Forces acting on the patella during maximal voluntary contraction of the quadriceps femoris muscle at different knee flexion/extension angles

From knee extension moments measured with a dynamometer, the quadriceps muscle force, the patellar ligament force and the reaction force in the patellofemoral joint at various knee angles (0-90 degrees) were estimated. The information needed to calculate the combined effect of both patellofemoral and tibiofemoral joint on the mechanical advantage of the muscle was obtained from lateral-view radiographs of autopsy knees. The results show that the smallest quadriceps force (2,000 N) is exerted at maximal extension, and the largest force (8,000 N) at about 75 degrees of flexion. The patellar ligament force reaches a maximum (5,000 N) at 60 degrees. The reaction force in the patellofemoral joint is the smallest (1,000 N) at extension and is of the same values as the muscle force in a range from 75 to 90 degrees. Especially at large flexion angles, the value of the estimated forces is considerably larger (by 100%) than reported in the literature. This difference is attributed to the influence of the patellofemoral joint on the mechanical advantage of the muscle, which has not been taken into account in other studies.     

A planar model of the knee joint to characterize the knee extensor mechanism

A simple planar static model of the knee joint was developed to calculate effective moment arms for the quadriceps muscle. A pathway for the instantaneous center of rotation was chosen that gives realistic orientations of the femur relative to the tibia. Using the model, nonlinear force and moment equilibrium equations were solved at one degree increments for knee flexion angles from 0 (full extension) to 90 degrees, yielding patellar orientation, patellofemoral contact force and patellar ligament force and direction with respect to both the tibial insertion point and the tibiofemoral contact point. The computer-derived results from this two-dimensional model agree with results from more complex models developed previously from experimentally obtained data. Due to our model's simplicity, however, the operation of the patellar mechanism as a lever as well as a spacer is clearly illustrated. Specifically, the thickness of the patella was found to increase the effective moment arm significantly only at flexions below 35 degrees even though the actual moment arm exhibited an increase throughout the flexion range. Lengthening either the patella or the patellar ligament altered the force transmitted from the quadriceps to the patellar ligament, significantly increasing the effective moment arm at flexions greater than 25 degrees. We conclude that the levering action of the patella is an essential mechanism of knee joint operation at moderate to high flexion angles.     

Prediction of antagonistic muscle forces using inverse dynamic optimization during flexion/extension of the knee.

This paper examined the feasibility of using different optimization criteria in inverse dynamic optimization to predict antagonistic muscle forces and joint reaction forces during isokinetic flexion/extension and isometric extension exercises of the knee. Both quadriceps and hamstrings muscle groups were included in this study. The knee joint motion included flexion/extension, varus/valgus, and internal/external rotations. Four linear, nonlinear, and physiological optimization criteria were utilized in the optimization procedure. All optimization criteria adopted in this paper were shown to be able to predict antagonistic muscle contraction during flexion and extension of the knee. The predicted muscle forces were compared in temporal patterns with EMG activities (averaged data measured from five subjects). Joint reaction forces were predicted to be similar using all optimization criteria. In comparison with previous studies, these results suggested that the kinematic information involved in the inverse dynamic optimization plays an important role in prediction of the recruitment of antagonistic muscles rather than the selection of a particular optimization criterion. Therefore, it might be concluded that a properly formulated inverse dynamic optimization procedure should describe the knee joint rotation in three orthogonal planes.     

Anterior hip joint force increases with hip extension, decreased gluteal force, or decreased iliopsoas force

Abnormal or excessive force on the anterior hip joint may cause anterior hip pain, subtle hip instability and a tear of the acetabular labrum. We propose that both the pattern of muscle force and hip joint position can affect the magnitude of anterior joint force and thus possibly lead to excessive force and injury. The purpose of this study was to determine the effect of hip joint position and of weakness of the gluteal and iliopsoas muscles on anterior hip joint force. We used a musculoskeletal model to estimate hip joint forces during simulated prone hip extension and supine hip flexion under four different muscle force conditions and across a range of hip extension and flexion positions. Weakness of specified muscles was simulated by decreasing the modeled maximum force value for the gluteal muscles during hip extension and the iliopsoas muscle during hip flexion. We found that decreased force contribution from the gluteal muscles during hip extension and the iliopsoas muscle during hip flexion resulted in an increase in the anterior hip joint force. The anterior hip joint force was greater when the hip was in extension than when the hip was in flexion. Further studies are warranted to determine if increased utilization of the gluteal muscles during hip extension and of the iliopsoas muscle during hip flexion, and avoidance of hip extension beyond neutral would be beneficial for people with anterior hip pain, subtle hip instability, or an anterior acetabular labral tear.     

