Murad Banaji

Relationship between activation of the sympathetic nervous system and renal blood flow autoregulation in cirrhosis

BACKGROUND & AIMS It has been proposed that activation of the sympathetic nervous system causes a rightward shift in the renal autoregulatory curve such that renal blood flow is critically dependent on renal perfusion pressure and that this contributes to the development of the hepatorenal syndrome. The aims of the study were to determine the relationship of renal blood flow and renal perfusion pressure in patients with liver cirrhosis and the effect on renal hemodynamics following insertion of a transjugular intrahepatic portosystemic shunt (TIPS). METHODS Fifty-six patients were recruited into groups (1) with no ascites, (2) with diuretic-responsive ascites, (3) with intractable ascites, (4) with type II hepatorenal syndrome, and (5) requiring a TIPSs for refractory ascites. We measured cardiac hemodynamics, renal blood flow, renal perfusion pressure, and portal pressure and norepinephrine levels and mathematically modeled the renal autoregulatory curve. RESULTS Renal blood flow correlated with renal perfusion pressure (r(2) = 0.78; P < .001) and inversely with the hepatic venous pressure gradient (r(2) = 0.61; P < .0001) and plasma norepinephrine levels (r(2) = 0.78; P < .0001). Norepinephrine levels increased with increasing disease severity, and this was associated with a rightward and downward shift of the renal blood flow/renal perfusion pressure autoregulatory curve. TIPS insertion reduced portal pressure and plasma norepinephrine levels (P < .001), and the renal blood flow/renal perfusion pressure curve was shifted upward. CONCLUSIONS The relationship between renal blood flow and renal perfusion pressure involves a critical interplay between the sympathetic nervous system and the kidney. TIPS insertion decreases sympathetic activation and improves renal function through positive effects on renal blood flow autoregulation.

A model of brain circulation and metabolism: NIRS signal changes during physiological challenges.

We construct a model of brain circulation and energy metabolism. The model is designed to explain experimental data and predict the response of the circulation and metabolism to a variety of stimuli, in particular, changes in arterial blood pressure, CO2 levels, O2 levels, and functional activation. Significant model outputs are predictions about blood flow, metabolic rate, and quantities measurable noninvasively using near-infrared spectroscopy (NIRS), including cerebral blood volume and oxygenation and the redox state of the CuA centre in cytochrome c oxidase. These quantities are now frequently measured in clinical settings; however the relationship between the measurements and the underlying physiological events is in general complex. We anticipate that the model will play an important role in helping to understand the NIRS signals, in particular, the cytochrome signal, which has been hard to interpret. A range of model simulations are presented, and model outputs are compared to published data obtained from both in vivo and in vitro settings. The comparisons are encouraging, showing that the model is able to reproduce observed behaviour in response to various stimuli.

P Matrix Properties, Injectivity, and Stability in Chemical Reaction Systems

In this paper we examine matrices which arise naturally as Jacobians in chemical dynamics. We are particularly interested in when these Jacobians are P matrices (up to a sign change), ensuring certain bounds on their eigenvalues, precluding certain behavior such as multiple equilibria, and sometimes implying stability. We first explore reaction systems and derive results which provide a deep connection between system structure and the P matrix property. We then examine a class of systems consisting of reactions coupled to an external rate-dependent negative feedback process and characterize conditions which ensure that the P matrix property survives the negative feedback. The techniques presented are applied to examples published in the mathematical and biological literature.

Monotonicity in chemical reaction systems

This article discusses the question of when the dynamical systems arising from chemical reaction networks are monotone, preserving an order induced by some proper cone. The reaction systems studied are defined by the reaction network structure while the kinetics is only constrained very weakly. Necessary and sufficient conditions on cones preserved by these systems are presented. Linear coordinate changes which make a given reaction system cooperative are characterized. Also discussed is when a reaction system restricted to an invariant subspace is cone preserving, even when the system fails to be cone preserving on the whole of phase space. Many of the proofs allow explicit construction of preserved cones. Numerous examples of chemical reaction systems are presented to illustrate the results.

Graphical methods for analysing feedback in biological networks-A survey

Observed phenotypes usually arise from complex networks of interacting cell components. Qualitative information about the structure of these networks is often available, while quantitative information may be partial or absent. It is natural then to ask what, if anything, we can learn about the behaviour of the system solely from its qualitative structure. In this article we review some techniques which can be applied to answer this question, focussing in particular on approaches involving graphical representations of model structure. By applying these techniques to various cellular network examples, we discuss their strengths and limitations, and point to future research directions.

