Generally, the transformation matrix above can be calculated, if coordinates of 3 or more markers are known in both coordinate systems A and B. The transformation matrix represents the solution to the following least squares problem (Sderkvist and Wedin, 1993):

; n 3 (2)

In the present investigation, a singular value decomposition method as described by Sderkvist and Wedin (1993) was employed to compute the transformation matrices. Typically, A is a local (segment-fixed) coordinate system, and B is the global coordinate system.

Based on these equations, the transformation matrices for the knee and AJC motion can be calculated based on bone [equations (9),(10)] and skin [equations (11),(10)] marker coordinates:

Cardanic angles were calculated to express the rotations at the knee joint and at the AJC during the stance phase of walking based on both bone markers and skin markers. Flexion/extension, ab/adduction, and internal/external tibiofemoral rotation were resolved from the matrices using the conventions of Grood and Suntay (1983). For the ankle joint complex, plantar/dorsiflexion, ab/adduction, and in/eversion were calculated according to Cole et al. (1993). This means that for the knee rotations flexion/extension occurred around a femoral fixed medio-lateral axis, ab/adduction around the floating axis, and internal/external knee rotation around the tibial fixed proximal-distal axis. At the AJC, plantar/dorsiflexion occurred around a medio-lateral tibial fixed axis, ab/adduction around the floating axis, and in/eversion around the longitudinal (antero-posterior) foot axis.

For simplicity, knee flexion/extension can be thought to occur in a sagittal plane, ab/adduction in a frontal plane, and internal/external knee rotation in a transverse plane. Knee abduction refers to an abduction of the tibia (shank) with respect to the femur (thigh), and similarly knee adduction refers to an adduction of the tibia (shank) relative to the femur (thigh). Internal knee rotation refers to an internal rotation of the tibia (shank) with respect to the femur (thigh), and similarly, external knee rotation refers to an external rotation of the tibia (shank) relative to the femur (thigh). For the AJC, plantar/dorsiflexion can be "simplified" as the rotation of the calcaneus (shoe) relative to the tibia occurring in a sagittal plane. Similarly, ab/adduction and in/eversion of the AJC can be simplified as the relative rotations occurring in a transverse and frontal plane, respectively. For a more detailed mathematical description of the calculations involved in determining the knee and AJC rotations, the reader is referred to Grood and Suntay (1983) and Cole and co-workers (1993).

Possible differences between the external and bone marker based knee and AJC rotations are the combined effect of the skin (external marker) movement artefact occurring at the two articulating segments. In order to determine separately the contribution of the thigh and shank to knee rotation errors, the effect of the skin movement at the thigh and tibia were calculated. For these calculations, the thigh (skin) motion relative to tibia (bone) motion was determined and subtracted from the bone marker based knee rotations (femur-tibia). In this manner, the erroneous effect of the thigh could be determined. Similarly, the effect of skin markers at the shank was determined by subtracting the femur-shank based knee rotations from the femur-tibia based rotations. For the AJC rotations, the contributions of the shank and the shoe/foot segments to the difference between skin and bone marker based kinematics were determined in analogy to the analysis of the tibiofemoral motion as described above.

Motion recordings of bone movement with the use of intracortical pins is a highly invasive procedure. It may be argued that the insertion of the pins may cause discomfort and the anesthetics may alter the subject’s perception. For two of the subjects (subject 2 and 4), a dry run with exactly the same motion recordings and skin markers was performed prior to surgery, in order to show quantitatively whether the subject’s gait was affected due to the insertion of the bone pins.

For the present study, it was assumed that the skin marker movement was not restricted by the insertion of the pins. In order to minimize this effect, skin markers were placed at least 5 cm away from the closest bone pin insertion. By manually moving the skin markers closest to the pin insertion, it appeared that the skin movement was not restricted at these locations due to the bone pin.

The calibration frame available at the site of the experiments was limited due to the few calibration points and its size. The accuracy of spatial reconstruction is reduced when a small number of calibration points are used (Hatze, 1988) or when markers are reconstructed that move outside the calibration volume (Wood and Marshall, 1986). Since the upper thigh markers moved outside the calibration volume, some errors may be introduced when using these markers to calculate skin marker based tibiofemoral joint motion. The magnitude and effect of these errors were determined by comparing joint motions based on all skin markers and the skin markers closest to the bone pins. Additionally, the residuals of the spatial reconstruction were calculated for each marker indicating the appropriateness of the DLT model for each of the skin and bone markers.

Problems were encountered with the femur pin in two subjects. In one subject (subject 2), the femur pin became loose after a few walking trials. The femur pin was then surgically removed and the experiments were continued with the remaining markers. Consequently, data of this subject will only be available to describe the AJC motion. It was suspected that the slit cut into the iliotibial band through which the femur pin was inserted may have been too small in subject 2. This may have caused large forces between the femur pin and the iliotibial band, eventually resulting in the loosening of the pin. In another subject (subject 4), it was observed that a "popping", a sudden rotation, of the femur pin occurred. This "popping" movement of the pin was in the order of 10^o flexion/extension, and appeared to occur in both directions during the swing phase when the knee underwent relatively large flexion angles. This popping movement did not represent true motion of the femur, since this sudden flexion movement would correspond to a large relative translation between the femoral head and the pelvis. Therefore, it was decided to discard the femur pin data for this subject. Consequently, tibiofemoral kinematics will only be presented for three subjects (subject 1, 3, and 5).

None of the subjects experienced pain and/or significant discomfort during the walking and running trials (chapters 4 to 6) used in this study. However, one subject did experience minor pain and discomfort in the distal part of the calcaneus during the later part of the experiments (barefoot running trials) which were not part of this project (see Fig. 17). During the motion trials, none of the subjects stated that his ability to walk or run normally (chapters 4 to 6) was affected by the pins

Qualitatively, the gait of all the subjects appeared to be the same with bone pin compared to the gait exhibited during the training sessions (used to familiarize the subjects with the walking and running (see chapters 4 to 6) procedure). The qualitative assessment of the subject’s gait was confirmed by comparing the skin marker based kinematics for walking with and without the bone pins. At the knee joint, the difference in both subjects at any instant during the stance phase did not exceed 2.1 for ab/adduction, 4.8 for internal/external knee rotation and 4.5 for flexion/extension. At the AJC, the absolute differences did not exceed 6.0 for in/eversion, 4.8 for ab/adduction and 4.8 for plantar/dorsiflexion.

These differences may be considered to be substantial, but the amplitude and shape of the curves were similar; the major part of the difference in skin based joint kinematics between the pin trials and the non-pin trials was a systematic shift between the two curves (Fig. 3). This systematic shift can be attributed to the different standing trials used for the pin and the non-pin walking trials. Knee rotations based on skin markers for the pin and the non-pin trials are displayed for one subject (subject 2) in Fig. 3. The trends were similar for the other subject and for the AJC motions, i.e. the shape and amplitude of the skin and bone marker based curves were similar.

The residuals of the DLT calculations are plotted in Fig. 4 for subjects 1, 3, and 5. The (skin) markers at the thigh were of primary interest since these markers were clearly outside the volume calibrated with the frame. The results (Fig. 4) show that only the residuals for thigh marker 1 (Th1, see Fig. 1) placed over the greater trochanter appeared to be consistently higher than the values of the other thigh markers (as well as the femur markers). This marker was only seen at the edge of the film in all three cameras where errors due to lens distortion can be expected to be high. This marker was excluded for the calculations of the knee motions even though the difference in knee rotations between calculations including and excluding this marker was found to be systematic and small (<2.5 for flexion, and <1.5 for internal/external rotation and ab/adduction).

Differences between skin and bone marker based tibiofemoral rotations may potentially be masked by inaccuracies in the DLT calculations for the markers moving outside the calibration volume, i.e. the thigh markers. In order to estimate this error source, the following calculations were made. First, the average residuals were calculated from Fig. 4 for all the femur and thigh markers (excluding the marker at the greater trochanter, Th1) during the stance phase. These values are displayed in Table 2. Taking the worst case (subject 1), the difference between femur and thigh markers was 5.6 (subject 1) which corresponds to 1.7 mm. Assuming an average marker distance of 150 mm, 1.7 mm uncertainty corresponds to roughly 0.6 (= arctan ) error in rotation. However, it should be realized this error is likely to be much smaller since the markers outside the calibration volume would be moved (distorted) in a similar, systematic manner which would result in less than the estimated 0.6 error in rotation. Based on these calculations, differences between external and skeletal marker based rotations exceeding 0.6 can not be explained by inaccuracies due to the DLT calculations.

Due to technical problems (overexposure, film frequency slowing down) in some subjects all three cameras were not available for the first or the last part of the stance phase of the walking trials. During these times, cameras 1 and 2 were typically the only cameras available. Since the angle between camera 1 and 2 was rather small (35, see Fig. 2), the spatial position of the markers can be expected to be less accurate. The transition from three to two cameras (and vice versa) typically caused "jumps" in the curves. Therefore, the times where only two cameras were available were marked in the following graphs (Fig. 5, Fig. 6), and all subsequent calculations (Table 3, Table 4) did not include these phases where only two cameras were available.

The individual knee rotations derived from skin and bone markers are depicted in Fig. 5. Additionally, average differences (root mean square, RMS), maximal differences and general curve agreement between tibiofemoral rotations derived from skin and bone markers are presented in Table 3. Generally, the difference in skin and bone marker based knee rotations between trials and within subjects was small (Fig. 5), i.e. the knee kinematics were very repeatable. The intersubject variability was typically much larger than the intrasubject variability (see Fig. 5).

The bone marker based knee ab/adduction movement patterns were different for the three subjects analyzed, i.e. no general ab/adduction pattern could be observed across subjects (Fig. 5). The ab/adduction range of motion (ROM) also varied across subjects; the ROM was about 5 for subjects 1 and 3, whereas the range of motion in ab/adduction was around 10 for subject 5. The difference between skin and bone marker based ab/adduction varied across subjects (Fig. 5). The best agreement was found in subject 1 where the difference between skin and bone marker based curves did not exceed 3.1 (Table 3). Additionally, the shape of the skin and bone marker based average curves was similar for subject 1, whereas in subject 3 and 5 poor agreement was found between the shape of the skin and bone marker based curves. The maximum difference between ab/adduction calculated from skin and bone markers was present in subject 5 where the maximal difference exceeded 5 (Table 3).

The patterns of internal/external knee rotation derived from bone markers varied across subjects, e.g. a pronounced initial internal tibial rotation with respect to the femur was present in subject 3, whereas for the other two subjects, no (subject 5) or only a small amount (subject 1) of initial internal knee rotation was observed (Fig. 5). The range of motion of internal/external (longitudinal) knee rotation derived from bone markers was around 5 for subject 1 and 5, whereas for subject 3, the range of motion was more than 10. Poor or virtually no agreement between skin and bone marker based kinematics was found in subject 1 and 5. On the other hand, relatively good agreement was present in subject 3, in particular for the time from 25% of stance phase to take-off. In all three subjects, the skin marker based internal/external rotation showed a distinct initial internal tibial rotation with respect to the femur, which was either not present at all or only to a much lesser extent in the bone motion. For all subjects, the maximal difference between knee rotation derived from skin and bone markers exceeded 7 (Table 3).

The shape of knee flexion/extension based on bone markers was similar for all subjects. The amplitude of the movement of flexion/extension, however, varied between subjects. Subjects 1 and 3 had much more flexion/extension movement from touchdown throughout the end of midstance. Generally, the agreement between bone and skin marker based knee flexion was good, especially during the first half of stance phase. The least agreement between flexion/extension derived from skin and bone markers was present in subject 5, where the maximum difference was as high as 5.8 (Table 3).

The individual AJC rotations derived from skin and bone markers are presented in Fig. 6, and for each subject, average (RMS) and maximal differences between skin and bone marker based rotations were calculated (Table 4). Similarly to the knee motions, the intrasubject differences between trials were small compared to the intersubject variability.

The shape of the bone marker based in/eversion curve was similar across all five subjects. An initial eversion movement was typically followed by an inversion movement towards the end of stance phase. The initial eversion calculated from the bone markers as the difference between the eversion at touchdown and maximal eversion (during the first 50% of stance) was in the same order of magnitude (5) for all subjects. On the other hand, initial eversion calculated from skin markers was much higher, and ranged between 10 and 16 depending on the subject. In all subjects, the eversion indicated by the skin markers was much higher than the eversion that actually took place between tibia and calcaneus. The difference between skin/shoe and bone marker based in/eversion was highest from around 20 to 60% of stance phase, and was in the order of magnitude of 5, a substantial difference considering the amplitude of this motion.

The tibiocalcaneal ab/adduction patterns of the bone motion were similar across subjects. An initial abduction during the first 20% of stance was generally followed by a slow adduction movement. The ab/adduction exhibited at the AJC was generally well reflected with the use of skin/shoe markers, in particular for three subjects (subjects 2, 3, and 4). For subject 1 and 5 more abduction was indicated with the skin/shoe markers. However, the shape of the average curves for skin and bone marker based kinematics were similar.

The shape of the plantar/dorsiflexion derived from bone markers was similar across subjects. Typically, the plantar/dorsiflexion curves had two peaks. The first plantarflexion peak occurred at around 10% of stance phase, whereas the maximum dorsiflexion movement typically occurred at 75% of stance phase. The difference between skin and bone marker based kinematics appeared to be systematic, in the sense that the amplitude of the movement was always higher for the skin marker based kinematics. That means that the maximum plantarflexion as well as the maximum dorsiflexion were overestimated when using skin markers. The overestimation of plantarflexion varied between subjects and could be as high as 5.8 as seen in subject 4 (Table 4). The overestimation of the maximum dorsiflexion movement which occurred around 75% of stance phase ranged from 1 (subject 2) to 8 (subject 3).

