A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construct

A three-dimensional model of the knee is developed to study the interactions between the muscles, ligaments, and bones during activity. The geometry of the distal femur, proximal tibia, and patella is based on cadaver data reported for an average-size knee. The shapes of the femoral condyles are represented by high-order polynomials; the tibial plateaux and patellar facets are approximated as flat surfaces. The contacting surfaces of the femur and tibia are modeled as deformable, while those of the femur and patella are assumed to be rigid. Interpenetration of the femur and tibia is taken into account by modeling cartilage as a thin, linear, elastic layer, mounted on rigid bone. Twelve elastic elements describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit modeled as a three-element muscle in series with tendon. The path of each muscle is approximated as a straight line, except where it contacts and wraps around bone and other muscles; changes in muscle paths are taken into account using data obtained from MRI. In the first part of this paper, the model is used to simulate passive knee flexion. Quantitative comparisons of the model results with experimental data reported in the literature indicate that the relative movements of the bones and the geometry of the ligaments and muscles in the model are similar to those evident in the real knee. In Part II, the model is used to describe knee-ligament function during anterior-posterior draw, axial rotation, and isometric knee-extension and knee-flexion exercises.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construction

A three-dimensional model of the knee is developed to study the interactions between the muscles, ligaments, and bones during activity. The geometry of the distal femur, proximal tibia, and patella is based on cadaver data reported for an average-size knee. The shapes of the femoral condyles are represented by high-order polynomials: the tibial plateaux and patellar facets are approximated as flat surfaces. The contacting surfaces of the femur and tibia are modeled as deformable, while those of the femur and patella are assumed to be rigid. Interpenetration of the femur and tibia is taken into account by modeling cartilage as a thin, linear, elastic layer, mounted on rigid bone. Twelve elastic elements describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit modeled as a three-element muscle in series with tendon. The path of each muscle is approximated as a straight line, except where it contacts and wraps around bone and other muscles; changes in muscle paths are taken into account using data obtained from MRI. In the first part of this paper, the model is used to simulate passive knee flexion. Quantitative comparisons of the model results with experimental data reported in the literature indicate that the relative movements of the bones and the geometry of the ligaments and muscles in the model are similar to those evident in the real knee. In Part II, the model is used to describe knee-ligament function during anterior-posterior draw, axial rotation, and isometric knee-extension and knee-flexion exercises.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 2: Analysis of Ligament Function

A three-dimensional model of the knee is used to study ligament function during anterior-posterior (a-p) draw, axial rotation, and isometric contractions of the extensor and flexor muscles. The geometry of the model bones is based on cadaver data. The contacting surfaces of the femur and tibia are modeled as deformable; those of the femur and patella are assumed to be rigid. Twelve elastic elements are used to describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit represented as a three-element muscle in series with tendon. The calculations show that the forces applied during a-p draw are substantially different from those applied by the muscles during activity. Principles of knee-ligament function based on the results of in vitro experiments may therefore be overstated. Knee-ligament forces during straight a-p draw are determined solely by the changing geometry of the ligaments relative to the bones: ACL force decreases with increasing flexion during anterior draw because the angle between the ACL and the tibial plateau decreases as knee flexion increases; PCL force increases with increasing flexion during posterior draw because the angle between the PCL and the tibial plateau increases. The pattern of ligament loading during activity is governed by the geometry of the muscles spanning the knee: the resultant force in the ACL during isometric knee extension is determined mainly by the changing orientation of the patellar tendon relative to the tibia in the sagittal plane; the resultant force in the PCL during isometric knee flexion is dominated by the angle at which the hamstrings meet the tibia in the sagittal plane.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 2: Analysis of Ligament Function

A three-dimensional model of the knee is used to study ligament function during anterior-posterior (a-p) draw, axial rotation, and isometric contractions of the extensor and flexor muscles. The geometry of the model bones is based on cadaver data. The contacting surfaces of the femur and tibia are modeled as deformable; those of the femur and patella are assumed to be rigid. Twelve elastic elements are used to describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit represented as a three-element muscle in series with tendon. The calculations show that the forces applied during a-p draw are substantially different from those applied by the muscles during activity. Principles of knee-ligament function based on the results of in vitro experiments may therefore be overstated. Knee-ligament forces during straight a-p draw are determined solely by the changing geometry of the ligaments relative to the bones: ACL force decreases with increasing flexion during anterior draw because the angle between the ACL and the tibial plateau decreases as knee flexion increases; PCL force increases with increasing flexion during posterior draw because the angle between the PCL and the tibial plateau increases. The pattern of ligament loading during activity is governed by the geometry of the muscles spanning the knee: the resultant force in the ACL during isometric knee extension is determined mainly by the changing orientation of the patellar tendon relative to the tibia in the sagittal plane; the resultant force in the PCL during isometric knee flexion is dominated by the angle at which the hamstrings meet the tibia in the sagittal plane.     

