This model implements the 1tissue compartment model for ^{1}H_{2}^{15}O water PET studies.
Additionally it is assumed that the true input curve has been convolved with a kernel
whereby the parameter t is called "Dispersion". This expression is incorporated into the 1tissue compartment model and solved using the Laplace transform to yield the equation below, as described by E. Meyer [16].
The original operational equation
has been modified to
to allow for a spillover term. The interpretation for a freely diffusible model is: K_{1} represents flow and k_{2} is flow divided by the partition coefficient p.
Unlike the standard compartment models in PKIN the model curve of the operational equation is not calculated by integrating a set of differential equations, but rather using the analytical solution given above. This convolution integral is approximated by summing up rectangles of 0.1sec in length, assuming that the acquisition time of dynamic water studies is short.
Note: The delay parameter is not part of the TAC model, but as usual must be enabled for fitting in the input curve model.
Abstract [16]
"The difference in tracer arrival times between the radial artery and the brain following i.v. injection of 15Olabeled water plus the difference in dispersion of the tracer bolus between these two sites have to be accounted for in order to quantify cerebral blood flow by the autoradiographic approach and positron emission tomography (PET). We describe a method that simultaneously corrects for these two effects by means of a fourparameter fit to the dynamically acquired data. Unlike with other methods, where the two corrections are performed sequentially, no additional measurement of the dispersion time constant is required. We have validated and tested the method by means of simulations and application to data from six human studies. The mean dispersion time constant of 4.0 +/ 1.2 sec, estimated by the new method for the six studies, is in fair agreement with estimates of 3 to 5 sec derived from cardiac PET."
Model Name 
Description 
As above, but the left ventricle input curve is linearly corrected for metabolites. 

1Tissue compartment model with two spillover terms. Has been developed for cardiac NH_{3}PET studies with bolus administration. 

2Tissue compartment model with metabolic trapping. Has been developed for cardiac NH_{3}PET studies with bolus administration. 

1compartment model for the quantification of myocardial perfusion with Rubidium82 PET data. 

Twocompartment model for the quantification of myocardial perfusion with Rubidium82 PET data. 

1Tissue compartment model with two spillover terms. Has been developed for cardiac H_{2}^{15}O PET studies with bolus administration. 

As above, but with geometrical spillover correction. 

1compartment model for the quantification of myocardial perfusion with ^{11}C Acetate PET data. 
Assumptions of the Cardiac Models
Exceptions to these rules are specified in the description of the individual models.