The rotational knee motions found in this study were generally in agreement with the tibiofemoral rotational kinematics reported in previous investigations (Lafortune et al., 1992a; Lafortune et al., 1994). The knee flexion/extension curves were similar in shape and magnitude to the data presented by Lafortune et al. (1992a). The range of motion in ab/adduction was much higher than the range of motion reported by Lafortune et al. (1992a). Their data indicated that almost no ab/adduction movement took place during stance. The difference between their results and the results of this study may be explained by differences in defining the anatomical coordinate systems of the tibia and femur (see chapter 6). Lafortune et al. (1992a) employed anatomical coordinate systems based on a roentgen-stereophotogrammetric analysis, whereas in the present study the anatomical coordinate systems were based on a "neutral" standing trial. It also appeared that the ab/adduction range measured for subject 5 was unphysiologically high. This may likely be the result of an alignment problem of the anatomical coordinate system causing cross-talk from the knee flexion/extension (see chapter 6).

In the study of Lafortune et al. (1992a), all five subjects clearly showed an initial internal tibial rotation with respect to the femur (internal knee rotation). Based on the curves presented by Lafortune and co-workers (1992a), the initial internal knee rotation was estimated to range from 2 to 6.3 across subjects. The results of this study showed minimal initial internal knee rotation of less than 2 for subject 1, a clear initial internal knee rotation of 5 for subject 3, and initial external knee rotation of approximately 4 for subject 5 (Fig. 5). The findings of this study show, therefore, more intersubject variability than the findings of Lafortune et al. (1992a). In order to discuss the results of the present investigation, the internal/external tibial and femoral rotations were also calculated with respect to the global laboratory coordinate system. The results showed that the tibia rotated internally from touchdown to about 25% of stance phase. This initial tibial rotation with respect to the global coordinate system was consistently present in all trials except in one trial of subject 3 where the tibia showed a short initial external rotation of less than 2 changing into internal tibial rotation of 4.4 after 7% of stance phase. The initial tibial rotation with respect to the laboratory coordinate system averaged 10.1, 5.6, and 8.9 for subject 1,3, and 5, respectively. This initial rotation was also present at the femur and averaged 8.6 (subject 1), 4.2 (subject 3), and 11.0 (subject 5). These results support the generally accepted paradigm of internal tibial rotation at and shortly after touch-down. However, this internal tibial rotation appears to be matched by internal femoral rotation. In subject 5, it was actually found that this internal rotation was larger at the femur which resulted in an external knee rotation.

Based on the results of this study, it can be concluded that skin markers as used in this study can only be used to reliably (maximal error < 20% of range of motion) determine flexion/extension at the tibiofemoral joint. For knee flexion/extension, the differences between bone and skin marker based knee kinematics was not only smallest in absolute terms, but especially in relation to the amplitude of the movement (signal to noise ratio). For knee ab/adduction and internal/external rotation, the error introduced as a result of the skin movement artefact can be almost as high as the motion measured. Therefore, knee ab/adduction and internal/external rotation calculated from skin markers as used in this study has to be interpreted with extreme caution in particular when differences across subjects are of interest. It may be argued that large differences within the same subject, e.g. a pre-intervention to a post-intervention comparison of a patient, may be detected in all knee rotations with the use of skin markers. However, the authors are convinced that such comparisons are not appropriate and suggest that the interpretations of such results may lead to wrong conclusions since the difference seen in the skin marker based kinematics may not reflect the true differences at the tibiofemoral joint. Statements other than that "there are differences" should be considered as overinterpretations. Additionally, the inability to reproduce the same anatomical coordinate system even within subjects may also cause or mask possible differences (see also chapter 6).

The discrepancies between skin and bone marker based kinematics for the knee joint (Fig. 5) are the combined effect of the skin movement artefact at the thigh and shank. Subject averages of the errors in knee rotations caused by the skin movement artefact at the thigh and tibia are depicted in Fig. 7. The curves show that most of the knee rotation errors occurred due to skin movement artefacts at the thigh. Shank induced errors were small, especially for knee ab/adduction (<2.6) and knee flexion/extension (<1.8). The magnitude of the errors due to skin movement artefact at the shank were in agreement with results from a previous investigation (Holden et al., 1994). Additionally, the results of Holden and co-workers (1994) also showed that the largest difference between rotational movement of the shank as determined from skin markers and tibia as determined from bone markers existed along the longitudinal axis of the lower leg. Based on the results of this investigation, it may be argued that the skin movement artefact at the shank can be neglected in comparison to the errors caused by the thigh. The result that thigh induced errors were much higher was expected. The thigh consists of much more soft tissue (muscles, adipose tissue) than the shank, and therefore, relative movement between skin and underlying bone was expected to be much higher than for the leg. Furthermore, the adherence or attachment of the soft tissue to the underlying bone may be different for the thigh and the shank. For example, the soft tissues over the femoral condyles may be rather thin but loose. On the other hand, the soft tissue over the tibia crest may be equally thin but relatively firmly attached to the bone.

No studies are known to the authors that investigated AJC (tibiocalcaneal) motion by actually measuring the motion of the respective bones during gait. Hence, gait analysis studies using external markers have to be used to compare the results of this study. Generally, the movement patterns of the skin marker based AJC motion was in agreement to what has been reported by Moseley and co-workers (1996). However, in the present study, the ranges of the AJC rotations were higher than the respective ranges presented by Moseley et al. (1996). This difference may be attributed to the fact the subjects in this study wore shoes, whereas in the other study the AJC rotations were determined when walking barefoot.

Unlike the rotations measured at the knee joint, the rotations at the AJC were more uniform across subjects. In general, the shape of the rotation curves were similar for all subjects, the only difference consisted in the magnitude, i.e. in the range of motion.

In absolute terms, the smallest difference between skin and bone marker based AJC motion was measured for ab/adduction. For subjects 2, 3 and 4, ab/adduction determined from skin and bone markers were almost identical. For subject 1 and 5, ab/adduction was overestimated by about 5. Hence, it can be concluded that ab/adduction patterns of the calcaneus with respect to the tibia can be determined reliably when using external (skin) markers as used in this investigation. For in/eversion, the skin and bone marker based results showed that the skin marker based in/eversion had similar patterns as the bone marker based in/eversion, however, with a higher amplitude. Similarly, the bone marker based plantar/dorsiflexion was well reflected by the skin marker based result, but again with a higher amplitude in both plantarflexion and dorsiflexion. The reason for the phenomenon that the calcaneus-tibia rotation were amplified when measured with external markers may be twofold. Firstly, the movement of the shoe may be different from the movement of the foot (Stacoff et al., 1992; Reinschmidt et al., 1992). This will be discussed in more detail later. Secondly, some of the movement between foot/shoe and shank may occur in the talonavicular joint rather than in the joints (talocalcaneal and talocrural joint) located between calcaneus and tibia.

The contribution of the shank and the shoe/foot segment to the difference between skin and bone marker based AJC kinematics was determined in analogy to the analysis for the tibiofemoral joint and is displayed in Fig. 8. Similar to the tibiofemoral joint, the least amount of error was introduced by the shank. The error due to the skin movement artefact at the shank was in the range of 2-3 and only exceeded 5 in in/eversion for one particular subject. The misreadings caused by the relative movement of the shoe markers with respect to the calcaneus were as high as 7, and were in the average always higher than the errors due to skin movement artefact at the shank. The error patterns caused by the shoe/foot segment were similar across all the subjects in all three AJC rotations. On the other hand, there were no apparent error patterns in the AJC kinematics for the errors caused by the shank. This observation was similar to what could be observed for the errors due to the shank at the tibiofemoral joint where again no apparent error patterns for the shank were found. On the other hand at the tibiofemoral joint, the error patterns caused by the thigh were somewhat similar across subjects (Fig. 7), but they were not as uniform across subjects as the error patterns caused by the shoe/foot at the AJC (Fig. 8). This observation implies that the skin movement artefact is more predictable for the AJC than for the knee joint. However, it has to be realized that the similarity in error patterns at the knee and AJC may be dependent on the homogeneity of the subjects analyzed. The subjects included in this study were rather homogenous. None of the subjects could be considered obese, they were all male, and they were all about the same age. The challenge of developing a model to correct for skin movement artefact for any subject would be to account for individual factors such as the amount of adipose tissue in the lower extremities and the movability of the skin with respect to the underlying tissue. This has also been pointed out by Holden and co-workers (1994) who suggested that a generalized model of soft tissue error (at the shank) has to account for individual subject differences.

The relative motion of skin with respect to the underlying bone can be caused by inertial effects, the non-rigid attachment of the skin to the bone, and by movement caused by muscle contractions underneath the skin. Artefacts due to inertial effects should primarily occur during the first 50 ms of stance phase, the impact phase, and should be minimal during the remaining stance and swing phase. Artefacts due to muscle activity can occur during the entire stance and swing phase. It is difficult to estimate the contribution of these effects on the relative movement between skin and underlying bone. Based on the qualitative observation of the films, it was felt that the skin movement artefact during the stance phase was mainly caused by muscle movements. Qualitative assessment also suggested that the skin artefacts due to muscle movements may even be higher during the swing phase than during the stance phase analyzed in this investigation. Another problem connected with movement due to muscle contraction is the standing trials being used to determine the anatomical position of the segments. During the standing trial, muscle can be expected to be in a state of low activity. However, during the stance phase of walking some muscles are always activated. Therefore, part of the skin movement artefact may simply be caused by the fact that standing trials were usually recorded with a different muscle activity as occurring during walking.

The skin movement artefacts at the shoe/foot segment have to be considered differently than the skin movement artefact occurring at the shank or tibia. A shell (shoe) is added on top of the skin which may introduce an additional relative motion. Therefore, the movement between shoe and calcaneus can be broken down into the relative movement between the shoe and foot and the movement between foot and calcaneus. Based on the data gathered in this study, it cannot be concluded if the skin movement artefact seen at the AJC was mainly due to the relative movement between the shoe and foot or due to the relative movement between foot and calcaneus. However, based on the fact that part of the heel counter had to be removed to accommodate the bone pin may suggest that the heel counters of these shoes were not very firm. This may have allowed for a considerable relative motion between the shoe and foot. The result that the movements based on the shoe markers were generally larger than the actual movement was in the same direction as the differences found in investigations comparing the rearfoot movement based on shoe and foot markers as viewed through windows cut into the shoe (Stacoff et al., 1992; Reinschmidt et al., 1992). It may be argued that the skin movement artefact caused by the relative motion between shoe and calcaneus was mainly caused by the relative motion between shoe and heel and not between heel and calcaneus. In other words, if windows were cut into the shoe and markers were attached to the skin of the heel, the tibiocalcaneal motion may have been better estimated than with the markers attached to the shoe.

The results of this study showed that tibiofemoral rotations determined with external markers as employed in this study have to be used and interpreted with caution for any type of gait analysis. Knee rotations other than flexion/extension are small and the errors induced through skin movement artefacts may well exceed the actual motion occurring at the tibiofemoral joint. For some subjects, there was no agreement in shape of ab/adduction or internal/external knee rotations as determined with skin and bone markers. Therefore, it is suggested that knee rotations other than flexion/extension cannot be reliably determined when using external skin markers. The segmental error analysis revealed that the discrepancies between skin and bone marker based kinematics were almost exclusively caused by the skin movement artefact occurring at the thigh. Therefore, external markers may still be used to measure the rotations of the tibia with respect to a laboratory coordinate system. This will be discussed in detail in chapter 7.

At the ankle joint complex, skin/shoe marker based kinematics gave a relatively good estimate of the actual tibiocalcaneal motion. In particular, the shape of in/eversion, ab/adduction, and plantar/dorsiflexion at the AJC was well reflected with the use of external markers. However, the AJC rotations are generally overestimated when using external markers. Therefore, skin/shoe markers may be used to "reflect" the AJC motion, however, absolute values have to be used and interpreted with caution.

Skin mounted markers are typically employed in kinematic gait analysis. However, large errors may be introduced as a result of the relative movement between skin and underlying bone. To date, knowledge about this skin movement artefact is limited, and no studies have been published which systematically investigated this error at the thigh, shank, and foot/shoe during a walking movement. The purpose of this study was to determine the errors in knee (tibiofemoral) and ankle joint complex, AJC, (tibiocalcaneal) rotations caused by the skin movement artefact during walking. Intracortical bone pins were inserted into the femur, tibia, and calcaneus of five subjects. Marker triads were attached to these pins, and additionally, six skin markers to the thigh, six to the shank, and three to the shoe. For each subject, three walking trials were filmed with three synchronized LOCAM cameras (50 Hz) to determine the 3-D position of the markers during stance phase. Flexion/extension, ab/adduction, and longitudinal rotation at the tibiofemoral joint as well as plantar/dorsiflexion, ab/adduction, and in/eversion at the AJC were calculated from both skin and bone markers. The results showed that the errors in knee rotations were mainly caused by the thigh markers. Knee flexion/extension was generally well reflected with the use of skin markers (mean difference 2.1). Depending on the subject, the agreement between skin and bone marker based kinematics for ab/adduction and internal/external knee rotation ranged from good to virtually no agreement, and in some subjects, the errors exceeded the actual motion. The errors in AJC rotations were mainly caused by the markers on the shoe/foot segment. The tibiocalcaneal motions were generally well reflected with external markers. However, tibiocalcaneal rotations derived from external markers typically exceeded the true bone motions. The results suggest that (a) knee rotations other than flexion/extension may be affected with substantial errors when using external markers, and (b) tibiocalcaneal motions are generally well reflected with external markers, but absolute values (amplitudes) have to be interpreted with caution.

