I. Introduction
Quantitative analysis in positron emission tomography (PET) is based on a relationship between a time-activity curve of an administered tracer (plasma time-activity curve; pTAC) and a time-activity curve in the target tissue (tissue time-activity curve, tTAC). For example, the following equation describes the relationship in [18F]fluorodeoxyglucose ([18F]FDG), which is a glucose analog and measures regional cerebral glucose metabolism [1]. C_{{\rm t}}(t)={k_1\over k_{2}+k_{3}}\left\{k_{3}+k_{2}\exp(-(k_{2}+k_{3})t)\right\}\otimes C_{{\rm p}}(t),\eqno{\hbox{(1)}}
where and are the tTAC and pTAC, respectively, and ⊗ is a convolution operation. to are kinetic parameters that describe the behavior of [18F]FDG. Especially, a combined parameter, , which is proportional to regional cerebral metabolite rate of glucose, is estimated as a slope using the Patlak Plot [2]. {C_{{\rm t}}(t)\over C_{{\rm p}}(t)}=K_{i}{\int\nolimits_{0}^{t} C_{{\rm p}}(u){\rm d}u\over C_{{\rm p}}(t)}+V,\eqno{\hbox{(2)}}
where is a constant intercept.