Principles of Blood Flow

Question 1

Characteristics of blood flow and motion throughout the circulation

Answer 1

Stage 1- steady laminar flow in rigid vessels, static driving pressure
Stage 2- High Reynold-s number flow Turbulence, dynamic pressure
Stage 3- Elastic vessel walls, pulsatile pressure
Stage 4- microcirculation, diffusion
-blood is a non-Newtonian fluid
-pressure changes cyclically by the periodic beating of the heart
-energy in the blood is composed of static (applied) pressure, gravitational force and motion of blood. Blood flows from higher to lower pressure
-blood vessels are elastic and change shape with changes in pressure
-pressure waves
-microscopic circulation and diffusion

Question 2

Flow

Answer 2

• flow in series of tubes is constant
• Q = Q1= Q2 = Q3 = Q4 = Q5 = Q
• this is connected series of tubes with different diameters
• image flow through aorta through arteries to the arterioles and then through capillaries back to the venules and then to the vena cava

Question 3

Blood flow

Answer 3

• Q, (L/min) is the quantity of blood passing a particular observation point in a given time interval
• volume flows are additive in a parallel circuit
• flow into a control region equals flow out if there are no sources or sinks (conservation of mass)
• flow across any total cross-sectional area is constant
• generalizes to any number of parallel branches
• parallel circuits can be complicated but flow is still additive

Question 4

Parallel architecture of the circulatory system

Answer 4

• rate of blood flow to each tissue is almost always precisely controlled by tissue need
• cardiac output is controlled mainly by sum of all local tissue flows
• arterial pressure regulation is generally independent of either local blood flow or cardiac output control

Question 5

Re-distribution of cardiac output to various organs during rest and exercise

Answer 5

• in order to avoid hypoxia, the flow of oxygen in the arteries to the tissues must be equal to or greater than the rate of oxygen consumption by the tissues
• in the parallel architecture of the cardiovascular system, the flow of oxygen is distibuted to each tissue at rest in accordance with metabolic activity of each tissue
• during exercise the fraction of cardiac output and hence the allocation of oxygen delivery to various tissues changes
• dramatic increases in blood flow to the skin, muscles and heart during exercise as the venous reserve is mobilized, blood flow to the brain is maintained

Question 6

Relationship between blood flow, velocity, and vessel cross-sectional area

Answer 6

• velocity is the rate of displacement of a particle of fluid with respect to time
• flow (Q) is rate of displacement of a volume of fluid with respect to time
• volume in a cylindrical tube is given by cross sectional area times the width, if fluid is incompressible and the tube is rigid, then the flow past successive cross sections must be equal
• Q = A x v, if Q1=Q2 then v1xA1 = v2xA2

Question 7

Blood flow through a vessel with variable cross section

Answer 7

• v= Q/A

- aorta and capillaries are in series, the total volume flow is the same for both

Question 8

Transit time

Answer 8

• the time required for a blood cell to travel between two points in the system
• estimated by velocity and length or from flow Q and volume of fluid in the vessel
• t= l/v; t=V/Q
• if arterial blood velocity averages 20 cm/sec between the aorta and the wrist, and the distance is 60 cm, then a red blood cell travels from the aorta and the wrist in 3 sec
• if capillary blood velocity is 500 micron/sec and capillary length is 0.5mm, then the capillary transit time is 1 sec, just enough time for the exchange of O2 and CO2
• the total circulation time for one pass through the entire systemic and pulmonary circulation is about 1 min

Question 9

Blood as a fluid

Answer 9

• steady flow of incompressible fluids in rigid, straight cylindrical tubes- good approximation
• assumptions that the flow is laminar with no slippage at the wall and the viscosity is constant across the diameter of vessel
• viscosity is related to how much a fluid resists shear forces and effects fluid flow where there are changes in velocity

Question 10

Relationship between blood flow and pressure

Answer 10

Q (flow) = Change in pressure/ Resistance

• energy to move blood through circulation comes from the driving contraction force generated by the left ventricle
• blood moves if the forces (pressures) at the ends of a region are different
• fluid moves (flows) from a region of high pressure to low (gradients)
• resistance to flow comes from walls of vessels and viscosity of blood (both are frictional forces)

Question 11

Poiseuille’s law

Answer 11

• Q= Change in pressure x (Pi x r^4/8 n(viscosity)L)
• cold water increases viscosity
• vasoconstriction reduces blood flow

Question 12

Pressure drop along a length of blood vessel

Answer 12

P2= P1 - (8nQ/pi r^4)L

• a greater pressure drop along the length of a vessel occurs in a longer vessel with a higher viscosity fluid and especially with a smaller radius
• the blood pressure drops more gradually along the length of large arteries, more rapidly along the length of small arterioles and capillaries, and then gradually along the length of the veins

Question 13

Total resistance for blood vessels in series

Answer 13

-R = (8)(pi)(n) (L/A^2)
-R total= R1 + R2 +R3
Rtotal = Change in P total/Q

Question 14

Total resistance for blood vessels in parallel

Answer 14

-Rtotal= Change of P/Qtotal
1/Rtotal= 1/R1 + 1/R2 + 1/R3
Rtotal= 8(pi)n(L/A^2)