Mathematical modelling of liver regeneration after intoxication with CCl4

Cell populations simulated in silico within SimulCell accurately reproduce the behaviour of experimental cell cultures

In silico simulations are used to understand cell behaviour by means of different approaches and tools, which range from reproducing average population trends to building lattice-based models to, more recently, creating populations of individual cell agents whose mass, volume and morphology behave according to more or less precise rules and models. In this work, a new agent-based simulator, SimulCell, was conceived, developed and used to predict the behaviour of eukaryotic cell cultures while growing attached to a flat surface. The system, starting from time-lapse microscopy experiments, uses growth, proliferation and migration models to create synthetic populations closely resembling original cultures. Support for cell-cell and cell-environment interaction makes cell agents able to react to changes in medium composition and other events, such as physical damage or chemical modifications occurring in the culture plate. The simulator is accessible through a web application and generates data that can be shown as tables and graphs or exported for further analyses.

From sampling to simulating: Single-cell multiomics in systems pathophysiological modeling

As single-cell omics data sampling and acquisition methods have accumulated at an unprecedented rate, various data analysis pipelines have been developed for the inference of cell types, cell states and their distribution, state transitions, state trajectories, and state interactions. This presents a new opportunity in which single-cell omics data can be utilized to generate high-resolution, high-fidelity computational models. In this review, we discuss how single-cell omics data can be used to build computational models to simulate biological systems at various scales. We propose that single-cell data can be integrated with physiological information to generate organ-specific models, which can then be assembled to generate multi-organ systems pathophysiological models. Finally, we discuss how generic multi-organ models can be brought to the patient-specific level thus permitting their use in the clinical setting.

Impact of heterogeneity in liver matrix and intrahepatic cells on the progression of hepatic fibrosis

Liver fibrosis is a disease with a high prevalence worldwide. The development of hepatic fibrosis results from a combination of factors within the liver, such as extracellular matrix (ECM) deposition, hepatic stellate cells (HSCs) activation, collagen cross-linking, and inflammatory response. Heterogeneity in fibrotic liver is the result of a combination of heterogeneity in the intrahepatic microenvironment as well as heterogeneous expression of fibrosis-associated enzymes and cells, complicating the study of the mechanisms underlying the progression of liver fibrosis. The role of this heterogeneity on the crosstalk between cells and matrix and on the fibrotic process is worth exploring. In this paper, we will describe the phenomenon and mechanism of heterogeneity of liver matrix and intrahepatic cells in the process of hepatic fibrosis and discuss the crosstalk between heterogeneous factors on the development of fibrosis. The elucidation of heterogeneity is important for a deeper understanding of the pathological mechanisms of liver fibrosis as well as for clinical diagnosis and targeted therapies.

On a deterministic mathematical model which efficiently predicts the protective effect of a plant extract mixture in cirrhotic rats

In this work, we propose a mathematical model that describes liver evolution and concentrations of alanine aminotransferase and aspartate aminotransferase in a group of rats damaged with carbon tetrachloride. Carbon tetrachloride was employed to induce cirrhosis. A second groups damaged with carbon tetrachloride was exposed simultaneously a plant extract as hepatoprotective agent. The model reproduces the data obtained in the experiment reported in [Rev. Cub. Plant. Med. 22(1), 2017], and predicts that using the plants extract helps to get a better natural recovery after the treatment. Computer simulations show that the extract reduces the damage velocity but does not avoid it entirely. The present paper is the first report in the literature in which a mathematical model reliably predicts the protective effect of a plant extract mixture in rats with cirrhosis disease. The results reported in this manuscript could be used in the future to help in fighting cirrhotic conditions in humans, though more experimental and mathematical work is required in that case.

Lumped parameter liver simulation to predict acute haemodynamic alterations following partial resections

Partial liver resections are routinely performed in living donor liver transplantation and to debulk tumours in liver malignancies, but surgical decisions on vessel reconstruction for adequate inflow and outflow are challenging. Pre-operative evaluation is often limited to radiological imaging, which fails to account for post-resection haemodynamic alterations. Substantial evidence suggests post-surgical increase in local volume flow rate enhances shear stress, signalling hepatic regeneration, but excessive shear stress has been postulated to result in small for size syndrome and liver failure. Predicting haemodynamic alterations throughout the liver is particularly challenging due to the dendritic architecture of the vasculature, spanning several orders of magnitude in diameter. Therefore, we developed a mathematical lumped parameter model with realistic heterogeneities capturing inflow/outflow of the human liver to simulate acute perfusion alterations following surgical resection. Our model is parametrized using clinical measurements, relies on a single free parameter and accurately captures established perfusion characteristics. We quantify acute changes in volume flow rate, flow speed and wall shear stress following variable, realistic liver resections and make comparisons with the intact liver. Our numerical model runs in minutes and can be adapted to patient-specific anatomy, providing a novel computational tool aimed at assisting pre- and intra-operative surgical decisions for liver resections.

