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WIREs Syst Biol Med
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The virtual liver: a multidisciplinary, multilevel challenge for systems biology

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Abstract The liver is the central metabolic organ in human physiology, with functions that are fundamentally important to the detoxification of xenobiotics (drugs), the maintenance of homeostasis of numerous blood metabolites, and the production of mediators of the acute phase response. Liver toxicity, whether actual or implied is the reason for the failure of a significant proportion of many promising novel medicines that consequently never reach the market, and diseases such as atherosclerosis, diabetes, and fatty liver diseases, that are a major burden on current health resources, are directly linked to functional and structural disorders of the liver. This article presents the concepts and approaches underpinning one of the most exciting and ambitious modeling projects in the field of systems biology and systems medicine. This major multidisciplinary research program is aimed at developing a whole‐organ model of the human liver, representing its central physiological functions under normal and pathological conditions The model will be composed of a larger battery of interconnected submodels representing liver anatomy and physiology, integrating processes across hierarchical levels in space, time, and structural organization. In this article, we outline the general architecture of the liver model and present first step taken to reach this ambitious goal. WIREs Syst Biol Med 2012 doi: 10.1002/wsbm.1158 This article is categorized under: Models of Systems Properties and Processes > Cellular Models Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Translational, Genomic, and Systems Medicine > Translational Medicine

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Modular composition of the whole‐organ model. The brownish marked part of the scheme refers to the modules operating on the level of a single liver unit. The output of the organ module is the integral output of the liver units. The module ‘body’ is not an integral part of the organ model. It is, however, indispensable in applications of the organ model aimed at predicting changes of the chemical composition of systemic blood. Without the module ‘body’, the chemical composition of systemic blood is an external input. Owing to the non‐hierarchical connections between modules (for reasoning see main text), there are three cyclic dependencies (indicated by 1, 2, and 3 at the connecting arrows .

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Module ‘cell’ [example: glucose metabolism in hepatocytes (HC)]. Reaction scheme of a kinetic model describing the metabolism of glucose in human HCs. The network comprises the synthesis and degradation of glycogen, glycolysis, and gluconeoegenesis. External compounds connecting this cellular module with the module ‘SU’ (Figure 5) are the metabolites glucose and lactate and the hormones insulin, glucagons, and epinephrine. Hormonal control is described by a transfer function (γ) relating the hormone level to the degree of phosphorylation of regulatory enzymes (marked in green) with insulin decreasing γ, and epinephrine and glucagon increasing γ. The rate equation for the phosphorylated and non‐phosphorylated form of interconvertible enzymes differs. Enzymes regulated by allosteric mechanisms are marked with red A. The time evolution of metabolite concentrations [xi] (I = 1,…,N) is governed by first‐order differential equations of the form: \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}\begin{equation*} \frac{\mathrm{d} [{x_{i}}]}{\mathrm{d}t}=\sum_j{v_{ij} ({[{x_{1}}],\ldots,[{x_{N}}]})} \end{equation*} \end{document} where vij denotes the rate with which the concentration of metabolite, xi is affected by chemical reactions and membrane transport processes. The index i lumps together the chemical identity of the metabolite and its compartmentalization (cytosol, mitochondrion, and extracellular space).

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Module ‘sinusoidal unit (SU)’. The space along the sinusoid is subdivided into (n) spatial compartments each compartment receiving blood from the preceding compartment and delivering it to the following one. Within a single compartment, blood compounds can be either taken up or released by the various liver cells: HCs, HEC, HKC, and HSC (ito). HCs of each compartment secrete bile components (cholesterol, bile acids, phospholipids, bilirubin, detoxified drugs).The chemical composition of the sinusoidal blood in compartment (i) at time (t) is described by the blood state function CBLi(t) comprising three different types of compounds (indicated by different colors): metabolites of the intermediary metabolism, signaling molecules (hormones and cytokines), and waste products. This module represents the exchange of compounds along the sinusoids between successive branching points of the sinusoidal network in the lobule model (Figure 4).

