1. Relationship between blood flow, vascular resistance and blood pressure
Kirk Levins

2. Blood Flow 1
Blood flow is defined as the quantity blood passing a given point in the circulation in a given period and is normally expressed in ml/min
Overall blood flow in the total circulation of an adult is about 5000 ml/min….The cardiac output

3. Equations of flow
Since flow is a measure of volume per unit time => Q=VA, where Q=Flow V=Velocity, A=Cross sectional area
Since the vascular system obeys an adaptation of Ohms law, known as Darcy’s law
=> Q=ΔP/R, where ΔP is the pressure differential and R is the resistance

4. Cross-sectional areas and Blood flow
- If all the systemic vessels of each type were put side by side, their approximate total cross-sectional areas for the average human being would be as follows:
Vessel
Cross-Sectional Area (cm2)
Aorta
2.5
Small arteries 20
Arterioles 40
Capillaries
2500
Venules
250
Small veins 80
Venae cavae 8
Because the same volume of blood must flow through each segment of the circulation each minute, the velocity of blood flow is inversely proportional to vascular cross-sectional area. Thus, under resting conditions, the velocity averages about 33 cm/sec in the aorta but only 1/1000 as rapidly in the capillaries, about 0.3 mm/sec.

6. Modes of flow in vessles
Blood flow can either be laminar or turbulent

7. Laminar Flow
When blood flows through a long smooth vessel it flows in straight lines, with each layer of blood remaining the same distance from the walls of the vessel throughout its length
When laminar flow occurs the different layers flow at different rates creating a parabolic profile
The parabolic profile arises because the fluid molecules touching the walls barely move because of adherence to the vessel wall. The next layer slips over these, the third layer slips over the second and so on.

8. Turbulent flow
When the rate of blood flow becomes too great, when it passes by an obstruction in a vessel, when it makes a sharp turn, or when it passes over a rough surface, the flow may then become turbulent
Turbulent flow means that the blood flows crosswise in the vessel as well as along the vessel, usually forming whorls in the blood called eddy currents. When eddy currents are present, the blood flows with much greater resistance than when the flow is streamline because eddies add tremendously to the overall friction of flow in the vessel.

9. Turbulent flow
The tendency for turbulent flow increases in direct proportion to the velocity of blood flow, the diameter of the blood vessel, and the density of the blood, and is inversely proportional to the viscosity of the blood, in accordance with the following equation:
Re=(v.d.ρ)/ η
where Re is Reynolds' number and is the measure of the tendency for turbulence to occur, ν is the mean velocity of blood flow (in centimeters/second), d is the vessel diameter (in centimeters), ρ is density, and η is the viscosity (in poise)
When Reynolds’ number increases above about 200 turbulent flow will result

10. Resistance Resistance is the impediment to blood flow in a vessel
Resistance cannot be measured by any direct means, instead, resistance must be calculated from measurements of blood flow and pressure difference between two points in the vessel such that:
Q=(PA-PV)/R
Where Q= Flow, PA-PV=difference between mean arterial and venous pressures, R=resistance
Resistance to blood flow within a vascular network is determined by the length and diameter of individual vessels, the organization of the vascular network , physical characteristics of the blood (viscosity, laminar flow vs turbulent flow, and extravascular mechanical forces acting upon the vasculature.

11. Regulation of blood pressure
Regulation of blood pressure involves the exercise of a number of different functions in different parts of the body. Their collective task is to maintain blood pressure value within a certain interval.
Blood pressure values are maintained within the relevant range by moment-to-moment regulation of cardiac output and of peripheral vascular resistance exerted primarily at the level of the arterioles, postcapillary venules and heart
The most important dimensions of this regulation are as follows:
– The heart contributes to the maintenance of blood pressure via cardiac output
– The kidney contributes by regulating the volume of the fluid present in the blood vessels.
– The internal cellular lining of the walls of the blood vessels regulates vascular resistance via local release of hormones such as endothlin-1 and nitric oxide.
– The baroreceptors are responsible for the rapid moment-to-moment adjustments in blood pressure affected by postural changes

12. Regulation of blood pressure

15. Conductance
Conductance is a measure of the blood flow through a vessel for a given pressure difference and is usually expressed in milliliters per second per millimeter of mercury pressure
Conductance is equal to the reciprocal of resistance

16. Conductance and vessel diameter
Slight changes in the diameter of a vessel cause tremendous changes in the vessel's ability to conduct blood when the blood flow is streamlined
Although the diameters of these vessels increase only fourfold, the respective flows are 1, 16, and 256 ml/mm, which is a 256-fold increase in flow. Thus, the conductance of the vessel increases in proportion to the fourth power of the diameter

17. Pouiseuille’s law
The relationship between conductance and diameter can be explained by considering the number of ‘layers’ of blood in a vessel. For a small vessel a large proportion of the blood is in contact with the wall of the vessel.
By integrating the velocities of all the concentric rings of flowing blood and multiplying them by the areas of the rings, one can derive the following formula, known as Poiseuille's law: Q = (π ΔPr4)/8 ηl
where Q is the rate of blood flow, ΔP is the pressure difference between the ends of the vessel, r is the radius of the vessel, l is length of the vessel, and η is viscosity of the blood.

18. Relationship between resistance and vessel radius

19. Pressure
Blood pressure means the force exerted by the blood against any unit area of the vessel wall
Blood pressure almost always is measured in millimeters of mercury (mm Hg)
Because the heart pumps blood continually into the aorta, the mean pressure in the aorta is high, averaging about 100 mm Hg
Heart pumping is pulsatile, the arterial pressure alternates between a systolic pressure level of 120 mm Hg and a diastolic pressure level of 80 mm Hg, as shown on the left
As the blood flows through the systemic circulation, its mean pressure falls progressively to about 0 mm Hg by the time it reaches the termination of the venae cavae where they empty into the right atrium of the heart.

21. Effect of pressure on vascular resistance and blood flow
Relationship between blood flow and pressure is exponential
Increase in arterial pressure not only increases the force that pushes blood through the vessels but also distends the vessels at the same time, which decreases vascular resistance.

22. Relationship between blood flow, vascular resistance and blood pressure
Blood flow through a blood vessel is determined by two factors:
(1) pressure difference of the blood between the two ends of the vessel, also sometimes called "pressure gradient" along the vessel, which is the force that pushes the blood through the vessel, and
(2) the impediment to blood flow through the vessel, which is called vascular resistance
Q=ΔP/R

23. Questions???