A brief overview of blood flow in arteries

Another possible application of a numerical code - such as a Navier-Stokes solver described here - is the computational modeling of blood flow in arteries. However, it should be noted that this summary is for illustration purposes only and it is not explored further. It is outlined here to demonstrate the applicability of such a code under different conditions. For example, fluid dynamics applications using different biofluids (i.e., blood instead of air) and wall boundary conditions (i.e., artrial walls with continuous compliance, which may or may not contain local blood flow blockages).

Studying blood flow in arteries belongs to the multidisciplinary field of bioengineering. It combines the knowledge base of engineering and medicine. Blood flow in arteries is covered under haemodynamics (Wilmer W. Nichols, Michael F. O'Rourke, "McDonald's Blood Flow in Arteries, Theoretical, Experimental and Clinical Principles", Third Edition, Lea & Febier, London, 1990) (Y.C. Fung, "Biomechanics, Circulation", Second Edition, Springer-Verlag, New York, 1997) (Y.C. Fung, "Biomechanics, Mechanical Properties of Living Tissues", Second Edition, Springer-Verlag, New York, 1993). Beside theoretical work, experimental studies and clinical measurements advanced our understanding in the past two centuries. With the development of modern computers, computational fluid dynamics (CFD) was added, as an independent field, to theoretical and experimental studies of fluid motion.
Numerical modeling of physical phenomena played an important role in the understanding of arterial flows as well.

While experiments can be expensive or measurement data hard to attain, properly validated computational simulations can hold the answer in characterizing conditions, such as flow and pressure, and can assist in the development of semi-empirical correlations.

Blood flow in arteries can be characterized by the combination of three key phenomena. It is an

internal laminar (or sometimes turbulent) flow - with and without flow blockages -
having compliant arterial wall boundaries,
where the blood flow is pulsatile in nature.

The classical picture used to explain the detailed characteristics of flowing blood is that of laminar Poiseuille flow. In this, the flow is compared to that of a fully developed viscous flow in a long, circular pipe with a constant flow rate and a parabolic velocity profile. The concept of Poiseuille flow, applies only under laminar, steady-state flow conditions. However, flow in the larger arteries is, in general, not Poiseuille flow. The primary reason for this is the unsteady nature of the flow, with the possibility of transition or at least transitory bursts of turbulence in the aorta. The branching, asymmetric nature of the vascular geometry means that the flow will be characterized fluid mechanically by entry phenomena, asymmetries in the velocity patterns, complicated secondary motions and even flow separation, all of which are far more difficult to analyze than simple steady-state fully developed Poiseuille flow. For
artery specific flow and geometry the entrance effect, characterized by the entry length, is at least 150 cm, which is far greater than the length of the aorta. The flow in the aorta thus cannot be characterized as fully developed. In fact, all the larger arteries of the circulatory system, including the epicardial coronary vessel, are subject to entrance effects. In the ascending aorta of large mammals viscous effects of the entrance region are confined to a thin-walled boundary layer. The core flow behaves in an inviscid manner, therefore, the flow is characterized as largely inviscid. On the other hand, in the case of fully viscous flow the flow is skewed towards the outer wall. An example for this is the flow in the left common coronary artery. In coronary arteries the Reynolds numbers are much lower, the viscous effects are more dominant and flow is laminar. The velocity profile in many regions will be more like a parabolic Poiseuille flow, except that there will be skewing of this profile due to vessel curvature and branching. Also, significant entrance effects may result in the blunting of the velocity profiles.

Associated with the flow in a bifurcation or curvature is the secondary motion induced by the curved path the fluid must follow. Secondary flows are characterized by a swirling, helical component superimposed on the main streamwise velocity along the tube axis. The most familiar example is that of steady flow in a pipe, a relevant example, since the arch of the aorta is in effect a pipe bend. Secondary motions are also produced by branching, where, just as in a curved pipe, the curvature associated with the change in flow direction is accompanied by a centrifugal pressure gradient. Although there have been numerous fluid-dynamic studies of secondary flow phenomena, instrumentation limitations have prevented any in vivo observations.

An additional complication introduced by the geometry of the arterial system in flow separation from and reattachment to the wall, causing recirculation zones. This phenomena in pulsatile flows is an extremely complex. The recirculation region is unsteady and the separation and reattachment points, if present, can change location or even disappear and then reappear as the flow pulses. The likelihood of separation occurring depends on how sharp a turn the flow must negotiate for the first location and the amount of flow drawn away through the branch for the second location. Even if flow separation does not occur, both these regions would be characterized as generally low in shear, followed by a rapid increase in shear to produce a locally elevated wall shear stress.

The issues addressed above need to be accounted for with suitable numerical models. Therefore, significant improvements to the current basic model are required to solve problems related to the blood flow phenomena.

last updated: January 11, 2000