  Significance: 2D fully convolutional neural networks have been shown capable
of producing maps of sO$_2$ from 2D simulated images of simple tissue models.
However, their potential to produce accurate estimates in vivo is uncertain as
they are limited by the 2D nature of the training data when the problem is
inherently 3D, and they have not been tested with realistic images.
  Aim: To demonstrate the capability of deep neural networks to process whole
3D images and output 3D maps of vascular sO$_2$ from realistic tissue
models/images.
  Approach: Two separate fully convolutional neural networks were trained to
produce 3D maps of vascular blood oxygen saturation and vessel positions from
multiwavelength simulated images of tissue models.
  Results: The mean of the absolute difference between the true mean vessel
sO$_2$ and the network output for 40 examples was 4.4% and the standard
deviation was 4.5%.
  Conclusions: 3D fully convolutional networks were shown capable of producing
accurate sO$_2$ maps using the full extent of spatial information contained
within 3D images generated under conditions mimicking real imaging scenarios.
This work demonstrates that networks can cope with some of the confounding
effects present in real images such as limited-view artefacts, and have the
potential to produce accurate estimates in vivo.
