A composite computational model of liver glucose homeostasis. II. Exploring system behaviour

Computational Modeling of Fructose Metabolism and Development in NAFLD

Non-alcohol fatty liver disease (NAFLD) is a common disorder that has increased in prevalence 20-fold over the last three decades. It covers a spectrum of conditions resulting from excess lipid accumulation in the liver without alcohol abuse. Among all the risk factors, over-consumption of fructose has been repeatedly reported in both clinical and experimental studies to be highly associated with the development of NAFLD. However, studying in vivo systems is complicated, time consuming and expensive. A detailed kinetic model of fructose metabolism was constructed to investigate the metabolic mechanisms whereby fructose consumption can induce dyslipidaemia associated with NAFLD and to explore whether the pathological conditions can be reversed during the early stages of disease. The model contains biochemical components and reactions identified from the literature, including ~120 parameters, 25 variables, and 25 first order differential equations. Three scenarios were presented to demonstrate the behavior of the model. Scenario one predicts the acute effects of a change in carbohydrate input in lipid profiles. The results present progressive triglyceride accumulations in the liver and plasma for three diets. The rate of accumulation was greater in the fructose diet than that of the mixed or glucose only models. Scenario two explores the variability of metabolic reaction rate within the general population. Sensitivity analysis reveals that hepatic triglyceride concentration is most sensitive to the rate constant of pyruvate kinase and fructokinase. Scenario three tests the effect of one specific inhibitor that might be potentially administered. The simulations of fructokinase suppression provide a good model for potentially reversing simple steatosis induced by high fructose consumption, which can be corroborated by experimental studies. The predictions in these three scenarios suggest that the model is robust and it has sufficient detail to present the kinetic relationship between fructose and lipid in the liver.

Mathematical modeling of the glucagon challenge test

A model for the homeostasis of glucose through the regulating hormones glucagon and insulin is described. It contains a subsystem that models the internalization of the glucagon receptor. Internalization is a mechanism in cell signaling, through which G-protein coupled receptors are taken from the surface of the cell to the endosome. The model is used to interpret data from a glucagon challenge test in which subjects have been under treatment with a novel glucagon receptor anti-sense drug which is aimed at reducing the number of receptors in the liver. It is shown how the receptor internalization results in tolerance of the blood glucose concentration to glucagon-induced hyperglycemia. We quantify the reduction of the number of receptors using the model and the data before and after treatment.

Model-based virtual patient analysis of human liver regeneration predicts critical perioperative factors controlling the dynamic mode of response to resection

BACKGROUND

Liver has the unique ability to regenerate following injury, with a wide range of variability of the regenerative response across individuals. Existing computational models of the liver regeneration are largely tuned based on rodent data and hence it is not clear how well these models capture the dynamics of human liver regeneration. Recent availability of human liver volumetry time series data has enabled new opportunities to tune the computational models for human-relevant time scales, and to predict factors that can significantly alter the dynamics of liver regeneration following a resection.

METHODS

We utilized a mathematical model that integrates signaling mechanisms and cellular functional state transitions. We tuned the model parameters to match the time scale of human liver regeneration using an elastic net based regularization approach for identifying optimal parameter values. We initially examined the effect of each parameter individually on the response mode (normal, suppressed, failure) and extent of recovery to identify critical parameters. We employed phase plane analysis to compute the threshold of resection. We mapped the distribution of the response modes and threshold of resection in a virtual patient cohort generated in silico via simultaneous variations in two most critical parameters.

RESULTS

Analysis of the responses to resection with individual parameter variations showed that the response mode and extent of recovery following resection were most sensitive to variations in two perioperative factors, metabolic load and cell death post partial hepatectomy. Phase plane analysis identified two steady states corresponding to recovery and failure, with a threshold of resection separating the two basins of attraction. The size of the basin of attraction for the recovery mode varied as a function of metabolic load and cell death sensitivity, leading to a change in the multiplicity of the system in response to changes in these two parameters.

CONCLUSIONS

Our results suggest that the response mode and threshold of failure are critically dependent on the metabolic load and cell death sensitivity parameters that are likely to be patient-specific. Interventions that modulate these critical perioperative factors may be helpful to drive the liver regenerative response process towards a complete recovery mode.

Computational Modeling in Liver Surgery

The need for extended liver resection is increasing due to the growing incidence of liver tumors in aging societies. Individualized surgical planning is the key for identifying the optimal resection strategy and to minimize the risk of postoperative liver failure and tumor recurrence. Current computational tools provide virtual planning of liver resection by taking into account the spatial relationship between the tumor and the hepatic vascular trees, as well as the size of the future liver remnant. However, size and function of the liver are not necessarily equivalent. Hence, determining the future liver volume might misestimate the future liver function, especially in cases of hepatic comorbidities such as hepatic steatosis. A systems medicine approach could be applied, including biological, medical, and surgical aspects, by integrating all available anatomical and functional information of the individual patient. Such an approach holds promise for better prediction of postoperative liver function and hence improved risk assessment. This review provides an overview of mathematical models related to the liver and its function and explores their potential relevance for computational liver surgery. We first summarize key facts of hepatic anatomy, physiology, and pathology relevant for hepatic surgery, followed by a description of the computational tools currently used in liver surgical planning. Then we present selected state-of-the-art computational liver models potentially useful to support liver surgery. Finally, we discuss the main challenges that will need to be addressed when developing advanced computational planning tools in the context of liver surgery.

