Bayesian inference for stable differential equation models with applications in computational neuroscience

Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations. The dynamics in these models are approximately linear around a stable fixed point of the system. We exploit this property to develop fast approximate methods for posterior inference. We first illustrate our approach using simulated EEG data on the Liley et al model, a mechanistic neural population model. Then we apply our methods to experimental EEG data from rats to estimate how parameters in the Liley et al model vary with level of isoflurane anaesthesia. More generally, stable differential equation models and the corresponding inference methods are useful for analysis of stationary time-series data. Compared to the existing state-of-the art, our methods are several orders of magnitude faster, and are particularly suited to analysis of long time-series (>10,000 time-points) and models of moderate dimension (10-50 state variables and 10-50 parameters.

Doula Services Within a Healthy Start Program: Increasing Access for an Underserved Population

Purpose: Women of color in the United States, particularly in high-poverty neighborhoods, experience high rates of poor birth outcomes, including cesarean section, preterm birth, low birthweight, and infant mortality. Doula care has been linked to improvements in many perinatal outcomes, but women of color and low-income women often face barriers in accessing doula support. Description: To address this issue, the New York City Department of Health and Mental Hygiene’s Healthy Start Brooklyn introduced the By My Side Birth Support Program in 2010. The goal was to complement other maternal home-visiting programs by providing doula support during labor and birth, along with prenatal and postpartum visits. Between 2010 and 2015, 489 infants were born to women enrolled in the program. Assessment: Data indicate that By My Side is a promising model of support for Healthy Start projects nationwide. Compared to the project area, program participants had lower rates of preterm birth (6.3 vs. 12.4%, p \u3c 0.001) and low birthweight (6.5 vs. 11.1%, p = 0.001); however, rates of cesarean birth did not differ significantly (33.5 vs. 36.9%, p = 0.122). Further research is needed to explore possible reasons for this finding, and to examine the influence of doula support on birth outcomes among populations with high rates of chronic disease and stressors such as poverty, racism, and exposure to violence. However, feedback from participants indicates that doula support is highly valued and helps give women a voice in consequential childbirth decisions. Conclusion: Available evidence suggests that doula services may be an important component of an effort to address birth inequities

Automatic simplification of differential equation models by a posteriori analysis

Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly large-scale and multiphysics, as increasing amounts of data are available on the properties and behaviour of biological systems. Often an observed behaviour of interest in a model may be written as a linear functional. A key question therefore is to determine which terms in the model have the greatest effect on functionals of interest.An approach for answering this question has recently been developed, called model reduction using a posteriori analysis. The method was initially developed for systems of nonlinear initial value ordinary differential equations, and automatically identifies regions of the computational domain and components of the model solution where an accurate mathematical representation of the model is required to accurately calculate a linear functional of interest. Initial-value ordinary differential equations can be written as a first-order derivative term plus an algebraic 'reaction' term. In previous work on model reduction using a posteriori analysis the algebraic 'reaction' term is removed from the equations in the reduced model.The first contribution of this thesis is to extend the method so that the first-order derivative term is removed from the differential equation instead of the algebraic 'reaction' term, resulting in a quasi-steady state approximation in automatically identified regions of the domain and components of the solution. The second contribution of this thesis is to extend the method to boundary value problems and partial differential equations. We consider differential equations with algebraic terms, first order terms and second order terms, any combination of which may be nonlinear. The method is used to automatically simplify several differential equation models including models of chemotaxis and tissue-level cardiac electrophysiology.</p

Automatic simplification of differential equation models by a posteriori analysis

Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly large-scale and multiphysics, as increasing amounts of data are available on the properties and behaviour of biological systems. Often an observed behaviour of interest in a model may be written as a linear functional. A key question therefore is to determine which terms in the model have the greatest effect on functionals of interest.An approach for answering this question has recently been developed, called model reduction using a posteriori analysis. The method was initially developed for systems of nonlinear initial value ordinary differential equations, and automatically identifies regions of the computational domain and components of the model solution where an accurate mathematical representation of the model is required to accurately calculate a linear functional of interest. Initial-value ordinary differential equations can be written as a first-order derivative term plus an algebraic 'reaction' term. In previous work on model reduction using a posteriori analysis the algebraic 'reaction' term is removed from the equations in the reduced model.The first contribution of this thesis is to extend the method so that the first-order derivative term is removed from the differential equation instead of the algebraic 'reaction' term, resulting in a quasi-steady state approximation in automatically identified regions of the domain and components of the solution. The second contribution of this thesis is to extend the method to boundary value problems and partial differential equations. We consider differential equations with algebraic terms, first order terms and second order terms, any combination of which may be nonlinear. The method is used to automatically simplify several differential equation models including models of chemotaxis and tissue-level cardiac electrophysiology.This thesis is not currently available via ORA

A local sensitivity analysis method for developing biological models with identifiable parameters: Application to cardiac ionic channel modelling

Computational cardiac models provide important insights into the underlying mechanisms of heart function. Parameter estimation in these models is an ongoing challenge with many existing models being overparameterised. Sensitivity analysis presents a key tool for exploring the parameter identifiability. While existing methods provide insights into the significance of the parameters, they are unable to identify redundant parameters in an efficient manner. We present a new singular value decomposition based algorithm for determining parameter identifiability in cardiac models. Using this local sensitivity approach, we investigate the Ten Tusscher 2004 rapid inward rectifier potassium and the Mahajan 2008 rabbit L-type calcium currents in ventricular myocyte models. We identify non-significant and redundant parameters and improve the models by reducing them to minimum ones that are validated to have only identifiable parameters. The newly proposed approach provides a new method for model validation and evaluation of the predictive power of cardiac models. © 2012 Elsevier B.V. All rights reserved