Mesh Morphing for Accelerated Representation of Patient-Specific Foot Geometry in Finite Element Analysis

Tadepalli, S C; Bafna, R; Erdemir, A; +Cavanagh, P R +University of Washington, Seattle, WA, Cleveland Clinic Foundation, Cleveland, OH [email protected] INTRODUCTION: Finite element (FE) models of the foot and footwear are useful to study the functional behavior of the foot-shoe interface. FE models of the foot of varying complexity, comprised entirely of tetrahedral/hexahedral elements or a combination of both, have been previously developed (13). Hexahedral elements have been shown to have superior performance compared to tetrahedral elements (4) and in FE analysis of the foot, this becomes apparent as the convergence behavior of simulations are hindered by large deformations, material incompressibility, and contact with high friction. De novo development of such complex patientspecific models comprised entirely of hexahedral elements is prohibitively time consuming. The present work explores the development of a semi-automated technique that can aid in the rapid creation of patient-specific FE models through morphing of stock (generic) meshes. The procedure is based on measurement of the patient’s plantar soft-tissue thickness at various locations obtained from clinically available imaging modalities. METHODS: A previously developed, forefoot mesh, fully comprised of hexahedral finite elements (26,324 elements generated using TrueGrid) was used in this study (5). This served as an initial stock mesh for the morphing process. The morphing algorithm was implemented in C++ using VTK and the graphical user interface was developed using KWWidgets (6). Morphing was based on overall foot dimensions and specific soft tissue thickness measurements at 10 points underneath the metatarsal heads and the proximal shafts. The morphing process was initiated with the selection of the landmarks on the plantar surface of the forefoot followed by the identification of the bony prominences (Figure 1 a, b). Then, an overall scaling of the generic mesh was performed so as to represent the patient-specific foot width and height. Later, based on the patient’s ultrasound or MRI data, the metatarsal bones were “moved” within the soft tissue boundaries so as to represent the patient-specific soft tissue thickness under each metatarsal head and proximal shaft. The remainder of the internal points (nodes) were smoothly interpolated using Bookstein’s thin plate spline algorithm (7). Mesh generation was followed by the model development process. For solving the model in ABAQUS, bones were modeled as rigid and soft tissue was modeled using a hyperelastic (Ogden) material model. Plantarflexion/dorsiflexion of the tarso-metatarsal and metatarsalphalangeal joints were represented by the hinge and the connector features available in ABAQUS (8) (Simulia, Providence, RI). Connector motion was fixed throughout the analysis and contact with a frictional coefficient of 0.5. To simulate the loading of the forefoot during ground contact, experimentally determined ground reaction forces of 485N vertical, 13N anterior/posterior and 11 N medial/lateral were applied to the midfoot of the model. RESULTS: Figure 1 shows cross sections of the forefoot before (Figure 1c) and after (Figure 1d) morphing. The change in tissue thickness under each MTH is shown in Figure 1e. A maximum error of 4.1% in tissue thickness was observed under the 3 metatarsal head in the morphed mesh. As can be clearly seen from the Figure 1(f) and (g), the plantar pressure distribution predicted by the simulation was changed markedly as a result of the change in the plantar soft tissue thickness. DISCUSSION: Custom software has been developed for morphing existing FE meshes of the forefoot to create patient–specific FE meshes. This technique primarily relies on measurements that can be obtained in the clinic via the use of the ultrasound. This approach has significantly reduced the time required to generate patient-specific FE meshes compared to conventional meshing techniques (~20 minutes compared to ~80 hours). Previously, mesh morphing has been successfully applied to model the human femur (9) and rat caudal vertebra (10) but, to our knowledge not to model embedded biological structures. This method enables accurate representation of soft tissue thickness which in the foot has been found to be a good predictor of peak plantar pressure (11) . Such patientspecific FE meshes will ultimately aid in the design of therapeutic footwear for diabetic patients. Efforts are underway to extend the method to the entire foot. Figure 1: (a) Fixed landmarks on the plantar surface of the forefoot. (b) Landmarks under the bony prominences. (c) Cross sectional view of the stock mesh (bones shown in orange, soft tissue shown in green). (d) Changes in tissue thickness under the metatarsal head before (black) and after the morphing (red). Delta t indicates the change in the thickness pre/post morphing (e) Cross sectional view depicting the thickness of the morphed mesh. (f) Plantar pressure distribution of the stock mesh. (g) Plantar pressure distribution of the morphed mesh.