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AME 60676 Biofluid & Bioheat Transfer

AME 60676 Biofluid & Bioheat Transfer. 3. Body thermo-fluid-mechanics. Objectives. Overview of blood behavior as it flows in blood vessels: Normal (physiologic) flow conditions Pathophysiologic conditions Blood flow past biomedical devices

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AME 60676 Biofluid & Bioheat Transfer

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  1. AME 60676Biofluid & Bioheat Transfer 3. Body thermo-fluid-mechanics

  2. Objectives • Overview of blood behavior as it flows in blood vessels: • Normal (physiologic) flow conditions • Pathophysiologic conditions • Blood flow past biomedical devices • Overview of the mechanics and mechanical properties of cardiovascular structures

  3. Outline • Blood characteristics • Viscous behavior • Pressure-flow relationships for non-Newtonian fluids • Blood vessel mechanics • Cardiac muscle mechanics • Heart valve mechanics

  4. 1. Blood characteristics Blood characteristics Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Viscous behavior

  5. Blood elements blood Plasma ( 55%) cellular elements ( 45%) water (92%) proteins (7%) others (1%) erythrocytes (RBCs) leukocytes (WBCs) thrombocytes (platelets) albumins (60%) globulins fibrinogen 90% of all proteins Blood characteristics Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Viscous behavior

  6. Blood elements • Erythrocytes (red blood cells) • Involved in transport of O2 and CO2 • Biconcave disc shape (maximizes surface-to-volume ratio) • Volume: 85 – 90 mm3 • Lifespan: 125 days • Concentration: 5 M/mm3 of whole blood 1 m 2 m 8 m Blood characteristics Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Viscous behavior

  7. Blood elements • Erythrocytes (red blood cells) • Production (erythropoiesis) • in bone marrow • requires hemoglobin and iron • Destruction • destroyed by macrophages • iron recycled in bone marrow into new hemoglobin Blood characteristics Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Viscous behavior

  8. Blood elements • Leukocytes (white blood cells) • Involved in phagocytosis and immune responses • Phagocytes • Removal of foreign bodies • Neutrophils, eosinophils, basophils • Immunocytes • lymphocytes • Concentration: 4k – 11k/mm3 of whole blood Blood characteristics Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Viscous behavior

  9. Blood elements • Leukocytes (white blood cells) • Neutrophils • Most abundant leukocyte • Key role in body’s defense against bacterial invasion • Neutrophilleukocytosis (> 7500/mm3) results from inflammation, necrosis Neutrophiland erythrocytes (McGraw-Hill) Blood characteristics Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Viscous behavior

  10. Blood elements • Leukocytes (white blood cells) • Eosinophils • Role in allergic response, defense against parasites • Detoxification of foreign proteins Eosinophil, neutrophil, erythrocytes and platelets (University of Texas) Blood characteristics Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Viscous behavior

  11. Blood elements • Leukocytes (white blood cells) • Basophils • Releases histamine in area of tissue damage • To increase blood flow • To attract other leukocytes Basophil, erythrocytes and platelets (University of Texas) Blood characteristics Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Viscous behavior

  12. Blood elements • Leukocytes (white blood cells) • Lymphocytes • Release of antibody molecules • Disposal of antigen • B lymphocytes (20%) • Produced in bone marrow • Antibody molecules synthesis (humoral immunity) • T lymphocytes (80%) • Produced in thymus gland • Attack virus-infected cells or regulate other immune cells (cell mediated immunity) Lymphocyte, erythrocytes and platelets (University of Texas) Blood characteristics Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Viscous behavior

  13. Blood elements • Thrombocytes (platelets) • Involved in blood clotting (formation of mechanical plugs in hemostatic response to injury) • Adhesion, secretion, aggregation, fusion • Size: 1-2m in diameter • Normal count: 250,000/mm3 of whole blood Platelets and erythrocytes (University of Texas) Blood characteristics Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Viscous behavior

