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

Evaluation of assumptions in foot and ankle biomechanical models

BACKGROUND

A variety of biomechanical models have been used in studies of foot and ankle disorders. Assumptions about the element types, material properties, and loading and boundary conditions are inherent in every model. It was hypothesized that the choice of these modeling assumptions could have a significant impact on the findings of the model.

METHODS

We investigated the assumptions made in a number of biomechanical models of the foot and ankle and evaluated their effects on the results of the studies. Specifically, we focused on: (1) element choice for simulation of ligaments and tendons, (2) material properties of ligaments, cortical and trabecular bones, and encapsulating soft tissue, (3) loading and boundary conditions of the tibia, fibula, tendons, and ground support.

FINDINGS

Our principal findings are: (1) the use of isotropic solid elements to model ligaments and tendons is not appropriate because it allows them to transmit unrealistic bending and twisting moments and compressive forces; (2) ignoring the difference in elastic modulus between cortical and trabecular bones creates non-physiological stress distribution in the bones; (3) over-constraining tibial motion prevents anticipated deformity within the foot when simulating foot deformities, such as progressive collapsing foot deformity; (4) neglecting the Achilles tendon force affects almost all kinetic and kinematic parameters through the foot; (5) the axial force applied to the tibia and fibula is not equal to the ground reaction force due to the presence of tendon forces.

INTERPRETATION

The predicted outcomes of a foot model are highly sensitive to the model assumptions.

The contribution of the ligaments in progressive collapsing foot deformity: A comprehensive computational study

The contribution of each of the ligaments in preventing the arch loss, hindfoot valgus, and forefoot abduction seen in progressive collapsing foot deformity (PCFD) has not been well characterized. An improved understanding of the individual ligament contributions to the deformity would aid in selecting among available treatments, optimizing current surgical techniques, and developing new ones. In this study, we evaluated the contribution of each ligament to the maintenance of foot alignment using a finite element model of the foot reconstructed from computed tomography scan images. The collapsed foot was modeled by simulating the failure of all the ligaments involved in PCFD. The ligaments were removed one at a time to determine the impact of each ligament on foot alignment, and then restored one at a time to simulate isolated reconstruction. Our findings show that the failure of any one ligament did not immediately lead to deformity, but that combined failure of only a few (the plantar fascia, long plantar, short plantar, deltoid, and spring ligaments) could lead to significant deformity. The plantar fascia, deltoid, and spring ligaments were primarily responsible for the prevention of arch collapse, hindfoot valgus, and forefoot abduction, respectively. Moreover, to produce deformity, a considerable amount of attenuation in the spring, tibiocalcaneal, interosseous talocalcaneal, plantar naviculocuneiform, and first plantar tarsometatarsal ligaments, but only a small amount in the plantar fascia, long plantar, and short plantar ligaments was needed. The results of this study suggest that the ability of a ligament to prevent deformity may not correlate with its attenuation in a collapsed foot.

Review of the Upright Balance Assessment Based on the Force Plate

Quantitative assessment is crucial for the evaluation of human postural balance. The force plate system is the key quantitative balance assessment method. The purpose of this study is to review the important concepts in balance assessment and analyze the experimental conditions, parameter variables, and application scope based on force plate technology. As there is a wide range of balance assessment tests and a variety of commercial force plate systems to choose from, there is room for further improvement of the test details and evaluation variables of the balance assessment. The recommendations presented in this article are the foundation and key part of the postural balance assessment; these recommendations focus on the type of force plate, the subject's foot posture, and the choice of assessment variables, which further enriches the content of posturography. In order to promote a more reasonable balance assessment method based on force plates, further methodological research and a stronger consensus are still needed.

Combination of PedCAT Weightbearing CT With Pedography Assessment of the Relationship Between Anatomy-Based Foot Center and Force/Pressure-Based Center of Gravity

BACKGROUND

A customized pedography sensor (Pliance; Novel, Munich, Germany) was inserted into a pedCAT (Curvebeam, Warrington, PA). The aim of this study was to analyze the relative position of the anatomical foot center (FC) and the pedographic center of gravity (COG). The hypothesis was that FC should be a good predictor of mediolateral position of COG but not longitudinal since hindfoot anatomy allows free anteroposterior movement but limited mediolateral movement.

METHODS

In 90 patients (180 feet), a pedCAT scan with simultaneous pedography with full weightbearing in a standing position was performed. The morphology-based definition of the FC was performed with the pedCAT data following the Torque Ankle Lever Arm System (TALAS) algorithm. The force/pressure-based COG was defined with the pedography data using a software-based algorithm. The distance between FC and COG and the direction of a potential shift (distal-proximal, mediolateral) was measured and analyzed. COG motion during data acquisition was recorded and analyzed. Mean age of patients was 53.8 (range, 17-84) years, and 57 (63%) were female.