The orientation of the distal part of the quadriceps femoris muscle as a function of the knee flexion-extension angle

Lateral view radiographs of ten autopsy knees were used to determine the orientation of the patellar ligament, patella and quadriceps tendon relative to tibia and femur at different flexion-extension angles (0-120 degrees) of the knee. The results show a linear relationship between the angle of flexion and the movement of the patellar ligament relative to the tibia and of the movement of the patella relative to tibia and femur. There is a non-linear relationship between angle of flexion and the movement of the quadriceps tendon relative to the patellar ligament, patella and femur. The angular changes between patella and patellar ligament are negligible. The complicated movements of the distal part of the quadriceps femoris muscle may significantly influence biomechanical parameters such as the forces acting at the patella and tibial tuberosity.     

The coupled motion of the femur and patella during in vivo weightbearing knee flexion

The movement of the knee joint consists of a coupled motion between the tibiofemoral and patellofemoral articulations. This study measured the six degrees-of-freedom kinematics of the tibia, femur, and patella using dual-orthogonal fluoroscopy and magnetic resonance imaging. Ten normal knees from ten living subjects were investigated during weightbearing flexion from full extension to maximum flexion. The femoral and the patellar motions were measured relative to the tibia. The femur externally rotated by 12.9 deg and the patella tilted laterally by 16.3 deg during the full range of knee flexion. Knee flexion was strongly correlated with patellar flexion (R(2)=0.91), posterior femoral translation was strongly correlated to the posterior patellar translation (R(2)=0.87), and internal-external rotation of the femur was correlated to patellar tilt (R(2)=0.73) and medial-lateral patellar translation (R(2)=0.63). These data quantitatively indicate a kinematic coupling between the tibia, femur, and patella, and provide base line information on normal knee joint kinematics throughout the full range of weightbearing flexion. The data also suggest that the kinematic coupling of tibia, femur, and patella should be considered when investigating patellar pathologies and when developing surgical techniques to treat knee joint diseases.     

Pattern of anterior cruciate ligament force in normal walking

The goal of this study was to calculate and explain the pattern of anterior cruciate ligament (ACL) loading during normal level walking. Knee-ligament forces were obtained by a two-step procedure. First, a three-dimensional (3D) model of the whole body was used together with dynamic optimization theory to calculate body-segmental motions, ground reaction forces, and leg-muscle forces for one cycle of gait. Joint angles, ground reaction forces, and muscle forces obtained from the gait simulation were then input into a musculoskeletal model of the lower limb that incorporated a 3D model of the knee. The relative positions of the femur, tibia, and patella and the forces induced in the knee ligaments were found by solving a static equilibrium problem at each instant during the simulated gait cycle. The model simulation predicted that the ACL bears load throughout stance. Peak force in the ACL (303 N) occurred at the beginning of single-leg stance (i.e., contralateral toe off). The pattern of ACL force was explained by the shear forces acting at the knee. The balance of muscle forces, ground reaction forces, and joint contact forces applied to the leg determined the magnitude and direction of the total shear force acting at the knee. The ACL was loaded whenever the total shear force pointed anteriorly. In early stance, the anterior shear force from the patellar tendon dominated the total shear force applied to the leg, and so maximum force was transmitted to the ACL at this time. ACL force was small in late stance because the anterior shear forces supplied by the patellar tendon, gastrocnemius, and tibiofemoral contact were nearly balanced by the posterior component of the ground reaction.     

