A generalized three-dimensional six-segment model of the ankle and the foot

Models estimating forces in internal structures of the ankle and the foot, use commonly one to three rigid body(ies) to mechanically represent the foot, and are limited to anterior-posterior movements. The purpose of this study was to develop a generalized three-dimensional representation of the ankle-foot complex resembling the actual functional anatomy for the estimation of the strain in ligaments at the tibio-talar and subtalar joint and for the estimation of bone-to-bone contact forces in the metatarso-phalangeal, the midtarsal, the subtalar, and the tibio-talar joints; and to investigate the influence of different model specifications on these estimates for a lateral side shuffle movement under two distinctly different conditions.

The model proposed in this study consisted of six rigid segments (segment 1: the phalangeals of the three medial rays, segment 2: the phalangeals of the two lateral rays, segment 3: the metatarsals of the three medial rays and the cuneiforms, segment 4: the metatarsals of the two lateral rays, the cuboid, and the navicular, segment 5: the calcaneus, segment 6: the talus) connected by joints allowing for three rotational degrees of freedom each. Ten long foot muscles and 5 ligamentous structures (the plantar aponeurosis, the anterior talo-fibular ligament, the calcaneo-fibular ligament, and two parts of the deltoid ligament) were included in the model. An inverse dynamics approach was used to derive the resultant joint forces and moments. Four different model specifications regarding the number of degrees of freedom at a joint, regarding unlimited or limited maximum muscle force, and regarding the distribution algorithm used to determine the muscle forces, were formulated. The 18DOF version of the model had three rotational degrees of freedom at each joint, no restriction to the maximum muscle force, and used a minimization algorithm to assign forces to the ten muscles. The 12DOF version of the model was similar to the 18DOF version with exception of the number of rotational degrees of freedom at three of the six joints (one rotational degree of freedom at the tibio-talar and at the metatarso-phalangeal joints). The 6DOF version considered each joint as a hinge joint and used Pierrynowski's (1982) muscle and neuro-physiological control model to calculate the forces in the ten muscles. The 1DOF version was similar to the 6DOF version but considered the foot as one rigid body with the tibio-talar joint as a hinge joint. Hicks' (1954) equation was used to calculate the force in the plantar aponeurosis.

The model was applied for a side shuffle movement performed by one subject under two different shoe conditions. A force distribution insole and four video cameras were used for the data acquisition.

The results showed that all four models estimated the same trend for the differences between the two shoe conditions. The magnitudes of the bone-to-bone contact force estimates varied greatly between the four models. The 18DOF and 12DOF models estimated excessive bone-to-bone contact forces. It was, therefore, speculated that the 6DOF model version with the muscle and the neuro-physiological control model was the most appropriate of the four versions for the representation of the foot as a mechanical system, considering the structures included in the model.

The representative application showed the model to be sensitive to small changes in the input variables, which makes the accuracy of the input variables a crucial factor. The results showed interesting differences between the two shoe conditions, especially in regard to ligament strain and the bone-to-bone contact forces. It was speculated that the model can provide new insight into the mechanisms causing injuries to the structures of the foot. The results of the study indicated that models should be used for comparative approaches and not for the determination of absolute magnitudes of internal forces.