Journal of Orthopaedic Research 8:312-382 Raven Press, Ltd., New York 0 1990 Orthopaedic Research Society
The Three-Dimensional Tracking Pattern of the Human Patella A. van Kampen and R. Huiskes Laboratory of Experimental Orthopaedics, Institute of Orthopaedics, University of Nijmegen, Nijmegen, The Netherlands
Summary: A study was undertaken to provide data on the three-dimensional tracking pattern of the patella, relative to the femur, in human knee-joint specimens. For this purpose, a highly accurate roentgen stereophotogrammetric analysis (RSA) method was applied. The three-dimensional motion patterns of the tibia and the patella were measured and represented in terms of three translations and three rotations each, during knee flexion in neutral (unloaded), endorotated, and exorotated pathways. We found that the patella displays complex but consistent three-dimensional motion patterns during flexion, which include flexion rotation, medial rotation, wavering tilt, and a lateral shift relative to the femur. The motion patterns are very much affected by tibial rotations accompanying flexion. Key Words: Patellar tracking mechanism.
Patellar pain syndromes are often assumed to be related to disturbances in the normal tracking mechanism of the patellofemoral joint. Chondromalacia patellae, for example, a condition in which abnormal changes of the patellar cartilage occur, is assumed to be caused by malalignment between the retropatellar cartilage surface and the femoral trochlea, resulting in abnormal pressure distributions and contact locations. During the last decade, research on the patellofemoral joint has been focussed on contact zones and pressure distributions, using various investigative methods (1,6,9). The data available on normal joint kinematics in the literature are scarce and not consistent. Veress et al. (19) measured patellar tracking patterns by analytical x-ray photogrammetry in four patients who had undergone a high tibial osteotomy. Sikorski et al. (18) introduced a radiological technique to measure
two rotational movements of the patella during knee flexion, and compared the movements of the patellae in patients suffering from chondromalacia to those in volunteers. Reider et al. (15) and Fujikawa et al. (5) measured patellar movements in vitro, the first using an orthogonal grid system and the second from replicas of the patella and the femoral trochlea. The results of these four studies are summarized in Table 1. The aim of the present study was to provide accurate data for normal, three-dimensional patellar tracking patterns. MATERIALS AND METHODS
The measuring system used in this study is based on roentgen stereophotogrammetric analysis (RSA), first introduced by Selvik in 1974 (17), and used in several of our recent studies (2,3,10,12). RSA offers a highly accurate three-dimensional technique to measure relative motions in joints, based on the reconstruction of spatial coordinates of markers implanted into bones, from their twodimensional projections from two roentgen tubes. The accuracy of the data acquisition depends on
Received August 18, 1988; accepted August 22, 1989. Address correspondence and reprint requests to Dr. A. van Kampen at Institute of Orthopaedics, University of Nijmegen, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands. Presented in part at the 31st Annual ORS, New Qrleans, 1986, and at the second congress of ESKA, Basel, 1986:
372
THREE-DIMENSIONAL TRACKING PATTERN OF PATELLA
3 73
TABLE 1. Summary of results from patella motion measurements published in the literature No. of specimens Authors
In vivo
Veress et al. Sikorski et al. Reider et al.
In vitro
Measurements Q-loading
Number
Range
4
Isometric
4
0-W
12
Isometric
3
60-90"
92 N
7
20
Fujikawa et al.
8
2G30 N
6
0-90"
25-130"
several factors, including the number of implanted markers, the relative positions of these markers in the object, and the accuracy of the film-digitizing procedure ( 11,20). To describe joint motions, Cartesian coordinate systems are applied to the femur, tibia, and patella (Fig. 1). Although it was not our primary objective to study tibiofemoral kinematics, tibial rotations were taken into account because of their possible influences on patellofemoral movements. The origin of the femoral coordinate system is located in the highest point of the intercondylar notch, at the cartilage border. The origin of the tibial coordinate system is located in the center of the tibial plateau,
A
Shift
Rotation
Neutral
Lateral
Unknown
not conclusive
Neutral
Unknown
Lateral
Medial
Fixed
Type I, lateral, 14 mm Type 11, medial, 7 mm Unknown
Lateral, 6"
Lateral, 12"
Lateral, 6"
Neutral, 0"
Lateral, 6.2"
Medial, 11"
Unknown
Tilt
just behind the insertion of the anterior cruciate ligament. The origin of the patellar coordinate system is in the center of the patella. The axes of the three systems are parallel in extension, in which case the x axes point medially, perpendicular to the sagittal plane; the y axes point superiorly, perpendicular to the horizontal plane; and the z axes point anteriorly, perpendicular to the frontal plane. During knee motion, the femur is considered as the space-fixed system, relative to which the tibial and patellar motions are described. Tibial rotations about the femoral x axis describe flexiodextension. Tibial rotations about the tibial y axis and z axis describe exo-/endorotation and varus/valgus rota-
shift
T
T
Average patellar movements
Tibia rotation
flexion
U
algus xt
right
left
'
rotation
FIG. 1. (A) The orientation and location of the coordinate axes of the patella for left and right knee specimens, as introduced for the present investigation. (B)Subsequent rotations around the axes represent patellar flexion ( x axis), patellar tilt (y axis), and patellar rotation (z axis). Translation along the x axis represents patellar shift. For reasons of clarity, the coordinate systems of the femur and the tibia are not shown.
