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."
x1 = Concentration of tracer in compartment 1
x2 = Concentration of tracer in compartment 2
Units of concentration = mass/volume (i.e. g/ml)
V1 = volume of compartment 1
V2 = volume of compartment 2
q1 = mass of tracer in compartment 1
q2 = mass of tracer in compartment 2
Conservation of Mass
d/dt(q1) = (mass entering in) - (mass exiting out)
d/dt(q1) = k12(q2) - k21(q1)
d/dt(q2) = k21(q1) - k12(q2);
where k12 and k21 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 q1 and q2?