FINITE ELEMENT MODELING OF THE SECOND RAY OF THE FOOT WITH FLEXOR MUSCLE LOADING

David R. Lemmon (1) , Christopher R. Jacobs (2), and Peter R. Cavanagh (1,2,3,4)
(1) Center for Locomotion Studies and Departments of (2) Orthopaedics and Rehabilitation, (3) Kinesiology, and (4) Medicine,
Penn State University, University Park, PA 16802 and Hershey, PA 17033

Presented at the 20th Annual Meeting of the American Society of Biomechanics
Atlanta, Georgia. October 17-19, 1996

INTRODUCTION

Finite element models have previously been developed to study the relationship between plantar pressure, soft tissue thickness, and footwear geometry (Lemmon et al. 1996). Work is currently under way to develop a more comprehensive model that will include loading of flexor muscles to the distal phalanges and the effect of these loads on the metatarsal head. In the current work , a finite element model has been constructed to investigate the feasibility of some key features of the comprehensive model. This model is a sagittal section of the second ray from the proximal second metatarsal to the distal end of the proximal phalanx. The model is based on the existing finite element models and is designed to test the addition of joint rotation and flexor muscle tendons interacting with the tissue.

REVIEW AND THEORY

A biomechanical analysis of forces acting on the metatarsals during normal walking was performed by Stokes, et al. (1979). This was a two-dimensional, sagittal plane analytical model of a typical ray including the phalanges. Metatarsal loading included axial and shear loads and a moment at the proximal end, and ground reaction force and lateral tendon loads to the metatarsal head.

Tendon loads were due to tension in the flexor digitorum longus (FDL) and flexor digitorum brevis (FDB) as they wrap around the metatarsal head. These flexors also applied a contact load at the metatarso-phalangeal joint due to their attachment to the phalanges. The finite element model in the current work applies these loads to the soft tissue continuum, and adds the proximal phalanx and corresponding joint forces.

Experiments have also been performed on cadaveric specimens to determine the loading of the metatarsal due to ground reaction forces and muscle loads. Sharkey, et al. (1995), applied simulated muscle loads in fresh cadaveric lower extremities. The specimens were rigidly mounted at the tibia such that the heel was elevated 10mm. An electric servo actuator applied tension to the Achilles tendon until measured vertical ground reaction force was 750N. This load was modulated as a 250N load was applied to the flexor digitorum longus (FDL), so that the ground reaction force remained 750N. Tests performed on nine feet yielded axial loads and plantar-dorsal moments in the second metatarsal of 450 ?303N, and 4.01 ?3.71N-m, respectively. These tests provide experimental data for validation of the current model.

PROCEDURES

The finite element model is a two-dimensional, plane strain sagittal section, and incorporates the second metatarsal, proximal phalanx, and plantar and dorsal soft tissue (Figure 1). The metatarso-phalangeal joint has been simplified by constructing a rigid body attached to the articular surface of the proximal phalanx, and to a node at the center of rotation. This center node is fixed in X- and Y- displacement to a coincident node of the metatarsal head, but is free to rotate about this node. In this way a hinge joint is formed that can transfer loads and produce reasonable kinematic motion in the joint. In addition to the continuum of soft tissue used in previous studies, an exemplar flexor tendon has been added. Flexor tendons in the forefoot pass over the condyle of the metatarsal heads, with some intervening soft tissue. Essentially, the tendon passes through the soft tissue continuum, so it is reasonable to assume that, in a two dimensional model, the tendon is superimposed on the continuum of plantar soft tissue. The tendon was represented in this model by quadrilateral continuum elements. This interaction was modeled by a sliding interface between the top surface of the tendon elements and the bottom surface of a line of elements intervening between the metatarsal head and tendon. The flexor tendon thus wraps around the metatarsal head. It is attached to the distal end of the proximal phalanx. Note that the actual FDL and FDB flexor tendons attach to the distal and middle phalanges, respectively, and that this is simply a representative model to test the feasibility of flexor tendon modeling.

