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From CT Scan to Plantar Pressure Map Distribution of a 3D Anatomic Human Foot

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From CT Scan to Plantar Pressure Map Distribution of a 3D Anatomic Human Foot Excerpt from the Proceedings of the COMSOL Conference 2010 Paris From CT Scan to Plantar Pressure Map Distribution of a 3D Anatomic Human Foot P. Franciosa, S. Gerbino* University of Molise, School of Engineering *Corresponding author: Via Duca degli Abruzzi - 86039 Termoli (CB) – Italy [email protected] Abstract: Understanding the stress-strain behav- methods, based on FE modeling, have also been ior of human foot tissues and pressure map dis- adopted. FE models of human foot have been tributions at the plantar interface is of interest developed under certain simplifications and as- into biomechanical investigations. In particular, sumptions (see [7] and [8]) such as: (i) simplified monitoring plantar pressure maps is crucial to or partial foot shape, (ii) assumptions of non- establishing the perceived human comfort of linear hyper-elastic material law, (iii) ligaments shoe insoles. and plantar fascia modeled as equivalent forces In this contest, a 3D anatomical detailed FE hu- or elastic beams/bars, (iiii) no friction or thermal man foot model was created, starting from CT effect, at plantar foot interface, accounted. (Computer Tomography) scans of a 29 years old Based on these assumptions, valuable 3D FE male. Anatomical domains related to bones and models were presented in the literature [9], [10]. soft tissues were generated, using segmentation In this contest, the geometrical complexity of techniques, and then processed into a CAD envi- foot structure was captured through reverse en- ronment to model 3D domains by using gineering methodologies, based on CT (Com- loft/sweep and boolean operations. Finally, FE puter Tomography) or MR (Magnetic Reso- model was generated into Comsol Multiphys- nance) scans. Starting from high resolution ics® 3.5a, by assigning contact pairs and defin- medical images, suitable FE models were gener- ing non-linear material laws. Particular attention ated by using segmentation procedures. was posed on fine tuning the calculation strongly In the present paper, how to face out the 3D dependent on the convergence parameters influ- geometry reconstruction of the human foot into enced by the contacts and hyper-elastic material Comsol Multiphisics® 3.5a is investigated. properties. Comsol Multiphisics® offers a direct link with two of the most powerful commercial tools able Keywords: CT scan, CAD foot model, hyper- to generate 3D tetrahedral mesh models starting elastic material, contact analysis, plantar pressure from stack-up images: ScanFE® (by Simple- map. ware®) and Mimics® (by Materialise®) [11]. However, as reported and experimented yet in 1. Introduction [12], so-imported mesh models cannot be edited in Comsol Multiphisics®. This program, when It was reported that the perceived comfort working on tessellated geometries, creates ra- related to the human foot can be associated to the tional Bezier patches, defining boundary or do- contact pressure generated at the plantar - insole main equations. Manipulating or editing those interface [1]. High values of pressure can gener- boundaries/domains, which requires geometry ate pain or pathologies due to the obstruction of decomposition analysis, is not allowed. blood circulation in areas with peak values of To avoid all these crucial issues, one should pressure. Experimental studies have pointed out create B-rep CAD geometry starting from seg- a relationship between perceived comfort and mented surfaces, extracted from stack-up images. plantar pressures [2], [3]. Over years, many re- If, on one hand, this stage may be time consum- searchers have addressed their attention on ing, on the other hand a suitable CAD geometry minimizing the plantar pressure, by varying in- model is finally available and ready to be post- sole footwear materials, thickness and anatomi- processed into any multiphysic simulation. cal shape [4], [5], [6]. The above approach was adopted, for exam- Recently, in order to give a valuable support ple, into [13], where, starting from MR scans, the to experimental investigations, computational foot geometry was created and then assembled into SolidWorks® CAD system. CAD model, the FE model was created directly In the present paper, the development of the into Comsol Multiphisics® for the non-linear detailed 3D anatomic FE model of a human foot analysis, by using the live-link between both is described. The balanced standing condition environments. Boundary conditions, contact and was simulated: the foot was supposed to be identity pairs were introduced. Domain equations touching an ideal-rigid ground. Hyper-elastic were set to simulate the non-linear hyper-elastic material law was assigned to soft tissues. Contact behavior of the foot soft tissue. pressures were calculated by adopting a non- linear static simulation. How to speed-up the 3. Foot Modeling solution convergence by fine-tuning non-linear tolerance, penalty factor and scaling value, was A CT (Toshiba® Aquilion 4 equipment) scan also highlighted. was performed on a 29 years old male (65 Kg). 