Chapter 8: Blood Rheology

Christina Kolyva

Blood Composition

• Whole blood consists of formed elements and plasma

• Formed elements: Red blood cells (RBCs) or erhythrocytes (99.9%)White blood cells (WBCs) or leukocytesPlatelets

• Plasma consists of: Water (92%)Plasma proteins (7%)Other solutes (1%)

• Hematocrit (H) is the percentage of whole blood occupied by cellular elements

0.1%

Red Blood Cells

• In adult males 1 μl of whole blood contains 4.5-6.3 billion RBCs• Shape: Biconcave disk-thin central region and thick outer margin. Why?• Composition: Only organelles related to transport of respiratory gases Hemoglobin (Hb) accounts for 95% of the cell’s intracellular proteins• Function:

• Production: No nuclei or ribosomes, so they cannot divide or produce their own proteins. Life span ~120 days

RBC formation (erythropoiesis) occurs in red bone marrow

2 2Hb O HbO H

32 2 2 3CO H O H CO H HCO

White Blood Cells

• In adults 1 μl of whole blood contains 6-9 thousand WBCs• Shape: Divided to granulocytes and agranulocytes• Composition: They do have a nucleus

They contain vesicles and lysosomes• Function: Defend the body against invasion by pathogens

Remove toxins, waste, abnormal or damaged cells• Production: They survive from days (N) to months or years (L)

Produced in the bone marrowLs also produced in lymphoid tissues

Neutrophil (50-70%)

Eosinophil (2-4%) Basophil (<1%)Monocyte (2-8%)

Lymphocyte (20-30%)

Platelets

• In adults 1 μl of whole blood contains 150-500 thousand platelets• Shape: Flattened disks, round when viewed from above• Composition: They do not have a nucleus

They carry enzymes and other substances important for the process of blood clotting

• Function: Transport chemicals for initiation and control of clottingForm temporary platelet plug in the walls of injured blood vesselsActively contract when the clot has been formed

• Production: They live for 9-12 daysProduced in the bone marrow by magakaryocytes

Plasma

• Composition: Contains significant quantities of dissolved proteinsAlbumins (60%): Important for the transport of fatty acids, thyroid hormones and steroid hormones. Also major contributors to the osmotic pressure of plasmaGlobulins (35%): Antibodies and transport proteinsFibrinogen: Important for blood clotting.Fit forms fibrin, which is the network for a blood clot

Also contains regulatory proteins, electrolytes, organic nutrients and organic waste

Viscosity

• Viscosity μ:

• Units: cP ( = )

dUτ μ μγ

dy

2 gr10

cm*s

Newtonian, Non-Newtonian behaviour

nτ kγ

0τ τ k γ

0τ τ kγ • Bingham fluids (2):

• Casson fluids (3):

• Pseudoplastics (4, 5):

Rheological curves = shear stress-shear rate curves

Apparent viscosity

• For non-newtonian fluids apparent viscosity μα is defined as the slope of

the rheological curve at a specific shear rate• Relative apparent viscosity is the ratio of the apparent viscosity of a solution divided by the apparent viscosity of the solvent

Viscometers

Blood viscosity

• Blood is a non-Newtonian fluid• Apparent blood viscosity depends on shear rate• Low shear rate=> Rouleaux formations and sedimentation=>high apparent viscosity• High shear rate=> the stacks break down=> newtonian behaviour

Blood viscosity

• The blood has yield stress

• Yield stress depends on H and also on the fibrinogen concentration in plasma

Empirical relation:

F0

(H 10)*(C 0.5)τ

100

Blood viscosity

• Relative viscosity depends also on H and on the flexibility of the RBCs

Blood viscosity

•The dependence on H is non-linear for tube sizes down to 9 μm. For smaller tubes the relation is linear

Blood viscosity

• Blood viscosity depends on plasma viscosity . The latter depends on the protein concentration of plasma

• Protein concentration of plasma also affects the flexibility of the RBCs and the interactions between them (adhesiveness, aggregation)

Blood viscosity

• Blood viscosity also depends on temperature, on the presence of platelets (thrombi formation) and on the presence of WBCs (but only at

pathological conditions)

• Conclusion? The parameters that determine plasma viscosity affect also each other. It is difficult to study each one separately

Model

• Blood is modeled as a Casson fluid: • When τ>>τ0 k= μα and blood behaves like a newtonian fluid

• At high shear rates μα can be calculated as:

0τ τ k γ

0α aα 1

μs μ

(1 H)

Fahraeus-Lindqvist effect

• The apparent viscosity of blood depends on the geometry of the instrument in which it is measured

Fahraeus effect

• Reduction in tube hematocrit in microvessels relative to the supply hematocrit

Blood rheology in the circulation

• High shear rates, therefore blood can be considered newtonian• In the capillaries though, the Fahraeus-Lindqvist effect must be taken into

account

Blood rheology in the circulation

• Isolated rat hearts-blood apparent viscosity was changes by adding albumin• Minimal resistance remained constant despite the changes in apparent viscosity

Blood rheology in the circulation

• Surface of endothelial cells is lined with glycocalyx

Blood rheology in the circulation

• Consists of membrane-bound molecules: glycoproteins, glycolipids, proteoglycans and proteins

Blood rheology in the circulation

• Implications of glycocalyx in blood rheology:• Decrease in H larger than predicted by the anatomical diameter• Increased resistance to flow• Shear stress on the endothelial surface is small-transmitted via the glycocalyx• Regulation of blood flow via changing the shape of the layer