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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Am J Physiol. Author manuscript; available in PMC 2010 December 22.
Published in final edited form as:
PMCID: PMC3008667
NIHMSID: NIHMS204002

Terminology for mass transport and exchange

Abstract

Virtually all fields of physiological research now encompass various aspects of solute transport by convection, diffusion, and permeation across membranes. Accordingly, this set of terms, symbols, definitions, and units is proposed as a means of clear communication among workers in the physiological, engineering, and physical sciences. The goal is to provide a setting for quantitative descriptions of physiological transport phenomena.

Keywords: circulatory transport, diffusion, capillary permeability, flow, irreversible thermodynamics, tracer washout, pharmacokinetics

THE SET OF SYMBOLS is an extension of those proposed by Wood (11), Gonzalez-Fernandez(3), Zierler (12), Kedem and Katchalsky (5), and Bassingthwaighte et al. (1). The extensions provide a set of symbols common to studies of transcapillary and cellular exchange and indicator-dilution studies. The rationale is to provide a self-consistent set of symbols covering broad aspects of circulatory flows, hydrodynamics, transcapillary and membrane transport. As the various previously rather separate aspects of these fields become intermeshed, the size of the required sets of symbols has enlarged to a point where the “standard” symbol for one group of users has a quite different “natural” meaning to another. This problem has necessitated some arbitrariness, but we have attempted to subscribe to the dominant usage so as to minimize changes in habits.

Care has been taken to provide each term with 1) a name, 2) a definition in words (and sometimes equations), 3) a unique symbol whenever possible, and 4) units mainly in centimeter-gram-second system but with some translation to approved International System of units (SI). Physical constants are listed separately.

An important feature of this list is the provision of operational terminology for the general description of the behavior of linear stationary systems. The use of the time-domain impulse response or transport function, h(t), etc., follows from the work of Stephenson (10), Meier and Zierler (6), and Zierler (12) and is reviewed by Bassingthwaighte and Goresky (2).

A system is diagramed in Figure 1. Most analysis is based on two fundamental assumptions, that the system is both linear and stationary. When both hold, superposition is applicable. In general, we also consider the system to be mass conservative; that is, indicator and solvent are neither formed nor consumed.

FIG. 1
Block diagram of a linear stationary system. Response to ideal impulse input δ(t) at the entrance is h(t), the transport function. When input is of another form, Cin(t), then outflow response Cout(t) is the convolution of Cin(t) and h(t).

A linear system is one in which inputs and outputs are additive. Defining Cin(t), as concentration-time curve at the input to a segment of the circulation and Cout(t) as the concentration-time curve occurring in response to it at the outlet, the relationship is denoted by

Cin(t)Cout(t)

Given a second pair with the same relationship Cin(t)Cout(t), then in a linear system, these can be summed or multiplied by a scalar

Cin(t)+Cin(t)Cout(t)+Cout(t)orkCin(t)kCout(t)linearity

A stationary system is one in which the distribution of transit times through the system is constant from moment to moment; that is, flows and volumes are constant everywhere in the system. Stationarity implies that the response to a given input is independent of a shift in the timing of the input by an arbitrary time, to,

IfCin(t)Cout(t)thenCin(to+t)Cout(to+t)stationarity

When the input system is an ideal unit impulse, the Dirac delta function, δ(t), then the output is the transport function, h(t). When the input is of general form, Cin(t), and h(t) is known, then the form of the output, Cout(t), can be calculated using the convolution integral given in Fig. 1.

A probability density function h(x) or w(x) is a weighting function or a frequency function that gives the probability of occurrence of an observation or measure as a linear function of the quantitative measure, x. The sum of probabilities of all the observations is unity; therefore the units of the density function are fraction per unit of the measure [e.g., the transport function h(t)]. A typical form of h(t) for transport through an organ is given in Fig. 2, accompanied by closely related general functions.

FIG. 2
Relationships between h(t), H(t), R(t), and η(t). Curve of h(t) is in this instance given by a unimodal density function having a relative dispersion of 0.33 and a skewness of 1.5. However, the theory is general and applies to h(t)s of all shapes. ...

