Question

Questions

Question 1.

Equation 1: Mean Arterial Blood Pressure = Cardiac Output X Total Peripheral Resistance

   Equation 2: Blood Flow = Δ Blood Pressure / Resistance

If you increase the radius of a blood vessel this leads to a decrease in the resistance to blood flow along that blood vessel. If the difference in blood pressure between the beginning and the end of this blood vessel does not change, then according to equation 2, blood flow should increase.

But, equation 1 suggests that if you decrease resistance then you should decrease blood pressure. According to equation 2, if you decrease blood pressure then blood flow should decrease.

Therefore, there appears to be a conflict between the two equations with a decrease in resistance (equation 2) leading to an increase in blood flow but also leading to a decrease in blood pressure (equation 1) which should, in turn, lead to a decrease in blood flow (equation 2). However, there is no conflict. Think carefully about what the two equations represent and indicate why this apparent conflict does not exist.

Answer 1

Blood flow refers to the movement of blood through a vessel, tissue, or organ, and is usually expressed in terms of volume of blood per unit of time

Blood pressure is the force exerted by the blood upon the walls of the blood vessels or the chambers of the heart, Arterial Blood Pressure is the pressure of blood flowing in the arteries of the systemic circulation. Mean arterial pressure (MAP) represents the “average” pressure of blood in the arteries

Cardiac output is the measurement of blood flow from the heart through the ventricles and is usually measured in liters per minute

Equation 1: Mean Arterial Blood Pressure = Cardiac Output X Total Peripheral Resistance

Equation 2: Blood Flow = Δ Blood Pressure / Resistance

Now if we rearrange the Eq 2, we will get: Δ Blood Pressure = Blood Flow X Resistance......Eq 3.

From Eq 3 states that an increase in resistance will increase the Blood pressure

Also, Poiseuille’s equation states that Blood flow = ​​π ΔP r^​4​​​​ / ​8ηλ.

• π is the Greek letter pi, used to represent the mathematical constant that is the ratio of a circle’s circumference to its diameter. It may commonly be represented as 3.14
• Δ Blood Pressure represents the difference in pressure.
  • r^4 is the radius (one-half of the diameter) of the vessel to the fourth power.
• η is the Greek letter eta and represents the viscosity of the blood.
• λ is the Greek letter lambda and represents the length of a blood vessel.

By rearranging it slightly to get Resistance and equating with eq 2,

Resistance = ​​​​8 η λ​​ / ​π r​^4

Now, the radius can be changed rapidly by vasoconstriction and vasodilation, thus dramatically impacting resistance and flow. Further, small changes in the radius will greatly affect the flow,

Thus we can see that there is no conflict