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Math Med Biol. 2019 Mar 14;36(1):93-112. doi: 10.1093/imammb/dqx022.

Simulated ablation for detection of cells impacting paracrine signalling in histology analysis.

Author information

Mathematical Institute, University of Oxford, Oxford, UK.
Department of Integrated Mathematical Oncology, Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA.
Institute of Molecular Systems Biology, Department of Biology, ETHZ, Zurich, Switzerland.
Department of Oncology, University of Oxford, Oxford, UK.
Cancer Research UK Cancer Therapeutics Unit, The Institute of Cancer Research, London, UK.
Department of Genetics, Institute for Cancer Research, Oslo University Hospital Radiumhospitalet, Oslo, Norway.
Department of Pathology, Oslo University Hospital, Oslo, Norway.
Department of Cancer Imaging and Metabolism, Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA.


Intra-tumour phenotypic heterogeneity limits accuracy of clinical diagnostics and hampers the efficiency of anti-cancer therapies. Dealing with this cellular heterogeneity requires adequate understanding of its sources, which is extremely difficult, as phenotypes of tumour cells integrate hardwired (epi)mutational differences with the dynamic responses to microenvironmental cues. The later comes in form of both direct physical interactions, as well as inputs from gradients of secreted signalling molecules. Furthermore, tumour cells can not only receive microenvironmental cues, but also produce them. Despite high biological and clinical importance of understanding spatial aspects of paracrine signaling, adequate research tools are largely lacking. Here, a partial differential equation (PDE)-based mathematical model is developed that mimics the process of cell ablation. This model suggests how each cell might contribute to the microenvironment by either absorbing or secreting diffusible factors, and quantifies the extent to which observed intensities can be explained via diffusion-mediated signalling. The model allows for the separation of phenotypic responses to signalling gradients within tumour microenvironments from the combined influence of responses mediated by direct physical contact and hardwired (epi)genetic differences. The method is applied to a multi-channel immunofluorescence in situ hybridisation (iFISH)-stained breast cancer histological specimen, and correlations are investigated between: HER2 gene amplification, HER2 protein expression and cell interaction with the diffusible microenvironment. This approach allows partial deconvolution of the complex inputs that shape phenotypic heterogeneity of tumour cells and identifies cells that significantly impact gradients of signalling molecules.


cancer; histology; image analysis; paracrine; signalling


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