Morphological aspects and biomechanical properties of the vertebroaxial joint (C2-C3).

The C2-C3 intervertebral joint must be regarded as a transitional area situated between the upper cervical spine where most rotation of the neck and little flexion and extension occur and the lower cervical spaces where chiefly motion in the sagittal plane and also somewhat rotation take place. Under normal circumstances the range of flexion-extension reaches 11 degrees, slighter than below (19.5 degrees at C5-C6); on the opposite, the range of rotation attains 7 degrees; less than above but much more than below (0 degrees at C5-C6). The motion in the sagittal and coronal planes is relatively poor because of the location of Penning's motor-axis of C2 which runs far from the vertebral body and the lowness of the intervertebral disc. However, the rotation of C2 with respect to C3 is fair by the peculiar inclination of the articular facets which slope sagittally but also coronally and trace a sphere whereupon C2 may move around its motor-centre in any plane. When C2-C3 is surgically fixed by bone graft, the lack of motion is completed by a "compensatory movement" in the upper cervical spaces and especially at the atlantooccipital joint for flexion-extension. In the same way, C2-C3 may improve its mobility especially in the sagittal plane when the inferior partner is blocked by surgical or arthritic fusion.     

Effect of knee joint flexion and femur rotation on retropatellar contact of the human knee joint]

The aim of the present study was to evaluate retropatellar contact characteristics at different angles of flexion of the knee joint. To this end, 6 cadaveric legs were examined using pressure sensitive film (Fuji Prescale type "super low") at angles of flexion of 45 degrees, 60 degrees, 90 degrees and 120 degrees both in neutral rotation and 10 degrees internal and external rotation of the femur in the same knee joints. A force of 140 N was applied to both the vastus medialis and lateralis, and a comparison made with a medially and a laterally dominating muscle force. The contact areas decreased with increasing angles of flexion. The medially dominating muscle traction increased the contact area. Comparison between internal and external rotation revealed a decrease in contact area on internal rotation. The pressure measurements were comparable in all loading situations. Comparison between neutral and medial traction revealed significant differences in contact area, pressure and force. The influence of femoral rotation showed no significant difference. A comparison of the different angles of flexion revealed only few significant differences. To prevent the development of retropatellar arthrosis, maximum contact areas are necessary. The study has shown an advantage for medially dominating muscle traction, and external rotation of the femur.     

Static optimization underestimates antagonist muscle activity at the glenohumeral joint: A musculoskeletal modeling study

Static optimization is commonly employed in musculoskeletal modeling to estimate muscle and joint loading; however, the ability of this approach to predict antagonist muscle activity at the shoulder is poorly understood. Antagonist muscles, which contribute negatively to a net joint moment, are known to be important for maintaining glenohumeral joint stability. This study aimed to compare muscle and joint force predictions from a subject-specific neuromusculoskeletal model of the shoulder driven entirely by measured muscle electromyography (EMG) data with those from a musculoskeletal model employing static optimization. Four healthy adults performed six sub-maximal upper-limb contractions including shoulder abduction, adduction, flexion, extension, internal rotation and external rotation. EMG data were simultaneously measured from 16 shoulder muscles using surface and intramuscular electrodes, and joint motion evaluated using video motion analysis. Muscle and joint forces were calculated using both a calibrated EMG-driven neuromusculoskeletal modeling framework, and musculoskeletal model simulations that employed static optimization. The EMG-driven model predicted antagonistic muscle function for pectoralis major, latissimus dorsi and teres major during abduction and flexion; supraspinatus during adduction; middle deltoid during extension; and subscapularis, pectoralis major and latissimus dorsi during external rotation. In contrast, static optimization neural solutions showed little or no recruitment of these muscles, and preferentially activated agonistic prime movers with large moment arms. As a consequence, glenohumeral joint force calculations varied substantially between models. The findings suggest that static optimization may under-estimate the activity of muscle antagonists, and therefore, their contribution to glenohumeral joint stability.     

