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Tibio-femoral loading during human gait and stair climbing
ELSEVIER
Journal of Orthopaedic Research
Journal of Orthopaedic Research 22 (2004) 625-632
www.elsevier.com/locate/orthres
Tibio-femoral loading during human gait and stair climbing William R. Taylor
a,
Markus 0. Heller
a,
Georg Bergmann ', Georg N. Duda
a,*
'' Rrseurch Laboratory, Traumu and Reconstructiw
Surgerj., Churiti, Huniholdr- University of' Berlin, Cumpus Vircliow,-Clinic. Augustenhurger Phr: I , D- 13353 Berlin, Germuny Biomechanics Lab., Depurtment of Orthopuediicy, Free Universitj, of Berlin, 12203 Berlin. Germuny
Abstract Surgical intervention of the knee joint routinely endeavors to recreate a physiologically normal joint loading environment. The loading conditions resulting from osteotomies, fracture treatment, ligament replacements, and arthroplasties of the knee are considered to have an impact on the long term clinical outcome; however, knowledge regarding in vivo loading conditions is limited. Using a previously validated musculoskeletal lower limb model, we predicted the tibio-femoral joint contact forces that occur in the human knee during the common daily activities of walking and stair climbing. The average resultant peak force during walking was 3.1 times body weight (BW) across four total hip arthroplasty patients. Inter-individual variations proved larger than the variation of forces for each patient repeating the same task. Forces through the knee were considerably larger during stair climbing than during walking: the average resultant peak force during stair climbing was 5.4 BW although peaks of up to 6.2 BW were calculated for one particular patient. Average anteroposterior peak shear components of 0.6 BW were determined during walking and 1.3 BW during stair climbing. These results confirm both the joint contact forces reported in the literature and the importance of muscular activity in creating high forces across the joint. The magnitudes of these forces, specifically in shear, have implications for all forms of surgical intervention in the knee. The data demonstrate that high contact and shear forces are generated during weight bearing combined with knee flexion angles greater than approximately 15". Clinically, the conditions that produce these larger contact forces should be avoided during post-operative rehabilitation. 0 2004 Orthopaedic Research Society. Published by Elsevier Ltd. All rights reserved. Keyivords: Joint contact forces; Tibio-femoral joint; Muscle forces
Introduction The action of muscles during normal activities produces bone loading and joint contact forces far in excess of body weight [10,32,42]. The loading within musculoskeletal structures influences biological processes including fracture healing [ 17,351, bone remodelling [29,36], and ligament repair [45]. Loading is also believed to play a role in the onset of osteoarthritis [7,26]. Surgical intervention of the knee, through osteotomy [6,18], ligament reconstruction [53], and joint replacement [50], routinely attempts to recreate a physiologically normal and stable loading environment. Surgical success is directly affected by the resulting local loading environment [6]. Defining 'normal' loading conditions
* Corresponding author. Tel.: +49-30-450-559079; fax: +49-30-450559969. E-muil uddress: [email protected] (G.N. Duda).
within the knee is difficult, however, as both intra- and inter-individual differences must be considered. Musculoskeletal loading is influenced by a number of inter-individual factors such as weight [26] and gender [21,38], as well as the activity being undertaken [10,11, 32,39,49]. Determining the in vivo loading environment in the human knee is difficult due to the combination of complex structural anatomy, complicated movements [44], and dynamic, often indeterminate muscle function. While direct measurement techniques such as instrumented prostheses have been employed to determine loading in the hip [ l l ] and spine [46], the results of instrumented implants in the knee remain to be seen [33]. As a result, mathematical models have been employed to estimate muscle and joint contact forces [8,20,34,43,54]. Different levels of loading have been reported for a variety of activities: peak tibio-femoral contact forces of approximately 2.8 times body weight (BW) exist in the knee during walking [3,30]; approximately 4.3 BW (assuming a 75 kg man) during squat, leg press and knee
0736-0266/$ - see front matter 0 2004 Orthopaedic Research Society. Published by Elsevier Ltd. All rights reserved doi: 10.1016/j.orthres.2003.09.003
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extension exercises [54]; and 2.6-7.5 BW at knee extension angles between 0" and 40" at varying angular velocities [8,34]. Shear forces are thought to be important for knee joint stability during rehabilitation after ligament reconstruction and total knee replacement surgery [25,27]. Shear forces of 0.9 BW during extension [8] and 0.580.68 BW during deep flexion have been reported [39]. Analysis of knee loading during equivalent exercises has produced much higher peak shear forces of up to 3.89 BW [34], demonstrating a lack of consensus on knee loading in the literature. While information regarding knee joint loading during such activities is important, understanding the loading that occurs during common daily activities such as walking and stair climbing [ 1,12,40,48] is essential for early rehabilitation from surgical interventions in order to know the magnitudes of forces that the reconstructed joint must withstand. The musculoskeletal model developed by Heller et al. [32] calculated hip contact forces that were compared with those measured in vivo for four patients during multiple trials of walking and stair climbing. The calculated peak hip contact forces both over and under estimated the measured forces, differing by a mean of 12'%during walking and 14Y1during stair climbing, but revealed good agreement in both pattern and magnitude for all activities in all patients. The aim of this study was therefore to examine the tibio-femoral joint contact forces that occur in vivo in an attempt to determine a normal range during walking and stair climbing. Specific attention was paid to the relationship between activity, joint flexion angles, and joint contact forces to avoid excessive loading of the knee and provide guidance for post-operative rehabilitation.
Fig. I . Image of patient stair climbing. Reflective markers were attached to the skin in order to measure the positions of each limb throughout the gait cycle. Simultaneously. the hip contact forces from an instrumented endoprosthesis were measured together with the ground reaction forces (force plate positioned under each step. not visible in image).
reflective markers attached to the patients' skin was used to determine movements of the lower limbs. Musculoskrletnl iuotlel
A musculoskeletal model of the human lower extremity (Fig. 2) was developed, based on CT-data from the Visible Human (VH: National Library of Medicine. Bethesda. MD). From the individual C T slice
Materials and methods Guit
criicrli,.si.\
A validated musculoskeletal model of the complete human lower limb was used in this study [32]. Clinical gait analysis was performed on a total offour total hip arthroplasty patients (average age 61 years; initials: IBL. HSR, PFL, and KWR). All subjects possessed an instrumented femoral prosthesis (average time after implantation: 17 months, range 11-31 months) for the measurement of in vivo hip contact forces [9,10.13]. For each patient, extensive anthropometric data were collected to determine bone dimensions. segment masses, center of gravity positions, and inertial parameters [22]. All subjects gave informed consent to participate in the experiments and to the publication of their images and names; the study was approved by the local ethics committee of the Free University of Berlin. Gait analysis (Fig. I ) was conducted for walking and stair climbing [lo] with each patient performing several trials of each activity. The beginning of the exercise was defined as the instant of heel strike (0% stride). During all activities, time dependent kinematic and kinetic data were gathered. Two force platforms (Kistler. Ostfildern, Germany) measured ground reaction forces. The in vivo hip contact force was measured in the femoral coordinate system [ I l l . An optical system (Vicon, Oxford Metrics, U K ) using six infrared cameras to detect 24
Fig. 2. Musculoskeletal model used for calculating muscle and joint contact forces, shown during several instances of the stair climbing activity for one patient. The geometry of the bones was derived from the Visible Human project (NLM. Bethesda. USA) and scaled to each individual patient. The lines connecting the bones represent the force vectors of the muscles acting on each segment.