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Center‐based models represent cells as intrinsic spherical objects with forces between their centers. Cell movement is mimicked by an equation of motion for all cells summarizing all forces on that cell and taking into account the active cell motion such as the cell micromotility. This includes friction forces of cells with the extracellular matrix, with the sinusoids and with parenchyma cells. The pair‐wise forces between two cells are calculated using the Johnson–Kendall–Roberts (JKR) model (upper left) motivated by micropipette experiments with S180 cells showing that the JKR‐model gives a good description of cells on short time scales. The JKR‐model approximates cells as isotropic homogeneous elastic sticky spheres.56 The y‐axis in the upper left picture is the interaction force Fij, (in nN), the x‐axis the scaled cell–cell center distance dij/l. l is the cell diameter at the beginning of the G1‐phase. Positive forces represent repulsion, negative forces adhesion. Cell–cell interaction displays a hysteresis: cells detach at a larger distance ( l) than the distance at which they had come into contact (dij = l). The JKR‐model permits to take into account the effect of cell stiffness (via the Young module), compressibility (via the Poisson ratio) and adhesion strength. Sinusoids are modeled by a chain of spheres linked by linear springs, anchored in the peri‐portal and central veins and characterized mainly by their Young modulus. A parenchyma cell (hepatocyte) in such a model grows in G1, S, and G2 phase of the cell cycle and deforms in M‐phase into a dumbbell until it divides (bottom left). The cell cycle is currently parameterized by the cell cycle duration, as well as the entrance probability or rate into the cell cycle. Right picture: A liver lobule in the model reconstructed from confocal laser scanning micrographs of mouse liver lobules. The dark red lines show peri‐portal veins (in three corners of the lobule), central vein (in the center of the lobule) and sinusoids linking peri‐portal field and central vein. Besides the peri‐portal vein, the artery (blue) and bilary ducts (green) are shown. Metabolic zonation is indicated by the expression level (high‐dark; low‐light) of the enzyme glutamine synthetase. With this model, a subsequently validated order mechanism during regeneration after CCl4‐induced damage in mouse liver could be predicted.48 Currently, we are able to model about 100 lobules with the same model approach. However, HSCs and HKCs will need to be integrated. On the level of the lobule architecture, the characteristic time scale is given by a typical cell cycle duration (about 24 h57). (Reprinted with permission from Ref 48. Copyright 2010 PNAS)

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Liver dissection, vascularization tree, and modeling microcirculation. On the coarse scale of organ level, the human liver is partitioned into lobes, whose blood flow and drainage results from the large vascular structures. By following bifurcations of the right, middle, and left hepatic vein as well as the portal vein, Coinaud divided the liver into eight independent segments. In Figure 3(a), the patient's individual partitioning of the liver into Coinaud segments based on a contrast enhanced CT scan is shown. However, for the construction of the multiscale model the resolution obtained from a patient's CT scan is way too coarse to generate an interface to the finer lobule scale. This gap in resolution is bridged with models that describe the morphology of hepatic blood vessels thus allowing for the enhancement of the real CT data with modeled vascular structures at lower scales (Figure 3(b)). The modeled vascular structures result from constructive algorithms,46,47 which minimize the intravascular volume as well as the energy needed for blood delivery. With the modeled mesoscale vasculature and the pressures at the entry of the hepatic vein, hepatic artery, and portal vein we can provide blood flow as well as drainage of molecular load of any kind to and from the liver units (2D configuration shown in Figure 3(c)). The liver units comprise several lobules and their SUs. Assuming equal distribution of the blood entering a liver unit to the SUs of all lobules, we consider the blood flow inside a SU as the smallest scale of perfusion (Figure 3(d)). The blood profile in the SU is obtained from a linear rotationally symmetric tubular model incorporating the lumen, the Disse space, and the endothelial fenestrations (Figure 3(e)). We assume a laminar blood flow in the lumen and diffusion inside the Disse space. In a more advanced version of the model we will also incorporate Stellate and Kupffer cells into this model. The connection to the HCs is realized in the lobule module of our multiscale model. Source: (a–c) Ole Schwen from Fraunhofer MEVIS.

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Whole‐body compartment modeling—physiologically based pharmacokinetic (PBPK) modeling. PBPK models represent the mass transfer of compounds in compartmental models of the mammalian body. Organ volumes, tissue composition into lipids, proteins and water, hematocrit values, and blood flows are parameterized using prior anatomical and physiological knowledge.39 Fully integrated models of the gastrointestinal (GI) tract use prior knowledge about transit times, volumes, and mucosa surfaces in different segments of the GI tract40 (a). The compartmental representation of organs in a generic PBPK model like the one used in PK‐Simˆ® can be quite complex itself, integrating knowledge about the relative volumes of the vascular space, the interstitial fluid, and the intracellular space as well as effective surface areas of the vascular endothelium and the cellular surfaces. Passive diffusive exchange across vascular endothelium is represented and active transport via transport proteins can be integrated as well as extra‐ and intracellular metabolization (b). For specific applications like the modeling of insulin control of glucose metabolism, PBPK models of compounds such as glucose, glucagon, and insulin can be coupled and integrated in one larger model representing processes like the insulin‐dependent uptake of glucose in muscle cells (c). Such models are then able to fully represent the systemic dynamics of the modeled compounds (d; experimental data from Ref 41). Model modules for biological processes at scales below the organ level can be integrated into PBPK models in a straight forward manner and computational platforms for such an integration are already available and in use.42 Source: (c and d) Stephan Schaller.

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Central physiological functions of liver. The liver receives blood supply from the systemic circulation via the liver arteries and the intestinal tract via the portal vein. The liver acts both as a filter removing pathogens, potentially toxic agents, waste products, and aged blood compounds and a bioreactor synthesizing numerous chemical compounds of the blood plasma. Excessive amounts of glucose, fatty acids, and some vitamins in the entering blood stream can be transiently stored (= buffering function). Production of bile represents the main exit pathway of cholesterol (in terms of bile acids) and hydrophobic drugs.

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