Subscripts

AArterial
BBlood
C or capCapillary, or the region of blood-tissue ex-
 change
cellCell
DDiffusive, or indicating a permeant tracer
ECFExtracellular fluid
FFlow or filtration
i,j Indices in series or summations or elements
 of arrays
in or iInto or inside or inflow
ISF or IInterstitial fluid space, the
 extravascular extracellular fluid
mMembrane
out or oOut of or outside or outflow
PPlasma
RBCRed blood cell
RReference, nonpermeant tracer
SSolute
TTotal
vVenous
WWater

Principal Symbols

aActivity, molar; a = [var phi]C, an activity coefficient
 times a concentration
AArea of indicator concentration-time curve excluding recirculation A=0C(t)dt,mol·s·l−1
CConcentration, mol/l; Cc(x, t) concentration
 in the capillary plasma at position x at time
 t (mol·1−1). Also [Na+] = sodium concentra-
 tion. The relationship between an outflow
 concentration-time curve Cout(t) and the
 inflow curve Cin(t) in a stationary system is
 given by the convolution integral: Cout(t)=0th(tτ)Cin(τ)dτ=Cin(t)h(t) where τ
 is a variable used in the integration. The
 asterisk denotes convolution
sConcentration of solute, the average of the
 concentrations on the two sides of a mem-
 brane, molal, used in irreversible thermo-
 dynamic equations. Note that this average
 does not represent the mean concentration
 within the membrane when both convection
 and diffusion occur through a channel of
 finite length
CVCoefficient of variation, dimensionless. See
 also RD; both are the standard deviation
 divided by the mean of a density function
DDiffusion coefficient, cm2·s−1; Do, in free
 (aqueous) solution; Db for observed bulk
 diffusion coefficient through tissue; Dcell for
 intracellular; DI for interstitial
EElectrical potential, volts; Em, membrane po-
 tential; EN, “Nernst” potential, occurring
 with a difference in concentration of an
 ion on the two sides of a membrane, EN =
 (RT/zF)loge(Cin,/Cout)
E(t)Extraction, dimensionless, is the fraction of a
 specific substance removed during transit
 through an organ. The calculation may be
 made relative to a reference substance that
 remains in the blood or relative to the inflow
 concentration. E(t) = [hR(t) – ho(t)]/hR(t)
 and is the instantaneous apparent frac-
 tional extraction of a permeating species,
 subscripted D, relative to a nonpermeating
 reference substance, subscripted R, at each
 time t, calculated from paired outflow dilu-
 tion curves. This differs from a steady-state
 extraction, E, calculated from the arterio-
 venous difference, E = (CA – Cv)/CA, for a
 substance that is consumed during transor-
 gan passage. E(tpeak) is the value of E(t)
 obtained at the time of the peak of the curve
 for the nonpermeating reference tracer,
 hR(t). Emax is the maximum value of the
 instantaneous extraction, E(t). Enet(t) is an
 integral extraction, 0t(hRhD)dτ0thRdτ=(RDRR)(1RR); when the
 reference tracer has all emerged, then
 Enet(t) = RD(t), the retained fraction of a
 permeant solute
ECFExtracellular fluid, interstitial fluid + plasma
fFrictional coefficient, g·cm equals (g·cm2 s−1)/(cm·
 s−1), following Spiegler (9)
fexclExcluded volume fraction, the fraction of sol-
 vent in a defined space that is not available
 to a particular solute, dimensionless
f iRelative regional flow in the jth region of an
 organ divided by the mean flow for the
 organ per gram of tissue, dimensionless
FFlow, cm3·s−1 or cm3·min−1
FBBlood flow to an organ, cm3·g−1·min−1
 (= F/W, where W = organ weight)
Fs, FpFlow of solute-containing mother fluid, cm3·
 g−1·min−1. When solute is excluded from
 red blood cells, Fs = FB(1 – Hct) = Fp, the
 plasma flow. (In modeling analysis, this is
 the flow of fluid containing solute available
 for exchange.)
FER(t)Fractional escape rate at time t for indicator
 contained in a system regardless of time of
 entry, s−1. With an impulse input, δ(t), then
 FER(t) = η(t), the emergence function. In
 general, FER = (dq/dt)/q = d logeq/dt,
 where q is the system’s content of a sub-
 stance and dq/dt = F[Cin(t) – Cout(t)]
h(t)Transport function, fraction/unit time (s−1),
 is the fraction of indicator injected at the
 inflow at t = 0, arriving at the outflow at
 time t. It is the unit impulse response, the
 frequency function of transit times, or the
 probability density function of transit
 times. The transport function, h(t), has the
 shape of the concentration-time curve that
 would be obtained by flow-proportional
 sampling at the output if indicator were
 injected in ideal fashion into the inflow, i.e.,
 across a cross section with indicator amount
 at each point in proportion to local flow, as
 defined by Gonzalez-Fernandez (3), and re-
 circulation absent. Under such conditions
 h(t) = F·C(t)/qo, where qo is the mass
 injected at t = 0. Subscripting denotes re-
 gion (e.g., A, V, or cap) or solute character-
 istic (R for intravascular or D for permeant)
H(t)Cumulative residence time distribution func-
 tion (dimensionless) of a system; it repre-
 sents the fraction of an ideally injected
 tracer that has exited from the system since
 t = 0. It is also the response to a step input.
 Formally, H(t)=0th(τ)dτ=1R(t),
 where R(t) is the residue function
HctHematocrit, the fraction of the blood volume
 that is erythrocytes, dimensionless
ISFInterstitial fluid, the extravascular extracel-
 lular fluid
JFlux, usually moles per unit surface area
 of membrane per second, mol·s−1·cm−2.
 Jnet 1→2 is net flux from side 1 to side 2. In
 the notation of irreversible thermody-
 namics the equations of Kedem and Katch-
 alsky (5) and Katchalsky and Curran (4)
 for water and solute transport across an
 ideal membrane composed of infinitely thin
 impermeant material pierced by aqueous
 channels (the K and K membrane) are
JV=LpΔp+LpDΔπJD=LDpΔp+LDΔπ

