Cardiovascular System

ML504: Medical Physics, 2013; Supriya Babu

Introduction

If body can be seen as a machine – billions of cells are engines

These engines must have Fuel from our food to supply energy

O2 to combine with food to release energy

A way to dispose of by-products of combustion

Cardiovascular system

There are three components of the cardiovascular system. Blood is the vehicle for transport. (7% of body mass)

It transports fuel from the digested food to the cells, transports oxygen from the air in the lungs so it can combine

with fuel to release energy, and it disposes of waste products – such as carbon dioxide from

the fuel engine and other metabolic wastes.

The circulatory system is the distribution system, and consists of a series of branched blood vessels.

The heart is the four-chambered pump composed mostly of cardiac muscle that enables this circulatory flow.

Some trivia

Heart is the first major organ to develop – four weeks after conception

Foramen oval Only 10% of blood circulated to lungs

Components

Blood Typical volume – 4.5 to 5 L Stroke volume – 80 ml

Volume distribution 80% in Systemic

15% in arteries 10% in capillaries 75% in Veins

20% in Pulmonary 7% in Pulm. Capillaries 93% divided between Pulm.

Arteries and Veins

Composition of Blood RBCs

45% of blood volume ~ 7m in diameter 5x106 cells/mm3 of blood

Plasma – 55% of blood volume WBCs

~ 9 to 15m in diameter 8000 cells/mm3 of blood Differential count

Platelets ~ 1 to 4m in diameter 3x105/mm3 of blood

Hormones, electrolytes

Circulatory system

Circulation to major organs

Function of heart

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Components of Cardiovascular System (CVS)

Heart – Double Pump – provides force

Two circulatory systems in series Pulmonary Systemic

Valves Pressure

LV – 125mmHg RV – 25 mmHg RA – 5-6 mmHg LA – 7-8 mmHg

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Measurement of Blood count using Coulter Counter

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Laser Flow Cell Counter – Flow Cytometry

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Capillary bed

Number - ~190/mm2

Average diameter ~20m

O2 and CO2 exchange Most probable distance

D that a molecule will travel after N collisions, with avg. dist. Between collisions being is given by: D = N

Starling’s law of capillary

Fluid movement through capillary Hydrostatic

pressure Forces fluid out of

capillary Osmotic pressure

Brings fluids in

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Work done by the heart

Muscle driving LV is 3 times thicker than RV Circular shape of LV is more efficient in producing high pressure than

elliptical shape of RV Work done = PV

Work done by heart

W = Pav Vstroke

Area under the curve For linear variation

Pav = (Pdiastole + Psystole) /2

= 100 mmHg = 1.33 × 104 N/m2

Vstroke = 80cm3 = 8 × 10−5 m3, W = (1.3 × 104)(8 × 10−5) = 1.06 J/cycle

With a heart rate of 60/min = 1/s, the rate the left ventricle does work is: Ppower,mech,av = (1.06 J per cycle)(1 cycle/s) = 1.06W.

Power and metabolic need

The efficiency () of converting metabolic energy into this mechanical work is approximately 20% (12–30%), and

the metabolic power needed to run the left ventricle is Ppower,metab,av = Ppower,mech,av/ = 5 W.

The heart pumps for about 1/3 of the cardiac cycle and rests for the other 2/3 of the time.

Therefore the peak powers are higher than these average values by a factor of 3, with Ppower,mech,peak = 1.5W and Ppower,metab,peak = 15 W.

The energy consumed to run the left ventricle is (86,400 s/day)(5W) = 4.32 × 105 J/day = 104 kcal/day.

Power and metabolic need

The right ventricle pumps the same volume per cardiac cycle (to maintain the steady-state flow throughout), at a pressure 1/5 times that of left ventricle, the work and all of these powers are smaller by a

factor of five. increases the required metabolic power by 20%. the pressures for the two atria are also relatively very

small With 20% muscle efficiency we expect to need ∼125

kcal/day to run the heart; With 10% muscle efficiency it would be ∼250 kcal/day.

Wave amplitude to cuff pressure and BP

Direct Measurement of BP

Effect of gravity

Pressure across blood vessel wall

Laplace Law The outward force/L = 2RP Inward force/L = Tension = 2T At equilibrium

2RP= 2T T = RP

Tension in aorta is 156,000 dynes/cm2

Tension in capillary is 24 dynes/cm2

A single layer of toilet tissue can withstand a tension of ~ 50,000 dynes/cm2

Pressure conditions in various blood vessels in CVS

Blood flow conditions in CVS

Bernoulli’s Equation

Bernoulli’s Principle (or equation) relates the average flow speed u, Pressure P, and height y

of an incompressible, non-viscous fluid in laminar, irrotational flow

Laminar/streamline & Turbulent

The Reynolds number Re is a dimensionless figure of merit that crudely divides the regimes of laminar and turbulent flow

where v = η/ρ is the coefficient of kinematic viscosity.

Re < 2,000 is laminar and that with Re > 2,000 is turbulent

(a)steady, laminar flow at low Re(b)short bursts of turbulence for

Re above the critical value(c) fully turbulent flow with

random motion of the dye streak for higher Re

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Difference

Silent Parabolic profile

of the flow velocity

More efficient

Sound can be heard due to vibrations

There is no set profile of velocity

Less efficient

Laminar Turbulent

Consequences of Laminar and turbulent blood flow

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Plasma Skimming Effect• Alters hematocrit at bifurcations

when flow distribution is asymmetric (Empirical Bifurcation Law)

• Leads to lowered apparent hematocrit at network exit

high saturationRBCs near centre

high hematocrit& oxygen saturation

low hematocrit& oxygen saturation

LAMINAR FLOW

Plasma skimming effect

Non-uniform distribution of RBCs Plasma Skimming Effect

Branching daughter vessel draws blood mainly from cell-free layer

Hematocrit of blood in the extremities (hands and feet) is higher

Laminar flow more efficient

Critical velocity (vc) is lower for blocked artery In aorta, vc is 0.4

m/sec Slope of curve in

laminar more than turbulent

Blood Flow: Poiseuille’s Law

Poiseuille’s Law

Assumptions for Poiseuille’s Law Length of tube must be much greater

than the radius Flow must be steady in time and laminar

velocity profile Fluid must be Newtonian Tube must be rigid

Heart Sounds Vibrations originating in the

heart and major vessels Frequency range from normal

heart: 20 Hz to 200 Hz Opening and closing of valves Murmurs: when there is

constriction Ex: Aortic valve is narrow

Sound heard depends on Design of stethoscope Pressure on chest and its

location Orientation of body Phase of breathing cycle

Phonocardiography

Physics of CV Diseases

Work done by heart = tension on muscles x

duration of its action High blood pressure muscle tension Tachycardia heart rate

Heart attack: blockage of one or more arteries that supply blood to heart

Infarction: cell death Anastomoses

Congestive Heart failure

Enlargement of heart Law of Laplace 2x Radius 2x tension in wall Stretched heart muscle is less efficient

Defective heart valves

Valve does not open wide enough: stenosis Work done against obstruction

Does not close enough: insufficiency Vol. of blood circulated is reduced

Aneurysm

Cerebrovascular Accident

Arteriosclerosis

Varicose Veins

Enlarged surface veins

Failure of one-way valves

Venous Pump