7. Arterial and Cardiac Indices

wave speed equation in the Mo-K equation

c²=Eh/pD

wave speed is a physical property of the arterial wall

wave speed equation regionally

c=∆L/∆t

wave speed equation locally using ultrasound measurements

c=±1/2 (d𝑈±/dln(𝐷)±)

Compliance Definition

the change in the cross sectional area in response to the change in pressure

Compliance Equation

Cs=(dA/dP) or (dV/dP) (cm²/mmHg)

dA, dV is the change in cross sectional area, volume and

dP is the change in pressure

Incremental/per cycle

Distensibility

the relative change in cross sectional area with respect to the original cross sectional area in response to change in pressure

Distensibility equation

Ds=(1/A)(dA/dP) (1/mmHg)

Ds=(Cs/A)=(compliance/A)

Why is distensibility a better measure as an Arterial Index than Compliance

Because compliance depends on vessel size, while distensibility corrects for size

arterial index

An arterial index is just a number used to describe the condition or mechanical behaviour of an artery

How is distensibility and wave speed related

Distensibility is directly related to wave speed and arterial stiffness through the B_H equation

c²=1/pDs

Pressure in the aortic root is…

the sum of the forward and reflected wave

How could reflected wave arrives back at the heart earlier

Human arteries become stiffer with age or disease, therefore pulse wave velocity (PWV-wave speed) increases, ad reflected wave arrives back at the heart earlier

What is the clinical implications of wave reflection; n=3

1. First, in the left panel, central systolic pressure and central pulse pressure is increased. This stresses cerebral blood vessels increases stroke risk

2. Second, there is an increase in left ventricular load (LV load). In the middle panel, the increase in LV load accelerates and increases LV hypertrophy. The area under the pressure-time curve systole is one definition of LV load.

3. Third, in the right panel, the pressure that is perfusing the coronary arteries during the critical diastole period is reduced, increasing the risk of myocardial ischemia’s

Earlier arrival of reflected waves is…

Bad as increasing arterial stiffness independently increases the risk of all major cardiovascular outcomes

Augmentation Index (a measure of reflected wave)

The index can be calculated as the ratio the increase in pressure due to reflected wave to the total pressure pulse

clear inflection point (Pi)

the arrival of reflected wave

Augmentation index equation

AIx=Ps-Pi/PP

Where Ps is systolic pressure

Pi is pressure at the inflection point

PP is the pulse pressure (Ps-Pd, systolic pressure - diastolic pressure)

Pressure reflection index

ratio of backward to forward pressure/diameter

Pressure reflection index equation

Rindex=P-/P+=D-/D+

dD+-

½ (dD+-D/2c dU)

D+-

T E t=0 dD +- +D(0)

dP+

½ (dP+pcdU)

P + - (t)

t=T E t=0 dP+= (t) +P0

Wave Intensity Reflection Index

ratio of backward to forward separated wave intensity

wave intensity reflection index equation

RdI=dI-/dI+

dI+-=+-1/4pc (dP+-pcdu)²

non invasive wave intensity reflection index equation

Rndl=ndI-/ndI+

ndI+-=+=1/4(D/2c) (dD+-D/2cDU)²

Cardiac Index

relates the cardiac output (CO) from left ventricle per minute to body surface area (BSA). This index relates cardiac performance to the size of the individual. The unit of measurement are (L/min/m2)

Cardiac Index Equation

CI=CO/BSA=SV*HR/BSA

Where

HR is heart rate

SV is stroke volume (end diastolic volume-end systolic volume)

CO is cardiac output and calculated: CO=HR x SV

Factors affected Heart Rate

hormones, fitness levels, age and autonomic levels

Factors affected Stroke Volume

gender, contractility, pre- and after- load and heart size

Stroke Volume Index (SVI)

Relates the volume pumped by the heart, stroke volume (SV) per beat to body surface area (BSA). This index relates cardiac performance to the size of the individual. The unit of measurement are (mL/m²)

Stroke Volume Index Equation

SVI=SV/BSA

SV is stroke volume (end diastolic volume - end systolic volume)

Equation for left ventricular stroke work

SV x (MAP - PAWP) x 0.0316

MAP is mean arterial pressure

PAWP is pulmonary artery wedge pressure

Normal Range: 58-104 gm-m/beat

Equation for left ventricle stroke work index (LVSWI)

SVI x (MAP-PAWP) x 0.0316

Normal range: 50-62 gm-m/m²/beat

Ejection Fraction

The ratio between volume of blood ejected by the ventricle during systole, Vs, to the volume of blood in the ventricle at end of diastole, Vd

Why does the ejection fraction considered as a crude parameter to assess the ventricle performance

difficulty and inaccuracy in measuring the left ventricular volume

ejection fraction equation

EF=Vd-Vs/Vd

Normal range:50%-80%

Shortening fraction

a left ventricle axis, SF, is the proportional decrease in the proportional decrease in the axis length during contraction compared to its length at end of diastole where it is completely stretched due to the filling, where X is the axis length: Base-Apex, Septum-free wall

Shortening fraction equation

SF=Xmax-Xmin/ Xmax

What happens during clamping

the contraction during systole and relaxation during diastole became in-coordinated and bi-phasic

MVO2 calculation

multiplying the flow rate of the left anterior descending coronary, Qcor, by the arteriovenous oxygen content difference

Left V O2 consumption equation

MVO2=Qcor*O2(A-V)

Where Qcor is coronary flow and O2 is the oxygen concentration, A is the arterial side and V is the venous side

Left Ventricle Parameters

See Image

Right Ventricle Equation

See Image

Schematic plot of a typical pressure-volume loop of the left ventricle

a. Passive filling phase (work done by blood on left ventricle)

b. isovolumetric contraction (no work done, elastic energy stored in heart muscle)

c. ejection phase (work done on blood by ventricle)

d. isovolumetric relaxation (no work done, but stored elastic energy is dissipated)

Ventricular Hydraulic work

W=[PUdt] T 0

Where T denotes the duration of the cardiac cycle

Measurements taken in the ascending aorta (where velocity(U) is measured)

Cardiac Power

W=[P dV] T 0

which is the area within the pressure-volume loop

What is an easier way to get cardiac power

W=DP dV

Simplify by integrating around the dashed rectangle

Using W= dP dV of avf human

1.5 J/cycle and 70 BPM corresponds to a power of 1.7 Watts

LV wall stress

a function of chamber size and configuration, thickness of the ventricular wall, and intra ventricular pressure

Average Meridional stress (Oa)

force per unit area acting at the mid plane to the heart, in the direction of the apex to base length

meridional wall forces equation

om=PRi²/(Ro-Ri)(Ro+Ri)

meridional wall forces assuming (Ro=Ri)=h equation

om=PRi²/2h(1+h/2Ri)