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.     

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.     

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.     

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.     

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 Coupling Analysis of the Biomechanical Functions of Human Foot Complex during Locomotion

This study represents a functional analysis of the human foot complex based on in-vivo gait measurements, finite element (FE) modeling and biological coupling theory, with the objective of achieving a comprehensive understanding of the impact attenuation and energy absorption functions of the human foot complex. A simplified heel pad FE model comprising reticular fiber structure and fat cells was constructed based on the foot pad Magnetic Resonance (MR) images. The model was then used to investigate the foot pad behaviors under impact during locomotion. Three-dimensional (3D) gait measurement and a 3D FE foot model comprising 29 bones, 85 ligaments and the plantar soft tissues were used to investigate the foot arch and plantar fascia deformations in mid-stance phase. The heel pad simulation results show that the pad model with fat cells (coupling model) has much stronger capacity in impact attenuation and energy storage than the model without fat cells (structure model). Furthermore, the FE simulation reproduced the deformations of the foot arch structure and the plantar fascia extension observed in the gait measurements, which reinforces the postulation that the foot arch structure also plays an important role in energy absorption during locomotion. Finally, the coupling mechanism of the human foot functions in impact attenuation and energy absorption was proposed.     

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.     

The Effects of Irreversible Electroporation on the Achilles Tendon: An Experimental Study in a Rabbit Model

Background

To evaluate the potential effects of irreversible electroporation ablation on the Achilles tendon in a rabbit model and to compare the histopathological and biomechanical changes between specimens following electroporation ablation and radiofrequency ablation.

Methods

A total of 140 six-month-old male New Zealand rabbits were used. The animals were randomly divided into two groups, 70 in the radiofrequency ablation group and 70 in the electroporation group. In situ ablations were applied directly to the Achilles tendons of rabbits using typical electroporation (1800 V/cm, 90 pulses) and radiofrequency ablation (power control mode) protocols. Histopathological and biomechanical evaluations were performed to examine the effects of electroporation ablation and radiofrequency ablation over time.

Results

Both electroporation and radiofrequency ablation produced complete cell ablation in the target region. Thermal damage resulted in tendon rupture 3 days post radiofrequency ablation. In contrast, electroporation-ablated Achilles tendons preserved their biomechanical properties and showed no detectable rupture at this time point. The electroporation-ablated tendons exhibited signs of recovery, including tenoblast regeneration and angiogenesis within 2 weeks, and the restoration of their integral structure was evident within 12 weeks.

Conclusions

When applying electroporation to ablate solid tumors, major advantage could be that collateral damage to adjacent tendons or ligaments is minimized due to the unique ability of electroporation ablation to target the cell membrane. This advantage could have a significant impact on the field of tumor ablation near vital tendons or ligaments.     

A closed-loop cadaveric foot and ankle loading model

Investigations of human foot and ankle biomechanics rely chiefly on cadaver experiments. The application of proper force magnitudes to the cadaver foot and ankle is essential to obtain valid biomechanical data. Data for external ground reaction forces are readily available from human motion analysis. However, determining appropriate forces for extrinsic foot and ankle muscles is more problematic. A common approach is the estimation of forces from muscle physiological cross-sectional areas and electromyographic data. We have developed a novel approach for loading the Achilles and posterior tibialis tendons that does not prescribe predetermined muscle forces. For our loading model, these muscle forces are determined experimentally using independent plantarflexion and inversion angle feedback control. The independent (input) parameters -- calcaneus plantarflexion, calcaneus inversion, ground reaction forces, and peroneus forces -- are specified. The dependent (output) parameters -- Achilles force, posterior tibialis force, joint motion, and spring ligament strain -- are functions of the independent parameters and the kinematics of the foot and ankle. We have investigated the performance of our model for a single, clinically relevant event during the gait cycle. The instantaneous external forces and foot orientation determined from human subjects in a motion analysis laboratory were simulated in vitro using closed-loop feedback control. Compared to muscle force estimates based on physiological cross-sectional area data and EMG activity at 40% of the gait cycle, the posterior tibialis force and Achilles force required when using position feedback control were greater.     

