A novel diffusion tensor based three-dimensional constitutive model for human breast tissue

There is a lack of understanding how human breast tissue internal structure connects to its bulk level 3D mechanical behaviors. An attractive method to quantify tissue structure is diffusion tensor imaging (DTMRI), which produces compact, local, quantitative information in the form of a second rank symmetric tensor D. As D contains rich information about local 3D tissue structure, we developed a novel constitutive model form for human fibroglandular (FG) and adipose (AD) breast tissues that directly utilized the complete $D$. Our modeling approach included separate extensional/compression and shear-like interactions terms. To develop the necessary mathematical forms we utilized a neural network modeling approach trained using pure-shear loading paths from the extant triaxial data for the AD and FG groups. A final model form was formulated and model parameters determined using the same data set. The resultant constitutive model was able to simulate the unique anisotropic tension/compression behaviors, including directionally dependent non-linearities for the FG tissue group. The constitutive model was validated in two steps. First, we used the model to predict D and compared it to D as measured directly by DTMRI on excised breast tissue, which compared very well. Secondly, validation of the predictive capabilities of the model were demonstrated by accurate predictions of breast tissue in simple compression for both AD and FG tissue groups. The present modeling approach was able to predict human breast tissue 3D mechanical behavior accurately, as well as shed insight into connections to the underlying tissue structure via the use of D.