Fundamentals of Biomedical Engineering

102	FUNDAMENTALS OF BIOMEDICAL ENGINEERING

130	Systolic
120	Pressure
110		Cuff Pressure
100
		Line
90
80
70		Diastolic Pressure
60
50
40
30
20
	Syphgmo m anometer	Stethoscope
	Cuff

Hand Bulb

Blood Pressure Measurement

2.The indirect method as described above is easy to use and can be automated. However it does not provide continuous recording of pressure variation. It also fails when the blood pressure of a patient is very low. Methods for direct blood measurement provide continuous recording of the blood pressure and they are more accurate than the indirect method. They require however that a blood vessel be punctured in order to introduce the sensor. The pulse pressure is the difference between systolic and diastolic pressure. Mean atrial pressure is diastolic pressure plus one third of pulse pressure.

3.Tension in the wall of blood vessel: A blood vessel can be considered a thin cylinder as thickness of the blood vessel is small as compared to its internal diameter (diameter > 15 × thickness of the wall). If the internal pressure in the blood vessel is

P1, σ = stress developed, D = diameter of vessel, t = thickness of the wall, then for equilibrium.

			Pi
			t
			D
	σ		σ
	P1 × D =		2 × σ × t
	or σ =	pi D	P1r where r = radius, t =
		2t

thickness and taken constant.

Hence the stress developed in the blood vessel is proportional to the product of the internal radius and pressure.

THE CARDIOVASCULAR SYSTEM AND BLOOD FLOW

103

4.Example: Let us find the stress in the blood vessels if 1 mm Hg = 130 N/m2 for (1) an aorta having mean internal pressure 110 mm Hg, t = 1.2 mm and diameter of 2.4 cm (2) a capillary having mean pressure of 20 mm Hg, t = 0.5 µm and diameter of 10 µm (3) the superior vena cava having mean internal pressure of 10 mm Hg, t = 0.15 cm and diameter of 0.03 m.

As found out	σ	= pi ×				D
						2 t
Case 1 :	σaorta	=	110×130×.024
			2 ×0.8012
		= 143 KN/m2
Case 2 :	σ	=			20 ×130 ×10–5
			2 ×0.5 ×10
	capillary
Case 3 :	σ	=	10 ×130× 0.03−5
				2 0.15 ×10
	venacava

= 26 KN/m2

BLOOD FLOW

1.Blood flow is highest in the pulmonary artery and the aorta as the blood leaves the heart from these two points. The flow at these points is called cardiac output. The cardiac output in a normal adult at rest varies from 3.5 to 5 litres/min. The stroke volume is the amount of the blood that comes out during each heart beat. If heart beat = 80 per min and cardiac output = 4 litres /min, then stroke

4

volume = 80 = 0.05 litres/beat. Similarly

cardiac index (n) is defined as the cardiac output per min per sq meter body surface area. The typical value of n is 3.3 litres/m2/ mm. The mean circulation time (≈ 60 sec) can be obtained by dividing cardiac output to the total amount of blood circulation. In the arteries, blood flow is pulsatile. During certain parts of the heart beat cycle, the

blood flow can occur in reverse direction. The elasticity of the walls of the blood vessels helps in smoothing out the pulsation and pressure of the blood. The capillaries can enlarge or constrict under the influence of certain drugs or when exposed to low temperatures. The blood flow reduces during vascoconstriction of the capillaries. The blood flow increases during vasodilation of the capillaries. Hence the status of the circulatory system can not be determined by measuring only blood pressure as it varies with the flow resistance of the capillaries. The basic theory of circulatory function is:

(a) The blood flow to each tissue of the body is always precisely controlled in relation to the tissue needs.

(b) The cardiac output is controlled primarily by the local tissue flow.

(c) The arterial pressure is independent of local blood flow or cardiac output.

(d) Veins besides transporting blood back to heart from the tissues, act as reservoir of blood. The veins can contract and expand as venous walls are thin which permit the veins to hold more blood or less blood depending upon the requirement of various systems.

