Professor The University of Texas at Austin Austin, Texas, United States
Introduction: : 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 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. Validation studies were then conducted and results evaluated and presented. We then used this approach to evaluate the effects of age on the resultant model parameters and related to structural changes .
Materials and
Methods: : Breast tissue was anatomically oriented 5mm x 5mm x 5mm specimens obtained from multiple healthy regions in the breast. To quantify the full 3D mechanical response of the breast tissue our unique full-3D triaxial testing methodology was used. Here, six independent pure shear protocols that combined all possible deformation combinations were used. The results of these experiments revealed that human breast tissue exhibited substantial non-linearity across all deformation modes. These included a nonlinear but also anisotropic responses. This result suggests some interesting mechanistic differences in the tension/compression behaviors of human breast tissues that need to be accounted for in material model development. We also subdivided the tissue into younger ( < 45) and older (>45) groups.
We developed a form for human breast tissue that incorporated the full diffusion tensor D, distinct from current uses of D wherein only the eigenvectors are used to define the local material axes. We take our starting point for model form from related work on meso-structural material models, wherein the response in a direction n is weighted by the mass fraction of material in that direction. To describe the kinematics in tension/compression along n we utilized the pseudo-invariant I4. Given the observed characteristics of the tension/compression responses we assumed the form of the mechanical response in any direction n will have different material constants in tension and compression. We then extended this base model to include additional shear-based interaction terms
Results, Conclusions, and Discussions:: The resultant constitutive model was able to simulate the unique anisotropic tension/compression behaviors, including directionally dependent non-linearities. It was observed that while the I4 model term captured the main responses, additional coupling terms were clearly needed (Figure 1). 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. Next, experimental results showed that older tissue exhibited more pronounced anisotropy. Model results clearly indicated that the young tissue was more isotropic, while older tissue was generally stiffer. Of particular interest was the complexity in the age-related changes, which was dominated in the anterior-posterior direction. These novel findings suggest that human breast tissue exhibits complex structural and mechanical behaviors, which change in a complex manner with age. 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.
Acknowledgements and/or References (Optional):: The Author gratefully acknowledge financial support from NIH/NIBIB grant R01EB032533.