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images, surfaces of all hip bones (left and right iliac bones and sacrum) and all the bones of the lower limb (femur, patella. tibia. fibula. and all the bones of the foot) were reconstructed [28]. Muscles were represented as straight lines spanning from origin to insertion based on literature descriptions [14.23], wrapped around the bones where necessary to approximate their real curved paths and to provide an adequate representation of their lever arms at the joints. Muscles with large attachment areas such as the abductors were modeled using more than one line of action, creating a total of 95 muscle fibers. Data on the physiological cross sectional area (PCSA) of the individual muscles were taken from the literature [15,23]. The hip, ankle, and tibio-femoral joints were modeled with 3 rotational degrees of freedom (DOF). Since tracking of the patella was not possible during gait analysis, its motion was determined from an in vitro experiment during a complete flexionxxtension cycle [24]. The VH dataset. including all muscle origins, insertions. and wrapping points, n'as then scaled to the anatomy of each individual patient using bony landmarks to obtain subject specific musculoskeletal models. Prominent bone landmark positions (e.g. joint centres and tuberosities) were measured from both the VH and individual subject anatomies. Lineal- 3-dimensional scaling was then performed according to the relevanl VH to patient ratios for each bone, muscle attachment site. and wrapping point. The PCSA of each muscle w d S scaled to each patient based on body weight. At the hip. the femoral anteversion. caput colum diaphyseal (CCD) angle. and neck-stem length were all determined to match each individual patient. The resultant inter-segmental forces and moments at the ankle. knee, and hip were computed from the kinematic and kinetic gait analysis data with respect to the local coordinate systems using an inverse dynamics approach [5,22] (Fig. 3). With the maximum obtainable force in each muscle constrained [I61 to 85'% of the physiologically attainable muscle force ( a value based on each muscle's
f -MR FOOI
Foot
-FR F O O ~ M R FOOI MR
GRF
1FR.
GRF
A
B
Fig. 3. (A) Mechanical model for calculation of the resultant forces and moments in the joints using inverse dynamic techniques. (B) In the exemplified time step, the resultant forces and moments are calculated for each joint. beginning with FR and resultant moment MR at the foot. The calculation takes into account the inertial properties (based upon the mass, m, and length, I ) of each segment and the ground reaction force (GRF).
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PCSA) [2]. the muscle force distribution surrounding the knee was computed for the tested activities in all patients using static optiniization techniques [I91 to minimize the square of the muscle stresses. A local coordinate system was then constructed on the surface of the tibia1 plateau at the center of the inter-condylar eminence. aligned with the shaft of the tibia, to calculate tibio-femoral contact forces. These forces were then compared with the in vivo measured joint contact forces for each of six repetitions throughout both walking and stair climbing for all four patients.
Results In general, all patients displayed double-peaked tibiofemoral loading curves for both walking and stair climbing (Figs. 4 and 5). Small intra-individual variations were observed for repetitions of the same activity, with comparatively greater inter-individual variation for different subjects repeating the same task. The average resultant peak tibio-femoral contact forces during walking were 3.33 (range 3.02-3.48), 3.23 (3.05-3.79), 3.02 (2.75-3.44), and 2.97 (2.74-3.22) BW, respectively, across the four patients (Table 1) with a single peak value of 3.79 BW in one subject (HSR). In two subjects (HSR and KWR), two distinct loading peaks were apparent, while the other two subjects possessed much smoother curves without this double peak characteristic. The intra-individual variation between repetitions of the same activity, however, remained low (Table 1). During stair climbing, the forces through the knee were considerably higher than during walking (Figs. 4 and 5). All patients demonstrated similar loading curves with a large first peak shortly after heel-strike, followed by a much smaller peak before toe-off. The maximum averaged forces for this activity were 5.88 (5.44-6.16), 5.23 (5.09-5.28), 5.09 (4.87-5.35), and 5.33 (4.69-5.78) BW for the four patients (Table l), although a peak of 6.16 BW was calculated for one particular trial (patient IBL). The intra-individual variations in joint contact forces were also low during the activity of stair climbing, although patient IBL displayed consistently higher second peaks than those observed for the other three subjects (Table 1). Based upon the average peak loading for each subject during walking, a comparison was made with the equivalent load situation during stair climbing (Fig. 4, horizontal dotted lines). When this load was projected downwards for all subjects (vertical dotted line), the loading in the knee was greatly increased when the flexion angle was larger than approximately 15" in a loaded state. The largest component of the joint contact force was in the direction of the long axis of the tibia throughout all trails of all patients. These force components reached values of 3.1 BW (individual forces of 3.2, 3.2, 3.0, 2.9 BW) and 5.1 BW (5.6, 4.7, 4.9, 5.0 BW) during walking and stair climbing, respectively.
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Walking
Stair Climbing
I
7 ,
IBL
HSR
0
PFL
I
"
I
0
Gait cycle (%)
100
0
100
Gait cycle (%)
Fig. 4. Average axial tibio-femoral contact forces from all 4 patients (abbreviations IBL, HSR, PFL and KWR) calculated throughout both walking and stair climbing are shown together with f one standard deviation (light grey lines) taken from repetitions of the same activity. Average Aexion angle at the knee is also shown for both activities. The dotted horizontal lines correspond to the average peak axial force during walking. When these same loads are horizontally projected to the situation during stair climbing, it can be seen that the flexion angle corresponds to an average of approximately 15" (dotted lines). The grey region shows the initial loading phase that produces greatly increased loading above that seen during walking. All forces are shown in body weight (BW). The flexion of the knee does not return to the initial state at 0" since only a single stair was climbed.
Average anteroposterior peak shear forces of 0.5 BW (0.5, 0.6, 0.4, and 0.5 BW) were determined during walking (Fig. 5). During stair climbing, these forces were more than doubled, averaging 1.3 BW (1.4, 1.5, 1.1, and 1.1 BW). Peak anteroposterior shear forces in single trials reached 0.8 BW during walking and 1.6 BW during stair climbing. Corresponding medial-lateral shear forces were similar in both magnitude and form for all patients. The average peak shear loading during walking was then compared to the equivalent shear load situation in each subject during stair climbing, in a process similar to that described above for axial loading. Once again, the shear loading in the knee was greatly increased when the flexion angle was greater than approximately 15" in a loaded state.
Discussion The goal of this study was to determine the tibiofemoral contact forces that occur during common daily activities. This study has established fundamental knowledge of the loading occurring in the human knee by employing a musculoskeletal model of the lower limb that has been previously validated at the hip for both walking and stair climbing. The results demonstrate both intra-individual variations of knee contact forces between repetitions of the same exercise but also interindividual variations between different patients performing the same task. The average peak resultant tibio-femoral contact forces calculated in this study ranged from 2.97 to 3.33 BW across different trials of all 4 patients during walk-
W.R. T u ~ ~ l oelr ul. I Journul of Orthopncdic Research 22 (2004) 625-632
Walking
629
Stair Climbing
mL
HSR
* 7 PFL
KWR
100 0
0
Gait cycle (%)
100
Gait cycle (%)
Fig. 5. Average anterior- posterior shear contact forces acting at the knee joint throughout the gait cycle for all patients during walking (left column) and stair climbing (right hand column) are shown together with ? one standard deviation (light grey lines). taken from repetitions of the same activity. The dotted horizontal lines correspond to the average peak shear forces during walking for each patient. When these same shear loads are projected to the situation during stair climbing, the corresponding flexion angle of the knee at this shear load corresponds to an average knee flexion OF approximately 15". All forces are shown in body weight (BW).
