Blood Flow in Vessels

Poiseuille’s Law

Blood flows through vessels that can be approximated as long, cylindrical tubes. Under conditions of steady, laminar flow, blood flow can be described by Poiseuille’s law.

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Fig 1 Poiseuille’s Law, simplified

According to this law, flow is directly proportional to radius⁴ and the pressure gradient and is inversely proportional to vessel length and fluid viscosity. Thus, the highest flow will occur in a wide, short vessel, with thin blood, and a large pressure gradient.

Flow 

Flow is defined as the volume of fluid passing a given point per unit time (e.g. mL/min or cm³/s).

In the cardiovascular system, flow may be described at different levels:

• Cardiac output (CO): flow from the left ventricle per minute
• Regional blood flow: flow to a specific organ (e.g. renal blood flow)

Both of these factors are important determinants of an organ’s functioning.

Pressure Gradient (ΔP)

Blood flows down a pressure gradient, from regions of higher pressure to regions of lower pressure. In practice, this means blood will flow from the high pressure arterial end of a vessel to the low pressure venous end. This pressure gradient is primarily created by the pumping action of the heart.

The pressure gradient (ΔP) provides the driving force for blood flow and is often approximated clinically as:

ΔP ≈ Mean arterial pressure (MAP) − venous pressure

Ohm’s Law

Resistance refers to all forces that oppose blood flow. The forces that drive and oppose blood flow in a system can be summarised by Ohm’s Law.

Flow = Δ Pressure / Resistance

where “resistance” are those factors mentioned above (radius, velocity and length).

This can be rearranged to calculate resistance as follows:

Resistance = Δ Pressure / Flow

This applies to the vascular system as a whole as well as regional blood flow. For example, renal blood flow will be determined by the difference in pressure between the renal artery and renal vein and the resistance of the renal vascular bed.

Resistance to flow

Combining Ohm’s Law and Poiseuille’s Law allows factors that affect resistance to blood flow to be determined.

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Fig 2 Ohm’s Law and Poiseuille’s Law combined and simplified to determine factors affecting resistance

Thus, resistance is increased by:

• Reducing vessel radius
• Increasing blood viscosity
• Increasing vessel length

Radius (the dominant factor)

Vessel radius has the greatest influence on resistance because it is raised to the fourth power: If vessel radius halves (2 → 1), then resistance increases 16-fold (2⁴)

Small changes in radius therefore cause large changes in flow. Unlike vessel length and viscosity, vessel radius is actively regulated by the nervous and endocrine systems via vasoconstriction and vasodilation.

Viscosity

Blood viscosity is normally constant.  However, it may increase in dehydration, smoking, or polycythaemia (elevated red blood cell count). Polycythaemia can be acquired in chronic smokers where chronic hypoxia is met with an increase in red blood cells in an attempt to deliver more oxygen to the tissues.

In all these cases, increased viscosity leads to increased resistance and reduced flow.

Length

Vessel length does not change acutely and contributes little to short-term regulation of flow. However, increased vessel length (e.g. in obesity) increases resistance and may contribute to hypertension. The length of blood vessels does not acutely change and is not under our control. As such it is often ignored in this equation.

Regional Blood Flow 

Not all blood follows the same route during each cardiac cycle. Different organs have different metabolic demands, and blood flow is redistributed accordingly.

Examples include:

• Exercise: blood is diverted from the gastrointestinal tract to skeletal muscle
• Hypertension: cerebral vessels constrict to protect the brain from excessive pressure

This redistribution occurs primarily through changes in arteriolar smooth muscle tone, altering local resistance.

Flow vs Velocity

Flow and velocity are related but distinct concepts:

A high flow can be achieved by a little volume moving at very high velocity or a very large volume moving at low velocity.

The relationship between flow, velocity, and vessel size is described by:

Flow = Cross-sectional area × Velocity

which can be rearranged to:

Velocity = Flow / Cross-sectional area

Blood velocity is directly proportional to the flow of blood and inversely proportional to the total cross-sectional area of the vessel network. As total cross-sectional area increases, velocity decreases.

Velocity Across the Vascular Tree

The above concept helps to understand changes in blood velocity through different parts of the circulation:

• Aorta and large arteries: high velocity, small total cross-sectional area
• Arterioles: falling velocity as total cross-sectional area increases
• Capillaries: lowest velocity due to the greatest total cross-sectional area
• Veins: velocity gradually increases again.

Created in BioRender

Fig 3 Diagram showing changes in velocity and surface area across the vascular system

Although individual capillaries have a very small radius, capillary beds are arranged in parallel, giving them a very large total cross-sectional area. This produces a low blood velocity, optimising the exchange of gases, nutrients, and waste products. Low capillary velocity is due to the large total area of the cross-section and not high resistance.

Patterns of Blood Flow

Laminar Flow

In most straight, smooth blood vessels, blood flows in a laminar pattern. Blood cells flow in unidirectional layers: cells nearer the endothelium have a lower velocity due to resistance from the wall itself; cells in the centre have a higher velocity due to lower resistance.

Turbulent Flow

Blood flow becomes turbulent when a vessels radius is reduced (e.g. atherosclerosis, calcification) or when vessel walls are irregular (e.g. bifurcation, abnormal vessel shape, presence of material in the lumen: cancer, atherosclerosis, aneurysm etc.).  Turbulent flow is chaotic and the blood cells bump into the vessel wall causing damage to both the blood cells and the wall.

This damage promotes the expression of pro-coagulative properties and removes normal anti-thrombin. Sometimes, turbulent flow can be heard (known as a ‘bruit’) over arteries with atherosclerotic plaques.

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Fig 4 (a). Laminar flow shows parallel layers; (b) Turbulent flow shows chaotic flow

Clinical Relevance

Virchow’s Triad

Virchow’s triad describes three factors that promote venous thrombosis:

• Stasis of blood flow: due to prolonged immobility, surgery or varicose veins
• Hyper-coagulability: due to smoking, cancer, sepsis, severe burns or increasing age. This can be caused by activation of the coagulation system, a change in the level of clotting factors in plasma or increased viscosity.
• Vessel wall injury: due to atherosclerosis, vessel bifurcations, turbulence. Turbulent flow disrupts the release of endothelial anti-thrombotic substances

All of these factors increase clot risk, potentially leading to conditions such as deep vein thrombosis.

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Fig 5 Virchow’s Triad