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Biomechanics of Circulation

15-Mark Answer

INTRODUCTION

Biomechanics of circulation refers to the application of physical and mechanical principles to understand how blood flows through the cardiovascular system. The key parameters are blood flow (Q), blood pressure (P), vascular resistance (R), compliance (C), viscosity (η), and velocity (v). These are governed by fundamental laws of fluid mechanics adapted for biological systems.

Costanzo Physiology 7th Ed., p. 125
Guyton & Hall Medical Physiology, p. 180

1. BLOOD FLOW (Q)

Blood flow is the volume of blood moving past a given point per unit time, expressed in mL/min or L/min.

Total cardiac output at rest ~ 5000-6000 mL/min.

The fundamental relationship (analogous to Ohm's Law in electricity):

Q = ΔP / R

Where:

Q = blood flow (mL/min)
ΔP = pressure difference between two ends of a vessel (mmHg)
R = vascular resistance

This means flow is directly proportional to the pressure gradient and inversely proportional to resistance. If pressure at both ends of a vessel is equal (ΔP = 0), there is NO flow regardless of the absolute pressure.

Guyton & Hall, p. 180

2. BLOOD PRESSURE

Blood pressure is the force exerted by blood per unit area of the vessel wall, measured in mmHg.

Pressure gradient across the systemic circulation:

Location	Mean Pressure (mmHg)
Aorta	100
Large arteries	100 (systolic 120, diastolic 80)
Arterioles	50
Capillaries	25
Venules	10
Vena cava	4
Right atrium	0-2

The greatest pressure drop occurs across the arterioles because they have the highest resistance (smallest radius, thick smooth muscle walls).

Arterial Pressure Components:

Systolic pressure: Highest pressure during ventricular ejection (~120 mmHg)
Diastolic pressure: Lowest pressure during ventricular relaxation (~80 mmHg)
Pulse pressure = Systolic - Diastolic = ~40 mmHg (reflects stroke volume)
Mean arterial pressure (MAP) = Diastolic pressure + 1/3 Pulse pressure ≈ 93 mmHg

MAP is not a simple arithmetic mean because the heart spends more time in diastole than systole.

Costanzo Physiology, p. 133-135

3. VASCULAR RESISTANCE

Resistance is the impedance to blood flow. It cannot be measured directly but is calculated as:

R = ΔP / Q

The unit is the Peripheral Resistance Unit (PRU): 1 mmHg per mL/sec.

Poiseuille's Equation

The factors determining resistance are described by the Hagen-Poiseuille equation:

R = 8ηl / πr⁴

Where:

η = viscosity of blood
l = length of vessel
r = radius of the vessel

Key implications:

Radius is the most powerful determinant - resistance is inversely proportional to r⁴. A 50% reduction in radius increases resistance 16-fold (2⁴); a 75% reduction (radius reduced to 1/4) increases resistance 256-fold (4⁴).
Resistance increases proportionally with vessel length.
Resistance increases with blood viscosity (e.g., in polycythemia, hematocrit ↑ → viscosity ↑ → resistance ↑).

This is why arterioles (smallest radius) are the primary site of vascular resistance and the main regulators of blood flow distribution.

Costanzo Physiology, p. 129

4. SERIES VS PARALLEL RESISTANCE

Vessels in Series:

Each organ's vasculature is arranged so blood flows from artery → arteriole → capillary → venule → vein sequentially. Total resistance adds up:

R_total = R₁ + R₂ + R₃ ...

Pressure drops progressively along this path.

Vessels in Parallel:

The major organ circulations (brain, kidney, muscle, coronary, skin) are arranged in parallel with each other. Total resistance is:

1/R_total = 1/R₁ + 1/R₂ + 1/R₃ ...

This means total peripheral resistance is less than any individual resistance. Adding parallel circuits decreases total resistance and increases total flow. This arrangement allows independent regulation of blood flow to each organ.