345 slices were captured with a slice distance of 2. Methodology Overview 1.0 mm (see Figure 2.a). Scans were made for both feet in their neutral Figure 1 depicts the general work-flow posture in which there is the least tension or adopted in the present research. pressure on tendons, muscles and bones. Foot CT scan images .DICOM format (Toshiba® Aquilion 4) 3D Image reconstruction .STL format (ScanIP® module 3.2) Figure 2.a. DICOM image CAD modeling live-link (SolidWorks® 2010) FE modeling (Comsol Multiphysics® 3.5a) 2D segmented regions 3D reconstructed domains Figure 2.b. Segmented regions and 3D reconstruction Figure 1. Work-flow methodology Medical images were, then, exported into A 29 years old male was submitted to a CT standard .DICOM format (image resolution scan. Medical images of both feet were imported 512x512 pixels) and processed by using into ScanIP® module of Simplewere® software, ScanIP® tools. Generally speaking, DICOM where bones and soft tissues were extracted by images are gray-based images. Different gray- adopting density-based segmentation procedures. levels correspond to different density materials At this stage boundary surfaces, into the tessel- (Figure 2.b). Looking at DICOM images the lated format, were generated. Those surfaces following regions can be distinguished: soft tis- were, then, exported into .STL format and im- sue, bone, ligaments, plantar fascia and carti- ported into SolidWorks® CAD system. Here, lages. In the present paper, only bones and soft solid domains were generated by adopting tissue were segmented. Ligaments and plantar loft/sweep and boolean operations. From this fascia were added at FEM stage as equivalent load conditions (see also Section 4); instead, lated surfaces), lofting/sweeping/filling surfaces cartilages were modeled separately at CAD were generated as also described in [14]. stage. In order to reduce the reconstruction ef- Figure 4 shows the typical work-flow (first fort, slice pixels related to left foot were re- metatarsal bone used as example) adopted to moved. Thus, in the following only the right foot generate solid domains, starting from cross- will be analyzed. section curves. Figures 3.a and 3.b show the assembled bone CAD procedure is based on the following structure and the soft tissue domain as seen into criteria: ScanIP® environment, respectively. Bone struc- • minimum number of surface patches; and, ture was composed of 19 bones: tibia, fibula, • surface patches large as much as possible. talus, calcaneus, cuboid, navicular, 3 cuneiforms All this assures more flexibility in handling 3D (bones of the metatarsus), 5 metatarsals (bones mesh and boundary conditions at FEM stage. of the metatarsus) and 5 components of the pha- langes (bones of the toes). Phalange bones (a proximal and a distal phalanx for the great toe; proximal, middle and distal phalanges for the second to fifth toes) were fused together since their relative motion do not affect plantar pres- sures. a. Bone structure b. Soft tissue Figure 5. 3D CAD domains generated into SolidWorks® Figure 5 depicts the so-reconstructed CAD geometry. Cartilages that were not extracted into a. Bone structure b. Soft tissue the segmentation phase were then modeled into Figure 3. Tessellated surfaces generated the CAD system in order to joint bones and fill into ScanIP® environment the cartilaginous space (see Figure 5.a). Boolean operations were used to ensure congruence One should note that the so-generated do- among the related interfacial surfaces. For in- mains are geometrically described by the tessel- stance, the whole bone structure was subtracted lated boundary surfaces. from the soft tissue. Finally, toes at soft tissue These tessellated models were then imported level were merged together (Figure 5.b). into SolidWorks® CAD system by using the SCANto3D® add-in module to process and fixed boundary (UFS) manage imported tessellated surfaces. y x z a b c Figure 4. Generation of CAD model. a: tessellated geometry; b: cross-section curves; c: 3D CAD model ground Starting from cross-sections (created as inter- section curves between cut planes and the tessel- Figure 6. FE model as seen into Comsol Multiphisics® 4. FE Modeling Constant Value Ebone (MPa) 7300.0 The foot CAD model was thus imported into Ecartilage (MPa) 10.0 ν Comsol Multiphisics® 3.5a, by using the live- bone 0.30 ν link connection with SolidWorks®. cartilage 0.40 Here, domain equations, boundary conditions Table 2. Material constants for bones and cartilages [7] and solver settings were provided. In the present paper the balanced standing 4.2 Boundary Conditions condition was simulated. The foot was supposed to touch an ideal-rigid flat ground. For this pur- During the balanced standing condition, a pose the “ground” domain was added to the FE vertical force, corresponding to one half of the model (see Figure 6). body weight (F =650/2 N), is transferred from w the body to the foot and then to the ground. 4.1 Domain Equations The plantar fascia stabilizes the longitudinal arch of the foot and supports the longitudinal Materials were assumed linear and isotropic, forces during the weight application phase [8].
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