Tumor Growth Modeling: State Estimation with Maximum Likelihood and Particle Filtering

Abstract

In this study, we combined the Maximum Likelihood Estimator from our previous works with a Sequential Importance Resampling (SIR) particle filter to estimate the states of the stochastic Gompertz tumor growth model. We also implemented a parallel version in CUDA for the SIR filter in order to reduce its execution time. Extensive simulations with synthetic data were run to examine whether the SIR filter can provide more accurate state estimates in respect to the Normalized Mean Squared Deviation criterion compared to those provided by the deterministic Gompertz model. Moreover, we monitored and compared the execution time of the SIR's parallel and sequential implementations for different numbers of particles. The results showed that the SIR filter can estimate the system's states very accurately, even at the early tumor growth stages. Additionally, the parallel implementation that ran on the GPU was way more efficient than the implementation that ran on the CPU. By combining the Maximum Likelihood Estimator (MLE) with an SIR filter, we were able to obtain very accurate estimates of the tumors' volume. Furthermore, the execution time for the SIR filter was significantly decreased by taking advantage of the GPUs ability to perform a very large number of computations in parallel.