Disproportional skeletal growth and markedly decreased bone mineral content in growth hormone receptor -/- mice

Growth hormone (GH) is important for skeletal growth as well as for a normal bone metabolism in adults. The skeletal growth and adult bone metabolism was studied in mice with an inactivated growth hormone receptor (GHR) gene. The lengths of femur, tibia, and crown-rump were, as expected, decreased in GHR-/- mice. Unexpectedly, GHR-/- mice displayed disproportional skeletal growth reflected by decreased femur/crown-rump and femur/tibia ratios. GHR-/- mice demonstrated decreased width of the growth plates in the long bones and disturbed ossification of the proximal tibial epiphysis. Furthermore, the area bone mineral density (BMD) as well as the bone mineral content (BMC)/body weight were markedly decreased in GHR-/- mice. The decrease in BMC in GHR-/- mice was not due to decreased trabecular volumetric BMD but to a decreased cross-sectional cortical bone area In conclusion, GHR-/- mice demonstrate disproportional skeletal growth and markedly decreased bone mineral content.     

A dynamic model of the knee and lower limb for simulating rising movements

A two-dimensional dynamical model of the human body was developed and used to simulate muscle and knee-ligament loading during a fast rising movement. The hip, ankle, and toes were each modeled as a simple hinge joint. Relative movements of the femur, tibia, and patella in the sagittal plane were described using a more detailed representation of the knee. The geometry of the model bones was adapted from cadaver data. Eleven elastic elements described the geometric and mechanical properties of the knee ligaments and joint capsule. The patella was assumed to be massless. Smooth hypersurfaces were constructed and used to calculate the position and orientation of the patella during a forward integration of the model. Each hypersurface was formed by applying the principle of static equilibrium to approximate patellofemoral mechanics during the simulation. The model was actuated by 22 musculotendinous units, each unit represented as a three-element muscle in series with tendon. A first-order process was assumed to model muscle excitation-contraction dynamics. Dynamic optimization theory was used to calculate the pattern of muscle excitations that produces a coordinated rising movement from an initial squatting position in minimum time. The calculations support the contention that squatting is a relatively safe exercise for rehabilitation following ACL reconstruction. ACL forces remain less than 20 N for the duration of the task.     

The effect of design variables of condylar total knees on the joint forces in step climbing based on a computer model.

The ability to climb a steep step or rise from a low chair after total knee replacement may be enhanced if the required force in the quadriceps muscle is reduced. This can potentially be achieved if the total knee produces a large lever arm measured from the femoral-tibial contact point to the patellar ligament. A reduced quadriceps force would also reduce the patello-femoral force and the femoral-tibial contact force. The contact point location is likely to be a function of the geometry of the femoral and tibial components in the sagittal plane, including the relative distal and posterior radii of the femoral profile, the location of the bottom-of-the-dish of the tibial surface, the radius of the tibial surface, and the presence or absence of the posterior cruciate ligament. A three-dimensional model of the knee was developed including the quadriceps and various ligaments. In the study, the motion was confined to flexion extension and displacement in the sagittal plane. The quadriceps was assumed to be the only muscle acting. A standard software package (Pro/Mechanica) was used for the analysis. For a femoral component with a smaller distal radius, there was 12% reduction in the quadriceps muscle force and up to 11% reduction in the patello-femoral force from about 100 up to 60 degrees flexion. However, apart from that, there were less than 10% differences in all the forces as a function of all of the design variables studied. This was attributed to the relatively small changes in the lever arm of the patella tendon, since the tendon moves in an anterior-posterior direction along with the femur. An additional factor explaining the results was the change in the anterior-posterior contact point as controlled by the forces in the patella tendon and in the soft tissues. The results imply that for a standard condylar replacement knee, the muscle and contact forces are not greatly affected by the geometrical design variables.     

Influence of patella alta on knee extensor mechanics

The purpose of this study was to compare the knee extensor mechanics in persons with and without patella alta. Thirteen subjects with patella alta and 14 subjects with normal patellar position participated in the study. Sagittal and axial MR images of the knee were acquired at 0°, 20°, 40°, and 60° of knee flexion. Measurements of actual moment arm, patellar ligament/quadriceps tendon force ratio, quadriceps effective moment arm, and joint reaction force/quadriceps force ratio were obtained. There were no differences between groups in terms of actual moment arm. However, subjects with patella alta had significantly larger patellar ligament/quadriceps tendon force ratios (1.04±0.02 vs. 0.92±0.02) and quadriceps effective moment arms (4.40±0.09 vs. 4.00±0.09 cm) when averaged across the range of knee flexion angles tested. There was no difference in the joint reaction force/quadriceps force ratio between groups. The observed differences in knee extensor mechanics suggest that individuals with patella alta have a more efficient knee extensor mechanism and would be expected to generate similar joint reaction forces per unit quadriceps force compared to subjects with normal patellar position. Therefore, persons with patella alta may experience less patellofemoral joint reaction force to overcome the same knee flexion moment in the range of 0°–60° of knee flexion.     

