Development of a Full Flexion 3D Musculoskeletal Model of the Knee Considering Intersegmental Contact During High Knee Flexion Movements

in Journal of Applied Biomechanics
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  • 1 University of Saskatchewan
  • 2 University of Waterloo

A musculoskeletal model of the right lower limb was developed to estimate 3D tibial contact forces in high knee flexion postures. This model determined the effect of intersegmental contact between thigh–calf and heel–gluteal structures on tibial contact forces. This model includes direct tracking and 3D orientation of intersegmental contact force, femoral translations from in vivo studies, wrapping of knee extensor musculature, and a novel optimization constraint for multielement muscle groups. Model verification consisted of calculating the error between estimated tibial compressive forces and direct measurements from the Grand Knee Challenge during movements to ∼120° of knee flexion as no high knee flexion data are available. Tibial compression estimates strongly fit implant data during walking (R2 = .83) and squatting (R2 = .93) with a root mean squared difference of .47 and .16 body weight, respectively. Incorporating intersegmental contact significantly reduced model estimates of peak tibial anterior–posterior shear and increased peak medial–lateral shear during the static phase of high knee flexion movements by an average of .33 and .07 body weight, respectively. This model supports prior work in that intersegmental contact is a critical parameter when estimating tibial contact forces in high knee flexion movements across a range of culturally and occupationally relevant postures.

There is no current 3D musculoskeletal (MSK) model of the knee that can incorporate the effects of intersegmental contact during high knee flexion postures. Intersegmental contact is a critical parameter when modeling high knee flexion movements (knee flexion exceeding 120°1,2) as its omission has been reported to result in overestimations of tibial compression and anterior–posterior shear forces as high as 1.99 and 0.54 body weight (BW), respectively.3 Prior 2D high knee flexion models4 that omit intersegmental contact predicted tibial compression as high as 5 kN or 7.3 BW during a maximum depth squat, which exceeds the 21 MPa tensile yield stress of both ultrahigh molecular weight polyethylene5 and the 15 to 20 MPa range known to damage cartilage and kill chondrocytes.6 However, overly conservative estimation of tissue loading is as detrimental as overestimation for menisci and cartilage growth.7,8 Development of the model presented in this study was motivated by this need for biofidelic tibial compressive and shear force magnitudes in applications such as tissue engineering of knee joint structures9,10 or estimating bone growth and prosthetic loosening in knee arthroplasty.11,12

Sagittal plane13 and finite element models3,14 have been previously reported but were based on sagittal plane kinematics.15 The model developed by Zelle et al consisted of a tibia and femur but used lumped muscle parameters to simplify geometry. Caruntu et al used a spring-damping model to estimate thigh–calf contact forces but neither reported magnitudes nor verified their predictions against empirical intersegmental contact data. Finally, Hirokawa and Fukunaga used thigh–calf contact parameters reported from Zelle et al but were limited to a 7 muscle sagittal plane model.

Recent work incorporating thigh–calf contact has been performed using 3D modeling approaches but it has been limited to peak knee flexion angles of approximately 120° or 130° during a heels-up squat. Using a uniaxial load cell, Dooley et al16 measured peak thigh–calf contact forces of ∼20% BW at ∼133° of knee flexion, reducing external knee flexion moments by 43% and 63% on the dominant and nondominant legs, respectively. Wu et al reported thigh–calf contact force magnitudes from a single male participant using an 11.2 cm2 pressure sensor (5101; Tekscan, Inc, Boston, MA) during a heels-up squat with pressure data input to AnyBody MSK modeling software.17 However, their report of thigh–calf contact onset at ∼90° of knee flexion and peak magnitudes of ∼300 N occurring at 120°18 contradict prior work.1,15,19 Similarly, it should be noted that in the work of Wu et al, a 57% reduction in tibiofemoral forces at ∼120° flexion was unexpected as Kingston and Acker, and Zelle et al reported <20 N of thigh–calf contact force at this angle (∼120°) and peak flexion angles of ∼150° in a similar movement.

Three critical modeling challenges specific to high knee flexion movements were considered in this model: 3D musculotendinous lines of action, specific muscle tension, and femoral translation relative to the tibia. There are no known reports of musculotendinous moment arms—for knee flexor and extensor muscles—in the high knee flexion range as current in vitro studies report from 0° to 120°20,21 or from 40° to 110°.22 Therefore, estimates of moment arms were computed using assumptions based on regional anatomy during these movements. There is also a wide range of muscle-specific tension values used in the modeling literature (eg, 30,23 61,24,25 or 8826 N/cm2), exceeding the 15 to 30 N/cm2 values reported for mammalian and human tissue.2730 Thus, the sensitivity and accuracy of modeled joint contact force estimates with respect to the specific tension were assessed in high knee flexion ranges. Finally, in vivo active and passive range of motion tests have reported femoral posterior translation (relative to the tibia) up to 2.8 cm at 162° of knee flexion using magnetic resonance imaging31 or 3.1 cm at 149.4° of knee flexion using fluoroscopy.32,33 Therefore, these translations of anatomical structures were incorporated when modeling high knee flexion postures.