To date, numerous studies have investigated the kinematics of the lower extremities and in particular the kinematics of the rearfoot with respect to the lower leg during running. These studies have been conducted for a number of reasons such as to gain a better understanding of the joint kinematics during running (Engsberg and Andrews, 1987), to determine the influence of running shoe parameters (e.g. Nigg and Morlock, 1987) or foot morpholgy (Nigg et al., 1993) on running kinematics, to investigate kinematic changes due to orthotics (e.g. Taunton et al., 1985), or to study a possible relationship between kinematic parameters and running injuries (e.g. Messier and Pittala, 1988). One of the main interest of these studies was to quantify the movement of the calcaneus with respect to the tibia. To approximate these bony movements, markers or linkages were typically attached to the leg as well as to the foot or the shoe. However, during a highly dynamic movement such as running, these external markers or linkages may move considerably with respect to the underlying bone. Therefore, a large error, typically referred to as the skin or shoe movement artefact, may be introduced as a result of this relative movement.

This skin movement artefact has motivated researchers to directly measure in-vivo skeletal motion during human ambulation (Levens et al., 1948; Karlsson, 1990; McClay, 1990; Murphy, 1990; Lafortune et al., 1992a; Cappozzo et al., 1996; Holden et al., 1994; Lafortune et al., 1994) even though procedures to directly measure in-vivo skeletal motion are typically highly invasive. Most of these studies were confined to slow movements such as walking, and to date, only one study determined the skeletal (patellofemoral, tibiofemoral) motion during running (McClay, 1990). However, no study has been conducted that determined the skeletal tibiocalcaneal motion during running.

The effect of the skin movement artefact on kinematics of the lower extremities has been determined in a few investigations looking at slow or quasi-static movements (Lafortune et al., 1992b; Cappozzo et al., 1996; Maslen and Ackland, 1994; Karlsson and Lundberg, 1994). Generally, large discrepancies were reported between the external marker and skeletal marker based motions during these slow movements. The effect of the skin movement artefact is highly dependent on the joint or joint complex in consideration. In chapter 3, it was shown that during walking tibiocalcaneal rotations (in/eversion, ab/adduction, plantar/dorsiflexion) were fairly well represented when using external markers; but, for tibiofemoral rotations, only flexion/extension was well represented when using external markers. In this context, it is of interest if external markers can also be used reliably to determine tibiocalcaneal motion during a more dynamic movement such as running.

Rearfoot (tibiocalcaneal) kinematics and in particular in/eversion of the rearfoot is believed to be important with respect to running injuries and the design of running shoes. However to date, it has not been shown how much rotation actually occurs between the calcaneus and tibia during running, and how accurately tibiocalcaneal rotations can be measured or estimated when using external markers. Therefore, the purpose of this investigation was (a) to determine tibiocalcaneal rotations during running as derived from bone markers, and (b) to compare the skeletal tibiocalcaneal rotations with rotations as derived from external markers attached to the shank and the shoe.

Five male subjects (age 28.6 4.3 yrs., weight 83.4 10.2 kg, height 185.1 4.5 cm) gave informed consent to participate in this study. The subjects had neither an injury at the time of testing nor an injury history which may have possibly lead to an abnormal running style. The experimental protocol was approved both by the ethics committees of The University of Calgary, Canada, and the Karolinska Hospital in Stockholm, Sweden. The experiments were conducted at the Department of Orthopaedics of the University Hospital in Huddinge, Sweden.

Intracortical Hofmann bone pins (2.5 mm diameter) were inserted into the posterolateral aspect of the calcaneus and into the lateral tibial condyle (Gerdy’s tubercle) in the subject’s right leg. Standard local anesthetic (Citanest 10 mg/ml) was applied at the insertion sites of the bone pins. To each of the bone pins, triads of reflective markers (10 mm diameter spheres) were attached. In addition to these bone pins, external markers were attached to the segments of interest: six external reflective markers (20 mm diameter spheres) were fixed to the skin of the shank at standardized locations, and three external markers were glued directly to the posterior aspect of the shoe (Fig. 1). The subjects wore standard running shoes (Adidas Equipment Cushioning 1994, Fig. 1), where a small half-circular piece (r = 12 mm) of the lateral heel cap (of the right shoe) was removed in order to accommodate the calcaneus pin. The subjects were barefoot in these shoes (they did not wear socks).

For each subject, one standing trial and five heel-toe running trials (2.9 0.2 m/s) were collected. Prior to the running trials and surgery, the subjects had ample time to familiarize themselves with the running procedure. The subjects were asked to land on a force plate (Kistler, Winterthur, Switzerland) with their right shoe. The force plate was embedded in the floor of a 10 m runway, and the speed was monitored with photo cells placed 70 cm in front and behind the force plate. The marker motions were recorded during the stance phase with the use of three high speed cine cameras (LOCAM) operating at a nominal frequency of 200 Hz. The cameras were placed at 10, 55 and 110 to the running direction (Fig. 2). The cameras were synchronized through small infrared lights visible in all cameras. The lights indicated the stance phase and they were triggered with a threshold detector connected to the force plate. Differences and fluctuations in camera speed were corrected using an internal LED producing small dots at the side of the film in 5 ms intervals. At the beginning of all trials, a high precision calibration frame with 6 control points was filmed to allow the three-dimensional reconstruction.

In addition to the five bone pin trials, two subjects (subjects 2 and 4) also performed three "pre-operative" runs and a standing trial prior to inserting the bone pins. For these pre-operative runs, the external markers were placed at the same locations as for the bone pin trials. The comparison of the tibiocalcaneal rotations based on external markers with and without bone pins was used to determine whether the insertion of the bone pins affected the "natural" running style of the subjects.

The films of the calibration, standing and running trials of each subject and camera were projected onto a digitizing board (GP-8, Sonic Digitizer, SAC) and manually digitized. Reflective markers at the edge of the force plate were used to control for shifting of the projected image with respect to the digitizing board. For filtering purposes, five frames before and five frames after stance phase were analyzed for each trial of each camera. If markers were not visible for less than five consecutive frames due to poor contrast or marker merging, the missing coordinates were linearly interpolated. Marker coordinates were normalized to 101 data points with respect to stance phase with 0% being touchdown and 100% being take-off. Camera coordinates were filtered with a bi-directional 4th order low-pass Butterworth filter with a cut-off frequency of 10 Hz determined from a residual analysis (Winter, 1990).

A standard direct linear transformation (DLT) using 11 coefficients (Abdel-Aziz and Karara, 1971) was used to calculate the spatial position of all the markers during the stance phase of running as well as during the standing trial. The anatomical segmental reference frames for the calcaneus, tibia, shoe, and shank were defined by using the standing trial where the subjects were instructed to align their lower limb segments with the global (film) reference frame. Coordinate transformations were applied to calculate the transformation matrix transforming the anatomical tibia (shank) reference frame into the anatomical calcaneus (shoe) reference frame. A singular value decomposition method (Sderkvist and Wedin, 1993) was employed to calculate the respective transformation matrices. For the transformation matrices concerning the shank, all skin markers were used that were visible in all the cameras during all frames of the stance phase. That means that depending on the subject, four to six shank markers were used for these calculations.

Intersegmental tibiocalcaneal motion which can be viewed as the combined motion of talocrural and talocalcaneal motion, was expressed by Cardanic angles using the sequences as proposed by Cole et al. (1993). That means that for the bone marker based rotations, plantar/dorsiflexion was calculated around the medio-lateral tibial fixed axis, ab/adduction around the floating axis, and in/eversion around the antero-posterior calcaneus axis. Similarly for the skin marker based tibiocalcaneal kinematics, plantar/dorsiflexion was resolved around the medio-lateral shank fixed axis, ab/adduction around the floating axis, and in/eversion around the antero-posterior shoe axis. Note that the terms shank and shoe will be used to refer to a body segment defined by external (surface) markers, and tibia and calcaneus will refer to the corresponding skeletal segments. The procedures involved with calculating the coordinate transformations and intersegmental motions were already described in detail in chapter 3.

A segmental error analysis was performed in order to determine the contribution of each segment to the difference in intersegmental rotations as derived from external and bone markers. For these calculations, the rotations of the shank with respect to the calcaneus were calculated and compared to the skeletal tibiocalcaneal rotations. Similarly, the rotations of the shoe with respect to the tibia was subtracted from the tibiocalcaneal rotations in order to determine the error caused by the relative movement of the shoe markers with respect to the underlying calcaneus.

The differences between bone and skin marker based tibiocalcaneal rotations (plantar/dorsiflexion, ab/adduction, in/eversion) were expressed in terms of the average (of single trials) root mean square (RMS) of the difference between the three rotation angles derived from bone and external markers at every instant in time during the stance phase of running. Additionally, the maximal RMS difference was calculated for each of the subjects during the stance phase of running.

The tibiocalcaneal rotations are presented in Fig. 10. In/eversion patterns were consistent across subjects. The position at touchdown ranged from neutral (0) to 5 inversion. In all subjects, an initial eversion took place reaching a maximal value at around 50% of stance phase. After the point of maximal eversion, the calcaneus continually inverted with respect to the tibia. Typically, this inversion motion was slightly higher than the initial eversion motion. At take-off, the calcaneus (relative to the tibia) was in an inverted position in all subjects and trials. The in/eversion excursion during the stance phase ranged between 10 (subject 3) and 17 (subject 1).

The ab/adduction patterns were similar across subjects, however, it appeared that the inter-subject variability in ab/adduction was greater than the inter-subject variability in/eversion and plantar/dorsiflexion. The range of motion in ab/adduction was small (average 7.5) compared to the other tibiocalcaneal rotations. All subjects showed an initial abduction followed by a larger adduction towards the end of stance phase.

All subjects landed in a close to neutral plantar/dorsiflexion position. In all subjects, a small initial plantarflexion movement was followed by a dorsiflexion movement reaching a maximum at around 50% of stance phase. During the second part of stance phase, all subjects exhibited a clear plantarflexion motion. The range in plantar/dorsiflexion averaged 32 over all subjects and trials.

Fig. 10: Tibiocalcaneal rotations during the stance phase of running based on bone (tibia, calcaneus) markers and external (shank, shoe) markers. Solid lines ( ) represent bone pin based kinematics, dashed lines (---) represent skin/shoe marker based kinematics. The averages of the five trials are displayed with thick lines. Movements labeled on the vertical axis indicate rotational movements in the positive direction of the vertical axis.

The skin and bone marker based tibiocalcaneal rotations are displayed in Fig. 10. Generally, the difference between the single trials was small both for skin and bone marker derived rotations for the same subject.

For all subjects, the in/eversion motion was typically overestimated when using external markers (Fig. 10). The average difference between the external and bone marker based in/eversion was 4.6 or 34.7% of the total range of in/eversion (Table 5). In all subjects, except subject 3, the difference between the external and bone marker based in/eversion was small during the touchdown and take-off phases; the largest difference occurred around the time when the calcaneus was maximally everted with respect to the tibia. In subject 3, it appeared that the skin marker based curves were shifted towards inversion which may have been caused by the fact that during the standing trial this subject may have been in a slightly everted (shoe) position. When accounting for this "shift", the difference between the skin and bone marker based kinematics would be very similar to the other four subjects.

Similarly to in/eversion, the maximal difference in ab/adduction derived from external and bone markers was highest around midstance, and the difference was typically small during both the touchdown and take-off phases. The mean difference between external and bone marker based ab/adduction was 3.6, or 51.2% of the total ab/adduction motion (Table 5).

The shape of the skin and bone marker based plantar/dorsiflexion were similar within the five subjects tested. However, the skin marker based plantar/dorsiflexion exhibited higher peaks, i.e. the initial plantarflexion occurring at approximately 10% of stance as well as the maximal dorsiflexion were overestimated when calculating plantar/dorsiflexion of the shoe with respect to the shank. The difference between external and bone marker based kinematics averaged 4.7 (14.1%) over the entire stance phase of all the subjects.

The results showed that tibiocalcaneal rotations determined from bone markers were highly repeatable within subjects. The tibiocalcaneal rotations were also similar across subjects (Fig. 10). More specifically, the patterns of in/eversion, ab/adduction and plantar/dorsiflexion were almost identical between the subjects, however, there were some differences in the amplitude of the respective rotations. For instance, all subjects showed a similar in/eversion pattern during the stance phase of their running trials, but the maximal eversion differed substantially between subjects (Table 6).

Since tibiocalcaneal motion during running has only been measured with the use of external markers, the results of this study cannot be directly compared to previous investigations. However, it can be reported that patterns of skin marker based in/eversion, ab/adduction and plantar/dorsiflexion motions of the present study were in agreement with other three-dimensional rearfoot analyses during running (Areblad et al., 1990; Soutas-Little et al., 1987; Nigg et al., 1993).

In all subjects and rotations (Fig. 10), some agreement was present between the rotations derived from external and bone markers. As a general rule, the external marker based rotations exhibited a similar pattern as the bone marker based rotations, though with a higher amplitude. This finding was similar to what has been found for walking (chapter 3). When comparing the shapes of the external and bone marker based curves, it appeared that the best agreement was present for plantar/dorsiflexion, whereas the least agreement existed for ab/adduction of the five subjects. This was also reflected in the relative RMS differences (Table 5). The difference between external and bone marker based rotations in relation to the range of motion was 14.1% for plantar/dorsiflexion, 34.7% for in/eversion and 51.2% for ab/adduction.

Due to the highly dynamic nature of running, one may expect that the effect of the skin (or external marker) movement artefact may be much higher for running compared to walking. However, the (RMS) differences between the skin and bone marker based rotations for running compared to walking (see Table 4) were only 1.2 higher for in/eversion, 1.1 higher for ab/adduction, and 1.6 higher for plantar/dorsiflexion.