ing. These forces concur with those previously reported in the literature 13,301, where peak forces of 2.7-2.8 BW were calculated for this activity, and are within the forces (2.6-7.5 BW) expected across a range of activities [8,34]. Contact forces of 5.09-5.88 BW have also been determined during stair climbing in this study, with individual peaks as high as 6.16 BW. Repetitions of each activity calculated for each individual produced relatively consistent peak joint loads (as shown by a maximum standard deviation of approximately 8% among all patients and activities), while the curves differed in form between each patient: during walking, two patients possessed two distinct loading peaks, while the other two subjects showed much smoother, flatter curves. Since the forces were normalized for the subject's weight, the variations in these calculated forces come from the different movements and ground reaction forces during each walk and from
the varying musculoskeletal geometries between individuals. This study has shown that the tibio-femoral forces seen during stair climbing were larger than those during walking consistently across all patients and all repetitions. The corresponding shear forces during stair climbing were more than double those during walking. The peaks in these contact forces also mainly occurred when the knee joint was under larger flexion angles and under loaded conditions (Figs. 4 and 5). These findings are supported by the results of previous studies [34,39], which also found that higher loads occurred under large knee flexion angles. With relative consistency, the loading during stair climbing greatly increased beyond the peak loads during walking when the knee was both loaded (i.e., during the stance phase) and the knee flexion angle was greater than approximately 15". Clinically, patients undergoing rehabilitation from knee ligament
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Table 1 Average resultant contact forces across the tibio-femoral joint over the complete gait cycle are shown for each patient together with the standard deviations of all six repetitions of each activity Gait cycle
Average resultant joint contact forces during walking (N)
Average resultant joint contact forces during stair climbing (N)
(1%))
IBL
TBL
HSR
PFL
0.64f0.19 0.79 f 0.10 0.41 f 0.09 I .64 2 0.32 1.70 f 0.20 1.08 f 0.07 2.86 f 0.3 1 3.01 2 0.30 2.05 f 0.21 10 3.02 f 0.22 3.23 f 0.31 2.77f0.19 15 2.78 f 0.24 2.90 f 0.27 3.05 f 0.18 20 2.21 20.25 2.68 f 0.25 2.94 f 0.21 25 2.57 k 0.25 2.67f 0.27 1.65f 0.22 30 2.62 k 0.32 1.58 f 0.13 2.60 f 0.30 35 2.78 f 0.24 2.24 f 0.32 2.64k 0.32 40 2.92f 0.39 2.60 f 0.27 3.07 f 0.14 45 2.30 f 0.19 3.33 k 0.1 7 2.91 f0.31 50 2.85 f 0.36 1.68 f 0.27 2.16k0.08 55 1.51 f 0 . 3 2 2.08 k 0.25 I .56? 0.36 60 1.04 f 0.16 0.60 f 0.17 0.41 f 0.05 65 0.29f 0.08 0.36 f 0.08 0.20 f 0.05 70 0.31 f 0.05 0.18k0.06 0.26 ? 0.04 75 0. I9 k 0.05 0.25 f 0.04 0.17f 0.03 80 0.16f0.02 0.18f0.04 0.23 f 0.04 85 0.43 f 0.04 0.25 f 0.04 0.31 ? 0.03 90 0.27 k 0.06 0.49 f 0.08 0.32f 0.04 95 Individual components of the forces are not presented here but 0
5
KWR
0.68 f 0.05 0.71 20.19 1.63 f 0.23 0.58 2 0.21 2.35 f 0.14 2.86 f 0.99 5.13 20.58 2.27 f 0.15 1.83 f 0.17 5.88f 0.25 1.47 ? 0.19 5.39 f 0.54 I .46 f 0.21 4.38 f 0.56 2.16 f 0.30 3.60f 0.42 2.79 f 0.26 3.20 f 0.50 2.9720.18 3.21 f 0.77 3.66 f 0.80 2.34 f 0.21 2.49 f 0.32 3.73 20.80 2.01 f 0.37 3.04 f 0.80 2.12f0.72 0.58 f 0.27 0.13 f 0.06 1.13 f 0.32 0.07f 0.02 0.77 f 0.17 0.09k 0.02 0.90 f 0.21 0.17 f 0.04 0.87f0.16 0.27 f 0.05 0.90 f 0.14 0.30 f 0.05 0.8520.19 are available upon request to the
surgery should attempt to avoid the large contact and shear forces that occur under these conditions. The calculated tibio-femoral contact forces in this study were larger than the corresponding peak contact loads measured at the hip [9-111. Peak in vivo measured hip contact force magnitudes of 2.9, 2.5, 2.1, and 2.4 BW (average 2.4 BW) were observed for normal walking and 2.7, 2.3, and 2.7 BW (average 2.5 BW-IBL not included) for stair climbing. A direct comparison of knee and hip contact forces in the same subject for the same trails and activities reveals an average 33% higher peak force in the knee during walking and an average increase of 1 16% during stair climbing over those seen at the hip. While the corresponding external loads (ground reaction forces) were approximately only a single BW [10,32], joint contact forces of many multiples of body weight demonstrate the importance of the muscles on the loading at the joint. In addition, despite relatively consistent inter-individual external loads, differences in gait patterns and varying muscle activation of each subject resulted in highly individualized joint loading (Figs. 4 and 5). The extensive increase in knee loading over and above the loading at the hip, specifically during stair climbing, has direct consequences for both primary stability and long term wear of implants in the knee and should be accounted for in the design stages of knee implants. Shear components of the knee contact forces are considered to be especially important for stability of the joint during rehabilitation after ligament reconstruction and total knee replacement surgery [25,27]. Average
HSR
PFL
KWR
0.35 f 0.08 1.38 f 0 . 4 4 4.06 f 0.34 5.23 f 0.07 4.91 f 0.20 3.97 k 0.20 3.12f0.28 2.45 2 0.35 2.142 0.31 2.07 f 0.30 2.08 f 0.41 1.89 f 0.35 0.58 ?r 0.32 0.13 f 0.03 0.15 ? 0.02 0.15 f 0.01 0. I4 L 0.02 0.20 f 0.07 0.27 f 0.03 0.23 f 0.04 authors.
0.42 f 0.10 1.37 f 0.47 3.74 2 0.40 5.09 f 0.22 5.06 f 0.25 4.15 f 0.45 3. I5 f 0.44 2.43 k 0.29 1.91 20.10 1.83 f 0 . 1 1 1.95 f 0.19 1.89 ?r 0.30 0.78 2 0.31 0.29 f 0.04 0.20 f 0.04 0.12 k 0.04 0.08 f 0.02 0.18 f 0.07 0.30 f 0.05 0.28 f 0.06
0.3 I f 0.06 1.92 f 1.03 4.47f 1.19 5.33 f 0.58 4.80 f 0.22 3.95 ?r 0.37 3.23 f 0 . 5 4 2.59 kO.71 2.31 2 0.40 2.13 k 0.26 2.12 f 0.26 2.16 f 0.29 I .63 f 0.92 0.72f0.51 0.08 f 0.02 0.12 f 0.04 0.15 ?r 0.05 0.21 f 0.08 0.26 f 0.06 0.19 f 0.07
anteroposterior peak shear forces of 0.6 BW during walking and 1.3 BW during stair climbing (Fig. 5) were observed for the four subjects tested in this study. Previous studies have reported shear forces of 0.9 BW during knee extension [8], 0.58-0.68 BW during deep flexion [39], up to 3.89 BW at angles beyond 50" during isokinetic eccentric efforts of the knee flexors [34], and 0.4-0.7 BW during running [47]. Although these studies did not reach a consensus on shear forces in the human knee, the shear forces for the four subjects reported in this study were well within the boundaries of the values reported in the literature and seem, therefore, to be in broad agreement. Shear forces are carried by the local soft tissues, including the anterior and posterior cruciate ligaments, collateral ligaments, and menisci. In this study, shear forces of up to 1.6 BW were observed during stair climbing. While the ultimate strength of the ACL is recognized as being much higher (2160 k 157 N [52]equivalent to 2.9 BW assuming a 75 kg man), and therefore the ligament alone is capable of carrying the shear forces seen here, any injury to the ACL would lead to a distribution of these shear forces to the surrounding soft tissue structures, particularly the menisci [41]. In the case of a completely ACL deficient knee, the transmission of these shear forces can potentially double the forces on the medial meniscus [41], almost certainly leading to their rapid degeneration and ultimate demise. It is therefore important to recognize the major role of the ACL as a structure for carrying the shear forces seen in this study.