In silico modeling for the hepatic circulation and transport: From the liver organ to lobules

The function of the liver depends critically on its blood supply. Numerous in silico models have been developed to study various aspects of the hepatic circulation, including not only the macro-hemodynamics at the organ level, but also the microcirculation at the lobular level. In addition, computational models of blood flow and bile flow have been used to study the transport, metabolism, and clearance of drugs in pharmacokinetic studies. These in silico models aim to provide insights into the liver organ function under both healthy and diseased states, and to assist quantitative analysis for surgical planning and postsurgery treatment. The purpose of this review is to provide an update on state-of-the-art in silico models of the hepatic circulation and transport processes. We introduce the numerical methods and the physiological background of these models. We also discuss multiscale frameworks that have been proposed for the liver, and their linkage with the large context of systems biology, systems pharmacology, and the Physiome project. This article is categorized under: Metabolic Diseases > Computational Models Metabolic Diseases > Biomedical Engineering Cardiovascular Diseases > Computational Models.

Predicting liver regeneration following major resection

Breakdown of synthesis, excretion and detoxification defines liver failure. Post-hepatectomy liver failure (PHLF) is specific for liver resection and a rightfully feared complication due to high lethality and limited therapeutic success. Individual cytokine and growth factor profiles may represent potent predictive markers for recovery of liver function. We aimed to investigate these profiles in post-hepatectomy regeneration. This study combined a time-dependent cytokine and growth factor profiling dataset of a training (30 patients) and a validation (14 patients) cohorts undergoing major liver resection with statistical and predictive models identifying individual pathway signatures. 2319 associations were tested. Primary hepatocytes isolated from patient tissue samples were stimulated and their proliferation was analysed through DNA content assay. Common expression trajectories of cytokines and growth factors with strong correlation to PHLF, morbidity and mortality were identified despite highly individual perioperative dynamics. Especially, dynamics of EGF, HGF, and PLGF were associated with mortality. PLGF was additionally associated with PHLF and complications. A global association-network was calculated and validated to investigate interdependence of cytokines and growth factors with clinical attributes. Preoperative cytokine and growth factor signatures were identified allowing prediction of mortality following major liver resection by regression modelling. Proliferation analysis of corresponding primary human hepatocytes showed associations of individual regenerative potential with clinical outcome. Prediction of PHLF was possible on as early as first postoperative day (POD1) with AUC above 0.75. Prediction of PHLF and mortality is possible on POD1 with liquid-biopsy based risk profiling. Further utilization of these models would allow tailoring of interventional strategies according to individual profiles.

Geometrical model of lobular structure and its importance for the liver perfusion analysis

A convenient geometrical description of the microvascular network is necessary for computationally efficient mathematical modelling of liver perfusion, metabolic and other physiological processes. The tissue models currently used are based on the generally accepted schematic structure of the parenchyma at the lobular level, assuming its perfect regular structure and geometrical symmetries. Hepatic lobule, portal lobule, or liver acinus are considered usually as autonomous functional units on which particular physiological problems are studied. We propose a new periodic unit-the liver representative periodic cell (LRPC) and establish its geometrical parametrization. The LRPC is constituted by two portal lobulae, such that it contains the liver acinus as a substructure. As a remarkable advantage over the classical phenomenological modelling approaches, the LRPC enables for multiscale modelling based on the periodic homogenization method. Derived macroscopic equations involve so called effective medium parameters, such as the tissue permeability, which reflect the LRPC geometry. In this way, mutual influences between the macroscopic phenomena, such as inhomogeneous perfusion, and the local processes relevant to the lobular (mesoscopic) level are respected. The LRPC based model is intended for its use within a complete hierarchical model of the whole liver. Using the Double-permeability Darcy model obtained by the homogenization, we illustrate the usefulness of the LRPC based modelling to describe the blood perfusion in the parenchyma.