Verification of MSK model predictions is a critical aspect in any computational model development cycle. Although there are no known instrumented implant data available from high knee flexion ranges, publicly available gold-standard data sets are available for ∼0° to 120° of knee flexion.34,35 The Grand Knee Challenge (https://simtk.org/projects/kneeloads) was a semiannual modeling competition where kinematic, kinetic, electromyography (EMG), and tibial compression data were provided to researchers.34 Similarly, Orthoload data sets (https://orthoload.com) will provide triaxial tibial forces—in addition to kinematic, kinetic, and EMG data—but these fulsome data sets are not yet publicly available.35 For the model developed in the current study, component verification will be performed to quantify prediction error of tibial compression against instrumented implant data from the fourth Grand Knee Challenge (https://simtk.org/projects/kneeloads).

In this study, we defined an MSK model of the pelvis and right lower limb that incorporates intersegmental contact variables. The objectives for this work were to quantify prediction error of tibial compression against a gold standard and to use this model to estimate 3D tibial contact forces during high knee flexion movements. Our main hypothesis was linked with the second objective; the inclusion of intersegmental contact would significantly decrease tibial contact forces when compared with estimates derived using the model with intersegmental contact omitted. Throughout this work, tibial contact forces are reported in the tibial/shank coordinate system.

Methods

This model of the pelvis and right lower limb contains 13 degrees of freedom across 3 joints (6 at the ankle, 4 at the knee, and 3 at the hip) and was coded in MATLAB 9.2 (R2017a; The MathWorks, Natick, MA). Three dimensional kinematic, kinetic, and intersegmental contact pressure data were used as inputs to the model.

Participants

Sixteen participants, 8 males and 8 females, were recruited as a sample of convenience from the university’s student body (Table 1). Exclusion criteria consisted of any low back or lower limb injury within the past year that required medical intervention or time off from work for longer than 3 days and any history of surgical interventions to the back or lower limb. All participants self-reported right-leg dominance and the ability to kneel to the ground without pain. Each participant read and signed an informed consent form approved by the University of Waterloo’s research ethics board.

Table 1

Mean (SD) Descriptive and Anthropometric Participant Information

ParameterFemales (n = 8)Males (n = 8)All (N = 16)
Age, y24.30 (4.50)26.30 (3.20)25.30 (3.90)
Height, m1.70 (0.10)1.80 (0.10)1.80 (0.10)
Mass, kg70.40 (10.70)88.60 (16.50)79.50 (16.40)
Body mass index, kg/m224.30 (3.80)27.00 (3.40)26.70 (3.80)
Thigh length, m0.41 (0.04)0.40 (0.04)0.40 (0.04)
Proximal thigh circumference, m0.60 (0.04)0.63 (0.09)0.61 (0.07)
Midthigh circumference, m0.53 (0.04)0.55 (0.12)0.54 (0.09)
Distal thigh circumference, m0.41 (0.04)0.42 (0.05)0.41 (0.04)
Shank length, m0.41 (0.03)0.41 (0.03)0.41 (0.03)
Proximal shank circumference, m0.35 (0.02)0.36 (0.04)0.35 (0.03)
Midshank circumference, m0.37 (0.03)0.39 (0.04)0.38 (0.03)
Distal shank circumference, m0.21 (0.02)0.23 (0.02)0.22 (0.02)

Note: Segmental circumferences were measured distally from the greater trochanter toward the lateral femoral condyle (thigh) or the lateral tibial condyle to the lateral malleolus (shank): proximal at 10%, mid at 50%, and distal at 90% of segment length.

