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Symbols and Units

 

 

 

 
ah, am, antransfer rate coefficients (Hodgkin-Huxley model)
bh, bm, bn - " -
ds, dvtwo-dimensional [m-2] and three-dimensional [m-3] Dirac delta functions
epermittivity [F/m]
Eelectromotive force (emf) [V]
Q conduction velocity (of wave) [m/s]
lmembrane length constant [cm] (~ Ö(rm/ri) = Ö(Rma/2ri))
µmagnetic permeability of the medium [H/m = Vs/Am]
µ, µ0electrochemical potential of the ion in general and in the reference state [J/mol]
nnodal width [µm]
rresistivity [Wm], charge density [C/m3]
rib, robintracellular and interstitial bidomain resistivities [kW·cm]
rmbbidomain membrane resistivity [kW·cm]
rtbbidomain total tme impedance [kW·cm]
ri, rointracellular and interstitial resistivities [kW·cm]
sconductivity [S/m]
sib, sibintracellular and interstitial bidomain conductivities [mS/cm]
si, sointracellular and interstitial conductivities [mS/cm]
tmembrane time constant [ms] (= rmcm in one-dimensional problem, = RmCm in two-dimensional problem)
f, q longitude (azimuth), colatitude, in spherical polar coordinates
F potential [V]
Fi, Fopotential inside and outside the membrane [mV]
FLEreciprocal electric scalar potential field of electric lead due to unit reciprocal current [V/A]
FLMreciprocal magnetic scalar potential field of magnetic lead due to reciprocal current of unit time derivative [Vs/A]
F, ytwo scalar functions (in Green's theorem)
csurface to volume ratio of a cell [1/cm]
wradial frequency [rad] (= 2pf )
Wsolid angle [sr (steradian) = m2/m2]
aradius [m], fiber radius [µm]
unit vector
Aazimuth angle in spherical coordinates [ ° ]
Across-sectional area [m²]
magnetic vector potential [Wb/m = Vs/m]
magnetic induction (magnetic field density) [Wb/m2 = Vs/m2]
LMreciprocal magnetic induction of a magnetic lead due to reciprocal current of unit time derivative [Wb·s/Am2 = Vs2/Am2]
cparticle concentration [mol/m3]
lead vector
ci,cointracellular and extracellular ion concentrations (monovalent ion) [mol/m3]
ckion concentration of the kth permeable ion [mol/m3]
cmmembrane capacitance per unit length [µF/cm fiber length]
Celectric charge [C (Coulomb) = As]
Cmmembrane capacitance per unit area (specific capacitance) [µF/cm²]
ddouble layer thickness, diameter [µm]
di,dofiber internal and external myelin diameters [µm]
doutward surface normal
DFick's constant (diffusion constant) [cm2/s = cm3/(cm·s)]
Delectric displacement [C/m2]
Eelevation angle in spherical coordinates [ ° ]
electric field [V/m]
LEreciprocal electric field of electric lead due to unit reciprocal current [V/Am]
LMreciprocal electric field of magnetic lead due to reciprocal current of unit time derivative [Vs/Am]
FFaraday's constant [9.649·104 C/mol]
Fmagnetic flux [Wb = Vs]
gK, gNa, gLmembrane conductances per unit length for potassium, sodium, and chloride (leakage) [mS/cm fiber length]
GK, GNa, GLmembrane conductances per unit area for potassium, sodium, and chloride (leakage) [mS/cm2]
GK max, GNa maxmaximum values of potassium and sodium conductances per unit area [mS/cm2]
Gmmembrane conductance per unit area [mS/cm2]
hdistance (height) [m]
hmembrane thickness [µm]
h, m, ngating variables (Hodgkin-Huxley model)
Hcthematocrit [%]
magnetic field [A/m]
LMreciprocal magnetic field of a magnetic lead due to reciprocal current of unit time derivative [s/m]
immembrane current per unit length [µA/cm fiber length] (= 2paIm)
irreciprocal current through a differential source element [A]
Ielectric current [A]
Iaapplied steady-state (or stimulus) current [µA]
Ii, Ioaxial currents [µA] and axial currents per unit area [µA/cm2] inside and outside the cell
iK, iNa, iLmembrane current carried by potassium, sodium, and chloride (leakage) ions per unit length [µA/cm fiber length]
IK, INa, ILmembrane current carried by potassium, sodium, and chloride (leakage) ions per unit area [µA/cm²]
ILlead current in general [A]
Immembrane current per unit area [µA/cm2] (= ImC + ImR), bidomain membrane current per unit volume [µA/cm³]
