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.

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

The development of poultry farms risk assessment tool for avian influenza in Imo State, Nigeria

Background: Nigeria was one of the 13 countries where avian influenza outbreak in poultry farms was reported during the 2006 avian influenza pandemic threat and was also the first country in Africa to report the presence of H5N1influenza among its poultry population. There are multiple hypotheses on how the avian influenza outbreak of 2006 was introduced to Nigeria, but the consensus is that once introduced, poultry farms and their workers were responsible for 70% of the spread of avian influenza virus to other poultry farms and the population. ^ The spread of avian influenza has been attributed to lack of compliance by poultry farms and their workers with poultry farm biosecurity measures. When poultry farms fail to adhere to biosecurity measures and there is an outbreak of infectious diseases like in 2006, epidemiological investigations usually assess poultry farm biosecurity—often with the aid of a questionnaire. Despite the importance of questionnaires in determining farm compliance with biosecurity measures, there have been few efforts to determine the validity of questionnaires designed to assess poultry farms risk factors. Hence, this study developed and validated a tool (questionnaire) that can be used for poultry farm risk stratification in Imo State, Nigeria. ^ Methods: Risk domains were generated using literature and recommendations from agricultural organizations and the Nigeria government for poultry farms. The risk domains were then used to develop a questionnaire. Both the risk domain and questionnaire were verified and modified by a group of five experts with a research interest in Nigeria's poultry industry and/or avian influenza prevention. Once a consensus was reached by the experts, the questionnaire was distributed to 30 selected poultry farms in Imo State, Nigeria that participated in this study. Survey responses were received for all the 30 poultry farms that were selected. The same poultry farms were visited one week after they completed the questionnaires for on-site observation. Agreement among survey and observation results were analyzed using a kappa test and rated as poor, fair, moderate, substantial, or nearly perfect; and internal consistency of the survey was also computed. ^ Result: Out of the 43 items on the questionnaire, 32 items were validated by this study. The agreement between the survey result and onsite observation was analyzed using kappa test and ranged from poor to nearly perfect. Most poultry farms had their best agreements in the contact section of the survey. The least agreement was noted in the farm management section of the survey. Thirty-two questions on the survey had a coefficient alpha > 0.70, which is a robust internal consistency for the survey. ^ Conclusion: This study developed 14 risk domains for poultry farms in Nigeria and validated 32 items from the original questionnaire that contained 43 items. The validated items can be used to determine the risk of introduction and spread of avian influenza virus in poultry farms in Imo State, Nigeria. After further validations in other states, regions and poultry farm sectors in Nigeria; this risk assessment tool can then be used to determine the risk profile of poultry farms across Nigeria.^

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

Charity care and community benefits by hospital type in Texas

Hospital care is the largest component of the health care sector. This industry is made up of for profit hospital (FPH) organizations, not for profit (NFP) hospitals, and government (GOV) run hospital facilities. Objectives of this analysis were: (a) to conduct a literature review on NFP hospital legislation at the state level in Texas and at the federal level in the broader U.S.; and (b) to describe the types of charity care and community benefits currently being provided: by NFP hospitals compared to FPH hospitals and GOV hospitals; by hospitals geographic proximity to the Texas-Mexico border; and by hospital community type (rural, suburban, and urban); and (c) propose specific policy changes that may be needed to improve the current Texas State statute. Methods. In describing the historical and current policy context of NFP hospital legislation in the United States, federal legislation was reviewed from 1913 to the present and Texas State legislation was reviewed from 1980 to the present. In describing the provision of charity care, data from the 2008 Annual Cooperative Hospital Survey were examined by hospital organizational type, size, proximity to the border, and community type using linear regression and chi-squared tests to assess differences in charity care and community benefits. Results. The data included 123 NFP hospitals, 114 GOV hospitals, and 123 FPH. Results. Small sized (p<0.001) and medium sized (p<0.001) NFP hospitals provide a greater percent of total charity care when compared to FPH hospitals and to both GOV and FPH hospitals respectively; however, no significant difference in total charity care was found among large sized NFP hospitals when compared to FPH hospitals alone (p=.345) and both GOV and FPH facilities (p=.214). The amount of charity care provided was not found to be different based on proximity to the border or community type. Community benefit planning and budgeting was found to be similar regardless of community type and proximity to the border. Conclusion. No differences in charity care in Texas were found for large sized NFP hospitals compared to FPH and GOV hospitals. Contrary to widely held beliefs, this study did not find the border region to provide a greater amount of charity care or bad debt. Charity care also did not vary by community type. These findings underscore the need for continued collection of transparent data from all hospitals in order to provide policy makers and consumers with information on utilization trends to ensure benefits are being provided to the community. Policy changes or revoking tax-benefits may occur as charity care utilization declines with the implementation of health reform in the next few years.^