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A . VAN KAMPEN AND R . HUISKES
tion, respectively (2). Patellar rotations about the femoral x axis describe patellar flexion (positive) or extension (negative). Rotation about the patellar y axis describes medial tilt (positive), when the medial patellar facet rotates towards the medial femoral condyle, or lateral tilt (negative), when the lateral patellar facet rotates towards the lateral femoral condyle. Rotation about the patellar z axis represents medial patellar rotation (positive), when the patellar apex turns towards the medial condyle, or lateral patellar rotation (negative), when the patellar apex turns towards the lateral condyle. Translation along the femoral x axis is denoted as patellar shift, positive towards medial and negative towards lateral. Translations along the y and z axes were also measured, but the results are not discussed here. Four fresh-frozen knee specimens from patients who underwent above-knee amputations for peripheral vascular disorders were used for this study. Although at preselection knees with roentgenological evidence of patellofemoral arthritis were excluded, all investigated knees showed some form of patellar cartilage damage at the time of preparation. After thawing, the knee specimens werc mounted in a motion rig, allowing for tibiofemoral flexion/ extension motions and prescribed tibial rotations (Fig. 2). During normal flexion-extension movements of the knee, the varus-valgus position of the tibia changes (2). Therefore, the tibial fixation clamp was constructed in such a way that these movements were free to occur during a flexion step. The clamp could be fixed in a specific position after each motion step. Torques for internal and
external rotation of the tibia were applied manually, using a torque wrench fixed to the tibial rod. Torques of zero and +-3 Nm were routinely applied during the flexion-motion steps. These torque values give a good description of the exo-/endorotation freedom of motion. The increase of freedom of motion with increasing torques is relatively small, due to the progressively increasing stiffness of the knee ligaments (2). The pulleys on the femoral side of the rig were used to guide the wires by which the four components of the quadriceps muscle are loaded in the principal fiber directions. The traction was divided equally over these components. A force of 28 N per component was chosen to just align the patella in the patellofemoral groove, similar to forces used in other studies concerning the patellofemoral joint (6,14,16). After insertion of five tantalum markers (0.8-1 .O mm), each in the femur, tibia, and patella, double roentgen exposures were taken of the specimens with the tibia extended (reference position) and after subsequent flexion steps of 15", up to maximal flexion of about 140". Each test series was carried out for the neutral (zero torque) flexion pathway, and for externally and internally rotated pathways ( 2 3 Nm tibial torques). The latter pathways are referred to here as the external and internal envelopes of passive tibiofemoral motion (2). RESULTS
The reproducibility of the data-acquisition procedure using RSA was determined using repeated reconstructions. The precision of the three-dimensional marker reconstruction was better than 50 Fm, resulting in a Euler rotation precision of approximately 0. I", which is similar to earlier findings (2,11,12,20). Tibia1 Movements
FIG. 2. Schematic drawing of the motion rig. (1) Clamp for flexionlextension along the rail. (2) Clamp for tibial internall external rotation and varuslvalgus rotation. (3) Wires, attached to the quadriceps muscle. (4) Pulleys to guide the wires in the different muscle directions. (5) The torque wrench.
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The envelopes of internal and external tibial rotation with torques of -+3 Nm, as a function of knee flexion, are represented in Fig. 3 , together with the unloaded neutral pathway. The tibial rotations in the neutral pathway tended to move towards internal in the first part of flexion, and towards external in the latter part. In specimen 105, however, the tibial rotations alternated around neutral. The so-called "screw home" rotation effect, the obligatory exorotation of the tibia towards full extension, was found in the four specimens in the
THREE-DIMENSIONAL TRACKING PATTERN OF PATELLA
375
In1 rot
I'
I
-
I
FIG. 3. The limits of internal (open circles) and external (closed circles) tibial rotation (*3 Nm torque) as a function of flexion, measured in four specimens. The neutral rotation pathways are represented by the black squares.
neutral and internal tibial rotation pathways only. It is evident, however, that this mechanism disappears when external rotation torques are applied to the tibia, indicating that it is not a property of the passive joint structures alone, as was also found in other studies (2). The total rotatory laxity ranged from 24-46" in the different specimens, probably depending on the tightness of the ligaments. The amount of rotational freedom does influence the amount of patellar movements, as will be shown later. Remarkable is the decrease of exorotation laxity in higher knee flexion, noticed in all specimens. Varus/valgus rotations of the tibia about the z axis (Fig. 4) show a slowly progressing positive direction, becoming obvious after 50" of knee flexion, being more pronounced along the exorotation envelope of motion in three specimens. Thus, in anatomical terms, knee flexion is coupled with a slight varus rotation of the tibia, which is increased by external rotation of the tibia. Except for the first 20" of knee flexion, the influence of tibial rotation on varus rotation is almost constant. The trends for the curves in three
specimens (103, 104, and 105) are remarkably similar, although absolute maximal values show notable differences. The varus/valgus motion in specimen 102 is almost negligible. It is interesting to note that this specimen stands apart, also, relative to the rotatory laxity. Patellar Movements Patellar flexion occurs in concert with knee flexion, as expected, but lags behind by about 20% (Fig. 5). The patellar flexion lag is more pronounced after about 105" of knee flexion. Along the external rotation pathway, the patellar flexion lag is reduced to about 10" in the first part of flexion. Maximal patellar flexion is reached simultaneously with maximal knee flexion. Overall, the influence of tibial rotations on patellar flexion is small. Patellar tilt can be described as wavering: during flexion, the patella wavers from a medial to a lateral tilted position and vice versa (Fig. 6). The patellar tilt is highly influenced by tibial rotations, espe-
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A . VAN KAMPEN AND R . HUISKES
vatus 101
16
-
-
16
8-
8-
-
0-
-8
-
-16
-
120
I50 knee flexion
h e f lexlon
-
-8
valgusaol
-16 valgus rot
102
103
varus 101
24
varus
I
101
1 l knee flexion
-8 -
-16
-
104
~
knee flexton o
-16 - 80
-24 valgus 101
105
FIG. 4. Varus/valgus laxity as a function of flexion, for the internal (open circles) and external (closed circles) pathways ( k 3 Nm), measured in four specimens.
cially towards full extension. This is understandable when thinking of the clinically moveable patella in extension, which becomes constrained in its patellofemoral groove with further knee flexion. Influences of tibial exorotations, in particular during the first part of knee flexion, are more pronounced than the influences of tibial endorotation. Along the external rotation envelope, medial tilt is converted to lateral tilt, or at least a less pronounced medial tilt. The trends of the curves in three specimens are remarkably similar (103, 104, and 105). Specimen 102 again behaves somewhat differently, the wavering tilt being less pronounced. An interesting phenomenon observed in three specimens (103, 104, and 105) occurs at greater knee flexion, at an average of 100". The patella shows a sudden jerk towards a medially tilted position, together with a crossing-over of the exo- and endorotation pathways, changing the relative positions of the curves. Patellar rotation is not significant in the first 40" of knee flexion (Fig. 7). With further flexion, the patella rotates medially . Along the internally rotated pathway, the medial patellar rotation is more pronounced. Maximal values of medial patellar ro-
J Orthop Res, Vol. 8, No. 3 , 1990
tation are reached in greater knee flexion. External rotation of the tibia reduces the medial patellar rotation. In one specimen (104), the external tibial rotation leads to a lateral patellar rotation. Relative to each other, however, not regarding the reference axes, the trends of the curves of the four specimens are again remarkably similar. It is interesting to note that the tibial rotations have a progressive influence on the patellar rotations in the second part of knee flexion, opposite to the tibial rotation influence on the patellar tilt. Patellar shift, or the translation of the patella along the x axis, shows a progressive lateralization with further knee flexion, after an initial medial shift in extension (Fig. 8). Along the tibial exorotation motion pathway, patellar lateralization is more pronounced, here again in the first part of knee flexion, similar to the tibial exorotation influence on the tilt. The influence of tibial exorotation on the patellar shift is more pronounced than the influence of the tibial endorotation. Although the number of specimens investigated was small, the results present true patellar motions, and a general conclusion on the patellar tracking
~
THREE-DIMENSIONAL TRACKING PATTERN OF PATELLA patella flexton
patella I lexton
I
‘patella flexion
377
I
I
DaIdla flexion
80
60
-
-
us 0
l
30
l
1
1
60
1
I
l
90
I
I
1
1
1
1
150
knecHexm
FIG. 5. Patellar flexion as a function of knee flexion. The open circles represent the internal tibial rotation pathways, and the closed circles represent the external tibial rotation pathways ( 2 3 Nm), measured in four specimens.
