Anesthetics And Red Blood Cell Rheology- Here Lecture Review

Question: The following data is obtained for the flow characteristics of a fluid. (rad s-1 ) 0 11.64 23.28 46.57 116.40 232.80 (Nm-2 ) 0.008 0.073 0.130 0.232 0.500 0.890 Plot shear stress (Nm-2 ) versus strain rate (rad s-1 ) and classify the material behaviour. Suggest a suitable constitutive law to predict material behaviour. Plot a graph of apparent fluid viscosity as a function of strain rate over the measured range. Blood flows at constant velocity through an inclined artery and drops a total vertical distance of 10 cm. At the entrance to this stretch of artery the blood pressure is 6.6 kPa. Assuming the total fluid energy to be unchanged, calculate the blood pressure on exiting this stretch. Some pathological conditions result in deposits forming on the walls of arteries reducing their internal cross-section available for blood flow. If such a condition results in the internal diameter of the aorta reducing by one quarter, calculate the increase in blood velocity and increase in pressure gradient required to ensure that the volumetric blood flow remains unchanged from that in a perfect aorta. Compare and contrast the arterial and venous circulatory systems. Include a discussion on the construction of the blood vessels, the flow conditions and all other relevant details. How does the composition of blood affect its rheological properties? Answer: The following is the graph drawn between shear stress and strain rate from the data given: In the above graph as there is an increase in shear stress, the shear strain rate is more than proportionally increased. The curve is cupped downwards and hence the material behavior can be confirmed as Dilatant(How Tion, Faiz, Zakaria Takashi, 2015). (ii) Constitutive equations are used to determine the relationship between shear stress and shear rate. The rheological behavior of blood is complex, and thus, a single equation cannot completely determine the various rheological variables. The following are some of the constitutive models to determine the material behavior (How Tion et al., 2015: Newtonian fluid model: this is applicable for high shear rates where the diameter of blood vessels is larger than blood cells. In this velocity is considered to be constant at all shear rates. Bingham fluid model: applicable at low shear rates and considers RBC aggregation. Thus, under yield stress (threshold shear stress) it behaves as a solid elastic material. Einstein model: this is valid for suspensions with a small percentage of particles. Quemada model: this can be applied to the blood data over a broad range of shear rates. Solution 2 The total fluid energy remains constant, and the velocity is constant. Hence, the blood pressure at the entrance and exit will be same. Therefore, the blood pressure at the exit is 6.6kPa. Solution 3 Diameter and pressure gradient are related as follows: D1 = d, D2 = d/4 P1= P1, P2= P2 D1 + P1 = D2+ P2 Pressure gradient, i.e., P2-P1 = d d/4 P=3d/4 Velocity and diameter are related similarly as: V12 + d1 =V22 + d2 V22 - V12=d1-d2 (V2-V1)2 = 3d/4 V2-V1 = 3d/4 Solution 4 The circulation of blood from the heart to the body parts and from the body parts to heart is done by blood vessels. The blood circulatory system is thus constituted by heart and blood vessels. Circulatory system can be classified as arterial circulatory system and venous circulatory system (Swift and Weinstein, 2009). Arterial circulation originates from the left heart and involves arteries such as the aorta, coronary arteries and pulmonary arteries. These vessels transport oxygen-rich blood, hormones, nutrients, etc.. from heart to various organs and peripheral tissues. The exception is pulmonary arteries, which carry less oxygenated blood from the right side of the heart to the lungs (Swift and Weinstein, 2009). The venous circulation is a low-pressure system that transports oxygen-depleted blood and waste through the veins and venules from different organs and tissues to the right side of the heart. Exceptionally, pulmonary veins carry oxygenated blood from the lungs to the left side of the heart(Coffman Lempert, 1975). The following table gives a comparison of arterial and venous circulation (Pilgrim and Meier, 2015): Arterial system Venous system Type of blood vessels Includes pulmonary arteries and systemic arteries Includes Superficial veins, deep veins, systemic veins and pulmonary veins Flow direction Blood is directed from the heart to various organs and tissues Blood from peripheral tissues and organs are transported to the heart Concentration of oxygen Oxygen rich blood is transported with the exception of pulmonary artery Low-oxygen or deoxygenated blood is carried with the exception of pulmonary vein Location Arteries are located deep in the body Veins are located superficially Anatomy The walls are made of thick elastic tissue and smooth muscle with more rigid walls to handle high pressure of blood Thin walled with less elastic tissue and very