The volumes of some compartment systems with sampling and loss from one compartment

If the concentrationc ₁(t)=∑ _i=1 ⁿ A _i exp (−α _i t) for one compartment, one presumes a linear catenaryn-compartment system without sinks and loss only from the same compartment, then the volumesV _i , rate constantsk _ij , and concentrationsc _i (t) in each compartment can be determined in terms of theA _i 's,A _i ′s, α _i ′s, the dose injectedD _o and the partition coefficientsr _ij =k _ij /k _ji . If the concentration would become uniform at equilibrium, then the total volume of distribution may be determined without knowledge ofr _ij or restriction to catenary configuration.