Bifurcated Topological Optimization for IVIM - Fadnavis, Shreyas; Endres, Stefan; Wen, Qiuting; Wu, Yu-Chien; Cheng, Hu; Koudoro, Serge; Rane, Swati; Rokem, Ariel; Garyfallidis, Eleftherios (Frontiers in Neuroscience, 2021)
In this work, we shed light on the issue of estimating Intravoxel Incoherent Motion (IVIM) for diffusion and perfusion estimation by characterizing the objective function using simplicial homology tools. We provide a robust solution via topological optimization of this model so that the estimates are reliable and is clinically usable. Estimating the tissue microstructure from diffusion MRI is in itself an ill-posed and a nonlinear inverse problem. Using variable projection functional (VarPro) to fit the standard bi-exponential IVIM model we perform the optimization using simplicial homology based global optimization to better understand the topology of the objective function surface. We theoretically show how the proposed methodology can recover the model parameters more accurately and consistently by casting it in a reduced subspace given by VarPro. Additionally, we demonstrate that the IVIM model parameters cannot be accurately reconstructed using conventional numerical optimization methods due to the presence of infinite solutions in subspaces. The proposed method helps uncover multiple global minima by analyzing the local geometry of the model enabling the generation of reliable estimates of model parameters.