Joana Sarah Grah, Department of Applied Mathematics and Theoretical Physics

Mathematical Methods for Automatic Detection and Tracking of Dividing Cancer Cells in Phase Contrast Microscopy

Joana Grah¹, Alexander Schreiner², Martin Burger³, Carola-Bibiane Schönlieb¹, Stefanie Reichelt²

1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge

2 Cancer Research UK Cambridge Institute

3 Institute for Computational and Applied Mathematics, Westfälische Wilhelms-Universität Münster, Germany

Abstract

Nowadays research in the biomedical sciences, including mitotic index analysis of cancer cells, strongly depends on the automated processing of digital microscopy images. The amount of data required for high quality analyses is constantly growing and there is an urgent need for suitable image enhancement and processing techniques which can help handling the big data in an automatic manner. We present a framework for automatic detection and analysis of mitotic cells and a new variational cell tracking method specifically designed for image sequences from phase contrast microscopy. By means of the circular Hough transform we are able to identify mitotic cells in a
large sequence of images. The resulting circle around the cell subsequently serves as an initial contour for tracking the cell through the whole mitosis cycle. To do so the tracking procedure is subdivided in two steps: First, the cell is tracked backwards in time until it reaches the start of the mitosis cycle. After that, it is tracked forwards in time until it divides or dies (end of the mitosis
cycle). From this analysis we determine the length of the mitotic phase and measure the mitotic index of the cell sample, that is the relative number of cells undergoing mitosis. All algorithms of this automated analyser of mitotic cells are featured in MitosisAnalyser, a user-friendly Graphical User Interface in MATLAB®.