Fast, Scalable Approximations to Posterior Distributions in Extended Latent Gaussian Models

We define a novel class of additive models, called Extended Latent Gaussian Models, that allow for a wide range of response distributions and flexible relationships between the additive predictor and mean response. The new class covers a broad range of interesting models including multi-resolution spatial processes, partial likelihood-based survival models, and multivariate measurement error models. Because computation of the exact posterior distribution is infeasible, we develop a fast, scalable approximate Bayesian inference methodology for this class based on nested Gaussian, Laplace, and adaptive quadrature approximations. We prove that the error in these approximate posteriors is op(1) under standard conditions, and provide numerical evidence suggesting that our method runs faster and scales to larger datasets than methods based on Integrated Nested Laplace Approximations and Markov Chain Monte Carlo, with comparable accuracy. We apply the new method to the mapping of malaria incidence rates in continuous space using aggregated data, mapping leukaemia survival hazards using a Cox Proportional-Hazards model with a continuously-varying spatial process, and estimating the mass of the Milky Way Galaxy using noisy multivariate measurements of the positions and velocities of star clusters in its orbit

Characterizing Dynamic Interactions between Ultradian Glucocorticoid Rhythmicity and Acute Stress Using the Phase Response Curve

The hypothalamic-pituitary-adrenal (HPA) axis is a dynamic oscillatory hormone signalling system that regulates the pulsatile secretion of glucocorticoids from the adrenal glands. In addition to regulation of basal levels of glucocorticoids, the HPA axis provides a rapid hormonal response to stress that is vitally important for homeostasis. Recently it has become clear that glucocorticoid pulses encode an important biological signal that regulates receptor signalling both in the central nervous system and in peripheral tissues. It is therefore important to understand how stressful stimuli disrupt the pulsatile dynamics of this system. Using a computational model that incorporates the crucial feed-forward and feedback components of the axis, we provide novel insight into experimental observations that the size of the stress-induced hormonal response is critically dependent on the timing of the stress. Further, we employ the theory of Phase Response Curves to show that an acute stressor acts as a phase-resetting mechanism for the ultradian rhythm of glucocorticoid secretion. Using our model, we demonstrate that the magnitude of an acute stress is a critical factor in determining whether the system resets via a Type 1 or Type 0 mechanism. By fitting our model to our in vivo stress-response data, we show that the glucocorticoid response to an acute noise stress in rats is governed by a Type 0 phase-resetting curve. Our results provide additional evidence for the concept of a deterministic sub-hypothalamic oscillator regulating the ultradian glucocorticoid rhythm, which constitutes a highly responsive peripheral hormone system that interacts dynamically with hypothalamic inputs to regulate the overall hormonal response to stress

Dynamic responses of the adrenal steroidogenic regulatory network

This is the final version of the article. Available from National Academy of Sciences via the DOI in this record.The hypothalamic-pituitary-adrenal axis is a dynamic system regulating glucocorticoid hormone synthesis in the adrenal glands. Many key factors within the adrenal steroidogenic pathway have been identified and studied, but little is known about how these factors function collectively as a dynamic network of interacting components. To investigate this, we developed a mathematical model of the adrenal steroidogenic regulatory network that accounts for key regulatory processes occurring at different timescales. We used our model to predict the time evolution of steroidogenesis in response to physiological adrenocorticotropic hormone (ACTH) perturbations, ranging from basal pulses to larger stress-like stimulations (e.g., inflammatory stress). Testing these predictions experimentally in the rat, our results show that the steroidogenic regulatory network architecture is sufficient to respond to both small and large ACTH perturbations, but coupling this regulatory network with the immune pathway is necessary to explain the dissociated dynamics between ACTH and glucocorticoids observed under conditions of inflammatory stress.This work was funded by the Medical Research Council (MRC) Grant MR/J008893/1 (to F.S., E.Z., J.J.W., Z.Z., J.R.T., and S.L.L.) and Fellowship MR/N008936/1 (to J.J.W.); the Wellcome Trust Grant WT105618MA (to J.J.W. and J.R.T.); and the Engineering and Physical Sciences Research Council (EPSRC) Grant EP/N014391/1 (to J.J.W., J.R.T., and S.L.L.)

Modelling the dynamic interaction of systemic inflammation and the hypothalamic-pituitary-adrenal (HPA) axis during and after cardiac surgery

Major surgery and critical illness produce a potentially life-threatening systemic inflammatory response. The hypothalamic–pituitary–adrenal (HPA) axis is one of the key physiological systems that counterbalances this systemic inflammation through changes in adrenocorticotrophic hormone (ACTH) and cortisol. These hormones normally exhibit highly correlated ultradian pulsatility with an amplitude modulated by circadian processes. However, these dynamics are disrupted by major surgery and critical illness. In this work, we characterize the inflammatory, ACTH and cortisol responses of patients undergoing cardiac surgery and show that the HPA axis response can be classified into one of three phenotypes: single-pulse, two-pulse and multiple-pulse dynamics. We develop a mathematical model of cortisol secretion and metabolism that predicts the physiological mechanisms responsible for these different phenotypes. We show that the effects of inflammatory mediators are important only in the single-pulse pattern in which normal pulsatility is lost—suggesting that this phenotype could be indicative of the greatest inflammatory response. Investigating whether and how these phenotypes are correlated with clinical outcomes will be critical to patient prognosis and designing interventions to improve recovery