The knee forces reported in this study were derived using a model which had been validated at the hip for walking and stair climbing against contact forces measured in 4 patients, each possessing an instrumented hip prosthesis [32]. Static optimization procedures were used to determine the contact forces at the knee joint. The difference between static and dynamic optimization techniques during gait is small [ 3 ] . Even though the optimization criterion used may have had a large influence on the forces in the individual muscle fibers, Brand and coworkers suggested that the optimization criterion has only a small influence on the calculated joint contact forces [15]. Our own studies have also shown that the joint contact force calculations are more sensitive to the gross anatomical structure (e.g., joint center, CCD angles, and offset) than the optimization criteria itself [31,32]. Since the participants in this study had all undergone hip replacement, their gait patterns and hence joint loading conditions could have differed from normal, unimpaired individuals. However, ground reaction forces, as well as joint resultant moments and angles during gait, return to those of healthy individuals within approximately half a year post-operatively [4]. The four patients were an average of 17 months post-operative, and the gait patterns appeared normal compared to literature data [lo]. Therefore, the presented data are assumed to be good estimates of loading conditions acting at the knee and only to a lesser degree affected by the hip athroplasty surgery. The methodology presented here, however, allowed data to be reported from a validated analysis of musculoskeletal loading. Since the muscle forces in the knee joint were calculated simultaneously with those in the hip joint and good resulting correlations of joint contact forces were achieved at the hip, the contact forces determined at the knee are also likely to be physiologically realistic for these individuals. The current musculoskeletal analysis reports a single resultant contact force across the knee joint, as a simplification of the forces that are carried across both femoral condyles. For further analysis of the soft tissue balance across the knee joint [37,51], determination of the distribution of the contact force across the condyles is of importance, especially for establishing the internal stress and strain loading environment of the individual structures within the joint. Despite these limitations, however, the model has determined highly individual muscle and joint contact forces, based on the individual anatomical considerations, gait movements, and ground reaction forces. This indicates the requirement for individualized analyses in order to achieve good estimates of both internal and external forces in vivo. This study has taken an existing model of the human lower extremity that has been validated at the hip during walking and stair climbing and used the model to examine the contact forces across the tibio-femoral joint. The magnitudes of these forces illustrate the impact of
muscle activity on knee joint loading. In this respect, surgical intervention should attempt to conserve the soft tissues in order to maintain a physiologically balanced loading environment. More specifically, loading during periods of knee flexion above approximately 15" rapidly increased both shear and contact loads in the knee over those seen during walking. These forces are potentially detrimental to post-operative rehabilitation and should therefore be avoided during early post-operative periods. Acknowledgements This study was supported by a grant from the German Research Foundation (number KFO 102/1). The authors would like to thank Dr. G . Deuretzbacher for providing the gait analysis data. References Aamodt A, Lund-Larsen J. Eine J. et al. Changes in proximal femoral strain after insertion of uncemented standard and customised femoral stems. An experimental study in human femora. J Bone Joint Surg Br 2001;83:921-9. An KN. Kwak BM. Chao EY. Morrey BF. Determination of muscle and joint forces: a new technique to solve the indeterminate problem. J Biomech Eng 1984:106:3647. Anderson FC. Pandy MG. Static and dynamic optimization solutions for gait are practically equivalent. J Biomech 2001; 34:153--61. Anderson L. Wesslau A. Boden H, Dalen N . Immediate or late weight bearing after uncemented total hip arthroplasty: a study of functional recovery. J Arthroplasty 2001: 16: 1063-5. Andrews JG. Biomechanical analysis of human motion. Kinesiology 1974:4:3242. Babis GC, An KN. Chao EY, et al. Double level osteotomy of the knee: a method to retain joint-line obliquity: clinical results. J Bone Joint Surg Am 2002:84-A:1380 8. Baliunas AJ. Hurwitz DE, Ryals AB, et al. Increased knee joint loads during walking are present in subjects with knee osteoarthritis. Osteoarthr Cartilage 2002: 10:573-9. Baltzopoulos V. Muscular and tibiofemoral joint forces during isokinetic concentric knee extension. Clin Biomech 1995;10:20814. Bergmann G. HlP98-Loading of the Hip Joint. 2001. Bergmann G. Deuretzbacher G , Heller M , et al. Hip contact forces and gait patterns from routine activities. J Biomech 2001; 34:859-71. Bergmann G , Graichen F. Rohlmann A. Hip joint loading during walking and running, measured in two patients. J Biomech 1993; 26:969-90. Bergmann G. Graichen F, Rohlmann A. Is staircase walking a risk for the fixation of hip implants'? J Biomech 1995;28:535-53. Bergmann G. Graichen F. Siraky J, et al. Multichannel strain gauge telemetry for orthopaedic implants. J Biomech 1988;21: 16976. Brand RA. Crowninshield RD. Wittstock CE, et al. A model of lower extremity muscular anatomy. J Biomech Eng 1982;104:30410. Brand RA. Pedersen DR. Friederich JA. The sensitivity of muscle force predictions to changes in physiologic cross-sectional area. J Biomech 1986:19:589-96.
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[I61 Challis JH. Producing physiologically realistic individual muscle force estimations by imposing constraints when using optimization techniques. Med Eng Phys 1997;19:253-61. [I71 Claes LE, Heigele CA, Neidlinger-Wilke C, et al. Effects of mechanical factors on the fracture healing process. Clin Orthop 1998;355(Suppl):132~7. [I81 Coventry MB. Upper tibia1 osteotomy for osteoarthritis. J Bone Joint Surg Am 1985;67-A:113640. [I91 Crowininshield RD. Use of optimization techniques to predict muscle forces. Trans ASME 1978;100:88-92. [20] Crowninshield RD, Brand RA. A physiologically based criterion of muscle force prediction in locomotion. J Biomech 1981;14:793801. Csintalan RP, Schulz MM. Woo J, et al. Gender differences in patellofemoral joint biomechanics. Clin Orthop 2002:260-9. Deuretzbacher G, Rehder U. Ein CAE-basierter Zugang zur dynamischen Ganzkorpermodellierung-Die KrHfte in der lumbalen Wirbelsiiule beini asymmetrischen Heben. Biomed Tech I995;40:93-8. Duda G N , Brand D. Freitag S, et al. Variability of femoral muscle attachments. J Biomech 1996;29:1183-90. Diirselen L. Claes L, Kiefer H. The influence of muscle forces and external loads on cruciate ligament strain. Am J Sports Med 1995;23:129-36. Fehring TK, Odum S, Griffin WL, et al. Early failures in total knee arthroplasty. Clin Orthop 2001:315-8. Felson DT. Weight and osteoarthritis. J Rheumatol 1995; 43(Suppl):7-9. Fischer LP, Guyot J, Gonon GP, et al. The role of the muscles and ligaments in stabilization of the knee joint. Anat Clin 1978;1:43 54. Geiger B. Three dimensional modeling of human organs and its application to diagnosis and surgical planning. Paris: Institut National de Recherche en Informatique et Automatique, 1993. Goodship AE, Cunningham JL, Kenwright J. Strain rate and timing of stimulation in mechanical modulation of fracture healing. Clin Orthop 1998;355(Suppl):105-15. Hardt DE. Determining Muscle forces in the leg during normal human walking-an application and evaluation of optimization methods. Trans ASME 1978;100:72-8. Heller MO. Bergmann G , Deuretzbacher G , et al. Influence of femoral anteversion on proximal femoral loading: measurement and simulation in four patients. Clin Biomech 2001:16:64& 9. Heller MO. Bergmann G, Deuretzbacher G, et al. Musculoskeletal loading conditions at the hip during walking and stair climbing. J Biomech 2001;34:883-93. Kaufman KR, Kovacevic N, Irby SE, Colwell CW. Instrumented implant for measuring tibiofemoral forces. J Bioniech 1996; 29:667 -7 1. Kellis E. Tibiofemoral joint forces during maximal isokinetic eccentric and concentric efforts of the knee flexors. Clin Biomech 2001: 16:229-36. Klein P, Schell H, Streitparth F, et al. The initial phase of fracture healing is specifically sensitive to mechanical conditions. J Orthop Res 2003;2 1:662-9.
