Physics of Blood flow in the circulation Hemodynamics Physics of Blood flow in the circulation

Circulatory System Heart: Has 2 collecting chambers - (Left, Right Atria) Has 2 Pumping chambers - (Left, Right Ventricles)

Circulation Schematic Left Side of Heart Pulmonary Vein Aorta A V Aortic Valve Mitral Valve Tissues Lungs Tricuspid Valve Pulmonary Valve V A Pulmonary Artery Right Side of Heart Sup. & Inf. Vena Cava

Heart Valves Atrioventricular (A-V) valves - separate Atria from Ventricles Bicuspid (Mitral) - Left Side Tricuspid - Right Side Semi-Lunar Valves - separate ventricles from Arteries

Opening, Closing of Valves - Depends on Pressure differences between blood in adjacent areas

Heart Sounds ‘Lubb’ (1st sound) - Closure of A-V valves ‘Dupp’ (2nd sound) - Closure of S-L valves Caused by Turbulence on closing. Anything extra ’Murmur’ (swishing of blood) Could be due to: Stenosis of Valves (calcification) Valves not closing properly (Incompetence, Insufficiency) Increases Pressure on heart

Blood Vessels Arteries Capillaries Veins Systemic Pathway: Left Ventricle Aorta Arteries Arterioles of Heart Venules Veins Right Atrium

Lumen of Coronary Artery

Blood Vessel Walls - Layers Arteries: Tunica Externa (Fibrous Connective Tissue) Tunica Media (Elastic Connective Tissue and/or Smooth Muscle) Tunica Intima (Endothelium) Capillaries: Endothelium Veins - same as Arteries except: Less smooth muscle in Tunica Media Have valves to control blood flow direction

Blood Composition: Approx 45% by Vol. Solid Components Red Blood Cells (12m x 2 m) White Cells Platelets Approx 55% Liquid (plasma) 91.5% of which is water 7% plasma proteins 1.5% other solutes

Blood Functions Transportation of blood gases, nutrients, wastes Homeostasis (regulation) of Ph, Body Temp, water content Protection

As a Result ……. Blood behaves as a simple Newtonian Fluid when flowing in blood vessels i.e. Viscous stresses  Viscosity, strain rate y u(y) No slip at wall

Viscosity of Blood = 3 3.5 times of water Blood acts as a non-newtonian fluid in smaller vessels (including capillaries)

Cardiac Output Flow of blood is usually measured in l/min Total amount of blood flowing through the circulation = Cardiac Output (CO) Cardiac Ouput = Stroke Vol. x Heart Rate = 5 l/min Influenced by Blood Pressure & Resistance Force of blood against vessel wall Blood viscosity Vessel Length Vessel Elasticity Vasconstriction / Vasodilation  with water retention  with dehydration, hemorrage

Overall Greater Pressure  Greater Blood Differences Flow Greater Resistance  Lesser Blood Flow

Elastic arterial walls expand and recoil Blood Pressure Driving force for blood flow is pressure created by ventricular contraction Elastic arterial walls expand and recoil continuous blood flow

Blood pressure is highest in the arteries (Aorta Blood pressure is highest in the arteries (Aorta!) and falls continuously . . . Systolic pressure in Aorta: 120 mm Hg Diastolic pressure in Aorta: 80 mm Hg Diastolic pressure in ventricle: ?? mm Hg

Ventricular pressure difficult to measure arterial blood pressure assumed to indicate driving pressure for blood flow Arterial pressure is pulsatile useful to have single value for driving pressure: Mean Arterial Pressure MAP = diastolic P + 1/3 pulse pressure

Pulse Pressure = systolic pressure - ?? = measure of amplitude of blood pressure wave

MAP influenced by Cardiac output Peripheral resistance MAP CO x Rarterioles Blood volume fairly constant due to homeostatic mechanisms (kidneys!!)

BP too low: Driving force for blood flow unable to overcome gravity O2 supply to brain  Symptoms?

BP too high: Weakening of arterial walls - Aneurysm Risk of rupture & hemorrhage Cerebral hemorrhage: ? Rupture of major artery:

BP estimated by Sphygmomanometry Auscultation of brachial artery with stethoscope Laminar flow vs. turbulent flow

Principles of Sphygmomanometry Cuff inflated until brachial artery compressed and blood flow stopped what kind of sound?

