In order to model the complete two-compartment system, we must be able
to solve equation (4). In section
2.2,
we solved the equation by multiplying by two different weights and
then dividing, and we can take a similar approach with the full
two-compartment equation. We can weight equation (4)
with *three* different weights and then integrate:

By multiplying equation (7) by
and equation (9) by
,
and then
subtracting the two, we may eliminate the *V*_{0} term. A similar
operation can be performed on equation (8) and
equation (9). This leaves two equations that do
not contain *V*_{0}. They may then be divided to produce:

The *K*_{1} term cancels out of both the numerator and denominator of
equation (10), leaving an equation that only involves
*k*_{2}. As with the equation in section 2.2,
this is very difficult to solve for *k*_{2}. Therefore, a look-up
table was again used. Once the table matching values of *k*_{2} with
values of the right hand side of equation (10) has been
created, we may evaluate *k*_{2} through simple lookup. With the
*k*_{2} data computed, finding *K*_{1} is simply a matter of
evaluating either the numerator or denominator of equation
(10) without cancelling *K*_{1}. With both *K*_{1} and
*k*_{2} known, we may find *V*_{0} by evaluating equation
(4).

Greg Ward <greg@bic.mni.mcgill.ca>

Sean Marrett <sean@bic.mni.mcgill.ca>