Stress analysis of the standing foot following surgical plantar fascia release

Plantar fascia release is a surgical alternative for patients who suffer chronic heel pain due to plantar fasciitis and are unaffected by conservative treatment. A computational (finite element) model for analysis of the structural behavior of the human foot during standing was utilized to investigate the biomechanical effects of releasing the plantar fascia. The model integrates a system of five planar structures in the directions of the foot rays. It was built according to accurate geometric data of MRI, and includes linear and non-linear elements that represent bony, cartilaginous, ligamentous and fatty tissues. The model was successfully validated by comparing its resultant ground reactions with foot-ground pressure measurements and its predicted displacements with those observed in radiological tests. Simulation of plantar fascia release (partial or total) was accomplished by gradually removing parts of the fascia in the model. The results showed that total fascia release causes extensive arch deformation during standing, which is greater than normal deformation by more than 2.5mm. Tension stresses carried by the long plantar ligaments increased significantly, and may exceed the normal average stress by more than 200%. Since the contribution of the plantar fascia to the foot's load-bearing ability is of major importance, its release must be very carefully considered, and the present model may be used to help surgeons decide upon the desired degree of release.     

Analysis of the human and ape foot during bipedal standing with implications for the evolution of the foot

The ratio of the power arm (the distance from the heel to the talocrural joint) to the load arm (that from the talocrural joint to the distal head of the metatarsals), or RPL, differs markedly between the human and ape foot. The arches are relatively higher in the human foot in comparison with those in apes. This study evaluates the effect of these two differences on biomechanical effectiveness during bipedal standing, estimating the forces acting across the talocrural and tarsometatarsal joints, and attempts to identify which type of foot is optimal for bipedal standing. A simple model of the foot musculoskeletal system was built to represent the geometric and force relationships in the foot during bipedal standing, and measurements for a variety of human and ape feet applied. The results show that: (1) an RPL of around 40% (as is the case in the human foot) minimizes required muscle force at the talocrural joint; (2) the presence of an high arch in the human foot reduces forces in the plantar musculature and aponeurosis; and (3) the human foot has a lower total of force in joints and muscles than do the ape feet. These results indicate that the proportions of the human foot, and the height of the medial arch are indeed better optimized for bipedal standing than those of apes, further suggesting that their current state is to some extent the product of positive selection for enhanced bipedal standing during the evolution of the foot.     

Tendon mineralization is progressive and associated with deterioration of tendon biomechanical properties,and requires BMP-Smad signaling in the mouse Achilles tendon injury model

Ectopic tendon mineralization can develop following tendon rupture or trauma surgery. The pathogenesis of ectopic tendon mineralization and its clinical impact have not been fully elucidated yet. In this study, we utilized a mouse Achilles tendon injury model to determine whether ectopic tendon mineralization alters the biomechanical properties of the tendon and whether BMP signaling is involved in this condition. A complete transverse incision was made at the midpoint of the right Achilles tendon in 8-week-old CD1 mice and the gap was left open. Ectopic cartilaginous mass formation was found in the injured tendon by 4 weeks post-surgery and ectopic mineralization was detected at 8 to 10 weeks post-surgery. Ectopic mineralization grew over time and volume of the mineralized materials of 25-weeks samples was about 2.5 fold bigger than that of 10-weeks samples, indicating that injury-induced ectopic tendon mineralization is progressive. In vitro mechanical testing showed that max force, max stress and mid-substance modulus in the 25-weeks samples were significantly lower than the 10-weeks samples. We observed substantial increases in expression of bone morphogenetic protein family genes in injured tendons 1 week post-surgery. Immunohistochemical analysis showed that phosphorylation of both Smad1 and Smad3 was highly increased in injured tendons as early as 1 week post-injury and remained high in ectopic chondrogenic lesions 4-weeks post-injury. Treatment with the BMP receptor kinase inhibitor (LDN193189) significantly inhibited injury-induced tendon mineralization. These findings indicate that injury-induced ectopic tendon mineralization is progressive, involves BMP signaling and associated with deterioration of tendon biomechanical properties.     