Cross-species analysis of hepatic cytochrome P450 and transport protein expression

Most drugs and xenobiotics are metabolized in the liver. Amongst others, different cytochrome P450 (CYP) enzymes catalyze the metabolic conversion of foreign compounds, and various transport proteins are engaged in the excretion of metabolites from the hepatocytes. Inter-species and inter-individual differences in the hepatic levels and activities of drug-metabolizing enzymes and transporters result from genetic as well as from environmental factors, and play a decisive role in determining the pharmacokinetic properties of a compound in a given test system. To allow for a meaningful comparison of results from metabolism studies, it is, therefore, of utmost importance to know about the specific metabolic properties of the test systems, especially about the levels of metabolic enzymes such as the CYPs. Using a targeted proteomics approach, we, therefore, compared the hepatic levels of important CYP enzymes and transporters in different experimental systems in vivo and in vitro, namely Wistar rats, C57/Bl6 mice, mice humanized for the two xeno-sensing receptors PXR (pregnane-X-receptor) and CAR (constitutive androstane receptor), mice with human hepatocyte-repopulated livers, human HepaRG hepatocarcinoma cells, primary human hepatocytes, and human liver biopsies. In addition, the effects of xenobiotic inducers of drug metabolism on CYP enzymes and transporters were analyzed in selected systems. This study for the first time presents a comprehensive overview of similarities and differences in important drug metabolism-related proteins among the different experimental models.

Modeling of Nanotherapy Response as a Function of the Tumor Microenvironment: Focus on Liver Metastasis

The tumor microenvironment (TME) presents a challenging barrier for effective nanotherapy-mediated drug delivery to solid tumors. In particular for tumors less vascularized than the surrounding normal tissue, as in liver metastases, the structure of the organ itself conjures with cancer-specific behavior to impair drug transport and uptake by cancer cells. Cells and elements in the TME of hypovascularized tumors play a key role in the process of delivery and retention of anti-cancer therapeutics by nanocarriers. This brief review describes the drug transport challenges and how they are being addressed with advanced in vitro 3D tissue models as well as with in silico mathematical modeling. This modeling complements network-oriented techniques, which seek to interpret intra-cellular relevant pathways and signal transduction within cells and with their surrounding microenvironment. With a concerted effort integrating experimental observations with computational analyses spanning from the molecular- to the tissue-scale, the goal of effective nanotherapy customized to patient tumor-specific conditions may be finally realized.

Holland C, Zaza A, Murad W, Hassan R, A. Ahmed Y, Abbas T, A. Abdelrahim E, Schneider KM, Matz-Soja M, Reinders J, Gebhardt R, Berres ML, Hatting M, Drasdo D, Saez-Rodriguez J, Trautwein C, G. Hengstler J. Influence of Liver Fibrosis on Lobular Zonation

Little is known about how liver fibrosis influences lobular zonation. To address this question, we used three mouse models of liver fibrosis, repeated CCl4 administration for 2, 6 and 12 months to induce pericentral damage, as well as bile duct ligation (21 days) and mdr2-/- mice to study periportal fibrosis. Analyses were performed by RNA-sequencing, immunostaining of zonated proteins and image analysis. RNA-sequencing demonstrated a significant enrichment of pericentral genes among genes downregulated by CCl4; vice versa, periportal genes were enriched among the upregulated genes. Immunostaining showed an almost complete loss of pericentral proteins, such as cytochrome P450 enzymes and glutamine synthetase, while periportal proteins, such as arginase 1 and CPS1 became expressed also in pericentral hepatocytes. This pattern of fibrosis-associated 'periportalization' was consistently observed in all three mouse models and led to complete resistance to hepatotoxic doses of acetaminophen (200 mg/kg). Characterization of the expression response identified the inflammatory pathways TGFβ, NFκB, TNFα, and transcription factors NFKb1, Stat1, Hif1a, Trp53, and Atf1 among those activated, while estrogen-associated pathways, Hnf4a and Hnf1a, were decreased. In conclusion, liver fibrosis leads to strong alterations of lobular zonation, where the pericentral region adopts periportal features. Beside adverse consequences, periportalization supports adaptation to repeated doses of hepatotoxic compounds.

Creation of Three-Dimensional Liver Tissue Models from Experimental Images for Systems Medicine

In this chapter, we illustrate how three-dimensional liver tissue models can be created from experimental image modalities by utilizing a well-established processing chain of experiments, microscopic imaging, image processing, image analysis and model construction. We describe how key features of liver tissue architecture are quantified and translated into model parameterizations, and show how a systematic iteration of experiments and model simulations often leads to a better understanding of biological phenomena in systems biology and systems medicine.

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.

