introduction.tex

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\section{Introduction} \label{sec:introduction}\vspace{-0.3cm}\vspace{0.2cm}
    \IEEEPARstart{T}{he} \gls{VT} estimated with an \gls{AIF} is utilised for quantification of many \gls{PET} tracers, including \gls{PBR28}. This, however, requires the concurrent measurement of the concentrations of unchanged radioligand in arterial plasma. Although insertion of an arterial catheter rarely results in clinically relevant adverse events, it is an invasive and laborious procedure. 
    
    \gls{IDIF} represents a promising alternative to arterial sampling~\cite{Zanotti-Fregonara2011}. However, its applicability in clinical research is hampered by several factors including the inaccuracy in the estimation of both shape and amplitude of the \gls{IF}; moreover \gls{IDIF} does not allow for radio-metabolites quantification~\cite{Sari2018Non-invasive11C-SB201745}. The application of \gls{ML} is expected to improve the accuracy of predicting the \gls{AIF} from \gls{PET} images~\cite{Kuttner2020, Ferrante2022PhysicallyImaging}. While these methods have shown promising results, the vast majority of these approaches have been developed for \gls{PET} tracers that do not produce radio-metabolites. Furthermore, even if the developed model shows sufficient prediction accuracy for unseen data, its applicability in the clinical setting remains questionable because of a lack of transparency or thorough evaluation~\cite{Salahuddin2022TransparencyMethods}. Bayesian networks offer the significant advantage of making probabilistic predictions based on available evidence. Specifically, a Bayesian network would output uncertainty estimates in addition to the model prediction. For this reason, they have the potential to overcome the key barrier to the responsible adoption of \gls{AI} in clinical practice~\cite{Prabhudesai2023LoweringAI}. 
    
    Here, we propose a Bayesian \gls{NN}-based method for predicting a metabolite corrected \gls{AIF}, while allowing for the estimation of uncertainty of the model's output.% Specifically for the \gls{AE}, although also present in the other networks, we try to enforce the low dimensional representation of the input data as disentangled and continuous. Furthermore, the network does not predict a single signal for each input; rather, it predicts a probability density function of potential signals, which allows for the estimation of uncertainty of the model's output.