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Department of Biophysics, Medical Faculty, Masaryk University in Brno
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Lectures on Medical Biophysics
Biophysics of cardiovascular system
Vascular Anatomy - click for details! PCSHeartbeating

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Lecture outline
̶Mechanical properties of blood vessels
̶Reynolds number
̶Blood flow in blood vessels
̶Peripheral resistance of blood vessels
̶Mechanical work and power of heart
̶Capillary ultrafiltration
̶Kidneys: renal work and glomerular ultrafiltration
̶Blood pressure measurement

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Mechanical properties of cardiovascular system
Closed circulation and transport system
̶Main parts:
ØHeart muscle (myocardium)
ØClosed system of blood vessels
ØBlood
Ø
̶Main functions:
ØSupplying cells by nutrients and oxygen,
ØTransport of hormones and other chemical signals,
ØRemoval of waste and side products from cells (tissues)
ØHeat transfer - thermoregulation

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Mechanical properties of blood vessels
Laplace law – mechanical stress of blood vessel walls is directly proportional to the pressure and
vessel radius
Tension T in walls of some blood vessels:
vessel
r(m)
p(kPa)
T(N·m-1)
aorta
0.012
13
156
artery
0.005
12
60
capillary
6 x 10-6
4
0.024
vein
0.005
2
10
vena cava
0.015
1.3
20

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Elastic and muscular blood vessels
6-6
Aorta behaves like typical elastic vessel
Arterioles are muscular vessels able of vasodilatation and vasoconstriction

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Reynolds number
̶Blood flow: laminar (ordered)
̶                  turbulent (chaotic, eddy)
̶Reynolds (1883)
̶Reynolds number (for a liquid flowing in a cylindrical tube):

r – liquid density, vm – mean flow rate, r – vessel radius, h – coefficient of dynamic viscosity
̶Critical flow rate:

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Blood flow in blood vessels
The differences between theoretical and real flow rate profiles are given mainly by the fact that
blood is a non-Newtonian liquid and is influenced by the distensibility and  compliance of the
vessel wall..
The flow rate profile changes during pulse wave.
We can obtain important diagnostic information from values of blood velocity and the shape of the
flow rate curve.

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Blood flow in an obstructed blood vessel
Fig. after Cameron et al., 1999
The upper curve represents blood flow in a vessel without atherosclerotic stenosis (narrowing), the
lower one in a vessel with stenosis.
We need bigger increase of pressure Dp for the same increase in blood flow DQ (volume per time
unit).
•
•

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Pressure in individual segments of blood circulation
blood circulation

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Peripheral impedance (resistance) of blood vessels
Analogy of electrical impedance (R = U/I)
Pressure p is an analogy of voltage U
Blood flow volume Q (m3·s-1) is an analogy of electric current I
R = Dp/Q
Considering the Hagen-Poiseuille formula for  flow volume:
•

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Peripheral resistance of blood vessels
obr
•Low vascular impedance
characteristic for brain, liver, spleen and kidney arteries
•High vascular impedance
characteristic for arteries of skeletal muscles
time
time

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Peripheral resistance of blood vessels
̶Percentage of total peripheral resistance estimated for individual segments of blood circulation:
Øarteries  .........    66 %
Ø(among those arterioles 40 %)
Øcapillaries ........     27 %
Øveins .............       7 %
̶In vasodilatation, R decreases – heart load decreases
̶In vasoconstriction, R increases – heart load increases

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Mechanical work and power of heart
•Mechanical work of heart muscle:
Some very small work dW is done against external pressure p during ejection of very small blood
volume dV:
dW = pdV
The whole work during a systole:
W = òpdV                    ?????
Very small part of this work is transformed into kinetic energy of the blood ejected.

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Estimation of heart work during one systole
̶p = const. Þ W = pmDV,
pm is mean blood pressure at the beginning of aorta
̶Left ventricle                      Right ventricle
 pm = 13.3 kPa        pm. = 2.7 kPa
 DV = 70 ml             DV  = 70 ml
  W = 0.93 J               W = 0.19 J
̶Mechanical energy of ejected blood volume Wk :
= 0.009 J                  = 0.0018 J
(since Wk = 1/2rvm2DV, r = 1·06x103 kg·m-3, vm. = 0.3 m·s-1, resp. 0.22 m·s-1 in pulmonary artery)
•

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Power of heart
̶Mechanical power of heart
(for pulse rate 70 min-1) ........ 1.3 W
̶Total power of heart
(at rest conditions) ......................13 W
̶Total power of human organism
(at rest conditions) ............................................115 W
̶
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Work and efficiency of myocardium
̶Energy necessary to maintain tonus of myocardium:
aòTdt
̶T – mechanical tension of heart walls (tonus) [N·m-1], t - time
̶Total energy necessary:
Ec = òpdV  +  aòTdt
̶Mechanical efficiency: W/Ec (max. 10 %)