_ _
~
[36] Lanyon LE, Rubin CT. Static vs dynamic loads as an influence on bone remodelling. J Biomech 1984;17:897-905. [37] Lu TW, O’Connor JJ, Taylor SJ, Walker PS. Validation of a lower limb model with in vivo femoral forces telemetered from two subjects. J Biomech 1998;31:63 9. [38] Marras WS, Davis KG, Heaney CA, et al. The influence of psychosocial stress, gender, and personality on mechanical loading of the lumbar spine. Spine 2000;25:3045-54. [39] Nagura T, Dyrby CO, Alexander EJ, Andriacchi TP. Mechanical loads at the knee joint during deep flexion. J Orthop Res 2002; 20:88 1-6. [40] O’Connor DO, Burke DW, Jasty M, et al. In vitro measurement of strain in the bone cement surrounding the femoral component of total hip replacements during simulated gait and stair-climbing. J Orthop Res 1996;14:769-77. [41] Papageorgiou CD, Gil JE, Kanamori A, et al. The biomechanical interdependence between the anterior cruciate ligament replacement graft and the medial meniscus. Am J Sports Med 2001; 29:226-31. 1421 Pauwels F. Uber die Bedeutung der Bauprinzipien des Stiitz- und Bewegungsapparates fur die Beanspruchung des Rohrenknochens. Acta Anat 1951;12:207-27. 1431 Piazza SJ, Delp SL. Three-dimensional dynamic simulation of total knee replacement motion during a step-up task. J Biomech Eng 2001; 123599-606. [44] Pinskerova V, Iwaki H, Freeman MA. The shapes and relative movements of the femur and tibia at the knee. Orthopiide 2000; 29:S3-5. [45] Provenzano PP, Martinez DA, Grindeland RE, et al. Hindlimb unloading alters ligament healing. J Appl Physiol 2003;94:314- 24. [46] Rohlmann A, Bergmann G , Graichen F. Loads on internal spinal fixators measured in different body positions. Eur Spine J 1999; 8:3549. [47] Scott SH, Winter DA. Internal forces of chronic running injury sites. Med Sci Sports Exer 1990:22:357-69. [48] Shelley FJ, Anderson D D , Kolar MJ, et al. Physical modelling of hip joint forces in stair climbing. Proc Inst Mech Eng [HI 1996;210:6S-8. [49] Simpson KJ, Pettit M. Jump distance of dance landings influencing internal joint forces: 11. Shear forces. Med Sci Sports Exer 1997;29:928-36. [50] Weidenhielm L, Svensson O K , Brostrom LkL. Surgical correction of leg alignment in unilateral knee osteoarthrosis reduces the load on the hip and knee joint bilaterally. Clin Biomech 1995;10:21721. [51] Wilson DR, Feikes JD, O’Connor JJ. Ligaments and articular contact guide passive knee flexion. J Biomech 1998;31:1127-36. [52] Woo SL, Hollis JM, Adams DJ, et al. Tensile properties of the human femur-anterior cruciate ligament- tibia complex. The effects of specimen age and orientation. Am J Sports Med 1991; 19:2 17-25 [53] Yagi M, Wong EK, Kanamori A, et al. Biomechanical analysis of an anatomic anterior cruciate ligament reconstruction. Am J Sports Med 2002;30:660 -6. [54] Zheng N, Fleisig GS, Escamilla R F , Barrentine SW. An analytical model of the knee for estimation of internal forces during exercise. J Biomech 1998;31:963-7.
Journal of Orthopaedic Research
Journal of Orthopaedic Research 22 (2004) 625-632
www.elsevier.com/locate/orthres
Tibio-femoral loading during human gait and stair climbing William R. Taylor
a,
Markus 0. Heller
a,
Georg Bergmann ', Georg N. Duda
a,*
'' Rrseurch Laboratory, Traumu and Reconstructiw
Surgerj., Churiti, Huniholdr- University of' Berlin, Cumpus Vircliow,-Clinic. Augustenhurger Phr: I , D- 13353 Berlin, Germuny Biomechanics Lab., Depurtment of Orthopuediicy, Free Universitj, of Berlin, 12203 Berlin. Germuny
Abstract Surgical intervention of the knee joint routinely endeavors to recreate a physiologically normal joint loading environment. The loading conditions resulting from osteotomies, fracture treatment, ligament replacements, and arthroplasties of the knee are considered to have an impact on the long term clinical outcome; however, knowledge regarding in vivo loading conditions is limited. Using a previously validated musculoskeletal lower limb model, we predicted the tibio-femoral joint contact forces that occur in the human knee during the common daily activities of walking and stair climbing. The average resultant peak force during walking was 3.1 times body weight (BW) across four total hip arthroplasty patients. Inter-individual variations proved larger than the variation of forces for each patient repeating the same task. Forces through the knee were considerably larger during stair climbing than during walking: the average resultant peak force during stair climbing was 5.4 BW although peaks of up to 6.2 BW were calculated for one particular patient. Average anteroposterior peak shear components of 0.6 BW were determined during walking and 1.3 BW during stair climbing. These results confirm both the joint contact forces reported in the literature and the importance of muscular activity in creating high forces across the joint. The magnitudes of these forces, specifically in shear, have implications for all forms of surgical intervention in the knee. The data demonstrate that high contact and shear forces are generated during weight bearing combined with knee flexion angles greater than approximately 15". Clinically, the conditions that produce these larger contact forces should be avoided during post-operative rehabilitation. 0 2004 Orthopaedic Research Society. Published by Elsevier Ltd. All rights reserved. Keyivords: Joint contact forces; Tibio-femoral joint; Muscle forces
Introduction The action of muscles during normal activities produces bone loading and joint contact forces far in excess of body weight [10,32,42]. The loading within musculoskeletal structures influences biological processes including fracture healing [ 17,351, bone remodelling [29,36], and ligament repair [45]. Loading is also believed to play a role in the onset of osteoarthritis [7,26]. Surgical intervention of the knee, through osteotomy [6,18], ligament reconstruction [53], and joint replacement [50], routinely attempts to recreate a physiologically normal and stable loading environment. Surgical success is directly affected by the resulting local loading environment [6]. Defining 'normal' loading conditions
* Corresponding author. Tel.: +49-30-450-559079; fax: +49-30-450559969. E-muil uddress: [email protected] (G.N. Duda).
