## 6 Mammary Tissue Modeling
### Forward Modeling  
To reveal the complex correlation between the breast thermal behavior and the underlying pathophysiological conditions, different numerical modeling techniques have been proposed. The principal ones are reviewed below. A 3D finite element model aimed at investigating the effect of the thermal and elastic properties of breast tissues on the thermal contrast of both healthy and cancerous breasts was developed by [PERSON] et al. [77]. In particular, the undeformed human breast was modeled as a hemispherical volume consisting of four concentric tissue layers with a uniform thickness, as depicted in Figure 8a. Then, gravity-induced deformation was introduced by applying both linear and non-linear elastic models. Moreover, both static and dynamic thermal conditions were considered in this work. The authors found that at the steady-state, for normal body posture (sitting or standing), gravity-induced breast  
Figure 8: Cross-section of 3D breast tissue multi-layer models with an embedded tumor: (**a**) concentric layers; (**b**) non-concentric layers. deformation yields an upper-lower asymmetric surface thermal contrast. Also, the surface temperature changes due to the lesion were more sensitive to tumor depth than its size. In dynamic conditions, the results obtained suggested that the tumor-induced thermal contrast exhibits an opposite initial change and delayed peak when compared to the deformation-induced thermal contrast on the breast surface. According to the authors, these lags of the thermal contrast are generally longer in deeper tumors that also show smaller peaks. A finite element model involving a realistic breast geometry based on 3D scanning of a mannequin was defined by [PERSON] et al. [78] to improve the accuracy and reliability of computer-aided diagnosis. To experimentally validate their model, the authors created a silicon rubber breast using 3D printing and molding techniques. Also, the presence of a tumor lesion was simulated through resistors placed within the silicone breast. This study revealed that 3D breast geometry and tumor size can give different temperature profiles, affecting the precision of computer-aided diagnosis of breast cancer. In fact, the authors reported that the maximum temperature difference between healthy and cancerous breasts can range from 0.34 to 1.37 \({}^{\circ}\)C when the cup sizes range from 120 to 260 mm and a tumor depth from 5 to 25 mm. A finite element, four-quadrant flexible breast model was developed by [PERSON] and [PERSON] [79]. These authors imagined the human breast divided into four quadrants, namely the upper-outer quadrant, the upper-inner quadrant, the lower-inner quadrant, and the lower-outer quadrant. In such a way, the thermal properties of the tissues in each quadrant could be changed selectively, yielding flexibility in the simulation. The suggested model not only incorporates three tissue layers (subcutaneous fat, a gland layer, and a core region) with different thicknesses, but it also includes the areaola region as a separate entity. Also, to define a more realistic geometry, the outer breast profile of a mannequin was traced with a CNC machine. The authors validated their model using experimental steady-state thermograms, and they reported a good overall match. A realistic computational thermal model of the human breast calibrated to real clinical data was developed by [PERSON] et al. [80] using high-resolution infrared images, real 3D breast geometries, and magnetic resonance imaging. For the purposes of their study, a female subject histologically diagnosed with breast cancer was enrolled. In particular, the real breast geometry was accurately derived using a 3D scanner. Additionally, magnetic resonance images were used to create the back surface of each breast based on the anatomic curvature of the pectoral muscle and to model the skin layer thickness around the nipple region, as well as to gain insight about the location and irregular geometry of the cancerous lesion.