patterns may be drawn, due to the high precision of the RSA measuring system. DISCUSSION The results found relative to the kinematics of the tibiofemoral articulation are in agreement with data from the literature (2,7,13). The total rotatory laxity as a function of flexion depends on the individual specimen. The reduction of total laxity with increased knee flexion that we noted was not consistently found previously, due to the fact that knee flexion up to 140” was not always investigated. A comparison between the specimens shows that two of the specimens (103 and 105) were remarkably similar in all of the movements. Relatively speaking, one specimen (104) showed the same tendencies, with slightly different tibial varus/valgus rotation and patellar rotations. Positioning of the specimens in the motion rig can cause slight differences in the reference axes of the different specimens (2). From these results, it seems that the ref-
erence axes of two specimens (103 and 105) were quite similar, and that the orientation of the reference axes of one specimen (104) was somewhat different. In one specimen (102), patellar excursions were less pronounced, probably due to the fact that this specimen exhibited a considerably lower total rotatory laxity of the tibia vs. the femur (about 50% less relative to specimen 104). Except for the patellar flexion, the patellar movements are influenced considerably by tibial rotations. The patellar tilt and the shift are more influenced by tibial rotations in the first part of flexion. This can be explained by the fact that in the first part of flexion, the patella is not yet confined to its femoral groove, thus giving room for patellar “play.” This play is affected by tibial rotations, through tensioning of the patellar ligament, of the lateral and medial retinaculae. In the second part of knee flexion, the structures around the patella are more tense, and the patella is pressed in its femoral groove, which reduces the possibilities for patellar play. The patellar rotations are more affected by
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A . VAN KAMPEN AND R . HUISKES
-20 J
l*Ie'll Ill1
tibial rotations at greater knee flexion, which can be explained as follows: in flexion, the retinaculae and especially the patellotibial bands are tense. Slight changes in tibial rotation can thus exert their influences on patellar rotations through the patellar ligament and patellotibial bands in greater knee flexion. The patellar flexion lag relative to the tibial flexion is probably due to the change in patellar ligament direction relative to the tibia, which changes from a relatively forward placement to a backward position with progressive knee flexion in the sagittal plane (4).The present results show that, by tibial exorotation, the flexion lag decreases. Tibial endorotation has a neglegible effect on patellar flexion, relative to the neutral tibial rotation pathway. This phenomenon is explained by the relative change in distance between the tuberosity and the patellar apex, and by the position of the patellar ligament in the sagittal plane. Normally, without tibial torques, the position of the tibial tuberosity is slightly laterally orientated, relative to the patella, in the frontal view. Tibial exorotation increases the projection of the distance between the tuberosity and the patellar
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101
FIG. 6. Patellar tilt, medialllateral, as a function of knee flexion. The open circles represent the internal tibial rotation pathways, and the closed circles represent the external tibial rotation pathways (+-3Nm), measured in four specimens.
apex on the sagittal (flexion) plane, and the patellar ligament moves backwards, thus reducing the flexion lag of the patella relative to the tibia. By tibial endorotation, the projection of the distance on the sagittal plane between the tibial tuberosity and the patellar apex remains relatively unchanged, as the position of the patellar ligament in the sagittal plane will be. An explanation for the wavering tilt, as detected here, can be found in the bony configurations of the distal femur that oppose the patella at different flexion angles. In the first part of knee flexion, the patella is opposite to the anteriorly reaching wall of the lateral condyle, inducing a medial tilt. The medial condyle reaches further caudally than the lateral one, causing a lateral tilt between 50-100" of knee flexion. Beyond 100" knee flexion, the patella shows a quite sudden inversion towards a medial tilt. This can be explained by the contact between the most medial part of the patella (the odd facet) and the medial femoral condyle (Fig. 9). This explanation is in accordance with studies on retropatellar cartilage contact areas (6,8), which show loading of the odd facet at about the same flexion angle. The
THREE-DIMENSIONAL TRACKING PATTERN OF PATELLA mcdial rotation
20
1
379
-
.
12 -
0'
16
-
8 -
-
,0- --_O
# ,
d
1
.p
I
,a
,*-
.-.-
**/-
*----*
'
medial rotation
medial rotation
1 1
FIG. 7. Patellar rotation, medialllateral, as a function of knee flexion. The open circles represent the internal tibial rotation pathways, and the closed circles represent the external tibial rotation pathways (k3 Nm), measured in four specimens.
direction of the patellar tilt depends partly on knee flexion and partly on tibial rotation. Exo- and endorotation influences on patellar tilt can be explained by stretching of the laterallmedial parapatellar structures and the pull of the patellar ligament, in combination with the articular constraints. Thus, in the first part of flexion, the tibial rotations result in a patellar tilt in corresponding directions (Fig. 10). In contrast, beyond about 100" of knee flexion, these tibial rotations lead to an inversion of patellar tilt. In greater knee flexion, with the patella deep between the femoral walls, traction on the medial side by tibial endorotation induces a lateral tilting of the patella, because the patella will ascend upon the wall of the medial femoral condyle. The flexion angle at which this crossing-over phenomenon occurs will depend on the slope and the height of the medial femoral condyle part, which forms the patellofemoral groove. The medial patellar rotation per se can be caused by the geometry of the femoral groove: the sulcus points slightly laterally, as seen from proximal to distal. Thus, with knee flexion, the patellar apex
will rotate medially through the pull of the patellar ligament. This also explains the increment of medial patellar rotation caused by internal tibial rotation, as an effect of further medialization of the patellar tendon (Fig. 11). All of the investigated specimens showed a lateral shift with increased knee flexion, due to the orientation of the femoral groove. The influences of the tibial rotations can be explained by a similar mechanism as the influences of the tibial rotation on the tilt (up to 100" knee flexion) and the patellar rotation (see also Fig. 12). Hence, stretching of the lateral parapatellar structures with lateralization of the patellar ligament by tibial exorotation will lead to a lateral patellar shift. Tibia1 endorotation will induce the opposite, a medial patellar shift. A comparison of the present results with data from the literature (Table 1) is only partly possible, because none of these studies included tibial rotation influences on the three-dimensional patellar tracking. As shown here, these effects can be very significant. Veress et al. (19) measured tilt only at three or four flexion angles, up to a maximum of
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A . VAN KAMPEN AND R . HUISKES
380
pathways (k3 Nm), measured in four specimens.
