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 V0 was negligibly small, in which case the CaV0 term is eliminated from equation (4). Taking equation (4) with CaV0eliminated, and integrating both sides from time 0 to the end of the last frame, we get:
We can then take this equation, and divide it by a weighted version of itself:
K1 cancels out of this equation, leaving us with an equation that only involves k2. 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 k2, so a different approach was taken. A look-up table was generated relating values of k2 to resulting values of the right hand side of equation (6). A linear interpolation was then performed to choose values of k2 from this look-up table for each point in the left hand side of equation (6).