RESULTS

The distance between FC and COG was 28.7 mm on average (range, 0-60). FC was distal to COG in 175 feet (97%; mean, 27.5 mm; range, -15 to 60) and lateral in 112 feet (62%; mean, 2.0 mm; range, -18 to 20).

CONCLUSIONS

There was a constant and major distal longitudinal shift of COG relative to FC and an inconstant minor mediolateral shift.

CLINICAL RELEVANCE

The data might be taken into consideration for planning and follow-up in foot and ankle surgery.

Age- and sex-associated morphological variations of metatarsal torsional patterns in humans

It has been demonstrated that the torsional patterns of the metatarsal heads are associated with the presence or absence of the medial longitudinal arch in hominoid feet. The relatively untwisted second metatarsal is unique in humans, but that of the African apes is much more inverted, suggesting that the torsion of the second metatarsal might represent the overall shape and flatness of the foot. Some clinical studies have recently argued that the onset of foot pathologies such as hallux valgus might be related to the torsional pattern of the metatarsals. However, to date, no studies have systematically investigated the morphological variations of the torsional patterns of human metatarsals. In this study, therefore, the aim was to clarify the age- and sex-associated variations in the torsional patterns of human metatarsals using three-dimensional computed tomography. The torsion angles of the five metatarsals were calculated by defining the dorsopalmar vector of the metatarsal base and the vector corresponding to the rotational axis of the metatarsal head. The present result demonstrated that the second metatarsals of females were significantly more inverted with increasing age. Flat foot is known to be most common in elderly women. Whether there is a cause-effect relationship between second metatarsal torsion and flattening of the medial longitudinal arch has yet to be answered, but this study suggested that torsion of the second metatarsal might possibly be used as an indicator for the early diagnosis of flat foot and associated foot pathologies. Clin. Anat. 30:1058-1063, 2017. © 2017 Wiley Periodicals, Inc.

A finite element model of flatfoot (Pes Planus) for improving surgical plan

Flatfoot is a foot condition caused by the collapse of the medial arch of the foot, and it can result in problems such as severe pain, swelling, abnormal gait, and difficulty walking. Despite being a very common foot deformity, flatfoot is one of the least understood orthopaedic problems, and the opinions regarding its optimal treatment vary widely. In this paper, an FE model of a flatfoot is proposed that is based on CT measurements. Surface meshes of the bones and soft tissue were generated from CT images and then simplified to reduce the node density. A total of 62 ligaments, 9 tendons, and the plantar fascia were modeled manually. Volume meshes of the different components were generated and combined to form the completed flatfoot model. A dynamic FE formulation was derived, and a balanced standing simulation was performed. The model was validated by comparing stress distribution results from the simulation to experimental data.

Plantar pressure relief under the metatarsal heads: therapeutic insole design using three-dimensional finite element model of the foot

Therapeutic footwear with specially-made insoles is often used in people with diabetes and rheumatoid arthritis to relieve ulcer risks and pain due to high pressures from areas beneath bony prominences of the foot, in particular to the metatarsal heads (MTHs). In a three-dimensional finite element study of the foot and footwear with sensitivity analysis, effects of geometrical variations of a therapeutic insole, in terms of insole thicknesses and metatarsal pad (MP) placements, on local peak plantar pressure under MTHs and stress/strain states within various forefoot tissues, were determined. A validated musculoskeletal finite element model of the human foot was employed. Analyses were performed in a simulated muscle-demanding instant in gait. For many design combinations, increasing insole thicknesses consistently reduce peak pressures and internal tissue strain under MTHs, but the effects reach a plateau when insole becomes very thick (e.g., a value of 12.7mm or greater). Altering MP placements, however, showed a proximally- and a distally-placed MP could result in reverse effects on MTH pressure-relief. The unsuccessful outcome due to a distally-placed MP may attribute to the way it interacts with plantar tissue (e.g., plantar fascia) adjacent to the MTH. A uniform pattern of tissue compression under metatarsal shaft is necessary for a most favorable pressure-relief under MTHs. The designated functions of an insole design can best be achieved when the insole is very thick, and when the MP can achieve a uniform tissue compression pattern adjacent to the MTH.