As mentioned earlier, it was found that tibiocalcaneal rotations were fairly well represented when using external markers, but they were generally overestimated. This overestimation in intersegmental motion can either be caused by the relative movement of the shank with respect to the tibia, or by the relative movement between the shoe and the calcaneus, or by a combination of both. The results of the segmental error analysis show that the difference in tibiocalcaneal kinematics between external and skeletal markers was mainly caused by the shoe segment or in other words by the relative movement between the shoe markers and the underlying calcaneus (Fig. 12). The errors due to the shank were in the order of a few degrees, and appeared to be almost constant during the stance phase. On the other hand, the errors due to the shoe were much higher. Additionally, all of the subjects showed a clear error pattern for the shoe which could not be reported for shank errors which appeared to be randomly distributed around zero.

The results of this study did not allow any conclusions to be drawn whether the shoe error was mainly due to relative movement between the shoe and (and the skin around) rearfoot or between the (skin around the) rearfoot and calcaneus. However, based on the fact that the heel counters of the shoes used were not very firm since part of it had to be removed to accommodate the bone pin, it could be speculated that the relative movement between the shoe and the foot was mainly responsible for the discrepancies between external and skeletal markers attached to the shoe and calcaneus, respectively.

The difference between skeletal and shoe marker based kinematics may have also been influenced by the location of the shoe markers. In the present investigations, two shoe markers were not directly attached to the heel counter; they were placed approximately 2 cm more anterior in order to decrease the likelihood of marker merging problems. It can be argued that these markers also tracked some midfoot movement. Hence, the differences between shoe marker and calcaneus marker based kinematics may have been smaller if all the markers were strictly placed over the heel counter of the running shoe. The effect of different shoe marker placements on 3-d rearfoot motion is currently under investigation.

The maximal eversion was highly overestimated when using the external shoe and shank markers. In some subjects, this overestimation exceeded 100% (Table 6). This implies that, when using similar markers and running shoes, all maximal eversion values should be considered as overestimations of the true calcaneus to tibia eversion. However, it can be argued that running shoes with relatively firm heel counters would allow less relative movement between shoe and foot. Hence, the differences between the true and externally measured maximal eversion may be smaller when testing shoes with relatively firm heel counters. On the other hand, if heel counters were very rigid, more slippage between shoe and foot could be expected (Gheluwe et al., 1995). Despite the fact that the shoes used may have allowed the heel to slip easily inside the shoe, it can be reported that considerable differences between the externally determined maximal eversion and the true bony eversion existed during the support phase of running. The fact that external markers overestimated the rearfoot (calcaneus) motion was in agreement with previous studies which reported that, during running and lateral movements, the maximal shoe eversion was higher than the maximal foot eversion tracked through windows cut into the shoe (Stacoff et al., 1992; Reinschmidt et al., 1992).

There was an apparent relationship between the external and skin marker based maximal eversion values (Fig. 11). This relationship appeared to be linear up to around 10 of skeletal maximal eversion (Fig. 11). For values higher than 10 there appeared to be an asymptotic behaviour, i.e. the difference between skeletal and external maximal eversion is increasing. The relationship found between external and skeletal marker based maximal eversions implies that external markers can be used to identify large inter-subject differences in skeletal tibiocalcaneal eversion. In other words, subjects with large maximal skeletal eversion can be identified with external markers. However, it has been shown that the difference between shoe markers and skin markers on the foot tracked through windows cut into the shoe is dependent on the type of shoe and specifically on the type of heel counter construction (Gheluwe et al., 1995). Therefore, the relationship between skeletal and external maximal eversion is likely to be shoe dependent, and as such, this relationship would only hold as long as the subjects would be wearing the same shoes.

The results of this study have shown that during running, external markers attached to the shoe and shank reflected the motion of the underlying bones, i.e. tibiocalcaneal rotations. However, the magnitude of the tibiocalcaneal rotations were generally overestimated when using external markers. When looking at a specific variable such as the maximal eversion, this overestimation exceeded 100% in some subjects, and there appeared to be a relationship between the maximal eversion calculated from skeletal and external markers. This relationship is likely to be influenced by the shoe and the location of the markers attached to the shoe. Further studies are needed to show whether changes in tibiocalcaneal motion due to different conditions, specifically due to different shoe conditions, can be detected when using external markers attached to the shoe and shank.

The objectives of this study were (a) to determine the tibiocalcaneal motion during running based on skeletal markers, and (b) to compare tibiocalcaneal motion based on skeletal markers with tibiocalcaneal motion based on external markers. Bone pins were inserted into the tibia and calcaneus of five subjects. The 3-d motion of markers attached to bone pins as well as of external markers attached to the shank and shoe were determined during the stance phase of five running trials. Intersegmental motion was expressed in terms of Cardanic angles (tibiocalcaneal in/eversion, ab/adduction, plantar/dorsiflexion). It was found that the in/eversion, ab/adduction, and plantar/dorsiflexion motions were similar across the subjects. The shape of the tibiocalcaneal rotation curves based on external markers were similar to those based on bone markers. However, the rotations were generally overestimated when using external markers, e.g. the average maximal eversion calculated from external markers was 16.0 whereas the skeletal maximal eversion was only 8.6. These discrepancies were mainly due to the relative movement between shoe markers and underlying calcaneus and not due to the skin movement artefact at the shank. The results of this study have shown that external markers attached to the rear part of the shoe and the shank are good indicators of tibiocalcaneal motion. However, quantitative results determined from external markers have to be used with caution since it was found that the tibiocalcaneal rotations were generally overestimated when using external markers.

The knee is the most affected site of running injuries (James et al., 1978; Clement et al., 1981). It has been speculated that part of these injuries may be caused by excessive or disturbed tibiofemoral rotation, specifically rotation about the long axis of the tibia with respect to the femur (James et al., 1978). In other words, these running injuries may be connected to excessive or "non-normal" knee motion, and thus, the assessment of knee kinematics during running may be essential for the understanding of the mechanisms of these running injuries. Consequently, kinematic knee assessment may help to design strategies for the prevention and treatment of such running injuries.

Even though most running injuries concern the knee joint (James et al., 1978; Clement et al., 1981), kinematic analyses of the lower extremities during running have typically concentrated on the foot/shoe and/or lower leg kinematics. This may be mainly due to the fact that external markers attached to the shoe or foot and to the lower leg are believed to provide a relatively good representation of the skeletal motion of the respective underlying skeletal structures. On the other hand, the thigh consists of much more soft tissue than the shank and foot, and therefore, surface markers attached to the thigh may not be able to provide a good estimation of the motion of the underlying bony structure, i.e. the femur.

One way to avoid the problem inherent with surface markers is to directly measure skeletal motion of the respective segments (Levens et al., 1948; Karlsson, 1990; McClay, 1990; Murphy, 1990; Lafortune et al., 1992a; Cappozzo et al., 1996; Holden et al., 1994; Lafortune et al., 1994). To date, for running, only one study has been conducted where the skeletal motion of the femur and tibia was determined directly with the use of markers attached to bone pins (McClay, 1990). However, such procedures using markers attached to bone pins are invasive, and as such, they are not suitable for routine kinematic running analyses. Therefore, one has to rely on external markers in order to estimate skeletal motion. In this context, it is of interest whether external markers attached to the shank and thigh may provide a good estimate of the skeletal tibiofemoral joint motion during running.

The purpose of this study was (a) to determine the effect of the skin movement artefact at the shank and the thigh on the calculation of tibiofemoral motion during running, and (b) to discuss the appropriateness of using external markers to estimate the skeletal tibiofemoral motion during running.

Three male subjects (age 25.7 2.1 yrs., mass 85.5 9.6 kg, height 186.7 9.6 cm) gave informed consent to participate in this study. The experimental protocol was approved both by the ethics committees of The University of Calgary, Canada, and the Karolinska Hospital in Stockholm, Sweden.

Intracortical Hofmann bone pins (2.5 mm diameter) were inserted under local anesthesia into the lateral tibial and femoral condyles of the subject’s right leg. Triads of reflective markers were attached to these pins. Additionally, six skin markers were attached each to the shank and thigh at standardized locations determined by the subject’s anatomical landmarks. The subjects were filmed with three high speed cine cameras set at a nominal speed of 200 Hz during the stance phase of five heel-toe running trials (2.9 0.2 m/s). During these heel-toe running trials, the subjects wore standard running shoes (Adidas Equipment Cushioning 1994, Fig. 1) and no socks. The running shoes were slightly altered by removing the lateral part of the "Achilles tendon protector", and by removing a half-circular (r = 12 mm) piece of the heel cap at the lateral part of the right shoe. These alterations were necessary in order to accommodate the calcaneus pin enabling the tracking of tibiocalcaneal rotations, for which the results were presented in the previous chapter (chapter 4).

A high precision calibration frame with six control points (0.5 x 0.5 x 0.5 m³) was filmed to allow for the spatial reconstruction. For each subject, a standing trial in a fully extended neutral knee position was recorded for which the subjects were asked to align themselves with the laboratory coordinate system. Camera positions, the method used to synchronize the three cameras and the exact location of the skin markers are described in detail elsewhere (see chapter 3). For one subject, skin marker based knee kinematics of three "preoperative" trials were also recorded prior to the insertion of the bone pins. The comparison between the skin marker based knee motion of the preoperative and bone pin trials was used to identify possible changes in running style due to psychological or proprioceptive effects caused by the insertion of the bone pins.

Each frame of the calibration, standing and running trials of each subject and camera was manually digitized. These camera coordinates were filtered with a bi-directional 4th order low-pass Butterworth filter. A suitable cut-off frequency (10 Hz) was determined from a residual analysis (Winter, 1990). Subsequently, marker coordinates were normalized with respect to stance phase.

The spatial position of all the markers during the stance phase of running as well as during the standing trial was calculated using a standard direct linear transformation (DLT) approach (Abdel-Aziz and Karara, 1971). The anatomical segmental reference frames of the tibia and femur (bone markers), and of the shank and thigh (skin markers) were defined based on the standing trial where it was assumed that these segmental reference frames coincided with the global film reference frame. A singular value decomposition method (Sderkvist and Wedin, 1993) was used to calculate the transformation matrices transforming the anatomical femur coordinate system into the anatomical tibial coordinate system as well as the anatomical thigh coordinate system into the anatomical shank coordinate system. From these transformation matrices, the intersegmental motion was expressed in terms of the Cardan angles, knee flexion/extension (femur fixed axis), ab/adduction (floating axis) and internal/external knee rotation (tibial fixed axis) using the conventions proposed by Grood and Suntay (1983). These knee rotations were calculated both based on external (thigh, shank) and skeletal (femur, tibia) marker based transformation matrices. Flexion, abduction and external rotation were chosen as positive. Knee abduction was defined as the abduction of the tibia with respect to the femur, and external knee rotation was defined as the external tibial rotation with respect to the femur.

The difference between the skin and bone marker based knee kinematics is the combined effect of the skin movement artefact at the shank and the thigh. In order to determine the effect of the skin movement artefact at the shank and thigh separately, a segmental error analysis was performed. For these calculations, the rotations of the shank with respect to the femur was subtracted from the skeletal tibiofemoral rotations in order to determine the error caused by skin movement artefact at the shank. Similarly, the effect of the thigh skin movement artefact was determined by subtracting the thigh-tibia rotations from the skeletal tibiofemoral rotations.

For the shank, only the markers that were visible throughout the entire stance phase in all cameras were included in the calculations presented in this investigation. Thus, depending on the subject, four to six shank markers were used (see chapter 4). For the thigh, no markers had to be excluded for the calculations because these markers were visible throughout the stance phase in all three cameras.

The difference between skin and bone marker based kinematics was quantified as the average root mean square difference (RMS) and the maximal difference between the knee rotations (flexion/extension, ab/adduction, internal/external rotation) derived from skin and bone markers during the stance phase of running. These differences were expressed in absolute terms () and in relation to the total range of motion of the respective rotation during the stance phase (%).

The calibration frame used, which was available at the site of the experiments was not optimal in the sense that the calibration frame had only a small number of calibration points (Hatze, 1988) and that the size of that frame was smaller then the volume in which the markers typically moved during the motion recordings (Wood and Marshall, 1986). This was of particular concern for the proximal thigh (skin) markers which were typically outside the calibrated volume. On the other hand, the corresponding skeletal (femur) markers were typically within the calibrated volume. Therefore, it may be argued that possible discrepancies between skin and bone marker based knee rotations may be at least partially caused by inaccuracies in determining the spatial position of markers outside the calibration volume^#. For that purpose, the norm of residuals of the spatial reconstruction were calculated for all markers to indicate the appropriateness of the DLT model for each of the skin and bone markers. Possible differences between average residuals of skeletal (femur pin markers) and skin (thigh) markers were then used to calculate or estimate the effect of this difference with respect to knee rotations (see also chapter 3).

The skin marker based knee rotations (flexion/extension, ab/adduction, internal/external rotation) are displayed in Fig. 13. The shape and amplitude of the average curves (thick lines) of the preoperative and bone pin trials were similar for flexion/extension, ab/adduction, and internal/external knee rotation. For all knee rotations, the small differences (< 3) appeared to be constant almost throughout the entire stance phase (Fig. 13). This systematic shift may be attributed to the different standing trials used to define the segmental anatomical reference frames for the preoperative and pin trials causing slight differences in the definition of the neutral position (Ramakrishnan et al., 1991). The similarity in shape and amplitude between the average curves of the preoperative and bone pin trials suggests that the insertion of the bone pins did not affect the running style of the subjects. This suggestion was in agreement to what has previously been shown for the tibiocalcaneal motion during running (chapter 4), and for both the tibiofemoral and tibiocalcaneal motion during walking (chapter 3).

