M.Sc Student M.Sc Thesis Bar-on Tomer Mathematical Problems in Bladder Cancer Department of Applied Mathematics PROF. Jacob Rubinstein

Abstract

Bladder cancer (BC) is an uncontrolled and unordered division of cells in the urine bladder, the mass of tissue created is called a Tumor or a Growth. The bladder itself is a muscular sac which is composed of three layers (from inner most to outer most) 1. The mucus layer 2. The connective layer 3. The muscle layer.

These three layers combined are referred to as the bladder wall. In this work will focus on a specific type of BC, Transitional Cell (urothelial) Carcinoma (TCC), a cancer category affecting the cells composing the bladder wall, and in that group we will focus on an early superficial stage: non muscle invasive bladder cancer (NMIBC), a stage in which the cancer hasn't reached the muscle layer. To treat TCC a surgical procedure is performed to remove the tumor followed by an adjuvant treatment for undetected and residual tumors. The most common adjuvant treatment is the Bacillus Calmette-Gurin

(BCG), a modified version of a tuberculosis vaccine.

This work encapsulate two main studies:

1.      An application of machine learning algorithms to a clinical database in order to find a criterion for predicting tumor recurrence in patients undergoing the BCG treatment. Several machine learning algorithms were tested and evaluated on the data base, Decision Tree, Multilayer Perceptron and K Nearest Neighbors. A special filter was devised to remove outliers from the database, which greatly improved prediction accuracy. It was found, by examining the Decision Tree output, that the neutrophil to lymphocyte ratio can help predict recurrence. Using optimization methods an algorithm was developed to find an optimal range for the neutrophil to lymphocyte ratio where the computer can predict recurrence in high precision.

2.      A dynamical system analysis of the BCG treatment. The BCG treatment is an immunotherapy method where a weakened strain of tuberculosis is introduced to the body. The bacteria infects the tumor cells which cause the body's immune system to eliminate the tumor cells. We improved an existing time dependent dynamical model, developed by Bunimovich and Mendrazitsky, describing the BCG mode of operation by adding spatial dependency. In both our model and the previous model we analyze the stability of the stationary "tumor free" solution. This expansion provides a stability criterion which shows the factors, mainly the bladder wall thickness, which may cause the treatment to fail. This stability criterion is an improvement over the previous model which shows general stability.