Segmental/Joint Kinematics

Kinematic data were recorded at 100 Hz from rigid body marker clusters on the pelvis, femur, shank, and foot using an optoelectronic system (Certus; NDI—Northern Digital Inc., Waterloo, ON) that was detailed in a previous study.36 In brief, participants performed 5 fully randomized repetitions of 6 high knee flexion movements (Figure 1): heels-up squat, flatfoot squat, dorsiflexed kneel, plantarflexed kneel, dorsiflexed unilateral kneel, and plantarflexed unilateral kneel. Each trial took 12 seconds to complete with participants moving at a self-selected pace. Trials consisted of stepping onto embedded force plates, descending to end range of motion, statically holding for 2 to 3 seconds, then ascending and walking backward off the force plates. Linear kinematic calculations were completed using standard procedures with angular kinematics determined from the segmental local coordinate system (Appendix A).37,38 Joint kinematics were extracted using a Cardan flexion/extension, abduction/adduction, and internal/external (ZXY) rotation sequence.37,39

Figure 1
Figure 1

—High knee flexion postures performed for the application of this model. Details regarding the processing of these data are reported in the study of Kingston and Acker.1 DK indicates dorsiflexed kneel; DUK, dorsiflexed unilateral kneel; FS, flatfoot squat; HS, heels-up squat; PK, plantarflexed kneel; PUK, plantarflexed unilateral kneel.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

Kinematic assumptions specific to high knee flexion movements were applied at the patella, knee, and hip joints. Patellar kinematics were modeled as we did not have the capability to track patellar movement in vivo. Therefore, each participant assumed 3 knee flexion angles (0°, 90°, and end range of motion in a heels-up squat) in a calibration trial while the tibial tuberosity and distal and proximal patellar points were manually palpated and digitized with respect to the shank local coordinate system. Patellar points were piecewise linearly interpolated to provide reference locations for attachment points of knee extensor muscles. Due to patellar tracking limitations, patellofemoral kinetic outcomes were beyond the scope of this work. Femoral anterior–posterior translation with respect to the tibial plateau was also modeled as a linear function of knee flexion angle. A posterior shift was applied to the femoral local coordinate system origin of 0 to 3 cm through the 0° to 180° knee flexion range to approximate in vivo data.31,33 This reduced the knee to a 4 degrees of freedom joint as medial–lateral and axial translations of the femur with respect to the tibia were constrained. Finally, the hip joint was limited to a 3 degrees of freedom joint to maintain joint spacing imposed during bone scaling.

Anatomical Geometry

Common anatomical points were used for segmental local coordinate system definitions (Appendix A) and to, first, scale published muscle origin/insertion data to publicly available bone geometries and, then, to scale this combined set of points to each participant. Muscle origin/insertion locations, VIA points, and physiological cross-sectional area were defined using cadaveric data.40 This muscle geometry was from the right leg of an embalmed male (age 77 y, height 1.74 m, and mass 105 kg) sectioned at the superior aspect of the L1 spinal body and included 56 muscle partitions (38 muscles in total) that were further segmented into 161 muscle elements.40 These muscle points were scaled to bone surfaces obtained from publicly available vertex-based object files of a single Japanese male patient.41 Rigid affine scaling42 was used to minimize the Euclidean distance between the following vertex locations and anatomical points (provided in the source muscle data): right/left anterior superior iliac spines, right/left posterior superior iliac spines (pelvis); greater trochanter, lateral/medial femoral epicondyles (thigh); lateral/medial tibial epicondyles, tibial tuberosity, lateral/medial malleoli (shank); and heel, first and fifth metatarsals (foot). Following this procedure, all points were scaled to participant data using the same method and anatomical locations (Figure 2).

Figure 2
Figure 2

—Anatomical geometry of musculoskeletal model. Black spheres are manually selected landmarks matching those from Horsman et al. Blue lines indicate muscle paths. Green spheres within a muscle path are scaled VIA points. Red lines are knee joint ligaments (not used in this iteration). The reader is referred to the online version of this paper for the color representation of this figure.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

Functional movements43,44 were performed by each participant for the hip and knee to calculate joint centers using the Symmetrical Centre of Rotation Estimation algorithm.45,46 This approach has a reported spatial accuracy equivalent to finite helical axis methods.47 Knee extensor muscles have a confluence at the proximal patella and conformed to a spherical wrapping surface (Figure 3B and 3C) if the perpendicular distance to a line of action from the sphere origin was less than its radius.17,48 The engagement of wrapping was determined using the vector quadruple product to determine 3D point–line distance for each frame. The wrapping sphere radius (Figure 3A) was determined as the perpendicular distance between the femoral groove and an axis defined between vertices of the medial and lateral femoral condyles.49 The tendon excursion method5052 was used to populate a muscle Jacobian matrix for each muscle element, allowing an estimate of musculotendinous moment arms.

