  Perfusion imaging is the current gold standard for acute ischemic stroke
analysis. It allows quantification of the salvageable and non-salvageable
tissue regions (penumbra and core areas respectively). In clinical settings,
the singular value decomposition (SVD) deconvolution is one of the most
accepted and used approaches for generating interpretable and physically
meaningful maps. Though this method has been widely validated in experimental
and clinical settings, it might produce suboptimal results because the chosen
inputs to the model cannot guarantee optimal performance. For the most critical
input, the arterial input function (AIF), it is still controversial how and
where it should be chosen even though the method is very sensitive to this
input. In this work we propose an AIF selection approach that is optimized for
maximal core lesion segmentation performance. The AIF is regressed by a neural
network optimized through a differentiable SVD deconvolution, aiming to
maximize core lesion segmentation agreement with ground truth data. To our
knowledge, this is the first work exploiting a differentiable deconvolution
model with neural networks. We show that our approach is able to generate AIFs
without any manual annotation, and hence avoiding manual rater's influences.
The method achieves manual expert performance in the ISLES18 dataset. We
conclude that the methodology opens new possibilities for improving perfusion
imaging quantification with deep neural networks.