Relative movements between the tibia and femur induced by external plantar shocks are controlled by muscle forces in vivo

The purpose of this study was to investigate the role of muscle activation on the relative motion between tibia and femur. Impacts were initiated under the heels of four volunteers in three different activation levels of muscles crossing the extended knee joint: 0%, 30% and 60% of previously performed maximal voluntary isometric contractions. Impact forces were measured and tibial and femoral accelerations and displacements were determined by means of accelerometry. The accelerometers were mounted on the protruding ends of intracortical pins, inserted into the distal aspect of the femur and proximal aspect of the tibia. Under the 0%-condition the impact force (475±64N) led to 2.3±1.2mm knee compression and to 2.4±1.9mm medio-lateral and 4.4±1.1mm antero-posterior shear. The impact forces increased significantly with higher activation levels (619±33N (30%), 643±147N (60%)), while the knee compression (1.5±1.2, 1.4±1.3mm) and both medio-lateral shear (1.8±1.4, 1.5±1.1mm) and antero-posterior shear (2.6±1.3, 1.5±1.1mm) were significantly reduced. This study indicated that muscles are effective in controlling the relative motion between tibia and femur when the knee is subjected to external forces.     

Gravitational force modulates muscle activity during mechanical oscillation of the tibia in humans

Mechanical oscillation (vibration) is an osteogenic stimulus for bone in animal models and may hold promise as an anti-osteoporosis measure in humans with spinal cord injury (SCI). However, the level of reflex induced muscle contractions associated with various loads (g force) during limb segment oscillation is uncertain. The purpose of this study was to determine whether certain gravitational loads (g forces) at a fixed oscillation frequency (30 Hz) increases muscle reflex activity in individuals with and without SCI. Nine healthy subjects and two individuals with SCI sat with their hip and knee joints at 90° and the foot secured on an oscillation platform. Vertical mechanical oscillations were introduced at 0.3, 0.6, 1.2, 3 and 5g force for 20 s at 30 Hz. Non-SCI subjects received the oscillation with and without a 5% MVC background contraction. Peak soleus and tibialis anterior (TA) EMG were normalized to M-max. Soleus and TA EMG were <2.5% of M-max in both SCI and non-SCI subjects. The greatest EMG occurred at the highest acceleration (5g). Low magnitude mechanical oscillation, shown to enhance bone anabolism in animal models, did not elicit high levels of reflex muscle activity in individuals with and without SCI. These findings support the g force modulated background muscle activity during fixed frequency vibration. The magnitude of muscle activity was low and likely does not influence the load during fixed frequency oscillation of the tibia.     

A three-dimensional anatomical model of the human patello-femoral joint,for the determination of patello-femoral motions and contact characteristics

