Principles of blood flow (Poiseuille's law)

Principles of blood flow (Poiseuille's law)

Principles of blood flow (Poiseuille's law)

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Ohm's Law for Fluids - The Basic Equation

  • Blood flow (Q) through a vessel is analogous to Ohm's law for electrical circuits, providing a fundamental model for hemodynamics.
  • The core relationship is defined by the formula: $Q = \Delta P / R$.
    • Q: Represents the flow rate of blood (e.g., L/min).
    • ΔP: The pressure gradient between two points in the vessel (P₁ - P₂). This is the driving force for flow.
    • R: The vascular resistance to blood flow.

⭐ The entire cardiovascular system's regulation is based on this principle. It's often expressed as Mean Arterial Pressure (MAP) = Cardiac Output (CO) × Systemic Vascular Resistance (SVR), a critical formula for understanding blood pressure control.

Blood flow diversion and Poiseuille's Law in treatment

Poiseuille's Law - The Radius Rules All

  • Defines the relationship between pressure, flow, and resistance for laminar flow in a cylindrical tube.
  • Resistance (R) is the key determinant, calculated as: $R = \frac{8 \eta L}{\pi r^4}$
    • Radius (r): The most powerful factor. Resistance is inversely proportional to the radius to the fourth power ($1/r^4$).
    • Viscosity ($\oldsymbol{\eta}$): Direct relationship. ↑ viscosity (e.g., polycythemia) → ↑ resistance → ↓ flow.
    • Length (L): Direct relationship. Longer vessels have higher resistance.

⭐ Halving the vessel radius increases resistance by 16-fold ($2^4$) and reduces flow by 16-fold, assuming a constant pressure gradient. This principle is critical in arteriolar regulation of blood pressure and flow.

📌 Mnemonic: Think of drinking through a straw. A wider (↑r) and shorter (↓L) straw with less thick (↓η) liquid allows for the easiest flow.

Resistance Networks - Series vs. Parallel

Parallel and Series Microvascular Network

FeatureSeries CircuitParallel Circuit
ArrangementBlood flows sequentially through vessels (one after another).Blood is distributed simultaneously among parallel vessels.
Total Resistance ($R_{total}$)Sum of individual resistances:
$R_{total} = R_1 + R_2 + ...$
Reciprocal of total is sum of reciprocals:
$1/R_{total} = 1/R_1 + 1/R_2 + ...$
EffectAdding a resistor total resistance.Adding a resistor total resistance.
AnatomyWithin organs (e.g., kidney: afferent arteriole → glomerulus → efferent arteriole).Systemic circulation (major arteries branching off aorta to supply organs).

Clinical Correlations - When Flow Goes Wrong

  • Radius ($r$): The most powerful determinant of flow ($Q \propto r^4$).

    • ↓r (Decreased Radius): Atherosclerosis, vasculitis, or arteriolar vasoconstriction dramatically ↓Q, leading to tissue ischemia or infarction.
    • ↑r (Increased Radius): Arteriolar vasodilation (e.g., during exercise, sepsis) significantly ↑Q locally.
  • Viscosity ($\[eta]$): Primarily determined by hematocrit.

    • ↑η (Increased Viscosity): Polycythemia, multiple myeloma, and dehydration lead to sluggish flow and ↑risk of thrombosis.
    • ↓η (Decreased Viscosity): Anemia can cause hyperdynamic circulation and systolic flow murmurs.

Atherosclerosis and blood flow reduction

⭐ A 50% reduction in vessel radius increases resistance 16-fold ($1/r^4$) and reduces flow to just ~6% of the original, highlighting the critical impact of stenosis.

High‑Yield Points - ⚡ Biggest Takeaways

  • Blood flow (Q) is directly proportional to the pressure gradient (ΔP) and radius to the fourth power (r⁴).
  • Flow is inversely proportional to viscosity (η) and vessel length (L).
  • Vessel radius is the most powerful determinant of flow; halving the radius increases resistance 16-fold.
  • Arterioles are the principal sites of systemic vascular resistance regulation.
  • Viscosity is primarily determined by hematocrit; ↑ hematocrit (polycythemia) ↑ viscosity and ↓ flow.

Practice Questions: Principles of blood flow (Poiseuille's law)

Test your understanding with these related questions

A 40-year-old female volunteers for an invasive study to measure her cardiac function. She has no previous cardiovascular history and takes no medications. With the test subject at rest, the following data is collected using blood tests, intravascular probes, and a closed rebreathing circuit: Blood hemoglobin concentration 14 g/dL Arterial oxygen content 0.22 mL O2/mL Arterial oxygen saturation 98% Venous oxygen content 0.17 mL O2/mL Venous oxygen saturation 78% Oxygen consumption 250 mL/min The patient's pulse is 75/min, respiratory rate is 14/ min, and blood pressure is 125/70 mm Hg. What is the cardiac output of this volunteer?

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Flashcards: Principles of blood flow (Poiseuille's law)

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_____ number predicts whether blood flow will be laminar or turbulent

TAP TO REVEAL ANSWER

_____ number predicts whether blood flow will be laminar or turbulent

Reynolds'

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