Effect of the blood function error on the estimated kinetic parameters with dynamic pet

PET is an imaging modality widely used in areas such as oncology, neurology, cardiology and neuropsychology/cognitive neuro-science. Dynamic PET, in contrast to static PET, can identify temporal variations in the radiotracer concentration. Mathematical modeling of the tissue of interest in dynamic PET can be simplified using compartment models as a linear system where the time activity curve of a specific tissue is the convolution of the tracer concentration in the plasma and the impulse response of the tissue containing kinetic parameters. Since the arterial sampling of blood to acquire the value of the tracer concentration is invasive, blind identification to estimate both the blood input function and the kinetic parameters has recently drawn attention. Several methods have been developed for this purpose, but the effect of the estimated blood on the estimation of the kinetic parameters is not studied. In this paper, we present a mathematical model to compute the error in the kinetic parameter estimates caused by the error in estimation of the blood input function. Computer simulations show that analytical expressions we derive are sufficiently close to results obtained from optimization. Our findings are conceptually important to observe the effect of the blood function on kinetic parameter estimation, but also practically useful to evaluate various blind methods.