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.

Application of Signal Advance Technology to Electrophysiology

Medical instrumentation used in diagnosis and treatment relies on the accurate detection and processing of various physiological events and signals. While signal detection technology has improved greatly in recent years, there remain inherent delays in signal detection/ processing. These delays may have significant negative clinical consequences during various pathophysiological events. Reducing or eliminating such delays would increase the ability to provide successful early intervention in certain disorders thereby increasing the efficacy of treatment. In recent years, a physical phenomenon referred to as Negative Group Delay (NGD), demonstrated in simple electronic circuits, has been shown to temporally advance the detection of analog waveforms. Specifically, the output is temporally advanced relative to the input, as the time delay through the circuit is negative. The circuit output precedes the complete detection of the input signal. This process is referred to as signal advance (SA) detection. An SA circuit model incorporating NGD was designed, developed and tested. It imparts a constant temporal signal advance over a pre-specified spectral range in which the output is almost identical to the input signal (i.e., it has minimal distortion). Certain human patho-electrophysiological events are good candidates for the application of temporally-advanced waveform detection. SA technology has potential in early arrhythmia and epileptic seizure detection and intervention. Demonstrating reliable and consistent temporally advanced detection of electrophysiological waveforms may enable intervention with a pathological event (much) earlier than previously possible. SA detection could also be used to improve the performance of neural computer interfaces, neurotherapy applications, radiation therapy and imaging. In this study, the performance of a single-stage SA circuit model on a variety of constructed input signals, and human ECGs is investigated. The data obtained is used to quantify and characterize the temporal advances and circuit gain, as well as distortions in the output waveforms relative to their inputs. This project combines elements of physics, engineering, signal processing, statistics and electrophysiology. Its success has important consequences for the development of novel interventional methodologies in cardiology and neurophysiology as well as significant potential in a broader range of both biomedical and non-biomedical areas of application.

Improving the accuracy of radiation pneumonitis dose response models

The prognosis for lung cancer patients remains poor. Five year survival rates have been reported to be 15%. Studies have shown that dose escalation to the tumor can lead to better local control and subsequently better overall survival. However, dose to lung tumor is limited by normal tissue toxicity. The most prevalent thoracic toxicity is radiation pneumonitis. In order to determine a safe dose that can be delivered to the healthy lung, researchers have turned to mathematical models predicting the rate of radiation pneumonitis. However, these models rely on simple metrics based on the dose-volume histogram and are not yet accurate enough to be used for dose escalation trials. The purpose of this work was to improve the fit of predictive risk models for radiation pneumonitis and to show the dosimetric benefit of using the models to guide patient treatment planning. The study was divided into 3 specific aims. The first two specifics aims were focused on improving the fit of the predictive model. In Specific Aim 1 we incorporated information about the spatial location of the lung dose distribution into a predictive model. In Specific Aim 2 we incorporated ventilation-based functional information into a predictive pneumonitis model. In the third specific aim a proof of principle virtual simulation was performed where a model-determined limit was used to scale the prescription dose. The data showed that for our patient cohort, the fit of the model to the data was not improved by incorporating spatial information. Although we were not able to achieve a significant improvement in model fit using pre-treatment ventilation, we show some promising results indicating that ventilation imaging can provide useful information about lung function in lung cancer patients. The virtual simulation trial demonstrated that using a personalized lung dose limit derived from a predictive model will result in a different prescription than what was achieved with the clinically used plan; thus demonstrating the utility of a normal tissue toxicity model in personalizing the prescription dose.