The numerical simulation of the diffusion MRI signal arising from complex tissue micro-structures is helpful for understanding and interpreting imaging data as well as for designing and optimizing MRI sequences. The discretization of the Bloch-Torrey equation by finite elements is a more recently developed approach for this purpose, in contrast to random walk simulations, which has a longer history. While finite elements discretization is more difficult to implement than random walk simulations, the approach benefits from a long history of theoretical and numerical developments by the mathematical and engineering communities. In particular, software packages for the automated solutions of partial differential equations using finite elements discretization, such as FEniCS, are undergoing active support and development. However, because diffusion MRI simulation is a relatively new application area, there is still a gap between the simulation needs of the MRI community and the available tools provided by finite elements software packages. In this paper, we address two potential difficulties in using FEniCS for diffusion MRI simulation. First, we simplified software installation by the use of FEniCS containers that are completely portable across multiple platforms. Second, we provide a portable simulation framework based on Python and whose code is open source. This simulation framework can be seamlessly integrated with cloud computing resources such as Google Colaboratory notebooks working on a web browser or with Google Cloud Platform with MPI parallelization. We show examples illustrating the accuracy, the computational times, and parallel computing capabilities. The framework contributes to reproducible science and open-source software in computational diffusion MRI with the hope that it will help to speed up method developments and stimulate research collaborations.

We present an adaptive finite element method for time-resolved simulation of aerodynamics without any turbulence-model parameters, which is applied to a benchmark problem from the HiLiftPW-3workshop to compute the flowpast a JAXA Standard Model (JSM) aircraft model at realistic Reynolds numbers. The mesh is automatically constructed by the method as part of an adaptive algorithm based on a posteriori error estimation using adjoint techniques. No explicit turbulence model is used, and the effect of unresolved turbulent boundary layers is modeled by a simple parametrization of the wall shear stress in terms of a skin friction. In the case of very high Reynolds numbers, we approximate the small skin friction by zero skin friction, corresponding to a free-slip boundary condition, which results in a computational model without any model parameter to be tuned, and without the need for costly boundary-layer resolution. We introduce a numerical tripping-noise term to act as a seed for growth of perturbations; the results support that this triggers the correct physical separation at stall and has no significant pre-stall effect. We show that the methodology quantitavely and qualitatively captures the main features of the JSM experiment-aerodynamic forces and the stall mechanism-with a much coarser mesh resolution and lower computational cost than the state-of-the-art methods in the field, with convergence under mesh refinement by the adaptive method. Thus, the simulation methodology appears to be a possible answer to the challenge of reliably predicting turbulent-separated flows for a complete air vehicle.

Radiofrequency catheter ablation (RFCA) is an effective treatment for cardiac arrhythmias. Although generally safe, it is not completely exempt from the risk of complications. The great flexibility of computational models can be a major asset in optimizing interventional strategies if they can produce sufficiently precise estimations of the generated lesion for a given ablation protocol. This requires an accurate description of the catheter tip and the cardiac tissue. In particular, the deformation of the tissue under the catheter pressure during the ablation is an important aspect that is overlooked in the existing literature, which resorts to a sharp insertion of the catheter into an undeformed geometry. As the lesion size depends on the power dissipated in the tissue and the latter depends on the percentage of the electrode surface in contact with the tissue itself, the sharp insertion geometry has the tendency to overestimate the lesion obtained, which is a consequence of the tissue temperature rise overestimation. In this paper, we introduce a full 3D computational model that takes into account the tissue elasticity and is able to capture tissue deformation and realistic power dissipation in the tissue. Numerical results in FEniCS-HPC are provided to validate the model against experimental data and to compare the lesions obtained with the new model and with the classical ones featuring a sharp electrode insertion in the tissue.

Radiofrequency catheter ablation (RFCA) is widely used for the treatment of various types of cardiac arrhythmias. Typically, the efficacy and the safety of the ablation protocols used in the clinics are derived from tests carried out on animal specimens, including swines. However, these experimental findings cannot be immediately translated to clinical practice on human patients, due to the difference in the physical properties of the types of tissue. Computational models can assist in the quantification of this variability and can provide insights in the results of the RFCA for different species. In this work, we consider a standard ablation protocol of 10 g force, 30 W power for 30 s. We simulate its application on a porcine cardiac tissue, a human ventricle and a human atrium. Using a recently developed computational model that accounts for the mechanical properties of the tissue, we explore the onset and the growth of the lesion along time by tracking its depth and width, and we compare the lesion size and dimensions at the end of the ablation.

Radiofrequency catheter ablation (RFCA) is an effective treatment for different types of cardiac arrhythmias. However, major complications can occur, including thrombus formation and steam pops. We present a full 3D mathematical model for the radiofrequency ablation process that uses an open-irrigated catheter and accounts for the tissue deformation, an aspect overlooked by the existing literature. An axisymmetric Boussinesq solution for spherical punch is used to model the deformation of the tissue due to the pressure of the catheter tip at the tissue-catheter contact point. We compare the effect of the tissue deformation in the RFCA model against the use of a standard sharp insertion of the catheter in the tissue that other state-of-the-art RFCA computational models use.