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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
8
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
9
Measurement of Blood count using Coulter Counter
10
Laser Flow Cell Counter – Flow Cytometry
11
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
13
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
26
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
28
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