less smooth muscle layer with less rigid walls Valves Absent (except for semilunar valves) Present especially in limbs Solution 5 Viscosity determines the rheology or flows behaviour of fluid. Blood, a two-phase liquid can be considered either as a suspension of cellular elements (majority red blood cells and to some extent leukocytes and platelets) in liquid phase plasma or as an emulsion under certain high shear stress condition. The consideration of blood either as a suspension or as an emulsion depends on the flow conditions and such transition is the main factor for its specific rheological behaviour (Franceschi, 2013). Blood can be considered as a non-Newtonian fluid whose viscosity does not remain constant and varies according to the flow conditions. With the increase in the shear force the viscosity of blood decreases and vice versa (How Tion et al., 2015). The Determinants of Blood Viscosity thus are plasma composition, properties of RBCs and properties of WBCs. Leukocyte concentration: Leukocytes contribute to a minor fraction of blood cell population and thus almost negligibly affects the viscosity of blood under bulk flow conditions. But hyperviscosity is seen when the concentration of leukocyte reaches near to erythrocytes, and this is experienced in various cases of leukemia. Increased leukocyte concentration leads to aggregation and slugging of WBCs and thus affects the rheology of blood (Determinants of Blood Viscosity, 2009). Plasma composition: The protein content of plasma determines the viscosity and increase in the content of proteins lead to hyperviscosity and thus affects the rheology of blood. A significant relative difference in the contribution of protein fractions to the viscosity is seen, and this is observed because of different molecular shape and size of plasma proteins. For example, fibrinogen contributes 22% to plasma viscosity even though it constitutes only 4% to total plasma protein content and globulin contributes to a larger extent to the viscosity because of higher molecular weight in comparison to albumin. The rheological properties of blood or plasma are also affected by the non-protein content of plasma, but this can be considered as a minor determinant (Determinants of Blood Viscosity, 2009). Red blood cell properties: The features of RBCs that contribute to the rheological behaviour of blood are deformability and aggregation. The ability of RBC to undergo a reversible change in the shape in response to deforming sources is defined as deformability. Deformability is a unique property contributing partly to the rheology of blood. Under high shear conditions, deformability contributes to thinning of blood, and this promotes the orientation of RBC to the blood flow. Under low shear stress, reversible RBC clumps are formed, and this denotes aggregation of red blood cells. Aggregation affects the particle size and increases the distortion of blood flow and also increases frictional resistance. Thus, RBC aggregation contributes to the non-Newtonian behaviour by increasing blood viscosity. The ratio of red blood cell volume to the whole blood volume is defined as Hematocrit value. This is a dynamic parameter that varies according to the fluid balance of the body. Hematocrit value reaches to higher value during pathological conditions and this causes increase in blood viscosity (Determinants of Blood Viscosity, 2009). Thus it can be concluded that alterations in hematocrit, RBC deformability and aggregation, plasma composition and leukocyte concentration affects the non-Newtonian rheological behaviour of blood (Determinants of Blood Viscosity, 2009). References Aydogan, B. and Aydogan, S. (2014). Anesthetics and red blood cell rheology. Korea-Australia Rheology Journal, 26(2), pp.205-208. Determinants of Blood Viscosity. (2009). Acta Medica Scandinavica, 180(S456), pp.14-16. Franceschi, C. (2013). Definition of the venous hemodynamics parameters and concepts. Veins and Lymphatics, 2(4), p.1. How Tion, P., Faiz, A., Zakaria, N. and Takashi, H. (2015). The Study of Flow Characteristics of Newtonian and Power-Law Non-Newtonian Fluids by Dam-Break Flow Model. AMM, 802, pp.51-56. MARIK, P. (2010). Hemodynamic parameters to guide fluid therapy. Transfusion Alternatives in Transfusion Medicine, 11(3), pp.102-112. Michael J. Simmonds, O. (2013). Blood rheology and aging. Journal of Geriatric Cardiology : JGC, [online] 10(3), p.291. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3796705/ [Accessed 12 Mar. 2016]. Pilgrim, T. and Meier, B. (2015). Once normal coronary arteries, always normal coronary arteries?. Cathet. Cardiovasc. Intervent., 85(3), pp.406-407. RESULTS OF BLOOD, PLASMA AND SERUM VISCOSITY MEASUREMENTS. (2009). Acta Medica Scandinavica, 180(S456), pp.46-50. Swift, M. and Weinstein, B. (2009). Arterial-Venous Specification During Development. Circulation Research, 104(5), pp.576-588. Sylvester, P., Gould, D. and Lee, L. (2013). The Cerebral Arterial System: A Visual Recall Device. MedEdPORTAL Publications.