Presentation on theme: "Physics in Medicine PH3708 Dr R.J. Stewart. Scope of Module Cardio-vascular system –Fluid flow in pipes, circulation system, pressure Membranes –Osmosis."— Presentation transcript:
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 the velocity gradient 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 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: l a P1P1 P2P2 P= P 1 - P 2
Volume Flow Rate Often convenient to define a resistance, R to flow, such that P=QR P 1 P 2 P 3 R1R1 R2R2 R3R3 P= P 1 + P 2 + P 3 =QR 1 +QR 2 +QR 3 =QR R=R 1 +R 2 +R 3 SeriesParallel R 1,Q 1 R 2,Q 2 Q=Q 1 +Q 2 = P/R 1 + P/R 2 = P/R R=1/R 1 +1/R 2
Resistance R The resistance decreases rapidly as a increases R = ΔP/Q = 8 l η / πa 4 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/ a 4 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: Systemic Circulation Lung Circulation Left side of heart Right side of heart
Transport System Structure of the Heart Inferior vena cava (from lower body) Superior vena cava (from upper body) Aorta
Transport System Branching of blood vessels –Ateries branch into arterioles, veins into venules Arteries Arterioles Capillaries Venules Veins Heart
Transport System Capillaries –Fine vessels penetrating tissues –Main route for gas/nutrient exchange with tissues –About 190/mm 2 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 10 6 mm 3 (density of muscle ~1gm/cm 3 or 1000 Kg/m 3 ), hence there are about 190km of capillaries with a surface area of ~12 m 2 assuming a typical capillary is 20 μm 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
Effect of gravity on pressure –Density of blood ~ 1.04x10 3 kg/m 3 –Distance heart-head~ 0.4 m –Heart-feet ~ 1.4 m – P = gh 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 = (a+g)h Pressure at head reduced. E.g., a = 3g P heart-head = 1.04x10 3 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 ~20 m in diameter, but very many hence total cross section equivalent to a tube 30 cm in diameter using estimate of 225 x 10 6 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 Flow rate Pressure Laminar Turbulent QcQc –Critical velocity V c = Q c /A –V c = K / R –For many fluids, K ~1000 –e.g, in the aorta (R~1cm), V c ~ 0.4m/s
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