90”. Yet, their figures show the same wavering tilt from medial to lateral with progressive knee flexion in three of four measured individuals. The overall finding of a lateral tilt by Reider et al. (15) is not supported by our results. In their experiment, the tibia was fixed, and the femur was free to flex and extend. Although the authors mention that the apparatus was constructed to allow for the “screw home” mechanism, further remarks in regard to femoral rotation freedom are not made. The patellar movements were described in relation to the tibia, instead of relative to the femur as in the present investigation, which could explain the different patellar tilt and patellar rotation established. The dif-
a
b
FIG. 9. Schematic drawing of the relation between patella and femur in extension (a), and 120” flexion (b). Loading of the medial odd facet occurs with a medial patellar tilt.
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n
n
FIG. 10. Influences of tibia1 rotations on patellar tilt (rotations around the y axis). Tibial exorotation induces lateral patellar tilt (left). Tibial endorotation induces medial patellar tilt (right), both caused by the direction of the pull of the patellar ligament.
THREE-DIMENSIONAL TRACKING PATTERN OF PATELLA
n
n
FIG. 11. Influences of tibial rotations on patellar rotation (rotation about the z axis). Tibial exorotation induces lateral patellar rotation (left).Tibial endorotation induces medial patellar rotation (right), both caused by the direction of the pull of the patellar ligament.
ferences in patellar rotation direction found by Fujikawa et al. (5) relative to the present results can be explained partly by the lower precision in the measurements and partly by different reference systems used. We conclude that the three-dimensional patellar tracking patterns are characterized by a progressive patellar flexion, a wavering patellar tilt, a medial patellar rotation, and a lateral patellar shift during
FIG. 12. Influences of tibial rotations on patellar shift (translation along the x axis). Tibial exorotation induces lateral patellar shift (left).Tibial endorotation induces medial patellar shift (right), both caused by the direction of the pull of the patellar ligament.
381
knee flexion. These patterns are highly influenced by tibial rotations: patellar tilt and shift more so in the first part of knee flexion, and patellar rotation more so in the second part of knee flexion. Comparing the shift and the tilt movements suggests that the patellar shift is coupled to the tilt or vice versa. The patellar rotations seem to follow the obligatory varus/valgus rotations of the tibia. The motion constraints of the patella are determined by the anatomical characteristics of the distal femur in relation to those of the patella and by the balance of forces along the soft tissues. Evidently, interindividual differences in this respect will be reflected in the motion patterns. Previous investigations concerning patellar tracking patterns, contact area determinations, or contact force measurements did not take tibial rotations into account. The present results emphasize their importance. Since patellar tracking patterns will only partly determine contact areas and forces, tibial rotations should be included in future investigations concerning the patellofemoral joint.
REFERENCES 1 . Ahmed AM, Yu A, Burke DL: In vitro measurement of static pressure distribution in synovialjoints. J Biomech Eng 105:226236, 1983 2. Blankevoort L, Huiskes R, Lange A de: The envelope of passive knee joint motion. J Biomech 21:707-720, 1988
3. Dijk van R: The behaviour of the cruciate ligaments in the human knee. Dissertation, University of Nijmegen, 1983 4. Eijden van TMGJ: The mechanical behaviour of the patellofemoral joint. Dissertation, University of Amsterdam, 1985 5. Fujikawa K, Seedhom BB, Wright V: Biomechanics of the patellofemoraljoint. Part I. Eng Med 12:3-11, 1983 6. Goodfellow J, Hungerford DS, Zindel M: Patellofemoral joint mechanics and pathology. Part I. Functional anatomy of the patellofemoral joint. J Bone Joinr Surg [Br] 58:287290, 1976 7. Hallen LG, Lindahl 0: The “screw-home’’ movements in the knee joint. Acta Orthop Scand 37:97-106, 1966 8. Hehne HJ, Schlageter MS, Hultzsch W, Rau WS: Experimentelle patellofemorale Kontaktflachen-messungen. Z Orthop 119:167-176, 1981 9. Huberti HH, Hayes WC: Patellofemoral contact pressures. J Bone Joint Surg [Am] 66:715-724, 1984 10. Huiskes R, Kremers J, Lange A de, Selvik G, Rens ThJG van, Woltring HJ: An analytical stereo-photogrammetric method to determine the 3-D geometry of articular surfaces. J Biomech 18559-570, 1985 1 1 . Lange A de, Huiskes R, Kauer JMG: Measurement errors in roentgenstereophotogrammetric joint-motion analysis. J Biomech (in press) 12. Lange A de, Kauer JMG, Huiskes R: Kinematic behaviour of the human wrist joint: a roentgenstereophotogrammetric analysis. J Orthop Res 3:5644, 1985 13. Markolf KL, Mensch JS, Amstutz HC: Stiffness and laxity of the knee-the contribution of the supporting structures. J Bone Joint Surg [Am] 58583-593, 1976
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14. Nakamura N, Ellis M, Seedhom BB: Advancement of the tibia1 tubercle, a biomechanical study. J Bone Joint Surg [Br] 67:255-260, 1985 15. Reider B, Marshall JL, Ring B: Patellar tracking. Clin Orthop Re1 Res 157:143-148, 1981 16. Seedhom BB, Takeda T, Tsubuku M, Wright V: Mechanical factors and patellofemoral osteo-arthrosis. Ann Rheum Dis 38~307-316, 1979 17. Selvik GA: Roentgenstereophotogrammetric method for the study of the kinematics of the skeletal system. Dissertation, AV Centralen, Lund, Sweden, 1974
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18. Sikorski JM, Peters J, Watt I: The importance of femoral rotation in chondromalacia patellae as shown by serial radiography J Bone Joint Surg [Brl 61:43542, 1979
19. Veress SA, Lippert FG, Hou MCY, Takamoto T: Patellar tracking patterns measurement by analytical x-ray photogrammetry. J Biomech 12:639-650, 1979 20. Woltring HJ, Huiskes R, Lange A de, Veldpans F: Finite centroid and helical axis estimation from noisy land mark measurements in the study of human joint kinematics. J Biomech 18:379-389, 1985
The Three-Dimensional Tracking Pattern of the Human Patella A. van Kampen and R. Huiskes Laboratory of Experimental Orthopaedics, Institute of Orthopaedics, University of Nijmegen, Nijmegen, The Netherlands
Summary: A study was undertaken to provide data on the three-dimensional tracking pattern of the patella, relative to the femur, in human knee-joint specimens. For this purpose, a highly accurate roentgen stereophotogrammetric analysis (RSA) method was applied. The three-dimensional motion patterns of the tibia and the patella were measured and represented in terms of three translations and three rotations each, during knee flexion in neutral (unloaded), endorotated, and exorotated pathways. We found that the patella displays complex but consistent three-dimensional motion patterns during flexion, which include flexion rotation, medial rotation, wavering tilt, and a lateral shift relative to the femur. The motion patterns are very much affected by tibial rotations accompanying flexion. Key Words: Patellar tracking mechanism.