Figure 3
Figure 3

—Determination of wrapping surface size and path of common knee extensor musculature. (A) Blue points represent vertices of the medial and lateral femoral condyles and femoral groove (perpendicular to the condylar axis). (B) Anterior view of wrapping sphere (cyan) with curved path (green points) connecting to the proximal patella (red point), distal patella (black point), and tibial tuberosity (magenta point). (C) Anterior–sagittal view. The reader is referred to the online version of this paper for the color representation of this figure.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

Intersegmental Contact

A resistive pressure sensor (3005 E-FScan; Tekscan, Inc) was used to measure intersegmental contact from a single repetition of each high knee flexion movement. Normal force 3D orientation, center of force, magnitude, and active area of intersegmental contact were input as a function of knee flexion angle.1 The 8-bit pressure sensor has a spatial resolution of 3.9 sensels/cm2 and a sensing region that was 15.75 cm wide by 39.62 cm long. It was conditioned to 103.4 kPa 10 times in 3-second cycles, equilibrated for 30 seconds at 3 points (34.5, 68.9, and 103.4 kPa), then calibrated following the manufacturer’s nonlinear (power) procedure.

Following calibration, the pressure sensor was attached to a 4-mm thick 23 × 19-cm polycarbonate sheet and a motion trial was collected synchronously with pressure data (Figure 4). These data were rounded to the nearest 0.25° of knee flexion for each frame and averaged if more than one value was present at a given angle. Intersegmental contact data were not used from the ascending phase of movement as these resistive pressure sensors are susceptible to drift during sustained loading5355; therefore, it was assumed that forces during the ascending phase of movement at a given flexion angle were identical to those measured at the same flexion angle in descent.

Figure 4
Figure 4

—Measurement of intersegmental force during a plantarflexed high knee flexion movement. The blue polygon represents the polycarbonate sheet tracked during motion trials, with magenta spheres depicting center of force locations. The measured values from the heel center of force were assumed to be in the plane of the polycarbonate sheet for participants who had heel–gluteal contact. Black arrows represent the total normal forces at each location, which were then applied to the tibia in the model. The reader is referred to the online version of this paper for the color representation of this figure.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

Inverse Dynamics

External reaction forces acting at joint centers were calculated using standard inverse dynamics approaches.56,57 Segmental mass and moments of inertia were estimated using segmental mass ratios and length ratios between segmental joint center locations.58 Gravitational force, ground reaction force measured from embedded force plates (OR6-7; AMTI, Watertown, MA), and intersegmental contact forces were modeled as forces external to appropriate segments. External joint moments about the ankle, knee, and hip were calculated using a standard inverse dynamics approach.56,57,59

Static Optimization

Muscle forces were estimated using static optimization for each frame of motion data. A cost function (CF, Equation 1) was minimized to solve for muscle forces that has been shown to promote cocontraction.6063 This optimization problem minimized CF using 161 individual muscle elements and was solved using the generalized nonlinear solver “fmincon” from the Matlab Optimization Toolbox (R2017a; The MathWorks). Possible muscle element force estimations were limited between zero and a predicted upper bound determined by multiplying the specific tension of a muscle by its physiological cross-sectional area. To determine the best specific tension for this model, 30,23 61,24,25 and 8826 N/cm2 specific tensions were considered. The specific tension that resulted in the greatest R2 and lowest root mean squared difference (RMSD) when compared with the gold standard was chosen. An equality constraint required that the muscles crossing each joint produced equivalent forces to oppose the joint moments computed by inverse dynamics at each frame (Equation 2).64

CF=m=1161(FmPCSAm)3
where CF is the instantaneous cost function, Fm is the force estimate of muscle element m, and PCSAm is the physiological cross-sectional area of muscle element m.
m=1161rmjFm=Mj
where rmj is the moment arm of muscle element m at joint j and Mj is the external joint moment at joint j computed from inverse dynamics.

Linear inequality constraints consisted of limiting the force estimation between elements in the same muscle partition to within 15%6567 of the muscle element at the centroid of the muscle. Similarly, a 15% limit on force estimation differences between the medial and lateral gastrocnemii was assumed due to selective recruitment of these muscles being unlikely.

The optimization solver requires an initial guess to drive the search algorithm; however, solutions using this approach are sensitive to these values.68,69 Therefore, we used the “MultiStart” solver from the Matlab Global Optimization Toolbox (R2017a; The MathWorks) to generate 1000 random initial guesses of Fm within estimate bounds. Once an optimal solution was found for the first frame of data, following iterations used the preceding solution as the initial guess.64 Activation and contraction dynamics7072 were not incorporated into this iteration of the model.