Proteomic Characterization of Primary Mouse Hepatocytes in Collagen Monolayer and Sandwich Culture

Dedifferentiation of primary hepatocytes in vitro makes their application in long-term studies difficult. Embedding hepatocytes in a sandwich of extracellular matrix is reported to delay the dedifferentiation process to some extent. In this study, we compared the intracellular proteome of primary mouse hepatocytes (PMH) in conventional monolayer cultures (ML) to collagen sandwich culture (SW) after 1 day and 5 days of cultivation. Quantitative proteome analysis of PMH showed no differences between collagen SW and ML cultures after 1 day. Glycolysis and gluconeogenesis were strongly affected by long-term cultivation in both ML and SW cultures. Interestingly, culture conditions had no effect on cellular lipid metabolism. After 5 days, PMH in collagen SW and ML cultures exhibit characteristic indications of oxidative stress. However, in the SW culture the defense system against oxidative stress is significantly up-regulated to deal with this, whereas in the ML culture a down-regulation of these important enzymes takes place. Regarding the multiple effects of ROS and oxidative stress in cells, we conclude that the down-regulation of these enzymes seem to play a role in the loss of hepatic function observed in the ML cultivation. In addition, enzymes of the urea cycle were clearly down-regulated in ML culture. Proteomics confirms lack in oxidative stress defense mechanisms as the major characteristic of hepatocytes in monolayer cultures compared to sandwich cultures. J. Cell. Biochem. 119: 447-454, 2018. © 2017 Wiley Periodicals, Inc.

Prediction of postoperative liver regeneration from clinical information using a data-led mathematical model

Although the capacity of the liver to recover its size after resection has enabled extensive liver resection, post-hepatectomy liver failure remains one of the most lethal complications of liver resection. Therefore, it is clinically important to discover reliable predictive factors after resection. In this study, we established a novel mathematical framework which described post-hepatectomy liver regeneration in each patient by incorporating quantitative clinical data. Using the model fitting to the liver volumes in series of computed tomography of 123 patients, we estimated liver regeneration rates. From the estimation, we found patients were divided into two groups: i) patients restored the liver to its original size (Group 1, n = 99); and ii) patients experienced a significant reduction in size (Group 2, n = 24). From discriminant analysis in 103 patients with full clinical variables, the prognosis of patients in terms of liver recovery was successfully predicted in 85-90% of patients. We further validated the accuracy of our model prediction using a validation cohort (prediction = 84-87%, n = 39). Our interdisciplinary approach provides qualitative and quantitative insights into the dynamics of liver regeneration. A key strength is to provide better prediction in patients who had been judged as acceptable for resection by current pragmatic criteria.

Toxicogenomics directory of chemically exposed human hepatocytes

A long-term goal of numerous research projects is to identify biomarkers for in vitro systems predicting toxicity in vivo. Often, transcriptomics data are used to identify candidates for further evaluation. However, a systematic directory summarizing key features of chemically influenced genes in human hepatocytes is not yet available. To bridge this gap, we used the Open TG-GATES database with Affymetrix files of cultivated human hepatocytes incubated with chemicals, further sets of gene array data with hepatocytes from human donors generated in this study, and publicly available genome-wide datasets of human liver tissue from patients with non-alcoholic steatohepatitis (NASH), cirrhosis, and hepatocellular cancer (HCC). After a curation procedure, expression data of 143 chemicals were included into a comprehensive biostatistical analysis. The results are summarized in the publicly available toxicotranscriptomics directory ( http://wiki.toxbank.net/toxicogenomics-map/ ) which provides information for all genes whether they are up- or downregulated by chemicals and, if yes, by which compounds. The directory also informs about the following key features of chemically influenced genes: (1) Stereotypical stress response. When chemicals induce strong expression alterations, this usually includes a complex but highly reproducible pattern named 'stereotypical response.' On the other hand, more specific expression responses exist that are induced only by individual compounds or small numbers of compounds. The directory differentiates if the gene is part of the stereotypical stress response or if it represents a more specific reaction. (2) Liver disease-associated genes. Approximately 20 % of the genes influenced by chemicals are up- or downregulated, also in liver disease. Liver disease genes deregulated in cirrhosis, HCC, and NASH that overlap with genes of the aforementioned stereotypical chemical stress response include CYP3A7, normally expressed in fetal liver; the phase II metabolizing enzyme SULT1C2; ALDH8A1, known to generate the ligand of RXR, one of the master regulators of gene expression in the liver; and several genes involved in normal liver functions: CPS1, PCK1, SLC2A2, CYP8B1, CYP4A11, ABCA8, and ADH4. (3) Unstable baseline genes. The process of isolating and the cultivation of hepatocytes was sufficient to induce some stress leading to alterations in the expression of genes, the so-called unstable baseline genes. (4) Biological function. Although more than 2,000 genes are transcriptionally influenced by chemicals, they can be assigned to a relatively small group of biological functions, including energy and lipid metabolism, inflammation and immune response, protein modification, endogenous and xenobiotic metabolism, cytoskeletal organization, stress response, and DNA repair. In conclusion, the introduced toxicotranscriptomics directory offers a basis for a rationale choice of candidate genes for biomarker evaluation studies and represents an easy to use source of background information on chemically influenced genes.