 where JD is a solute velocity relative to the
 solvent velocity, Jv, which is in turn relative
 to the membrane. [Although these expres-
 sions are incomplete in that the forces on
 the membrane, in effect a second solute,
 should also be considered (8), they provide
 an elementary conceptual approach to an
 idealized system.] Jv and JD may be
 properly regarded as flows rather than mass
 fluxes
J V Solvent velocity or volume flux per unit mem-
 brane surface area relative to a membrane,
 cm·s−1 or cm3 · s−1 per cm2 area
JV=JWV~W+JSV~SJWV~W
J D Solute movement relative to solvent, cm3 ·s−1
 per cm2 surface area or cm·s−1. For the
 Kedem-Katchalsky (K-K) ideal membrane
 JD=JSCSV~WJW See JS
J W Water flux across a membrane, mol·s−1·cm−2.
 For the K-K membrane JW=V~SJSV~W
J S Solute flux across a membrane, mol·s−1·cm−2.
 For the K-K membrane JS=CS(1σ)JV.
 Also
JSCs=(Lp+LDp)Δp+(LpD+LD)Δπ,orJS=CS(1σ)JV+ωΔπ
k Rate constant for an exchange process, usu-
 ally s−1; k(C) is concentration-dependent
 rate
k F Filtration coefficient, cm3·s−1·cmm−2 (mmHg)−1;
 kF = Lp. See Lp and also PF
K m Michaelis constant, molar. For a reaction
E+Sk1k1ESk2E+P

 then Km = (k−1 + k2)/k1, which in the limit
 where k2 << k−1 becomes the original appar-
 ent dissociation constant, k−1/k1, which at
 equilibrium = [E]·[S]/[ES]. (E, enzyme; S,
 substrate; P, product)
l, LLength, cm
L Conductance (general) per unit area as in J =
 LX; flux = conductance times driving force
L p Pressure filtration coefficient or hydraulic
 conductance; the flow of pure solvent across
 a membrane per unit area per unit pressure
 difference, e.g., cm·s−1(mmHg)−1; also, Lp=V~PFRT=kF
L pD Osmotic coefficient; the flow of solution across
 a membrane per unit area per unit osmotic
 pressure difference. Same units as Lp; also,
 LpD = σLp
L Dp Ultrafiltration coefficient; the conductance
 for the hydrostatically driven flow of solute
 relative to that of solvent, per
 unit area per unit hydrostatic pressure difference. Same
 units as Lp. By Onsager reciprocity, LDp =
 LpD. (For an ideal semipermeable mem-
 brane, σ = 1, ω = 0, and −LpD = Lp = LD =
 LDp)
LD Coefficient for diffusional mobility per unit
 osmotic pressure. Same units as LP. See ω
 and P
MMolarity, moles of solute per liter of solution.
 Also mM, 10−3 M and μM, 10−6 M. (Molality
 is moles of solute per kilogram of solvent.
 The use of molal units gives consistency in
 transient states; for example, the molal con-
 centration of solute 1 is not changed by the
 removal of solute 2, but the molar concen-
 tration may be raised or lowered)
MeanX, the mean of a density function, ω(x), is
 calculated by
x=0xw(x)dx/0w(x)dxor=ixiw(xi)Δxiiw(xi)Δxi