within the knee is difficult, however, as both intra- and inter-individual differences must be considered. Musculoskeletal loading is influenced by a number of inter-individual factors such as weight [26] and gender [21,38], as well as the activity being undertaken [10,11, 32,39,49]. Determining the in vivo loading environment in the human knee is difficult due to the combination of complex structural anatomy, complicated movements [44], and dynamic, often indeterminate muscle function. While direct measurement techniques such as instrumented prostheses have been employed to determine loading in the hip [ l l ] and spine [46], the results of instrumented implants in the knee remain to be seen [33]. As a result, mathematical models have been employed to estimate muscle and joint contact forces [8,20,34,43,54]. Different levels of loading have been reported for a variety of activities: peak tibio-femoral contact forces of approximately 2.8 times body weight (BW) exist in the knee during walking [3,30]; approximately 4.3 BW (assuming a 75 kg man) during squat, leg press and knee
0736-0266/$ - see front matter 0 2004 Orthopaedic Research Society. Published by Elsevier Ltd. All rights reserved doi: 10.1016/j.orthres.2003.09.003
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extension exercises [54]; and 2.6-7.5 BW at knee extension angles between 0" and 40" at varying angular velocities [8,34]. Shear forces are thought to be important for knee joint stability during rehabilitation after ligament reconstruction and total knee replacement surgery [25,27]. Shear forces of 0.9 BW during extension [8] and 0.580.68 BW during deep flexion have been reported [39]. Analysis of knee loading during equivalent exercises has produced much higher peak shear forces of up to 3.89 BW [34], demonstrating a lack of consensus on knee loading in the literature. While information regarding knee joint loading during such activities is important, understanding the loading that occurs during common daily activities such as walking and stair climbing [ 1,12,40,48] is essential for early rehabilitation from surgical interventions in order to know the magnitudes of forces that the reconstructed joint must withstand. The musculoskeletal model developed by Heller et al. [32] calculated hip contact forces that were compared with those measured in vivo for four patients during multiple trials of walking and stair climbing. The calculated peak hip contact forces both over and under estimated the measured forces, differing by a mean of 12'%during walking and 14Y1during stair climbing, but revealed good agreement in both pattern and magnitude for all activities in all patients. The aim of this study was therefore to examine the tibio-femoral joint contact forces that occur in vivo in an attempt to determine a normal range during walking and stair climbing. Specific attention was paid to the relationship between activity, joint flexion angles, and joint contact forces to avoid excessive loading of the knee and provide guidance for post-operative rehabilitation.
Fig. I . Image of patient stair climbing. Reflective markers were attached to the skin in order to measure the positions of each limb throughout the gait cycle. Simultaneously. the hip contact forces from an instrumented endoprosthesis were measured together with the ground reaction forces (force plate positioned under each step. not visible in image).
reflective markers attached to the patients' skin was used to determine movements of the lower limbs. Musculoskrletnl iuotlel
A musculoskeletal model of the human lower extremity (Fig. 2) was developed, based on CT-data from the Visible Human (VH: National Library of Medicine. Bethesda. MD). From the individual C T slice
Materials and methods Guit
criicrli,.si.\
A validated musculoskeletal model of the complete human lower limb was used in this study [32]. Clinical gait analysis was performed on a total offour total hip arthroplasty patients (average age 61 years; initials: IBL. HSR, PFL, and KWR). All subjects possessed an instrumented femoral prosthesis (average time after implantation: 17 months, range 11-31 months) for the measurement of in vivo hip contact forces [9,10.13]. For each patient, extensive anthropometric data were collected to determine bone dimensions. segment masses, center of gravity positions, and inertial parameters [22]. All subjects gave informed consent to participate in the experiments and to the publication of their images and names; the study was approved by the local ethics committee of the Free University of Berlin. Gait analysis (Fig. I ) was conducted for walking and stair climbing [lo] with each patient performing several trials of each activity. The beginning of the exercise was defined as the instant of heel strike (0% stride). During all activities, time dependent kinematic and kinetic data were gathered. Two force platforms (Kistler. Ostfildern, Germany) measured ground reaction forces. The in vivo hip contact force was measured in the femoral coordinate system [ I l l . An optical system (Vicon, Oxford Metrics, U K ) using six infrared cameras to detect 24
Fig. 2. Musculoskeletal model used for calculating muscle and joint contact forces, shown during several instances of the stair climbing activity for one patient. The geometry of the bones was derived from the Visible Human project (NLM. Bethesda. USA) and scaled to each individual patient. The lines connecting the bones represent the force vectors of the muscles acting on each segment.
W.R. T U J ~etOof. ~ I Joirrnirl of Orthoprrctlic Re.~c~nr.ch 22 (2004) 62.5 632
images, surfaces of all hip bones (left and right iliac bones and sacrum) and all the bones of the lower limb (femur, patella. tibia. fibula. and all the bones of the foot) were reconstructed [28]. Muscles were represented as straight lines spanning from origin to insertion based on literature descriptions [14.23], wrapped around the bones where necessary to approximate their real curved paths and to provide an adequate representation of their lever arms at the joints. Muscles with large attachment areas such as the abductors were modeled using more than one line of action, creating a total of 95 muscle fibers. Data on the physiological cross sectional area (PCSA) of the individual muscles were taken from the literature [15,23]. The hip, ankle, and tibio-femoral joints were modeled with 3 rotational degrees of freedom (DOF). Since tracking of the patella was not possible during gait analysis, its motion was determined from an in vitro experiment during a complete flexionxxtension cycle [24]. The VH dataset. including all muscle origins, insertions. and wrapping points, n'as then scaled to the anatomy of each individual patient using bony landmarks to obtain subject specific musculoskeletal models. Prominent bone landmark positions (e.g. joint centres and tuberosities) were measured from both the VH and individual subject anatomies. Lineal- 3-dimensional scaling was then performed according to the relevanl VH to patient ratios for each bone, muscle attachment site. and wrapping point. The PCSA of each muscle w d S scaled to each patient based on body weight. At the hip. the femoral anteversion. caput colum diaphyseal (CCD) angle. and neck-stem length were all determined to match each individual patient. The resultant inter-segmental forces and moments at the ankle. knee, and hip were computed from the kinematic and kinetic gait analysis data with respect to the local coordinate systems using an inverse dynamics approach [5,22] (Fig. 3). With the maximum obtainable force in each muscle constrained [I61 to 85'% of the physiologically attainable muscle force ( a value based on each muscle's
f -MR FOOI
Foot
-FR F O O ~ M R FOOI MR
GRF
1FR.
GRF
A
B
Fig. 3. (A) Mechanical model for calculation of the resultant forces and moments in the joints using inverse dynamic techniques. (B) In the exemplified time step, the resultant forces and moments are calculated for each joint. beginning with FR and resultant moment MR at the foot. The calculation takes into account the inertial properties (based upon the mass, m, and length, I ) of each segment and the ground reaction force (GRF).
627
PCSA) [2]. the muscle force distribution surrounding the knee was computed for the tested activities in all patients using static optiniization techniques [I91 to minimize the square of the muscle stresses. A local coordinate system was then constructed on the surface of the tibia1 plateau at the center of the inter-condylar eminence. aligned with the shaft of the tibia, to calculate tibio-femoral contact forces. These forces were then compared with the in vivo measured joint contact forces for each of six repetitions throughout both walking and stair climbing for all four patients.