Variables during swing associated with decreased impact peak and loading rate in running

When the foot impacts the ground in running, large forces and loading rates can arise that may contribute to the development of overuse injuries. Investigating which biomechanical factors contribute to these impact loads and loading rates in running could assist clinicians in developing strategies to reduce these loads. Therefore, the goals of our work were to determine variables that predict the magnitude of the impact peak and loading rate during running, as well as to investigate how modulation of knee and hip muscle activity affects these variables. Instrumented gait analysis was conducted on 48 healthy subjects running at 3.3 m/s on a treadmill. The top four predictors of loading rate and impact peak were determined using a stepwise multiple linear regression model. Forward dynamics was performed using a whole body musculoskeletal model to determine how increased muscle activity of the knee flexors, knee extensors, hip flexors, and hip extensors during swing altered the predictors of loading rate and impact peak. A smaller impact peak was associated with a larger downward acceleration of the foot, a higher positioned foot, and a decreased downward velocity of the shank at mid-swing while a lower loading rate was associated with a higher positioned thigh at mid-swing. Our results suggest that an alternative to forefoot striking may be increased hip flexor activity during swing to alter these mid-swing kinematics and ultimately decrease the leg's velocity at landing. The decreased velocity would decrease the downward momentum of the leg and hence require a smaller force at impact.     

The biomechanical model of the long finger extensor mechanism and its parametric identification

The extensor mechanism of the finger is a structure transmitting the forces from several muscles to the finger joints. Force transmission in the extensor mechanism is usually modeled by equations with constant coefficients which are determined experimentally only for finger extension posture. However, the coefficient values change with finger flexion because of the extensor mechanism deformation. This induces inaccurate results for any other finger postures. We proposed a biomechanical model of the extensor mechanism represented as elastic strings. The model includes the main tendons and ligaments. The parametric identification of the model in extension posture was performed to match the distribution of the forces among the tendons to experimental data. The parametrized model was used to simulate three degrees of flexion. Furthermore, the ability of the model to reproduce how the force distribution in simulated extensor mechanism changes according to the muscle forces was also demonstrated. The proposed model could be used to simulate the extensor mechanism for any physiological finger posture for which the coefficients involved in the equations are unknown.     

Optimal foot shape for a passive dynamic biped

Passive walking dynamics describe the motion of a biped that is able to "walk" down a shallow slope without any actuation or control. Instead, the walker relies on gravitational and inertial effects to propel itself forward, exhibiting a gait quite similar to that of humans. These purely passive models depend on potential energy to overcome the energy lost when the foot impacts the ground. Previous research has demonstrated that energy loss at heel-strike can vary widely for a given speed, depending on the nature of the collision. The point of foot contact with the ground (relative to the hip) can have a significant effect: semi-circular (round) feet soften the impact, resulting in much smaller losses than point-foot walkers. Collisional losses are also lower if a single impulse is broken up into a series of smaller impulses that gradually redirect the velocity of the center of mass rather than a single abrupt impulse. Using this principle, a model was created where foot-strike occurs over two impulses, "heel-strike" and "toe-strike," representative of the initial impact of the heel and the following impact as the ball of the foot strikes the ground. Having two collisions with the flat-foot model did improve efficiency over the point-foot model. Representation of the flat-foot walker as a rimless wheel helped to explain the optimal flat-foot shape, driven by symmetry of the virtual spoke angles. The optimal long period foot shape of the simple passive walking model was not very representative of the human foot shape, although a reasonably anthropometric foot shape was predicted by the short period solution.     

Finite element analysis of plantar fascia under stretch-the relative contribution of windlass mechanism and Achilles tendon force

Stretching plays an important role in the treatment of plantar fasciitis. Information on the internal stresses/strains of the plantar fascia under stretch is useful in enhancing knowledge on the stretch mechanisms. Although direct measurement can monitor plantar fascia changes, it is invasive and gathers only localized information. The purpose of this paper was to construct a three-dimensional finite element model of the foot to calculate the stretch effects on plantar fascia and monitor its stress/strain distributions and concentrations. A three-dimensional foot model was developed and contained 26 bones with joint cartilages, 67 ligaments and a fan-like solid plantar fascia modeling. All tissues were idealized as linear elastic, homogeneous and isotropic whilst the plantar fascia was assigned as hyperelastic to represent its nonlinearity. The plantar fascia was monitored for its biomechanical responses under various stretch combinations: three toe dorsiflexion angles (windlass effect: 15 degrees , 30 degrees and 45 degrees ) and five Achilles tendon forces (100, 200, 300, 400 and 500N). Our results indicated that the plantar fascia strain increased as the dorsiflexion angles increased, and this phenomenon was enhanced by increasing Achilles tendon force. A stress concentration was found near the medial calcaneal tubercle, and the fascia stress was higher underneath the first foot ray and gradually decreased as it moved toward the fifth ray. The current model recreated the position of the foot when stretch is placed on the plantar fascia. The results provided a general insight into the mechanical and biomechanical aspects of the influences of windlass mechanism and Achilles tendon force on plantar fascia stress and strain distribution. These findings might have practical implications onto plantar fascia stretch approaches, and provide guidelines to its surgical release.     

