Numerical Simulation of Mechanical Interaction
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Journal of Information & Computational Science 1: 1 (2004) 15– 19 Available at http://www.joics.com Numerical Simulation of Mechanical Interaction betweenLower-limb and Compression Stocking , X. Dai, Y. Li∗R. Liu, Y. L. Kwok Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hong Kong, China Received 11 June 2004; revised 2 September 2004 Abstract Stocking compression exerted on lower limb is effective to prevent and manage various venous diseases, such as varicose vein, oedema, and deep vein thrombosis. Different diseases and different stage of a disease may require compression of different degrees. The purpose of this study is to theoretically examine the pressure distribution on leg and the mechanical state of the leg under stocking pressure. A FEM approach is used to simulate the dynamic put-on process of a knee-length stocking. A biomechanical solid model consisting of soft tissue and bones is built for the lower leg, and an orthotropic shell model is built for the stocking. With this approach, a stocking simulation involving different materials, and a lower leg was carried out. Reasonable pressure and stress distributions in the stocking and the lower leg are obtained. The comparison between the simulated pressure values and the respective measured results confirms that this approach is able to predict the pressure of stockings exerted on the legs. Keywords: Biomechanical model; Pressure distribution; Compression stocking 1 Introduction For over 150 years, compression stocking has been used as a treatment for venous and lymphatic disorders, such as deep vein thrombosis(DVT), superficial phlebitis, as well as in chronic conditions, such as leg ulcers, lymph-edema, and so on [3, 5]. Different diseases and different stage of a disease may require compression of different degrees. Compression stocking may be designed to apply graduated or uniform compression. Graduated compression refers to the application of varying degrees of constant compression to different segments of the leg, with pressure being greatest at the ankle and gradually decreasing proximally. Graduated Compression Stockings(GCS) have been reported that can enhance venous return, reduce stasis by providing graded compression with the greater pressure applied more distally . As a key factor in the compression therapy, the pressure itself has not been investigated sufficiently. The pressure exerted by a GCS may vary among individuals, different levels of a same leg, and even different regions at a same level. Although there are several approaches that have been reported to model the soft tissue deformation under external pressure [2, 1, 4], there is still few effective methods to evaluate the pressure exerted by GCS, and the mechanism of the compression therapy is still not clear. Our aim is to theoretically investigate the interaction between a leg and a GCS, to predict the pressure accurately, and further to fundamentally un-derstand the mechanism of the compression therapy exerted by stockings. For these purposes, we develop a contact model to simulate the mechanical interaction between a stocking and a leg. A knee-length GCS is modelled numerically to derive pressure distribution and compared with experimental measurement. 2 Biomechanical Model 2.1 3-D geometric models of lower leg and stocking The legging of a compression stocking is usually a round-knitted tube, after fitted to a leg, it will take the shape of the leg surface. To obtain this 3-dimentional leg-fitted shape, and also the actual mechanical state for the stocking, a common way is to simulate a dynamic putting-on process. A simplified model including soft tissue and two bones(the medial tibia and the lateral fibula) is used to model a lower leg during standing still. The geometrical model of a lower leg is reconstructed from Magnetic Resonance Imaging(MRI) coronal images. Fig. 1(a) shows the soft tissue layer of the lower leg. (a) Lower leg (b) Legging of stocking Fig. 1 Geometrical models We use a kind of commercial GCS with medical effect to prevent and manage varicose vein as a sample, and simulate its dynamic wearing on the leg. The stocking size is chosen properly according to the lower leg’s dimension. The legging of the stocking is of cylindrical shape. We build a cylindrical tube shown in Fig. 1(b) as the initial geometry of the legging, and its size is taken from the actual sample. 2.2 Material properties We made an assumption that the medial tibia and the lateral fibula do not deform due to wearing stocking, so the bones are assumed to be rigid. The soft tissue material is assumed to be Part W(tonne/mm) E 1 (MPa) E 2 (MPa) G 12 (MPa) υ 1 t(mm) Ankle 2.1 × 10 − 10 0.098 0.147 0.052 0.113 0.8 Calf 2.10 × 10 − 10 0.093 0.059 0.029 0.369 0.76 homogeneous, isotropic and linear elastic. For the soft tissue, Young’s modulus, Poisson ratio, and mass density are taken as 0.01MPa, 0.49, and 9.37 × 10− 10 tonne/mm 3 respectively [2, 6]. Since knitted fabrics often have significantly different mechanical properties in wale and course directions, the material property for stocking is defined as orthotropic and linearly elastic. Two kinds of knit stitches are used for the ankle part and the calf part of the legging of the sample stocking respectively as illustrated in Fig. 1(b). Hence the two parts have different mechanical properties. All the parameters used in the numerical analysis are listed in Table 1, where E 1 and E 2 denote the Young’s moduli in the course and wale directions respectively, G 12 and υ 1 are the shear modulus and Poisson ratio, and t denotes the fabric thickness. 