Figure 1 - Sagittal plane FE model of the second ray with added flexor tendon.

During solutions, nodes at the proximal end were tied to a rigid surface. This rigid surface was also tied to a node lying at the intersection of the proximal metatarsal and that metatarsal's neutral axis. This node was fixed by boundary conditions in displacement and rotation, which in turn fixed the rotation and displacement of all the nodes on the proximal end. The advantage of this arrangement over previous methods of restraining the proximal end is that both reaction forces and reaction moments can be determined from static solutions. These reactions are similar to those borne by the cuneiform joint at the proximal end of the metatarsal.

Loading of the model was applied through a rigid surface in contact with the plantar surface. In this way known or measured ground reaction forces can be applied to the model and plantar pressures can be determined. In the model solutions, no friction was used in the contact surface, and the foot was allowed to make or break contact with the ground.

Material properties used in the model include a Young's modulus and Poisson's ratio obtained from published values for bone. The flexor tendon had stiffness one tenth the stiffness used for bone. The soft tissue continuum was given second order polynomial hyperelastic behavior as defined by the Abaqus "hyperelastic" material model. Coefficients obtained from compression of the heel plantar fat pad were used to approximate the sub-metatarsal material.

RESULTS AND DISCUSSION

The model was tested by applying loads and determining reaction forces measured by Sharkey, et al. (1995). A 188N ground reaction load to the second ray was determined by weighting the loads to the five rays as follows: 3-2-1-1-1 for the first through fifth rays, respectively. Loading to the flexor tendon was directed along a 10 degree angle from the X (horizontal) axis, and its magnitude was varied until the axial load and bending moment in the metatarsal was within the range measured by Sharkey, et al. (1995). Figure 2 shows Y direction normal stress contours in the soft tissue from two load cases: one with no load on the flexor tendon, an the other with a 250 N load at a 10 degree angle with the ground surface. Without the load in the flexor tendon, the phalanx is free to extend dorsally as the soft tissue beneath it is compressed.

Figure 2 - Stress contours on deformed geometry for the two FDL loading conditions. Highest stress contours were 900 kPa in the unloaded flexor condition.

Peak normal interface stress (plantar pressure) is seen to be located near the metatarsal head. The normal reaction force in the metatarsal was 59 N and the moment was 10.34 Nm. When a 250 N load was applied to the flexor tendon, the axial reaction force in the metatarsal increased to 306 N and the bending moment decreased to 7.64 Nm, which correspond to the range of values obtained by Sharkey, et al. (1995). The tension in the flexor tendon served to counter the moment in the metatarsal created by the vertical load, and at the same time, to apply an additional axial load. The plantar pressure distribution shown in the figure reveals a shift in focal plantar pressure toward the proximal phalanx. It is believed that this shift in loading does occur during gait. There is also a dramatic reduction in the magnitude of the peak pressure - indicative of the load sharing between the sub-metatarsal head and sub-phalangeal regions as a result of muscle action. Additional refinement of the model, such as adding the middle and distal phalanges, should further improve the prediction of plantar pressure distribution.

Figure 3 - Normal interface stress (plantar pressure) for the two FDL loading conditions. Stress is in kPa.

REFERENCES

Lemmon , D.R., Shiang, T.Y., Hashmi, A., Ulbrecht, J.S., Cavanagh, P.R., J. Biomechanics, (In Review).

Sharkey, N.A., Ferris, L., Smith, T.S., Matthews, D.K., Journal of Bone and Joint Surgery, 77-A(7):1050-1057, 1995.

Stokes, I.A.F., Hutton, W.C., Stott, J.R.R., J. Anatomy, 129(3):579-590, 1979.

ACKNOWLEDGMENT

The authors would like to acknowledge helpful discussions with Dr. Neil Sharkey which led to the refinement of this model.