Equations

Question 1

Cardiac

Answer 1

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