Journal of Biomechanics 38 (2005) 1045���1054 Three-dimensional finite element analysis of the foot during standing���a material sensitivity study Jason Tak-Man Cheunga, MingZhang a,*, Aaron Kam-Lun Leunga, Yu-Bo Fanb a Jockey Club Rehabilitation Engineering Centre, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China b Laboratory of Biomechanical Engineering, Department of Applied Mechanics, Sichuan University, Chengdu 610065, China Accepted 26 May 2004 Abstract Information on the internal stresses/strains in the human foot and the pressure distribution at the plantar support interface under loadingis useful in enhancingknowledge on the biomechanics of the ankle���foot complex. While techniques for plantar pressure measurements are well established, direct measurement of the internal stresses/strains is difficult. A three-dimensional (3D) finite element model of the human foot and ankle was developed usingthe actual geometry of the foot skeleton and soft tissues, which were obtained from 3D reconstruction of MR images. Except the phalanges that were fused, the interaction among the metatarsals, cuneiforms, cuboid, navicular, talus, calcaneus, tibia and fibula were defined as contact surfaces, which allow relative articulating movement. The plantar fascia and 72 major ligaments were simulated using tension-only truss elements by connecting the correspondingattachment points on the bone surfaces. The bony and ligamentous structures were embedded in a volume of soft tissues. The encapsulated soft tissue was defined as hyperelastic, while the bony and ligamentous structures were assumed to be linearly elastic. The effects of soft tissue stiffeningon the stress distribution of the plantar surface and bony structures during balanced standingwere investigated. Increases of soft tissue stiffness from 2 and up to 5 times the normal values were used to approximate the pathologically stiffened tissue behaviour with increasing stages of diabetic neuropathy. The results showed that a five-fold increase in soft tissue stiffness led to about 35% and 33% increase in the peak plantar pressure at the forefoot and rearfoot regions, respectively. This corresponded to about 47% decrease in the total contact area between the plantar foot and the horizontal support surface. Peak bone stress was found at the third metatarsal in all calculated cases with a minimal increase of about 7% with soft tissue stiffening. r 2004 Elsevier Ltd. All rights reserved. Keywords: Foot model Ankle Plantar pressure Soft tissue stiffness 1. Introduction Heel pain and ulceration of the diabetic foot are the most common complaints amongpatients with foot and ankle problems (Selth and Francis, 2000 Holewski et al., 1989). Patients with diabetes-related peripheral neuro- pathy are susceptible for developingulcers on the plantar foot surface, which frequently leads to hospita- lization and amputations of the lower extremities. One of the major causes of diabetic ulceration and painful heel syndrome is thought to be the presence of abnormally high plantar pressures (Holewski et al., 1989 Lobmann et al., 2001 Mueller et al., 1994 Onwuanyi, 2000 Reiber et al., 2002 Sage et al., 2001), which can be attributed from bony prominences, calluses, structural deformities or poor footwear fitting. Diabetic foot ulcers are highly associated with chronic pressure callus (Murray et al., 1996 Pitei et al., 1999 Sage et al., 2001), which is mainly a result of abnormal plantar tissue stiffeningin patients with neuropathy. Knowledge on the effect of soft tissue compliance or other structural characteristics on the stress distribution of the plantar foot surface and bony structures is essential to achieve an appropriate individualised treat- ment strategy such as an orthotic design. The pressure distributions between the foot and different supports were measured experimentally with ARTICLE IN PRESS *Correspondingauthor. Tel.: +852-27664939 fax: +852-23624365. E-mail address: rcmzhang@polyu.edu.hk (M. Zhang). 0021-9290/$- see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2004.05.035

the use of in-shoe pressure sensors and pedobarograph (Cavanagh et al., 1987 Lavery et al., 1997 Patil et al., 2002 Raspovic et al., 2000 Lord and Hosein, 2000 Lord et al., 1986). Due to the difficulties and lack of better technology for the experimental measurement, the load transfer mechanism and internal stress states within the soft tissues and the bony structures were not well addressed. In order to supplement these experiments, researchers have turned to computational methods. The finite element (FE) analysis has been an adjunct to experi- mental approach to predict the load distribution between the foot and different supports, which offer additional information such as the internal stresses/ strains of the ankle���foot complex. A number of foot models have been developed based on certain assump- tions such