Validation of lumbar spine loading from a musculoskeletal model including the lower limbs and lumbar spine

Low back mechanics are important to quantify to study injury, pain and disability. As in vivo forces are difficult to measure directly, modeling approaches are commonly used to estimate these forces. Validation of model estimates is critical to gain confidence in modeling results across populations of interest, such as people with lower-limb amputation. Motion capture, ground reaction force and electromyographic data were collected from ten participants without an amputation (five male/five female) and five participants with a unilateral transtibial amputation (four male/one female) during trunk-pelvis range of motion trials in flexion/extension, lateral bending and axial rotation. A musculoskeletal model with a detailed lumbar spine and the legs including 294 muscles was used to predict L4-L5 loading and muscle activations using static optimization. Model estimates of L4-L5 intervertebral joint loading were compared to measured intradiscal pressures from the literature and muscle activations were compared to electromyographic signals. Model loading estimates were only significantly different from experimental measurements during trunk extension for males without an amputation and for people with an amputation, which may suggest a greater portion of L4-L5 axial load transfer through the facet joints, as facet loads are not captured by intradiscal pressure transducers. Pressure estimates between the model and previous work were not significantly different for flexion, lateral bending or axial rotation. Timing of model-estimated muscle activations compared well with electromyographic activity of the lumbar paraspinals and upper erector spinae. Validated estimates of low back loading can increase the applicability of musculoskeletal models to clinical diagnosis and treatment.     

Determination of trunk muscle forces for flexion and extension by using a validated finite element model of the lumbar spine and measured in vivo data

Muscle forces stabilize the spine and have a great influence on spinal loads. But little is known about their magnitude. In a former in vitro experiment, a good agreement with intradiscal pressure and fixator loads measured in vivo could be achieved for standing and extension of the lumbar spine. However, for flexion the agreement between in vitro and in vivo measurements was insufficient. In order to improve the determination of trunk muscle forces, a three-dimensional nonlinear finite element model of the lumbar spine with an internal fixation device was created and the same loads were applied as in a previous in vitro experiment. An extensive adaptation process of the model was performed for flexion and extension angles up to 20 degrees and -15 degrees, respectively. With this validated computer model intra-abdominal pressure, preload in the fixators, and a combination of hip- and lumbar flexion angle were varied until a good agreement between analytical and in vivo results was reached for both, intradiscal pressure and bending moments in the fixators. Finally, the fixators were removed and the muscle forces for the intact lumbar spine calculated. A good agreement with the in vivo results could only be achieved at a combination of hip- and lumbar flexion. For the intact spine, forces of 170, 100 and 600 N are predicted in the m. erector spinae for standing, 5 degrees extension and 30 degrees flexion, respectively. The force in the m. rectus abdominus for these body positions is less than 25 N. For more than 10 degrees extension the m. erector spinae is unloaded. The finite element method together with in vivo data allows the estimation of trunk muscle forces for different upper body positions in the sagittal plane. In our patients, flexion of the upper body was most likely a combination of hip- and lumbar spine bending.     

Trunk strength,muscle activity and spinal loads in maximum isometric flexion and extension exertions: A combined in vivo-computational study

Determination of the trunk maximum voluntary exertion moment capacity and associated internal spinal forces could serve in proper selection of workers for specific occupational task requirements, injury prevention and treatment outcome evaluations. Maximum isometric trunk exertion moments in flexion and extension along with surface EMG of select trunk muscles are measured in 12 asymptomatic subjects. Subsequently and under individualized measured harness-subject forces, kinematics and upper trunk gravity, an iterative kinematics-driven finite element model is used to compute muscle forces and spinal loads in 4 of these subjects. Different co-activity and intra-abdominal pressure levels are simulated. Results indicate significantly larger maximal resistant moments and spinal compression/shear forces in extension exertions than flexion exertions. The agonist trunk muscles reach their maximum force generation (saturation) to greater extent in extension exertions compared to flexion exertions. Local lumbar extensor muscles are highly active in extension exertions and generate most of the internal spinal forces. The maximum exertion attempts produce large spinal compression and shear loads that increase with the antagonist co-activity level but decrease with the intra-abdominal pressure. Intra-abdominal pressure decreases agonist muscle forces in extension exertions but generally increase them in flexion exertions.     

