Physics in Medicine

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

2. 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

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

4. 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

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 2πrΔx 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. 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:

10. 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

11. 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.

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

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 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.

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 120 mmHg systole and 80 mmHg diastole for a healthy young person

19. Pressure

20. 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

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. 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

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