The model predicts that the total contact force across the TC joint reaches maximum values of 5.4 BW during walking and 11.1 BW during running (Fig. 6). Across the CC joint, maximum loads are 4.2 and 7.9 BW, for walking and running (Fig. 6). For both joints, the peaks occur at 70% of stance for walking and at 60% of stance for running. Slightly elevated TC joint loading of 3.1 BW is observed for the high impact load.
The compressive principal stress trajectories extend from the subtalar joint surface posterior to the insertion of the Achilles tendon and anterior toward the superior surface of the calcaneocuboid joint (Fig. 8 a). Tensile trajectories extend along the inferior aspect of the calcaneus (Fig. 8b). A 20-mm thick sagittal CT scan section of the calcaneus and a 3.5-mm thick histologic section illustrate the correspondence between bone architecture and the principal stress trajectories (Fig. 8c and 8d).
This study demonstrates that the magnitude of loading in the hindfoot increases throughout the gait cycle, peaking in the later portion of stance. The shape of the force-time curve for all of the variables examined in this study corresponds qualitatively with the moment about the ankle joint, which is calculated from the external GRF. As the moment arm of the GRF, extending from the center of rotation of the ankle to the location of the center of pressure, increases during gait, the moment increases, which is balanced internally by the force in the Achilles tendon. Comparison of the results for walking versus those for running show that the peak ligament and tendon forces during running are scaled from those during walking by a factor of two at the two gait speeds analyzed. This corresponds to the scale factor, for these trials, of the peak moments about the ankle joint.
Low-magnitude loading during the early stance phase suggests that the vertical impact peak does not play an important role in stress generation in the calcaneus. The results for the high-impact case show only slight increases in the talocalcaneal joint contact force magnitudes early in the gait cycle. For the kinematic data analyzed, the impact peak occurs as the line of action of the GRF passes close to the center of the ankle joint, resulting in only small magnitude moments being generated about the ankle joint. Increasing the magnitude of the GRF during this portion of gait only increases the TC joint load, with no effect on the other loads evaluated in the model. The exact etiology of injuries to the foot during gait, and during running in particular, is unknown, making it difficult to conclude that this portion of gait is insignificant. However, if the likelihood of injury is related to force magnitude, then the greatest potential for injury is during mid-to-late stance when maximal calcaneal loading occurs, as has been suggested by Scott and Winter (27).
The results demonstrated quantitative agreement with previous numerical models and in vivo measurements. During running, the model of Scott and Winter (27) found peak Achilles tendon loads of 6.1–8.2 BW, ankle compressive joint loads of 10.3–14.1 BW, and plantar fascial loads of 1.3–2.9 BW, with the maximum values occurring in late mid stance, compared with our model predictions of 7.7, 11.1, and 3.7 BW, respectively. Komi (18) measured the force in the Achilles tendon in vivo during walking and running. From a curve fit of his data relating running velocity to Achilles tendon force, we found that our model prediction of 7.7 BW closely agrees with the experimental result of 7.5 BW. Additionally, the patterns of loading throughout the stance phase of gait predicted by our model agree with the in vivo force profile in the Achilles tendon during both walking and running (18).
The results suggest that the load conditions at late mid stance, 70% for walking and 60% for running, will provide the largest and perhaps most influential stimulus to the bone tissue during the gait cycle. This result may be somewhat approximate due to the relatively low number of sampling points used in our analysis. Based on these results, we would expect that bone remodeling simulations would be able to predict many of the bone morphological features based on the application of the peak-load case alone. The peak SE for running was four times that for walking, suggesting that calcaneal bone density in runners would be much higher than in a nonrunning population. Whalen et al. (33) hypothesized that stress magnitudes have a greater influence on bone mass than the number of cycles of loading. Although the number of running cycles per day for a typical runner is much less than the number of walking cycles, the running cycles, due to the large magnitude SE, could be influential in determining the bone mass or density distribution.
The geometry of the calcaneal model was represented in the mid-sagittal plane and did not consider the effect of out-of-plane loading. Because locomotion is primarily forward motion, we would expect that the majority of muscle and soft tissue action is in the plane of progression of the body during walking. Eng and Winter (10) performed a three-dimensional kinematic analysis of the lower limbs and determined that the magnitude of the sagittal plane moment was > 10 times that of the moments generated in the frontal and transverse planes and that 93% of the work performed at the ankle joint occurred in the sagittal plane. These results indicate that modeling the calcaneus in the sagittal plane is a reasonable assumption in terms of the directions of major load application.
We assumed that the center of rotation of the ankle joint and the end of the Achilles tendon were fixed, modeling the ankle joint as a single degree-of-freedom hinge. The extent to which the COR of the ankle joint translates during normal gait is still a subject of some debate. Anthropometric data suggests that the talocrural joint can be considered to be a single-axis joint (16), although in vivo kinematic analysis suggests that the COR does move somewhat within the sagittal plane during weight-bearing activities (25). In vivo magnetic resonance imaging (MRI) imaging (24) of ankle motion demonstrated a significant increase in the Achilles tendon moment arm and small variations in the location of the COR within the talar body during passive plantarflexion from 100 to 150 degrees; however, within the range of normal ankle flexion during stance (60° in dorsiflexion to 110° in plantarflexion (19)), the study of Rugg et al. (24) did not show significant changes in the tendon moment arm length or the location of the COR. Carrier et al. (7) examined the relationship between muscle and GRF moment arms in the foot and found that the change of the Achilles moment arm during stance, of less than 15%, is insignificant relative to the change in the moment arm of the GRF, which changes by as much as a factor of 20. Given the existing information regarding the location of the COR and the change in the Achilles tendon moment arm during gait, fixing both of these for the analysis is a reasonable approximation.
In the present study, we have developed a two-dimensional contact-coupled model of the foot that incorporates experimentally measured kinetic and kinematic data to examine the internal loading of the foot during walking and running. This biomechanical model allowed for direct application of the external ground reaction force, such that a priori assumptions regarding the calcaneal boundary conditions were not needed. This work represents an important first step in understanding the loading on the calcaneus, how loads vary during the gait cycle, and the resulting stress distributions within the calcaneus. This work is not only valuable to the field of foot mechanics, providing insight into the relationship between external loading and internal force generation in the foot, but is also of value to the study of functional bone adaptation, providing a model that can be applied clinically to examine the relationship between activities loading the foot and the generation of bone stresses.
We thank Scott Tashman for his collaboration on the gait analysis and for the use of his lab. We also thank Chye Yan and Cliff Les for their assistance.
This work was supported by the American Association of University Women, Veterans Affairs grants (B802-RA and A501–3RA), and NASA (NCC2–5121).
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