A musculoskeletal shoulder simulation of moment arms and joint reaction forces after medialization of the supraspinatus footprint in rotator cuff repair

A non-anatomical reinsertion of the supraspinatus medially to the original footprint to avoid over-tensioning of the tendon in large and retracted tears is one surgical option in rotator cuff (RC) repair. The purpose of the study was to determine the biomechanical effects on the glenohumeral joint with regard to this surgical technique. A modified musculoskeletal computational shoulder model was used to evaluate the change in moment arms and muscle forces of the RC and the co-contracting muscles and the alteration of the joint reaction forces (compressive and shear forces) after reinsertion of the supraspinatus 5?mm, 10?mm, 15?mm and 20?mm medially to the original footprint. A medialization of the supraspinatus reduces its moment arm in glenohumeral abduction. In case of a medialization of the attachment of 15?mm and 20?mm, the supraspinatus restricts glenohumeral abduction at 54° and 68°. In glenohumeral forward flexion and in lower degrees of internal rotation the moment arm of the supraspinatus increases for a medialized tendon attachment and decreases in external rotation in relation to the anatomical condition. A medialization of the supraspinatus insertion point yields in an increase in muscle force for abduction, internal and external rotation. In the present model a medially non-anatomic reinsertion reduces significantly the compressive glenohumeral joint reaction and the glenohumeral stability. Moreover, the results show that a medialization of the supraspinatus leads to a reduction of the supraspinatus moment arm especially in abduction. This leads to an increase of a compensatory supraspinatus load for stabilization the humerus in space, which may potentially cause a postoperative overload of the tendon-bone-complex.     

The importance of quadriceps and hamstring muscle loading on knee kinematics and in-situ forces in the ACL

This study investigated the effect of hamstring co-contraction with quadriceps on the kinematics of the human knee joint and the in-situ forces in the anterior cruciate ligament (ACL) during a simulated isometric extension motion of the knee. Cadaveric human knee specimens (n = 10) were tested using the robotic universal force moment sensor (UFS) system and measurements of knee kinematics and in-situ forces in the ACL were based on reference positions on the path of passive flexion/extension motion of the knee. With an isolated 200 N quadriceps load, the knee underwent anterior and lateral tibial translation as well as internal tibial rotation with respect to the femur. Both translation and rotation increased when the knee was flexed from full extension to 30 of flexion; with further flexion, these motion decreased. The addition of 80 N antagonistic hamstrings load significantly reduced both anterior and lateral tibial translation as well as internal tibial rotation at knee flexion angles tested except at full extension. At 30 of flexion, the anterior tibial translation, lateral tibial translation, and internal tibial rotation were significantly reduced by 18, 46, and 30%, respectively (p<0.05). The in-situ forces in the ACL under the quadriceps load were found to increase from 27.8+/-9.3 N at full extension to a maximum of 44.9+/-13.8 N at 15 of flexion and then decrease to 10 N beyond 60 of flexion. The in-situ force at 15 was significantly higher than that at other flexion angles (p<0.05). The addition of the hamstring load of 80 N significantly reduced the in-situ forces in the ACL at 15, 30 and 60 of flexion by 30, 43, and 44%, respectively (p<0.05). These data demonstrate that maximum knee motion may not necessarily correspond to the highest in-situ forces in the ACL. The data also suggest that hamstring co-contraction with quadriceps is effective in reducing excessive forces in the ACL particularly between 15 and 60 of knee flexion.     

Spinal constraint modulates head instantaneous center of rotation and dictates head angular motion

The head is kinematically constrained to the torso through the spine and thus, the spine dictates the amount of output head angular motion expected from an input impact. Here, we investigate the spinal kinematic constraint by analyzing the head instantaneous center of rotation (HICOR) with respect to the torso in head/neck sagittal extension and coronal lateral flexion during mild loads applied to 10 subjects. We found the mean HICOR location was near the C5-C6 intervertebral joint in sagittal extension, and T2-T3 intervertebral joint in coronal lateral flexion. Using the impulse-momentum relationship normalized by subject mass and neck length, we developed a non-dimensional analytical ratio between output angular velocity and input linear impulse as a function of HICOR location. The ratio was 0.65 and 0.50 in sagittal extension and coronal lateral flexion respectively, implying 30% greater angular velocities in sagittal extension given an equivalent impulse. Scaling to subject physiology also predicts larger required impulses given greater subject mass and neck length to achieve equivalent angular velocities, which was observed experimentally. Furthermore, the HICOR has greater motion in sagittal extension than coronal lateral flexion, suggesting the head and spine can be represented with a single inverted pendulum in coronal lateral flexion, but requires a more complex representation in sagittal extension. The upper cervical spine has substantial compliance in sagittal extension, and may be responsible for the complex motion and greater extension angular velocities. In analyzing the HICOR, we can gain intuition regarding the neck’s role in dictating head motion during external loading.     

