1D Modeling of Blood Flow in Networks

Download or read book 1D Modeling of Blood Flow in Networks written by Xiaofei Wang and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The vascular network consists of a very large number of segments with various properties and thus the pulsatile blood flow inside is very complicated. With the time-domain-based nonlinear 1D model, this thesis studies the blood flow in networks, focusing on the numerical computing and several applications.With assumptions of long wave and axisymmetric velocity profile, the 1D governing equations of mass and momentum are derived by integrating the continuity and Navier-Stokes equations along the radius.A Kelvin-Voigt viscoelastic model is adopted for the constitutive equation of the tube.This leads to a nonlinear hyperbolic-parabolic system, which is then solved with four numerical schemes, namely: MacCormack, Taylor-Galerkin, Monotonic Upwind Scheme for Conservation Law (MUSCL) and local discontinuous Galerkin.The schemes are implemented in MATLAB and the numerical solutions are checked favorably against analytical, semi-analytical solutions and clinical observations.Among the numerical schemes, comparisons are made in four important aspects: accuracy, ability to capture shock-like phenomena, computational speed and implementation complexity. The suitable conditions for the application of each scheme are discussed.After this, a general purpose C++ code is developed and tested on several networks:a circle of arteries, a human systemic network with 55 arteries and a mouse kidney with more than one thousand segments. The time dependent distribution of pressure in the networks is visualized and the propagation patterns of the waves are well captured.Good speedup is achieved by parallelizations of the code.The developed code is applied in three studies.First, the coefficients of fluid friction and wall viscosity are determined with aides of a well defined experimental setup.Because both the two factors damp the pulse waves, they are difficult to evaluate separately.We estimate them in pairs by fitting the 1D viscoelastic model against pressure waves measured on the experimental setup. The fitted values of viscoelastic parameters are consistent with values estimated with other methods.The effect of wall viscosity on the pulse wave has been shown in the same order of that of fluid viscosity.Second, with time series of pressure and diameter measured in several locations of the sheep arterial network,the viscoelasticity parameters are estimated.With those values, the pulse waves in the sheep network are simulated and the effect of viscoelasticity is investigated.Numerical solutions show that the viscoelasticity damps significantly the high frequency components of the pulse waves.Third, we simulate the change of blood flow induced by the axillofemoral and femoral-femoral anastomoses with a severe iliac stenosis.The influence of the bypassing path is studied.