Hemodynamics and Factors Affecting Blood Flow Amir Golnabi ENGS 166 Spring 2008

Outline: Blood Flow Blood Pressure –Facts –Mean Arterial Pressure –Total Blood Volume Vascular Resistance –Size Of The Lumen –Blood Viscosity –Total Length of Blood Vessel Conclusion –Rate of Blood Flow References

Blood Flow: Blood flow: Amount of blood that flows through any tissue in a given period of time (mL/min) Total blood flow: Volume of blood that circulates through the systemic and pulmonary blood vessels each minute → Cardiac Output (CO) Cardiac output (CO) = heart rate (HR) x stroke volume (SV) Distribution of CO into different body tissues: 1. Pressure difference of different parts of the body Pressure ↑ → Blood Flow ↑ 2. Resistance of specific blood vessels to blood flow Resistance ↑ → Blood Flow ↓

1. Blood Pressure (BP): Blood flow: ↑ Pressure → ↓ Pressure BP: Contraction of the ventricles → hydrostatic pressure exerted by blood on the walls of a blood vessel. Normal BP in a young adult at rest: – 110 mmHg during ventricular contraction, systole – 70 mmHg during ventricular relaxation, diastole – Systemic Circulation: Tortora, Gerard, and Bryan Derrickson. Principles of Anatomy and Physiology. Wiley,

Blood Pressure (cont.): Mean Arterial Pressure (MAP): The average blood pressure in arteries → closer to diastolic pressure during the greater portion of the cardiac cycle MAP = diastolic BP + 1/3(systolic BP – diastolic BP) (80 + 1/3(120 – 80)) = 93 mmHg CO = HR x SV CO = MAP/R where R is the vascular resistance MAP = CO x R SV ↑ or HR ↑ → CO ↑ and if R stays constant → MAP ↑

Blood Pressure (cont.): Total volume of blood in the cardiovascular system: 5 liters of blood in total – Modest decrease in BV → Homeostatic mechanism – More than 10% → BP ↓ – Water retention → BP ↑

2. Vascular Resistance: Friction between blood and the walls of blood vessels: resists to blood flow Vascular resistance depends on three factors: (1) Size of the blood vessels (2) Blood viscosity (3) Total blood vessels length

2.1. Size of Blood Vessels: Size of the lumen of a blood vessel ↓ → Resistance to blood flow ↑ “forth power law”: the resistance increases in proportion to the inverse of the forth power of the diameter: Vasoconstriction: Narrowing of the vessels resulting from contraction of the muscular wall of the vessels Vasodilation: Widening of the vessels resulting from relaxation of the muscular wall of the vessels constant fluctuations → Resistance → BP

2.2. Blood Viscosity: Shearing force F Different layers of the blood move with different velocities causing a shearing action (friction) between them Rate of shear (γ) is the relative displacement of one fluid layer with respect to the next –slope of the velocity profile: v/h Blood moves by the action of shear stress – the force per area, τ = F/A Viscosity: – η = shear stress / shear rate = τ / γ

2.2. Blood Viscosity (cont.): Blood: – Plasma: Poise – Hematocrit (Ht): normally about 46% for men and 38% for women Factors: – Size of blood vessels ↓ → Velocity (shear rate) ↑ → Viscosity ↓ – Temperature ↓ → Viscosity ↑ 1ºC ↓ → Viscosity ↑ by 2%

2.3. total length of blood vessel: Resistance to blood flow through a vessel ≈ total length of blood vessel Hypertension → additional blood vessels in the adipose tissue → total blood vessel length is longer → resistance to blood flow ↑ → blood pressure ↑ For each extra kilogram of fat, an estimated 650 km (about 400 miles) of additional blood vessels can develop in our body!!!

Rate of Blood Flow Poiseuille’s Law: – F: rate of blood flow – ∆P: pressure difference between two ends of the vessel – r: radius of the vessel – η: blood viscosity – l: length of the vessel

References: "An Introduction to Blood Pressure". Maryland Virtual High School of Science and Mathematics. 04/27/2008. Bipin, Upadhyay. "BLOOD VISCOSITY FUNCTIONAL PARAMETERS". COLLEGE OF BIOMEDICAL ENGINEERING AND APPLIED SCIENCES. 04/28/2008. Freeman, Scott. Biological Science. Upper Saddle River, NJ: Pearson Prentice Hall, Guyton, Arthur, and John Hall. Textbook of Medical Physiology. PA: Elsevier, Purves, William K.; David Sadava, Gordon H. Orians, H. Craig Heller (2004). Life: The Science of Biology, 7th, Sunderland, Mass: Sinauer Associates, 954. Tortora, Gerard, and Bryan Derrickson. Principles of Anatomy and Physiology. Wiley, 2006.