Table 2

CFD—a glossary of selected useful terminology

Analytical solutionRelatively simple models can be described by solving a number of equations using mathematical analysis techniques such as calculus or trigonometry. The solution is analytical because an exact solution can be obtained through algebraic manipulation of the equations (cf. numerical solution).
Bernoulli equation:
Embedded Image Rearranged and simplified:
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The Bernoulli equation relates blood pressure (P) and flow velocity (V). The total energy of flowing blood comprises hydrostatic (P), kinetic ((1/2)ρV2) and potential (ρgh where ρ is fluid density, g is gravity and h is height) energies, the sum of which is conserved. Therefore, an increase in flow velocity must be accompanied by a decrease in pressure, and vice versa. Gravitational effects (ρgh) are usually neglected in a supine vessel. The simplified and rearranged equation is used routinely to calculate transvalvular pressure gradients from flow velocity. The Bernoulli equation ignores energy loss due to viscous friction (see Poiseuille equation) and turbulence, and assumes steady flow.
Boundary conditionsA set of parameters or relationships which describe the physiological conditions (haemodynamic or structural) acting at the boundaries of a modelled segment, representing the interaction of the model with its distal compartments.
DiscretisationTo divide into discrete elements or time periods.
Electrical analogueAn electrical circuit design used to represent a compartment of the circulation, using, for example, ‘voltages’ (pressures), ‘current’ (flow) and resistors. They lack spatial dimensions and are therefore also referred to as dimensionless or ‘zero-D’ (0D) models.
In silico‘Represented or simulated in a computer’, comparable to in vivo and in vitro.
Multi-scale modelA model which integrates models of different length- and or time-scales.
Newtonian and non-Newtonian fluidAs blood is a suspension, non-Newtonian behaviour is particularly important within the capillaries where the size of (solid) blood cells is large relative to vessel calibre, resulting in a non-linear relationship between shear-stress and viscosity. In larger blood vessels Newtonian fluid behaviour is often assumed whereby viscosity is constant, independent of the shear-stress acting on the fluid.
Numerical solutionIn more complex models the mathematics becomes too complicated for analytical techniques and numerical techniques are used instead. Rather than generating an exact solution, the result is an approximation, albeit within very close bounds under certain circumstances. Typically, iterative methods are employed to produce a solution to the equations that converges around the true values. Used to resolve complicated, non-linear, transient (time-varying) analyses for example, 3D-CFD models.
Poiseuille equation:
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Rearranged:
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The Poiseuille equation describes blood flow (Q), along a vessel in relation to viscosity (μ), vessel geometry (length (L) and radius (r)) and the driving pressure gradient (ΔP). According to Poiseuille, flow is strongly dependent upon vessel radius (fourth power). Poisuille's equation considers viscous (frictional) energy losses.
SegmentationThe process by which relevant structures in medical images are identified, isolated and converted into computer representations.
WindkesselGerman for ‘air-chamber’. Windkessel models are relatively simple zero-D models used to represent the resistive and compliant properties of the arterial vasculature.
WorkflowA sequence of applications (computational tools) which are executed sequentially to manipulate medical data to build a model and perform computational analyses. Typically this involves medical imaging, segmentation, discretisation, CFD simulation and post-processing, that is, from clinical imaging to results. Sometimes referred to as a tool-chain.
  • CFD, computational fluid dynamics.