Verification

Estimates of tibial compression from the MSK model were compared with in vivo data from the fourth Grand Knee Challenge data set as means of component validation.34 These data were collected from an older male participant (height 1.68 m and mass 66.7 kg) who had undergone a total hip and knee arthroplasty and whose knee contained an instrumented tibial plateau. Given that there are no verification data available in high knee flexion ranges, this verification step was performed to assess inverse dynamic and optimization face validity. Vertex-based object files of participant bones and computer aided design (CAD) files of the implant were publicly available.34 Manually selected landmarks were used to scale MSK origin and insertion points from the Horsman et al data set using the procedures described earlier. Time-synchronized data were provided for marker trajectories, tibial compression forces (eKnee), and ground reaction force. Kinematic variables were calculated identically to previously defined methods,37,39 except for the foot segment as the participant was shod. This resulted in the same points for the long axis of the foot (heel and toe), but a “lateral mid-foot” marker was used in place of the distal head of the fifth metatarsal. Anatomical landmarks were extracted from a static pose trial with functional joint centers determined (flexion–extension trial for the knee and star arc pattern for the hip) using the Symmetrical Centre of Rotation Estimation method.45,46

External kinetics were calculated and used as inputs to the static optimization procedure to estimate tibial compression in 2-legged squatting and walking. eKnee data were converted to a single compression force using validated regression equations for this implant.73 Model performance was assessed by RMSD and coefficient of determination (R2) between MSK compression estimates and eKnee data as these were typical outcome measures used to evaluate Grand Knee Challenge models.34

Statistical Analysis

All statistical procedures were performed using SPSS (version 20.0; IBM Corp Released 2011. IBM SPSS Statistics for Windows, Armonk, NY). To test the hypothesis that the inclusion of intersegmental contact would significantly decrease tibial contact forces, three 6 × 2 two-way repeated-measures analysis of variance—with fixed effects of movement and intersegmental contact (none/included) and a random effect of participant—were used across mean tibial compression, anterior–posterior, and medial–lateral shear values from the static phase of high knee flexion movements. The α level for all comparisons was preset at .05 with Bonferroni adjustments to account for multiple comparisons and simple main effect analysis performed on significant interaction terms.

Results

Verification of tibial compression estimates from this model against the gold standard implant data had a strong correlation (R2 of .83) with an RMSD of .47 BW across 5 normal walking trials (Figure 5). During repeated bodyweight squatting trials (to ∼110° of knee flexion) using a specific tension of 30 N/cm2, this model had a similarly strong correlation (R2 of .93) with an RMSD of .16 BW (Figure 6).

Figure 5
Figure 5

—Compression estimations compared with instrumented tibia measurements from 5 walking trials from Fregley et al. Mean values are dotted lines with ± 1 SD highlighted by colored bands. BW indicates body weight; RMS, root mean square. The reader is referred to the online version of this paper for the color representation of this figure.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

Figure 6
Figure 6

—Compression estimations using varying specific muscle tension values of 30, 61, or 88 N/cm2 from Carbone et al, Arnold et al, Delp et al, and Dickerson et al, respectively. Instrumented tibia measurements (eKnee) were reported from cyclic ∼95° knee flexion movements from Fregley et al. BW indicates body weight; RMS, root mean square. The reader is referred to the online version of this paper for the color representation of this figure.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

Incorporating intersegmental contact significantly reduced anterior–posterior and medial–lateral shear when compared with ignoring this external force (Table 2). An example tibial contact force waveform is presented for heels-up squat (Figure 7), with remaining movements provided in Appendix B. A summary of intersegmental contact values during the static phase of high knee flexion movements is provided in Table 3. Tibial compression had a main effect of movement (P = .001) with post hoc tests indicating a 2.01 BW lower compression during the flatfoot squat movement when compared with plantarflexed unilateral kneel (P = .008), but no other significant differences were found in axial forces. Tibial anterior–posterior shear had an interaction effect between movement and intersegmental contact (P < .001). Simple main effects revealed that with intersegmental contact, there were decreases in posterior shear of 0.25 BW in heels-up squat (P = .017), 0.21 BW in plantarflexed kneel (P = .024), 0.42 BW in dorsiflexed unilateral kneel (P = .008), and 0.42 BW in plantarflexed unilateral kneel (P < .001). Finally, tibial medial–lateral shear also had an interaction effect between movement and intersegmental contact (P < .001). Simple main effects revealed increases in lateral shear of 0.05 BW in dorsiflexed kneel (P = .39) and 0.08 BW in dorsiflexed unilateral kneel (P = .014) with intersegmental contact.

