MODELING THERMOGRAPHY OF THE TUMOROUS HUMAN BREAST: FROM FORWARD PROBLEM TO INVERSE PROBLEM SOLVING Li Jiang 1 , Wang Zhan 2 , Murray H. Loew 1 1 George Washington Univ., Washington, DC, USA. 2 Univ. of California, San Francisco, CA, USA. ABSTRACT The abnormal thermogram has been shown to be a reliable indicator of a high risk of breast cancer. Nevertheless, a major weakness of current infrared breast thermography is its poor sensitivity for deeper tumors. Numerical modeling for breast thermography provides an effective tool to investigate the complex relationships between the breast thermal behaviors and the underlying pathophysiological conditions. Conventional “forward problem” modeling cannot be used to directly improve the tumor detectability, however, because the underlying tissue thermal properties are generally unknown. Based on our new comprehensive forward modeling, we propose an “inverse problem” modeling technique that aims to estimate tissue thermal properties from the breast surface thermogram. Our data suggest that the estimation of tumor-induced thermal contrast can be significantly improved by using the proposed inverse problem solving techniques to provide the individual-specific thermal background, especially for deeper tumors. Index Terms — breast tumor, forward problem, inverse problem, numerical modeling, thermogram 1. INTRODUCTION Infrared thermal imaging shows promise to be a noninvasive and effective adjunctive modality for early breast cancer screening [1-3]. Widespread clinical adoption of breast thermography, however, is still hindered by its poor sensitivity to deeper or smaller tumors [1-3]. To address this problem, various numerical modeling techniques for breast thermography have been developed to investigate the complex relationships between the breast thermal behavior and the underlying pathophysiological conditions [4, 5]. Along with the existing methods, we have developed a set of new modeling techniques to take into account some subtle factors that were usually ignored in previous studies, yet contribute to the thermal behavior on the breast surface. These factors include the gravity-induced elastic deformations of the breast, the nonlinear elasticity of soft tissues, and the dynamic nature of the thermogram [6-8]. It should be noted, however, that current techniques target only the so-called “forward problem” of thermography modeling, i.e., to estimate the temperature distribution from known thermal properties of the normal and/or tumorous tissues. In practice, however, it is difficult to use those techniques to directly improve the tumor detectability, because the thermal properties of the breast tissues are usually unknown in the clinical setting [1-3, 9]. In fact, the thermal property parameters were generally specified as population averages, which might substantially depart from individual values [1-3, 9]. This leads to a major barrier to accurate estimation of the tumor-induced thermal contrast (TITC) on the breast surface, because of the uncertainty of corresponding non-tumor thermal background, which needs to be subtracted from the thermogram. Our new breast tissue finite-element methods aim to extend the “forward’ modeling into the realm of the “inverse problem” solving [10], namely to estimate the thermal properties of the breast tissues from the observed surface temperature distribution. To address the intrinsic ill-posed nature of the inverse problem, we applied a spatial constraint to three major thermal properties, i.e., thermal conductivity, blood perfusion, and metabolic heat generation, for each breast tissue type. Superior to previous inverse problem attempts [11], our approach is the only one using a 3D model and that accounts for tissue thermal properties. We expect that, by using the proposed inverse problem techniques, the estimation of the TITC can be significantly improved, especially for deeper tumors. 2. METHODS 2.1. Forward Thermography Modeling The forward thermal modeling was based on the static Pennes’s equation [12], 0 ) (        a b b T T c q T k Z U to obtain the breast temperature distribution T , from the known tissue thermal properties of thermal conductivity k, volumetric metabolic heat generation rate q, and blood perfusion rate Ȧ, respectively. The b c , b U , and a T represent the blood heat capacity, the blood density, and the arterial blood temperature, respectively. Using tetrahedron finite element (FE) meshing as described in [6], we can rewrite the algebraic thermal FE equations as P KT  for solving for the unknown temperature vector T. K is the thermal characteristic matrix of the breast; it incorporates the 205 978-1-4244-4126-6/10/$25.00 ©2010 IEEE ISBI 2010