Patellar pain syndromes are often assumed to be related to disturbances in the normal tracking mechanism of the patellofemoral joint. Chondromalacia patellae, for example, a condition in which abnormal changes of the patellar cartilage occur, is assumed to be caused by malalignment between the retropatellar cartilage surface and the femoral trochlea, resulting in abnormal pressure distributions and contact locations. During the last decade, research on the patellofemoral joint has been focussed on contact zones and pressure distributions, using various investigative methods (1,6,9). The data available on normal joint kinematics in the literature are scarce and not consistent. Veress et al. (19) measured patellar tracking patterns by analytical x-ray photogrammetry in four patients who had undergone a high tibial osteotomy. Sikorski et al. (18) introduced a radiological technique to measure
two rotational movements of the patella during knee flexion, and compared the movements of the patellae in patients suffering from chondromalacia to those in volunteers. Reider et al. (15) and Fujikawa et al. (5) measured patellar movements in vitro, the first using an orthogonal grid system and the second from replicas of the patella and the femoral trochlea. The results of these four studies are summarized in Table 1. The aim of the present study was to provide accurate data for normal, three-dimensional patellar tracking patterns. MATERIALS AND METHODS
The measuring system used in this study is based on roentgen stereophotogrammetric analysis (RSA), first introduced by Selvik in 1974 (17), and used in several of our recent studies (2,3,10,12). RSA offers a highly accurate three-dimensional technique to measure relative motions in joints, based on the reconstruction of spatial coordinates of markers implanted into bones, from their twodimensional projections from two roentgen tubes. The accuracy of the data acquisition depends on
Received August 18, 1988; accepted August 22, 1989. Address correspondence and reprint requests to Dr. A. van Kampen at Institute of Orthopaedics, University of Nijmegen, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands. Presented in part at the 31st Annual ORS, New Qrleans, 1986, and at the second congress of ESKA, Basel, 1986:
372
THREE-DIMENSIONAL TRACKING PATTERN OF PATELLA
3 73
TABLE 1. Summary of results from patella motion measurements published in the literature No. of specimens Authors
In vivo
Veress et al. Sikorski et al. Reider et al.
In vitro
Measurements Q-loading
Number
Range
4
Isometric
4
0-W
12
Isometric
3
60-90"
92 N
7
20
Fujikawa et al.
8
2G30 N
6
0-90"
25-130"
several factors, including the number of implanted markers, the relative positions of these markers in the object, and the accuracy of the film-digitizing procedure ( 11,20). To describe joint motions, Cartesian coordinate systems are applied to the femur, tibia, and patella (Fig. 1). Although it was not our primary objective to study tibiofemoral kinematics, tibial rotations were taken into account because of their possible influences on patellofemoral movements. The origin of the femoral coordinate system is located in the highest point of the intercondylar notch, at the cartilage border. The origin of the tibial coordinate system is located in the center of the tibial plateau,
A
Shift
Rotation
Neutral
Lateral
Unknown
not conclusive
Neutral
Unknown
Lateral
Medial
Fixed
Type I, lateral, 14 mm Type 11, medial, 7 mm Unknown
Lateral, 6"
Lateral, 12"
Lateral, 6"
Neutral, 0"
Lateral, 6.2"
Medial, 11"
Unknown
Tilt
just behind the insertion of the anterior cruciate ligament. The origin of the patellar coordinate system is in the center of the patella. The axes of the three systems are parallel in extension, in which case the x axes point medially, perpendicular to the sagittal plane; the y axes point superiorly, perpendicular to the horizontal plane; and the z axes point anteriorly, perpendicular to the frontal plane. During knee motion, the femur is considered as the space-fixed system, relative to which the tibial and patellar motions are described. Tibial rotations about the femoral x axis describe flexiodextension. Tibial rotations about the tibial y axis and z axis describe exo-/endorotation and varus/valgus rota-
shift
T
T
Average patellar movements
Tibia rotation
flexion
U
algus xt
right
left
'
rotation
FIG. 1. (A) The orientation and location of the coordinate axes of the patella for left and right knee specimens, as introduced for the present investigation. (B)Subsequent rotations around the axes represent patellar flexion ( x axis), patellar tilt (y axis), and patellar rotation (z axis). Translation along the x axis represents patellar shift. For reasons of clarity, the coordinate systems of the femur and the tibia are not shown.