Rodent models and imaging techniques to study liver regeneration

The liver has the unique capability of regeneration from various injuries. Different animal models and in vitro methods are used for studying the processes and mechanisms of liver regeneration. Animal models were established either by administration of hepatotoxic chemicals or by surgical approach. The administration of hepatotoxic chemicals results in the death of liver cells and in subsequent hepatic regeneration and tissue repair. Surgery includes partial hepatectomy and portal vein occlusion or diversion: hepatectomy leads to compensatory regeneration of the remnant liver lobe, whereas portal vein occlusion leads to atrophy of the ipsilateral lobe and to compensatory regeneration of the contralateral lobe. Adaptation of modern radiological imaging technologies to the small size of rodents made the visualization of rodent intrahepatic vascular anatomy possible. Advanced knowledge of the detailed intrahepatic 3D anatomy enabled the establishment of refined surgical techniques. The same technology allows the visualization of hepatic vascular regeneration. The development of modern histological image analysis tools improved the quantitative assessment of hepatic regeneration. Novel image analysis tools enable us to quantify reliably and reproducibly the proliferative rate of hepatocytes using whole-slide scans, thus reducing the sampling error. In this review, the refined rodent models and the newly developed imaging technology to study liver regeneration are summarized. This summary helps to integrate the current knowledge of liver regeneration and promises an enormous increase in hepatological knowledge in the near future.

How predictive quantitative modelling of tissue organisation can inform liver disease pathogenesis

From the more than 100 liver diseases described, many of those with high incidence rates manifest themselves by histopathological changes, such as hepatitis, alcoholic liver disease, fatty liver disease, fibrosis, and, in its later stages, cirrhosis, hepatocellular carcinoma, primary biliary cirrhosis and other disorders. Studies of disease pathogeneses are largely based on integrating -omics data pooled from cells at different locations with spatial information from stained liver structures in animal models. Even though this has led to significant insights, the complexity of interactions as well as the involvement of processes at many different time and length scales constrains the possibility to condense disease processes in illustrations, schemes and tables. The combination of modern imaging modalities with image processing and analysis, and mathematical models opens up a promising new approach towards a quantitative understanding of pathologies and of disease processes. This strategy is discussed for two examples, ammonia metabolism after drug-induced acute liver damage, and the recovery of liver mass as well as architecture during the subsequent regeneration process. This interdisciplinary approach permits integration of biological mechanisms and models of processes contributing to disease progression at various scales into mathematical models. These can be used to perform in silico simulations to promote unravelling the relation between architecture and function as below illustrated for liver regeneration, and bridging from the in vitro situation and animal models to humans. In the near future novel mechanisms will usually not be directly elucidated by modelling. However, models will falsify hypotheses and guide towards the most informative experimental design.

Method for finding metabolic properties based on the general growth law. Liver examples. A general framework for biological modeling

We propose a method for finding metabolic parameters of cells, organs and whole organisms, which is based on the earlier discovered general growth law. Based on the obtained results and analysis of available biological models, we propose a general framework for modeling biological phenomena and discuss how it can be used in Virtual Liver Network project. The foundational idea of the study is that growth of cells, organs, systems and whole organisms, besides biomolecular machinery, is influenced by biophysical mechanisms acting at different scale levels. In particular, the general growth law uniquely defines distribution of nutritional resources between maintenance needs and biomass synthesis at each phase of growth and at each scale level. We exemplify the approach considering metabolic properties of growing human and dog livers and liver transplants. A procedure for verification of obtained results has been introduced too. We found that two examined dogs have high metabolic rates consuming about 0.62 and 1 gram of nutrients per cubic centimeter of liver per day, and verified this using the proposed verification procedure. We also evaluated consumption rate of nutrients in human livers, determining it to be about 0.088 gram of nutrients per cubic centimeter of liver per day for males, and about 0.098 for females. This noticeable difference can be explained by evolutionary development, which required females to have greater liver processing capacity to support pregnancy. We also found how much nutrients go to biomass synthesis and maintenance at each phase of liver and liver transplant growth. Obtained results demonstrate that the proposed approach can be used for finding metabolic characteristics of cells, organs, and whole organisms, which can further serve as important inputs and constraints for many applications in biology (such as protein expression), biotechnology (synthesis of substances), and medicine.

