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Abstract Tikhonov regularization is commonly used in the solution of linear discrete ill-posed problems. It is known that iterated Tikhonov regularization often produces approximate solutions of higher quality than (standard) Tikhonov regularization. This paper discusses iterated Tikhonov regularization for large-scale problems with a general regularization matrix. Specifically, the original problem is reduced to small size by application of a fairly small number of steps of the Arnoldi or Golub-Kahan processes, and iterated Tikhonov is applied to the reduced problem. The regularization parameter is determined by using an extension of a technique first described by Donatelli and Hanke for quite special coefficient matrices. Convergence of the method is established and computed examples illustrate its performance. 

Abstract Diffusion MRI (dMRI) has become a crucial imaging technique in the field of neuroscience, with a growing number of clinical applications. Although most studies still focus on the brain, there is a growing interest in utilizing dMRI to investigate the healthy or injured spinal cord. The past decade has also seen the development of biophysical models that link MR-based diffusion measures to underlying microscopic tissue characteristics, which necessitates validation through ex vivo dMRI measurements. Building upon 13 years of research and development, we present an open-source, MATLAB-based academic software toolkit dubbed ACID: A Comprehensive Toolbox for Image Processing and Modeling of Brain, Spinal Cord, and Ex Vivo Diffusion MRI Data. ACID is an extension to the Statistical Parametric Mapping (SPM) software, designed to process and model dMRI data of the brain, spinal cord, and ex vivo specimens by incorporating state-of-the-art artifact correction tools, diffusion and kurtosis tensor imaging, and biophysical models that enable the estimation of microstructural properties in white matter. Additionally, the software includes an array of linear and nonlinear fitting algorithms for accurate diffusion parameter estimation. By adhering to the Brain Imaging Data Structure (BIDS) data organization principles, ACID facilitates standardized analysis, ensures compatibility with other BIDS-compliant software, and aligns with the growing availability of large databases utilizing the BIDS format. Furthermore, being integrated into the popular SPM framework, ACID benefits from a wide range of segmentation, spatial processing, and statistical analysis tools as well as a large and growing number of SPM extensions. As such, this comprehensive toolbox covers the entire processing chain from raw DICOM data to group-level statistics, all within a single software package. 

Background and objective: Wall shear stress (WSS) has been known to play a critical role in the development of several complications following coronary artery stenting, including in-stent restenosis and thrombosis. Computational fluid dynamics is often used to quantify the post-stenting WSS, which may potentially be used as a predictive metric. However, large-scale studies for WSS-based risk stratification often neglect the footprint of the stent due to reconstruction challenges. The primary objective of this study is to statistically evaluate the impact of the stent footprints (Xience and Resolute stents) on the computed endothelial WSS and quantitatively identify the relationship between these local hemodynamic alterations and the global properties of the vessel, such as curvature, on WSS. The ultimate goal is to evaluate whether and when it is worth including the footprint of the stent in an in-silico study to compute the WSS reliably. Methods: A previously developed semi-automated reconstruction approach for patient-specific coronaries was employed as a part of the SHEAR-STENT trial. A subset of patients was analyzed (N=30), and CFD simulations were performed with and without the stent to evaluate the impact of the stent footprint on WSS. Due to the computationally expensive nature of transient analyses, a sub-cohort of ten patients were used to assess the reliability of WSS obtained from steady computations as a surrogate for the time-averaged results. Global and local vessel curvature data were extracted for all cases and evaluated against stent-induced alterations in the WSS. The differences between the Xience and Resolute stent platforms were also examined to quantify each stent's unique WSS footprint. Results: Results from the surrogate analysis indicate that steady WSS serves as an excellent approximation of the time-averaged computations. The presence of either stent footprint causes a statistically significant decrease in the space-averaged WSS, and a significant increase in the endothelial regions exposed to very low WSS as well (<0.5 Pa). Negative correlations were observed between vessel curvature and WSS differences, indicating that macroscopic vessel characteristics play a more prominent role in determining endothelial WSS at higher curvature values. In our pool of cases, comparison of Xience and Resolute stents revealed that the Resolute platform seems to lead to lower space-averaged WSS and an increase in areas of very low WSS. Conclusion: These results outline (1) the necessity of including the stent footprint for accurate in-silico WSS analysis; (2) the global features of stented arteries serving as the dominant determinant of WSS past a certain curvature threshold; and (3) the Xience stent resulting in a milder presence of hemodynamically unfavorable WSS regions compared to the Resolute stent. Keywords: Computational fluid dynamics; Drug-eluting stents; In-silico clinical trials; Percutaneous coronary intervention; Wall shear stress. 

We consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage to enable rapid decision-making and be able to react to changes in the parameter in the online stage. To tackle the curse of dimensionality arising when the state and/or parameter are high-dimensional, we represent the policy using neural networks. We compare two training paradigms: First, our model-based approach leverages the dynamics and definition of the objective function to learn the value function of the parameterized optimal control problem and obtain the policy using a feedback form. Second, we use actor-critic reinforcement learning to approximate the policy in a data-driven way. Using an example involving a two-dimensional convection-diffusion equation, which features high-dimensional state and parameter spaces, we investigate the accuracy and efficiency of both training paradigms. While both paradigms lead to a reasonable approximation of the policy, the model-based approach is more accurate and considerably reduces the number of PDE solves.