Basic Terms and Definitions

Space:  the terms "space" and "volume" will be used interchangeably in reference to the same thing.  The contents of a space may be a heterogenous or homogenous mixture.

Compartment and Compartmentation:   a compartment is an amount of a certain matter that acts kinetically like a distinct, homogenous, well-mixed amount of that matter.  The standard diagrammatic representation for compartmental systems is a box to represent a compartment and arrows to represent transfer of material into and/or out of compartments.  Each arrow may be labeled with the fractional transfer coefficient, which is the fraction of the compartment from which the arrow originates, transferred per unit time.  To further clarify the distinction between a space and a compartment, consider a compound A exchanging between two physiological spaces by diffusion;  this is regarded as a two compartment system since q1 and q2 are the amounts of A in spaces 1 and 2, respectively.  Suppose then that compound A reacts with compound B to form a complex AB, the result of this reaction is a four-compartment system with q1 and q2 as the amounts of A in spaces 1 and 2, respectively, and q3 and q4 being the amounts of AB in spaces 1 and 2, respectively.  Hence, within one physical volume, two different chemical combinations of an element, each uniformly distributed, can be represented by a compartment.  

Pool:  the term designates an amount of given material. A pool may consist of more than one compartment and may be distributed in more than one space so as to be more general than the terms "space" or "compartment."

Volume of Distribution:  Consider any closed system.  The volume of distribution is a hypothetical volume in which a given compound concentration c is distributed uniformly within a given system A.  The volume of distribution of the compound is A/c. Thus, the volume of distribution of compound X is the "hypothetical volume in which it would be distributed if its concentration wherever it was distributed, were the same as at the sampling site."  In an open system, we have to assume that there is a continuous injection of compound X at a constant rate until the concentration at the sampling site remains constant. The volume of distribution is the amount in the system at the time of measurement (total injected minus the total excreted) divided by the concentration of X in the sample.

Turnover Rate and Turnover Time:  For a system in a steady state, the rate at which material leaves or enters a compartment is the turnover rate;  this has the units mass/time.  The size of a compartment divided by the turnover rate gives the turnover time.

Radioisotopes and Units:  Used as tracers in compartmental analysis experiments.  The units of radioactivity are disintegration per unit time.  The standard unit is the curie, which is 3.7 x 1010 disintegrations per second.  Immediate measurements are measured in units counts per unit time.  Specific activity refers to a measure of radioactivity per unit mass or per mole of a substance.  "Trace" amounts of isotopes are used within a system so as to not disturb the steady state of the system.  Usually the amount added to a compartment is much less than 1% of the size of the compartment.  The amount added to a biological system should be small enough so that the emitted radiation does not appreciably affect the integrity or functioning of the living system.

Apparent Exchangeable Mass:  suppose an injection  of radioactive tracer is injected into given volume as in the case with the volume of distribution scenario.  "The mass obtained by dividing the amount of labeled compound in the system, measured in units of radioactivity, by the specific activity at the sampling site is the apparent exchangeable mass."  This too is a hypothetical quantity because we are assuming that the labeled molecules have been uniformly mixed with the unlabeled molecules of the compound.

Isotope Fractionation:  When radioisotopes are used as tracers, a question as to whether there is a discrimination in favor of or against the labeled compound within the system needs to be taken into account.  In other words, the mass differences between the tracer 's and their normal corresponding isotope can significantly affect diffusion and rates of chemical reactions because these rates are dependent upon the masses of the compounds involved.  If the mass differences are small, the effects are usually small, but isotope fractionation effects must be kept in mind when interpreting the result of experiments with tracers.