 Same as α1
ni Same as α1 Moles of substance i in a solution. See mole
 fraction xi
N Number of observations or number of ele-
 ments in a series, i = 1 to N
ppressure, mmHg or Pa (1 Torr = 1 mmHg).
 See osmotic pressure, π
P Permeability coefficient for a solute traversing
 a membrane, cm·s−1; equivalent to a diffu-
 sion coefficient for a solute in a membrane
 divided by the thickness. P = ωRT. P0, PL,
 permeabilities at the arterial and venous
 end of a capillary of length L, respectively.
 P(x) for 0 < x < L for permeability at
 position x. (Usually observed as a product,
 PS, with the membrane surface area, S)
PePeclet number, ratio of a convective to a dif-
 fusive velocity, dimensionless
P F Filtration permeability, LpRTV~w, cm·s−1.
 [The conversion factor RTV~w at 20°C, from
 the experimental units for Lp or kF, is (18.36
 mmHg·cm3·mol−1)/( 18 cm3·mol−1) equals
 1.02 mmHg]
PS Permeability-surface area product of a barrier,
 cm3·g−1·s−1 or cm3·g−1·min−1. PScap for
 capillary (the same as capillary diffusion
 capacity), PScell for parenchymal cell
qMass, g or mol. q(t) is mass (or content of
 tracer) in region or organ (at time t). q0,
 mass of indicator injected at t = 0
r, R Radius or radial distance, cm. RC, capillary
 radius
RDRelative dispersion(dimensionless)=SDmean=μ2α1. Same as coefficient of var-
 iation
R(t)Residue function (dimensionless) is the com-
 plement of H(t), i.e., R(t) = 1 – H(t). It
 represents the fraction of injectate in the
 system at time t after an impulse input at
 time zero, i.e., the probability of a tracer
 residing in the system for time t or greater
S Surface area. SC and Scell for capillary and cell
 surface areas, cm2·g tissue−1
SDStandard deviation = square root of the vari-
 ance of a density function, μ212. Also SD=α2α12 (units are those of the independent variable)
SEMStandard error of the SD=N, where
 N = number of observations
t, ΔtTime, s; Δt is a finite time interval
t Mean transit time, s. t=0th(d)dt=0R(t)dt
t a Appearance (a) time; the time at which the
 first detectable indicator (or a concentra-
 tion of, for example, 1% of the peak) passed
 through the system
t 0 Zero time; midpoint of pulse injection for in-
 dicator-dilution studies or beginning of con-
 stant-rate injection
t peak Time from injection to peak of indicator-di-
 lution curve (modal time)
VVolume, cm3 or ml; in a solution, V=ΣniV~i,
 the sum of the products of the mole fraction
 times the partial molar volume for each
 contained species
VregionAnatomic volumes within regions of an organ,
 i.e., VC, capillary; VI, interstitial fluid; Vcell,
 parenchymal cells, cm3·(g tissue of the
 organ)−1
vregionFractional regional volumes of distribution
 available to a particular solute, i.e., vC,
 within the capillary; vI, interstitial fluid
 space; and vcell, parenchymal cells. At equi-
 librium, for a substance passively exchang-
 ing between plasma and ISF, vI is the ratio
 of the concentration in VI to that in the
 plasma and is equal to the partition co-
 efficient λ = CI/Cp. For steady-state proc-
 esses producing transmembrane fluxes,
 the effective volume of distribution is not
 the same as the equilibrium ratio, i.e.,
 vI ≠ λ
ν F Velocity of fluid flow, cm·s−1
V’Volumes of distribution, cm3·g−1. VC, in cap-
 illary; VI, in ISF; and Vcell, in parenchymal
 cell. These are the anatomic volumes times
 the fractional volume of distribution, e.g.,
 VI=vIVI. Commonly used ratios are γ=VIVc and ϴ=VcellVC
V~i Partial molar volume of solute i, cm3/mol; the
 increment in the volume of a solution per
 mole of added solute, e.g., V~w18cm3mol1
WMass, g (“weight,” mass times gravitational
 acceleration)
ω(x)Weighting function or probability density
 function of variable x
ωi or
ωi(f)
Weighting or fraction of total in the ith group.
 Units are fraction per unit of f. Given a
 density function of regional flows, ω(f), in
 its finite histogram representation ωiΔfi, is
 the fraction of the mass of the organ having
 a flow fi, the average of the flows grouped
 as the ith class. The fraction of the total
 flow going to the regions falling into the ith
 class is ωifiΔfi
x Distance, cm; e.g., distance along the capillary
 from inflow, x = 0, to outflow, x = L
x Mean of a density function, ω(x); see mean
 and moments, α
X Generalized driving force
xi Mole fraction of component i; i.e., moles of
 the ith component divided by the total moles
 in the system, = ni/n, where n is the total
z Valence of an ionic solute, number of unpaired electrons (or missing electrons) per molecule