The norm of residuals for the external and skeletal markers during the stance phase are depicted in Fig. 14 for subject 1, 3, and 5. The (skin) markers at the thigh were of primary concern as these markers were clearly outside the volume calibrated with the frame. he thigh marker 1 (=Th1, see Fig. 1) placed over the greater trochanter appeared to be consistently higher than the values of the other thigh markers (as well as the femur markers) (Fig. 14); a finding similarly to what has been found for walking. This marker was only seen at the edge of the film in all three cameras where errors due to lens distortion can be expected to be high. As in the walking trials (chapter 3), it was decided to exclude this marker for the calculations of the knee rotations.

Differences between skin and bone marker based tibiofemoral rotations may potentially be influenced by inaccuracies in the DLT calculations for the markers moving outside the calibration volume, i.e. the thigh markers. In order to estimate this error source, the average residuals were calculated from Fig. 4 for all the femur and thigh markers (excluding the marker at the greater trochanter, Th1) during the stance phase. It was found that the difference between the mean thigh and femur markers were highest in subject 1, where the residuals of the femur markers averaged 9.1, and the residuals for the thigh markers averaged 12.6 (Table 7). The difference between these values (3.5) is in units of the digitizing board corresponding to approximately 1.05 mm. Assuming an average intermarker distance at the thigh of 15 cm, the 1.05 mm would roughly correspond to an error of 0.4 (= arctan ). Therefore, differences between skin and bone marker based kinematics in excess of 1 (or 0.4) cannot only be caused by the inaccuracies in the spatial reconstruction of the thigh markers. In other words, differences between skin and bone marker derived tibiofemoral rotations have to be attributed to other error sources (skin movement artefact).

The difference between the external and bone marker based ab/adduction was highly subject dependent (Fig. 15). For subject 1, the difference between the external and skeletal ab/adduction was larger than the actual motion; the average difference during stance was 155% of the skeletal range of ab/adduction (Table 8). For subject 3, there was some agreement, especially during midstance, between the externally and skeletally derived ab/adduction. In subject 5, relatively good agreement was present throughout the stance phase of running (Fig. 15). The mean and maximum difference in ab/adduction during stance averaged over all subjects was 4.1 and 6.6, respectively (Table 8).

Similar to the ab/adduction, the agreement between the skin and bone marker based internal/external knee rotation was highly subject dependent. Relatively good agreement could be reported for subject 1 (Fig. 15, Table 8), whereas the least agreement was measured for subject 5. Interestingly, the subject showing the least agreement for ab/adduction (subject 1) exhibited the best agreement for internal/external knee rotation and vice versa (subject 5). The mean and maximum difference in internal/external knee rotation during stance averaged over all subjects was 4.4 and 9.0, respectively (Table 8).

The shape of the flexion/extension curves derived from skin and bone markers were similar for all subjects (Fig. 15). When looking at the difference between external and skeletal knee flexion/extension in relative terms, the difference during the stance phase averaged 21% whereas for ab/adduction and internal/external knee rotation the difference was higher than 60% (Table 8).

The errors due to skin movement artefact at the shank did not exceed 5 for all subjects and rotations during the stance phase of the running trials (Fig. 16). For the shank induced error in ab/adduction and internal/external knee rotation, there were no apparent systematic error patterns across subjects. The error curves of the different subjects appeared to be "scattered" around the zero line, and for the ab/adduction the errors particularly in two subjects were almost constant throughout the stance phase. Only for flexion/extension, the errors caused by the skin movement artefact at the shank showed a somewhat similar behaviour across subjects (Fig. 16).

For all knee rotations, the maximal errors due to the skin movement artefact at the thigh were consistently higher than the maximal errors induced by the shank (Fig. 16). For the thigh errors, similar error patterns across subjects were found for the ab/adduction and the internal/external knee rotations. For example, the external knee rotation was overestimated in all subjects at touchdown, i.e. the external markers at the thigh indicated the knee in a more externally rotated position at touchdown. Since the external knee rotation caused by the skin movement artefact at the thigh decreased towards midstance, particularly in two subjects (Fig. 16), this error pattern would cause a systematic overestimation of the initial internal knee rotation typically associated with the initial phases of stance during running.

The differences found between the skin and bone marker based tibiofemoral rotations were well in excess of the difference which was introduced as a result of inaccuracies of the spatial reconstruction of the thigh markers. Therefore, the discrepancies between skin and bone marker derived tibiofemoral rotations can almost entirely be attributed to the skin movement artefact which is discussed in detail in the following paragraphs.

The results of this study have shown that the flexion/extension curves derived from external markers agreed well with the flexion/extension curves obtained from the skeletal markers. For all subjects, the shape and magnitude of the flexion/extension curves derived from the two different methods were similar. However, the skin marker based curves appeared to be shifted with respect to bone marker based curves. It can be speculated that this shift is associated with the difference in muscle activation between the standing and running trial. During the standing trial, the thigh and shank muscles can be expected to be in a state of low activity. On the other hand, during stance, some muscles are highly activated. Since muscle activity is likely to result in relative movement between the marker and the underlying bone, the muscle activity during stance may have partially accounted for the shift between the skin and bone marker based tibiofemoral flexion/extension. The shift found between the skin and bone marker based flexion/extension curves also suggested that variables calculated from these curves should be rather based on relative motion rather than on absolute positions, e.g. the range from touchdown to maximum flexion should be used instead of the (absolute) maximum flexion value.

In contrast to flexion/extension, the agreement between skin and bone marker based kinematics for ab/adduction and internal/external knee rotation was poor. In some subjects and rotations (ab/adduction for subject 5, internal/external knee rotation for subject 1, Fig. 15) there was some agreement between the skin and bone marker derived kinematics; but generally, the skin marker based ab/adduction and internal/external knee rotation did not reflect the "true" skeletal knee movement. Additionally, the difference between the skin and bone marker based ab/adduction and internal/external knee rotation did not appear to be systematic across subjects. In other words, the difference between external and skeletal kinematics was highly subject dependent.

The fact that the external markers were only able to provide a good representation of the skeletal motion for knee flexion/extension was in agreement with the results for walking (chapter 3). Additionally, as one may expect, the skin movement artefact errors in all rotations were consistently higher for running (Table 8) than for walking (see chapter 3, Table 3).

The differences found between the skin and bone marker based kinematics can either be caused by the skin movement artefact at the shank, the skin movement artefact at the thigh or by a combination of both. The results of this study have shown that the discrepancies between the external and the skeletal knee motion were mainly caused by the skin movement artefact at the thigh. This result was in agreement with what has been found for walking (see chapter 3). Similar error patterns across subjects were only observed for the shank induced flexion/extension error, and the thigh induced ab/adduction and internal/external knee rotation errors (Fig. 16). Since no similar error patterns were present for all the other rotations, the authors speculate that it would be very difficult to develop a correction algorithm which could be applied to any particular subject, especially when considering that there were no clear shank and thigh error patterns across all subjects and rotations even for the relatively uniform sample of subjects used in this study (same gender, no obese subjects).

Based on the results of this study, external markers attached to the shank and thigh cannot be used to reliably determine ab/adduction and internal/external knee rotation. In the past, different methods have been suggested to overcome or minimize the problem of the skin movement artefact during human ambulation. These methods include the use of rigid skin frames (Karlsson, 1990; Ronsky and Nigg, 1991; Angeloni et al., 1993), the use of a solidification method (Chze et al., 1995), or methods of direct skeletal measurements (Levens et al., 1948; Tashman et al., 1995). The use of a rigid frame or the application of a solidification method may provide a better estimation of the skeletal knee joint motion during running. However, it can be speculated that such procedures would only slightly diminish the discrepancies between the skin and bone marker based rotations since these methods mainly eliminate or reduce the motion of the markers relative to each other. However, the rigid skin frame or the three (or more) markers yielding the best rigid model (Chze et al., 1995) are likely to move as a whole with respect to the underlying bone. Therefore, such methods may only marginally improve the results.

The application of direct measurement with the use of bone pins is limited due its invasiveness. A promising method which is able to directly measure skeletal motion during routine human gait analysis has recently been presented (Tashman et al., 1995). Tashman and co-workers (1995) developed a biplanar video fluoroscopy system allowing tracking of skeletal kinematics during gait. The challenge of this technique will be to identify the exact location of bony landmarks in the two x-ray views. This identification problem can be avoided with the use of bone implanted pellets (tantalum markers). However, the implantation of such pellets is an invasive procedure, which together with the exposure to radiation associated with the fluoroscopy would limit the application of this method.

The results have also clearly shown that the discrepancies between skin and bone marker derived knee rotations were predominantly caused by the skin movement artefact at the thigh. This result indirectly implies that the tibial rotation (with respect to a laboratory coordinate system) may be well represented when using external markers. This will be discussed in more detail in chapter 7.

In conclusion, the results of this study have shown that external markers can only be used to reliably determine the skeletal tibiofemoral flexion/extension. For ab/adduction and internal/external knee rotation, the skin marker based rotations cannot be used as an indicator of the skeletal motion. In these rotations, the difference between the skin and bone marker based kinematics may easily exceed the actual motion.

It is not known how well surface markers attached to the shank and thigh represent the skeletal tibiofemoral (knee) joint motion during running. Hence, the purpose of this investigation was to compare the skin marker derived tibiofemoral motion with the skeletal tibiofemoral motion during running. In addition to skin markers attached to the shank and thigh, triads of reflective markers were attached to bone pins inserted into the tibia and femur of three subjects. Three-dimensional kinematics of the stance phase of five running trials were recorded for each subjects using high speed cine cameras (200 Hz). The knee motion was expressed in terms of Cardan angles (flexion/extension, ab/adduction, internal/external knee rotation) calculated from both the external and skeletal markers. It was found that good agreement was present between the skin and bone marker based knee flexion/extension. For ab/adduction and internal/external rotation, the difference between skeletal and external motion was large considering the small amplitude of these motions, and in some subjects, this difference exceeded the skeletal range of motion of these rotations during the stance phase. Based on the results of this study, it was concluded that knee ab/adduction and internal/external knee rotation during running may be affected with substantial errors when using skin markers.

This chapter discusses methodological problems and aspects associated with this project. The specific purposes are:

1. to present and discuss the problems encountered with the attachment of the femur pin,
2. to discuss uncertainties in determining anatomical coordinate systems and assess the influence of these uncertainties on the measured (tibiofemoral) joint motion,
3. and to present and discuss tibiofemoral rotations and translations during running in view of the methodological concerns presented in (a) and (b).

As pointed out earlier (see chapters 3 & 5), problems with the femur pin attachment were encountered in two subjects, subject 2 and subject 4. In subject 2, the femur pin became loose during the first motion recording (walking) trials. Therefore, it was decided to surgically remove this pin and to continue motion recording with the remaining tibia and calcaneus pin. In subject 4, a phenomenon which can be described as femur "popping" was observed during the course of the experiments. This "popping" can be described as a sudden rotation of the pin (about its long axis) relative to the thigh in the order of 10 when the knee underwent large flexion angles during the swing phase of walking or running. This "popping movement" cannot represent true motion of the femur, because this sudden rotation would correspond to a large relative translation between the femoral head and the pelvis. This "popping movement" was detected when viewing the film before starting the data analysis.

Both of these "instability" problems of the femur pin encountered in subject 2 and 4 were attributed to the influence of the iliotibial band. In order to access the femur in the proximal region of the lateral condyle, the pin was inserted through the iliotibial band. Possible impingement (and friction) problems between femur pin and iliotibial band were attempted to be minimized by cutting a slit (10 to 15 mm in proximal/distal direction) into the iliotibial band at the time of pin insertion. It was speculated that in subject 2 and 4, the slit cut into the iliotibial band was either too small, or that the iliotibial band moved considerably in an anterior-posterior (femoral) direction relative to the insertion site of the femur pin. The latter may mainly be expected to occur during large knee flexion angles when the tibial insertion point of the iliotibial band moves away in a posterior direction with respect to the femur. This would possibly explain why these impingement problems in subject 4 were only encountered when large flexion angles were present.

McClay (1990) used a similar insertion site for the femur pin and also reported on an "impingement problem" in the subject used for the pilot study. That subject demonstrated a stiff-legged walking and running gait, and was unable to flex the knee upon request. The subject was painfree, and it was assumed that the femur pin was hindering normal movement by its introduction into the iliotibial band. McClay (1990) also speculated that the well-developed thigh musculature and strong iliotibial band in that particular subject may have contributed to this problem. For the following subjects, the surgical technique was changed to minimize the restriction problem. The pin was inserted when the knee was flexed and a longitudinal incision into iliotibial band was made (McClay, 1990). Using this approach, McClay (1990) found that restriction problems did not occur anymore in the following four subjects. Even though applying the same technique in the present study (incision into the iliotibial band, insertion of pin in flexed position), impingement problems could not be prevented in some subjects.

The rejection of the femur pin data of subject 2 and 4 was based on observations made during the course of the experiments and made during the inspection of the films, respectively. However, in the remaining subjects, there may still have been a problem with the attachment of the femur pin which may not have been easily detected by visual inspection of the films. Therefore, in order to find out possible problems with the femur pin attachment, the standing trials collected during the course of the experiment were analyzed.

For every subject, eight standing trials corresponding to different movement and shoe conditions were collected always immediately prior to a set of specific movement measurements (Fig. 17). These standing trials were distributed over a period of approximately 90 minutes. For these standing trials, the subjects were asked to stand in a fully extended knee position with a hip-wide stance aligning their lower extremity segments with respect to the force plate representing the laboratory coordinate system. The alignment was monitored and the subjects were asked to realign themselves if the lower extremities and in particular the shoes (e.g. standing in a slightly abducted position) were not in alignment with the laboratory coordinate system. For the results presented in the previous chapters, only trials 1 and 2 were used corresponding to the standing trials collected prior to the walking and running trials, respectively (Fig. 17). Standing trials 3 to 8 were used for another project where the kinematic influence of various shoe design parameters was tested. Trial 5 corresponded to a barefoot standing trial, whereas in all the other trials shoes were worn.

