A free boundary problem model of ductal carcinoma in situ

Abstract

Ductal carcinoma in situ (DCIS) refers to a specific diagnosis of cancerthat is isolated within the breast duct, and has not spread to otherparts of the breast. We modify a model proposed by Byrne and Chaplainfor the growth of a tumour consisting of live cells (nonnecrotic tumour)to describe the tumour growth inside a cylinder, a model mimickingthe growth of a ductal carcinoma. The model is in the form of a freeboundary problem. The analysis of stationary solutions of the problemshows interesting results that are similar to the patterns found in DCIS.