  14. 2. Viscous behavior Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  15. Plasma • Density: 1035 kg/m3 • Dynamic viscosity:  0.0012 kg/(m.s) Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  16. Whole blood • Density:ρ = 1060 kg/m3 (water: 1000 kg/m3) • Dynamic viscosity: = 0.003 – 0.004 kg/(m.s) (water: 0.001 kg/(m.s)) • Non-Newtonian fluid: : strain rate T: temperature H: hematocrit (volume percent of blood occupied by formed elements; normal: 40% - 45%) Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  17. Whole blood • Nonlinear behavior at low shear rates • Existence of a minimum yield stress • Casson’s fluid behavior: yield stress yield stress Shear stress normalized to plasma viscosity vs. rate of shear (Whitmore, 1968) Square root of shear stress normalized to plasma viscosity vs. square root of shear rate (Whitmore, 1968)  Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  18. Whole blood • Apparent viscosity: • Apparent viscosity increases as shear rate decreases • Asymptotic behavior as >>1 0.035 Apparent viscosity vs. shear rate (Whitmore, 1968) Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  19. Whole blood • Effect of hematocrit • Blood viscosity increases with hematocrit • Blood viscosity decreases with shear rate • RBC structure (flexible membrane) minimizes viscosity Apparent blood viscosity normalized to plasma viscosity vs. hematocrit (Whitmore, 1968) Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  20. Whole blood • Effect of plasma protein content • Globulin tends to increase blood viscosity • Albumin tends to lower blood viscosity • Fibrinogen lowers blood viscosity but to a lower extent due to low concentration Apparent blood viscosity vs. shear rate for different plasma protein contents (Flow properties of blood, 1960) Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  21. Whole blood • Yield stress • Mainly dependent on fibrinogen content and hematocrit CF: fibrinogen content (g / 100mL) H: hematocrit (%) • Normal value: 0.7 dyne/cm2 • Effect on capillary blood flow Flow initiated when: Yield stress vs. fibrinogen content and hematocrit (Merill et al., 1965) Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  22. Fahraeus-Lindqvist effect • Definition: apparent viscosity of blood increases with the increase in vessel diameter • Migration of the RBCs from vessel wall to center of the vessel (due to BL effect, spinning) • Existence of 2 flow regions: • cell-free plasma region near the wall • core region near the centerline of the vessel Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  23. Fahraeus-Lindqvist effect • Cell-free marginal layer model red blood cells vessel wall core region cell-free region flow direction From local flow analysis:  In large vessels: In small vessels: Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  24. Fahraeus-Lindqvist effect • Sigma effect • For small vessel diameters (capillaries), continuum hypothesis is not valid • Need to discretize the velocity profile in different concentric layers Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  25. Rouleaux and aggregates • More aggregates at lower shear rates • N cells in a rouleaux will cause a greater disturbance than N individual cells  rouleaux increase apparent viscosity Rouleaux of human red cells (Fung, 1993) Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  26. Red blood cell deformation t = 10 N.m-2 t = 300 N.m-2 • Under high shear rates: • blood aggregate size ↓ • viscosity ↓ • RBC deformation becomes more evident • RBCs elongate and line up along flow direction RBC deformation under shear stress (Caro, 1978) Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  27. 3. Pressure-flow relationships for non-Newtonian fluids Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  28. Power law fluid K: flow consistency index (Pa.sn) n: behavior index (dimensionless)  0.75 for human whole blood • n = 1: Newtonian fluid • n < 1: pseudoplastic (shear-thinning) behavior • n > 1: dilatant (shear-thickening) behavior Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  29. Power law fluid K: flow consistency index (Pa.sn) n: behavior index (dimensionless)  0.75 for human whole blood • Velocity profile: • Volume flow rate:  Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  30. Bingham plastic y: yield stress K: viscosity coefficient • Velocity profile: • Radius at which yield stress is attained: u(r) Rc uc Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  31. Bingham plastic y: yield stress K: viscosity coefficient • Volume flow rate: u(r) Rc uc Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  32. Casson’s fluid(preferred whole blood model) • Velocity profile: • Radius at which yield stress is attained: y: yield stress K: viscosity coefficient Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  33. Casson’s fluid(preferred whole blood model) • Volume flow rate: y: yield stress K: viscosity coefficient Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  34. Whole blood model: summary • Non-Newtonian behavior (Casson’s fluid) • Apparent viscosity is high at low shear rates (RBC aggregation) • Shear thinning behavior (as shear rate , apparent viscosity ) Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  35. Hemolysis • Blood cell damage (destruction or activation) • Depends on: • Shear stress magnitude • Exposure time • RBC hemolysis: • Hemoglobin release in plasma (anemia) • Platelet activation: • Adherence of activated platelets to subendothelial structures (thrombus formation) Shear stress vs. exposure time for hemolysis of RBCs and platelet destruction Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  36. 