Table 2

Mean Tibial Contact Forces—in Body Weight—During the Static Phase of High Knee Flexion Movements

MovementCOMPaAPML
NOTCNOTCNOTC
Heels-up squat3.23 (1.49)2.96 (1.52)−0.27 (0.13)0.02 (0.29)0.05 (0.08)0.06 (0.07)
Flatfoot squat1.98 (1.48)1.99 (1.43)−0.09 (0.24)0.00 (0.22)0.03 (0.06)0.03 (0.04)
Dorsiflexed kneel4.50 (2.25)4.38 (2.32)−0.26 (0.31)−0.05 (0.28)0.07 (0.08)0.12 (0.07)
Plantarflexed kneel3.25 (2.14)3.26 (2.16)−0.28 (0.20)0.07 (0.31)0.10 (0.07)0.13 (0.05)
Dorsiflexed unilateral kneel4.13 (2.09)4.18 (1.92)−0.48 (0.22)−0.06 (0.30)0.01 (0.14)0.10 (0.09)
Plantarflexed unilateral kneel4.02 (2.03)3.97 (2.00)−0.47 (0.20)−0.05 (0.41)0.07 (0.10)0.09 (0.07)

Abbreviations: AP, anterior (+)/posterior (−) shear; COMP, tibial compression (+); ML, medial (−)/lateral (+) shear. Note: Brackets indicate 1 SD. Calculations that did not include intersegmental contact (NO) and those that did (TC).

aA main effect of movement with bold pairs indicating interaction effects of movement and intersegmental contact identified at a movement level by simple main effects.

Figure 7
Figure 7

—Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during an HS. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; HS, heels-up squat; ML, medial/lateral; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

Table 3

Mean (SD) Values of Intersegmental Contact Parameters During High Knee Flexion Movements

MovementOnset, degMaximum angle, degForce, NForce, %BWArea, cm2CoF, mm
Heels-up squat119.8 (14.2)155.7 (5.6)146.5 (116.3)27.2 (14.5)105.7 (31.4)62 (6)
Flatfoot squat116.6 (14.3)150.0 (6.6)195.9 (121.3)24.7 (14.8)118.7 (21.4)64 (3)
Dorsiflexed kneel126.5 (6.4)140.1 (13.9)211.4 (131.0)26.7 (17.4)115.9 (37.5)62 (7)
Plantarflexed kneel119.7 (8.7)142.7 (17.9)219.9 (93.2)26.8 (12.9)123.6 (18.3)68 (7)
Dorsiflexed unilateral kneel120.7 (7.8)151.7 (6.7)376.4 (264.9)47.4 (35.0)136.6 (48.6)62 (7)
Plantarflexed unilateral kneel119.4 (5.3)154.4 (6.3)384.0 (260.4)47.3 (33.2)127.5 (47.9)70 (9)

Note: Onset is the knee flexion angle when thigh–calf contact begins, maximum angle is the peak knee flexion angle achieved during the static phase, force is the normal force magnitude with respect to the measured intersegmental contact plane, area is the measured contact area, and CoF is the center of force location distal from the functional knee joint center about the long axis of the tibia.

Discussion

In this study, we present an MSK model of the pelvis and right lower limb that incorporates intersegmental contact variables. We validated the model by quantifying prediction error of tibial compression, to the maximal knee flexion angle data that are available, against a gold standard. The objective of using this model was to estimate 3D tibial contact forces during high knee flexion movements to determine the effect of including intersegmental contact forces in the estimation. We hypothesized that the inclusion of intersegmental contact would significantly decrease tibial contact forces when compared with estimates derived using the model with intersegmental contact omitted. Tibial compression estimates strongly fit implant data during walking (R2 = .83) and squatting (R2 = .93) with an RMSD of .47 and .16 BW, respectively. When incorporating intersegmental contact as an external force, significant reductions in posterior shear were observed in 4 movements with small increases in tibial lateral shear in dorsiflexed movements.

Limitations of this study include no verification data above ∼120° of knee flexion, soft tissue artifact, the exclusion of knee capsular ligaments, assumptions of intersegmental contact parameters, and no estimation of knee joint contact area. There are no in vivo tibial contact data currently available above ∼120° due to mechanical constraints of instrumented artificial knee designs.73 Soft tissue deformation of the thigh segment during high knee flexion postures introduces additional uncertainty in kinematic measurements. There are no data currently available to quantify error of surface markers compared with skeletal structures in high knee flexion movements, but fulsome efforts have been made in lower knee flexion angles.74 Although external force and moment calculations—which are inputs to the MSK model—would be affected by this error, it would be consistent between our 2 conditions. This model excluded knee capsule ligaments; however, prior in vitro work suggests low force contributions of the anterior cruciate ligament (<40 N), posterior cruciate ligament (<20 N), medial collateral ligament (<10 N), and lateral collateral ligament (<5 N) above 90° of knee flexion.75 Intersegmental contact pressure distributions used in this study were measured against a polycarbonate sheet and modeled as a function of knee flexion angle. This assumes an approximately constant external force during the static phase of movements and “mirrored” loading during the ascending phase as only the descent phase was measured. Finally, the current model does not have the capability to estimate contact area between femoral condyles and the tibial plateau. This does not allow us to comment on stress of knee joint tissues and is a required future improvement for clinical applications of this model.

