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:
DP Qi = volumetric flow to organ “i”
Qi = ------- DP = 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