Arterial System & Hemodynamics

Arterial system

Pressures in the circulation

Arterial pressure during diastole

Pulse pressure and work of the heart

Hemodynamics is the study of the physical

principles that govern blood flow in the

cardiovascular system.

Factors affecting resistance to flow

Laminar & turbulent flow

Tension, pressure and radius

Arterial system

The arterial system consists of:

Elastic arteries: major distribution vessels with a large component of elastic

tissue and low resistance: aorta, brachiocephalic, common carotid, subclavian

and pulmonary arteries.

Muscular arteries: distributing branches with more muscular tissue and less

elastic tissue: radial, femoral, coronary and cerebral arteries.

Arterioles: terminal branches that supply the capillaries.

= MAP Mean & pulse pressures in the circulation Systolic pressure

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Shaded area = systolic pressure - diastolic = pulse pressure

Diastolic pressure

Pulse pressure depends on stroke volume and aortic compliance

Peak systolic pressure & pulse pressure are determined by stroke volume & aortic compliance.

Compliance depends on the elastic tissue of the aorta.

Pulse pressure = peak systolic minus diastolic pressure.

A decrease in aortic compliance will result in a higher peak systolic pressure & pulse pressure (assuming stroke volume is unchanged).

Stroke volume

Pulse pressure Mean arterial pressure

Aortic compliance

Aortic valve closure

Arterial pressure is maintained during diastole by recoil of the aorta

The stroke volume is ejected during the rapid ejection period & is accommodated by expansion of the aorta.Aortic pressure is maintained during diastole by recoil of the aorta as blood flows to the periphery.Because of the elasticity of the aorta and large arteries, the pulsatile pressure signal is gradually dampened so that flow is steady (not pulsatile) in the venules.

During diastole the aortic valve is closed and recoil of the elastic aorta drives blood to the periphery

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diastoleLeft Ventricle

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Central and peripheral aortic pressures

Simultaneously recorded pressures from the aortic root (Ao) and femoral artery (FA) demonstrate delayed transmission and a higher systolic pressure in the femoral artery.

Although peak pressure is higher in the femoral artery than the aorta, average driving pressure (MAP) is higher in the aorta than the femoral artery.

There is smoothing of the pressure waveform and loss of the dicrotic notch between the aorta and femoral artery.

UpToDate®

The work of the heart consists of pumping volume against pressure

Work = force (f) operating over distance (dl): W = (f)( dl)

For work done by a piston with area A moving against pressure P,

For the left ventricle:

P = afterload = arterial pressure when the aortic valve is open &

V = stroke volume, so

cardiac work = stroke volume x afterload

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Systolic and pulse pressures increase with age

Determinants of pulse pressure:Stroke volumeAortic compliance

Aging & atherosclerosis aortic compliance systolic pressure & pulse pressure cardiac work due to systolic pressure

A decrease in aortic compliance or an increase in afterload increase cardiac work

Cardiac work = stroke volume x afterload.

Cardiac work stroke volume x systolic BP.

Increasing systolic pressure increases cardiac work.

Compliance of the aorta minimizes peak systolic pressure & cardiac work.Cardiac work increases with age, & in hypertension, aortic stenosis or coarctation.

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C = DV/DP

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Difference in aortic compliance in young versus old subjects

Arterial, arteriolar & capillary resistance

The resistance of an individual vessel is inversely proportional to radius so

R artery < R arteriole < R capillary

The total resistance of a category of vessels is determined by the total cross

sectional area of all the vessels and the radius of the individual vessels.

Comparing arteries & arterioles supplying an organ, the total resistance of the

arterioles is greater than the resistance of the arteries.

Comparing arterioles & capillaries, the total cross sectional area of the capillaries

is so much greater than the area of the arterioles that the total resistance of the

capillaries is less than the resistance of the arterioles.

The greatest pressure drop in the circulation is across the arterioles.

Series & parallel resistances

Resistances in series are additive; total resistance equals the sum of individual resistances.

Resistances in parallel add as the inverse sum, like parallel electrical circuits:

Most vessels of a given category are arranged in parallel.

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Conductance is the inverse of resistance.

For Parallel circuits conductances are additive

Ctotal = C1 + C2 + C3

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Series and parallel resistance

Parallel resistances in the systemic circulation

Aorta

Arteries to stomach, spleen, pancreas, gut

Arteries to CNS

Hepatic artery

Arteries to limbs & trunk

Renal arteries

Coronary arteriesArterial beds are arranged in parallel

Venous pressure is small compared to arterial pressure.

Blood pressure is nearly the same in all large arteries, so DP is the same in all vascular beds:

DP = MAP – VP MAP and

MAP = CO X TPR

The resistance of each arterial bed is set by its own arteriolar tone

TPR is less than the resistance of any single arterial bed.

For example:

TPR = MAP/CO

Renal resistance = MAP/renal flow

And renal flow < CO so

Renal resistance > TPR

There are multiple parallel paths for blood flow so total peripheral resistance is less than resistance in any one bed.

Laminar & turbulent flow

Normal flow in the circulation is laminar.

