Learning Objectives
By the end of this section, the learner should be able to:
- Define volumetric flow rate and describe its relationship to velocity and cross-sectional area.
- Explain the determinants of vascular resistance using Poiseuille’s law.
- Compare the total resistance in vessels arranged in series versus parallel.
- Apply the pressure–flow–resistance relationship to the cardiovascular system.
- Describe how vessel radius, viscosity, and vascular arrangement influence blood flow.
Basic Definitions
Volumetric flow rate (Q):
The volume of blood flowing per unit time.
Q=v×AQ = v \times A
Where:
- v = flow velocity
- A = cross-sectional area
As the total cross-sectional area increases, the flow velocity decreases.
Pressure Gradient and Flow
- Blood flow is driven by a pressure gradient (ΔP), moving from high pressure to low pressure.
- The relationship between pressure, flow, and resistance is:
ΔP=Q×R\Delta P = Q \times R
This relationship is analogous to Ohm’s law in electrical circuits (V = I × R).
Vascular Resistance
Resistance (R) is determined by Poiseuille’s law:
R=8ηLπr4R = \frac{8 \eta L}{\pi r^4}
Where:
- η = blood viscosity
- L = vessel length
- r = vessel radius
Key principle:
- Resistance is inversely proportional to the fourth power of the radius.
R∝1r4R \propto \frac{1}{r^4}
➡️ Small changes in vessel radius cause large changes in resistance and flow.
Resistance in Vessel Networks
Vessels in Series
- Total resistance is the sum of individual resistances:
RT=R1+R2+R3+…R_T = R_1 + R_2 + R_3 + \dots
- Example: sequential arterial segments
Vessels in Parallel
- Total resistance is less than the resistance of any single vessel:
1RT=1R1+1R2+1R3+…\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots
- Example: capillary beds
- Parallel arrangement reduces total resistance and increases total flow.
Physiological Correlations
Capillaries:
-
- Have the largest total cross-sectional area
- Exhibit the lowest flow velocity, facilitating gas and nutrient exchange
Arterioles:
-
- Contribute the most to total peripheral resistance (TPR)
- Primary site of blood flow regulation
Veins:
-
- Serve as the main blood reservoir
- Provide most of the body’s blood storage capacity
Blood Viscosity
- Viscosity depends mainly on hematocrit.
Increased viscosity:
- Polycythemia
- Hyperproteinemic states (e.g., multiple myeloma)
Decreased viscosity:
- Anemia
Changes in viscosity directly affect vascular resistance and flow.
