A Multiscale Triphasic Biomechanical Model for Tumors’ Classification K. Barber and C.S. Drapaca, PhD Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA 16802, USA ABSTRACT The aim of this paper is to formulate a novel mathematical model that will be able to differentiate not only between normal and abnormal tissues, but, more importantly, between benign and malignant tumors. We present some very promising preliminary results of a multiscale triphasic model for biological tissues that couple the electro-chemical processes that take place in tissue’s microstructure and tissue’s biomechanics. The multiscaling is based on a recently developed homogenization technique for materials with evolving microstructure. 1. INTRODUCTION The ever-growing field of non-invasive diagnostic technologies is continually providing new insights into in vivo biological processes, requiring joint efforts among researchers in medicine, science, and engineering. One of these emerging technologies, Magnetic Resonance Elastography (MRE), uses an imaging technique to measure the elasticity of biological tissues subject to mechanical stresses [4, 5]. The resulting strains are measured using magnetic resonance imaging and the related elastic modulus is computed from models of tissues mechanics. The elastic modulus contains important information about the pathology of the imaged tissues. Thus, MRE can help in tumor detection, determination of characteristics of disease, and in assessment of rehabilitation. It was noticed experimentally that most biological tissues have incompressible viscoelastic features: they have a certain amount of rigidity that is characteristic of solid bodies, but, at the same time, they flow and dissipate energy by frictional losses as viscous fluids do [1, 2]. The incompressibility assumption for soft tissues is based on the fact that most tissues are made primarily of water. In addition, since the displacements in MRE are very small (on the order of microns), a linear constitutive law is usually assumed. However, despite the richness of the data set, the variety of processing techniques and the simplifications made in the biomechanical model, it remains a challenge to extract accurate results at high resolution in complex, heterogeneous tissues from the intrinsically noisy data. Therefore, any improvement in the MRE data processing with the help of biomechanics and computational methods will be of significant importance to modern medicine. Fig.1: (a) Benign tumor: the fibrous connective tissue capsule (orange) separates the inside benign cells (black boundaries) from the outside normal cells (yellow). (b) Malignant tumor: the irregularly-shaped cancer cells (red boundaries) are anisotropic and diffuse. (inspired from [10]) The aim of this paper is to formulate a new mathematical model that will be able to differentiate not only between normal and abnormal tissues, but, more importantly, between benign (not cancerous) and malignant (cancerous) tumors. As it can be seen in Figure 1, benign tumors are localized, self-contained (encapsulated), with smooth boundaries, and tend to be more isotropic. On the other hand, malignant tumors are not localized, diffuse, have irregular boundaries, and are anisotropic. The biomechanical models used so far in MRE are classic macroscopic models that do not incorporate any relevant information about the biochemical and mechanical processes that take place in tissue’s microstructure and thus fail to properly classify T. Proulx (ed.), Mechanics of Biological Systems and Materials, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series 9999, DOI 10.1007/978-1-4614-0219-0_14, © The Society for Experimental Mechanics, Inc. 2011 105
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