Predicting tumor sizes of ductal carcinoma in situ from immunohistochemical images using a novel approach of mathematical pathology: preliminary results, potentials and challenges ahead*

Differential equation models have recently drawn increasing attentions as a useful tool to help advance the knowledge in cancer research. However, challenges remain for applying such models to clinical practices on a patient-specific basis to assist surgical decisions. Clinical diagnoses essentially at a single time point are often insufficient to fully constrain the time-dependent differential equations. Here we present a novel mathematical pathology approach, identifying robust indicators for time-invariant predictions of the model that can be used for surgical planning. We demonstrate this approach by predicting the sizes of ductal carcinoma in situ by calibrating model parameters from immunohistochemical images. Our preliminary studies of 17 excised tumor cases resulted in a better agreement with the actual measured sizes than the other estimates available to us, showing the potential of our approach for patient-specific cancer diagnosis. Conversely, our studies also revealed challenges to overcome before we can take this approach to the next level.