estimation of pc-mri pressure map using integral form of governing equations and spline segments

in this paper, the boundary-based estimation of pressure distribution in the cardiovascular system is investigated using two dimensional flow images. the conventional methods of non-invasive estimation of pressure distribution in the cardiovascular flow domain use the differential form of governing equations. this study evaluates the advantages of using the integral form of the equations in these calculations. the concepts provided with the boundary element method (bem) together with the boundary-based image segmentation tools are used to develop a fast calculation method. boundary-based segmentation provides bem with domain pixel extraction, boundary meshing, wall normal vector calculation, and accurate calculation of boundary element length. the integral form of the governing equations are reviewed in detail and the analytic value of integral constants at singular points are provided. the pressure data on boundary nodes are calculated to obtain the pressure data at every point in the domain. therefore, the calculation of domain pressure could be considered as a post-processing procedure, which is an advantage of this approach. both the differential and integral-based formulations are evaluated using mathematical couette test flow image whose pressure domain is available. the resulting pressure distributions from both methods will be compared. according to the results obtained from this study, the use of bem for estimating pressure values from a non-invasive flow image has the following advantages: reduced computational domain from two to one dimension, flexible calculation of pressure data at arbitrary points or at finer spatial resolutions, robustness against noise, less concern for its stability and compatibility, accuracy, and lower meshing attempts.