2 Scope of Module Cardio-vascular system Membranes Fluid flow in pipes, circulation system, pressureMembranesOsmosis and solute transportTransmission of electrical signalsNerves, ECGOptical Fibres and Endoscopy
3 Scope of Module Ultrasound Radioisotope imaging and radiology Imaging and Doppler measurementsRadioisotope imaging and radiologyX-ray generation and imagingNMR imaging
4 Module Resources Web Page: Books: Books:Good general books: “Physics of the Body”, Cameron, Skofronick and Grant “Medical Physics”, J.A. PopeOther 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. 8In considering the circulation of blood, one essentially considers the flow of a viscous fluid through pipes of different diametersDefine: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 differenceAssume: 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 gradientViscosity
7 ViscosityThe 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|2r2a
8 Volume Flow RateThe 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:laP1P2DP= P1 - P2
10 Volume Flow RateOften convenient to define a resistance, R to flow, such that DP=QRSeriesParallelDP1DP2DP3R1R2R3R1,Q1R2,Q2DP= DP1 + DP2 + DP3=QR1+QR2+QR3=QR\R=R1+R2+R3Q=Q1+Q2=DP/R1+DP/R2=DP/R\1/R=1/R1+1/R2
11 Resistance RThe 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/stoppedParallel, flow partially reduced, increased in other parts of the network
13 Transport System A closed double-pump system: Left side of heart Lung CirculationSystemicCirculationRight 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 venulesArteriesArteriolesHeartCapillariesVeinsVenules
16 Transport System Capillaries Fine vessels penetrating tissues Main route for gas/nutrient exchange with tissuesAbout 190/mm2 in cut muscle surfaceSphincter 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 PressuresLarge pressure variations throughout the system (note 1 kPa = 7.35 mm Hg)17 kPa (125 mmHg) after left ventricle2 kPa (15 mm Hg) after systemic system3.4 kPa (25 mmHg) after right ventricleBlood pressure monitor on arm measures mmHg systole and 80 mmHg diastole for a healthy young person
20 Pressure Effect of gravity on pressure Density of blood ~ 1.04x103 kg/m3Distance heart-head~ 0.4 mHeart-feet ~ 1.4 mDP = rgh9.3 kPa13.3 kPa26.7 kPa13.3 kPa13.1 kPa13.2 kPa
21 Pressure Consequences Varicose veins Normally (e.g., during walking) muscle action helps return venous blood from the legsOne-way valves in leg veins to prevent backward flowDefective valves means pooling of blood in leg veins
22 Pressure Acceleration Consider upward acceleration, a - augments gravityeffective gravity = a+gPressure difference = r(a+g)hPressure at head reduced.E.g., a = 3gDPheart-head = 1.04x103 x4gx0.4 = 16 kPaPressure 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/sSurprising - continuity should imply higher flowRecall 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 effectNarrowing of tube gives increased velocity, but reduced pressureIncreasing 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, KCritical velocity Vc = Qc/AVc = Kh/rRFor many fluids, K ~1000e.g, in the aorta (R~1cm), Vc ~ 0.4m/sFlow ratePressureLaminarTurbulentQc
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 regionDuring exercise, 4-5 time increase in blood flow requiredObstructed vessel may not be able to deliverChest pains and heart attack!
27 Further ReadingAll in Physics of the Body, Cameron, Skofronick and Grant, Ch. 8,Measurement of blood pressureSection 8.4Physics of heart diseaseSection 8.10