Table 3

A summary of the various orders of CFD modelling applied to the cardiovascular system

ModelFigureCFD solutionDescription/examplesTypical solution time
0D *No spatial dimension. Physiological variables such as pressure (P), flow (Q) and resistance (R) are assumed spatially uniform within the model, varying only as a function of time (t), eg, Solved with ordinary differential (0D NS) equations
Lump together distributed physiological systems into a single description. They describe the global behaviour of the modelled segment. The 0D Windkessel model (pictured) is often used to represent the compliant and resistive nature of the arterial circulation. 0D models are frequently used to model components of the cardiovascular system or to improve boundary conditions for 3D models of arterial, ventricular or venous pathophysiology.5 47Immediate solution
1D Physiological variables are solved as a function of a single spatial variable, typically length (x), eg, Solved with partial differential (1D NS) equations
Used to represent wave propagation characteristics and wave reflection. 1D models may also be used to provide boundary conditions for higher order models in order to increase refinement of the solution, especially where the effects of wave reflection are significant.45 46S (static)
Min (transient)
2D Physiological variables are solved as a function of two spatial variables, typically length and distance from centreline (r) eg, Solved with axisymmetric NS equations
Able to resolve the solution in 2D. Used less often now than previously due to ready availability of improved computer processing and 3D solvers. Examples include the simulation of para-prosthetic valve haemolysis and improvement of the assessment of the proximal flow convergence zone in the clinical evaluation of regurgitant valve disease.48
3D Physiological variables are solved as a function of all three spatial variables, including the angle around the centreline axis (θ) eg, Solved with full 3-D NS equations
Full 3D CFD can resolve the physiological solution in all dimensions including time. Examples are more widely reviewed in the main body of the text.Order of minutes for steady- state
Order of hours or days for transient
• *Hydro-electrical analogue diagrams are often used to describe physiological components such as resistance, pressure (voltage), compliance (capacitance), and flow (current).

• †Solution times vary according to complexity of the model and the mathematical solution. The times presented are approximate and are based on a model of coronary physiology.5

• CFD, computational fluid dynamics; NS, Navier-Stokes; 0D, zero dimensional; 1D, one dimensional; 2D, two dimensional; 3D, three dimensional.