Visual Exploration of Simulated and Measured Blood Flow - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 291

decreases the numerical computation time. With all boundary conditions defined,
the flow can be computed based on the 3D unsteady Navier-Stokes equations for an
incompressible Newtonian fluid. Typically, common CFD solvers are used for this
step, for example ANSYS Fluent or OpenFOAM. The resulting velocity and pressure
of the blood flow can subsequently be used for further analysis. For example, the
computation of the dimensionless Reynolds number [ 6 ]. The Reynolds (Re) number
characterizes the local flow behaviour in terms of laminar (Re < 300) or turbulent

(Re 300). In addition to velocity and pressure values, other hemodynamic quanti-

ties are obtained during the simulation. An important quantity is the wall shear stress
( WSS ), which represents the tangential force produced by blood moving across the
vessel surface. It is known that WSS has an influence on the tissue structure of the
vessel wall and it is likely that WSS plays an important role in initiation, growth
and rupture of cerebral aneurysms [ 32 ]. The WSS can be computed based on the
velocity field and the geometry [ 6 , 17 ]. Figure 25.1 b shows the result of such a CFD
simulation using the inlet pressure and velocity based on a typical heart rate. This
simulation is based on 124 time steps. For each time step, a grid size of 500,000 cells
was used to accurately represent the vascular structure resulting in close to 900 MB
of data. CFD simulations give blood flow information at high resolution. However,
CFD simulations are based on models with assumptions and simplifications which
make it difficult to obtain patient-specific accurate results.

>

25.3 Blood Flow Measurement

25.3.1 Acquisition Methods

Measured blood flow information is mostly obtained by quantitative ultrasound (US)
acquisition (see Chap. 5 ) . US is a cost-effective modality, providing flow informa-
tion at high spatiotemporal resolution. However, US acquisition requires a skilled
operator, is generally subject to a substantial amount of noise, and volumetric mea-
surements of the vector velocity field are not possible. Consequently, this modality
is less suitable for challenging cardiovascular conditions. Alternatively, computed
tomography provides a limited number of blood flow acquisition sequences while
delivering better signal-to-noise ratios. CT has the drawback of not measuring flow
directly and exposing the patient to harmful radiation, which is impermissible for
young patients. Instead, we focus on non-invasive Phase-Contrast (PC) MRI acqui-
sition, which is the only modality providing volumetric quantitative measurements
of blood flow velocities throughout the cardiac cycle. A typical size of such a vol-
umetric data is 150 × 150 × 50 voxels with velocity vectors with a resolution of

2 5mm per voxel, and a time series of 20-25 steps per cardiac cycle.

Phase-contrast MRI sequences enable acquisition of flow data that is linearly
related to the actual blood flow velocities, capturing both speed and direction. This
linear relation is described by the velocity encoding (VENC) acquisition parameter,
representing the largest speed that can be measured unambiguously and is typically

× 2 × 2 .