The Lattice Boltzmann Method as a General Framework for Blood Flow Modelling and Simulations - Bioanalysis Advanced Materials Methods and Devices - page 150

In the past, the LB method has been applied to a broad range of fluid-dynamic
problems, including turbulence and multiphase flows [ 41 ], as well as in blood flow
simulations in steady and pulsatile regimes and with non-Newtonian flows through
stenoses [ 32 ]. A direct benefit of the joint use of simulation and imaging techniques is
to understand the connection between fluid-mechanical flow patterns and plaque
formation and evolution, with important implications for predicting the course of
atherosclerosis and possibly preventing or mitigating its effects, in particular by non-
invasively and inexpensively screening large numbers of patients for incipient arterial
disease, and to intervene at clinical level prior to the occurrence of a catastrophic
event. One option is to obtain the arterial wall shape, plaque morphology, and lumen
anatomy from the non-invasive multi-detector computed tomography (MDCT) imag-
ing technique, as in the newest systems with 320-detector rows, a technology that
enables 3D acquisition of the entire arterial tree in a single heart beat and high
accuracy of nominal resolution of 0. 1 mm [ 36 ].
The LB method is particularly flexible for handling complex arterial geometries,
since most of its simplicity stems from an underlying Cartesian mesh over which
fluid motion is represented. LB is based on moving information along straight-line
trajectories, associated with the constant speed of fictitious molecules which char-
acterize the state of the fluid at any instant and spatial location. This picture stands
in sharp contrast with the fluid-dynamic representation, in which, by definition,
information moves along the material lines defined by fluid velocity itself, usually a
very complex space-time-dependent vector field. This main asset has motivated the
increasing use over the last decade of LB techniques for large-scale simulations of
complex hemodynamic flows [ 29 , 12 , 27 , 3 ].
The main aim of this chapter is to show that the inclusion of crucial components
such as RBC and the glycocalyx, can be done within a single unified computational
framework. This would allow us to reproduce blood rheology in complex flows and
geometrical conditions, including the non-trivial interplay between erythrocytes and
wall structure. The possibility of embedding suspended bodies in the surrounding
plasma and the glycocalyx representation over an undulated endothelial wall
addresses major steps forward to model blood from a bottom-up perspective, in
order to avoid unnecessary and sometimes wrong assumptions in blood dynamics.
10.2 The Lattice Boltzmann Framework
In the last decade, the LB method has captured increasing attention from the
fluid-dynamics community as a competitive computational alternative to the
discretization of the Navier-Stokes equations of continuum mechanics. LB is a
hydrokinetic approach and a minimal form of the Boltzmann kinetic equation, based
on the collective dynamics of fictitious particles on the nodes of a regular lattice.
The dynamics of fluid particles is designed in such a way as to obey the basic
conservation laws ensuring hydrodynamic behavior in the continuum limit, in which
the molecular mean free path is much shorter than typical macroscopic scales [ 41 ].