Muscle-driven finite element simulation of human foot movements

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.     

Magnetic resonance imaging of the ankle joint and foot: possible diagnostic errors

The paper deals with the visualizing study of the ankle joint and foot by MRI and with the problems in the interpretation of magnetic resonance images in health. For this, 50 healthy volunteers without diseases and lesions of the ankle joint and foot were examined. The study was performed by using flexible superficial coils and T1-, T2-, and proton-weighed pulse-sequences in the orthogonal projections. The articular surfaces and cavity of the ankle joint were evaluated. The specific features of visualization of the muscles and tendons of this area and the pattern of fluid under their membranes were explored. The typical location of the "magic corner" phenomenon was revealed. The individual specific features of identification of the ligaments of the ankle joint and foot and plantar aponeurosis were defined. The features of visualization of bones simulating abnormalities were studied. A category of normalcy in the MRI of the ankle joint and foot was formulated.     

Deformation and stress distribution of the human foot after plantar ligaments release: A cadaveric study and finite element analysis

The majority of foot deformities are related to arch collapse or instability, especially the longitudinal arch. Although the relationship between the plantar fascia and arch height has been previously investigated, the stress distribution remains unclear. The aim of this study was to explore the role of the plantar ligaments in foot arch biomechanics. We constructed a geometrical detailed three-dimensional (3-D) finite element (FE) model of the human foot and ankle from computer tomography images. The model comprised the majority of joints in the foot as well as bone segments, major ligaments, and plantar soft tissue. Release of the plantar fascia and other ligaments was simulated to evaluate the corresponding biomechanical effects on load distribution of the bony and ligamentous structures. These intrinsic ligaments of the foot arch were sectioned to simulate different pathologic situations of injury to the plantar ligaments, and to explore bone segment displacement and stress distribution. The validity of the 3-D FE model was verified by comparing results with experimentally measured data via the displacement and von Mise stress of each bone segment. Plantar fascia release decreased arch height, but did not cause total collapse of the foot arch. The longitudinal foot arch was lost when all the four major plantar ligaments were sectioned simultaneously. Plantar fascia release was compromised by increased strain applied to the plantar ligaments and intensified stress in the midfoot and metatarsal bones. Load redistribution among the centralized metatarsal bones and focal stress relief at the calcaneal insertion were predicted. The 3-D FE model indicated that plantar fascia release may provide relief of focal stress and associated heel pain. However, these operative procedures may pose a risk to arch stability and clinically may produce dorsolateral midfoot pain. The initial strategy for treating plantar fasciitis should be non-operative.     

Parametric study of orthopedic insole of valgus foot on partial foot amputation

Orthopedic insole was important for partial foot amputation (PFA) to achieve foot balance and avoid foot deformity. The inapposite insole orthosis was thought to be one of the risk factors of reamputation for foot valgus patient, but biomechanical effects of internal tissues on valgus foot had not been clearly addressed. In this study, plantar pressure on heel and metatarsal regions of PFA was measured using F-Scan. The three-dimensional finite element (FE) model of partial foot evaluated different medial wedge angles (MWAs) (0.0°–10.0°) of orthopedic insole on valgus foot. The effect of orthopedic insole on the internal bone stress, the medial ligament tension of ankle, plantar fascia tension, and plantar pressure was investigated. Plantar pressure on medial heel region was about 2.5 times higher than that of lateral region based on the F-Scan measurements. FE-predicted results showed that the tension of medial ankle ligaments was the lowest, and the plantar pressure was redistributed around the heel, the first metatarsal, and the lateral longitudinal arch regions when MWA of orthopedic insole ranged from 7.5° to 8.0°. The plantar fascias maintained about 3.5% of the total load bearing on foot. However, the internal stresses from foot bones increased. The simulation in this study would provide the suggestion of guiding optimal design of orthopedic insole and therapeutic planning to pedorthist.     

