Identifying the necrotic zone boundary in tumour spheroids with pair-correlation functions

Automatic identification of the necrotic zone boundary is important in the assessment of treatments on in vitro tumour spheroids. This has been difficult especially when the difference in cell density between the necrotic and viable zones of a tumour spheroid is small. To help overcome this problem, we developed novel one-dimensional pair-correlation functions (PCFs) to provide quantitative estimates of the radial distance of the necrotic zone boundary from the centre of a tumour spheroid. We validate our approach on synthetic tumour spheroids in which the position of the necrotic zone boundary is known a priori. It is then applied to nine real tumour spheroids imaged with light sheet-based fluorescence microscopy. PCF estimates of the necrotic zone boundary are compared with those of a human expert and an existing standard computational method.