Blood is a suspension of cells in plasma. The viscosity of blood depends on the viscosity of the plasma, in combination with the hematocrit and proteins Blood cells behave as suspended particles and increase the viscosity of blood. Fibrinogen due to its asymmetry and high density imparts maximum viscosity to the blood.

 Deformability of Erythrocytes  Haematocrit

Erythrocyte when freely suspended assumes biconcave discoid shape indicative of large excess of its surface area over its volume Shape change of erythrocytes under applied forces is reversible and the biconcave-discoid shape is maintained after the removal of the deforming forces In other words, erythrocytes behave like elastic bodies, while they also resist to shape change under deforming forces

 Erythrocyte deformability refers to the cellular properties of erythrocytes which determine the degree of shape change under a given level of applied force  Erythrocytes change their shape extensively under the influence of applied forces in fluid flow or while passing through microcirculation.

 Erythrocyte deformability is an important determinant of blood viscosity  Deformability of erythrocytes affects viscosity of blood in small vessels where erythrocytes are forced to pass through blood vessels with diameters smaller than their size  In sickle cell anaemia, deformability of erythrocytes is reduced thereby increasing viscosity of blood

The viscoelasticity of blood is traceable to the elastic red blood cells, which occupy about half the volume. When the red cells are at rest they tend to aggregate and stack together In order for blood to flow freely, the size of these aggregates must be reduced, which in turn provides some freedom of internal motion. The forces that disaggregate the cells also produce elastic deformation and orientation of the cells

 Viscosity of blood also varies with changing haematocrit  When the haematocrit rises, the friction between the successive layers of blood increases. Hence with increasing haematocrit the viscosity of the blood rises drastically

 Inflammation causes loss of plasma into the tissues. This leads to slowing of blood flow, disturbance in the axial flow, rouleaux formation and increase in viscosity  Blood viscosity is increased in diabetes mellitus, multiple myloma, jaundice, leukaemia, asphyxia, vomiting and diarrhea Typical mammalian erythrocytes: (a) seen from surface; (b) in profile, forming rouleaux

 Temperature  Flow rate At low flow rates, cell to cell and protein to cell adhesive interactions increase which can cause the red blood cells to adhere to one another

Fahreus-Lindqvist Effect:  Relative viscosity of water, serum or plasma is not altered when they are made to flow through tubes of different sizes  But the relative viscosity of blood is altered when it passes through tubes of different sizes i.e. blood flow in very minute vessels exhibit far less viscous effect than it does in large vessels. This is called Fahreus-Lindqvist Effect

in particular there's a decrease of viscosity of blood as it moves from larger vessels to smaller ones (only if the vessel diameter is between 10 and 300 micrometers). The viscosity decreases with decreasing capillary radius r. This decrease was most pronounced for capillary diameters < 0.5mm

Reasons for Fahreus-Lindqvist Effect: Segre–Silberberg effect, Plasma Skimming Change in haematocrit

 For deformable particles (such as red blood cells) flowing in a tube, there is a net hydrodynamic force that tends to force the particles towards the center of the vessels with diameter between 10 and 300 micrometers This is known as the Segre–Silberberg effect.

 On average, there will be more red blood cells near the center of the capillary than very near the wall, leaving plasma at the wall of the vessel  There is a cell free layer near the vessel wall. This redistribution is known as “plasma skimming”

 In larger vessels such as aorta and its major branches, the cell free layer is only a small % of complete blood stream, so it does not effect the viscosity of blood much  However in arterioles (<300µm) and capillaries, this layer becomes a great % of the total volume contained within the vessel, so fluid viscosity as a whole decreases in these vessels

 Newtons law of motion under translational and rotational motion  If the red blood cell is not located directly within the flow centerline (assuming that the flow is fully developed and parabolic, then the forces induced by the fluid velocity will be different on each end of the red blood cell. Due to this influence of forces, the red blood cell will tend to rotate towards the higher flow region  Recall that the higher fluid velocity has a lower shear stress and therefore higher shear stress would be localized closer to the vessel wall

 This continues until the forces acting o the red cell are balanced and do not cause rotation  Therefore red cells move to the lower shear stress region which have high velocities in order to balance forces.

 Another reason for Fahreus-Lindqvist Effect is change in haematocrit as the vessel diameter decreases  The haematocrit in capillaries e.g. is lower than in the arteries. This is because red blood cells are fairly restricted to the centerline (higher velocity flow) in capillaries and plasma is slowest at the vessel wall  With an inflow haematocrit of 40-50%, capillary haematocrit is about 10-20%

 Analogous to Ohms law for electrical circuits (V=IR) Poiseuille law can be written as ∆P = Q R Where R is the resistance to blood flow

 Vascular resistance is a term used to define the resistance to flow that must be overcome to push blood through the circulatory system.  The resistance offered by the peripheral circulation is known as the systemic vascular resistance ( SVR )  The systemic vascular resistance may also be referred to as the total peripheral resistance

 In fluid dynamics, the Hagen–Poiseuille equation is a physical law that states that for steady laminar flow of a Newtonian fluid through a cylindrical tube, the pressure drop in the tube is directly proportional to the volume flow rate Q, length of the tube, viscosity of fluid and inversely proportional to fourth power of radius of tube Where ∆P is the pressure drop L is the length of pipe, ƞ is the dynamic viscosity, Q is the volumetric flow rate and r is the radius of the pipe L r P1P1 P2P2  P= P 1 - P 2

 R= 8 L η / π r 4  Resistance is dependent on the vessel’s dimensions and the viscosity of blood according to Poiseuille law  A narrowing of an artery leads to a large increase in the resistance to blood flow because of 1/ r 4 term  Vasoconstriction (i.e., decrease in blood vessel diameter) increases SVR, whereas vasodilation (increase in diameter) decreases SVR  Peripheral resistance can be equated to DC resistance in electrical circuits

 Arrangement of vessels also determines resistance.  When the vessels are arranged in series, the total resistance to flow through all the vessels is the sum of individual resistances, whereas when they are arranged in parallel the reciprocal of the total resistance is the sum of all the reciprocals of the individual resistance  Less resistance is offered to blood flow when vessels are arranged in parallel rather than in series

P1P1 P2P2 P3P3 R1R1 R2R2 R3R3  P=  P 1 +  P 2 +  P 3 =QR 1 +QR 2 +QR 3 =QR  R=R 1 +R 2 +R 3 SeriesParallel R 1,Q 1 R 2,Q 2 Q=Q 1 +Q 2 =  P/R 1 +  P/R 2 =  P/R  R=1/R 1 +1/R 2 Resistances in series add directly while resistances in parallel add in reciprocals