1. Physics in Medicine
PH3708
Dr R.J. Stewart

2. Scope of Module Cardio-vascular system Membranes
Fluid flow in pipes, circulation system, pressure
Membranes
Osmosis and solute transport
Transmission of electrical signals
Nerves, ECG
Optical Fibres and Endoscopy

3. Scope of Module Ultrasound Radioisotope imaging and radiology
Imaging and Doppler measurements
Radioisotope imaging and radiology
X-ray generation and imaging
NMR imaging

4. Module Resources Web Page: Books:
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

5. 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

6. 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

7. 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 πrΔx η |dv/dr| 2r 2a

8. 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

9. Volume Flow Rate Poiseulle’s Equation
Volume flow rate, Q, related to pressure difference DP, length l and radius a by: l a P1 P2
DP= P1 - P2

10. Volume Flow Rate
Often convenient to define a resistance, R to flow, such that DP=QR
Series
Parallel
DP1
DP2
DP3 R1 R2 R3
R1,Q1
R2,Q2
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

11. Resistance R
The resistance decreases rapidly as a increases R = ΔP/Q = 8 l η / πa 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.

12. 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

13. Transport System A closed double-pump system: Left side of heart Lung
Circulation
Systemic
Circulation
Right side of heart

14. Transport System Structure of the Heart Aorta Superior vena cava
(from upper body)
Inferior vena cava
(from lower body)

15. Transport System Branching of blood vessels
Ateries branch into arterioles, veins into venules
Arteries
Arterioles
Heart
Capillaries
Veins
Venules

16. 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

17. Transport System Blood is in capillary bed for a few seconds
1Kg of muscle has a volume of about mm3 (density of muscle ~1gm/cm3 or Kg/m3 ), hence there are about 190km of capillaries with a surface area of ~12 m2 assuming a typical capillary is 20μm in diameter.

18. 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 mmHg systole and 80 mmHg diastole for a healthy young person

19. Pressure

20. 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
9.3 kPa
13.3 kPa
26.7 kPa
13.3 kPa
13.1 kPa
13.2 kPa

21. 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

22. 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!

23. 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

24. 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

25. 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
Flow rate
Pressure
Laminar
Turbulent Qc

26. 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!

27. 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