An Eulerian formulation for the computational modeling of phase-contrast MRI

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.

Do blood flow patterns in the left atriums differ between left upper lobectomy and other lobectomies? A computational study

Background

Left atrial (LA) hemodynamics after lung lobectomies with pulmonary vein (PV) resection is widely understood to be a risk factor for LA thrombosis. A recent magnetic resonance imaging study showed that left upper lobectomy (LUL) with left superior pulmonary vein resection tended to cause LA flow patterns distinct from those of other lobectomies, with flow disturbances seen near the PV stump. However, little is known about this flow pattern because of severe image resolution limitations. The present study compared flow patterns in the LA after LUL with the flow patterns of other lobectomies using computational simulations.

Methods

The computational simulations of LA blood flow were conducted on the basis of four-dimensional computed tomography images of four lung cancer patients prior to lobectomies. Four kinds of PV resection cases were constructed by cutting each one of the PVs from the LA of each patient. We performed a total of five cases (pre-resection case and four PV resection cases) in each patient and evaluated global flow patterns formed by the remaining PV inflow, especially in the upper LA region.

Results

LUL tended to enhance the remaining left inferior PV inflow, with impingements seen in the right PV inflows in the upper LA region near the PV stump. These flow alterations induced viscous dissipation and the LUL cases had the highest values compared to other PV resection cases, especially in the LV systole in three patients, and reached three to four times higher than those in pre-resection cases. However, in another patient, these tendencies were weaker when PV inflow was stronger from the right side than from the left side, and the degree of flow dissipation was lower than those in other PV resection cases.

Conclusion

These findings suggest marked variations in LA flow patterns among patients after lobectomies and highlights the importance of patient-specific assessment of LA hemodynamics after lobectomies.

On the Impact of Left Upper Lobectomy on the Left Atrial Hemodynamics

The left atrium (LA) functions to transport oxygenated blood from the pulmonary veins (PVs) to the left ventricle (LV). LA hemodynamics has received much attention because thrombosis in the LA in pathological states, such as atrial fibrillation, is a major factor leading to thromboembolic stroke. In the last 5 years, multiple cohort studies have revealed that left upper lobectomy (LUL) with PV resection risks thrombus formation in the PV stump even in the normal LA without a history of cardiac disease; the causal mechanism is, however, an open question. The present study investigated the potential effect of an LUL on LA hemodynamics associated with thrombus formation through computational simulation using four-dimensional computed tomography (4D-CT) images. Time series of patient-specific LA geometries before and after LUL were extracted from the 4D-CT images and these motions were estimated through non-rigid registration. Adopting the LA geometries and prescribed moving wall boundary conditions, the LA blood flow was determined using a Cartesian-grid computational fluid dynamics solver. The obtained results show that the LUL resulted in blood flow impingement from the left and right PV inflows into the LA upper region throughout most of the cardiac cycle. This characteristic alteration of the LA hemodynamics generated fine-scale vortices with viscous energy dissipations, enhancing the flow stasis associated with thrombus formation in the PV stump. These findings show that an LUL affects the hemodynamics not only in the PV stump but also throughout the LA region. They also highlight the importance of computational analysis of LA hemodynamics in understanding the underlying mechanism of LUL-induced thrombus formation.

Computational modeling of braided-stent deployment for interpreting the mechanism of stent flattening

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.

A Highly Automated Computational Method for Modeling of Intracranial Aneurysm Hemodynamics

Intracranial aneurysms manifest in a vast variety of morphologies and their growth and rupture risk are subject to patient-specific conditions that are coupled with complex, non-linear effects of hemodynamics. Thus, studies that attempt to understand and correlate rupture risk to aneurysm morphology have to incorporate hemodynamics, and at the same time, address a large enough sample size so as to produce reliable statistical correlations. In order to perform accurate hemodynamic simulations for a large number of aneurysm cases, automated methods to convert medical imaging data to simulation-ready configuration with minimal (or no) human intervention are required. In the present study, we develop a highly-automated method based on the immersed boundary method framework to construct computational models from medical imaging data which is the key idea is the direct use of voxelized contrast information from the 3D angiograms to construct a level-set based computational “mask” for the hemodynamic simulation. Appropriate boundary conditions are provided to the mask and the dynamics of blood flow inside the vessels and aneurysm is simulated by solving the Navier-Stokes equations on the Cartesian grid using the sharp-interface immersed boundary method. The present method does not require body conformal surface/volume mesh generation or other intervention for model clean-up. The viability of the proposed method is demonstrated for a number of distinct aneurysms derived from actual, patient-specific data.