This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

Phase-contrast magnetic resonance (MR) imaging is a well-known but undervalued method of obtaining quantitative information on blood flow. Applications of this technique in cardiovascular MR imaging are expanding. According to the sequences available, phase-contrast measurement can be performed in a breath hold or during normal respiration. Prospective as well as retrospective gating techniques can be used. Common errors in phase-contrast imaging include mismatched encoding velocity, deviation of the imaging plane, inadequate temporal resolution, inadequate spatial resolution, accelerated flow and spatial misregistration, and phase offset errors. Flow measurements are most precise if the imaging plane is perpendicular to the vessel of interest and flow encoding is set to through-plane flow. The sequence should be repeated at least once, with a high encoding velocity used initially. If peak velocity has to be estimated, flow measurement is repeated with an adapted encoding velocity. The overall error of a ...

https://pubs.rsna.org/doi/pdf/10.1148/radiographics.22.3.g02ma11651

Cardiovascular Flow Measurement with Phase-Contrast MR Imaging: Basic Facts and Implementation

Amyloid deposition is present in 20-50% of nondemented older adults yet the functional consequences remain unclear. The current study found that amyloid accumulation is correlated with functional disruption of the default network as measured by intrinsic activity correlations. Clinically normal participants (n = 38, aged 60-88 years) were characterized using (11)C-labeled Pittsburgh Compound B positron emission tomography imaging to estimate fibrillar amyloid burden and, separately, underwent functional magnetic resonance imaging (fMRI). The integrity of the default network was estimated by correlating rest-state fMRI time courses extracted from a priori regions including the posterior cingulate, lateral parietal, and medial prefrontal cortices. Clinically normal participants with high amyloid burden displayed significantly reduced functional correlations within the default network relative to participants with low amyloid burden. These reductions were also observed when amyloid burden was treated as a continuous, rather than a dichotomous, measure and when controlling for age and structural atrophy. Whole-brain analyses initiated by seeding the posterior cingulate cortex, a region of high amyloid burden in Alzheimer's disease, revealed significant disruption in the default network including functional disconnection of the hippocampal formation.

https://www.jneurosci.org/content/jneuro/29/40/12686.full.pdf

Disruption of Functional Connectivity in Clinically Normal Older Adults Harboring Amyloid Burden

The authors present a unique application of polyvinyl alcohol (PVA) cryogel as an anthropomorphic, elastic, vascular phantom material that can be used in MR imaging. The composition consists of two nontoxic ingredients: water and PVA. The biomechanical and MR properties can be adjusted to be similar to those of excised porcine aortas by varying the number of freeze-thaw cycles to which the PVA solution is exposed. The authors present the T1, T2, shrinkage, and tensile properties of PVA cryogel tubes as a function of freeze-thaw cycles. MR images of a dual elastic aortic phantom undergoing pulsatile motion are shown.

Polyvinyl alcohol cryogel: An ideal phantom material for MR studies of arterial flow and elasticity

Background In the patient with mitral regurgitation who is being considered for valvular surgery, cardiac catheterization is usually performed to quantify the severity of regurgitation and to determine its influence on left ventricular volumes and systolic function. Magnetic resonance imaging (MRI) potentially provides a rapid, noninvasive method of acquiring these data. Thus, this study was done to determine whether MRI can reliably measure the magnitude of mitral regurgitation and evaluate the effect of regurgitation on left ventricular volumes and systolic function. Methods and Results Twenty-three subjects (14 women and 9 men 15 to 72 years of age) with (n=17) or without (n=6) mitral regurgitation underwent MRI scanning followed immediately by cardiac catheterization. The presence (or absence) of valvular regurgitation was determined, and left ventricular volumes and regurgitant fraction were quantified during each procedure. There was excellent correlation between invasive and MRI assessments of left...

Magnetic Resonance Imaging Assessment of the Severity of Mitral Regurgitation Comparison With Invasive Techniques

RATIONALE AND OBJECTIVES.One promising approach to flow quantification uses the velocity-dependent phase change of moving protons. A velocity-encoding phase subtraction technique was used to measure the velocity and flow rate of fluid flow in a phantom and blood flow in volunteers.METHODS.In a model

Thomas A. Grist

Papers

Magnetic Resonance Imaging of Blood Flow with a Phase Subtraction Technique: In Vitro and In Vivo Validation