Results In general, all patients displayed double-peaked tibiofemoral loading curves for both walking and stair climbing (Figs. 4 and 5). Small intra-individual variations were observed for repetitions of the same activity, with comparatively greater inter-individual variation for different subjects repeating the same task. The average resultant peak tibio-femoral contact forces during walking were 3.33 (range 3.02-3.48), 3.23 (3.05-3.79), 3.02 (2.75-3.44), and 2.97 (2.74-3.22) BW, respectively, across the four patients (Table 1) with a single peak value of 3.79 BW in one subject (HSR). In two subjects (HSR and KWR), two distinct loading peaks were apparent, while the other two subjects possessed much smoother curves without this double peak characteristic. The intra-individual variation between repetitions of the same activity, however, remained low (Table 1). During stair climbing, the forces through the knee were considerably higher than during walking (Figs. 4 and 5). All patients demonstrated similar loading curves with a large first peak shortly after heel-strike, followed by a much smaller peak before toe-off. The maximum averaged forces for this activity were 5.88 (5.44-6.16), 5.23 (5.09-5.28), 5.09 (4.87-5.35), and 5.33 (4.69-5.78) BW for the four patients (Table l), although a peak of 6.16 BW was calculated for one particular trial (patient IBL). The intra-individual variations in joint contact forces were also low during the activity of stair climbing, although patient IBL displayed consistently higher second peaks than those observed for the other three subjects (Table 1). Based upon the average peak loading for each subject during walking, a comparison was made with the equivalent load situation during stair climbing (Fig. 4, horizontal dotted lines). When this load was projected downwards for all subjects (vertical dotted line), the loading in the knee was greatly increased when the flexion angle was larger than approximately 15" in a loaded state. The largest component of the joint contact force was in the direction of the long axis of the tibia throughout all trails of all patients. These force components reached values of 3.1 BW (individual forces of 3.2, 3.2, 3.0, 2.9 BW) and 5.1 BW (5.6, 4.7, 4.9, 5.0 BW) during walking and stair climbing, respectively.
W.R. Tuylor et ul. I JournuI o j Orihoprrrdic Research 22 (2004) 6 2 5 4 3 2
628
Walking
Stair Climbing
I
7 ,
IBL
HSR
0
PFL
I
"
I
0
Gait cycle (%)
100
0
100
Gait cycle (%)
Fig. 4. Average axial tibio-femoral contact forces from all 4 patients (abbreviations IBL, HSR, PFL and KWR) calculated throughout both walking and stair climbing are shown together with f one standard deviation (light grey lines) taken from repetitions of the same activity. Average Aexion angle at the knee is also shown for both activities. The dotted horizontal lines correspond to the average peak axial force during walking. When these same loads are horizontally projected to the situation during stair climbing, it can be seen that the flexion angle corresponds to an average of approximately 15" (dotted lines). The grey region shows the initial loading phase that produces greatly increased loading above that seen during walking. All forces are shown in body weight (BW). The flexion of the knee does not return to the initial state at 0" since only a single stair was climbed.
Average anteroposterior peak shear forces of 0.5 BW (0.5, 0.6, 0.4, and 0.5 BW) were determined during walking (Fig. 5). During stair climbing, these forces were more than doubled, averaging 1.3 BW (1.4, 1.5, 1.1, and 1.1 BW). Peak anteroposterior shear forces in single trials reached 0.8 BW during walking and 1.6 BW during stair climbing. Corresponding medial-lateral shear forces were similar in both magnitude and form for all patients. The average peak shear loading during walking was then compared to the equivalent shear load situation in each subject during stair climbing, in a process similar to that described above for axial loading. Once again, the shear loading in the knee was greatly increased when the flexion angle was greater than approximately 15" in a loaded state.
Discussion The goal of this study was to determine the tibiofemoral contact forces that occur during common daily activities. This study has established fundamental knowledge of the loading occurring in the human knee by employing a musculoskeletal model of the lower limb that has been previously validated at the hip for both walking and stair climbing. The results demonstrate both intra-individual variations of knee contact forces between repetitions of the same exercise but also interindividual variations between different patients performing the same task. The average peak resultant tibio-femoral contact forces calculated in this study ranged from 2.97 to 3.33 BW across different trials of all 4 patients during walk-
W.R. T u ~ ~ l oelr ul. I Journul of Orthopncdic Research 22 (2004) 625-632
Walking
629
Stair Climbing
mL
HSR
* 7 PFL
KWR
100 0
0
Gait cycle (%)
100
Gait cycle (%)
Fig. 5. Average anterior- posterior shear contact forces acting at the knee joint throughout the gait cycle for all patients during walking (left column) and stair climbing (right hand column) are shown together with ? one standard deviation (light grey lines). taken from repetitions of the same activity. The dotted horizontal lines correspond to the average peak shear forces during walking for each patient. When these same shear loads are projected to the situation during stair climbing, the corresponding flexion angle of the knee at this shear load corresponds to an average knee flexion OF approximately 15". All forces are shown in body weight (BW).
ing. These forces concur with those previously reported in the literature 13,301, where peak forces of 2.7-2.8 BW were calculated for this activity, and are within the forces (2.6-7.5 BW) expected across a range of activities [8,34]. Contact forces of 5.09-5.88 BW have also been determined during stair climbing in this study, with individual peaks as high as 6.16 BW. Repetitions of each activity calculated for each individual produced relatively consistent peak joint loads (as shown by a maximum standard deviation of approximately 8% among all patients and activities), while the curves differed in form between each patient: during walking, two patients possessed two distinct loading peaks, while the other two subjects showed much smoother, flatter curves. Since the forces were normalized for the subject's weight, the variations in these calculated forces come from the different movements and ground reaction forces during each walk and from
the varying musculoskeletal geometries between individuals. This study has shown that the tibio-femoral forces seen during stair climbing were larger than those during walking consistently across all patients and all repetitions. The corresponding shear forces during stair climbing were more than double those during walking. The peaks in these contact forces also mainly occurred when the knee joint was under larger flexion angles and under loaded conditions (Figs. 4 and 5). These findings are supported by the results of previous studies [34,39], which also found that higher loads occurred under large knee flexion angles. With relative consistency, the loading during stair climbing greatly increased beyond the peak loads during walking when the knee was both loaded (i.e., during the stance phase) and the knee flexion angle was greater than approximately 15". Clinically, patients undergoing rehabilitation from knee ligament
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Table 1 Average resultant contact forces across the tibio-femoral joint over the complete gait cycle are shown for each patient together with the standard deviations of all six repetitions of each activity Gait cycle
Average resultant joint contact forces during walking (N)
Average resultant joint contact forces during stair climbing (N)
(1%))
IBL
TBL
HSR
PFL