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tion, respectively (2). Patellar rotations about the femoral x axis describe patellar flexion (positive) or extension (negative). Rotation about the patellar y axis describes medial tilt (positive), when the medial patellar facet rotates towards the medial femoral condyle, or lateral tilt (negative), when the lateral patellar facet rotates towards the lateral femoral condyle. Rotation about the patellar z axis represents medial patellar rotation (positive), when the patellar apex turns towards the medial condyle, or lateral patellar rotation (negative), when the patellar apex turns towards the lateral condyle. Translation along the femoral x axis is denoted as patellar shift, positive towards medial and negative towards lateral. Translations along the y and z axes were also measured, but the results are not discussed here. Four fresh-frozen knee specimens from patients who underwent above-knee amputations for peripheral vascular disorders were used for this study. Although at preselection knees with roentgenological evidence of patellofemoral arthritis were excluded, all investigated knees showed some form of patellar cartilage damage at the time of preparation. After thawing, the knee specimens werc mounted in a motion rig, allowing for tibiofemoral flexion/ extension motions and prescribed tibial rotations (Fig. 2). During normal flexion-extension movements of the knee, the varus-valgus position of the tibia changes (2). Therefore, the tibial fixation clamp was constructed in such a way that these movements were free to occur during a flexion step. The clamp could be fixed in a specific position after each motion step. Torques for internal and
external rotation of the tibia were applied manually, using a torque wrench fixed to the tibial rod. Torques of zero and +-3 Nm were routinely applied during the flexion-motion steps. These torque values give a good description of the exo-/endorotation freedom of motion. The increase of freedom of motion with increasing torques is relatively small, due to the progressively increasing stiffness of the knee ligaments (2). The pulleys on the femoral side of the rig were used to guide the wires by which the four components of the quadriceps muscle are loaded in the principal fiber directions. The traction was divided equally over these components. A force of 28 N per component was chosen to just align the patella in the patellofemoral groove, similar to forces used in other studies concerning the patellofemoral joint (6,14,16). After insertion of five tantalum markers (0.8-1 .O mm), each in the femur, tibia, and patella, double roentgen exposures were taken of the specimens with the tibia extended (reference position) and after subsequent flexion steps of 15", up to maximal flexion of about 140". Each test series was carried out for the neutral (zero torque) flexion pathway, and for externally and internally rotated pathways ( 2 3 Nm tibial torques). The latter pathways are referred to here as the external and internal envelopes of passive tibiofemoral motion (2). RESULTS
The reproducibility of the data-acquisition procedure using RSA was determined using repeated reconstructions. The precision of the three-dimensional marker reconstruction was better than 50 Fm, resulting in a Euler rotation precision of approximately 0. I", which is similar to earlier findings (2,11,12,20). Tibia1 Movements
FIG. 2. Schematic drawing of the motion rig. (1) Clamp for flexionlextension along the rail. (2) Clamp for tibial internall external rotation and varuslvalgus rotation. (3) Wires, attached to the quadriceps muscle. (4) Pulleys to guide the wires in the different muscle directions. (5) The torque wrench.
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The envelopes of internal and external tibial rotation with torques of -+3 Nm, as a function of knee flexion, are represented in Fig. 3 , together with the unloaded neutral pathway. The tibial rotations in the neutral pathway tended to move towards internal in the first part of flexion, and towards external in the latter part. In specimen 105, however, the tibial rotations alternated around neutral. The so-called "screw home" rotation effect, the obligatory exorotation of the tibia towards full extension, was found in the four specimens in the
THREE-DIMENSIONAL TRACKING PATTERN OF PATELLA
375
In1 rot
I'
I
-
I
FIG. 3. The limits of internal (open circles) and external (closed circles) tibial rotation (*3 Nm torque) as a function of flexion, measured in four specimens. The neutral rotation pathways are represented by the black squares.
neutral and internal tibial rotation pathways only. It is evident, however, that this mechanism disappears when external rotation torques are applied to the tibia, indicating that it is not a property of the passive joint structures alone, as was also found in other studies (2). The total rotatory laxity ranged from 24-46" in the different specimens, probably depending on the tightness of the ligaments. The amount of rotational freedom does influence the amount of patellar movements, as will be shown later. Remarkable is the decrease of exorotation laxity in higher knee flexion, noticed in all specimens. Varus/valgus rotations of the tibia about the z axis (Fig. 4) show a slowly progressing positive direction, becoming obvious after 50" of knee flexion, being more pronounced along the exorotation envelope of motion in three specimens. Thus, in anatomical terms, knee flexion is coupled with a slight varus rotation of the tibia, which is increased by external rotation of the tibia. Except for the first 20" of knee flexion, the influence of tibial rotation on varus rotation is almost constant. The trends for the curves in three
specimens (103, 104, and 105) are remarkably similar, although absolute maximal values show notable differences. The varus/valgus motion in specimen 102 is almost negligible. It is interesting to note that this specimen stands apart, also, relative to the rotatory laxity. Patellar Movements Patellar flexion occurs in concert with knee flexion, as expected, but lags behind by about 20% (Fig. 5). The patellar flexion lag is more pronounced after about 105" of knee flexion. Along the external rotation pathway, the patellar flexion lag is reduced to about 10" in the first part of flexion. Maximal patellar flexion is reached simultaneously with maximal knee flexion. Overall, the influence of tibial rotations on patellar flexion is small. Patellar tilt can be described as wavering: during flexion, the patella wavers from a medial to a lateral tilted position and vice versa (Fig. 6). The patellar tilt is highly influenced by tibial rotations, espe-
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A . VAN KAMPEN AND R . HUISKES
vatus 101
16
-
-
16
8-
8-
-
0-
-8
-
-16
-
120
I50 knee flexion
h e f lexlon
-
-8
valgusaol
-16 valgus rot
102
103
varus 101
24
varus
I
101
1 l knee flexion
-8 -
-16
-
104
~
knee flexton o
-16 - 80
-24 valgus 101
105
FIG. 4. Varus/valgus laxity as a function of flexion, for the internal (open circles) and external (closed circles) pathways ( k 3 Nm), measured in four specimens.
cially towards full extension. This is understandable when thinking of the clinically moveable patella in extension, which becomes constrained in its patellofemoral groove with further knee flexion. Influences of tibial exorotations, in particular during the first part of knee flexion, are more pronounced than the influences of tibial endorotation. Along the external rotation envelope, medial tilt is converted to lateral tilt, or at least a less pronounced medial tilt. The trends of the curves in three specimens are remarkably similar (103, 104, and 105). Specimen 102 again behaves somewhat differently, the wavering tilt being less pronounced. An interesting phenomenon observed in three specimens (103, 104, and 105) occurs at greater knee flexion, at an average of 100". The patella shows a sudden jerk towards a medially tilted position, together with a crossing-over of the exo- and endorotation pathways, changing the relative positions of the curves. Patellar rotation is not significant in the first 40" of knee flexion (Fig. 7). With further flexion, the patella rotates medially . Along the internally rotated pathway, the medial patellar rotation is more pronounced. Maximal values of medial patellar ro-
J Orthop Res, Vol. 8, No. 3 , 1990
tation are reached in greater knee flexion. External rotation of the tibia reduces the medial patellar rotation. In one specimen (104), the external tibial rotation leads to a lateral patellar rotation. Relative to each other, however, not regarding the reference axes, the trends of the curves of the four specimens are again remarkably similar. It is interesting to note that the tibial rotations have a progressive influence on the patellar rotations in the second part of knee flexion, opposite to the tibial rotation influence on the patellar tilt. Patellar shift, or the translation of the patella along the x axis, shows a progressive lateralization with further knee flexion, after an initial medial shift in extension (Fig. 8). Along the tibial exorotation motion pathway, patellar lateralization is more pronounced, here again in the first part of knee flexion, similar to the tibial exorotation influence on the tilt. The influence of tibial exorotation on the patellar shift is more pronounced than the influence of the tibial endorotation. Although the number of specimens investigated was small, the results present true patellar motions, and a general conclusion on the patellar tracking
~
THREE-DIMENSIONAL TRACKING PATTERN OF PATELLA patella flexton
patella I lexton
I
‘patella flexion
377
I
I
DaIdla flexion
80
60
-
-
us 0
l
30
l
1
1
60
1
I
l
90
I
I
1
1
1
1
150
knecHexm
FIG. 5. Patellar flexion as a function of knee flexion. The open circles represent the internal tibial rotation pathways, and the closed circles represent the external tibial rotation pathways ( 2 3 Nm), measured in four specimens.