Slowly release pressure in cuff: turbulent flow

Pressure at which . . . . . . sound (= blood flow) first heard: . . . sound disappeared:

Pressure can be stated in terms of column of fluid. Pressure Units mm Hg cm H2O PSI ATM 50 68 0.9 0.065 100 136 1.9 0.13 200 272 3.8 0.26 300 408 5.7 0.39 400 544 7.6 0.52

Pressure = Height x Density or P = gh If Right Atrial pressure = 1 cm H2O in an open column of blood  Pressure in feet = 140 cm H2O  Rupture  Venous Valves Density of blood = 1.035 that of water Incompetent venous valves  Varicosities Actual Pressure in foot = 4-5 cm H2O

Dynamic Fluid Mechanics Blood flowing through circulation follows physical principles of pressure, flow Under conditions of constant flow, velocity must increase to allow the same flow through a smaller space i.e. the continuity equation

(This is the usual pattern of flow in the vascular system.) Types of Blood Flow Laminar: When velocity of blood flow is below a critical speed, the flow is orderly and streamlined (This is the usual pattern of flow in the vascular system.) Turbulent: disorderly flow with eddies & vortices

R = Velocity * Diameter * Density / Viscosity Turbulent flow is noisy In the vascular system high flow velocities cause turbulent flow and produce sound The murmur heard when blood flows through a narrowed heart valve is due to turbulent flow To determine whether flow is laminar or turbulent, calculate the Reynolds Number (R) (dimensionless no.) R = Velocity * Diameter * Density / Viscosity Values below 2000 define laminar flow

Energy = [V2/2g] + [P/r] + H = Constant Bernoulli Equation When blood flows through an artery, the total energy of the fluid at any point is assumed to be constant i.e. The sum of energy stored in pressure, energy provided by flow and potential energy due to the height of the blood above a reference point is constant Energy = [V2/2g] + [P/r] + H = Constant In an arterial stenosis, the increase in velocity causes a fall in pressure in the stenosis

Pressure = Flow x Resistance Poiseulle equation: Pressure drop across a length of vessel Radius Flow Length of Vessel

This is most effective in the arterioles For a given pressure, there is greater flow when the blood vessel is short and wide and the blood is thin Since BP is constant most of the time, flow is controlled by small changes in r--the vessel radius This is most effective in the arterioles Resistance is measured in Wood units Pulmonary = (PA pressure - LA pressure) / CO resistance e.g. R = (14 mm Hg - 7 mm Hg) / 5 l/min = 1.4 Wood units Pulmonary Artery

Pressures in the circulation Pressures in the arteries, veins and heart chambers are the result of the pumping action of the heart The right and left ventricles have similar waveforms but different pressures The right and left atria also have similar waveforms with pressures that are similar but not identical

5. Then the aortic valve closes and LV pressure falls to LA pressure 3. As blood enters the aorta, the aortic pressure begins to rise to form the systolic pulse 4. As the LV pressure falls in late systole the aortic pressure falls until the LV pressure is below the aortic diastolic press. 2. Pressure rises until the LV pressure exceeds the aortic pressure 5. Then the aortic valve closes and LV pressure falls to LA pressure  The blood begins to move from the ventricle to the aorta 1. The LV pressure begins to rise after the QRS wave of the ECG

The first wave of atrial pressure (the A wave) is due to atrial contraction The second wave of atrial pressure (the V wave) is due to ventricular contraction

Normal Pressures RV and pulmonary systolic pressure are 12-15 mm Hg Pulmonary diastolic pressure is 6-10 mm Hg LA pressure is difficult to measure because access to the LA is not direct

AS produces a pressure gradient between the aorta and LV The severity of AS is determined by the pressure drop across the aortic valve or by the aortic valve area The high velocity of blood flow through the narrowed valve causes turbulence and a characteristic murmur AS can be diagnosed with a stethoscope i.e. For blood to move rapidly through a narrowed aortic valve orifice, the pressure must be higher in the ventricle

AV Area The AV area can be calculated from pressure and cardiac output The calculate the AV area, use the Gorlin equation In the formula, flow is calculated for the time of systole since systolic time is the only time in the heart cycle when blood flows across the AV Flow Mean Gradient between LV and Aorta AV Area

Pressure Measurement Accurate pressure measurements are essential to understanding the status of the circulation In 1733 Steven Hales connected a long glass tube directly to the left femoral artery of a horse and measured the height of a column of blood (8 feet, 3 inches) to determine mean BP Direct pressure measurements are made frequently in the cardiac catheterization laboratory, the ICU and the OR

A tube is inserted into an artery and connected to an electrical strain gauge that converts pressure into force that is sensed electrically The output of the transducer is an electrical signal that is amplified and recorded on a strip chart For correct pressure measurements the cannula and transducer must be free of air, the cannula should be stiff and short

Cardiac Output (CO)Measurement The measurement of blood flow through the circulation is usually done clinically using either the Fick method The Fick method states that the cardiac output is equal to the oxygen consumption divided by the arterial-venous oxygen difference CO = Oxygen consumption / A-V O2

The measurement is done by determining the oxygen consumption using respiratory gas measurements and the O2 content of arterial and mixed venous blood The mixed venous blood sample is obtained from a PA with a catheter The arterial sample can be drawn from any artery