(e) Circulatory shock is caused by decreased cardiac output. It can be due to cardiac abnormalities that decrease the ability of heart to pump blood. It can be also due to the factors that decrease the vanous return flow. The most common cause is trauma to the body as hemorrhage is caused by the trauma.

2.As we have seen in chapter 2, Newtonian fluids obey Newton’s viscosity equation and viscosity does not change with the rate of deformation. Non Newtonian fluids do not follow the linear relationship between shear stress and the rate of deformation i.e.

104	FUNDAMENTALS OF BIOMEDICAL ENGINEERING

τ

(Shear stress)

Plastic Fluid

c

ti

s

la

lP

a

d

n

e

Id

i

u

u

l

F

d

y

n

i

d

a

n

µ

o

=

t

w

τ

id

e

N

lu

F

n

n

o

ia

N

n

to

w

e

N

			1
		<			u
		n
	d				d
n						y
a
				µ d
			=
			τ

	Dilatant Fluid		n
	τ = µ	du
			and n > 1
		dy

Inviscid & Ideal Fluid

du

dy (Strain Rate)

Fluid Classifications

Stenosis

Separation of Blood FLow

du

τ ≠ µ dy . Blood is also a non Newtonian fluid. The Reynold number is the ratio of

inertial forces to viscous forces Re = ρVD

µ

where ρ = density, V = velocity D = diameter and µ = viscosity. When Reynolds number is large, inertial forces are large as compared to viscous forces and the inertial forces tend to diffuse the fluid particles, causing intense mixing of the fluid, which is characteristic of turbulence. In bloodflow situations, laminar flow continue to occur at Reynolds number as high as 10,000. Hence the blood flow is laminar in the blood vascular system except only in the aorta during a small fraction of each cycle when

flow is turbulent. The turbulent blood flow may also arise due to a stenosis or obstruction in the circulatory system. Stenosis may also take place in the valves.

3.Synovial fluid: Articulating cavity of synovial joint contains synovial fluid. A knee joint configuration is shown in the figure. Jointing bones have articular cartilage at their ends. Cartilage is collagen rich tissue which has two main properties. Firstly it can maintain shape and secondly it provides bearing surfaces at joints. Cartilage has porous nature. Joint cartilage has a very low coefficient of friction (less than 0.01). The squeezc film effect between cartilage and synovial fluid is considered to give low coefficient of friction. Hence the effective viscosity of the synovial fluid near the articular cartilage is abnormally high. There

THE CARDIOVASCULAR SYSTEM AND BLOOD FLOW

105

is also possibility of increasing concentration of suspended particles (hyaluronic acid molecules) in synovial fluid due to filtration in porous cartilage and its surface topography which provide boosted joint lubrication. The articular surfaces are protected due to the boosted lubrication.

Fem ur

Articular

Cartilage Articulating

Cavity with

synovial fluid

Tibia

Fibula

Knee Joint : Synovial Fluid

which arises from rhythmic action of the heart. The pressure and volume increase during systole which gradually decrease during diastole.

(g) The blood has unusual fluid properties. The blood consists of millions of different corpuscles suspended in the plasma. These corpuscles can deform when these are required to pass through the blood vessels having diameter smaller than their own.

(h) The blood vessels can contract or enlarge as explained earlier. The veins can enlarge to act as reservoir to store more blood.

5.Hagen-poiseuille flow: The flow of blood in arteries was investigated by the physician Poiseuille. He considered laminar flow through a horizontal round blood vessel as shown in the figure. The flow moves in cylindrical laminae.

4. Special characteristics of blood flow are: (a) the Reynolds number of the blood is high

(range 10,000) which results into a larger entry length (the length in which 99% of the final velocity profile is achieved). In most cases in the blood vessels the fully developed flow is never reached as the blood vessels start branching before this stage is attained.

(b) The blood is flowing through the blood vessels which have different properties. The reason for the different properties is that the blood vessels are formed of different substances such as elastin, collagen and smooth muscles.

(c) Unusual large bifurcation or branching of the blood vessels. There are million of blood vessels in the blood circulating system.

(d) The blood vessels have to bend into unusual curvature in the blood circulating system which leads to secondary flow in some cases.