Foot arch deformation and plantar fascia loading during running with rearfoot strike and forefoot strike: A dynamic finite element analysis

Forefoot strike becomes popular among runners because it facilitates better impact attenuation. However, forefoot strike may overload the plantar fascia and impose risk of plantar fasciitis. This study aimed to examine and compare the foot arch deformation and plantar fascia tension between different foot strike techniques in running using a computational modelling approach. A three-dimensional finite element foot model was reconstructed from the MRI of a healthy runner. The foot model included twenty bones, bulk soft tissue, ligaments, tendons, and plantar fascia. The time-series data of segmental kinematics, foot muscle force, and ankle joint reaction force were derived from a musculoskeletal model of the same participant based on the motion capture analysis and input as the boundary conditions for the finite element analysis. Rearfoot strike and forefoot strike running were simulated using a dynamic explicit solver. The results showed that, compared to rearfoot strike, forefoot strike reduced the foot arch height by 9.12% and increased the medial longitudinal arch angle by 2.06%. Forefoot strike also increased the plantar connective tissues stress by 18.28–200.11% and increased the plantar fascia tensile force by 18.71–109.10%. Although it is currently difficult to estimate the threshold value of stress or force that results in injury, forefoot strike runners appeared to be more vulnerable to plantar fasciitis.     

A procedure for estimating the relevant forces in the human knee using a four-bar mechanism

Knee injuries, especially those that affect the cruciate and lateral ligaments, are one of the most serious and frequent pathologies that affect the lower human extremity. Hence, the aim of this study is to develop a dynamic model for the lower extremity capable of estimating forces, forces in the cruciate and collateral ligaments and those normal to the articular cartilage, generated in the knee. The proposed model considers a four-bar mechanism in the knee, a spherical joint in the pelvis and a revolute one in the ankle. The four-bar mechanism is obtained by a synthesis process. The dynamic model includes the inertial properties of the femur, tibia, patella and the foot, the ground reaction force and the most important muscles in the knee. Muscle forces are estimated using an optimisation technique. Results from the application of the model on a real human task are presented.     

Searching for the “sweet spot”: the foot rotation and parallel engagement of ankle ligaments in maximizing injury tolerance

Ligament sprains, defined as tearing of bands of fibrous tissues within ligaments, account for a majority of injuries to the foot and ankle complex in field-based sports. External rotation of the foot is considered the primary injury mechanism of syndesmotic ankle sprains with concomitant flexion and inversion/eversion associated with particular patterns of ligament trauma. However, the influence of the magnitude and direction of loading vectors to the ankle on the in situ stress state of the ligaments has not been quantified in the literature. The objective of the present study was to search for the maximum injury tolerance of a human foot with an acceptable subfailure distribution of individual ligaments. We used a previously developed and comprehensively validated foot and ankle model to reproduce a range of combined foot rotation experienced during high-risk sports activities. Biomechanical computational investigation was performed on initial foot rotation from \(20{^{\circ }}\) of plantar flexion to \(15{^{\circ }}\) of dorsiflexion, and from \(15{^{\circ }}\) of inversion to \(15{^{\circ }}\) of eversion prior to external rotation. Change in initial foot rotation shifted injury initiation among different ligaments and resulted in a wide range of injury tolerances at the structural level (e.g., 36–125 Nm of rotational moment). The observed trend was in agreement with a parallel experimental study that initial plantar flexion decreased the incidence of syndesmotic injury compared to a neutral foot. A mechanism of distributing even loads across ligaments subjected to combined foot rotations was identified. This mechanism is potential to obtain the maximum load-bearing capability of a foot and ankle while minimizing the injury severity of ligaments. Such improved understanding of ligament injuries in athletes is necessary to facilitate injury management by clinicians and countermeasure development by biomechanists.     

A biomechanical model of the foot: the role of muscles,tendons, and ligaments

A biomechanical model of the foot is developed and analyzed to determine the distribution of support under the metatarsal heads, the tension in the plantar aponeurosis, and the bending moment at each of the joints of the foot. This model is an extension of our earlier work to include the role of muscles, tendons, and ligaments. Two cases are presented: in the first the center of gravity of the body is over the mid foot, and in the second, the center of gravity is anterior, over the metatarsals, and no support is provided by the heel. The model shows the extent to which the muscles reduce the force in the supporting ligaments at each of the joints and decrease the tension in the plantar aponeurosis, and that this effect is more pronounced when the center of gravity of the body is moved forward.     