Greek symbols

α0, α1, αnMoments about zero for a probability density
 function. (Units are tn when t is the inde-
 pendent variable.) [α0 = area; α1 = mean;
 for the density function h(t), αn=0+tnh(t)dt. See central moments, μ
β n–2 Dimensionless parameters of shape of density
 function calculated from the central mo-
 ments, =μnSDn=μnμ2n2. “β1” is skewness
 (or asymmetry); β1 is zero for all symmet-
 rical functions, positive for right skewness.
 β2” is kurtosis (or flatness). β2 = 3.0 for
 normal density function; β2 > 3 for lepto-
 kurtosis (highpeakedness), and <3 for
 platykurtosis
γ Ratio of interstitial volume of distribution
 to intracapillary volume of distribution,
 VIVcap
Δ Difference
δ(t)Unit impulse func-
 tion, or Dirac delta function, has unity area, an infinite amplitude
 at t = 0, and is zero at all other times. It is
 the limit of any symmetrical unimodal den-
 sity function of unity area as its width ap-
 proaches zero. For delta function occurring
 at a nonzero time t0, it is written δ(tt0)
[sm epsilon] Epsilon, vanishingly small difference
ζ Tortuosity of diffusion pathway. ζ is ratio of
 apparent path length to measured length of
 diffusion pathway, dimensionless; thus the
 effective diffusion coefficient, D = D02
 where D is the free aqueous diffusion coef-
 ficient
η Viscosity, poise (P) = dyn/cm2 = g·s−1·cm−1.
 Water viscosity = 0.01002 P at 20°C.
 Plasma viscosity ≈ 0.011
η(t)Equals h(t)/R(t) (fraction/s); the emergence
 function, the specific fractional escape rate
 following an impulse input. Of the particles
 residing in the system for t seconds after
 entering, η(t) is the fraction that will depart
 or escape in the tth second. In chemical
 engineering it is known as the intensity
 function (7), and in population statistics as
 the risk function, the death rate of those
 living at age t. Also, η(t) = (dR/dt)/R(t) =
 −d logeR(t)/dt. See FER(t)
Θ Ratio of intracellular volume of distribution
 to intracapillary volume of distribution,
 VcellVcap, dimensionless
λ, λij Partition coefficient, a dimensionless ratio
 of Bunsen solubility coefficients in two
 phases. λij is the ratio of solubility in region
 or solvent i to the solubility in region j. The
 reference region j is usually the plasma. At
 equilibrium, λij is the ratio of concentra-
 tions
μ Chemical potential for a solute in a solution,
 N·m−2; μ = μ0 + RT In a, where the activity
 a is a concentration times an activity coef-
 ficient and μ0 is the potential at a reference
 state of temperature and pressure
μ n nth central moment of a density function,
 h(t), a moment around the mean, t. μn=(tt)nh(t)dt. Units are those of t to
 the nth power
μ2, μ3, μ4μ2 is variance, the second moment of a density
 function around the mean, =α2α12. Also
 μ3=α33α1α2+2α13 and μ4=α44α1α3+6α12α2. See also βn
π Osmotic pressure, Pa or N·m−2 or mmHg, is
 the pressure that would have to be exerted
 on a solution to prevent pure water from
 entering it from across an ideal semiperme-
 able membrane, i.e., a membrane permeable
 to solvent only. π = CRT is Van’t Hoff’s
 law for ideal dilute solutions, and across a
 membrane impermeable to solute. π =
 [var phi]CRT is preferred to account for activity
 coefficients less than unity. When the sol-
 ute can permeate the membrane, the effec-
 tive π = σ[var phi]CRT. Osmotic pressure, a colli-
 gative property of solutions, is related to
 actual pressure rn the same fashion as a
 freezing point is to actual temperature. On-
 cotic pressure is a term, now obsolete al-
 though historically useful, for the osmotic
 pressure associated with the presence of
 large, relatively impermeant molecules such
 as plasma proteins. It should now be re-
 placed by more exact terms, e.g., across
 some specific membrane the effective Δπ
 equals RTφi=1i=NσiϕiΔCi, where the effects of
 concentration differences for a set of N
 solutes are summed.
ρ Density, g·cmm−3. (Specific gravity is density
 relative to density of water)
σ Reflection coefficient, in notation of irrevers-
 ible thermodynamics, dimensionless; σ =
 –LpD/Lp or, experimentally, σ = –JD/Jv for
 ΔC8 = 0. The effective osmotic pressure
 across a membrane is σΔπ, mmHg; i.e., σ =
 (observed osmotic pressure)/CRT
τCCapillary mean transit time, tc, used in Krogh
 cylinder capillary-tissue models with plug
 flow velocity profiles
[var phi] Activity coefficient, the ratio of apparent
 chemically effective concentration to the
 actual concentration in a solution, in the
 absence of chemical binding, dimensionless.
 The osmotic activity coefficient [var phi] = π/CRT
ψ Electrical potential, V
ω Solute permeability coefficient, ω = P/RT,
 mol·cm−2. s−1 ·(mmHg)−1. In the notation of
 irreversible thermodynamics ω = (LD – RT/F
 σ2Lp)C̄s, where C̄s, is the average solute con-
 centration across the membrane

