Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

A Bayesian approach to estimating the regression coefficients of a multinomial logit model

A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^

EVALUATION OF THE EFFECTIVENESS OF ANISOTROPIC ANALYTICAL ALGORITHM IN FLATTENED AND FLATTENING-FILTER-FREE BEAMS FOR HIGH ENERGY LUNG DOSE DELIVERY USING THE RADIOLOGICAL PHYSICS CENTER LUNG PHANTOM

The effectiveness of the Anisotropic Analytical Algorithm (AAA) implemented in the Eclipse treatment planning system (TPS) was evaluated using theRadiologicalPhysicsCenteranthropomorphic lung phantom using both flattened and flattening-filter-free high energy beams. Radiation treatment plans were developed following the Radiation Therapy Oncology Group and theRadiologicalPhysicsCenterguidelines for lung treatment using Stereotactic Radiation Body Therapy. The tumor was covered such that at least 95% of Planning Target Volume (PTV) received 100% of the prescribed dose while ensuring that normal tissue constraints were followed as well. Calculated doses were exported from the Eclipse TPS and compared with the experimental data as measured using thermoluminescence detectors (TLD) and radiochromic films that were placed inside the phantom. The results demonstrate that the AAA superposition-convolution algorithm is able to calculate SBRT treatment plans with all clinically used photon beams in the range from 6 MV to 18 MV. The measured dose distribution showed a good agreement with the calculated distribution using clinically acceptable criteria of ±5% dose or 3mm distance to agreement. These results show that in a heterogeneous environment a 3D pencil beam superposition-convolution algorithms with Monte Carlo pre-calculated scatter kernels, such as AAA, are able to reliably calculate dose, accounting for increased lateral scattering due to the loss of electronic equilibrium in low density medium. The data for high energy plans (15 MV and 18 MV) showed very good tumor coverage in contrast to findings by other investigators for less sophisticated dose calculation algorithms, which demonstrated less than expected tumor doses and generally worse tumor coverage for high energy plans compared to 6MV plans. This demonstrates that the modern superposition-convolution AAA algorithm is a significant improvement over previous algorithms and is able to calculate doses accurately for SBRT treatment plans in the highly heterogeneous environment of the thorax for both lower (≤12 MV) and higher (greater than 12 MV) beam energies.