Development of a patient-specific anatomical foot model from structured light scan data

The use of anatomically accurate finite element (FE) models of the human foot in research studies has increased rapidly in recent years. Uses for FE foot models include advancing knowledge of orthotic design, shoe design, ankle–foot orthoses, pathomechanics, locomotion, plantar pressure, tissue mechanics, plantar fasciitis, joint stress and surgical interventions. Similar applications but for clinical use on a per-patient basis would also be on the rise if it were not for the high costs associated with developing patient-specific anatomical foot models. High costs arise primarily from the expense and challenges of acquiring anatomical data via magnetic resonance imaging (MRI) or computed tomography (CT) and reconstructing the three-dimensional models. The proposed solution morphs detailed anatomy from skin surface geometry and anatomical landmarks of a generic foot model (developed from CT or MRI) to surface geometry and anatomical landmarks acquired from an inexpensive structured light scan of a foot. The method yields a patient-specific anatomical foot model at a fraction of the cost of standard methods. Average error for bone surfaces was 2.53 mm for the six experiments completed. Highest accuracy occurred in the mid-foot and lowest in the forefoot due to the small, irregular bones of the toes. The method must be validated in the intended application to determine if the resulting errors are acceptable.     

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 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.     

Kinematics of the human ankle complex in passive flexion; a single degree of freedom system

The restoration of original range and pattern of motion is the primary goal of joint replacement and ligament reconstruction. The objective of the present work is to investigate whether or not a preferred path of joint motion at the intact human ankle complex is exhibited during passive flexion. A rig was built to move the ankle complex through its range of flexion while applying only the minimum necessary load to drive ankle flexion. Joint motion was constrained only by the articular surfaces and the ligaments. The movements of the calcaneus, talus and fibula relative to the stationary tibia in seven cadaveric specimens were tracked with a stereophotogrammetric system. It was shown that the calcaneus follows a unique path of unresisted coupled motion relative to the tibia and that most of the motion occurred at the ankle, with little motion at the subtalar level. The calcaneofibular and the tibiocalcaneal ligaments showed near-isometric pattern of rotations. All specimens showed motion of the axis of rotation relative to the bones. Deviations from the unique path due to the application of load involved mostly subtalar motion and were resisted. The ankle complex exhibits one degree of unresisted freedom, the ankle behaving as a single degree of freedom mechanism and the subtalar as a flexible structure. We deduced that the calcaneofibular and tibiocalcaneal ligaments together with the articular surfaces guide ankle passive motion, other ligaments limit but do not guide motion.     

Subject-specific models of the hindfoot reveal a relationship between morphology and passive mechanical properties

The morphology of the bones, articular surfaces and ligaments and the passive mechanical characteristics of the ankle complex were reported to vary greatly among individuals. The goal of this study was to test the hypothesis that the variations observed in the passive mechanical properties of the healthy ankle complex are strongly influenced by morphological variations. To evaluate this hypothesis six numerical models of the ankle joint complex were developed from morphological data obtained from MRI of six cadaveric lower limbs, and from average reported data on the mechanical properties of ligaments and articular cartilage. The passive mechanical behavior of each model, under a variety of loading conditions, was found to closely match the experimental data obtained from each corresponding specimen. Since all models used identical material properties and were subjected to identical loads and boundary conditions, it was concluded that the observed variations in passive mechanical characteristics were due to variations in morphology, thus confirming the hypothesis. In addition, the average and large variations in passive mechanical behavior observed between the models were similar to those observed experimentally between cadaveric specimens. The results suggest that individualized subject-specific treatment procedures for ankle complex disorders are potentially superior to a one-size-fits-all approach.     

A Phase-Dependent Hypothesis for Locomotor Functions of Human Foot Complex

The human foot is a very complex structure comprising numerous bones, muscles, ligaments and synovial joints. As the only component in contact with the ground, the foot complex delivers a variety of biomechanical functions during human locomotion, e.g. body support and propulsion, stability maintenance and impact absorption. These need the human foot to be rigid and damped to transmit ground reaction forces to the upper body and maintain body stability, and also to be compliant and resilient to moderate risky impacts and save energy. How does the human foot achieve these apparent conflicting functions？ In this study, we propose a phase-dependent hypothesis for the overall locomotor functions of the human foot complex based on in-vivo measurements of human natural gait and simulation results of a mathematical foot model. We propse that foot functions are highly dependent on gait phase, which is a major characteristics of human locomotion. In early stance just after heel strike, the foot mainly works as a shock absorber by moderating high impacts using the viscouselastic heel pad in both vertical and horizontal directions. In mid-stance phase （-80% of stance phase）, the foot complex can be considered as a springy rocker, reserving external mechanical work using the foot arch whilst moving ground contact point forward along a curved path to maintain body stability. In late stance after heel off, the foot complex mainly serves as a force modulator like a gear box, modulating effective mechanical advantages of ankle plantiflexor muscles using metatarsal-phalangeal joints. A sound under- standing of how diverse functions are implemented in a simple foot segment during human locomotion might be useful to gain insight into the overall foot locomotor functions and hence to facilitate clinical diagnosis, rehabilitation product design and humanoid robot development.     