The model’s tibial contact force estimates were within reported instrumented implant values for a variety of low- to mid-range knee flexion activities.35,73,7678 For example, the model’s estimations of peak tibial contact forces were slightly above magnitudes observed during stair ambulation76 and 1 to 2 BW higher than peak loading when standing from a chair at a knee flexion angle of ∼80°.35 The only known study that estimated tibial contact forces in high knee flexion—and modeled thigh–calf contact—predicted peak decreases of 1.99 BW in compression and 0.54 BW in posterior shear.3 Our maximum mean RMSD compressive force reduction was considerably smaller (.27 BW), but we reported similar changes in posterior shear with a maximum mean RMSD of .30 BW. This disagreement with previous outcomes is a likely result of our intersegmental force and contact area magnitudes being lower than previous reports15,19 as our sensor was of higher resolution.1

Tibial contact force estimates including intersegmental contact from this model appear to be more biologically feasible than prior 2D reports. Our peak tibial compression and shear estimates are almost half4,12 or 1 to 3 BW12,79,80 lower than sagitttal plane high knee flexion models that did not account for intersegmental contact. Assuming joint contact areas measured in prostheses,73,81 the peak compressive and shear force magnitudes reported by Nagura et al were in excess of the 21 MPa tensile yield stress of both ultrahigh molecular weight polyethylene5 and the 15 to 20 MPa range known to damage cartilage and kill chondrocytes.6 A volumetric contact model was outside the scope of this study, but our peak tibial compression and anterior–posterior shear estimates were comparable with Zelle et al, which included an intersegmental contact parameter and mid-range (up to ∼120° of knee flexion) implant data.34,35

Prior work has highlighted the need for accurate tibial compressive and shear force magnitudes to improve tissue engineering of knee joint structures9,10 and robustness to prosthetic loosening.11,12 Further verification of our reported magnitudes is needed as, unlike some biological tissues, overly conservative estimation of tissue loading is as detrimental as overestimation in terms of predicting effects on menisci and cartilage growth.7,8 Findings from this study are a substantial first step toward improving our understanding of the tibial loading environment during high knee flexion exposures. In some instances, the inclusion of thigh–calf contact significantly reduced posterior shear in this study. As individuals can regularly perform high knee flexion activities with negligible acute tissue damage, we feel the inclusion of intersegmental contact is necessary for cumulative tissue and joint contact models of the knee.

Including 3D intersegmental contact forces when estimating tibial contact forces using a high knee flexion model resulted in a significant decrease in posterior shear and increase in lateral shear in select movements. Tibial posterior shear had peak forces of approximately 0.5 BW when thigh–calf contact was neglected but was reduced by a peak mean RMSD of .43 BW in unilateral kneeling movements by including thigh–calf contact. Although tibial lateral shear was significantly increased in dorsiflexed kneeling movements, the biological effect of a 0.08 BW change is presumed to be negligible. There were no significant differences in tibial compression as a result of including intersegmental contact. These results suggest that intersegmental contact could significantly reduce the exposure of knee tissues to anterior–posterior shear stress; however, estimates of tibiofemoral contact area would be required to confirm this possibility.

Acknowledgments

The authors would like to acknowledge Shabnam Pejhan and Jeffery Barrett for their guidance on optimization implementation and many thoughtful discussions on modeling assumptions and limitations. This work was funded by NSERC Discovery Grant #418647. The authors have no conflicts of interest to disclose.