Elastic mechanisms in primate locomotion

Tendons that stretch elastically and recoil, as the forces on them rise and fall, can save energy in running by enabling the animal to make do with shorter or slower muscle fascicles, that can generate force more economically. Non-human primates have rather long fascicles and thick tendons in their distal leg muscles and so seem poorly adapted to save energy in this way. Additional savings are made possible by the elastic compliance of ligaments in the foot. Though tendon and ligament compliance tend to save energy, the compliance of branches tends to increase the energy cost of arboreal locomotion.     

Pre-impact lower extremity posture and brake pedal force predict foot and ankle forces during an automobile collision

BACKGROUND: The purpose of this study was to determine how a driver's foot and ankle forces during a frontal vehicle collision depend on initial lower extremity posture and brake pedal force. METHOD OF APPROACH: A 2D musculoskeletal model with seven segments and six right-side muscle groups was used. A simulation of a three-second braking task found 3647 sets of muscle activation levels that resulted in stable braking postures with realistic pedal force. These activation patterns were then used in impact simulations where vehicle deceleration was applied and driver movements and foot and ankle forces were simulated. Peak rearfoot ground reaction force (F(RF)), peak Achilles tendon force (FAT), peak calcaneal force (F(CF)) and peak ankle joint force (F(AJ)) were calculated. RESULTS: Peak forces during the impact simulation were 476 +/- 687 N (F(RF)), 2934 +/- 944 N (F(CF)) and 2449 +/- 918 N (F(AJ)). Many simulations resulted in force levels that could cause fractures. Multivariate quadratic regression determined that the pre-impact brake pedal force (PF), knee angle (KA) and heel distance (HD) explained 72% of the variance in peak FRF, 62% in peak F(CF) and 73% in peak F(AJ). CONCLUSIONS: Foot and ankle forces during a collision depend on initial posture and pedal force. Braking postures with increased knee flexion, while keeping the seat position fixed, are associated with higher foot and ankle forces during a collision.     

Stress deprivation simultaneously induces over-expression of interleukin-1beta, tumor necrosis factor-alpha, and transforming growth factor-beta in fibroblasts and mechanical deterioration of the tissue in the patellar tendon

To test the hypothesis that stress deprivation induces over-expression of cytokines in the patellar tendon, 40 rats were divided into the following two groups. In the stress-shielded group, we slackened the patellar tendon in the right knee by drawing the patella toward the tibial tubercle with flexible wires. In the control group, we performed a sham operation on the right knee. Animals were killed at 2 or 6 weeks for immunohistological evaluation and biomechanical examination. For IL-1beta, TNF-alpha and TGF-beta, the ratio of positively stained specimens to total specimens was significantly higher in the stress-shielded tendons than in the control tendons. The elastic modulus of the stress-shielded tendon was significantly lower than that of the control tendon, while the cross-sectional area of the stress-shielded tendon was significantly greater than that of the control tendon. Therefore, the present study indicated that stress shielding induced the over-expression of IL-1beta, TNF-alpha and TGF-beta in patellar tendon fibroblasts with mechanical deterioration of the tendon. Regarding clinical relevance, the present study suggests a possible application of an anti-IL-1beta or anti-TNF-alpha strategy for reducing the mechanical deterioration of tendons and ligaments in response to stress deprivation, although this study did not directly show that over-expression of IL-1beta or TNF-alpha in response to stress deprivation was the causation of mechanical deterioration of tendons.