Volumetric Blood Flow Rate (Q)
Volumetric blood flow rate ($Q$) is a hydrodynamic parameter that characterizes the volume of fluid passing through a vessel cross-section per unit time. This parameter is typically measured in milliliters per minute (mL/min).
Volumetric flow rate is calculated using Poiseuille's law. According to this law, flow rate is determined by the pressure gradient divided by vascular resistance:
$Q = (P_1 - P_2) / R$
Where:
- $Q$ = volumetric blood flow rate (mL/min)
- $P_1 - P_2$ = pressure gradient between the start and end of the vascular bed (mmHg)
- $R$ = hydrodynamic resistance (dyn·s/cm⁵)
It is important to remember that blood flow rate directly depends on the vessel lumen and varies significantly across different segments. However, according to the continuity equation, volumetric flow rate remains constant across all vessels of the same total caliber.
Distribution of Volumetric Flow Rate Across Organs
Organ perfusion is uneven and depends on functional activity. Below are normal resting volumetric blood flow rates for various organs (mL/min):
| Organ | Blood Flow Rate (mL/min) |
|---|---|
| Thyroid gland | 560 (highest intensity) |
| Kidneys | 420 |
| Liver | 150 |
| Heart (coronary vessels) | 85 |
| Spleen | 70 |
| Brain | 65 |
| Intestines | 50 |
| Stomach | 35 |
| Limb skeletal muscles (at rest) | 2–3 |
Linear Blood Flow Velocity (V) and the Continuity Equation
Linear blood flow velocity ($V$) is the distance a specific blood particle travels per unit time. It is calculated by the formula:
$V = Q / (\pi r^2)$
Where $Q$ is the volumetric flow rate and $\pi r^2$ is the cross-sectional area of a specific vessel.
A fundamental principle of hemodynamics is the continuity equation. It states that if a fluid moves at a constant volumetric flow rate through a system of tubes of varying diameter, the linear velocity of the fluid is inversely proportional to the total cross-sectional area of those tubes ($S$).
$S_1 V_1 = S_2 V_2$
Key rules for the vascular bed:
- Volumetric flow rate does not change along the length of the vascular tree.
- Linear velocity depends exclusively on the total cross-sectional area of all vessels of a given caliber.
- The larger the total lumen area, the lower the linear velocity.
Linear Velocity Dynamics Across Vascular Segments
A graph of velocity versus total cross-sectional area shows a clear inverse relationship:
- Aorta and arteries: Total cross-sectional area is minimal here, so linear velocity is maximal. During ventricular ejection, it reaches 50–60 cm/s, averaging 25–40 cm/s in the aorta and major arteries.
- Arterioles: The flow profile transitions from pulsatile (pulsating) to continuous.
- Capillaries: This segment exhibits a sharp peak in total cross-sectional area. Consequently, linear velocity drops to an absolute minimum of 0.5 mm/s. This dramatic reduction is critical for ensuring efficient metabolic exchange between blood and tissues.
- Veins: Total luminal area begins to decrease compared to the capillary network (though it still exceeds that of the arterial system). Due to the convergence of venules into larger veins and venae cavae, velocity moderately increases, reaching up to 20 cm/s.
Velocity Profile Within a Vessel
Blood flow within a single vessel is non-uniform. Due to frictional forces between blood elements and the vessel wall, a laminar velocity profile is formed:
- Maximum particle velocity is observed strictly in the center of the vessel.
- Minimum velocity is recorded directly at the endothelial walls.
This distribution creates a parallel shearing force directed along the inner vessel wall surface—a phenomenon known as shear stress.