Quantification of Biomedical Data with Stochastic Parametric Models and Numerical Optimization

Abstract

Accurate and robust quantification of measurement data is a key factor in biomedical research. However, the quantification is complicated by random noise, limited resolution and indirect nature of measurements.

In this study we quantified biomedical data by modeling the target, the acquisition process and the noise contamination. By combining these three components we built the model for the acquired data. The indirect acquisition was modeled as a forward projection from the target to the data. The random noise was handled by using stochastic model and treating the data as a single realization from the model. The data model was determined through adjustable parameters and the most likely parameters in terms of the acquired noisy data were searched for.

The search for best parameters in our stochastic parametric models led to mathematically inconvenient and challenging optimization problems. The most common challenges in our applications were multiple local optima, very large number of parameters, unknown gradient function and lack of reliable initialization. In order to solve these issues, we developed customized numerical optimization techniques by modifying standard algorithms and combining different types of optimization. The optimization techniques were implemented to distributed computing environment which enabled us to solve problems with very large number of parameters and amount of data.

By modeling static fluorescence microscopy images we achieved results which we could not obtain with the conventional methods and which in part helped to reveal significant differences between treatment groups. By modeling dynamic fluorescence microscopy data we managed to compensate cell movement and inhomogeneous fluorescence distribution well during the quantification. The results with simulated data imply that our method is very robust and accurate. With positron emission tomography (PET) data we were able to solve the huge parameter optimization problem which allowed us to quantify regional parameter heterogeneity with a novel approach. Overall, we believe that the stochastic parametric modeling is a very accurate and robust method to quantify biomedical data.