Protocols for staining of bile canalicular and sinusoidal networks of human, mouse and pig livers, three-dimensional reconstruction and quantification of tissue microarchitecture by image processing and analysis

Histological alterations often constitute a fingerprint of toxicity and diseases. The extent to which these alterations are cause or consequence of compromised organ function, and the underlying mechanisms involved is a matter of intensive research. In particular, liver disease is often associated with altered tissue microarchitecture, which in turn may compromise perfusion and functionality. Research in this field requires the development and orchestration of new techniques into standardized processing pipelines that can be used to reproducibly quantify tissue architecture. Major bottlenecks include the lack of robust staining, and adequate reconstruction and quantification techniques. To bridge this gap, we established protocols employing specific antibody combinations for immunostaining, confocal imaging, three-dimensional reconstruction of approximately 100-μm-thick tissue blocks and quantification of key architectural features. We describe a standard procedure termed ‘liver architectural staining’ for the simultaneous visualization of bile canaliculi, sinusoidal endothelial cells, glutamine synthetase (GS) for the identification of central veins, and DAPI as a nuclear marker. Additionally, we present a second standard procedure entitled ‘S-phase staining’, where S-phase-positive and S-phase-negative nuclei (stained with BrdU and DAPI, respectively), sinusoidal endothelial cells and GS are stained. The techniques include three-dimensional reconstruction of the sinusoidal and bile canalicular networks from the same tissue block, and robust capture of position, size and shape of individual hepatocytes, as well as entire lobules from the same tissue specimen. In addition to the protocols, we have also established image analysis software that allows relational and hierarchical quantifications of different liver substructures (e.g. cells and vascular branches) and events (e.g. cell proliferation and death). Typical results acquired for routinely quantified parameters in adult mice (C57Bl6/N) include the hepatocyte volume (5,128.3 ± 837.8 μm³) and the fraction of the hepatocyte surface in contact with the neighbouring hepatocytes (67.4 ± 6.7 %), sinusoids (22.1 ± 4.8 %) and bile canaliculi (9.9 ± 3.8 %). Parameters of the sinusoidal network that we also routinely quantify include the radius of the sinusoids (4.8 ± 2.25 μm), the branching angle (32.5 ± 11.2°), the length of intersection branches (23.93 ± 5.9 μm), the number of intersection nodes per mm³ (120.3 × 103 ± 42.1 × 10³), the average length of sinusoidal vessel per mm³ (5.4 × 10³ ± 1.4 × 10³mm) and the percentage of vessel volume in relation to the whole liver volume (15.3 ± 3.9) (mean ± standard deviation). Moreover, the provided parameters of the bile canalicular network are: length of the first-order branches (7.5 ± 0.6 μm), length of the second-order branches (10.9 ± 1.8 μm), length of the dead-end branches (5.9 ± 0.7 μm), the number of intersection nodes per mm³ (819.1 × 10³ ± 180.7 × 10³), the number of dead-end branches per mm³ (409.9 × 10³ ± 95.6 × 10³), the length of the bile canalicular network per mm³ (9.4 × 10³ ± 0.7 × 10³ mm) and the percentage of the bile canalicular volume with respect to the total liver volume (3.4 ± 0.005). A particular strength of our technique is that quantitative parameters of hepatocytes and bile canalicular as well as sinusoidal networks can be extracted from the same tissue block. Reconstructions and quantifications performed as described in the current protocols can be used for quantitative mathematical modelling of the underlying mechanisms. Furthermore, protocols are presented for both human and pig livers. The technique is also applicable for both vibratome blocks and conventional paraffin slices.

Mathematical model of liver regeneration in human live donors

Liver regeneration after injury occurs in many mammals. Rat liver regenerates after partial hepatectomy over a period of 2 weeks while human liver regeneration takes several months. Notwithstanding this enormous difference in time-scales, with new data from five human live liver transplant donors, we show that a mathematical model of rat liver regeneration can be transferred to human, with all biochemical interactions and signaling unchanged. Only six phenomenological parameters need change, and three of these parameter changes are rescalings of rate constants by the ratio of human lifespan to rat lifespan. Data from three donor subjects with approximately equal resections were used to fit the three parameters and the data from the other two donor subjects was used to independently verify the fit.