patterns may be drawn, due to the high precision of the RSA measuring system. DISCUSSION The results found relative to the kinematics of the tibiofemoral articulation are in agreement with data from the literature (2,7,13). The total rotatory laxity as a function of flexion depends on the individual specimen. The reduction of total laxity with increased knee flexion that we noted was not consistently found previously, due to the fact that knee flexion up to 140” was not always investigated. A comparison between the specimens shows that two of the specimens (103 and 105) were remarkably similar in all of the movements. Relatively speaking, one specimen (104) showed the same tendencies, with slightly different tibial varus/valgus rotation and patellar rotations. Positioning of the specimens in the motion rig can cause slight differences in the reference axes of the different specimens (2). From these results, it seems that the ref-
erence axes of two specimens (103 and 105) were quite similar, and that the orientation of the reference axes of one specimen (104) was somewhat different. In one specimen (102), patellar excursions were less pronounced, probably due to the fact that this specimen exhibited a considerably lower total rotatory laxity of the tibia vs. the femur (about 50% less relative to specimen 104). Except for the patellar flexion, the patellar movements are influenced considerably by tibial rotations. The patellar tilt and the shift are more influenced by tibial rotations in the first part of flexion. This can be explained by the fact that in the first part of flexion, the patella is not yet confined to its femoral groove, thus giving room for patellar “play.” This play is affected by tibial rotations, through tensioning of the patellar ligament, of the lateral and medial retinaculae. In the second part of knee flexion, the structures around the patella are more tense, and the patella is pressed in its femoral groove, which reduces the possibilities for patellar play. The patellar rotations are more affected by
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A . VAN KAMPEN AND R . HUISKES
-20 J
l*Ie'll Ill1
tibial rotations at greater knee flexion, which can be explained as follows: in flexion, the retinaculae and especially the patellotibial bands are tense. Slight changes in tibial rotation can thus exert their influences on patellar rotations through the patellar ligament and patellotibial bands in greater knee flexion. The patellar flexion lag relative to the tibial flexion is probably due to the change in patellar ligament direction relative to the tibia, which changes from a relatively forward placement to a backward position with progressive knee flexion in the sagittal plane (4).The present results show that, by tibial exorotation, the flexion lag decreases. Tibial endorotation has a neglegible effect on patellar flexion, relative to the neutral tibial rotation pathway. This phenomenon is explained by the relative change in distance between the tuberosity and the patellar apex, and by the position of the patellar ligament in the sagittal plane. Normally, without tibial torques, the position of the tibial tuberosity is slightly laterally orientated, relative to the patella, in the frontal view. Tibial exorotation increases the projection of the distance between the tuberosity and the patellar
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101
FIG. 6. Patellar tilt, medialllateral, as a function of knee flexion. The open circles represent the internal tibial rotation pathways, and the closed circles represent the external tibial rotation pathways (+-3Nm), measured in four specimens.
apex on the sagittal (flexion) plane, and the patellar ligament moves backwards, thus reducing the flexion lag of the patella relative to the tibia. By tibial endorotation, the projection of the distance on the sagittal plane between the tibial tuberosity and the patellar apex remains relatively unchanged, as the position of the patellar ligament in the sagittal plane will be. An explanation for the wavering tilt, as detected here, can be found in the bony configurations of the distal femur that oppose the patella at different flexion angles. In the first part of knee flexion, the patella is opposite to the anteriorly reaching wall of the lateral condyle, inducing a medial tilt. The medial condyle reaches further caudally than the lateral one, causing a lateral tilt between 50-100" of knee flexion. Beyond 100" knee flexion, the patella shows a quite sudden inversion towards a medial tilt. This can be explained by the contact between the most medial part of the patella (the odd facet) and the medial femoral condyle (Fig. 9). This explanation is in accordance with studies on retropatellar cartilage contact areas (6,8), which show loading of the odd facet at about the same flexion angle. The
THREE-DIMENSIONAL TRACKING PATTERN OF PATELLA mcdial rotation
20
1
379
-
.
12 -
0'
16
-
8 -
-
,0- --_O
# ,
d
1
.p
I
,a
,*-
.-.-
**/-
*----*
'
medial rotation
medial rotation
1 1
FIG. 7. Patellar rotation, medialllateral, as a function of knee flexion. The open circles represent the internal tibial rotation pathways, and the closed circles represent the external tibial rotation pathways (k3 Nm), measured in four specimens.
direction of the patellar tilt depends partly on knee flexion and partly on tibial rotation. Exo- and endorotation influences on patellar tilt can be explained by stretching of the laterallmedial parapatellar structures and the pull of the patellar ligament, in combination with the articular constraints. Thus, in the first part of flexion, the tibial rotations result in a patellar tilt in corresponding directions (Fig. 10). In contrast, beyond about 100" of knee flexion, these tibial rotations lead to an inversion of patellar tilt. In greater knee flexion, with the patella deep between the femoral walls, traction on the medial side by tibial endorotation induces a lateral tilting of the patella, because the patella will ascend upon the wall of the medial femoral condyle. The flexion angle at which this crossing-over phenomenon occurs will depend on the slope and the height of the medial femoral condyle part, which forms the patellofemoral groove. The medial patellar rotation per se can be caused by the geometry of the femoral groove: the sulcus points slightly laterally, as seen from proximal to distal. Thus, with knee flexion, the patellar apex
will rotate medially through the pull of the patellar ligament. This also explains the increment of medial patellar rotation caused by internal tibial rotation, as an effect of further medialization of the patellar tendon (Fig. 11). All of the investigated specimens showed a lateral shift with increased knee flexion, due to the orientation of the femoral groove. The influences of the tibial rotations can be explained by a similar mechanism as the influences of the tibial rotation on the tilt (up to 100" knee flexion) and the patellar rotation (see also Fig. 12). Hence, stretching of the lateral parapatellar structures with lateralization of the patellar ligament by tibial exorotation will lead to a lateral patellar shift. Tibia1 endorotation will induce the opposite, a medial patellar shift. A comparison of the present results with data from the literature (Table 1) is only partly possible, because none of these studies included tibial rotation influences on the three-dimensional patellar tracking. As shown here, these effects can be very significant. Veress et al. (19) measured tilt only at three or four flexion angles, up to a maximum of
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A . VAN KAMPEN AND R . HUISKES
380
pathways (k3 Nm), measured in four specimens.