Guyton & Hall, p. 182-183

5. VASCULAR COMPLIANCE (CAPACITANCE)

Compliance describes the distensibility of blood vessels:

C = ΔV / ΔP

Where C = compliance, ΔV = change in volume, ΔP = change in pressure.

Veins are highly compliant (~8x more than arteries) - they hold ~64% of total blood volume at low pressure → called the unstressed volume (venous reservoir).

Arteries are less compliant - they hold blood under high pressure → called the stressed volume.

Clinical significance:

Aging reduces arterial compliance (arteries become stiffer) → same stroke volume now produces a higher pulse pressure → systolic hypertension in the elderly.
Venoconstriction (decreased venous compliance) shifts blood from veins to arteries → increases venous return → increases preload → increases cardiac output (Starling mechanism).

Costanzo Physiology, p. 131-132

6. VELOCITY OF BLOOD FLOW

Velocity (v) is different from flow (Q). Velocity is the speed at which blood travels along a vessel.

v = Q / A

Where A = cross-sectional area of the vessel.

Key concept: As vessels branch and their total cross-sectional area increases, velocity decreases - even though flow (volume/min) is constant. This is why:

Blood moves fastest in the aorta (~50 cm/s) - small total area
Blood moves slowest in capillaries (~0.03 cm/s) - enormous total cross-sectional area (~4500 cm²)
Slow capillary velocity allows time for nutrient and gas exchange

Costanzo Physiology, p. 126

7. LAMINAR vs. TURBULENT FLOW

Laminar Flow (Normal):

Under normal physiological conditions, blood flows in concentric cylindrical layers (laminae):

The outermost layer (adjacent to vessel wall) moves slowest due to friction
The central layer (axial stream) moves fastest
Red blood cells accumulate at the center - this is called axial streaming
The plasma-rich zone near the wall explains the Fahraeus-Lindqvist effect: apparent viscosity decreases in very small vessels (<300 μm diameter)

Turbulent Flow (Abnormal):

Turbulence occurs when flow exceeds a critical velocity. It is predicted by the Reynolds number (Re):

Re = ρvd / η

Where ρ = blood density, v = velocity, d = vessel diameter, η = viscosity.

Re < 2000: Laminar flow
Re > 3000: Turbulent flow
Re between 2000-3000: transitional zone

Turbulent flow generates audible sounds (bruits or murmurs) - the basis of Korotkoff sounds in blood pressure measurement, and pathological heart murmurs. Turbulence increases energy expenditure and reduces efficiency of flow.

8. CLINICAL APPLICATIONS

Condition	Biomechanical Change
Hypertension	↑ TPR (arteriolar constriction) → ↑ MAP
Atherosclerosis	↓ r⁴ (plaque narrows lumen) → ↑ R by 256× with 75% stenosis
Polycythemia	↑ viscosity (η) → ↑ R → ↑ cardiac workload
Anemia	↓ viscosity → ↓ R → ↑ flow (compensatory)
Arterial aging	↓ compliance → ↑ pulse pressure → isolated systolic HTN
Heart failure	↓ stroke volume → ↓ pulse pressure
Shock	↓ ΔP → ↓ Q → reflex arteriolar constriction ↑ R to maintain MAP

SUMMARY TABLE

Parameter	Formula	Key Determinants
Blood Flow (Q)	Q = ΔP/R	Pressure gradient, resistance
Resistance (R)	R = 8ηl/πr⁴	Radius (r⁴), viscosity, length
Compliance (C)	C = ΔV/ΔP	Vessel wall elasticity
Velocity (v)	v = Q/A	Cross-sectional area
MAP	DBP + 1/3 PP	Diastole, stroke volume, HR
Reynolds No.	Re = ρvd/η	Velocity, diameter, viscosity

CONCLUSION

The biomechanics of circulation is governed by the interplay of pressure gradients, vascular resistance, vessel compliance, blood viscosity, and flow velocity. The arterioles are the primary resistance vessels controlling tissue blood flow distribution. Vessel radius (via the 4th-power law of Poiseuille) is the single most powerful regulator of resistance. Vascular compliance determines how vessels buffer pulsatile pressure into steady flow. Understanding these principles is the foundation for interpreting cardiovascular physiology and the pathophysiology of diseases like hypertension, atherosclerosis, and heart failure.