(e) The turbulent flow may arise due to a stenosis or obstruction in the circulating system. It may also be due to the defective valves.

(f) The blood has unusual pulsating nature

Cylindrical Laminae

Laminar Flow Through Round Artery

The equilibrium of a cylinder of radius r and length dx is considered with pressure P at right and P – δP at left when the blood flow is from right to left. The net pressure force at the ends must be equal to the shear force.

	P πr2 – ( P + δp) πr2 – = τ 2πr.dx
	or τ =	dp			r	...(i)
		dx		2
	dp		R
	maximum shear stress τ = – dx			when r = R.
		2

Velocity Profile : Laminar Flow of Blood

106	FUNDAMENTALS OF BIOMEDICAL ENGINEERING

The velocity distribution can be obtained by the relationship

	τ		dU
		=	µ dy
but	y	=	R – r
	dy	=	– dr

Using this, we get τ = µ	dU	...(ii)
	dr

Putting value from eqn. (ii) in eqn. (i)

	dU	=		τ				dP
	dr							dx r
			2µ
or	U	=		1				dP			r2 + A (on integrating)
			4µ						dx
Condition; r =			R then U = 0
hence	A	=	–				1 dp				R2
					4µ				dx
U =			1					dp		(R2– r2)
				4µ dx

The velocity profile in a fully developed laminar artery flow is a paraboloid of revolution. At the centre line (r = 0), the velocity is maximum.

U		=		1	dp	R2
	max		4µ		dx
							r 2
or	U =		Umax 1–
							R

Total discharge (Q) through the artery

Q = ∫ dq =

R

r2

∫

1–

2

2πrdr .Umax

R

0

Q = 2 π U

R2

=

ð

dP

R4

max

4

8µ

dx

The average velocity (Umean) is given by

	Q			1	dP		R2		Umax
Umean =			=					=
	ðR	2		8µ					2
					dx

6.The proper functioning of all parts of the body depends on adequate supply of blood to these parts. If the blood supply to any part is reduced by a narrowing of the blood vessel, the function of that part can be severely affected. Incase the blood flow in a certain vessel is completely blocked due to blood clot or thrombosis, the tissues in the area supplied by the blood vessel will die. The brain stroke takes place when the blood vessel of the brain is blocked. The heart attack similarly takes place when there is an obstruction in the coronary arteries that supply blood to the heart muscle. A reduction in the blood flow of the coronary arteries can cause a severe chest pain which is called angina pectoris. A clot in the blood vessels in the lung is called an embolism.

7.Blood flow cannot be measured easily. The blood flow meters are based on the principle of (1) electromagnetic induction (2) ultrasound reflection (3) radiographic principle (4) dye dilution (5) chamber plethysmography. The magnetic and ultrasound blood flow meters actually measure the velocity of the blood stream. A transducer is used that envelope an excised blood vessel to measure the mean velocity of the blood stream. The flow of the blood can be worked out. In an ultrasonic blood flow meter, a beam of ultrasonic energy is used to measure the velocity of flowing blood. A pulsed beam is directed through a blood vessel and transit time is measured. Transit time is shortened if blood flow is in same direction as that of the pulsed beam otherwise transit time is lengthened. In radiographic method, blood is made visible by X-rays by the contrast medium and the movement of the blood can be measured. The dye dilution method measures the blood flow instead of the blood velocity as done

THE CARDIOVASCULAR SYSTEM AND BLOOD FLOW

by the earlier described methods. The dye is injected at a constant infusion rate I (gms/ min). A detector measures the dye concentration down stream. Concentration increases and finally reaches a constant value Co (gms/litre). The blood flow F (litres/min) = I /Co. In chamber plethysmography the

107

venous occlusion cuff is inflated to stop blood return from the veins of the forearm. Arterial flow causes the increase in volume of the forearm segment which the chamber measures. The flow of the blood is proportional to the change in the volume of the chamber.

