Physics in Medicine - University of Reading

Physics in Medicine - University of Reading

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 Imaging and Doppler measurements Radioisotope imaging and radiology X-ray generation and imaging NMR imaging 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 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 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

x the velocity gradient dv F dr Viscosity v(r ) F Viscosity

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

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 Rate Poiseulles Equation Volume flow rate, Q, related to pressure difference P, length l and radius a by: a 4 Q

P 8l a P1 P2 l P= P1 - P2 Volume Flow Rate Often convenient to define a resistance, R to flow, such that P=QR

R1 Series R2 Parallel R3 P1 P2 P3

P= P1 + P2 + P3 =QR1+QR2+QR3 =QR R=R1+R2+R3 R1,Q1 R2,Q2 Q=Q1+Q2 =P/R1+P/R2 =P/R R=1/R1+1/R2

Resistance R The resistance decreases rapidly as a increases R = P/Q = 8 l / a4 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 Effect of restrictions and blockages: Series, whole flow is reduced/stopped

Parallel, flow partially reduced, increased in other parts of the network Transport System A closed double-pump system: Left side of heart Lung Circulation Right side of heart Systemic Circulation

Transport System Structure of the Heart Aorta Superior vena cava (from upper body) Inferior vena cava (from lower body) Transport System Branching of blood vessels Ateries branch into arterioles, veins into

venules Arteries Arterioles Heart Capillaries Veins Venules 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 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 20m in diameter. 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

Pressure Pressure Effect of gravity on pressure Density of blood ~ 1.04x103 kg/m3 Distance heart-head~ 0.4 m Heart-feet ~ 1.4 m

9.3 kPa P = gh 13.1 kPa 13.3 kPa 13.3 kPa 13.2 kPa 26.7 kPa 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 Pressure Acceleration Consider upward acceleration, a - augments gravity effective gravity = a+g Pressure difference = (a+g)h

Pressure at head reduced. E.g., a = 3g Pheart-head = 1.04x103 x4gx0.4 = 16 kPa Pressure from heart = 13.3 kPa head receives no blood - Blackout! 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 ~20m 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 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 Constrictions Transition from laminar to turbulent flow characterised by Reynolds Number, K r Qc i na For many fluids,

K ~1000 e.g, in the aorta (R~1cm), Vc ~ 0.4m/s t n e l u Turb Lam

Vc = K/R Flow rate Critical velocity Vc = Qc/A Pressure 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 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

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