Modeling of non-Newtonian blood rheology with applications to arterial flow simulations
Date
2015
Authors
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Journal ISSN
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Publisher
University of Delaware
Abstract
This thesis aims at improving the accuracy of blood flow simulations by offering
a faithful representation of the human blood rheology. A central component of this
work has been the establishment of a connection between the physiological conditions
in blood and the exhibited rheology. This connection, along with the macroscopic
approach which is adopted so as to describe the structural changes within blood that
dictate the key rheological properties, namely the viscosity and yield stress, can be a
powerful tool in the hands of physicians and medical scientists who might require
detailed and reliable information of the exhibited hemodynamics in the arterial network.
Thus, this work can be potentially used for the improvement of diagnostic methods in
cardiovascular-related diseases.
Throughout this thesis particular emphasis has been placed on adhering to a
systematic approach, a practice that is warranted for the modeling of systems as
complex, and highly coupled, as the flow of blood in the human arterial network. The
first step has been the development of a parametric model for the description of the
steady state rheology in simple shear flows. Under physiological conditions, we have
shown that the Casson constitutive equation describes best the rheology of blood. The
proposed model connects the involved parameters, the Casson viscosity and yield stress,
to the physiological conditions, the hematocrit, temperature and fibrinogen
concentration. Yield stress has been modeled as critical, percolation type phenomenon
with an onset that corresponds to a critical hematocrit. The highlight of this work has
been the quantification of the dependence of yield stress, and the critical hematocrit, on
the fibrinogen concentration.
Following the development of the parametric Casson model for physiological
conditions we extended our analysis to pathological cases, whereby we examined the
effect of both high and low values of cholesterol and triglycerides to the steady shear
flow properties. We showed that while the Casson model continues to describe well the
blood rheology, its model parameters, i.e. the yield stress and model viscosity, need to
be significantly modified from their physiological expressions. The new
parametrization involves indices, formed from the supplied cholesterol and triglycerides
information. Namely, we found that the indices of interest are all ratios: total cholesterol
to high density lipoproteins (HDL), low density lipoproteins (LDL) to HDL, and total
triglyceride to HDL. While these indices arose naturally in the fitting of the data, they
all have been previously identified as important in medical evaluations of CVDs.
Upon completion of the steady state analysis, we focused on the modeling of
blood in transient shear flows. We have developed a scalar, structural, parameter
thixotropic model capable of describing the transient shear rheology. The thixotropic
model introduces only three additional parameters, with a specific physical meaning (a
zero shear rate maximum strain, and two kinematic coefficients) and a known order of
magnitude. Even more importantly, at steady state the thixotropic model reduces to the
parametric Casson for low and moderate shear rates, therefore ensuring the previously
emphasized systematic analysis, while at high shear rates it reduces to a Newtonian
model, which is consistent with data from literature that have, however, never been
predicted theoretically. The thixotropic model has been extensively validated against
triangular step-change, rectangular step-change, and large amplitude oscillatory
(LAOS) data, and it offers, at a minimum, a reasonable, semi-quantitative fit.
Finally, we have examined the impact of the described rheology on simulations
of arterial flow. Namely, we have carried out CFD simulations of blood flow in the left
coronary artery (LCA), considering two separate cases: a healthy LCA artery, and a
pathological one with a stenosis causing ~82% blockage in the left anterior descending
(LAD) branch of the LCA. In this study we further developed a previously proposed
methodology for the proper implementation of outflow boundary conditions (OBCs) in
simulations of arterial flow, while also applying a numerical analysis technique which
accelerated significantly the convergence rate of the proposed scheme. The results were
presented via two comparative cases. For the healthy LCA artery, we compared the
predictions of a Newtonian-based simulation to those that resulted from the application
of the Casson parametric model. The obtained pressure and flow profiles, as well as the
wall shear stress (WSS), which is the most important parameter in CVD related
hematological studies, were shown to be significantly different in the two cases. This
highlights the importance of incorporating the rheology of blood in CFD simulations.
Then, for the pathological geometry we compared the results obtained with and without
the application of the proposed scheme for the proper implementation of OBCs. Again,
the marked differences in the simulation output in the two cases highlights the need for
adopting the proposed methodology in arterial flow simulations.