	M agnet
N	Blood Vessel

Blood

Flow

S

V

A column of conductive blood

Magnetic Flow Meter

Voltage induced is proportional to the velocity of the blood

		Signal with
		frequency (F)
Flow		Doppler shift
		of frequency (Fb)
		is proportional
		to velocity of the blood
	D	Detector detects signal’s
		carrying frequency F + Fb or
		F – Fb depending direction of
		Flow

Blood Flow Meter

Dye Dilution Method

108	FUNDAMENTALS OF BIOMEDICAL ENGINEERING

V olume Calibrator

V enous OOcclusionclusio ncuff

P r es s ure

T rans ducer

Chamber	H and bulb

R ecorder

8.Solved example: A patient has cardiac output of 4.2 litres/min and heart rate of 84 beats/min and a blood volume of 5 litre. Find out (1) the stroke volume (2) the mean circulation time (3) the mean velocity in the aorta if it has a diameter of 32 mm.

The stroke volume = Cardiac output/min beats/min

4.2 litres/min

=84 beats/min

=0.05 litres

The blood volume

The circulation time = cardiac output/min 5litre

=4.2 litres/min

=1.19 min

Flow = Area × mean velocity = AV

DIABETES AND BLOOD SUGAR

1.Diabetes is a chronic and incurable disease in which excess sugar is present in the blood. Sugar (glucose) is necessary to provide energy to cells of the body. Insulin produced by the pancreatic cells of the body that convert the glucose in the blood into energy. In diabetes, the pancreatic cells produce little or no insulin or the body does not respond properly to the insulin, resulting in glucose levels building up in the blood. The body loses its primary source of energy. Excess blood sugar levels over a period of time harm the eyes, kidneys, heart, nerves and blood circulation to limbs besides starving the cells of the body.

Velocity =

Flow

=

4.2 litres /min

A

Area =

ðD2

4

=

4.2 10m–3/ min

4.2 × 4 ×10

π×(0.032)2

0.32 2

ð

4

4.2 ×4 ×10–3

π×10.24 ×10–4

= 5.22 m/min

Diabetes and Blood Sugar

THE CARDIOVASCULAR SYSTEM AND BLOOD FLOW

109

OBJECTIVE TYPE QUESTIONS

Fill in the gaps
1. The blood has carrier of ----------	supply
(a) fuel (b) water

2.The rhythmic pressure is maintained by the contraction and expansion of the -----------

(a) artery (b) heart

3.The heart beats without rest about 1,00,000

	times per ------------		(a) day (b) week
4.	The average heart rate is ------------			beats
	per min (a) 75 (b) 150
5.	Arteries, arterioles and capillaries form ----
	------	systems (a) diffusing (b) distribution
6.	The veins form		------------- system
	(a) dispatching (b) collecting
7.	The left heart receives blood from the
	pulmonary -----		(a) vein (b) artery
8.	The -----	heart is larger and stronger as it is
	a pressure pump (a) left (b) right
9.	The --------	heart is a volume pump

(a) left (b) right

10.The heart is divided into four chambers by -

----- (a) epicardium (b) septum

11.The inferior and superior vena cava open

into ------ atrium (a ) left (b) right

12. The right atrioventicular orifice is guarded by ---------- valve. (a) tricuspid (b) dicuspid

13.The pulmonary orifice is guarded by pulmonary valve which consists of ---------

semilunar cusps (a) two (b) three

14.The left atrioventricular orifice is guarded

	by the -------------	valve (a) mitral
	(b) tricuspid
15.	SA node is also called ---------		(a) pulse
	maker (b) pacemaker
16.	The propogation of excitation is delayed at
	AV node so that--------	can be filled up with
	the blood from the --------		(a) atria, vena
	cava (b) ventricles, atria

17.The sympathetic nervous system ----- the heart rate (a) quickens (b) slows down

18.The Vagus nerve of the parasympathetic nervous system ---- the heart rate

(a) quicken (b) slows down

19.The ---- state of a cell is called polarised (a) resting (b) action

20.The process of gaining an action potential on excitation is called -------(a) polarisation (b) depolarization

21.After sodium pumping the cell is -------- to the resting potential (a) depolarized

