Cardiovascular Equations - University of Arizona



Cardiovascular Equations

Conduction Velocity:

A d2V Θ = conduction velocity I = capacitance

Θ2 = ---- ----- A = cross-sectional area d2V/dt2 = second derivative

2RI dt2 R = resistance of membrane voltage to time

Law of Laplace:

2HT P = pressure T = wall tension

P = ------ H = wall thickness r = chamber radius

r

Stroke Work:

1 SW = stroke work

SW = (Pafterload)(SV) + --- mv2 Pafterload = afterload pressure

2. mv2/2 = kinetic energy

SV = stroke volume

SW = (MAP)(SV) MAP = mean arterial pressure

Efficiency:

SW CE = cardiac efficiency

CE = ------- SW = stroke work

QO2 QO2 = oxygen consumption

Cardiac Output:

CO = cardiac output

CO = HR (EDV – ESV) HR = heart rate

EDV = end diastolic volume

CO = (HR)(SV) ESV = end systolic volume

SV = stroke volume

Ejection Fraction:

EF = ejection fraction

EF = (EDV – ESV)/EDV ESV = end systolic volume

EDV = end diastolic volume

Flow through a tube:

VF = volumetric flow

VF = vA v = velocity

A = cross-sectional area

Darcy’s Law:

MAP CO = cardiac output

CO = ---------- MAP = mean arterial pressure

TPR TPR = total peripheral resistance

Poiseuille’s Law:

8ηl R = resistance r = tube radius

R = -------- η = viscosity

πr4 l = tube length

Reynold’s Number:

vDρ NRe = Reynold’s number ρ = density

NRe = --------- v = fluid velocity η = viscosity

η D = tube diameter

Vascular Compliance:

C = compliance

C = V/P V = volume

P = pressure

Organ Blood Flow:

(P Qi = volumetric flow to organ “i”

Qi = ------- (P = perfusion pressure

Ri Ri = resistance to organ “i”

Solute Exchange:

JS = solute flux CC = [solute] in capillary

JS = PSS (CC-CI) PS = permeability coefficient CI = [solute] in interstitium

S = capillary surface area for exchange

Starling Equation:

JF = transcapillary flux

JF = LPS [(PC-PT)- σ(ΠC-ΠT)] LP = hydraulic conductivity σ = plasma protein reflection coefficient

S = capillary surface area for exchange

PC = capillary hydrostatic pressure

PT = tissue hydrostatic pressure

ΠC = capillary oncotic pressure

ΠT = tissue oncotic pressure

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