A new in vivo technique for 3-dimensional analysis of the translation of femoral condyles and the menisci responding to antagonistic muscle forces]

The aim of our study was to develop a 3-D MR-based technique for the analysis of meniscal and femoral translations during flexion of the knee, and under the influence of antagonistic muscle forces in healthy subjects. In an open MR system, 5 knees were examined at 30 degrees and 90 degrees flexion using a T1-weighted 3-D gradient echo sequence. A force of 30 Newtons, first in the extending and then in the flexing direction, was applied to the distal lower leg. After three-dimensional reconstruction, the minimal distances between the centre of the tibial plateau and the posterior edge of the menisci and femoral condyles were determined. At 30 degrees flexion, the minimum distance for the meniscus was larger medially than laterally (23.2 +/- 1.8 mm vs. 16.2 +/- 3.3 mm), and this also applied to the condyles (25.1 +/- 1.5 vs. 19.0 +/- 3.0 mm). During flexion to 90 degrees, a posterior translation of 0.5 +/- 0.2 mm was observed for the lateral, and of 3.4 +/- 1.2 mm for the medial, meniscus. The condyles demonstrated a different posterior translation (lateral 2.2 +/- 0.56 mm; medial 1.8 +/- 1.9 mm). No obvious differences were found between extension and flexion muscle activity for the different positions of the knee. In the present study, a new 3-D technique is presented for the analysis of the femoral and meniscal translation at various positions of the knee, and under muscle activity. The results suggest different translation for the menisci and condyles.     

The interaction of muscle moment arm,knee laxity,and torque in a multi-scale musculoskeletal model of the lower limb

IntroductionMusculoskeletal modeling allows insight into the interaction of muscle force and knee joint kinematics that cannot be measured in the laboratory. However, musculoskeletal models of the lower extremity commonly use simplified representations of the knee that may limit analyses of the interaction between muscle forces and joint kinematics. The goal of this research was to demonstrate how muscle forces alter knee kinematics and consequently muscle moment arms and joint torque in a musculoskeletal model of the lower limb that includes a deformable representation of the knee.MethodsTwo musculoskeletal models of the lower limb including specimen-specific articular geometries and ligament deformability at the knee were built in a finite element framework and calibrated to match mean isometric torque data collected from 12 healthy subjects. Muscle moment arms were compared between simulations of passive knee flexion and maximum isometric knee extension and flexion. In addition, isometric torque results were compared with predictions using simplified knee models in which the deformability of the knee was removed and the kinematics at the joint were prescribed for all degrees of freedom.ResultsPeak isometric torque estimated with a deformable knee representation occurred between 45° and 60° in extension, and 45° in flexion. The maximum isometric flexion torques generated by the models with deformable ligaments were 14.6% and 17.9% larger than those generated by the models with prescribed kinematics; by contrast, the maximum isometric extension torques generated by the models were similar. The change in hamstrings moment arms during isometric flexion was greater than that of the quadriceps during isometric extension (a mean RMS difference of 9.8 mm compared to 2.9 mm, respectively).DiscussionThe large changes in the moment arms of the hamstrings, when activated in a model with deformable ligaments, resulted in changes to flexion torque. When simulating human motion, the inclusion of a deformable joint in a multi-scale musculoskeletal finite element model of the lower limb may preserve the realistic interaction of muscle force with knee kinematics and torque.     

A global optimization method for prediction of muscle forces of human musculoskeletal system

Inverse dynamic optimization is a popular method for predicting muscle and joint reaction forces within human musculoskeletal joints. However, the traditional formulation of the optimization method does not include the joint reaction moment in the moment equilibrium equation, potentially violating the equilibrium conditions of the joint. Consequently, the predicted muscle and joint reaction forces are coordinate system-dependent. This paper presents an improved optimization method for the prediction of muscle forces and joint reaction forces. In this method, the location of the rotation center of the joint is used as an optimization variable, and the moment equilibrium equation is formulated with respect to the joint rotation center to represent an accurate moment constraint condition. The predicted muscle and joint reaction forces are independent of the joint coordinate system. The new optimization method was used to predict muscle forces of an elbow joint. The results demonstrated that the joint rotation center location varied with applied loading conditions. The predicted muscle and joint reaction forces were different from those predicted by using the traditional optimization method. The results further demonstrated that the improved optimization method converged to a minimum for the objective function that is smaller than that reached by using the traditional optimization method. Therefore, the joint rotation center location should be involved as a variable in an inverse dynamic optimization method for predicting muscle and joint reaction forces within human musculoskeletal joints.     