A population of patient-specific adult acquired flatfoot deformity models before and after surgery

Following IRB approval, a cohort of 3-D rigid-body computational models was created from submillimeter MRIs of clinically diagnosed Adult Acquired Flatfoot Deformity patients and employed to investigate postoperative foot/ankle function and surgical effect during single-leg stance. Models were constrained through physiologic joint contact, passive soft-tissue tension, active muscle force, full body weight, and without idealized joints. Models were validated against patient-matched controls using clinically utilized radiographic angle and distance measures and plantar force distributions in the medial forefoot, lateral forefoot, and hindfoot. Each model further predicted changes in strain for the spring ligament, deltoid ligament, and plantar fascia, as well as joint contact loads for three midfoot joints, the talonavicular, navicular-1st cuneiform, and calcaneocuboid. Radiographic agreement ranged across measures, with average absolute deviations of <5° and <4 mm indicating generally good agreement. Postoperative plantar force loading in patients and models was reduced for the medial forefoot and hindfoot concomitant with increases in the lateral forefoot. Model predicted reductions in medial soft-tissue strain and increases in lateral joint contact load were consistent with in vitro observations and elucidate the biomechanical mechanisms of repair. Thus, validated rigid-body models offer promise for the investigation of foot/ankle kinematics and biomechanical behaviors that are difficult to measure in vivo.

Validation of a population of patient-specific adult acquired flatfoot deformity models

Adult acquired flatfoot deformity (AAFD) is a degenerative disease resulting in malalignment of the mid- and hindfoot secondary to posterior tibial tendon dysfunction and increasing implication of ligament pathologies. Despite the complex 3D nature of AAFD, 2D radiographs are still employed to diagnose and stage the disease. Computer modeling techniques allow for accurate 3D recreations of musculoskeletal systems for the investigation of biomechanical factors contributing to disease. Following Institutional Review Board approval, the lower limbs of six diagnosed AAFD sufferers were imaged with MRI, photographs, and X-ray. Next, a radiologist graded the MRI attenuation of eight soft-tissues implicated in AAFD. Six patient-specific rigid-body models were then created and loaded according to patient weight, graded soft-tissues, and extrinsic muscles. Model function was validated using clinically relevant kinematic measures in three planes. Agreement varied depending on the measure, with average absolute deviations of < 7° for angles and <4 mm for distances. Additionally, the clinically favored AP talonavicular coverage angle, ML talo-1st metatarsal angle, and ML 1st cuneiform height showed strong correlations of R(2) = 0.63, 0.75, and 0.85, respectively. Thus, computer modeling offers a promising methodology for the non-invasive investigation of in vivo kinematic behavior in pathologic feet and, once validated, may further be used to investigate biomechanical parameters that are difficult to measure clinically.

Flexion strength of the toes in the normal foot. An evaluation using magnetic resonance imaging

Flexion of the toes may be active from muscle contraction or passive from the reversed windlass function of the plantar aponeurosis. The aim of this study was to estimate the flexion moments the muscles of the foot and long digital flexors may be capable of generating and compare these calculations with published data. Magnetic resonance images were used to measure the maximal cross-sectional area of the foot muscles and long digital flexors, along with the radius of curvature of the metatarsal heads. Using known physiological data the maximal flexion moments the muscles may be able to generate at the metatarsophalangeal (MTP) joints were calculated. The methodology overestimates muscle strength and flexion moments at the metatarsophalangeal joints. The calculated maximal flexion moment at the 1st MTP joint is 4.27-6.84 Nm, for the 2nd, 3rd and 4th MTP joints 3.06-4.91 Nm, and the 5th MTP joint 0.47-0.75 Nm. The flexion moments the muscles may generate at the MTP joints do not account for the flexion forces seen in normal walking. Given that maximal strength is not used in normal walking, we conclude that the reversed windlass mechanism of the plantar aponeurosis must be important in normal function of the toes.

Effects of custom and semi-custom foot orthotics on second metatarsal bone strain during dynamic gait simulation

BACKGROUND

Stress fractures of the lower extremity are common in military and running populations. Research on the effectiveness of orthotics in modifying bone strain is limited. Our hypothesis was that custom and semi-custom foot orthotics would equally decrease bone strain of the second metatarsal.

MATERIALS AND METHODS

Eight cadaver specimens were cast for two types of orthotics, a custom and semi-custom device, using neutral plaster casts. Cadaver specimens, mounted to a dynamic gait simulator, walked over a force platform while force and bone strain data were collected. Peak bone strains, strain rates and tendon forces during the stance phase for each condition were analyzed using repeated measures analysis of variance and effect sizes.