Physical Units, Constants

AAmpere, unit of electrical current, coulomb
 per second (C·s−1)
Å Ångstrom, 10−10 m or 0.l nm
CCharge, coulomb, ampere· second (A. s)
°KDegrees of temperature, Kelvin (absolute); °C
 for degrees Celsius = 273.15 + °K
dynDyne, force, g·cm·s−2 = 10−5 N (newton)
eqEquivalent weight = molecular weight/va-
 lence. One equivalent carries 9.65 × 104 C
 of charge
eElementary charge, 1.6021892 × 10−19 C
ergEnergy, dyn·cm = g·cm2·s−2 = 10−7 J
FFaraday constant, 9.648456 × 104 elementary
 charge. eq−1 = 96,484.6 C· mol−1 = NAe
g Acceleration due to gravity = 980.665 cm·s−2
hPlanck’s constant (energy quantum) =
 6.626176 × 10−27 erg·s = 6.626 × 10−34 J·s
η Viscosity; 1 poise (P) = 1 cm−1· g·s−1 = 0.1
 Pascal·second (Pa·s)
ICurrent, amperes
JJoule = Watt·second (W ·s) = ampere·volt·
 second (A·V·s) = 107 erg = 107 cm2g·s−2
kBoltzmann constant, 1.380662 × 10−23 J. °K−1
 = R/NA, the gas constant over Avogadro’s
 number = 1.37900 × 10−16 cm2·g·s−2·°K−1
1, literLiter = 1 dm3 = 1,000 cm3. Also milliliter (ml)
 and microliter (μl)
MMol/l (molarity)
mol/kgMol solute/kg solvent (molality)
NNewton = 105 dyn = 105 cm·g·s−2
N A Avogadro’s number, 6.022045 × 1023 mol−1,
 the number of molecules contained in 1 mol
ns, nwNumber of moles of solute and water
PPressure (= force per unit area), N·m−2 or Pa
 (Pascal). (1 Pa [equivalent] 1 N·m−2 [equivalent] 10 g·cm−1·s−2
 [equivalent] 10−2 mbar [equivalent] 0.10197 mmH20 [equivalent] 7.5 ×
 10−3 mmHg [equivalent] 9.869 × 10−6 atm; or 1 atm =
 101325 Pa = 760 Torr; 1 cmH20 (at density
 1 g·cm−3) = 98.0665 Pa = 981 g·cm−1·s−2;
 1 mmHg = 1.00000014 Torr = 133.322 Pa
 = 1,333 g·cm−1 · s−2
ρ Density, g·cm−3. Water (3.98°C, 1 atm) =
 0.999972 g·cm−3. Mercury (0°C, 1 atm) =
 13.59508 g·c−3
R Resistance, electrical (Ω), or electrophysiolog-
 ical (Ω/cm2) or vascular (a pressure divided
 by a flow)
R Universal gas constant = 8.31441 J.mol−1
 °K−1 = 8.3144 × 107 cm2 ·g·s−2 ·mol−1 °K−1
 = 0.082 1· atm· mol−1 °K−1 = 0.0623 mmHg·
 mmol−1· °K−1 = 8.31441 × 10−7 erg·mol−1·
 °K−1
RT Energy/mol, gas constant × absolute temper-
 ature; e.g., at 37°C or 310.16°K, RT = 19.34
 × 106 mmHg· cm3· mol−1
RT/F 24.84 mV at 15°C.26.62 mV at 37°C. Values
 of loge,10 RT/F at 15, 20, 25, 30, and 37°C
 are 57.2, 58.2, 59.2, 60.2, and 61.3 mV
STPStandard temperature and pressure (ice point
 of water, 0°C = 273.16°K; 760 mmHg = 1
 atm = 1.01325 × 106 dyn·cm−2 = 1.013 ×
 105 N· m−2)
T Temperature, absolute, in degrees Kelvin
 (°K); 0°C = 273.16 °K
VVolts; millivolt, mV; microvolt, μV
V i Partial molar volume, ml/m01 =
 ([partial differential]V/[partial differential]ni)T,p,njj≠i = change of volume of total
 system per mole additional solute i, at T, p,
 and constant presence of other components
 j, and at the particular concentration ni/V.
 (VW is the partial molar volume of water;
 close to 18 ml/mol for physiological solu-
 tions)
WattUnit of power, joules per second, J·s−1
WorkWork is energy × time or force × distance ×
 time, erg·s or J· s or cm2g·s−1
Ω Ohm, unit of electrical resistance; V/I

