In this paper we present random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a novel transit model for solving the interaction of random walkers with a membrane. This hybrid model is based on treating the membrane permeability and the step change in diffusion coefficient as two interactions separated by an infinitesimally small layer. By conducting an extensive analytical flux analysis, the performance of our hybrid model is compared with a commonly used membrane transit model (reference model). Numerical simulations demonstrate the limitations of the reference model in dealing with step changes in diffusivity and show the capability of the hybrid model to overcome this limitation and to offer substantial gains in computational efficiency. The suitability of both random walk transit models for the application to simulations of diffusion tensor cardiovascular magnetic resonance (DT-CMR) imaging is assessed in a histology-based domain relevant to DT-CMR. In order to demonstrate the usefulness of the new hybrid model for other possible applications, we also consider a larger range of permeabilities beyond those commonly found in biological tissues.

Abstract:Cushioning is an important aspect in hydraulic cylinder performance. The piston has to be decelerated before it strikes the end cap in order to avoid stresses in the cylinder components and reduce vibration that can be transmitted to the machine. One of the least-studied methods is internal cushioning by grooves in the piston. In this method, the flow is throttled with adequately designed grooves when the piston reaches the outlet port position. The purpose of the present work is to present a method to estimate the pressure-drop coefficients for a certain design of piston grooves in order to provide a model to develop a dynamic system simulation of the cushion system. The method is based on a computational fluid dynamic simulation of flow through piston grooves to the outlet port for each piston's static position. The results are compared with experimental measurements, and a correction, based on Reynolds number, is proposed. Good agreement, below 16%, was obtained for all the positions but particularly for the last grooves, for which the numerical result's deviation to the experimental measurements was less than 10%. In general, the numerical simulation tended to underestimate the pressure drop for the first grooves and overestimate the calculation for the last grooves.

Purpose To study the sensitivity of diffusion tensor cardiovascular magnetic resonance (DT‐CMR) to microvascular perfusion and changes in cell permeability. Methods Monte Carlo (MC) random walk simulations in the myocardium have been performed to simulate self‐diffusion of water molecules in histology‐based media with varying extracellular volume fraction (ECV) and permeable membranes. The effect of microvascular perfusion on simulations of the DT‐CMR signal has been incorporated by adding the contribution of particles traveling through an anisotropic capillary network to the diffusion signal. The simulations have been performed considering three pulse sequences with clinical gradient strengths: monopolar stimulated echo acquisition mode (STEAM), monopolar pulsed‐gradient spin echo (PGSE), and second‐order motion‐compensated spin echo (MCSE). Results Reducing ECV intensifies the diffusion restriction and incorporating membrane permeability reduces the anisotropy of the diffusion tensor. Widening the intercapillary velocity distribution results in increased measured diffusion along the cardiomyocytes long axis when the capillary networks are anisotropic. Perfusion amplifies the mean diffusivity for STEAM while the opposite is observed for short diffusion encoding time sequences (PGSE and MCSE). Conclusion The effect of perfusion on the measured diffusion tensor is reduced using an increased reference b‐value. Our results pave the way for characterization of the response of DT‐CMR to microstructural changes underlying cardiac pathology and highlight the higher sensitivity of STEAM to permeability and microvascular circulation due to its longer diffusion encoding time.