RESULTS

Condition effects were present for tension strain, shear strain, compression rate and shear rate. Specifically, custom orthotics significantly decreased the aforementioned bone strains and strain rates (< or = 0.01 for all) and the semi-custom orthotic decreased tension strains and shear strain rates (p = 0.05 and 0.03, respectively). The effect of custom and semi-custom devices only differed significantly for compression and shear strain (p= 0.04 and 0.02, respectively) with custom orthotics having a greater effect.

CONCLUSION

Both custom and semi-custom orthotics modified the second metatarsal bone strain and strain rate. The use of custom orthotics during simulated walking decreased second metatarsal bone strains and strain rates more effectively than semi-custom orthotics.

CLINICAL RELEVANCE

Orthotics may minimize the strain magnitudes and rates of the second metatarsal in walking and therefore are a feasible treatment option for the treatment and prevention of stress injury to the second metatarsal.

A biomechanical analysis of posterior tibial tendon dysfunction, medial displacement calcaneal osteotomy and flexor digitorum longus transfer in adult acquired flat foot

BACKGROUND

Biomechanical models have been used to study stress in the metatarsals, subtalar motion, lateral column lengthening and subtalar arthroereisis. Posterior tibial tendon dysfunction has been associated with increased loads in the arch of the acquired flat foot. We examine whether a 10 millimeter (mm) medial displacement calcaneal osteotomy and flexor digitorum longus transfer to the navicular reduces these increased loads in the flat foot.

METHODS

The response of a normal foot, a foot with posterior tibial tendon dysfunction, and a flat foot to an applied load of 683Newton was analyzed using a multi-segment biomechanical model. The distribution of load on the metatarsals, the moment about each joint, the force on each of the plantar ligaments and the muscle forces were computed.

FINDINGS

Posterior tibial tendon dysfunction results in increased load on the medial arch, which may cause the foot to flatten. A 10mm medial displacement calcaneal osteotomy substantially decreases the load on the first metatarsal and the moment at the talo-navicular joint and increases the load on the fifth metatarsal and the calcaneal-cuboid joint. Adding the flexor digitorum longus transfer to the medial displacement calcaneal osteotomy has only a small effect on the flattened foot.

INTERPRETATION

Our biomechanical analysis illustrates that when the foot becomes flat, the force on the talo-navicular joint increases substantially from its value for the normal foot, and that medial displacement calcaneal osteotomy can reduce this increased force back toward the value occurring in the normal foot. This study provides a biomechanical rationale for medial displacement calcaneal osteotomy treatments for posterior tibial tendon dysfunction.

In vivo tests of an improved method for functional location of the subtalar joint axis

The subtalar joint is important in frontal plane movement and posture of the hindfoot. Abnormal subtalar joint moments caused by muscle forces and the ground reaction force acting on the foot are thought to play a role in various foot deformities. Calculating joint moments typically requires knowledge of the location of the joint axis; however, location of the subtalar axis from measured movement is difficult because the talus cannot be tracked using skin-mounted markers. The accuracy of a novel technique for locating the subtalar axis was assessed in vivo using magnetic resonance imaging. The method was also tested with skin-mounted markers and video motion analysis. The technique involves applying forces to the foot that cause pure subtalar joint motion (with negligible talocrural joint motion), and then using helical axis decomposition of the resulting tibiocalcaneal motion. The resulting subtalar axis estimates differed by 6 degrees on average from the true best-fit subtalar axes in the MRI tests. Motion was found to have been applied primarily about the subtalar joint with an average of only 3 degrees of talocrural joint motion. The proposed method provides a potential means for obtaining subject-specific subtalar axis estimates which can then be used in inverse dynamic analyses and subject-specific musculoskeletal models.

A biomechanical analysis of the effect of lateral column lengthening calcaneal osteotomy on the flat foot

BACKGROUND

Biomechanical models have been used to study the plantar aponeurosis, medial arch height, subtalar motion, medial displacement calcaneal osteotomy, subtalar arthroereisis and the distribution of forces in the normal and flat foot. The objective was to examine the hypothesis that increased load on the medial arch in the adult flat foot can be reduced through a 10mm lateral column lengthening calcaneal osteotomy 10 mm proximal from the calcaneal cuboid joint.

METHODS

A three dimensional multisegment biomechanical model was used with anatomical data from a normal foot, a flat foot and a foot corrected with a 10mm lateral column lengthening calcaneal osteotomy. The response of a normal foot, a flat foot and a flat foot with a 10mm lateral column lengthening calcaneal osteotomy to an applied load of 683 N was analyzed using the biomechanical model. Data for the biomechanical model was obtained from a cadaver foot using the direct linear transformation method. Direct linear transformation uses multiple cameras to determine the spatial location of anatomical landmarks.

