Stress distribution of the foot during mid-stance to push-off in barefoot gait: a 3-D finite element analysis
Introduction
The foot is one of the most important weight-bearing, and shock-absorbing structures in the human body during ambulation. It has been pointed out by many researchers that biomechanical factors play an important role on the etiology, treatment, and prevention of many foot disorders [1], [2]. Therefore, it is essential to understand the biomechanics associated with the normal foot before any foot orthosis or surgical intervention can be applied.
The biomechanics of the foot and footwear has been better understood owing to the recent scientific advances in both measurement instrumentation and theoretical methodology. In recent literatures, many experimental techniques were developed and employed for the quantification of foot biomechanics, such as gait analysis [3], pressure sensing platforms [4], in-shoe pressure transducers [5], [6], [7], pressure sensitive films [8], cadaveric experiments [9], [10], and in vivo force measurements [11]. The above-mentioned measurement techniques are commonly used in predicting joint kinetics and quantifying plantar pressure distributions. However, bones, soft tissue, and associated joint stresses inside the foot were less investigated and remained unclear. It is very difficult to quantify the in vivo bone and soft tissue stress with the existing experimental techniques. As for in vitro studies, the loading conditions were often different from the actual physiological loading situation as the foot structure was compromised. Therefore, no overall stress distribution of the whole foot is known using the currently available measuring techniques.
Besides the experimental techniques, many theoretical models, such as kinematic models [12], mathematical models [13], [14], and finite element models [15], [16], [17], [18] of the foot had been developed. Finite element method has been used increasingly in many biomechanical investigations with great success due to its capability of modeling structures with irregular geometry and complex material properties, and the ease of simulating complicated boundary and loading conditions in both static and dynamic analyses. Therefore, it has become a suitable method for the investigation of foot stress distributions. Although many finite element analyses of the foot or footwear were performed in previous literatures, many were 2-D approximations [17] with only part of the foot discussed [18]. Even with 3-D finite element models [15], [16], only simplified geometry and static loading conditions were discussed. Therefore, a more detailed finite element model is essential to provide an overall representation of the foot.
The objective of this research was to establish a preliminary 3-D finite element model of a normal foot, and to estimate the stress distribution in the foot during mid-stance to push-off phase during barefoot gait. In the finite element foot model, major bones and soft tissues of the foot were identified based on the computed tomographic (CT) sectional images. Quasi-static loading condition simulating barefoot gait during mid-stance (starting from heel-off) to push-off was applied and the stress distributions both in the plantar region and the interior bones were quantified. Experimental plantar pressure results from previous literature for normal barefoot gait were compared with the results from our finite element analysis for validation purpose.
Section snippets
Finite element model generation
The right foot of a 24-year-old male subject without any foot pathology was chosen for the construction of the finite element model. CT scan images of the foot were obtained in order to provide geometric information of the foot. The subject was lying in supine position with a custom-molded ankle-foot orthosis (AFO) to place the foot in a neutral position during CT scanning. A series of 136 scans at 2 mm interval was made in the frontal plane direction. The resolution for each of the CT scan was
Results
Unlike other experimental measurements, the finite element analysis has the benefit of quantifying the overall deformation, stress, and strain distributions of a structure to be analyzed. Following the analysis, we chose to display the normal stress at the plantar surface and the von Mises equivalent stress at the skeletal parts of the foot at four different loading instants (0.03, 0.06, 0.09, and 0.12 s). The stress distributions of the plantar surface (normal stress) and the bones (von Mises
Discussion
Several observations were found from the plantar stress distributions during mid-stance to push-off phase. The peak plantar stress occurred under the second metatarsal at t=0.03 s and t=0.06 s. At t=0.09 s and 0.12 s, the peak stress shifted to the plantar region under the other metatarsals. It was found that the peak stress region occurred in the forefoot and shifted from the plantar region under the second metatarsal towards the other metatarsals from mid-stance to push-off phase.
In order to
Conclusion
The present study provides a preliminary computational model that is capable of estimating both the plantar foot pressure and the stress in the bone. Although many assumptions were still inevitable in the current model, it can provide quantitative analysis of normal and pathological foot and ankle motion. In the future, when this preliminary model is further improved, it would be possible to identify areas of increased pressure and correlate the pressure with foot pathology. Potential
Acknowledgments
This study was supported by the grant from the National Science Council of the Republic of China (grant no. NSC-89-2614-E-033-001). The computing facilities provided by the National Center for High-Performance Computing are greatly appreciated.
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