The stability of the femur and tibia pin attachment was determined by comparing the knee positions during these standing trials (for subject 1, 3 and 5). For this purpose, standing trial 2, which was employed to define neutral for all the running trials (see chapter 5), was used as the reference trial to which the positions of all the other standing trials were related. The calculations involved were the same as presented previously for the tibiofemoral motion treating the standing trials 1, and 3 to 8 as if they were knee positions occurring during movement. Additionally, during the standing trials (1, 3 to 8) the position of the femur and tibia was also calculated with respect to the position of the femur and tibia during the standing trial 2. This was done in order to find out if possible attachment problems can be related to either the femur pin or the tibia pin.

Relatively large deviations in the standing positions over time (>10) were observed in subject 1 and 5 (Fig. 18). In subject 1, a more or less gradual increase in flexion position could be observed, whereas for subject 5, a gradual increase towards a more extended knee position appeared to be present. By examining the corresponding femur positions (Fig. 19) and tibia positions (Fig. 20) it was apparent that for both subjects, these deviations were caused by the femur pin. This was also confirmed by (visually) examining the film sequences of these standing trials. The visual inspection also suggested that in these subjects the marker triads attached to the femur pin either made a clockwise or counter-clockwise rotation around the bone pin axis (screwing in or screwing out). For completeness, the stability of the calcaneus pin was also assessed in these three subjects using the same approach as for the femur and tibia pin. No evidence was found in any of the three subjects suggesting that the attachment was not stable.

Based on these results (Fig. 18 - Fig. 20), it can be concluded that in subject 1 and 5, the femur pin moved (rotational drift) gradually with respect to the bone during the duration of the 90 minute protocol. On the other hand, there was no evidence of a loosening or a drift for the femur pin attachment in subject 3.

In order to determine the implications of the "rotational drifts" in the femur pin attachment found in subject 1 and 5 with respect to the results presented in the previous chapters, the exact chronological sequence of trials and events is important (Fig. 17). For each subject, the three walking trials took place between standing trial 1 (used to define neutral for the walking trials) and 2, and the five running trials took place between standing trial 2 (used to define neutral for the running trials) and 3. It is also important to note that the subjects were typically sitting down after completing the motion trials (Fig. 17). Since all positions displayed in Fig. 18 were calculated with respect to standing trial 2, the knee position for the standing trial 1 directly reflects the change in alignment from before to after the walking trials. Similarly, the knee position for trial 3 reflects the change in standing position from before to after the running trials (Fig. 18). First of all, the changes in knee position from standing trial to the next standing trial are rather small (Fig. 18) in both subject 1 and 5. Furthermore, it is speculated that the "rotational drift" of the pin happened after the motion measurements when the subject was sitting down, and therefore going through a relatively large flexion where the risk of impingement problem between iliotibial band and femur pin is expected to be high. Another possibility could also be that a gradual rotational drift occurred between trials. Such an effect would be evident as a gradual change in knee kinematics from single trial to single trial. However, such an effect could not be observed. Based on all these considerations, it was concluded that the tibiofemoral joint kinematics presented in the previous chapters for subject 1 and 5 were not significantly affected by this femur pin "drifting". However, in the worst and unlikely case, if the pin rotated (drifted) between the standing trial and the first motion trial, alignment errors in the order of magnitude of 5 or less (estimated based on Fig. 18) would have to be expected.

One way to overcome the "impingement" problem between femur pin and iliotibial band would be to choose other locations to access the femur with a bone pin. Femur pins placed at either the medial condyle (Levens et al., 1948; Lafortune, 1984) or at the greater trochanter (Murphy, 1990) would not have the impingement problem with moving structures (muscles, tendons). However, a placement at the medial femoral condyle would require that the marker clusters attached to that pin would have to be projected anteriorly (or posteriorly) in order not to interfere with the other leg during locomotion (Lafortune, 1984). Even with the use of a counter-arm design as employed by Lafortune (1984) for walking, vibration problems (due to inertia) during running would be very likely with the use of such a design (McClay, 1990). Therefore, such a placement does not appear to be adequate for analyses of highly dynamic movements such as running. The problem of using a bone pin at the greater trochanter lies in the long distance between the attachment site and the location of the knee joint. For instance, assuming a femur length of 45 cm, a 1 error in determining the orientation of the femur pin would result into a translation error at the knee joint of 8 mm. Consequently, the femur pin location chosen for the present project seems to be the most appropriate despite the problems encountered with the femur pin. In this context, it is also important to note that the subject who showed the femur pin "popping" also experienced slight complications. This subject resumed running activities within a week after the experiments, and thereafter developed an inflammation of the iliotibial band. This suggests that proper healing of this structure after such experiments is required before resuming athletic activities.

For three-dimensional intersegmental motion measurements, the choice of anatomical coordinate systems is of great importance (Blankevoort et al., 1988; Pennock and Clark, 1990; Ramakrishnan et al., 1991; Cappozzo et al., 1995). Using a joint coordinate system (JCS) as in this project, Cardan angles and the corresponding translations are highly dependent on the choice of anatomical coordinate systems in both segments. Consequently, angles and translations calculated using a JCS are highly susceptible to alignment errors and uncertainties in defining the anatomical coordinate systems (Blankevoort et al., 1988; Pennock and Clark, 1990; Ramakrishnan et al., 1991). For instance, Ramakrishnan and co-workers (1991) found that during a full gait cycle, perturbations of 15 of the anatomical thigh coordinate system around its longitudinal axis caused almost no effects on the flexion/extensions, errors in ab/adduction of up to 12, and a shift in internal/external knee rotation curves of about 10 to 15. The methodological concern associated with the definition of anatomical coordinate systems makes it very difficult to compare results across studies using different definitions of anatomical coordinate systems (Pennock and Clark, 1990). Additionally, inter-subject comparisons may also be difficult to make since subtle differences may easily be caused by small deviations in anatomical reference frame alignment across subjects or specimens (Blankevoort et al., 1988).

For the determination of skin movement artefact as presented in the previous three chapters, the dependency of the joint rotations on the definition of anatomical coordinate systems is not of a major concern. Mainly intra-subject comparisons were made and the same standing trials were used to define both the skin and bone marker based anatomical coordinate systems. However, when comparing joint kinematics across subjects, this is a concern since differences across subjects may be partially (or totally) caused by slight differences in defining the anatomical coordinate systems. This is especially a concern for the presentation of (skeletal) tibiofemoral rotations where uncertainties in defining the anatomical coordinate systems may also cause more or less cross-talk. The cross-talk problem is discussed in detail in the following paragraphs.

Since the values used for this specific example correspond to (estimated) realistic values with respect to this project, the cross-talk during the stance phase of running can be expected to easily fall within the range of 5 for both ab/adduction and internal/external knee rotations.

Due to the dependency of Cardan angles on the choice of anatomical coordinate systems, other concepts, such as (finite or instantaneous) helical axes, have been chosen to represent the three-dimensional joint motion (e.g. Blankevoort et al., 1990; Murphy, 1990). The finite helical axis representation describes motion steps as a rotation about and a translation along an axis. Although the direction and position of a helical axis are represented with respect to a coordinate system (either fixed in the distal or proximal segment), both position and direction can be described relative to anatomical landmarks embedded in one of the segments, in which case the precise determination of the coordinate axes is of less importance (Blankevoort et al., 1990). The direction and location can even be displayed graphically onto a knee model (Blankevoort et al., 1990) or onto radiographic pictures (Lundberg, 1989), and in these cases the finite helical axis descriptors are totally independent of the choice of coordinate systems. However, finite helical axis descriptors have also the disadvantage that they may be less "appealing" to clinicians, and that they are highly susceptible to measurement errors if the rotations are of small amplitude (Woltring et al., 1985).

It is actually planned to use the data gathered in this project to calculate finite helical axes during running and to project these axes onto radiographic pictures which were taken for all subjects to define coordinate systems using a roentgen-stereophotogrammetric analysis. Unfortunately, this can only be done for subject 3, for whom the femur pin attachment appeared to be stable during the entire course of the experiments.

Recently, Woltring (1994) suggested to use helical angles to describe joint motion. Helical angles use a similar approach as the joint coordinate system (Grood and Suntay, 1983), but instead of extracting Cardan angles from the transformation matrix, Woltring (1994) suggested to determine "helical angles". Helical angles are calculated by multiplying the unit vector of the helical axis with the amount of rotation occurring around that helical axis. However, this approach also relies on proper definition of the two anatomical coordinate systems. In his publication, Woltring (1994) acknowledged the problem of cross-talk from knee flexion/extension into ab/adduction and into internal/external knee rotation caused by misalignments between the true anatomical system and the calculated one. Woltring (1994) used an interesting approach to correct for cross-talk caused by misalignment of the anatomical coordinate systems. Misalignments were corrected by either minimizing only the ab/adduction or the ab/adduction and the internal/external knee rotation at the time of maximum flexion. Woltring (1994) concluded that this approach worked well from a numerical point of view, but may be questionable from anatomical point of view.

The purpose of this section is to present and discuss the skeletal tibiofemoral rotations and translations occurring during the stance phase of running. The following results regarding the tibiofemoral kinematics have to be viewed under the reservations discussed in the previous section (alignment of anatomical coordinate systems, cross-talk).

The methods and data which will be presented are exactly the same as in the previous chapter, except that in addition to the standing trial based tibial and femoral anatomical coordinate systems, a roentgen-stereophotogrammetric analysis (RSA) was used to define the anatomical coordinate system of the femur and tibia. In contrast to standing trial based coordinate systems used in the previous chapter, RSA based coordinate systems allow the definition of anatomically meaningful origins of the two coordinate systems which in turn allows quantification of joint translations. For all five subjects included in this project, radiographic pictures for the RSA were either collected prior or after the motion measurements. This, of course, required that the attachment of the bone pins did not change throughout the experiments. Since the tibia and femur pins only appeared to be stable for subject 3 (as discussed earlier), tibiofemoral rotations and translations using RSA based coordinate systems will only be presented for this subject. For the rotations, however, the results of subjects 1 and 5 will also be used as already presented in the previous chapter focusing on the difference between external and skeletal tibiofemoral kinematics.

The same definition and procedure as used by Lafortune et al. (1992a) was employed for the RSA based definition of anatomical coordinate systems for the femur and tibia. Briefly, two radiographs were taken, one from a lateral and one from a anterior view of the knee joint. In addition to the three femoral bone pin markers (FM1 to FM3, Fig. 21) and three tibial bone pin markers (TM1 to TM3, Fig. 21), a number of anatomical points were digitized in these views enabling to define anatomical femoral and tibial reference frames. For the femoral anatomical coordinate system, the deepest point of the intercondylar notch (F1) was digitized and chosen as the origin of that coordinate system. Then a point F2 lying on a line parallel to the femur long axis and going through point F1 was used to define the proximal-distal axis (y-axis) of the femoral coordinate system. The medio-lateral femoral axis (z-axis) was defined by projecting the line connecting the most distal point on the medial (F3) and lateral (F4) femoral condyles onto a plane going through the origin (F1) and being normal to the y-axis. The remaining axis was then calculated using the cross product of the unit vectors of the two axes already defined.

For the tibial coordinate system, the most proximal point of the medial intercondylar eminence (T1, Fig. 21) was selected as the origin of the tibial coordinate system. A second point T2, lying on a line parallel to the longitudinal axis of the tibia and going through T1, was used to define the proximal-distal y-axis. The medio-lateral axis was determined by projecting the estimated centers of the medial (T3) and lateral (T4) tibial articular surfaces onto the plane going through T1 and being perpendicular to the proximal-distal axis. The remaining anterior-posterior axis was then again calculated using the cross product.

Using coordinate transformations (Sderkvist and Wedin, 1993), the femur pin markers were then expressed in the RSA femoral coordinate system, and similarly, the tibia pin markers were expressed in the RSA tibial coordinate system (see also appendix). The following calculations were then exactly as if these coordinates were the coordinates recorded during the standing trial (see chapter 3). The joint translations along the femur fixed flexion axis (medio-lateral shift), along the floating ab/adduction axis (anterior-posterior drawer), and along the tibial fixed internal/external rotation axis (compression/distraction) were calculated. Since the medio-lateral shift and the compression/distraction magnitudes are dependent upon the rotation around the floating axis, these translations were adjusted accordingly (Grood and Suntay, 1983; Lafortune et al. 1992a). The terms medio-lateral shift, and anterior-posterior drawer always refer to translations of the tibia with respect to the femur. The terms medio-lateral shift, anterior-posterior drawer and compression/distraction may not be directly "translated" into the equivalent clinical terms. For instance, compression/distraction does not refer to the compression/distraction experienced between the contact areas of the articulating surfaces of the tibia and femur. Compression/distraction as used in this study refers to the entire tibiofemoral joint structure as being shortened or stretched in a direction parallel to the long axis of the tibia (Lafortune et al., 1992a).

The ab/adduction patterns varied considerably between the subjects (Fig. 22). The ab/adduction were similar in subject 3 and 5, whereas the amplitude of this motion was higher for subject 5. Both subjects 3 and 5 showed an initial abduction movement occurring from 0% to 40% of stance followed by an adduction motion until the end of stance. This initial abduction motion averaged 6 for subject 3, and 9 subject 5. On the other hand, subject 1 showed a small initial adduction movement of 4, followed by smaller abduction and adduction motions. Towards the end of stance phase, subject 1 exhibited an average adduction motion in the order of magnitude of 3. As found for flexion/extension, the RSA based and standing trial based ab/adduction agreed well for subject 3, and the only difference consisted again of a constant shift between the two average curves.

