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Physics in Medicine PH3708 Dr R.J. Stewart

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**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

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**Scope of Module Ultrasound Radioisotope imaging and radiology**

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

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**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

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**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

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**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

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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

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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

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**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

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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

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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.

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**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

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**Transport System A closed double-pump system: Left side of heart Lung**

Circulation Systemic Circulation Right side of heart

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**Transport System Structure of the Heart Aorta Superior vena cava**

(from upper body) Inferior vena cava (from lower body)

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**Transport System Branching of blood vessels**

Ateries branch into arterioles, veins into venules Arteries Arterioles Heart Capillaries Veins Venules

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**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

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**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.

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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

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Pressure

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**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

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**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

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**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!

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**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

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**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

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**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

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**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!

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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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Dynamics of Blood Flow 26.3.12. Transport System A closed double-pump system: Systemic Circulation Lung Circulation Left side of heart Right side of heart.

Dynamics of Blood Flow 26.3.12. Transport System A closed double-pump system: Systemic Circulation Lung Circulation Left side of heart Right side of heart.

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