Are hamstrings activated to counteract shear forces during isometric knee extension efforts in healthy subjects?

The hamstring muscles have the potential to counteract anterior shear forces at the knee joint by co-contracting during knee extension efforts. Such a muscle recruitment pattern might protect the anterior cruciate ligament (ACL) by reducing its strain. In this study we investigated to what extent co-activation of the knee flexors during extension efforts is compatible with the hypothesis that this co-activation serves to counteract anterior tibial shear forces during isometric knee extension efforts in healthy subjects. To this aim, it is investigated whether co-activation varies with the required knee extension moment, with the knee joint angle, and with the position of the external flexing force relative to the knee joint. With unaltered moment and muscle activation, distal positioning of the flexing force on the tibia causes higher resultant (muscular plus external) forward shear forces at the knee as compared to proximal positioning. In ten subjects, knee flexor and extensor EMG was measured during a quasi-isometric positioning task for a range (5-50 degrees) of knee flexion angles. It was found that the co-activation of the knee flexors increased with the extension moment, but this increase was less than proportional (p<0.001). The extension moment increased 2.7 to 3.4 times, whereas the activation of Biceps Femoris and Semitendinosus increased only a factor 1.3 to 2.0 (joint angle dependent). Furthermore, a strong increase in co-activation was seen near full extension of the knee joint. The position of the external extension load on the tibia did not affect the level of co-contraction. It is argued that these results do not suggest a recruitment pattern that is directed at reduction of anterior shear forces in the knee joint during sub-maximal isometric knee extension efforts in healthy subjects.     

Dynamic joint and muscle forces during knee isokinetic exercise

Isokinetic exercise has been commonly used in knee rehabilitation, conditioning and research in the past two decades. Although many investigators have used various experimental and theoretical approaches to study the muscle and joint force involved in isokinetic knee extension and flexion exercises, only a few of these studies have actually distinguished between the tibiofemoral joint forces and muscle forces. Therefore, the objective of this study was to specify, via an eletromyography(EMG)-driven muscle force model of the knee, the magnitude of the tibiofemoral joint and muscle forces acting during isokinetic knee extension and flexion exercises. Fifteen subjects ranging from 21 to 36 years of age volunteered to participate in this study. A Kin Com exercise machine (Chattecx Corporation, Chattanooga, TN, U.S.A.) was used as the loading device. An EMG-driven muscle force model was used to predict muscle forces, and a biomechanical model was used to analyze two knee joint constraint forces; compression and shear force. The methods used in this study were shown to be valid and reliable (r > 0.84 andp < 0.05). The effects on the tibiofemoral joint force during knee isokinetic exercises were compared with several functional activities that were investigated by earlier researchers. The muscle forces generated during knee isokinetic exercise were also obtained. Based on the findings obtained in this study, several therapeutic justifications for knee rehabilitation are proposed.     

Realistic loading conditions for upper body bending

Different modes of load applications are used to simulate flexion and extension of the upper body. It is not clear which loading modes deliver realistic results and allow the comparison of different studies.In a numerical study, a validated finite element model of the lumbar spine, ranging from the vertebra L1 to the disc L5–S1 was employed. Each of six different loading modes was studied for simulating flexion and extension, including pure moments, an eccentric axial force, using a wedged fixture, and applying upper body weight plus follower load plus muscle forces. Intersegmental rotations, intradiscal pressures and facet joint contact forces were calculated. Where possible, results were compared to data measured in vivo.The results of the loading modes studied show a large variance for some values. Outcome measures such as flexion angle and intradiscal pressure differed at a segment by up to 44% and 88%, respectively, related to their maximum values. Intradiscal pressure is mainly determined by the magnitude of the applied compressive force. For flexion maximum contact forces between 0 and 69 N are predicted in each facet joint for different loading modes. For both flexion and extension, applying upper body weight plus follower load plus muscle forces as well as a follower load together with a bending moment delivers results which agreed well with in vivo data from the literature.Choosing an adequate loading mode is important in spine biomechanics when realistic results are required for intersegmental rotations, intradiscal pressure and facet joint contact forces. Only then will results of different studies be comparable.     

A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.