FINDINGS

Load on the first metatarsal increases to 37% body weight in the flat foot compared to 12% for the normal foot and the moment about the talo-navicular joint increases from 5.6 N m to 21.6 N m. Lateral column lengthening shifts the load toward the lateral column, decreasing load on the first metatarsal to 10% and decreasing the moment about the talo-navicular joint to 8.1 N m.

INTERPRETATION

The analysis shows that a 10mm lateral column lengthening calcaneal osteotomy reduces the excess force on the medial arch in an adult flat foot and adds biomechanical rationale to this clinical procedure.

The Pathomechanics of Plantar Fasciitis

Plantar fasciitis is a musculoskeletal disorder primarily affecting the fascial enthesis. Although poorly understood, the development of plantar fasciitis is thought to have a mechanical origin. In particular, pes planus foot types and lower-limb biomechanics that result in a lowered medial longitudinal arch are thought to create excessive tensile strain within the fascia, producing microscopic tears and chronic inflammation. However, contrary to clinical doctrine, histological evidence does not support this concept, with inflammation rarely observed in chronic plantar fasciitis. Similarly, scientific support for the role of arch mechanics in the development of plantar fasciitis is equivocal, despite an abundance of anecdotal evidence indicating a causal link between arch function and heel pain. This may, in part, reflect the difficulty in measuring arch mechanics in vivo. However, it may also indicate that tensile failure is not a predominant feature in the pathomechanics of plantar fasciitis. Alternative mechanisms including 'stress-shielding', vascular and metabolic disturbances, the formation of free radicals, hyperthermia and genetic factors have also been linked to degenerative change in connective tissues. Further research is needed to ascertain the importance of such factors in the development of plantar fasciitis.

A biomechanical model of the effect of subtalar arthroereisis on the adult flexible flat foot

OBJECTIVE

The hypothesis tested was that the increased load on the medial arch in the adult flat foot can be reduced through a 6 mm subtalar arthroereisis.

DESIGN

A three-dimensional multisegment biomechanical model was used in conjunction with experimental data and data from the literature.

BACKGROUND

Biomechanical models have been used to study the plantar fascia, medial arch height, subtalar motion, medial displacement calcaneal osteotomy and distribution of forces in the foot.

METHODS

Responses of a normal foot, a flat foot, and a flat foot with a subtalar arthroereisis to an applied load of 683 N were analyzed and the distribution of support among the metatarsal heads and the moment about various joints were computed.

RESULTS

The flattened foot results in an increase in the load on the head of the first metatarsal from 10% to 24% of the body weight, and an increase in the moment about the talo-navicular joint from 3.4 to 11.9 Nm. Insertion of a 6 mm cylinder into the sinus tarsi, subtalar arthroereisis, results in a shift of the load back toward the lateral column, decreasing the load on the first metatarsal to 6% of the body weight and decreasing the moment about the talo-navicular joint to 6.0 Nm.

CONCLUSIONS

Our analysis indicates that a 6 mm subtalar arthroereisis in an adult flat foot model decreases the load on the medial arch.

Sagittal Movement of the Medial Longitudinal Arch Is Unchanged in Plantar Fasciitis

BACKGROUND

Although a lowered medial longitudinal arch has been cited as a causal factor in plantar fasciitis, there is little experimental evidence linking arch motion to the pathogenesis of the condition. This study investigated the sagittal movement of the arch in subjects with and without plantar fasciitis during gait.

METHODS

Digital fluoroscopy was used to acquire dynamic lateral radiographs from 10 subjects with unilateral plantar fasciitis and 10 matched control subjects. The arch angle and the first metatarsophalangeal joint angle were digitized and their respective maxima recorded. Sagittal movement of the arch was defined as the angular change between heel strike and the maximum arch angle observed during the stance phase of gait. The thickness of the proximal plantar fascia was determined from sagittal sonograms of both feet. ANOVA models were used to identify differences between limbs with respect to each dependent variable. Relationships between arch movement and fascial thickness were investigated using correlations.

RESULTS

There was no significant difference in either the movement or maximum arch angle between limbs. However, subjects with plantar fasciitis were found to have a larger metatarsophalangeal joint angle than controls (P < 0.05). Whereas the symptomatic and asymptomatic plantar fascia were thicker than those of control feet (P < 0.05), significant correlations were noted between fascial thickness and peak arch and metatarsophalangeal joint angles (P < 0.05) in the symptomatic limb only.

CONCLUSIONS

Neither abnormal shape nor movement of the arch are associated with chronic plantar fasciitis. However, arch mechanics may influence the severity of plantar fasciitis, once the condition is present. Digital flexion, in contrast, has a protective role in what might be a bilateral disease process.