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Physics in Medicine. PH3708 Dr R.J. Stewart. Scope of Module. Cardio-vascular system Fluid flow in pipes, circulation system, pressure Membranes Osmosis and solute transport Transmission of electrical signals Nerves, ECG Optical Fibres and Endoscopy. Scope of Module. Ultrasound

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physics in medicine

Physics in Medicine

PH3708

Dr R.J. Stewart

scope of module
Scope of Module
  • Cardio-vascular system
    • Fluid flow in pipes, circulation system, pressure
  • Membranes
    • Osmosis and solute transport
  • Transmission of electrical signals
    • Nerves, ECG
  • Optical Fibres and Endoscopy
scope of module3
Scope of Module
  • Ultrasound
    • Imaging and Doppler measurements
  • Radioisotope imaging and radiology
  • X-ray generation and imaging
  • NMR imaging
module resources
Module Resources
  • Web Page:
    • http://www.rdg.ac.uk/physicsnet/units/3/ph3708/ph3708.htm
  • Books:
    • Good general books: “Physics of the Body”, Cameron, Skofronick and Grant “Medical Physics”, J.A. Pope
    • Other more specialised books are given in the unit description and will be referred to where necessary
cardiovascular system
Cardiovascular System
  • Physics of the Body, Cameron, Skofronick and Grant, Ch. 8
  • In considering the circulation of blood, one essentially considers the flow of a viscous fluid through pipes of different diameters
  • Define:
    • Viscosity: arises from frictional forces associated with the flow of one layer of liquid over another
viscosity
Viscosity
  • Consider a circular cross section pipe:
    • Flow through pipe due to pressure difference
    • Assume: flow at walls of pipe = 0, maximum in the centre (arrows in figure represent velocity)
    • Frictional force per unit area, F, proportional to the velocity gradient

Viscosity

viscosity7
Viscosity
  • The slower moving fluid outside the central (shaded) region exerts a viscous drag across the cylindrical surface at radius r. For a length Δx of pipe the area of surface is 2πrΔx. The force points in the opposite direction to the direction of fluid motion and is of magnitude 2πrΔx η |dv/dr|

2r

2a

volume flow rate
Volume Flow Rate
  • The average flow from the heart is the stroke volume (the volume of blood ejected in each beat) x number of beats per second. This is ~ 60 (ml/beat) x 80 (beats/min) = 4800 ml/min
volume flow rate9

a

P1

P2

l

DP= P1 - P2

Volume Flow Rate
  • Poiseulle’s Equation
    • Volume flow rate, Q, related to pressure difference DP, length l and radius a by:
volume flow rate10

R1

R2

R3

R1,Q1

DP1

DP2

DP3

R2,Q2

Volume Flow Rate
  • Often convenient to define a resistance, R to flow, such that DP=QR

Series

Parallel

DP= DP1 + DP2 + DP3

=QR1+QR2+QR3

=QR

\R=R1+R2+R3

Q=Q1+Q2

=DP/R1+DP/R2

=DP/R

\1/R=1/R1+1/R2

resistance r
Resistance R
  • The resistance decreases rapidly as a increases R = ΔP/Q = 8 l η / πa4 The units of R are Pa m-3 s A narrowing of an artery leads to a large increase in the resistance to blood flow, because of 1/ a4 term.
volume flow rates
Volume Flow Rates
  • Effect of restrictions and blockages:
    • Series, whole flow is reduced/stopped
    • Parallel, flow partially reduced, increased in other parts of the network
transport system

Left side of heart

Systemic

Circulation

Lung

Circulation

Right side of heart

Transport System
  • A closed double-pump system:
transport system14
Transport System
  • Structure of the Heart

Aorta

Superior vena cava

(from upper body)

Inferior vena cava

(from lower body)

transport system15
Transport System
  • Branching of blood vessels
    • Ateries branch into arterioles, veins into venules

Arteries

Arterioles

Heart

Capillaries

Veins

Venules

transport system16
Transport System
  • Capillaries
    • Fine vessels penetrating tissues
    • Main route for gas/nutrient exchange with tissues
    • About 190/mm2 in cut muscle surface
    • Sphincter muscles (S) control flow
transport system17
Transport System
  • Blood is in capillary bed for a few seconds
  • 1Kg of muscle has a volume of about 106 mm3 (density of muscle ~1gm/cm3 or 1000 Kg/m3 ), hence there are about 190km of capillaries with a surface area of ~12 m2 assuming a typical capillary is 20μm in diameter.
pressures
Pressures
  • Large pressure variations throughout the system (note 1 kPa = 7.35 mm Hg)
    • 17 kPa (125 mmHg) after left ventricle
    • 2 kPa (15 mm Hg) after systemic system
    • 3.4 kPa (25 mmHg) after right ventricle

Blood pressure monitor on arm measures 120 mmHg systole and 80 mmHg diastole for a healthy young person

pressure20

9.3 kPa

13.3 kPa

13.2 kPa

13.3 kPa

13.1 kPa

26.7 kPa

Pressure
  • Effect of gravity on pressure
    • Density of blood ~ 1.04x103 kg/m3
    • Distance heart-head~ 0.4 m
    • Heart-feet ~ 1.4 m
    • DP = rgh
pressure21
Pressure
  • Consequences
    • Varicose veins
      • Normally (e.g., during walking) muscle action helps return venous blood from the legs
      • One-way valves in leg veins to prevent backward flow
      • Defective valves means pooling of blood in leg veins
pressure22
Pressure
  • Acceleration
    • Consider upward acceleration, a - augments gravity
    • effective gravity = a+g
    • Pressure difference = r(a+g)h
      • Pressure at head reduced.
      • E.g., a = 3g
      • DPheart-head = 1.04x103 x4gx0.4 = 16 kPa
      • Pressure from heart = 13.3 kPa \head receives no blood - Blackout!
rate of blood flow
Rate of blood flow
  • Blood leaves heart at ~ 30 cm/s
  • In capillaries, flow slows to ~ 1mm/s
    • Surprising - continuity should imply higher flow
    • Recall individual capillaries only ~20mm in diameter, but very many hence total cross section equivalent to a tube 30 cm in diameter using estimate of 225 x 106 capillaries in body
effect of constrictions
Effect of Constrictions
  • Bernoulli effect
    • Narrowing of tube gives increased velocity, but reduced pressure
  • Increasing velocity at obstruction leads to a transition from laminar to turbulent flow
effect of constrictions25

Turbulent

Qc

Flow rate

Laminar

Pressure

Effect of Constrictions
  • Transition from laminar to turbulent flow characterised by Reynold’s Number, K
  • Critical velocity Vc = Qc/A
  • Vc = Kh/rR
  • For many fluids,K ~1000
  • e.g, in the aorta (R~1cm), Vc~ 0.4m/s
effect of constrictions26
Effect of Constrictions
  • Apparent that one can get a rapid increase in flow as a function of pressure in the laminar region, but relatively slow in turbulent region
    • During exercise, 4-5 time increase in blood flow required
    • Obstructed vessel may not be able to deliver
      • Chest pains and heart attack!
further reading
Further Reading
  • All in Physics of the Body, Cameron, Skofronick and Grant, Ch. 8,
  • Measurement of blood pressure
    • Section 8.4
  • Physics of heart disease
    • Section 8.10