as simplified geometry, limited relative joint movement, ignorance of certain ligamentous structures and simplified material properties (Chen et al., 2001 Gefen, 2000 Gefen, 2003 Jacob and Patil, 1999 Kitagawa et al., 2000 Nakamura et al., 1981). The models developed by Jacob and Patil (1999) and Gefen (2003) have been employed to investigate the biomecha- nical effects of soft tissue stiffeningin the diabetic feet. Their models predicted that the peak plantar pressure was found to increase with soft tissue stiffness but with minimal effect on the bony structures. Gefen (2003) further speculated that the development of diabetic- foot-related infection and injury was more likely initiated by micro-damage of tissue from intensified stress in the deeper subcutaneous layers rather than the skin surface. It has been shown in the literature that FE models can contribute in familiarizingthe effects of thickness and stiffness of plantar soft tissue on plantar pressure distribution (Gefen, 2003 Jacob and Patil, 1999 Lemmon et al., 1997). A detailed model of the human foot and ankle, incorporatingrealistic geometrical properties of both bony and soft tissue components is needed to provide a more realistic representation of the foot and the supportingconditions, in order to enhance the understandingof the ankle���foot biomechanics (Camacho et al., 2002 Kirby, 2001). For the sake of convergence of solution and minimizingcomputational efforts, most of the linearly elastic FE foot models reported so far (Chen et al., 2001 Chu et al., 1995 Jacob and Patil, 1999) assigned relatively stiff mechanical properties for soft tissue, where the Young���s moduli were selected as being 1 MPa or larger. These values of Young���s moduli are much larger than those obtained from in vivo experimental measurements of plantar soft tissue, ranging from 0.05 to 0.3 MPa under strains of 10���35% (Gefen et al., 2001b Zhenget al., 2000). For FE models usinga nonlinear material model for plantar soft tissue (Gefen et al., 2000 Gefen, 2003 Nakamura et al., 1981 Lemmon et al., 1997), the adopted stress���strain beha- viour varied as a result of the intrinsic variation of individual tissue, measurement techniques and environ- ment. The stress���strain response of plantar soft tissue was often obtained from either indentation or compres- sion test of in vivo or cadaveric specimens (Gefen et al., 2001a Klaesner et al., 2002 Lemmon et al., 1997 Nakamura et al., 1981 Miller-Younget al., 2002). In the literature, there is still a lack of material sensitivity study to quantify the effects of soft tissue stiffeningon plantar pressure distribution usinga geometrical accurate three- dimensional (3D) foot model. The objective of this study was to develop a comprehensive FE model of the foot and ankle, using 3D actual geometry of both skeletal and soft tissues components and to investigate the effect of soft tissue stiffness on the plantar pressure distributions and the internal load transfer between bony structures. 2. Methods The geometry of the FE model was obtained from 3D reconstruction of MR images from the right foot of a normal male subject of age 26, height 174 cm and weight 70kg. Coronal MR images were taken with intervals of 2mm in the neutral unloaded position. The images were segmented using MIMICS v7.10 (Materialise, Leuven, Belgium) to obtain the boundaries of skeleton and skin surface. The boundary surfaces of the skeletal and skin components (Fig. 1a) were processed usingSolidWorks 2001 (SolidWorks Corporation, Massachusetts) to form solid models for each bone and the whole foot surface. The solid model was then imported and assembled in the FE package ABAQUS (version 6.4, Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI, USA). The FE model, as shown in Figs. 1b and c, consisted of 28 bony segments, including the distal segments of the tibia and fibula and 26 foot bones: talus, calcaneus, cuboid, navicular, 3 cuneiforms, 5 metatarsals and 14 components of the phalanges. The phalanges were fused together with 2mm thick solid elements, which simu- lated the connection of the cartilage and other connective tissues. The interaction amongthe metatar- sals, cuneiforms, cuboid, navicular, talus, calcaneus, tibia and fibula were defined as contact surfaces, which allow relative articulatingmovement. To simulate the frictionless contact between the joint surfaces, ABA- QUS automated surface-to-surface contact option was used. Compressive stiffness resemblingthe cartilage structure (Athanasiou et al., 1998) was prescribed between each pair of joint contact surfaces to simulate the coveringlayers of articular cartilage. Except the collateral ligaments of the phalanges and other con- nective tissue, a total number of 72 ligaments and the plantar fascia were included and defined by connecting ARTICLE IN PRESS J.T.-M. Cheung et al. / Journal of Biomechanics 38 (2005) 1045���1054 1046