Hemodynamics and Factors Affecting Blood Flow

Amir GolnabiENGS 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:

Torto

ra, G

erard, and B

ryan D

errickson. P

rinciples of A

natom

y and P

hysiology. W

iley, 2006. 747.

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

4

1

dR

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: 0.015 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%

Ht.plasma 521

Poise.... 03204605210150

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

l

rPF

8

4

References:

•"An Introduction to Blood Pressure". Maryland Virtual High School of Science and

Mathematics. 04/27/2008 <http://mvhs.shodor.org/edgrid/bloodpressure/bptoblt.pdf>.

•Bipin , Upadhyay. "BLOOD VISCOSITY FUNCTIONAL PARAMETERS". COLLEGE OF

BIOMEDICAL ENGINEERING AND APPLIED SCIENCES. 04/28/2008

<http://www.biomedical.edu.np/biomed_files/>.

•Freeman, Scott. Biological Science. Upper Saddle River, NJ: Pearson Prentice Hall,

2005.

•Guyton, Arthur, and John Hall. Textbook of Medical Physiology. PA: Elsevier, 2006.

•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.