Time-Varying Flow of Blood in Vivo

The most obvious feature of the circulation is the pulse. Pulsatile flow can be analyzed as containing steady plus harmonic components. The heartbeat of 60-120 beats per minute gives a fundamental Fourier component of 1 to 2 Hz. Because the flow is time varying, pressure-flow relations are a function of both the shear viscosity and the shear elasticity of the blood. The viscoelasticity of blood has a direct effect on the propagation of the pulse throughout the arterial system [1]. Blood flow in vivo covers a wide range of shear rates and varied vascular geometry (smooth wall of uniform diameter, tapered vessels, bifurcations, side branches, stenoses).

Red Cell Concentration and Deformation

Normal human blood contains a high concentration of red blood cells (RBC), which are elastic elements. The maximum theoretical volume concentration of red cells without squeezing and deforming is 58%. Because normal cell concentration is in the range from 30 to 60%, flow cannot occur through the varied geometry of the circulation without elastic cell deformation and orientation and hence storage of elastic energy in the cells.

Blood flows only because the RBC are deformable and can be reoriented to slide on the low viscosity plasma. The elastic deformability of cells means that energy can be stored in and recovered from cell deformation. The elastic energy is measurable when flow changes with time. Oscillatory flow is particularly useful for measuring this energy and characterizing viscoelastic properties of blood.