A free boundary problem model of ductal carcinoma in situ

Ductal carcinoma in situ (DCIS) refers to a specific diagnosis of cancer that is isolated within the breast duct, and has not spread to other parts of the breast. We modify a model proposed by Byrne and Chaplain for the growth of a tumour consisting of live cells (nonnecrotic tumour) to describe the tumour growth inside a cylinder, a model mimicking the growth of a ductal carcinoma. The model is in the form of a free boundary problem. The analysis of stationary solutions of the problem shows interesting results that are similar to the patterns found in DCIS.