4. Blood vessel mechanics Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  37. Blood vessel components • Elastin fibers: all vessels but capillaries and venules • Collagen fibers: stiffer but slack • Smooth muscle • Endothelial cells Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  38. Blood vessel components • Elastin + collagen function: to maintain a steady tension within the vessels to act against the transmural pressure • Smooth muscle function: to provide an active tension by means of contraction under physiological control (vascular resistance regulated primarily in smaller arteries and arterioles) • Endothelial cells: sensors, no mechanical function Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  39. Blood vessel behavior • Structure contribution to material behavior • Stress-strain behavior • Individual components: linear elastic materials • Individual fiber combination: bilinear curve • Tissue-level: nonlinear behavior elastin fibers collagen fibers Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  40. Blood vessel behavior • Elastic modulus • Elastin fiber: 106 dynes/cm2 • Collagen fiber: 109 dynes/cm2 • Smooth muscle: depends on muscle state • Typical stress-strain curve for blood vessel: collagen collagen + elastin collagen fiber i+1 collagen fiber i collagen fiber i+2 elastin Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  41. Material characterization considerations • Testing protocol requirements: • Preconditioning over several loading-unloading cycles (compensate for hysteresis) • Physiological environment • Controlled ionic content, moisture, temperature, … • Test on native blood vessels: • long segments to neglect end-effects • compensate for effect of smooth muscle relaxation/contraction Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  42. Material characterization considerations • Assumptions: • Knowledge of p, R, t  E Thin-walled tube t/R < 0.1 Thick-walled tube t/R > 0.1 Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  43. Material characterization considerations • Assumptions: • Homogeneity, isotropy, compressibility • Non homogeneous material (different layers, different components) • Anisotropic material:  information reported in Poisson’s ratio  • Incompressible material ( = 0.5) radial circumferential longitudinal increasing E Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  44. Residual stresses • Arterial wall tissue is not stress-free at zero transmural load Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  45. Residual stresses • Magnitude described in terms of opening angle of sector shape • Residual strains computed by measuring circumferential lengths of intima and adventia in uncut and cut configurations • Function of: • Anatomical location • Species • Location of radial cut Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac muscle mechanics Heart valve mechanics Blood characteristics

  46. 5. Cardiac muscle mechanics Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac musle mechanics Heart valve mechanics Blood characteristics

  47. Material characterization • Diastolic and systolic contractile properties • Orthotropic material: force-deformation behavior stiffer along fibers than in transverse direction intercalated disk (sectioned) intercalated disk mitochondria nucleus cardiac muscle cell contractile fibers Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac musle mechanics Heart valve mechanics Blood characteristics

  48. Material characterization • Fiber orientation varies along wall thickness  Tests performed on papillary muscles (longitudinal fiber orientation) intercalated disk (sectioned) intercalated disk mitochondria nucleus cardiac muscle cell contractile fibers Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac musle mechanics Heart valve mechanics Blood characteristics

  49. Material characterization • Non linear exponential stress-strain behavior • Effects of contractile properties: • Muscle contraction  muscle shortening shortening velocity Vmax maximal isometric force afterload Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac musle mechanics Heart valve mechanics Blood characteristics

  50. Material characterization • Non linear exponential stress-strain behavior • Effects of contractile properties: • Effect of preload shortening velocity Vmax Increasing preload afterload Viscous behavior Non-Newtonian models Blood vessel mechanics Cardiac musle mechanics Heart valve mechanics Blood characteristics

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