Biophysics of Circulatory System

Overview

Function:

  • to serve the needs of the body tissue
  • to transport
    • nutrients to the body tissue
    • waste products away
    • hormones from one area of the body to another one
    • to maintain an appropriate environment
  • optimal function of the cells = survival
  • blood flow rate is controlled as a function of the actual needs
  • additional function (e.g.: the kidney): 
    • blood flow rate is >> of effective metabolic requirements
    • excretory functions require large volumes to be filtered each minute

What are the mechanisms for controlling blood volume and flow?

Physical characteristics

Pulmonary circulation

Systemic circulation (greater/peripheral)

  • circular closed loop
  • made of several circuits in parallel
  • DIFFERENT types of vessels are organised in SERIES
  • SIMILAR types of vessels are found in PARALLEL

Arteries: pressure reservoir

  • transport blood under high pressure
  • strong vascular wall
  • high blood velocity (fast route)

Arterioles: act as control conduits

  • release blood to capillaries
  • muscular wall (contraction/dilation regulates blood flow)

Capillaries: exchange fluids/metabolites/hormones/gas etc.

  • at the tissue level between blood and the interstitial fluid
  • thin wall
  • capillary pores (semi-permeable)

Venules: collect blood from the capillaries

Veins: conduits of transport of blood back to the heart

  • blood (volume) reservoir
  • low pressure -> thin wall, large lumen, no elastic layer

Amount of blood volume

  • Pulmonary circulation: 9%
  • Heart: 7%
  • Systemic circulation: 84%
    • Arteries: 13%
    • Arterioles and capillaries: 7%
    • Veins, venules, and venous sinuses: 64%

Cross sectional area

  • Arteries: 0.5
  • Arterioles: 10
  • Capillaries: 59
  • Venules: 29
  • Veins: 1,5

Blood velocity

Principle of conservation of mass

F = v x A —> v = F/A

Arteries: 33cm/sec, Capillaries: 0.33 mm/sec (1/1000)

  • While each branching originates smaller vessels, the sum of cross-sectional area progressively increases
  • Velocity of blood flow depends on the total cross-sectional area

Regulation mechanisms

Three basic principles

  1. Blood flow controlled according to the tissue need
    • Rest vs. Exercise: tissues may need up to 20-30 fold increase of blood flow
    • however CO can increase up to 4-7 folds
    • Microvessels act directly on the local blood flow (dilation/contraction)
    • Nervous system plays a role through nervous control
  2. CO = Sum of all the local flows —> the heart pumps what it “receives” ..however CO can increase up to 4-7 folds
  3. Arterial blood pressure is independent of local blood flow and/or CO
    • if arterial pressure falls down nervous reflexes (within sec)
    • a)  ++heart force pumping
    • b)  ++veins contraction -> ++blood volume back to the heart
    • c)  ++arterioles contraction -> ++blood storage in the large arteries -> ++arterial pressure

The Ohm’s Law

  • Pressure, Flow, and Resistance
  • Flow depends on
    • Pressure difference
    • Impediment to flow (vascular resistance)
    • F = (Pin – Pout)/R = ΔP/R
    • Note: pressure gradient is not absolute pressure
  • blood flows according to gradient
  • pressure decreases because of vascular resistance
  • shear stress: friction of blood elements against the vascular wall
  • main pressure drop occurs in arterioles
  • progressive switch from pulsatile to steady state (compliace)
  • P ≈ 0 in the vena cava and right atrium
  • depicted is average pressure
  • see P drop in the pulmonary circuit

What is pressure?

  • blood pressure is the force exerted by the blood against unit of area of the vessel wall
  • P = F/A
  • P = 50 mmHg —> the force needed to push a column of Hg against gravity up to a level of 50 mm

What is resistance?

  • is the impediment to blood flow in a vessel
  • Remember: blood flows according to P gradient, P decreases because of vascular R, shear stress is the friction of blood elements against the vascular wall
  • If ++R —> –ΔP —> –F
  • In systemic circulation: CO ≈ 100 mL/sec and ΔP from the arteries to the veins is 100mmHg
  • R = ΔP/F —> 100mmHg / 100 mL/sec —> R = 1 PRU
    • Vasconstriction —> ++R = 4 PRU (max)
    • Dilation —> – R = 0.2 PRU (min)
  • In Pulmonary circulation CO ≈ 100 mL/sec and ΔP from the pulmonary artery to the left atrium is 16-2 =14mmHg
  • R = ΔP/F —> 14mmHg / 100 mL/sec —> R = 0.14 PRU

The Poiseuille’s Law
F = (Pin – Pout)/R = ΔP/R = (πΔP x r^4)/(8ηL)
R = 8ηL/πr^4

  • depends on geometry (L, r) and viscosity (η)
  • increases linearly with L and η
  • decreases with 4th power of r

Flow characteristics

  • Laminar
    • Parabolic velocity profile
    • friction progressively decreases from the vascular wall to the center of the vessel
    • the fluid touching the wall moves slowly because of friction but the next layer slips over the previous one and so on
  • Turbolent
    • Disordered velocity profile
    • the blood flows along the vessel and crosswise in the vessel (spirals/eddy currents)
    • obstruction (sudden ++velocity),  sharp turn (directional change, bifurcation),  sudden change in vessel diameter,  pulsatility
  • Reynolds number —> Re = (v x D x ρ)/η
    • 200<Re —> Laminar (small vessels (arterioles, capillaries))
    • 200<Re<400 —> transitional
    • Re>400 —> turbulent (large vessels (large arteries: Re >10^3)

Autoregulation

  • how pressure influences resistance and flow) ex: arterial vasoconstriction
  • Vasconstriction
    • —> ++P —> ++F
    • —> ++R —> –F
  • Vascular DISTENSIBILITY allows storing large amount of blood (that can be called into use when necessary)
  • Veins are much more distensible than arteries (8x)
  • Compliance = Increase in Vol / Increase in P
    • i.e., ability of a vessel to expand when the internal pressure varies
  • Immediate elastic distention is followed by stress-relaxation Effect of smooth muscle cells
  • Attenuation of pulsatility
    • it is an effect of vascular compliance of the arterial tree that progressively attenuates pressure pulsations
    • the greater the compliance the smaller the velocity of propagation
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