imC, imI, imRcapacitive, ionic, and resistive components of the membrane current per unit length [µA/cm fiber length] (= 2paImC , = 2paImI , = 2paImR )
ImC, ImI, ImRcapacitive, ionic, and resistive components of the membrane current per unit area [µA/cm²]
Irtotal reciprocal current [A]
Irhrheobasic current per unit area [µA/cm2]
Isstimulus current per unit area [µA/cm2]
j, jkionic flux, ionic flux due to the kth ion [mol/(cm2·s)]
jD, jeionic flux due to diffusion, due to electric field [mol/(cm2·s)]
electric current density [A/m2]
dvsource element
iimpressed current density [µA/cm2], impressed dipole moment per unit volume [µA·cm/cm3]
i, ointracellular and interstitial current densities [µA/cm2]
iF, iVflow (flux) and vortex source components of the impressed current density [µA/cm2]
ir, itradial and tangential components of the impressed current density [µA/cm2]
Llead field in general [A/m2]
LEelectric lead field due to unit reciprocal current [1/m2]
LIlead field of current feeding electrodes for a unit current [1/m2] (in impedance measurement)
LMmagnetic lead field due to reciprocal current of unit time derivative [s/m2]
Kconstant
K(k), E(k)complete elliptic integrals
jsecondary current source for electric fields [µA/cm2]
llength [m], internodal spacing [µm]
liter
Linductance [H = Wb/A = Vs/A]
magnetic dipole moment of a volume source [Am2]
Mvector magnitude in spherical coordinates
M1, M2, M3peak vector magnitudes during the initial, mid, and terminal phases of the QRS-complex in ECG [mV] and MCG [pT]
nnumber of moles
surface normal (unit length)
jsurface normal of surface Sj directed from the primed region to the double-primed one
pelectric dipole moment per unit area [Am/m2 = A/m]
electric dipole moment of a volume source [Am]
Ppressure [N/m²]
PCl, PK, PNamembrane permeabilities of chloride, potassium and sodium iones [m/s]
rradius, distance [m], vector magnitude in spherical polar coordinates
rcorrelation coefficient
radius vector
ri, roaxial intracellular and interstitial resistances per unit length [kW/cm fiber length] (ri = 1/si pa2)
rmmembrane resistance times unit length [kW·cm fiber length] (= Rm/2pa)
Rgas constant [8.314 J/(mol·K)]
Ri, Roaxial resistances of the intracellular and interstitial media [kW]
Rmmembrane resistance times unit area (specific resistance) [kW·cm2]
Rsseries resistance [MW]
SCl, SK, SNaelectric current densities due to chloride, potassium and sodium ion fluxes [µA/cm2]
ttime [s]
Ttemperature [ ° C], absolute temperature [K]
uionic mobility [cm2/(V·s)]
vvelocity [m/s]
vvolume [m3]
Vvoltage [V]
V 'deviation of the membrane voltage from the resting state [mV] (= Vm - Vr )
Vcclamp voltage [mV]
VLlead voltage in general [V]
VLElead voltage of electric lead due to unit reciprocal current [V]
VLMlead voltage of magnetic lead due to reciprocal current of unit time derivative [V]
VK, VNa, VLNernst voltages for potassium, sodium, and chloride (leakage) ions [mV]
Vmmembrane voltage [mV] (= Fi - Fo)
Vr , Vthresting and threshold voltages of membrane [mV]
VRreversal voltage [mV]
VZmeasured voltage (in impedance measurement) [V]
Wwork [J/mol]
X, Y, Zrectangular coordinates
zvalence of the ions
Zimpedance [W]

 

The List of Symbols and Units includes the main symbols existing in the book. Symbols, which appear only in one connection or are obvious extensions of those in the list, are not necessarily included. They are defined in the text as they are introduced.

The dimensions for general variables follow the SI-system.
The dimensions for variables used in electrophysiological measurements follow, for practical reasons, usually the tradition in this discipline. Lower case symbols are used in the one-dimensional problem, where they are defined "per unit length". Upper case symbols are used in the two-dimensional problem, where they are defined "per unit area". Upper case symbols may also represent a variable defined "for the total area". (As usual in the bioelectric literature, the symbol "I" is used for membrane currents also in the two-dimensional problem, though in physics current density is represented with the symbol "J".).

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