The patterns and magnitude of ab/adduction during stance was in total disagreement with the only other running study reporting skeletal knee ab/adduction (McClay, 1990). McClay (1990) found that all four subjects exhibited a similar pattern: an initial adduction motion averaging 6 from touchdown to around 40% of stance, followed by a gradual abduction (8) until the end of stance. None of the subjects in the present study showed a similar pattern. Part of these differences may be attributed to the fact that the coordinate system definitions used in McClay (1990) were based on RSA whereas in this study they were based on a neutral standing trial. However, interestingly even the RSA based curves for subject 3 did not agree at all with McClay’s data, although the anatomical reference frames for both the femur and tibia were defined using exactly the same method.

Due to the ligamentous restrictions imposed by the medial and lateral collateral ligaments and due to the geometry of the knee joint, the ab/adduction motion at the knee joint is very limited. The range of motion of knee ab/adduction is approximately 5, whereas the possible range of motion of the other rotations are much higher; the ranges of motion of flexion/extension and internal/external knee rotation are approximately 150 and 35, respectively (Frank et al., 1995). It can be speculated that the range of motion of ab/adduction is even smaller during running when the knee joint is loaded and stabilized by muscular forces. However, the ranges of motion in ab/adduction for some subjects found in this study and in the study by McClay (1990) well exceeded 5. This suggests that the ab/adduction motion measured may not be the "true" ab/adduction motion. Due to the small magnitude, the ab/adduction motions are highly influenced by alignment problems of the anatomical coordinate systems. The effect of alignment problems and resulting cross-talk may exceed and mask the actual ab/adduction motion. In this context, it is interesting to note that in the two subjects showing a considerable amount of ab/adduction (subjects 3 & 5, Fig. 22), the patterns of ab/adduction were very similar to the flexion/extension motion giving rise to speculations that the relatively large ab/adduction motions were mainly caused by cross-talk.

The internal/external knee rotation patterns were fairly similar across subjects. From touchdown to midstance, all subjects showed an initial internal knee rotation (Fig. 22). However, the magnitude of that motion ranged considerably between subjects: Almost no initial knee rotation was present in subject 5 (2), whereas the initial internal knee rotation was very pronounced in the other two subjects (9 for subject 1), 7 for subject 3). The subjects exhibited an external knee rotation during the second half of stance. For all subjects, this external knee rotation towards the end of stance exceeded the initial internal knee rotation leaving the knee in a more externally rotated position at take-off as compared to touchdown. The patterns and magnitudes of internal/external knee rotation found in this study compared favourably to the patterns and magnitudes presented in the study by McClay (1990) with the exception that in that study the magnitude of the initial internal knee rotations was higher than the magnitude of external knee rotation during the second half of stance.

Again, it has to be realized that at least part of the differences found between subjects for the internal/external knee rotations may be attributed to small deviations and inconsistencies in defining the anatomical coordinate systems and resulting cross-talk. For subject 3, the internal/external knee rotation curves based on RSA and the neutral standing trial were again very similar and an obvious shift between the two average curves can be reported (Fig. 22). However, in contrast to flexion/extension and ab/adduction, there was a noticeable difference in amplitude; the initial internal knee rotation based on RSA and the neutral standing trial averaged 11 and 7, respectively.

On a different note, one of the five trials in subject 5 appeared to be an outlier (Fig. 22). Since this particular trial was trial number 1 in the series of the five trials, it was first suspected that between trial 1 and the following four trials the femur pin may have moved. However, the same trial also produced an "outlier" for the skin marker based curves (see Fig. 15), and therefore, the possibility of a moving (femur) pin between these trials was excluded.

When comparing the ab/adduction and internal/external knee rotation curves with the flexion/extension curves within the same subject, it is apparent that most of these curves resemble the flexion/extension patterns. In other words, the ab/adduction and internal/external knee rotation curves are the same as the flexion/extension curves with different amplitudes. It appeared that only the ab/adduction in subject 1 and the internal/external knee rotation in subject 5 did not have this "pattern agreement". The similarities between the flexion/extension curves and the other curves within the same subject suggested that there may have been some cross-talk. On the other hand, it may also be argued that the knee rotations are coupled, in the sense that for instance, an internal knee rotation takes place when the knee undergoes a flexion motion (Blankevoort et al., 1988). Based on the data presented in this study, it is difficult to estimate how much of the non-primary knee rotations (ab/adduction, internal/external knee rotation) is due to a "real" rotation and how much can be attributed to alignment problems of the anatomical reference frames. More research is needed to establish reliable and meaningful coordinate systems in order to make valid comparisons across subjects. On the other hand, it may also be argued that Cardan angles using a joint coordinate system (Grood and Suntay, 1983) may not be appropriate to determine knee rotations other than flexion/extension.

The tibiofemoral joint translations of the five trials for subject 3 are depicted in Fig. 23. Since the origin of the femoral and tibial anatomical coordinate systems did not have coincident origins, there is an "off-set" present in these graphs. In other words, already in a "neutral" position the origins of the two reference frames would be some distance apart from each other. Therefore, the change in movement should be considered rather than the absolute values displayed on the vertical axes (Fig. 23).

The anterior/posterior drawer curves indicate that during the first 5% of stance almost no movement took place (Fig. 23). Thereafter, the origin of the tibial reference frame moved 4 mm posteriorly with respect to the femur. From around 40% to 80% of stance, an anterior movement of the tibia (5 mm) took place, followed by a fast posterior movement of the tibia towards the end of stance.

The distraction/compression pattern was very similar to the anterior/posterior drawer pattern (Fig. 23). Almost no compression/distraction movement took place during the 10% of stance. From 10% to 40% of stance, a distraction movement (5.6 mm) took place between the origins of the tibial and femoral reference frame. This distraction movement was followed by a larger compression movement (6.8 mm). During the final 20% of stance, a distraction movement of 2.8 mm was observed between the origins of the two coordinate systems.

The medio-lateral shift was the translatory motion with the least amount of movement excursion during stance (Fig. 23). No consistent medio-lateral motions across the five single trials was present during the first 15% of stance. Thereafter, the tibia underwent a lateral shift averaging 3.6 mm. From 40% to 80% of stance, the origin of the tibial reference frame shifted medially (4.1 mm) with respect to the femoral reference frame. During the last 20% of stance, the tibia shifted again in a lateral direction (1.8 mm).

All tibiofemoral translations (Fig. 23) exhibited a striking similarity with the knee flexion extension behaviour (Fig. 22). This has also been found in previous investigations determining the skeletal tibiofemoral translations during walking and running (Lafortune, 1984; McClay, 1990). The striking similarity between the translations and the knee flexion is not surprising. Even though the orientation and location of the anatomical tibial and femoral reference frames were based on anatomical considerations, the points chosen as the origins of the femoral and tibial reference frames can be considered to be "arbitrary". That means that they are likely not to reflect an "average" knee joint center. If the origins of the two coordinate systems do not coincide with an "average" joint center or if such an "average" joint center does not exist, the translations are very much dependent on the rotations. In other words, cross-talk exists in the sense that translations would be registered even though a pure rotation took place. The methodological concerns regarding the sensitivity of the tibiofemoral translations with respect to the definition of the anatomical coordinate systems has been pointed out previously (Blankevoort et al., 1988). Blankevoort and co-workers (1988) suggested that relative translations of a point on the femur with respect to a point located at the tibia would be more meaningful than translations calculated along the axis of a joint coordinate system.

The joint translations as calculated for subject 3 (Fig. 23) will not be further discussed since it is believed that these results are primarily a function on how the anatomical coordinate systems were defined, and the physiological meaning of these results are limited. For a comprehensive interpretation of the joint translations, meaningful distances between points located in the femur and tibia should be calculated (Blankevoort et al, 1988). This was attempted in the present study by calculating the distance between average femoral and tibial attachment sites of the anterior cruciate ligament (ACL). These points were identified and digitized on the radiographic pictures (RSA) which allowed the calculation of the distance between these points during the stance phase of running. As expected, the translations were much smaller than the translations shown in Fig. 23. However, the changes in distance between the average femoral and tibial ACL attachment sites were in the range of the accuracy of the motion measurement system used (1.5 mm), and therefore, the author did not feel comfortable presenting that data. In order to calculate such small changes, a closer camera view of the knee joint would have been required to attain a better accuracy enabling to calculate such small changes.

The knee rotations were presented for three subjects and the knee translations for one subject during the stance phase of running. It was found that the non-primary knee rotations (ab/adduction, internal/external knee rotation) as well as the translations were highly influenced by the knee flexion/extension patterns during the stance phase of running. Based on the results of this study, it cannot be concluded how much of these rotations and translations were "real" and how much was due to the definition of the anatomical coordinate systems used in this investigation ("cross-talk"). Further research is needed to establish reliable, reproducible and meaningful anatomical coordinate systems for both femur and tibia. It can also be argued that Cardan angles calculated using joint coordinate systems (JCS) may not be the method of choice to determine the non-primary knee rotations. It was concluded that joint translations determined using a JCS may only have limited physiological meaning. For future studies, it is suggested to calculate meaningful distances between points located in the two bodies, such as the insertion sites of ligaments. Such distances are believed to provide a more comprehensive and physiologically meaningful translations than translations measured using a joint coordinate system.

The purpose of this chapter is (a) to discuss the implications of the results of this project with respect to future studies using external markers to estimate the skeletal joint motions at the lower extremities, and (b) to make suggestions for future research in the area of skin (or external marker) movement artefact. The implications and possible future work will be discussed separately for the shoe/foot (calcaneus), the shank (tibia) and the thigh (femur).

The results of the previous chapters (chapters 3&4) have shown that:

These findings imply that shoe markers may not provide an accurate representation of the skeletal calcaneal kinematics. Hence, skeletal kinematics should not be predicted from markers attached to the shoe. Based on the results of this study and based on the review of literature, two approaches (considerations) are suggested for future studies:

The results of this project have shown that for both the tibiocalcaneal (ankle-joint complex) and tibiofemoral (knee) rotations, the skin movement artefact caused by the shank markers was almost negligible in comparison to the external marker movement artefact caused by the shoe or the thigh markers. In order to find out how accurately the rotations of the tibia can actually be determined with skin markers, the tibial rotations were calculated with respect to the laboratory coordinate system both based on external and skeletal markers.

Tibial rotations during running were calculated for the five subjects for which AJC (tibiocalcaneal) rotations were presented in chapter 4. The rotations of the tibia with respect to the laboratory coordinate system were determined using Cardan angles. For these calculations, the longitudinal tibial rotation occurred around the proximal-distal (longitudinal) axis of the tibia, tibial ab/adduction around the floating axis, and tibial flexion/extension around the z-axis (axis perpendicular to running direction and vertical laboratory axis) of the laboratory (or film) coordinate system. The kinematics were determined based both on skeletal and skin markers. For the skin markers, all markers were used which were visible throughout the entire stance phase (see chapter 4). That means, that depending on the subject, four shank markers (subject 1), five shank markers (subject 3), or all six shank markers were used (subjects 2, 4 & 5).

During midstance, when the foot is on the ground, the rotation of tibia with respect to the laboratory coordinate system and with respect to the foot can be expected to be very similar.

The longitudinal tibial rotation based on skeletal and bone markers are depicted in Fig. 24. For all subjects, excellent agreement between the skin and bone marker based tibial rotation was found with respect to the amplitude as well as with respect to the shape of the curves (Fig. 24). This was also reflected in the small mean (RMS) differences and maximal differences between the skeletal and skin marker derived tibial rotations (Table 9).

The differences found in this study between skin and bone marker based tibial rotations were slightly lower than the differences found in a previous study comparing skin and bone marker based tibial rotations during walking (Holden et al., 1994). From the curves of the three subject presented in Holden et al. (1994), the maximal difference during stance was estimated to be 3.8 (averaged across the three subjects), whereas in the present study the maximal differences averaged 2.6 (Table 9). It is surprising that the differences were actually lower for running (present study) than for walking (Holden et al., 1994). However, it is suggested that the smaller difference for running can be explained by subject differences and differences in number and placement of skin markers used rather than by the different movements (running vs. walking).

The results of this study have shown that rotation of the tibia along its longitudinal axis is well represented with the use of skin markers as employed in this study. It is speculated that the representation of the skeletal tibial rotation could even be improved when all skin markers would be placed directly over the tibia instead of also placing markers over other structures, i.e. the fibula (lateral shank markers: S1 to S3, see Fig. 1).

The results of this project have shown that skin movement artefact occurring at the thigh is a major problem. Rotations other than flexion/extension cannot be reliably determined when using skin markers.

For the results presented in the previous chapters, five skin markers (Th2 to Th6) were used to calculate the skin marker based rotations. However, some markers may move more than others with respect to the underlying bone, and therefore, a better representation of the skeletal kinematics may be obtained when excluding such ("bad") markers from the calculations. The purpose of the following paragraphs is to come up with some recommendations regarding marker placements at the thigh. For that purpose, two type of analyses were performed, a quantitative analysis and a qualitative analysis.

In addition to the different thigh marker combination, the MTE was also calculated for three running trials with shoe 4 (see Fig. 17) for the three subjects with valid femur pin data. For these running trials, the subjects wore a thigh skin frame (Fig. 25). The center part of the frame (arranged in a proximal-distal direction) consisted of a strip of plastic (Sanssplint™) which was 20 cm in length and 5 cm in width. At the each end of this strip, separate strips of thermoplast were secured, encompassing most of the thigh. Three skin markers were attached to the frame as depicted in Fig. 25. The skin frame was attached to the thigh with double sided tape and additionally, the distal and proximal "circumferential" strips were closed at the posterior part with tape. Prior to the motion recordings and the insertion of the bone pins, the thigh frame was fitted to each of the subjects in order to ensure an optimal fit.