The object of this study is to develop a three-dimensional mathematical model of the patello-femoral joint, which is modelled as two rigid bodies representing a moving patella and a fixed femur. Two-point contact was assumed between the femur and patella at the medial and lateral sides and in the analysis, the femoral and patellar articular surfaces were mathematically represented using Coons' bicubic surface patches. Model equations include six equilibrium equations and eleven constraints: six contact conditions, four geometric compatibility conditions, and the condition of a rigid patellar ligament; the model required the solution of a system of 17 nonlinear equations in 17 unknowns, its response describing the six-degress-of-freedom patellar motions and the forces acting on the patella. Patellar motions are described by six motion parameters representing the translations and rotations of the patella with respect to the femur. The forces acting on the patella include the medial and lateral component of patello-femoral contact and the patellar ligament force, all of which were represented as ratios to the quadriceps tendon force. The model response also includes the locations of the medial and lateral contact points on the femur and the patella. A graphical display of its response was produced in order to visualize better the motion of the components of the extensor mechanism.Model calculations show good agreement with experimental results available from the literature. The patella was found to move distally and posteriorly on the femoral condyles as the knee was flexed from full extension. Results indicate that the relative orientation of the patellar ligament with respect to the patella remains unchanged during this motion. The model also predicts a patellar flexion which always lagged knee flexion.Our calculations show that as the angle of knee flexion increased, the lateral contact point moved distally on the femur without moving significantly either medially or laterally. The medial contact point also moved distally on the femur but moved medially from full extension to about 40° of knee flexion, then laterally as the knee flexion angle increased. The lateral contact point on the patella did not change significantly in the medial and lateral direction as the knee was flexed; however, this point moved proximally toward the basis of the patella with knee flexion. The medial contact point also moved proximally on the patella with knee flexion, and in a similar manner the medial contact point on the patella moved distally with flexion from full extension to about 40° of flexion. However, as the angle of flexion increased, the medial contact point did not move significantly in the medial-lateral direction.Model calculations also show that during the simulated knee extension exercise, the ratio of the force in the patellar ligament to the force in the quadriceps tendon remains almost unchanged for the first 30° of knee flexion, then decreases as the angle of knee flexion increases. Furthermore, model results show that the lateral component of the patello-femoral contact force is always greater than the medial component, both components increasing with knee flexion.     

Simultaneous prediction of muscle and contact forces in the knee during gait

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process.     

Doublet stimulation protocol to minimize musculoskeletal stress during paralyzed quadriceps muscle testing.

With long-term electrical stimulation training, paralyzed muscle can serve as an effective load delivery agent for the skeletal system. Muscle adaptations to training, however, will almost certainly outstrip bone adaptations, exposing participants in training protocols to an elevated risk for fracture. Assessing the physiological properties of the chronically paralyzed quadriceps may transmit unacceptably high shear forces to the osteoporotic distal femur. We devised a two-pulse doublet strategy to measure quadriceps physiological properties while minimizing the peak muscle force. The purposes of the study were 1) to determine the repeatability of the doublet stimulation protocol, and 2) to compare this protocol among individuals with and without spinal cord injury (SCI). Eight individuals with SCI and four individuals without SCI underwent testing. The doublet force-frequency relationship shifted to the left after SCI, likely reflecting enhancements in the twitch-to-tetanus ratio known to exist in paralyzed muscle. Posttetanic potentiation occurred to a greater degree in subjects with SCI (20%) than in non-SCI subjects (7%). Potentiation of contractile rate occurred in both subject groups (14% and 23% for SCI and non-SCI, respectively). Normalized contractile speed (rate of force rise, rate of force fall) reflected well-known adaptations of paralyzed muscle toward a fast fatigable muscle. The doublet stimulation strategy provided repeatable and sensitive measurements of muscle force and speed properties that revealed meaningful differences between subjects with and without SCI. Doublet stimulation may offer a unique way to test muscle physiological parameters of the quadriceps in subjects with uncertain musculoskeletal integrity.     

Bone Mass and Bone Quality Are Altered by Hypoactivity in the Chicken

Disuse induces a rapid bone loss in adults; sedentarity is now recognized as a risk factor for osteoporosis. Hypoactivity or confinement also decrease bone mass in adults but their effects are largely unknown and only few animal models have been described. We have used 10 chickens of the rapidly growing strain 857K bred in a large enclosure (FREE group); 10 others were confined in small cages with little space to move around (HYPO group). They were sacrificed at 53 days and femurs and tibias were evaluated by texture analysis, dual energy X-ray densitometry, microcomputed tomography (microCT) and histomorphometry. Hypoactivity had no effect on the length and diameter of the bones. Bone mineral density (BMD), microCT (trabecular bone volume and trabecular microarchitecture) and texture analysis were always found significantly reduced in the animals of the HYPO group. BMD was reduced at both femur and tibia diaphysises; BMD of the metaphysis was significantly reduced in the femur but not in the tibia. An increase in osteoid volume and surfaces was noted in the HYPO group. However, there was no alteration of the mineral phase as the osteoid thickness did not differ from control animals. Bone loss was much more pronounced at the lower femur metaphysis than at the upper metaphysis of the tibia. At the tibia, only microarchitectural changes of trabecular bone could be evidenced. The confined chicken represents a new method for the study of hypodynamia since these animals do not have surgical lesions.     