2.3 Finite element analysis 2.3.1 Model discretization The model was elaborated using the ABAQUS 6.4 FE software package. Automatic division was used to generate meshes of 4-node linear tetrahedron solid elements for bone and soft tissue respectively with the global seed size of 8mm, as well as a mesh of 4-node quadrilateral membrane elements for the legging, whose global seed size is 3mm. Each node has three degrees of freedom. 2.3.2 Contact constraints The interface between a legging and a lower limb is considered as surface-to-surface contact, the surfaces can undergo finite sliding relative to each other. Finite sliding allows arbitrary motion of the surfaces forming the contact pair. A penalty method is employed to enforce a kinematical constraint that the slave surface nodes(inner surface of legging) do not penetrate the master surface(lower leg surface). Forces(pressures) that are a stiff linear function of the penetration distance(overclosure) are applied to the slave nodes to oppose the penetration into the master faces, while equal and opposite forces act on the master surface at the penetration point. And then the master surface contact forces are distributed to the nodes of the master faces being penetrated. 2.3.3 Boundary condition We assumed that the medial tibia and the lateral fibula do not deform due to wearing sock, therefore the displacements of all the nodes on the two bones are constrained in all directions as boundary condition in the simulation. For the legging, along the lower leg length direction, the displacements of both the top and the bottom welts are defined while in the cross-sectional plane they can deform freely according to the shape of the lower leg. 2.3.4 Numerical solution The geometric non-linearity due to the large deformation of the stocking, and the boundary non-linearity due to the discontinuous contact constraints make the mechanical simulation com- plicated. ABAQUS/Explicit, which is well suited for nonlinear analysis, is used to solve the dynamic system. Page 4 18 X. Dai et al. /Journal of Information & Computational Science 1: 1 (2004) 15– 19 3 Experimental Results and Discussions Fig. 2 shows two frames taken from the dynamic wearing simulation, the top frame is during the putting-on process, and the bottom one is the final completed state. From these figures we can notice that once the contact occurs, the interaction between the lower leg and the stocking stretches the stocking, meanwhile inducing pressure on the lower leg. As the contact area in- creases, the pressure also spreads. As the stocking becomes much more stretched, the pressure value increases. However, even at the final state, the pressure does not distribute uniformly all over the lower leg. Due to the complicated geometrical feature of the lower leg surface, the legging is not in contact with the underlying leg everywhere. (a) Stress in Stocking (b)Pressure on leg surface Fig. 2 Dynamic wearing of a stocking on a leg (a) Measurement position (b) Pressure values Fig. 3 Pressure exerted on leg At the final wearing completed state, the ankle part shows significant higher stress than that at the calf part due to the difference of mechanical properties of the materials used for the two parts. It results in that the pressure value decreases as going up from the ankle to the calf. This pressure gradient is usually demanded in compression therapy. Page 5 X. Dai et al. /Journal of Information & Computational Science 1: 1 (2004) 15– 19 19 To confirm the simulated results, the wear trial of the stocking on the subject whose leg is scanned for the simulation is carried out, and the pressure in situ is measured. The measurement positions are illustrated in Fig. 3(a). Comparing the measured pressure values to the respective simulated results, good agreement is obtained as shown in Fig. 3 (b), where “ M” and “ S” denote measured pressure and simulated pressure respectively. 4 Conclusion The dynamic putting-on simulation demonstrates that the pressure exerted on leg is induced due to the fabric stretch, and its value depends on fabric tension and the curvature of the leg surface. The comparison between the simulated results and the experimental measurements confirms that the model is able to assess the pressure with satisfied accuracy. With the stocking wearing model, the overall pressure distribution can be predicted in a quick and easy way. It will be helpful in the clinical practice and the design of compression stockings. Through this model, the further investigation on the internal mechanical state of the leg is expected to help us understand the mechanism of compression therapy. Acknowledgment We would like to thank the Hong Kong Polytechnic University for the funding of this research through the project G-YD31 entitled “ Biomechanical Sensory Functional Design of Socks” . References  R. G. M. Breuls et al., A theoretical analysis of damage evolution in skeletal muscle tissue with reference to pressure ulcer development, J. Biomech. Eng 125 (12) (2003) 902-909.  G. H. Dai, J. P. Gertler and R. D. 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