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

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Physics in Medicine PH3708 Dr R.J. Stewart

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

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

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

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 the velocity gradient Viscosity

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

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 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

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

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.

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 Systemic Circulation Right side of heart

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 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.

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

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 DP = rgh 9.3 kPa 13.3 kPa 26.7 kPa 13.3 kPa 13.1 kPa 13.2 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 = 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 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
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 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

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