Estimation of Tumor Size Evolution Using Particle Filters

Parameter estimation in high-intensity focused ultrasound therapy

Hyperthermia using High-Intensity Focused Ultrasound (HIFU) is an acoustic therapy for cancer treatment. This technique consists of an increase in the temperature field of the tumor to achieve coagulative necrosis and immediate cell death. Therefore, for having a successful treatment, the physical problem requires to know several properties due to the high variability from individual to individual, or even for the same individual under different physiological conditions. This article presents a numerical simulation of hyperthermia therapy for cancer treatment using HIFU, as well as the estimation of parameters that influence the physical problem. Two mathematical models were considered to solve the forward problem. The acoustic model based on acoustic pressure performs a frequency-domain study, and the bioheat transfer model a time-dependent study. These models were solved using Comsol Multiphysics® software in a 2D-axisymmetric rectangular domain to determine the temperature field. Parameter estimation was coded in Matlab Mathworks® environment using a Bayesian approach. The Markov Chain Monte Carlo method by the Metropolis-Hastings algorithm was implemented, and the simulated temperature measurements were considered. Results suggest that specific HIFU therapy can be performed for each patient by estimating appropriate parameters for cancer treatment and provides the possibility to define procedures before and during the treatment.

An O(log2N) Fully-Balanced Resampling Algorithm for Particle Filters on Distributed Memory Architectures

Resampling is a well-known statistical algorithm that is commonly applied in the context of Particle Filters (PFs) in order to perform state estimation for non-linear non-Gaussian dynamic models. As the models become more complex and accurate, the run-time of PF applications becomes increasingly slow. Parallel computing can help to address this. However, resampling (and, hence, PFs as well) necessarily involves a bottleneck, the redistribution step, which is notoriously challenging to parallelize if using textbook parallel computing techniques. A state-of-the-art redistribution takes O((log2N)2) computations on Distributed Memory (DM) architectures, which most supercomputers adopt, whereas redistribution can be performed in O(log2N) on Shared Memory (SM) architectures, such as GPU or mainstream CPUs. In this paper, we propose a novel parallel redistribution for DM that achieves an O(log2N) time complexity. We also present empirical results that indicate that our novel approach outperforms the O((log2N)2) approach.

State and Parameter Estimation of a Mathematical Carcinoma Model under Chemotherapeutic Treatment

One challenging aspect of therapy optimization and application of control algorithms in the field of tumor growth modeling is the limited number of measurable physiological signals—state variables—and the knowledge of model parameters. A possible solution to provide such information is the application of observer or state estimator. One of the most widely applied estimators for nonlinear problems is the extended Kalman filter (EKF). In this study, a moving horizon estimation (MHE)-based observer is developed and compared to an optimized EKF. The observers utilize a third-order tumor growth model. The performance of the observers is tested on measurements gathered from a laboratory mice trial using chemotherapeutic drug. The proposed MHE is designed to be suitable for closed-loop applications and yields simultaneous state and parameter estimation.

Simultaneous Model Selection and Model Calibration for the Proliferation of Tumor and Normal Cells During In Vitro Chemotherapy Experiments

In vitro experiments were conducted in this work to analyze the proliferation of tumor (DU-145) and normal (macrophage RAW 264.7) cells under the influence of a chemotherapeutic drug (doxorubicin). Approximate Bayesian Computation (ABC) was used to select among four competing models to represent the number of cells and to estimate the model parameters, based on the experimental data. For one case, the selected model was validated in a replicated experiment, through the solution of a state estimation problem with a particle filter algorithm, thus demonstrating the robustness of the ABC procedure used in this work.