Since the time required to perform a least squares curve fitting would
be prohibitive, a simpler approach to solving the problem is required.
One technique is to use a weighted integration method. We initially
approached the problem by assuming that *V*_{0} was negligibly small,
in which case the
*C*_{a}*V*_{0} term is eliminated from equation
(4). Taking equation (4) with *C*_{a}*V*_{0}eliminated, and integrating both sides from time 0 to the end of the
last frame, we get:

(5) |

We can then take this equation, and divide it by a weighted version of itself:

*K*_{1} cancels out of this equation, leaving us with an equation
that only involves *k*_{2}. The left side of equation
(6) is easily evaluated by integrating the PET data.
The right side of equation (6) is not easily solved for
*k*_{2}, so a different approach was taken. A look-up table was
generated relating values of *k*_{2} to resulting values of the
right hand side of equation (6). A linear
interpolation was then performed to choose values of *k*_{2} from
this look-up table for each point in the left hand side of equation
(6).

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

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