A Computational Model of Hepatic Energy Metabolism: Understanding Zonated Damage and Steatosis in NAFLD

In non-alcoholic fatty liver disease (NAFLD), lipid build-up and the resulting damage is known to occur more severely in pericentral cells. Due to the complexity of studying individual regions of the sinusoid, the causes of this zone specificity and its implications on treatment are largely ignored. In this study, a computational model of liver glucose and lipid metabolism is presented which treats the sinusoid as the repeating unit of the liver rather than the single hepatocyte. This allows for inclusion of zonated enzyme expression by splitting the sinusoid into periportal to pericentral compartments. By simulating insulin resistance (IR) and high intake diets leading to the development of steatosis in the model, we identify key differences between periportal and pericentral cells accounting for higher susceptibility to pericentral steatosis. Secondly, variation between individuals is seen in both susceptibility to steatosis and in its development across the sinusoid. Around 25% of obese individuals do not show excess liver fat, whilst 16% of lean individuals develop NAFLD. Furthermore, whilst pericentral cells tend to show higher lipid levels, variation is seen in the predominant location of steatosis from pericentral to pan-sinusoidal or azonal. Sensitivity analysis was used to identify the processes which have the largest effect on both total hepatic triglyceride levels and on the sinusoidal location of steatosis. As is seen in vivo, steatosis occurs when simulating IR in the model, predominantly due to increased uptake, along with an increase in de novo lipogenesis. Additionally, concentrations of glucose intermediates including glycerol-3-phosphate increased when simulating IR due to inhibited glycogen synthesis. Several differences between zones contributed to a higher susceptibility to steatosis in pericentral cells in the model simulations. Firstly, the periportal zonation of both glycogen synthase and the oxidative phosphorylation enzymes meant that the build-up of glucose intermediates was less severe in the periportal hepatocyte compartments. Secondly, the periportal zonation of the enzymes mediating β-oxidation and oxidative phosphorylation resulted in excess fats being metabolised more rapidly in the periportal hepatocyte compartments. Finally, the pericentral expression of de novo lipogenesis contributed to pericentral steatosis when additionally simulating the increase in sterol-regulatory element binding protein 1c (SREBP-1c) seen in NAFLD patients in vivo. The hepatic triglyceride concentration was predicted to be most sensitive to inter-individual variation in the activity of enzymes which, either directly or indirectly, determine the rate of free fatty acid (FFA) oxidation. The concentration was most strongly dependent on the rate constants for β-oxidation and oxidative phosphorylation. It also showed moderate sensitivity to the rate constants for processes which alter the allosteric inhibition of β-oxidation by acetyl-CoA. The predominant sinusoidal location of steatosis meanwhile was most sensitive variations in the zonation of proteins mediating FFA uptake or triglyceride release as very low density lipoproteins (VLDL). Neither the total hepatic concentration nor the location of steatosis showed strong sensitivity to variations in the lipogenic rate constants.

Sensitivity Analysis of an ENteric Immunity SImulator (ENISI)-Based Model of Immune Responses to Helicobacter pylori Infection

Agent-based models (ABM) are widely used to study immune systems, providing a procedural and interactive view of the underlying system. The interaction of components and the behavior of individual objects is described procedurally as a function of the internal states and the local interactions, which are often stochastic in nature. Such models typically have complex structures and consist of a large number of modeling parameters. Determining the key modeling parameters which govern the outcomes of the system is very challenging. Sensitivity analysis plays a vital role in quantifying the impact of modeling parameters in massively interacting systems, including large complex ABM. The high computational cost of executing simulations impedes running experiments with exhaustive parameter settings. Existing techniques of analyzing such a complex system typically focus on local sensitivity analysis, i.e. one parameter at a time, or a close “neighborhood” of particular parameter settings. However, such methods are not adequate to measure the uncertainty and sensitivity of parameters accurately because they overlook the global impacts of parameters on the system. In this article, we develop novel experimental design and analysis techniques to perform both global and local sensitivity analysis of large-scale ABMs. The proposed method can efficiently identify the most significant parameters and quantify their contributions to outcomes of the system. We demonstrate the proposed methodology for ENteric Immune SImulator (ENISI), a large-scale ABM environment, using a computational model of immune responses to Helicobacter pylori colonization of the gastric mucosa.

A composite computational model of liver glucose homeostasis. I. Building the composite model

A computational model of the glucagon/insulin-driven liver glucohomeostasis function, focusing on the buffering of glucose into glycogen, has been developed. The model exemplifies an 'engineering' approach to modelling in systems biology, and was produced by linking together seven component models of separate aspects of the physiology. The component models use a variety of modelling paradigms and degrees of simplification. Model parameters were determined by an iterative hybrid of fitting to high-scale physiological data, and determination from small-scale in vitro experiments or molecular biological techniques. The component models were not originally designed for inclusion within such a composite model, but were integrated, with modification, using our published modelling software and computational frameworks. This approach facilitates the development of large and complex composite models, although, inevitably, some compromises must be made when composing the individual models. Composite models of this form have not previously been demonstrated.