Acknowledgments

The authors greatly appreciate the efforts of Geraldine Crooker in the preparation of this terminology.

REFERENCES

1. Bassingthwaighte JB, Chinard FP, Crone C, Lassen NA, Perl W. Definitions and terminology for indicator dilution methods. In: Crone C, Lassen NA, editors. Capillary Permeability. Munksgaard; Copenhagen: 1970. pp. 665–669.
2. Bassingthwaighte JB, Goresky CA. Handbook of Physiology. Sect. 2, The Cardiovascular System. Vol. IV, The Microcirculation. Bethesda, MD: Modeling in the analysis of solute and water exchange in the microvasculature.Am. Physiol. Sot. 1984:549–626. chapt. 13.
3. Gonzalez-Fernandez JM. Theory of the measurement of the dispersion of an indicator in indicator-dilution studies. Circ. Res. 1962;10:409–428. [PubMed]
4. Katchalsky A, Curran PF. Nonequilibrium Thermody-namics in Biophysics. Harvard Univ. Press; Cambridge, MA: 1965.
5. Kedem O, Katchalsky A. Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. Biochim. Biophys. Acta. 1958;27:229–246. [PubMed]
6. Meier P, Zierler KL. On the theory of the indicator-dilution method for measurement of blood flow and volume. J. Appl. Physiol. 1954;6:731–744. [PubMed]
7. Shinnar R, Naor P. Residence time distributions in systems with internal reflux. Chem. Eng. Sci. 1967;22:1369–1381.
8. Silberberg A. The mechanics and thermodynamics of separation flow through porous, molecularly disperse, solid media—the Poiseuille Lecture 1981. Biorheology. 1982;19:111–127. [PubMed]
9. Spiegler KS. Transport process in ionic membranes. Trans. Faraday Sot. 1958;54:1408–1428.
10. Stephenson JL. Theory of the measurement of blood flow by the dilution of an indicator. Bull. Math. Biophys. 1948;10:117–121. [PubMed]
11. WOOD EH. Definitions and symbols for terms commonly used in relation to indicator-dilution curves. Circ. Res. 1962;10:379–380.
12. Zierler KL. Equations for measuring blood flow by external monitoring of radioisotopes. Circ. Res. 1965;16:309–321. [PubMed]