References:

Costanzo, L.S. Physiology, 7th Ed. (Chapter 4: Cardiovascular Physiology), pp. 125-140
Guyton, A.C. & Hall, J.E. Textbook of Medical Physiology, pp. 180-186

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BIOMECHANICS OF CIRCULATION

FUNCTION OF CIRCULATION

Circulation serves four main functions:

Transport nutrients to tissues
Take away waste products from tissues
Conduct hormones from one part of the body to another
Maintain an appropriate environment in all tissue fluids for survival and function of cells

CIRCULATION

Circulation is of two types:

Systemic circulation - carries oxygenated blood from left heart to body tissues
Pulmonary circulation - carries deoxygenated blood from right heart to lungs

FUNCTIONAL PARTS OF CIRCULATION

(a) Arteries - Transport blood under high pressure to the tissues. They are thick-walled, with extensive elastic tissue and smooth muscle to withstand high pressure.

(b) Arterioles - Last small branches of the arterial system. They act as control valves through which blood is released into the capillaries. Their walls have extensive smooth muscle which can completely close or dilate the vessel several-fold.

(c) Capillaries - Their walls are thin and permeable to small molecular substances. They help exchange of fluid, nutrients, electrolytes, hormones, and other substances between blood and interstitial fluid.

(d) Venules - Collect blood from the capillaries.

(e) Veins - Transport blood from tissues back to heart. Also act as a controllable reservoir for extra blood.

VOLUME OF BLOOD IN DIFFERENT PARTS OF CIRCULATION

Part	% of Total Blood Volume
Systemic circulation	84%
Pulmonary vessels	9%
Heart	7%

BASIC THEORY OF CIRCULATION

(1) Blood flow to each tissue is controlled according to its needs

Each tissue regulates its own blood supply based on metabolic demand
Increased activity → increased O₂ demand → increased blood flow
This is achieved by autoregulation

(2) Cardiac output is determined by tissue needs

The heart pumps the amount of blood returned to it
Increased tissue blood flow → increased venous return → increases cardiac output through Frank-Starling mechanism

Cardiac Output = Heart Rate × Stroke Volume

(3) Arterial pressure is regulated independently

The body maintains arterial pressure within a narrow range to ensure adequate perfusion of vital organs
Normal blood pressure = 120/80 mmHg

Regulation:

Short term - Baroreceptors at carotid sinus and aortic arch
Long term - Kidneys; Renin-Angiotensin-Aldosterone System (RAAS)

INTERRELATIONSHIP AMONG PRESSURE, BLOOD FLOW, AND RESISTANCE

Haemodynamic Principle

Flow is determined by 2 factors:

Q = ΔP / R

Where:

Q = Blood flow
ΔP = Pressure difference between two ends of vessel (P₁ - P₂) = pressure gradient
R = Vascular resistance

The pressure gradient is the driving force and resistance opposes flow. If ΔP = 0, there is no flow even if absolute pressure is high.

BLOOD FLOW

Definition: Quantity of blood that passes a given point in circulation in a given period of time.

Units: millilitres or litres per minute (mL/min or L/min)

Methods for Measuring Blood Flow:

Electromagnetic flowmeter
Ultrasonic Doppler flowmeter

Types of Blood Flow

Laminar Flow	Turbulent Flow
Streamlined / normal flow	Blood flows in irregular, chaotic patterns
Parabolic velocity profile	Produces murmurs and bruits
Velocity at centre of vessel is far greater than at outer edges	Occurs when blood passes an obstruction in the vessel, makes a sharp turn, or passes over a rough surface
After parabolic interface, fluid adjacent to wall is hardly moved; slightly away is moved small distance; centre moves greatest distance	Causes energy loss and reduces flow efficiency

Parabolic velocity profile during laminar flow:

vessel wall ________________________
                →→→→ (fastest at centre)
              →→→
            →→
wall ________________________
         Velocity →

BLOOD PRESSURE

Definition: Force exerted by blood against any unit area of vessel wall.