Laminar (or streamlined) flow exhibits maximal velocity at the center of the vessel, and concentric thin layers of plasma with gradually decreasing velocity toward the walls of the vessel. Laminar flow is silent.

Plasma flowing closest to the vessel wall exerts a drag on the wall (shear stress) that influences endothelial function.

Turbulent flow exhibits irregular radial mixing of blood as overall flow occurs in the longitudinal direction.

Turbulent flow usually causes vibrations that are audible with the stethoscope as murmurs or bruits.

The pressure gradient required to drive turbulent flow is greater than that required to drive laminar flow so turbulence increases cardiac work.

Turbulent

Laminar

Causes of turbulent flow

Examples of turbulent flow:Flow across an obstruction (aortic stenosis, coarctation)Abnormally high flow velocity (high CO & reduced viscosity in severe anemia)Regurgitant flow across an incompetent heart valveAbnormal shunt from a high to low pressure chamber (ventricular septal defect)Presence of turbulent flow increases the likelihood of development of blood clots

Flow in the vascular system is normally laminar.Turbulence occurs if Reynold’s number (NR) exceeds 3000:

Factors predisposing to development of turbulence in flowing fluid include:Greater density (r)larger vessel diameter (D)High velocity (v)Low viscosity (h)

In addition, turbulence is likely in the presence of abrupt changes in vessel diameter or irregularities in vessel walls as may occur with atherosclerosis or other pathology.

Dv

NR

Viscosity and hematocrit

Viscosity of a fluid is its resistance to flow resulting from molecular cohesion.Blood is a complex mixture of fluid and cells; blood viscosity increases with hematocrit.

Resistance to blood flow is proportional to viscosity ():

4πr

8LηR

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Hematocrit

Normal hematocrit

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polycythemia

Viscosity of whole blood (solid line) relative to plasma (dashed line) as a function of hematocrit

Vessel diameter and viscosity of blood

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Vessel diameter, mm

Blood viscosity decreases in vessels with diameter < 0.3 mm (300 mm)

Mechanism is complicated but the effect reduces resistance to blood flow.

Most of the resistance in the systemic circulation is from arterioles with small

diameters. Lower resistance reduces the work of the heart.

Viscosity increases at low temperature, & may reduce blood flow in the

extremities & contribute to frost bite.

Law of Laplace

The law of Laplace states that tension (T) in the wall of a blood vessel equals the product of transmural pressure (P) and radius (r):

Tension is a force acting tangential to the surface of a cylinder.

P is transmural pressure (internal pressure minus external)

Transmural pressure equals blood pressure minus tissue pressure. Extravascular tissue pressure is small & can be ignored so

P T

)r)(Palminralu(intT

PrT

Law of Laplace and tension in blood vessel walls

Radius Tension Amount of

mm Hg dynes/cm2 dynes/cm. Elastic tissueElastic arteries I00 130,000 1.3 cm 270,000 ++++Distributing arteries 90 120,000 0.5 cm 60,000 +++Arterioles 60 80,000 0.15 mm - 62 mm 1,200 - 500 elastic intima Capillaries 30 40,000 4 mm 16 None Venules 20 26,000 10mm 26 None Veins 15 20,000 200 mm 400 + Vena cava 10 13,000 1.6 cm 21,000 ++

Intravascular Pressure

T = Pr

The amount of elastic tissue in the vessel wall correlates with the wall tension.

Elastic tissue maintains wall integrity against the outward force of the pressure.

The table shows that a very small tension in the wall of the capillaries suffices to withstand the intraluminal pressure. For comparison, the breaking strength of a strip of Kleenex one cm wide is about 50,000 dynes per cm, over 3000 times as great as the tension required to maintain a capillary wall.

Compliance of the aorta as an example of an elastic artery

In this figure smooth muscle is relaxed pharmacologically so the vessel’s compliance is due primarily to the compliance of the elastic tissue. Compliance of elastic arteries is nearly constant over the physiological range of pressure.

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Compliance decreases slightly at higher pressures

Slope = Compliance = DV/DP

Compliance in the vena cava as an example of a large vein

In this figure smooth muscle is relaxed; the compliance is due primarily to the changes vessel geometry.

Slope = Compliance = DV/DP

Maximal physiological pressure

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Compliance decreases as cross section becomes circular

Contribution of collagen & elastic fibers to passive tension development

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Relative radius, %

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T= Pr

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Intact artery

Passive tension development (smooth muscle relaxed) with increasing radius in

an intact artery or an artery with only collagen fibers (elastic fibers digested) or

only elastic fibers (collagen fibers digested).

Arterial segment studied in vitro by injecting fluid & measuring radius & tension.

Collagen fibers are least compliant, develop greatest tension for a given radius.

Wall tension and pathological changes

T = Pr

Arteries: If weakening of the wall causes dilatation (aneurism) , as the radius

increases the tension required to maintain wall integrity increases. If the wall is

too weak to maintain the tension, it will rupture.

The heart: Pathological dilation of the heart as occurs in heart failure increases

the radius of the ventricles. As a result, more tension must be generated to

create a given pressure, increasing the work of the heart & causing

progression of heart failure.