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Angiogenesis is a key phenomenon for tumour progression, diagnosis andtreatment in brain tumours and more generally in oncology. Presently, itsprecise, direct quantitative assessment can only be done on whole tissuesections immunostained to reveal vascular endothelial cells. But this is atremendous task for the pathologist and a challenge for the computer sincedigitised whole tissue sections, whole slide images (WSI), contain typicallyaround ten gigapixels.  We define and implement an algorithm that determines automatically, on a WSIat objective magnification $40\times$, the regions of tissue, the regionswithout blur and the regions of large puddles of red blood cells, andconstructs the mask of blur-free, significant tissue on the WSI. Then itcalibrates automatically the optical density ratios of the immunostaining ofthe vessel walls and of the counterstaining, performs a colour deconvolutioninside the regions of blur-free tissue, and finds the vessel walls inside theseregions by selecting, on the image resulting from the colour deconvolution,zones which satisfy a double-threshold criterion. A mask of vessel wall regionson the WSI is produced. The density of microvessels is finally computed as thefraction of the area of significant tissue which is occupied by vessel walls.  We apply this algorithm to a set of 186 WSI of paediatric brain tumours fromWorld Health Organisation grades I to IV. The segmentations are of very goodquality although the set of slides is very heterogeneous. The computation timeis of the order of a fraction of an hour for each WSI on a modest computer. Thecomputed microvascular density is found to be robust and strongly correlateswith the tumour grade.  This method requires no training and can easily be applied to other tumourtypes and other stainings.

Automatic quantification of the microvascular density on whole slide images, applied to paediatric brain tumours