**Two-Compartment Linear
System**

## "If the rates of change of all the state variables of a system can be written as sums of processes none of which is of higher than first order, the system is a linear system and is described by a set of linear differential equations."

## x

_{1}= Concentration of tracer in compartment 1## x

_{2}= Concentration of tracer in compartment 2## Units of concentration = mass/volume (i.e. g/ml)

## V

_{1}= volume of compartment 1## V

_{2}= volume of compartment 2## q

_{1}= mass of tracer in compartment 1## q

_{2}= mass of tracer in compartment 2

## Conservation of Mass

d/dt(q_{1}) = (mass entering in) - (mass exiting out)## d/dt(q

_{1}) = k_{12}(q_{2}) - k_{21}(q_{1})## d/dt(q

_{2}) = k_{21}(q_{1}) - k_{12}(q_{2});## where k

_{12}and k_{21}are rate constants. The first subscript for k denotes the destination and the latter the origin of the directional flow .## How should we solve for q

_{1}and q_{2}?

B.3-a