Relations describing fluid flow in cylindrical tubes were formulated by Poiseuille approximately 150 years ago, resulting in the well-known Poiseuille Equation. The experiments underlying this formulation were conducted using simple fluids and the viscosity concept was introduced in the equation as a constant, being directly proportional to flow resistance. This was an oversimplification for blood flow and experimental work in the early 1900's revealed that blood viscosity could not be represented with a constant, but rather depended on flow conditions (i.e., tube diameter, flow rate). Blood viscosity expressed as apparent viscosity (i.e., the empirical ratio of the volumes of water and blood which would flow in a given time under the same specified conditions) was reported to take values between 5-100, depending on the velocity of flow and diameter of the tube [1]. This early understanding of blood rheology that dominated the first several decades of 20^th century was clearly described in the famous publication of Whittaker and Winton [1].

This publication is not primarily famous for this description of the shear rate dependence of blood viscosity, but rather because it pointed out that measurements of blood viscosity in cylindrical tubes could not be used to predict its effects on in vivo blood flow [1]. Whittaker and Winton compared the apparent viscosity of blood under a constant pressure difference as determined by simultaneously measuring flow through a dog hind limb preparation and a glass viscometer arranged in parallel. The results clearly indicated that the apparent viscosity of blood determined using the flow rate through the hind limb was lower than the value obtained using the glass viscometer (Figure 1). The differences between apparent viscosity values measured in vivo and ex vivo were more prominent at higher hematocrit values [1].

This approach for calculating apparent viscosity using pressure drop and flow rate data measured in vivo has been used by other investigators under various conditions and in different experimental settings [2, 3]. These investigations were usually done using isolated organs [2] or specially designed arterio-venous shunts to allow the measurements of pressure and flow through a calibrated tube [3]. Additionally, the role of hemorheological parameters in determining pressure-flow relationship in various organs [4-8] or under various pathophysiological conditions [9] have been investigated.