0.64f0.19 0.79 f 0.10 0.41 f 0.09 I .64 2 0.32 1.70 f 0.20 1.08 f 0.07 2.86 f 0.3 1 3.01 2 0.30 2.05 f 0.21 10 3.02 f 0.22 3.23 f 0.31 2.77f0.19 15 2.78 f 0.24 2.90 f 0.27 3.05 f 0.18 20 2.21 20.25 2.68 f 0.25 2.94 f 0.21 25 2.57 k 0.25 2.67f 0.27 1.65f 0.22 30 2.62 k 0.32 1.58 f 0.13 2.60 f 0.30 35 2.78 f 0.24 2.24 f 0.32 2.64k 0.32 40 2.92f 0.39 2.60 f 0.27 3.07 f 0.14 45 2.30 f 0.19 3.33 k 0.1 7 2.91 f0.31 50 2.85 f 0.36 1.68 f 0.27 2.16k0.08 55 1.51 f 0 . 3 2 2.08 k 0.25 I .56? 0.36 60 1.04 f 0.16 0.60 f 0.17 0.41 f 0.05 65 0.29f 0.08 0.36 f 0.08 0.20 f 0.05 70 0.31 f 0.05 0.18k0.06 0.26 ? 0.04 75 0. I9 k 0.05 0.25 f 0.04 0.17f 0.03 80 0.16f0.02 0.18f0.04 0.23 f 0.04 85 0.43 f 0.04 0.25 f 0.04 0.31 ? 0.03 90 0.27 k 0.06 0.49 f 0.08 0.32f 0.04 95 Individual components of the forces are not presented here but 0
5
KWR
0.68 f 0.05 0.71 20.19 1.63 f 0.23 0.58 2 0.21 2.35 f 0.14 2.86 f 0.99 5.13 20.58 2.27 f 0.15 1.83 f 0.17 5.88f 0.25 1.47 ? 0.19 5.39 f 0.54 I .46 f 0.21 4.38 f 0.56 2.16 f 0.30 3.60f 0.42 2.79 f 0.26 3.20 f 0.50 2.9720.18 3.21 f 0.77 3.66 f 0.80 2.34 f 0.21 2.49 f 0.32 3.73 20.80 2.01 f 0.37 3.04 f 0.80 2.12f0.72 0.58 f 0.27 0.13 f 0.06 1.13 f 0.32 0.07f 0.02 0.77 f 0.17 0.09k 0.02 0.90 f 0.21 0.17 f 0.04 0.87f0.16 0.27 f 0.05 0.90 f 0.14 0.30 f 0.05 0.8520.19 are available upon request to the
surgery should attempt to avoid the large contact and shear forces that occur under these conditions. The calculated tibio-femoral contact forces in this study were larger than the corresponding peak contact loads measured at the hip [9-111. Peak in vivo measured hip contact force magnitudes of 2.9, 2.5, 2.1, and 2.4 BW (average 2.4 BW) were observed for normal walking and 2.7, 2.3, and 2.7 BW (average 2.5 BW-IBL not included) for stair climbing. A direct comparison of knee and hip contact forces in the same subject for the same trails and activities reveals an average 33% higher peak force in the knee during walking and an average increase of 1 16% during stair climbing over those seen at the hip. While the corresponding external loads (ground reaction forces) were approximately only a single BW [10,32], joint contact forces of many multiples of body weight demonstrate the importance of the muscles on the loading at the joint. In addition, despite relatively consistent inter-individual external loads, differences in gait patterns and varying muscle activation of each subject resulted in highly individualized joint loading (Figs. 4 and 5). The extensive increase in knee loading over and above the loading at the hip, specifically during stair climbing, has direct consequences for both primary stability and long term wear of implants in the knee and should be accounted for in the design stages of knee implants. Shear components of the knee contact forces are considered to be especially important for stability of the joint during rehabilitation after ligament reconstruction and total knee replacement surgery [25,27]. Average
HSR
PFL
KWR
0.35 f 0.08 1.38 f 0 . 4 4 4.06 f 0.34 5.23 f 0.07 4.91 f 0.20 3.97 k 0.20 3.12f0.28 2.45 2 0.35 2.142 0.31 2.07 f 0.30 2.08 f 0.41 1.89 f 0.35 0.58 ?r 0.32 0.13 f 0.03 0.15 ? 0.02 0.15 f 0.01 0. I4 L 0.02 0.20 f 0.07 0.27 f 0.03 0.23 f 0.04 authors.
0.42 f 0.10 1.37 f 0.47 3.74 2 0.40 5.09 f 0.22 5.06 f 0.25 4.15 f 0.45 3. I5 f 0.44 2.43 k 0.29 1.91 20.10 1.83 f 0 . 1 1 1.95 f 0.19 1.89 ?r 0.30 0.78 2 0.31 0.29 f 0.04 0.20 f 0.04 0.12 k 0.04 0.08 f 0.02 0.18 f 0.07 0.30 f 0.05 0.28 f 0.06
0.3 I f 0.06 1.92 f 1.03 4.47f 1.19 5.33 f 0.58 4.80 f 0.22 3.95 ?r 0.37 3.23 f 0 . 5 4 2.59 kO.71 2.31 2 0.40 2.13 k 0.26 2.12 f 0.26 2.16 f 0.29 I .63 f 0.92 0.72f0.51 0.08 f 0.02 0.12 f 0.04 0.15 ?r 0.05 0.21 f 0.08 0.26 f 0.06 0.19 f 0.07
anteroposterior peak shear forces of 0.6 BW during walking and 1.3 BW during stair climbing (Fig. 5) were observed for the four subjects tested in this study. Previous studies have reported shear forces of 0.9 BW during knee extension [8], 0.58-0.68 BW during deep flexion [39], up to 3.89 BW at angles beyond 50" during isokinetic eccentric efforts of the knee flexors [34], and 0.4-0.7 BW during running [47]. Although these studies did not reach a consensus on shear forces in the human knee, the shear forces for the four subjects reported in this study were well within the boundaries of the values reported in the literature and seem, therefore, to be in broad agreement. Shear forces are carried by the local soft tissues, including the anterior and posterior cruciate ligaments, collateral ligaments, and menisci. In this study, shear forces of up to 1.6 BW were observed during stair climbing. While the ultimate strength of the ACL is recognized as being much higher (2160 k 157 N [52]equivalent to 2.9 BW assuming a 75 kg man), and therefore the ligament alone is capable of carrying the shear forces seen here, any injury to the ACL would lead to a distribution of these shear forces to the surrounding soft tissue structures, particularly the menisci [41]. In the case of a completely ACL deficient knee, the transmission of these shear forces can potentially double the forces on the medial meniscus [41], almost certainly leading to their rapid degeneration and ultimate demise. It is therefore important to recognize the major role of the ACL as a structure for carrying the shear forces seen in this study.
The knee forces reported in this study were derived using a model which had been validated at the hip for walking and stair climbing against contact forces measured in 4 patients, each possessing an instrumented hip prosthesis [32]. Static optimization procedures were used to determine the contact forces at the knee joint. The difference between static and dynamic optimization techniques during gait is small [ 3 ] . Even though the optimization criterion used may have had a large influence on the forces in the individual muscle fibers, Brand and coworkers suggested that the optimization criterion has only a small influence on the calculated joint contact forces [15]. Our own studies have also shown that the joint contact force calculations are more sensitive to the gross anatomical structure (e.g., joint center, CCD angles, and offset) than the optimization criteria itself [31,32]. Since the participants in this study had all undergone hip replacement, their gait patterns and hence joint loading conditions could have differed from normal, unimpaired individuals. However, ground reaction forces, as well as joint resultant moments and angles during gait, return to those of healthy individuals within approximately half a year post-operatively [4]. The four patients were an average of 17 months post-operative, and the gait patterns appeared normal compared to literature data [lo]. Therefore, the presented data are assumed to be good estimates of loading conditions acting at the knee and only to a lesser degree affected by the hip athroplasty surgery. The methodology presented here, however, allowed data to be reported from a validated analysis of musculoskeletal loading. Since the muscle forces in the knee joint were calculated simultaneously with those in the hip joint and good resulting correlations of joint contact forces were achieved at the hip, the contact forces determined at the knee are also likely to be physiologically realistic for these individuals. The current musculoskeletal analysis reports a single resultant contact force across the knee joint, as a simplification of the forces that are carried across both femoral condyles. For further analysis of the soft tissue balance across the knee joint [37,51], determination of the distribution of the contact force across the condyles is of importance, especially for establishing the internal stress and strain loading environment of the individual structures within the joint. Despite these limitations, however, the model has determined highly individual muscle and joint contact forces, based on the individual anatomical considerations, gait movements, and ground reaction forces. This indicates the requirement for individualized analyses in order to achieve good estimates of both internal and external forces in vivo. This study has taken an existing model of the human lower extremity that has been validated at the hip during walking and stair climbing and used the model to examine the contact forces across the tibio-femoral joint. The magnitudes of these forces illustrate the impact of
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