Tumor Control Probability modeling and Data Fitting

Immanuel Edi Wibowo

Wednesday, May 22, 2019, 14:30

Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany

Prostate cancer is the most common of cancer in men. Nowadays, radiotherapy has become a primary treatment for cancer therapy. To measure the effectiveness of the patient treatment, Tumor Control Probability (TCP) is commonly an assessment method. This thesis aims to model and t the TCP Poisson distribution based model with four dierent optimization methods. Thus we can determine the most suitable optimization method for TCP modeling based on the patients' clinical data.

In the analysis, we involved published clinical data from 110 patients withprostate cancer which consist of a summary of the treatment plans for each patient. Subsequently, the data was used to t the model. A Poisson distribution model was used to present the TCP model. We t the TCP models to external radiation treatment therapy outcome of prostate cancer based on dose distribution from the Dose Volume Histogram (DVH). By using the negative log-likelihood technique, we t the patient clinical data to obtain the outcome scores of the radiation treatment therapy. To dene the TCP model, we used two dierent mathematical models. The rst TCP model used radiobiological parameters such as density(), alpha(), and alpha-beta ratio (=) as optimizer variables. Second TCP model used  , D50, and alpha-beta ratio(=) as optimizer variables. We estimated the radiobiological parameters by using the optimizing methods such as Limited Memory Broyden-Fletcher Goldfarb- Shanno (L-BFGS), Nelder-Mead (NM) Simplex Optimization, Simulated An-nealing (SA), and Particle Swarm Optimization (PSO). In the L-BFGS and NM Simplex optimization, a few initial start conditions were used to solve the local optima problem. In this project, we also implemented a sensitivity analysis to analyze the outcome which might occur within a dierent = ratio parameter values. To study the population size management in PSO, we implemented PSO with dierent number of particles which were involved. We assessed the tting quality between the models by using normal Gaussian distribution and the Pearson Chi-Square test.

At L-BFGS and NM Simplex optimization, we alternatively tried to trade-off an optimization result against time-consuming. As a consequence, L-BFG and NM Simplex new optimization results showed improvement. However, the optimization time increased signicantly. We show that TCP modeling can be dened with two dierent models, even though it shows a dierenttting quality result. In the report, we presented the optimization result table from four dierent optimization methods, PSO number of particles analysis table and initial temperature SA analysis. Besides, we also analyzed the goodness of model t in the report.

In this thesis, we represent several conclusions. First, it shows that increasing the number of particles in the PSO algorithm method would not give a significant optimization result impact on the TCP;D50 likelihood model. Besides, it may be useless since a signicant number of particles which are involved in the process would increase the optimization time. Second, in the optimization process comparison, PSO method had the potential to be the best tness optimization of these four algorithms. The method can reach optimum condence area with less time; however, it takes more times to reach the nal optimization result. Thus, we are not able to say that the method is an ecient algorithm since it had mid-range optimization time in the end. Furthermore, algorithm tting using the SA method is the most ecient, since it can reach an optimum solution with less optimization time. Finally, the TCP;D50 likelihood model was able to achieve a better tting quality result than the TCP; likelihood model.