A second analysis was also performed to assess how much each thigh marker moved with respect to the underlying femur (using again the same data as used for chapter 5). For this analysis, all of the thigh marker positions were expressed in a femur coordinate system based on the three markers attached to the pins. The difference of these thigh marker positions during the stance phase compared to during the standing trials was determined as a measure on how much these markers moved at each instant in time during the stance of the running trials. An average relative marker movement (RMM) of each marker was then calculated during the stance phase from all the five running trials and from all the three subjects (subjects 1, 3, & 5) for which valid femur pin data was available.

The results of the mean thigh errors in terms of rotations are presented in Table 10. All MTE values were between 2 and 5 except when using the thigh marker combination Th4-Th5-Th6. The results for the Th4-Th5-Th6 combination were excepted as these markers were more or less on a line (colinear), which results in a poor description of a rigid body in space. The best skin marker combination was Th2-Th3-Th6. However, this combination was only marginally better than other combinations. The skin frame used did not produce less error. However, it must be mentioned that this skin frame was used during different running trials with a different shoe (shoe 4). Shoe 4 had a much stiffer midsole than the shoe 1. This may have affected the amount of the skin movement artefact at the thigh and therefore these results cannot be compared directly.

The results of the relative movement of each of the thigh markers with respect to the underlying bone confirmed the results found for the rotational errors of the different possible combinations as presented in Table 10. Markers Th2, Th3 and Th6 had also the least amount of RMM (Table 11). This error analysis is limited as errors can be expected to increase the further away the markers are from the location of the bone markers used to define the skeletal femoral coordinate system. This increase in error is due to two reasons. First, small inaccuracies (caused e.g. by digitizing errors) in the definition of the directions of the bone-embedded femoral coordinate system are amplified the further away the markers are. For instance, a 2 rotational error in defining the femoral coordinate system causes an error of 1.7 mm (= sin(2) * 50 mm) for a marker at a distance of 5 cm. On the other hand, if the marker is 40 cm away, such a rotational deviation would result in 14 mm error in determining the RMM of such a marker. Secondly, the further the thigh markers are away from the bone markers, the more they are affected by the inaccuracies in the DLT calculations (outside calibration volume). Due to these reasons, it is suggested that the results (RMM) of the markers furthest away from the bone markers are not reliable (Th1, Th3).

One problem inherent with both quantitative variables used (MTE and RMM), is that results may be masked or affected by the DLT inaccuracies of the thigh markers. Due to this limitation, recommendations with respect to marker placements at the thigh could not be made exclusively based on these analyses. Hence, in addition to the quantitative analysis, a qualitative analysis was performed.

For the qualitative analysis, all the running trials used in this study were examined carefully on the films. The following observations were made:

• Generally, the lateral markers (Th1, Th2, Th3) appeared to be more stable than the markers placed in front of the thigh (Th4, Th5, Th6). This observation was in agreement with the finding of Cappozzo et al. (1996).
• The thigh marker Th4 (middle front marker) showed generally the greatest wobbling of all thigh markers.
• The marker placed at the greater trochanter appeared to be the best marker based on the observation of the films. This finding is in disagreement with the RMM results (Table 11), however as mentioned earlier, it is very likely that the RMM results for this marker cannot be trusted (DLT problems, large distance from bone markers). Interestingly, the observation that the greater trochanter marker appeared to be a good location is somewhat in disagreement to the conclusions made in a previous study (Cappozzo et al., 1996). Cappozzo and co-workers (1996) suggested that skin markers above anatomical landmarks (including the greater trochanter) are unsuitable for marker placements.
• Based on the observation of the film, the following ranking was made (from best to worst):

1. Th1
2. Th3 and Th6
3. Th2 and Th4
4. Th5

• Interestingly, the marker placed in the middle front (Th5) showing the most relative movement (wobbling) with respect to the underlying also appeared to influence the adjacent marker on the lateral side (Th2).
• The skin frame reduced the relative movement between the markers attached to it. However, the skin frame appeared to move as one unit with respect to the underlying bone, especially during the period when the thigh muscles were activated.
• The key reason for the above observations appeared to be the location of muscles and muscle activities. Markers placed on tendinous structures (Th3, Th6) appeared to be more stable than markers placed directly on muscles (Th5 placed on the muscle belly of the rectus femoris). Based on these considerations, locations on muscles (muscle bellies) should be avoided particularly if the muscles are rather large and are activated and deactivated during the movement in consideration.

The use of skin markers at the thigh appears to be very problematic when accurate three-dimensional kinematics is required. The limited results as presented in the previous paragraphs suggest that markers should not be placed on muscles that are activated during the movement in consideration. It is suggested that for any type of kinematic analysis involving the thigh, a number of markers (grid of markers) should be attached to the thigh and the subject(s) should be filmed or videotaped during the movement. A simple qualitative analysis (as performed in this study) may help to exclude obviously poor marker placements which introduce large differences between external and skeletal kinematics.

As for running, it is suggested that the markers Th2-Th3-Th6 provide the best (although still a rather poor) representation of the skeletal femoral kinematics. Markers placed directly over the muscle belly of the rectus femoris (Th5) should definitely be avoided.

Further research is needed to gain a better understanding of the skin movement artefact at the thigh and to establish methods that are able to provide an improved representation of skeletal (femoral) kinematics during highly dynamic movements such as running. For that purpose, future studies should be conducted which focus on the skin movement artefact at the thigh, and evaluate a greater number of skin markers to create recommendations for suitable skin marker locations on the thigh.

The author questions whether external markers, even when used in conjunction with a correction algorithm or a method to reduce the skin movement artefact, can (ever) be used to obtain an accurate representation of the skeletal femoral kinematics during a highly dynamic movement such as running. In that sense, the development of minimally invasive in-vivo measurements as for instance suggested by Tashman and co-workers (1996) may be a more promising avenue for future research aimed at accurate kinematic assessments involving the femur.

The objectives of this study were to determine the three-dimensional skeletal tibiocalcaneal (ankle joint complex, AJC) and tibiofemoral (knee) motion during the stance phase of walking and running with shoes, and to compare this to the respective motion determined from external markers. Five male subjects (age 28.6 4.3 years) participated in the study. All subjects were injury free at the time of testing and none of the subjects had an injury history which may have resulted in an abnormal gait. Under local anesthesia, intracortical bone pins (2.5 mm diameter) were inserted into the lateral femoral and tibial condyles, and into the postero-lateral aspect of the calcaneus of the subject’s right leg. Triads of reflective markers were attached to these pins, and additionally, six skin markers were attached to the thigh, six skin markers to the shank, and three markers were fixed to the shoe. For each subject, three walking and five running trials were recorded during the stance phase of walking and running using three high speed cine cameras (LOCAM) operating at 50 Hz for walking and 200 Hz for running. For these trials, the subjects wore standard running shoes (Adidas Equipment Cushioning 1994) without socks. The position of the simultaneously collected skeletal and externally mounted markers were digitized manually for each of the cameras. The three-dimensional coordinates of all the markers were calculated using a standard DLT (direct linear transformation) approach. A "neutral" standing trial collected prior to the motion trials was used to define the anatomical references frames of the various segments. Additionally, a set of radiographs were also taken either prior or after the motion measurements enabling the additional definition of RSA (roentgen-stereophotogrammetric analysis) based anatomical coordinate systems for the femur and tibia. Cardan angles (and respective translations) were used to express the intersegmental knee and AJC motion. Knee flexion/extension, ab/adduction, and internal/external knee rotation as well as AJC plantar/dorsiflexion, ab/adduction and in/eversion were calculated both from skeletal and external markers.

The comparison between skin marker based kinematics of bone pin trials and "dry runs" collected prior to the insertion of the pins revealed that the running style of the subjects was not significantly affected by the insertion of the bone pins. Problems with the femur pin attachment were encountered in some subjects. For one subject, a loosening of the pin was detected during the experiment whereas for another subject a non-rigid femur pin attachment was detected when observing the films prior to data analysis. Consequently, tibiofemoral motion based on skin and skeletal markers were only determined from the remaining three subjects. An analysis of all the standing trials collected during the course of the experiment also suggested that the femur pin drifted (rotational drift) in two of the remaining subjects. However, this rotational drift was small for the time span during which data for this project was collected. Therefore, these two subjects could still be included in the analysis.

For walking and running, the skeletal tibiofemoral (AJC) rotations were generally well reflected with external markers. However, the skeletal rotations were typically overestimated when using external markers. For instance, during running, the maximal initial eversion occurring from touchdown to midstance averaged 16.0 when using external markers. However, the same variable determined from skeletal markers was only 8.6. A segmental error analysis revealed that the differences found between the external and bone marker based kinematics were primarily caused by the relative movement of the shoe markers with respect to the underlying calcaneus. It was speculated that the artefact caused by the relative movement between shoe and calcaneus was mainly caused by the relative movement between shoe and heel and not between heel and calcaneus. Therefore, heel markers tracked through windows cut into the shoe may provide a better estimate of the calcaneal motion than markers directly attached to the shoe as used in this study.

Both during walking and running, good agreement was found between knee flexion/extension derived from skin and bone markers. For the other knee rotations however, the agreement between the rotations calculated from external and skeletal markers ranged from good to virtually no agreement. For ab/adduction and internal/external knee rotations, the differences were large considering the small amplitude of these rotations, and in some subjects, these errors exceeded the actual skeletal motion. A segmental error analysis showed that the discrepancies between external and skeletal kinematics was mainly caused by the skin movement artefact at the thigh. The errors caused by the skin movement artefact at the shank were almost negligible in comparison to the skin movement artefact at the thigh.

Methodological problems were also identified concerning the use of Cardan angles to describe the three-dimensional motion of the tibiofemoral joint. Internal/external knee rotation and particularly ab/adduction can be expected to be small, and these rotations are highly influenced by cross-talk (from knee flexion/extension) resulting from alignment problems of the anatomical coordinate systems. For instance, 5.6 ab/adduction and 6.7 internal/external knee rotation would be registered during a pure knee flexion motion of 30 if the uncertainty in the defining the anatomical coordinate system (of either the femur or tibia) was only 6 for internal/external knee rotation and 3 for ab/adduction. The values used for this specific example correspond to estimated values for knee flexion occurring during the stance phase of running (30 flexion), and to uncertainties in alignment (6 in internal/external knee rotation, 3 for ab/adduction) when using the procedures employed in this project.

Problems were also identified with the representation of joint translations using a joint coordinate system. These translations highly depend on the definition of the anatomical coordinate systems. Additionally, these translations are also highly dependent on the knee flexion/extension motion. Therefore, the physiological meaning of such joint translations may be questioned. For future studies, it is suggested to calculate meaningful distances between points embedded in both segments such as distances between femoral and tibial insertion sites of ligaments.

Based on the results of this project, it was concluded that during walking and running:

• tibiocalcaneal rotations are generally well represented with the use of external markers, but absolute values have to be interpreted with caution since the tibiocalcaneal rotations can be expected to be overestimated when using external markers, and that
• knee rotations other than flexion/extension may be affected with substantial errors when using skin markers.

In the following, the methods which were used to calculate intersegmental joint motions will be described in detail.

Segmental coordinate systems (anatomical reference frames) are needed to determine the relative position of two adjacent segments of the human body. For this project, anatomical reference frame were determined with two different methods:

• Neutral Position:

A standing trial or a defined neutral position is used to align the segmental (anatomical) coordinate system to the global (lab) coordinate system. Such coordinate systems cannot be used to calculate meaningful relative translations between two adjacent segments. Furthermore, anatomical coordinate systems that are based on a standing trial do not account for "misalignment" of different segments with respect to each other (e.g. varus/valgus positions).

• Roentgen Stereo Analysis (RSA):

An anatomical reference frame can be determined with the use of digitized landmarks and/or directions in the radiographic reference frame. Anatomical reference frames based on RSA account for subject difference in alignment, but their definition is "arbitrary", i.e. depends on how medio-lateral, proximal-distal, and anterior-posterior axes are defined in the RSA views.

 

The subject has the segments in a neutral (standing) position where it is assumed that the segments are aligned with the global (laboratory) coordinate system:

rG = rS

Definition of an anatomical (femur, tibia, and calcaneus) reference frame with the use of digitized anatomical landmarks or directions (in radiographic reference frame).

rA = [TRA] rR

[TRA] can be determined with the use of the "Sderkvist algorithm" (Sderkvist and Wedin, 1993).

Example: sderkvist([0 0 0,1 0 0, 0 1 0; new origin RSA coordinates, point 1/0/0 in new anatom. coord. system expressed in RSA coordinates,...])

Determination of absolute and relative orientation of two adjacent segments. As an example, the femur, tibia, thigh and shank segments will be used:

known: rG, rA of the markers

unknown: transformation matrix, TAG

rGsegment = [TAsegmentGsegment] rAsegment

[TAG] ([TAsegmentGsegment]) can again be determined with the use of the "Sderkvist algorithm".

 

JCS as proposed by Grood and Suntay (1983), and Cole et al. (1993) were used.

Rzxy =

• Determination of a, b, and g:Solve for a, b, and g using appropriate elements of the matrix above
• Determination of translations:ant.-posterior drawer (x)=Hx

compr./distraction (y) = Hy + sinb Hz

medio-lateral shift (z) = Hz + sinb Hy

Note that the translations (except along the floating axis) have to be corrected fo the rotation about the floating axis (Grood and Suntay, 1983; Lafortune, 1984).