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