Mathematical modeling of regenerative processes

In many animals, regenerative processes can replace lost body parts. Organ and tissue regeneration consequently also hold great medical promise. The regulation of regenerative processes is achieved through concerted actions of multiple organizational levels of the organism, from diffusing molecules and cellular gene expression patterns up to tissue mechanics. Our intuition is usually not adapted well to this degree of complexity and the quantitative aspects of the regulation of regenerative processes remain poorly understood. One way out of this dilemma lies in the combination of experimentation and mathematical modeling within an iterative process of model development/refinement, model predictions for novel experimental conditions, quantitative experiments testing these predictions, and subsequent model refinement. This interdisciplinary approach has already provided key insights into smaller scale processes during embryonic development and a so-far limited number of more complex regeneration processes. This review discusses selected theoretical and interdisciplinary studies and is structured along the three phases of regeneration: (1) initiation of a regeneration response, (2) tissue patterning during regenerate growth, (3) arresting the regeneration response. Moreover, we highlight the opportunities provided by extensions of mathematical models from developmental processes toward the study of related regenerative processes.

Recent advances in 2D and 3D in vitro systems using primary hepatocytes, alternative hepatocyte sources and non-parenchymal liver cells and their use in investigating mechanisms of hepatotoxicity, cell signaling and ADME

This review encompasses the most important advances in liver functions and hepatotoxicity and analyzes which mechanisms can be studied in vitro. In a complex architecture of nested, zonated lobules, the liver consists of approximately 80 % hepatocytes and 20 % non-parenchymal cells, the latter being involved in a secondary phase that may dramatically aggravate the initial damage. Hepatotoxicity, as well as hepatic metabolism, is controlled by a set of nuclear receptors (including PXR, CAR, HNF-4α, FXR, LXR, SHP, VDR and PPAR) and signaling pathways. When isolating liver cells, some pathways are activated, e.g., the RAS/MEK/ERK pathway, whereas others are silenced (e.g. HNF-4α), resulting in up- and downregulation of hundreds of genes. An understanding of these changes is crucial for a correct interpretation of in vitro data. The possibilities and limitations of the most useful liver in vitro systems are summarized, including three-dimensional culture techniques, co-cultures with non-parenchymal cells, hepatospheres, precision cut liver slices and the isolated perfused liver. Also discussed is how closely hepatoma, stem cell and iPS cell-derived hepatocyte-like-cells resemble real hepatocytes. Finally, a summary is given of the state of the art of liver in vitro and mathematical modeling systems that are currently used in the pharmaceutical industry with an emphasis on drug metabolism, prediction of clearance, drug interaction, transporter studies and hepatotoxicity. One key message is that despite our enthusiasm for in vitro systems, we must never lose sight of the in vivo situation. Although hepatocytes have been isolated for decades, the hunt for relevant alternative systems has only just begun.

Systems toxicology from genes to organs

This unique overview of systems toxicology methods and techniques begins with a brief account of systems thinking in biology over the last century. We discuss how systems biology and toxicology continue to leverage advances in computational modeling, informatics, large-scale computing, and biotechnology. Next, we chart the genesis of systems toxicology from previous work in physiologically based models, models of early development, and more recently, molecular systems biology. For readers interested in further details this background provides useful linkages to the relevant literature. It also lays the foundations for new ideas in systems toxicology that could translate laboratory measurements of molecular responses from xenobiotic perturbations to adverse organ level effects in humans. By providing innovative solutions across disciplinary boundaries and highlighting key scientific gaps, we believe this chapter provides useful information about the current state, and valuable insight about future directions in systems toxicity.

Systems biology tools for toxicology

An important goal of toxicology is to understand and predict the adverse effects of drugs and other xenobiotics. For pharmaceuticals, such effects often emerge unexpectedly in man even when absent from trials in vitro and in animals. Although drugs and xenobiotics act on molecules, it is their perturbation of intracellular networks that matters. The tremendous complexity of these networks makes it difficult to understand the effects of xenobiotics on their ability to function. Because systems biology integrates data concerning molecules and their interactions into an understanding of network behaviour, it should be able to assist toxicology in this respect. This review identifies how in silico systems biology tools, such as kinetic modelling, and metabolic control, robustness and flux analyse, may indeed help understanding network-mediated toxicity. It also shows how these approaches function by implementing them vis-à-vis the glutathione network, which is important for the detoxification of reactive drug metabolites. The tools enable the appreciation of the steady state concept for the detoxification network and make it possible to simulate and then understand effects of perturbations of the macromolecules in the pathway that are counterintuitive. We review how a glutathione model has been used to explain the impact of perturbation of the pathway at various molecular sites, as would be the effect of single-nucleotide polymorphisms. We focus on how the mutations impact the levels of glutathione and of two candidate biomarkers of hepatic glutathione status. We conclude this review by sketching how the various systems biology tools may help in the various phases of drug development in the pharmaceutical industry.