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Capillary ultrafiltration
pressure [kPa]
arterial end
venous end
hydrostat. pressure
4.7
2.3
oncotic pressure
-3.5
-3.5
filtration pressure
1.2
filtrate enters interstitium
-1.2
filtrate leaves interstitium

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Filtration process in capillary loop
6-7
Oncotic pressure = 3.5 kPa
Hydrostatic pressure:
= 4.7 kPa
= 2.3 kPa
filtration pressure
capillary

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!!!!!!!!!!!!!
Group of starving children. Where's your god now?
Oedemas arise due to low protein level in blood plasma, which causes low oncotic pressure and
increases so the filtration pressure.

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Kidneys: renal work and glomerular ultrafiltration
̶The osmotic work necessary to transfer a substance from a medium with substance concentration
C2 to the medium with substance concentration C1. (It is transfer of needful substances from
primary urine back to the blood.)
̶
W = 2.3 nRT logC1/C2
̶Glomerular ultrafiltration:
Hydrostatic pressure in glomerular capillaries is about 6.6 kPa (50 mmHg). The following pressures
have opposite effect: hydrostatic pressure in Bowman’s capsule – 1.3 kPa (10 mm Hg) and oncotic
pressure of plasma proteins – 3.3 kPa (25 mm Hg), so the resulting filtration pressure in
glomerulus is 2 kPa (15 mmHg) under normal circumstances.

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Glomerulus
http://coe.fgcu.edu/faculty/greenep/kidney/Glomerulus.html
glomer3
- 3.3 kPa
-1.3 kPa
+6.6 kPa
+2.0 kPa

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Blood pressure measurement
̶Pressure is  defined as a force  acting on unit area  in a gas or liquid.
p = F/A                [N·m-2],
where F is the force acting on the area A.
̶In the SI system, the pressure is measured in N·m-2, the unit is called pascal [Pa].
̶The most common way of indicating pressure in medicine is by  the height of mercury column in
millimetres - mmHg.
̶1 mmHg = 1 torr = 133.3 Pa
[USEMAP]

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Blood pressure measurement
̶In arteries, the blood pressure oscillates  between a maximum value, i.e. systolic  pressure, and
a minimum  value of  the pressure,  i.e. diastolic blood pressure.
̶The time-course of the blood pressure changes is periodical but non-sinusiodal.
̶The difference between the  systolic and diastolic pressures is maximal at the beginning of
aorta;  the pressure fluctuates in the range of 10.5 to 16 kPa, i.e. 80 to 120 mmHg.
̶The mean value of blood pressure in lung artery represents only one fifth of the blood pressure in
the aorta.

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Riva-Rocci method
a211
An inflatable cuff with manometer is put on the arm above the elbow (heart level), inflated to a
pressure higher than the systolic pressure in a. brachialis. Blood flow is stopped. The pressure in
the cuff is gradually decreased. At systolic pressure, blood starts to flow through the artery. The
turbulent flow produces acoustic noise - Korotkoff sounds, audible in a stethoscope placed in the
elbow pit. As pressure in the cuff is decreased the sounds become louder, culminate and gradually
decrease, disappearing altogether at the diastolic pressure (laminar flow renewed). The maximum
loudness is at mean arterial pressure.

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Riva-Rocci method
̶The Riva-Rocci method can be objectified and automatised for patient monitoring. The cuff is
regularly inflated by a small compressor (e.g., every ten minutes) and the Korotkoff sounds are
recorded by a microphone. Measured values of systolic and diastolic pressures can be displayed (in
simple devices) or stored in the instrument memory and evaluated later. This method is called
Holter monitoring of blood pressure.
̶In small children, this auscultation method can fail. In this case, we can use the Doppler flow
detectors to detect blood flow in the artery compressed by the cuff.
̶

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Direct measurement of blood pressure
̶Invasive measurement of BP is a direct method. A thin, flexible catheter or probe must be inserted
into the blood vessel. Its free end usually is connected to a transducer (capacity or
piezoelectric) but it is also possible to insert a piezoelectric transducer directly into the
vessel. This method is rather risky, so that it is used relatively seldom. However, it is the only
method which allows measurements of  pressure in veins or inside the heart.

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Author:
Vojtěch Mornstein
Content collaboration
C.J. Caruana, I. Hrazdira,
language revision: C.J. Caruana
Last revision October 2021, additon of soundtrack November 2020