The physical and mechanical effects of suspension-induced osteopenia on mouse long bones.

The present investigation addresses the extent of tail-suspension effects on the long bones of mice. The effects are explored in both sexes, in both forelimb and hindlimb bones, and in both diaphyseal and metaphyseal/epiphyseal bones. Two weeks of suspension provided unloading of the femora and tibiae and an altered loading of the humeri. Whole-bone effects included lower mass (approximately 10%) and length (approximately 4%) in the bones of suspended mice compared to controls. The geometric and material properties of the femora were considered along the entire length of the diaphysis and in the metaphysis/epiphysis portions as a unit. Geometric effects included lower cross-sectional cortical area (16%), cortical thickness (25%) and moment of inertia (21%) in the femora of suspended mice; these differences were observed in both distal and proximal portions of the femur diaphysis. The relative amount of bone comprising the middle 8 mm of the diaphysis was greater (3%) in the control mice than in the suspended mice. Significant mass differences between the group in the metaphysis/epiphysis were not observed. Material effects included lower %ash (approximately 2%) in the femora and tibiae as well as in the humeri of suspended mice compared to controls. With respect to the measured physical and material properties, suspension produced similar bone responses in male and female mice. The effects of suspension are manifested largely through geometric rather than through material changes.     

Patella tendon moment arm function considerations for human vastus lateralis force estimates

In vivo muscle forces are typically estimated using literature-based or subject-specific moment arms (MAs) because it is not possible to measure in vivo muscle forces non-invasively. However, even subject-specific muscle-tendon MAs vary across contraction levels and are impossible to determine at high contraction levels without techniques that use ionized radiation. Therefore, different generic MA functions are often used to estimate in vivo muscle forces, which may alter force predictions and the shape of the muscle’s force-length relationship. The aim of this study was to examine the influence of different literature-based patella tendon MA functions on the vastus lateralis (VL) force-angle relationship. Participants (n = 11) performed maximum voluntary isometric knee extension contractions at six knee flexion angles, ranging from 40° to 90°. To estimate in vivo VL muscle force, the peak knee extension torque at each joint angle was multiplied by the VL’s physiological cross-sectional area (PCSA) relative to the quadriceps’ PCSA (34%) and then divided by the angle-specific patella tendon MA for 19 different functions. Maximum VL force was significantly different across MA functions (p ≤ 0.039) and occurred at different knee flexion angles. The shape of the VL force-angle relationship also differed significantly (p < 0.01) across MA functions. According to the maximum force generated by VL based on its literature-derived PSCA, only the VL force-angle relationships estimated using geometric imaging-based MA functions are feasible across the knee angles studied here. We therefore recommend that an average of these MA functions is calculated to estimate quadriceps muscle forces if subject-specific MAs cannot be determined.     

Orientation of tendons in vivo with active and passive knee muscles

Tendon orientations in knee models are often taken from cadaver studies. The aim of this study was to investigate the effect of muscle activation on tendon orientation in vivo. Magnetic resonance imaging (MRI) images of the knee were made during relaxation and isometric knee extensions and flexions with 0 degrees , 15 degrees and 30 degrees of knee joint flexion. For six tendons, the orientation angles in sagittal and frontal plane were calculated. In the sagittal plane, muscle activation pulled the patellar tendon to a more vertical orientation and the semitendinosus and sartorius tendons to a more posterior orientation. In the frontal plane, the semitendinosus had a less lateral orientation, the biceps femoris a more medial orientation and the patellar tendon less medial orientation in loaded compared to unloaded conditions. The knee joint angle also influenced the tendon orientations. In the sagittal plane, the patellar tendon had a more anterior orientation near full extension and the biceps femoris had an anterior orientation with 0 degrees and 15 degrees flexions and neutral with 30 degrees flexions. Within 0 degrees to 30 degrees of flexion, the biceps femoris cannot produce a posterior shear force and the anterior angle of the patellar tendon is always larger than the hamstring tendons. Therefore, co-contraction of the hamstring and quadriceps is unlikely to reduce anterior shear forces in knee angles up to 30 degrees . Finally, inter-individual variation in tendon angles was large. This suggests that the amount of shear force produced and the potential to counteract shear forces by co-contraction is subject-specific.