GIDDINGS, V. L., G. S. BEAUPRÉ, R. T. WHALEN, and D. R. CARTER. Calcaneal loading during walking and running. Med. Sci. Sports Exerc., Vol. 32, No. 3, pp. 627–634, 2000.
Purpose: This study of the foot uses experimentally measured kinematic and kinetic data with a numerical model to evaluate in vivo calcaneal stresses during walking and running.
Methods: External ground reaction forces (GRF) and kinematic data were measured during walking and running using cineradiography and force plate measurements. A contact-coupled finite element model of the foot was developed to assess the forces acting on the calcaneus during gait.
Results: We found that the calculated force-time profiles of the joint contact, ligament, and Achilles tendon forces varied with the time-history curve of the moment about the ankle joint. The model predicted peak talocalcaneal and calcaneocuboid joint loads of 5.4 and 4.2 body weights (BW) during walking and 11.1 and 7.9 BW during running. The maximum predicted Achilles tendon forces were 3.9 and 7.7 BW for walking and running.
Conclusions: Large magnitude forces and calcaneal stresses are generated late in the stance phase, with maximum loads occurring at ∼70% of the stance phase during walking and at ∼60% of the stance phase during running, for the gait velocities analyzed. The trajectories of the principal stresses, during both walking and running, corresponded to each other and qualitatively to the calcaneal trabecular architecture.
Experimental determination of the ground reaction force (GRF) vector has allowed investigators to characterize the patterns of external load application to the foot during gait; however, the internal musculoskeletal forces that accompany these external loads and the relationship between the two are not as well understood. Better understanding of the internal loads generated by normal daily loading events such as walking and running can further our understanding of the relationship between bone structure and function. The calcaneus has become an important peripheral site for osteoporosis assessment (4,30,36). A model that relates kinetic and kinematic measurements to loads generated in the calcaneus during daily activities could be used to study the contribution of mechanics to bone development and maintenance. In addition, understanding the relationship between gait and force transmission in the foot is essential for devising methods of injury prevention and treatment.
The parameters that characterize the GRF profile for walking and running are largely dependent on gait velocity (1,5,17). During walking, there is an initial small peak in the vertical GRF, generated after ground contact and termed the “impact” peak, followed by a bimodal waveform with peaks ranging from 1.0 to 1.5 body weights (BW) (1,5,34). The profile for running has a more distinct initial impact peak, usually followed by a single maximum peak achieved at mid stance, ranging from 2.0 to 3.5 BW (5,9,20,34). Measurement of the GRF has been used extensively to evaluate causal factors for gait related injuries; however, the relationship between foot kinematics and kinetics and the resulting stresses in ligaments, joints, and bones is still unknown.
Invasive in vivo studies provide valuable information for validation of numerical models but are of limited practicality because they are difficult to perform and raise ethical questions. Computational modeling provides an alternative to in vivo experiments. Numerous biomechanical models have been developed to examine muscle forces during quasi-static walking and running (6,23,27–29,31). The objectives of these models are to solve the indeterminacy problem associated with the large number of unknown parameters and to estimate the internal loading. Seireg and Arvikar (28) utilized minimization of muscle forces and joint moments to solve for muscle and joint reaction forces in the lower extremity during walking. They found that the predicted muscle and joint reaction forces correlated with EMG data. Equilibrium methods have been applied to study the forces in the foot both during walking (23,29,31) and running (6,27). Procter and Paul (23) focused their analysis on the ankle joint, looking at the joint reaction and muscle/tendon forces during walking. They grouped muscles and weighted the forces based on the average tendon cross-sectional area. Scott and Winter (27) divided the lower leg into four static systems, using equilibrium methods to solve for muscle and ankle joint loads during running. Although all of these analyses provide information regarding the loading in and around the ankle joint, none offer a comprehensive analysis that includes an examination of the bone stresses.
Several finite element (FEM) models have been developed to examine the stress patterns in the calcaneus during loading (14,21,37). One of the main difficulties of constructing a FEM model of a biological structure is determining the physiological loading and constraining the structure without imposing nonphysiologic boundary conditions. Yettram and Camilleri (37) used an optimization routine to determine the loading on a two-dimensional FEM model of the calcaneus during static standing. They found qualitative agreement between the resulting stress trajectories and the orientation of apatite crystals in the calcaneus. Oxnard (21) and Hsu (14) examined the stress patterns in the calcaneus at three periods of the stance phase of walking: heel-strike, mid stance, and toe-off. Based on the similarity between the patterns of von Mises stress in the calcaneal models and the distribution of areal densities in the mid-sagittal plane, Hsu concluded that the patterns formed by the trabeculae in the calcaneus are predominantly influenced by the forces and the stresses induced during the toe-off phase of walking or running. Although this work represents an important first effort at numerical modeling of the calcaneus, it does have three limitations: 1) the loads applied to the calcaneus were assumed from the predictions of several different numerical models, thereby combining estimates of loading that do not guarantee equilibrium; 2) the displacement constraint across the calcaneocuboid joint, which enforces static equilibrium, results in stress artifacts and nonphysiologic tensile joint reaction forces; and 3) foot kinematics were not considered when determining the lines of action of muscle forces, ligament forces, joint distributed loads, or the GRF. Additionally, none of the FEM analyses performed to date examine the loading that occurs during running or present a methodology that couples kinematic and kinetic experimental data for evaluating calcaneal loading throughout the gait cycle.
The purpose of the present study was to develop a model of the calcaneus that does not require a priori assumptions regarding applied loads and joint pressures. This model was used to examine the loading on the calcaneus throughout the gait cycle for both walking and running using externally measured ground reaction forces and high speed cineradiography, to capture the positions of the skeletal structures directly in relation to the ground reaction force, as input into the model. The goal of this analysis was to evaluate the contribution of different loading events on the resulting joint contact forces, ligament and tendon loads, and bone stresses.
Biomechanical Engineering Division, Mechanical Engineering Department, Stanford University, Stanford, CA; Rehabilitation Research and Development Center, Veterans Affairs Health Care System, Palo Alto, CA; and Life Sciences Division, NASA Ames Research Center, Mountain View, CA
Submitted for publication April 1998.
Accepted for publication July 1999.
Address for correspondence: Virginia Giddings, Exponent Failure Analysis Associates, 149 Commonwealth Drive, Menlo Park, CA 94025. E-mail: firstname.lastname@example.org.