Poster P9 - A NOVEL DIFFUSION TENSOR MYOCARDIAL MATERIAL MODEL USING NEURAL NETWORKS FOR FORM DETERMINATION

Introduction: Cardiac tissue is a very complex structure with large degrees of anisotropy found throughout the tissue. The accurate modeling of the tissue is critical to improving the treatment of cardiac pathologies. Structural information can be extracted in vivo using Diffusion Tensor Magnetic Resonance Imaging (DTMRI) data, which can be obtained non-invasively. By introducing a neural network to represent the strain energy function as first introduced by Linke et al. with constitutive neural networks, modern automatic differentiation tools can be utilized to determine the material parameters in the inverse model. This freedom allows for generalized model form determination by letting the form be determined by the data. Moreover, the spatially varying diffusion tensor, D, can enter the material model with no prior assumptions, and the data will show how the structural tensor can be best incorporated into the model. This is a very important step as form determination for hyperelastic biological tissues remains a major hurdle in accurate simulation of disease and surgical planning.

Materials and

Methods: The inverse model framework starts by acquiring force-displacement pairs either from synthetic or real data. A generic form is given to the inverse model containing invariants and pseudoinvariants for anisotropy. A finite element solution is found where the material is modeled as nearly incompressible. The parameters are then trained by minimizing the mean squared error between the force data and the prediction of the model. The gradients can be obtained from the JAX-FEM solver through automatic differentiation. As the parameters are trained, certain ones will fall to zero showing little contribution from certain terms, recovering the form of the model.

Results, Conclusions, and Discussions: The above method was tested on the Li model, which only uses eigenvectors of D, and data presented in the work on left ventricular myocardium modeling. After the method was validated on the Li model, a new form is proposed using the full diffusion tensor to model the same data. The benefits of the method allow the data to show us how D should be incorporated. To allow for local heterogeneity, D is normalized and incorporated as a weighting distribution, integrated over the sphere. This form suggests the use of exponential I4 term where a good fit was achieved with only three material constants. The method presented is able to recover material constants for known material models through the data. The data centric method allows us to extend the material model to account for the full structural tensor D. By using all the information of D, the model is no longer locally homogeneous due to its spatial variation. The final form then becomes much simpler to model highly anisotropic materials.

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