90”. Yet, their figures show the same wavering tilt from medial to lateral with progressive knee flexion in three of four measured individuals. The overall finding of a lateral tilt by Reider et al. (15) is not supported by our results. In their experiment, the tibia was fixed, and the femur was free to flex and extend. Although the authors mention that the apparatus was constructed to allow for the “screw home” mechanism, further remarks in regard to femoral rotation freedom are not made. The patellar movements were described in relation to the tibia, instead of relative to the femur as in the present investigation, which could explain the different patellar tilt and patellar rotation established. The dif-
a
b
FIG. 9. Schematic drawing of the relation between patella and femur in extension (a), and 120” flexion (b). Loading of the medial odd facet occurs with a medial patellar tilt.
J Orthop Res, Vol. 8, No. 3 , 1990
n
n
FIG. 10. Influences of tibia1 rotations on patellar tilt (rotations around the y axis). Tibial exorotation induces lateral patellar tilt (left). Tibial endorotation induces medial patellar tilt (right), both caused by the direction of the pull of the patellar ligament.
THREE-DIMENSIONAL TRACKING PATTERN OF PATELLA
n
n
FIG. 11. Influences of tibial rotations on patellar rotation (rotation about the z axis). Tibial exorotation induces lateral patellar rotation (left).Tibial endorotation induces medial patellar rotation (right), both caused by the direction of the pull of the patellar ligament.
ferences in patellar rotation direction found by Fujikawa et al. (5) relative to the present results can be explained partly by the lower precision in the measurements and partly by different reference systems used. We conclude that the three-dimensional patellar tracking patterns are characterized by a progressive patellar flexion, a wavering patellar tilt, a medial patellar rotation, and a lateral patellar shift during
FIG. 12. Influences of tibial rotations on patellar shift (translation along the x axis). Tibial exorotation induces lateral patellar shift (left).Tibial endorotation induces medial patellar shift (right), both caused by the direction of the pull of the patellar ligament.
381
knee flexion. These patterns are highly influenced by tibial rotations: patellar tilt and shift more so in the first part of knee flexion, and patellar rotation more so in the second part of knee flexion. Comparing the shift and the tilt movements suggests that the patellar shift is coupled to the tilt or vice versa. The patellar rotations seem to follow the obligatory varus/valgus rotations of the tibia. The motion constraints of the patella are determined by the anatomical characteristics of the distal femur in relation to those of the patella and by the balance of forces along the soft tissues. Evidently, interindividual differences in this respect will be reflected in the motion patterns. Previous investigations concerning patellar tracking patterns, contact area determinations, or contact force measurements did not take tibial rotations into account. The present results emphasize their importance. Since patellar tracking patterns will only partly determine contact areas and forces, tibial rotations should be included in future investigations concerning the patellofemoral joint.
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3. Dijk van R: The behaviour of the cruciate ligaments in the human knee. Dissertation, University of Nijmegen, 1983 4. Eijden van TMGJ: The mechanical behaviour of the patellofemoral joint. Dissertation, University of Amsterdam, 1985 5. Fujikawa K, Seedhom BB, Wright V: Biomechanics of the patellofemoraljoint. Part I. Eng Med 12:3-11, 1983 6. Goodfellow J, Hungerford DS, Zindel M: Patellofemoral joint mechanics and pathology. Part I. Functional anatomy of the patellofemoral joint. J Bone Joinr Surg [Br] 58:287290, 1976 7. Hallen LG, Lindahl 0: The “screw-home’’ movements in the knee joint. Acta Orthop Scand 37:97-106, 1966 8. Hehne HJ, Schlageter MS, Hultzsch W, Rau WS: Experimentelle patellofemorale Kontaktflachen-messungen. Z Orthop 119:167-176, 1981 9. Huberti HH, Hayes WC: Patellofemoral contact pressures. J Bone Joint Surg [Am] 66:715-724, 1984 10. Huiskes R, Kremers J, Lange A de, Selvik G, Rens ThJG van, Woltring HJ: An analytical stereo-photogrammetric method to determine the 3-D geometry of articular surfaces. J Biomech 18559-570, 1985 1 1 . Lange A de, Huiskes R, Kauer JMG: Measurement errors in roentgenstereophotogrammetric joint-motion analysis. J Biomech (in press) 12. Lange A de, Kauer JMG, Huiskes R: Kinematic behaviour of the human wrist joint: a roentgenstereophotogrammetric analysis. J Orthop Res 3:5644, 1985 13. Markolf KL, Mensch JS, Amstutz HC: Stiffness and laxity of the knee-the contribution of the supporting structures. J Bone Joint Surg [Am] 58583-593, 1976
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14. Nakamura N, Ellis M, Seedhom BB: Advancement of the tibia1 tubercle, a biomechanical study. J Bone Joint Surg [Br] 67:255-260, 1985 15. Reider B, Marshall JL, Ring B: Patellar tracking. Clin Orthop Re1 Res 157:143-148, 1981 16. Seedhom BB, Takeda T, Tsubuku M, Wright V: Mechanical factors and patellofemoral osteo-arthrosis. Ann Rheum Dis 38~307-316, 1979 17. Selvik GA: Roentgenstereophotogrammetric method for the study of the kinematics of the skeletal system. Dissertation, AV Centralen, Lund, Sweden, 1974
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18. Sikorski JM, Peters J, Watt I: The importance of femoral rotation in chondromalacia patellae as shown by serial radiography J Bone Joint Surg [Brl 61:43542, 1979
19. Veress SA, Lippert FG, Hou MCY, Takamoto T: Patellar tracking patterns measurement by analytical x-ray photogrammetry. J Biomech 12:639-650, 1979 20. Woltring HJ, Huiskes R, Lange A de, Veldpans F: Finite centroid and helical axis estimation from noisy land mark measurements in the study of human joint kinematics. J Biomech 18:379-389, 1985