(b) repolarized

22.The dub sound is introduced by the heart by the closing of the valves (a) atrio ventricular (b) semilunar and aortic

23.The 'lub' sound is produced by the heart by the closing of the ------ valves (a) atrio ventricular (b) Semilunar and aortic

24.The lub is the -----heart sound (a) first (b) second

25.The dub is the -- heart sound (a) first (b) second

26.The first heart sound occurs at the time of the -------- part of the ECG (a) PQR

(b) QRS

27.The second heart sound occurs at the -----

----- of the ‘T’ wave of the ECG (a) start (b) end

28.The blood pressure is measured by an indirect method using a -----manometer (a) cuff (b) sphygmo

29.------- pressure is the difference between systolic and diastolic pressure (a) pulse (b) heart

30.The systolic period is completed with the closing of the -------- valve (a) mitral

(b) aortic

110	FUNDAMENTALS OF BIOMEDICAL ENGINEERING

31.The systolic period starts with the closing of the valve (a) mitral (b) aortic

32.The action potential is about --------- millivolt (a) –70 (b) +20

33.The resting potential is about ---------millivolt (a) –70 (b) +20

34.The walls of the left ventricle is -------times thicker than the walls of the right ventricle (a) two (b) three

35.	The pressure in the left ventricle can be ---
	-------times higher than the right ventricle
	(a) four (b) six
36.	The walls of ---------	are thicker and ridged
	as composed to the wall of --------
	(a) ventricle, atrium (b) atrium, ventricle
37.	The delay line is at	------- node (a) SA
	(b) AV
38.	From the AV node the cardiac impulse is
	conducted to-------	(a) the bundle of His

(b) The purkinje fibre

						ANSWERS
1.	(a)	2.	(b)	3.	(a)	4.	(a)	5.	(b)	6.	(b)	7.	(a)
8.	(a)	9.	(b)	10.	(b)	11.	(b)	12.	( a)	13.	(b)	14.	(a)
15.	(b)	16.	(b)	17.	(a)	18.	(b)	19.	(a)	20.	(b)	21.	(b)
22.	(b)	23.	(a)	24.	(a)	25.	(b)	26.	(b)	27.	(b)	28.	(b)
29.	(a)	30.	(b)	31.	(a)	32.	(b)	33.	(a)	34.	(b)	35.	(b)
36.	(a)	37.	(b)	38.	(a)

	THE RESPIRATORY
	SYSTEM

To attain knowledge, add things everyday. To attain wisdom, remove things every day.

INTRODUCTION

THE RESPIRTORAY TRACT

1.Respiration consists of two phases viz. inspiration and expiration. Inspiration and expiration are accomplished by the alternate increase and decrease of the capacity of thoracic cavity. The respiration rate is 16 to 20 per minutes in adults. It is faster in children and slower in the aged. During inspiration, air is taken in the lungs and the blood is oxygenated. During expiration, the lungs eliminate carbon dioxide in a controlled manner. Oxygen is required to sustain life as oxygen combines with hydrogen, carbon and other nutrients in order to generate heat and energy. This is called the process of metabolism which is taking place in the cells. Carbon dioxide and waste are produced from the metabolism. The respiration is the entire process of taking in oxygen as a part of air from the atmosphere, transporation of oxygen to the cells and transportion of carbon dioxide from the cells to the atmosphere.

1.The right and left lungs are elastic bags which are soft and spongy. They are located in a closed cavity which is called thoracic cavity. The right lung has three lobes while the left lung has two lobes. The lungs can shrink to one-third or less in volume. Air enters into the lungs through the air passage formed by the nasal cavities, pharynx, larynx, trachea, bronchi and bronchioles. The trachea (wind pipe) connects the larynx (voice box) to the left and right bronchus. The epiglottis is a valve above the larynx which prevents any liquid or food from entering into the larynx. Each principal bronchus enters into the corresponding lung. Each principal bronchus on entering the lung divides into secondary bronchus which passes to a lobe of the lung. A secondary bronchus gives off tertiary bronchi. Each tertiary (segmental) bronchus goes to a structurally and functionally independent