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—Lower Limb Segmental Local Coordinate System Definitions
Pelvis
 OriginMidpoint between the left and right anterior superior iliac spines
z-axisVector from the origin toward the right ASIS
y-axisCross product of temporary vector from the origin to the midpoint of left and right PSIS and z-axis
x-axisCross product of y-axis and z-axis
Thigh
 OriginFunctional knee joint center33
z-axisCross product of the x-axis by y-axis
y-axisVector from origin to functional hip joint center34
x-axisCross product of the y-axis and a temporary vector from the origin to the lateral greater trochanter
Shank
 OriginMidpoint of malleoli
z-axisCross product of x-axis by y-axis
y-axisVector from the midpoint between the malleoli to the functional knee joint center
x-axisCross product of the y-axis and a temporary vector pointing from the origin to lateral malleoli
Foot
 OriginHeel
z-axisCross product of x-axis by y-axis
y-axisVector from the origin to the toe
x-axisCross product of the y-axis and temporary vector pointing from the origin to the midpoint of the malleoli
—Time Series Estimates of Tibial Contact Force Magnitudes With and Without Intersegmental Contact

Figure A1
Figure A1

—Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during an FS. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; FS, flatfoot squat; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

Figure A2
Figure A2

—Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during a DK. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; DK, dorsiflexed kneel; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

Figure A3
Figure A3

—Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during a PK. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; PK, plantarflexed kneel; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

Figure A4
Figure A4

—Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during a DUK. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; DUK, dorsiflexed unilateral kneel; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

Figure A5
Figure A5

—Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during a PUK. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; PUK, plantarflexed unilateral kneel; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

Citation: Journal of Applied Biomechanics 36, 6; 10.1123/jab.2019-0335

If the inline PDF is not rendering correctly, you can download the PDF file here.

Kingston is with the Canadian Centre for Health and Safety in Agriculture, University of Saskatchewan, Saskatoon, SK, Canada. Kingston and Acker are with the Department of Kinesiology, University of Waterloo, Waterloo, ON, Canada.

Acker (stacey.acker@uwaterloo.ca) is corresponding author.
  • View in gallery

    —High knee flexion postures performed for the application of this model. Details regarding the processing of these data are reported in the study of Kingston and Acker.1 DK indicates dorsiflexed kneel; DUK, dorsiflexed unilateral kneel; FS, flatfoot squat; HS, heels-up squat; PK, plantarflexed kneel; PUK, plantarflexed unilateral kneel.

  • View in gallery

    —Anatomical geometry of musculoskeletal model. Black spheres are manually selected landmarks matching those from Horsman et al. Blue lines indicate muscle paths. Green spheres within a muscle path are scaled VIA points. Red lines are knee joint ligaments (not used in this iteration). The reader is referred to the online version of this paper for the color representation of this figure.

  • View in gallery

    —Determination of wrapping surface size and path of common knee extensor musculature. (A) Blue points represent vertices of the medial and lateral femoral condyles and femoral groove (perpendicular to the condylar axis). (B) Anterior view of wrapping sphere (cyan) with curved path (green points) connecting to the proximal patella (red point), distal patella (black point), and tibial tuberosity (magenta point). (C) Anterior–sagittal view. The reader is referred to the online version of this paper for the color representation of this figure.

  • View in gallery

    —Measurement of intersegmental force during a plantarflexed high knee flexion movement. The blue polygon represents the polycarbonate sheet tracked during motion trials, with magenta spheres depicting center of force locations. The measured values from the heel center of force were assumed to be in the plane of the polycarbonate sheet for participants who had heel–gluteal contact. Black arrows represent the total normal forces at each location, which were then applied to the tibia in the model. The reader is referred to the online version of this paper for the color representation of this figure.

  • View in gallery

    —Compression estimations compared with instrumented tibia measurements from 5 walking trials from Fregley et al. Mean values are dotted lines with ± 1 SD highlighted by colored bands. BW indicates body weight; RMS, root mean square. The reader is referred to the online version of this paper for the color representation of this figure.

  • View in gallery

    —Compression estimations using varying specific muscle tension values of 30, 61, or 88 N/cm2 from Carbone et al, Arnold et al, Delp et al, and Dickerson et al, respectively. Instrumented tibia measurements (eKnee) were reported from cyclic ∼95° knee flexion movements from Fregley et al. BW indicates body weight; RMS, root mean square. The reader is referred to the online version of this paper for the color representation of this figure.

  • View in gallery

    —Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during an HS. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; HS, heels-up squat; ML, medial/lateral; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

  • View in gallery

    —Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during an FS. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; FS, flatfoot squat; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

  • View in gallery

    —Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during a DK. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; DK, dorsiflexed kneel; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

  • View in gallery

    —Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during a PK. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; PK, plantarflexed kneel; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

  • View in gallery

    —Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during a DUK. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; DUK, dorsiflexed unilateral kneel; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

  • View in gallery

    —Mean model estimates of TC (+), anterior (+)/posterior (−) shear, and medial (−)/lateral (+) shear forces during a PUK. Shaded regions represent ±1 SD. AP indicates anterior; BW, body weight; PUK, plantarflexed unilateral kneel; TC, tibial compression. The reader is referred to the online version of this paper for the color representation of this figure.

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