Local and global stability of equilibria for a class of chemical reaction networks

A class of chemical reaction networks is described with the property that each positive equilibrium is locally asymptotically stable relative to its stoichiometry class, an invariant subspace on which it lies. The reaction systems treated are characterized primarily by the existence of a certain factorization of their stoichiometric matrix and strong connectedness of an associated graph. Only very mild assumptions are made about the rates of reactions, and, in particular, mass action kinetics are not assumed. In many cases, local asymptotic stability can be extended to global asymptotic stability of each positive equilibrium relative to its stoichiometry class. The results are proved via the construction of Lyapunov functions whose existence follows from the fact that the reaction networks define monotone dynamical systems with increasing integrals.

Computational modelling of the piglet brain to simulate near-infrared spectroscopy and magnetic resonance spectroscopy data collected during oxygen deprivation

We describe a computational model to simulate measurements from near-infrared spectroscopy (NIRS) and magnetic resonance spectroscopy (MRS) in the piglet brain. Piglets are often subjected to anoxic, hypoxic and ischaemic insults, as experimental models for human neonates. The model aims to help interpret measurements and increase understanding of physiological processes occurring during such insults. It is an extension of a previous model of circulation and mitochondrial metabolism. This was developed to predict NIRS measurements in the brains of healthy adults i.e. concentration changes of oxyhaemoglobin and deoxyhaemoglobin and redox state changes of cytochrome c oxidase (CCO). We altered and enhanced the model to apply to the anaesthetized piglet brain. It now includes metabolites measured by 31P-MRS, namely phosphocreatine, inorganic phosphate and adenosine triphosphate (ATP). It also includes simple descriptions of glycolysis, lactate dynamics and the tricarboxylic acid (TCA) cycle. The model is described, and its simulations compared with existing measurements from piglets during anoxia. The NIRS and MRS measurements are predicted well, although this requires a reduction in blood pressure autoregulation. Predictions of the cerebral metabolic rate of oxygen consumption (CMRO2) and lactate concentration, which were not measured, are given. Finally, the model is used to investigate hypotheses regarding changes in CCO redox state during anoxia.

Some Results on Injectivity and Multistationarity in Chemical Reaction Networks

The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on the nature of the network and the reaction rates. The results are primarily linear algebraic or matrix-theoretic, with some graph-theoretic results also mentioned. Several results appear in, or are close to, results in the literature. Here, we emphasize the connections between the results and, where possible, present elementary proofs which rely solely on basic linear algebra and calculus. A number of examples are provided to illustrate the variety of subtly different conclusions which can be reached via different computations. In addition, many of the computations are implemented in a web-based open source platform, allowing the reader to test examples including and beyond those analyzed in the paper.

CONVERGENCE IN STRONGLY MONOTONE SYSTEMS WITH AN INCREASING FIRST INTEGRAL

In this paper we generalise a useful result due to J. Mierczynski which states that for a strictly cooperative system on the positive orthant, with increasing first integral, all bounded orbits are convergent. Moreover there can be no more than one equilibrium on any level set, and any equilibrium attracts its entire level set. Here, more general state spaces and more general orderings are considered. Let Y be a subset of K which is a subset of R^n, where Y and K are proper cones. Given a local semiflow φ on Y which is strongly monotone with respect to K, and which preserves a K-increasing first integral, we show that every bounded orbit converges. Again, there can be no more than one equilibrium on any level set, and each equilibrium attracts its entire level set. An application from chemical dynamics is provided.

CoNtRol: an open source framework for the analysis of chemical reaction networks

UNLABELLED We introduce CoNtRol, a web-based framework for analysis of chemical reaction networks (CRNs). It is designed to be both extensible and simple to use, complementing existing CRN-related tools. CoNtRol currently implements a number of necessary and/or sufficient structural tests for multiple equilibria, stable periodic orbits, convergence to equilibria and persistence, with the potential for incorporation of further tests. AVAILABILITY AND IMPLEMENTATION Reference implementation: reaction-networks.net/control/. Source code and binaries, released under the GPLv3: reaction-networks.net/control/download/. Documentation: reaction-networks.net/wiki/CoNtRol.