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Purpose: Computational simulation of phase-contrast MRI (PC-MRI) is an attractive way to physically interpret properties and errors in MRI-reconstructed flow velocity fields. Recent studies have developed PC-MRI simulators that solve the Bloch equation, with the magnetization transport being modeled using a Lagrangian approach. Because this method expresses the magnetization as spatial distribution of particles, influences of particle densities and their spatial uniformities on numerical accuracy are well known. This study developed an alternative method for PC-MRI modeling using an Eulerian approach in which the magnetization is expressed as a spatially smooth continuous function., Methods: The magnetization motion was described using the Bloch equation with an advection term and computed on a fixed grid using a finite difference method, and k-space sampling was implemented using the spoiled gradient echo sequence. PC-MRI scans of a fully developed flow in straight and stenosed cylinders were acquired to provide numerical examples., Results: Reconstructed flow in a straight cylinder showed excellent agreement with input velocity profiles and mean errors were less than 0.5% of the maximum velocity. Numerical cases of flow in a stenosed cylinder successfully demonstrated the velocity profiles, with displacement artifacts being dependent on scan parameters and intravoxel dephasing due to flow disturbances. These results were in good agreement with those obtained using the Lagrangian approach with a sufficient particle density., Conclusion: The feasibility of the Eulerian approach to PC-MRI modeling was successfully demonstrated., (© 2024 The Author(s). Magnetic Resonance in Medicine published by Wiley Periodicals LLC on behalf of International Society for Magnetic Resonance in Medicine.)

Purpose: Phase-contrast MRI (PC-MRI) of cerebrospinal fluid (CSF) velocity is used to evaluate the characteristics of intracranial diseases, such as normal-pressure hydrocephalus (NPH). Nevertheless, PC-MRI has several potential error sources, with eddy-current-based phase offset error being non-negligible in CSF measurement. In this study, we assess the measurement error of CSF velocity maps obtained using 4D flow MRI and evaluate correction methods., Methods: CSF velocity maps of 10 patients with NPH were acquired using 4D flow MRI (velocity-encoding = 5 cm/s). Distributed phase offset error was estimated for a whole 3D background field by polynomial fitting using robust regression analysis. This estimated phase offset error was then used to correct the CSF velocity maps. The estimated error profiles were compared with those obtained using an existing 2D correction approach involving local background information near the region of interest., Results: The residual standard error of the polynomial fitting against the phase offset error extracted from the measured velocities was within 0.2 cm/s. The spatial dependencies of the phase offset errors showed similar tendencies in all cases, but sufficient differences in these values were found to indicate requirement of velocity correction. Differences of the estimated errors among other correction approaches were in the order of 10 -2 cm/s, and the estimated errors were in good agreement with those obtained using existing approaches., Conclusion: Our method is capable of estimating the measurement error of CSF velocity maps obtained from 4D flow MRI and provides quantitatively reasonable characteristics for the main CSF profile in the cerebral aqueduct in patients with NPH., (© 2021 International Society for Magnetic Resonance in Medicine.)

This study develops a computational model of the braided stent for interpreting the mechanism of stent flattening during deployment into curved arteries. Stent wires are expressed using Kirchhoff's rod theory and their mechanical behavior is treated using a corotational beam formulation. The equation of motion of the braided stent is solved in a step-by-step manner using the resultant elastic force and mechanical interactions of wires with friction. Examples of braided-stent deployment into idealized arteries with various curvatures are numerically simulated. In cases of low curvature, the braided stent expands from a catheter by releasing the bending energy stored in stent wires, while incomplete expansion is found at both stent ends (ie, the fish-mouth phenomenon), where relatively little bending energy is stored. In cases of high curvature, much torsional energy is stored in stent wires locally in the midsection of the curvature and the bending energy for stent self-expansion is not fully released even after deployment, leading to stent flattening. These findings suggest that the mechanical state of the braided stent and its transition during deployment play an important role in the underlying mechanism of stent flattening. NOVELTY STATEMENT: This study developed a computational mechanical model of the braided stent for interpreting stent flattening, which is a critical issue observed during deployment into highly curved arteries. Mechanical behaviors of the stent wires are appropriately treated by corotational beam element formulation with considering multiple contacts. We conducted numerical examples of the stent deployment into curved arteries and found that the mechanical state of the braided stent during deployment associated with occurrences of the stent flattening. We believe this finding gives new insight into the mechanism of stent flattening and would advance the design of the stent and its deployment protocol., (© 2020 John Wiley & Sons, Ltd.)

This paper presents a novel data assimilation method for patient-specific blood flow analysis based on feedback control theory called the physically consistent feedback control-based data assimilation (PFC-DA) method. In the PFC-DA method, the signal, which is the residual error term of the velocity when comparing the numerical and reference measurement data, is cast as a source term in a Poisson equation for the scalar potential field that induces flow in a closed system. The pressure values at the inlet and outlet boundaries are recursively calculated by this scalar potential field. Hence, the flow field is physically consistent because it is driven by the calculated inlet and outlet pressures, without any artificial body forces. As compared with existing variational approaches, although this PFC-DA method does not guarantee the optimal solution, only one additional Poisson equation for the scalar potential field is required, providing a remarkable improvement for such a small additional computational cost at every iteration. Through numerical examples for 2D and 3D exact flow fields, with both noise-free and noisy reference data as well as a blood flow analysis on a cerebral aneurysm using actual patient data, the robustness and accuracy of this approach is shown. Moreover, the feasibility of a patient-specific practical blood flow analysis is demonstrated., (Copyright © 2017 John Wiley & Sons, Ltd.)

We examined the deformation behavior of a red blood cell (RBC) in various flow fields to determine whether the extent of RBC deformation is correlated with the shear stress used as a hemolysis index. The RBC model was introduced to a simple shear flow (Couette flow) and to slightly complex flows (unsteady shear flows and stenosed flows). The RBC deformation was assessed by the maximum first principal strain over the RBC membrane and compared with the shear stress. Although the results were consistent under steady Couette flow, this was not the case under unsteady Couette flow or stenosed flow due to the viscoelastic nature of the RBC deformation caused by fluid forces. These results suggest that there is a limitation in accurately estimating the mechanical damage of RBCs solely from a macroscopic flow field, indicating the necessity of taking into account the dynamic deformation of RBCs to provide a better estimation of hemolysis., (Copyright © 2013 John Wiley & Sons, Ltd.)

We developed a mechanical model of a red blood cell (RBC) that is capable of expressing its characteristic behaviors in shear flows. The RBC was modeled as a closed shell membrane consisting of spring networks in the framework of the energy minimum concept. The fluid forces acting on RBCs were modeled from Newton's viscosity law and the conservation of momentum. In a steady shear flow, the RBC model exhibited various behaviors, depending on the shear rate; it tumbled, tank-treaded, or both. The transition from tumbling to tank-treading occurred at a shear rate of 20 s( - 1). The simulation of an RBC in steady and unsteady parallel shear flows (Couette flows) showed that the deformation parameters of the RBC were consistent with experimental results. The RBC in Poiseuille flow migrated radially towards the central axis of the flow channel. Axial migration became faster with an increase in the viscosity of the media, qualitatively consistent with experimental results. These results demonstrate that the proposed model satisfies the essential conditions for simulating RBC behavior in blood flow. Finally, a large-scale RBC flow simulation was implemented to show the capability of the proposed model for analyzing the mesoscopic nature of blood flow., (Copyright © 2012 John Wiley & Sons, Ltd.)