Standard units of pressure:

mmHg (millimetres of mercury)
cmH₂O (centimetres of water)

High Fidelity Methods for Measuring Blood Pressure

Works on 3 basic principles:

Works on capacitance - membrane moves closer to metal plate, increasing capacitance
Works on inductance - iron slug displaced into coil, changing inductance
Works on resistance - stretched wire changes resistance

RESISTANCE TO BLOOD FLOW

Calculated from measurement of blood flow and pressure difference in vessel
Unit is Peripheral Resistance Unit (PRU)

Total Peripheral Resistance (TPR) = mmHg / mL per sec

Normal value = 1 PRU

Calculated as:

Mean arterial pressure ≈ 100 mmHg
Cardiac output ≈ 100 mL/s

TPR = 100/100 = 1 PRU

Conductance

Conductance = ease with which blood flows through a vessel
Opposite of resistance
High conductance = blood flows easily
Low conductance = blood flow is difficult

According to Poiseuille's law: Flow ∝ diameter⁴

Diameter	Flow
1	1
2	16
4	256

Because: 1⁴ = 1, 2⁴ = 16, 4⁴ = 256

Conductance ∝ diameter⁴

POISEUILLE'S LAW ★

Describes the relationship between blood flow and physical properties of blood vessel.

Q = π ΔP r⁴ / 8ηl

Where:

Q = Blood flow
ΔP = Pressure difference
r = Radius of vessel
η = Viscosity of blood
l = Length of vessel

EFFECT OF BLOOD HEMATOCRIT AND VISCOSITY

Hematocrit = % of blood that is cells

Average men: 42
Average women: 38
Greater the % of hematocrit → more friction between layers of blood
Viscosity ↑ as hematocrit ↑
Viscosity of normal blood is about 3× greater than viscosity of water
Each RBC exerts frictional drag against adjacent cells and wall of vessel

Blood Viscosity in Microcirculation

More resistance in circulatory system occurs in very small blood vessels. Three factors - hematocrit, plasma protein, and vessel size - affect blood viscosity in these vessels:

(1) Fahraeus-Lindqvist Effect

Blood flow in minute tubes exhibits far less viscous effect than it does in large vessels
In small vessels (<300 μm), velocity of blood flow is slow (<1 mm/sec) → viscosity can increase as much as 10-fold

(2) Viscosity of blood increases tremendously as its velocity of flow decreases

Velocity of blood flow in small vessels is slow (<1mm/sec)
Viscosity can increase as much as 10-fold

(3) Cells often become stuck at constriction on small vessels

Blood flow becomes blocked for a fraction of a second or much longer
This increases the viscosity

Effect of Pressure on Resistance

Increase in arterial pressure not only increases the force to push blood through vessels, but also distends the vessels → which decreases resistance
Strong sympathetic stimulation constricts the vessels → blood flow can decrease to as low as zero for short periods despite high arterial pressure

REYNOLDS NUMBER (Re) - Turbulent Flow

Re = ρvd / η

Where:

Re = Reynolds number
ρ = Density of blood
v = Velocity of blood flow
d = Diameter of vessel
η = Viscosity of blood
Re < 2000 → Laminar flow
Re > 3000 → Turbulent flow

SUMMARY

The biomechanics of circulation governs how blood moves through the cardiovascular system using the principles of flow (Q = ΔP/R), Poiseuille's law (Q = πΔPr⁴/8ηl), and vascular resistance. The arterioles are the primary resistance vessels acting as control valves. Blood viscosity (influenced by hematocrit) and vessel radius (raised to the 4th power) are the most important determinants of resistance. Laminar flow is normal; turbulence occurs at high Reynolds numbers and produces audible murmurs. Arterial pressure is maintained by short-term baroreceptor reflexes and long-term RAAS mechanisms to ensure adequate tissue perfusion.

Reference: Textbook of Medical Physiology by Guyton, 9th Edition

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