A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint

We present here a three-dimensional FE model of the healthy human knee that included the main structures of the joint: bones, all the relevant ligaments and patellar tendon, menisci and articular cartilages. Bones were considered to be rigid, articular cartilage and menisci linearly elastic, isotropic and homogeneous and ligaments hyperelastic and transversely isotropic. Initial strains on the ligaments and patellar tendon were also considered. This model was validated using experimental and numerical results obtained by other authors. Our main goal was to analyze the combined role of menisci and ligaments in load transmission and stability of the human knee. The results obtained reproduce the complex, nonuniform stress and strain fields that occur in the biological soft tissues involved and the kinematics of the human knee joint under a physiological external load.     

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.     

Bed rest attenuates sympathetic and pressor responses to isometric exercise in antigravity leg muscles in humans

Although spaceflight and bed rest are known to cause muscular atrophy in the antigravity muscles of the legs, the changes in sympathetic and cardiovascular responses to exercises using the atrophied muscles remain unknown. We hypothesized that bed rest would augment sympathetic responses to isometric exercise using antigravity leg muscles in humans. Ten healthy male volunteers were subjected to 14-day 6 degrees head-down bed rest. Before and after bed rest, they performed isometric exercises using leg (plantar flexion) and forearm (handgrip) muscles, followed by 2-min postexercise muscle ischemia (PEMI) that continues to stimulate the muscle metaboreflex. These exercises were sustained to fatigue. We measured muscle sympathetic nerve activity (MSNA) in the contralateral resting leg by microneurography. In both pre- and post-bed-rest exercise tests, exercise intensities were set at 30 and 70% of the maximum voluntary force measured before bed rest. Bed rest attenuated the increase in MSNA in response to fatiguing plantar flexion by approximately 70% at both exercise intensities (both P < 0.05 vs. before bed rest) and reduced the maximal voluntary force of plantar flexion by 15%. In contrast, bed rest did not alter the increase in MSNA response to fatiguing handgrip and had no effects on the maximal voluntary force of handgrip. Although PEMI sustained MSNA activation before bed rest in all trials, bed rest entirely eliminated the PEMI-induced increase in MSNA in leg exercises but partially attenuated it in forearm exercises. These results do not support our hypothesis but indicate that bed rest causes a reduction in isometric exercise-induced sympathetic activation in (probably atrophied) antigravity leg muscles.     

Foot modeling affects ankle sagittal plane kinematics during jump-landing

The foot-ankle complex is a key-element to mitigate impact forces during jump-landing activities. Biomechanical studies commonly model the foot as a single-segment, which can provide different ankle kinematics compared to a multi-segmented model. Also, it can neglect intersegmental kinematics of the foot-ankle joints, such as the hindfoot-tibia, forefoot-hindfoot, and hallux-forefoot joints, that are used during jump-landing activities. The purpose of this short communication was to compare ankle kinematics between a three- and single-segmented foot models, during forward and lateral single-leg jump-landings. Marker trajectories and synchronized ground reaction forces of 30 participants were collected using motion capture and a force plate, during multidirectional single-leg jump-landings. Ankle kinematics were computed using a three- (hindfoot-tibia) and a single-segmented (ankle) foot models, at initial contact (IC), peak vertical ground reaction force (PvGRF) and peak knee flexion (PKF). Repeated measures ANOVAs were conducted (p < 0.05). The findings of this study showed that during lateral and forward jump-landing directions, the three-segmented foot model exhibited lower hindfoot-tibia dorsiflexion angles (PvGRF and PKF, p < 0.001) and excursions (sagittal: p < 0.001; frontal: p < 0.05) during the weightbearing acceptance phase than the single-segmented model. Overall, the two foot models provided distinctive sagittal ankle kinematics, with lower magnitudes in the hindfoot-tibia of the three-segmented foot. Furthermore, the three-segmented foot model may provide additional and representative kinematic data of the ankle and foot joints, to better comprehend its function, particularly in populations whose foot-ankle complex plays an important role (e.g., dancers).