A Proper Orthogonal Decomposition-based inverse material parameter optimization method with applications to cardiac mechanics

We are currently witnessing the advent of a revolutionary new tool for biomedical research. Complex mathematical models of "living cells" are being arranged into representative tissue assemblies and utilized to produce models of integrated tissue and organ function. This enables more sophisticated simulation tools that allows for greater insight into disease and guide the development of modern therapies. The development of realistic computer models of mechanical behaviour for soft biological tissues, such as cardiac tissue, is dependent on the formulation of appropriate constitutive laws and accurate identification of their material parameters. The main focus of this contribution is to investigate a Proper Orthogonal Decomposition with Interpolation (PODI) based method for inverse material parameter optimization in the field of cardiac mechanics. Material parameters are calibrated for a left ventricular and bi-ventricular human heart model during the diastolic filling phase. The calibration method combines a MATLAB-based Levenberg Marquardt algorithm with the in-house PODIbased software ORION. The calibration results are then compared against the full-order solution which is obtained using an in-house code based on the element-free Galerkin method, which is assumed to be the exact solution. The results obtained from this novel calibration method demonstrate that PODI provides the means to drastically reduce computation time but at the same time maintain a similar level of accuracy as provided by the conventional approach

Splitting methods with variable metric for KL functions

We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the Kurdyka-Lojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a critical point of f and obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward method with variable metric and relative errors. As an example, a nonsmooth and nonconvex version of the Levenberg-Marquardt algorithm is detailled

Comprehensive maximum likelihood estimation of diffusion compartment models towards reliable mapping of brain microstructure

open4siDiffusion MRI is a key in-vivo non invasive imaging capability that can probe the microstructure of the brain. However,its limited resolution requires complex voxelwise generative models of the diffusion. Diffusion Compartment (DC) models divide the voxel into smaller compartments in which diffusion is homogeneous. We present a comprehensive framework for maximum likelihood estimation (MLE) of such models that jointly features ML estimators of (i) the baseline MR signal,(ii) the noise variance,(iii) compartment proportions,and (iv) diffusion-related parameters. ML estimators are key to providing reliable mapping of brain microstructure as they are asymptotically unbiased and of minimal variance. We compare our algorithm (which efficiently exploits analytical properties of MLE) to alternative implementations and a state-of-theart strategy. Simulation results show that our approach offers the best reduction in computational burden while guaranteeing convergence of numerical estimators to the MLE. In-vivo results also reveal remarkably reliable microstructure mapping in areas as complex as the centrum semiovale. Our ML framework accommodates any DC model and is available freely for multi-tensor models as part of the ANIMA software (https://github.com/Inria-Visages/Anima-Public/wiki).Stamm, Aymeric; Commowick, Olivier; Warfield, Simon K.; Vantini, SimoneStamm, Aymeric; Commowick, Olivier; Warfield, Simon K.; Vantini, Simon

Restarted Nonnegativity Preserving Tensor Splitting Methods via Relaxed Anderson Acceleration for Solving Multi-linear Systems

Multilinear systems play an important role in scientific calculations of practical problems. In this paper, we consider a tensor splitting method with a relaxed Anderson acceleration for solving multilinear systems. The new method preserves nonnegativity for every iterative step and improves the existing ones. Furthermore, the convergence analysis of the proposed method is given. The new algorithm performs effectively for numerical experiments