Advances in the regulation of liver regeneration

Liver regeneration is known to be a process involving highly organized and ordered tissue growth triggered by the loss of liver tissue, and remains a fascinating topic. A large number of genes are involved in this process, and there exists a sequence of stages that results in liver regeneration, while at the same time inhibitors control the size of the regenerated liver. The initiation step is characterized by priming of quiescent hepatocytes by factors such as TNF-α, IL-6 and nitric oxide. The proliferation step is the step during which hepatocytes enter into the cell cycle's G1 phase and are stimulated by complete mitogens including HGF, TGF-α and EGF. Hepatic stimulator substance, glucagon, insulin, TNF-α, IL-1 and IL-6 have also been implicated in regulating the regeneration process. Inhibitors and stop signals of hepatic regeneration are not well known and only limited information is available. Furthermore, the effects of other factors such as VEGF, PDGF, hypothyroidism, proliferating cell nuclear antigen, heat shock proteins, ischemic-reperfusion injury, steatosis and granulocyte colony-stimulating factor on liver regeneration are also systematically reviewed in this article. A tissue engineering approach using isolated hepatocytes for in vitro tissue generation and heterotopic transplantation of liver cells has been established. The use of stem cells might also be very attractive to overcome the limitation of donor liver tissue. Liver-specific differentiation of embryonic, fetal or adult stem cells is currently under investigation.

A cell-based simulation software for multi-cellular systems

CellSys is a modular software tool for efficient off-lattice simulation of growth and organization processes in multi-cellular systems in 2D and 3D. It implements an agent-based model that approximates cells as isotropic, elastic and adhesive objects. Cell migration is modeled by an equation of motion for each cell. The software includes many modules specifically tailored to support the simulation and analysis of virtual tissues including real-time 3D visualization and VRML 2.0 support. All cell and environment parameters can be independently varied which facilitates species specific simulations and allows for detailed analyses of growth dynamics and links between cellular and multi-cellular phenotypes.

Availability: CellSys is freely available for non-commercial use at http://msysbio.com/software/cellsys. The current version of CellSys permits the simulation of growing monolayer cultures and avascular tumor spheroids in liquid environment. Further functionality will be made available ongoing with published papers.

Contact:hoehme@izbi.uni-leipzig.de; dirk.drasdo@inria.fr

Supplementary information:Supplementary data are available at Bioinformatics online.

Prediction and validation of cell alignment along microvessels as order principle to restore tissue architecture in liver regeneration

Only little is known about how cells coordinately behave to establish functional tissue structure and restore microarchitecture during regeneration. Research in this field is hampered by a lack of techniques that allow quantification of tissue architecture and its development. To bridge this gap, we have established a procedure based on confocal laser scans, image processing, and three-dimensional tissue reconstruction, as well as quantitative mathematical modeling. As a proof of principle, we reconstructed and modeled liver regeneration in mice after damage by CCl(4), a prototypical inducer of pericentral liver damage. We have chosen the regenerating liver as an example because of the tight link between liver architecture and function: the complex microarchitecture formed by hepatocytes and microvessels, i.e. sinusoids, ensures optimal exchange of metabolites between blood and hepatocytes. Our model captures all hepatocytes and sinusoids of a liver lobule during a 16 days regeneration process. The model unambiguously predicted a so-far unrecognized mechanism as essential for liver regeneration, whereby daughter hepatocytes align along the orientation of the closest sinusoid, a process which we named "hepatocyte-sinusoid alignment" (HSA). The simulated tissue architecture was only in agreement with the experimentally obtained data when HSA was included into the model and, moreover, no other likely mechanism could replace it. In order to experimentally validate the model of prediction of HSA, we analyzed the three-dimensional orientation of daughter hepatocytes in relation to the sinusoids. The results of this analysis clearly confirmed the model prediction. We believe our procedure is widely applicable in the systems biology of tissues.

Simulating microdosimetry in a virtual hepatic lobule

The liver plays a key role in removing harmful chemicals from the body and is therefore often the first tissue to suffer potentially adverse consequences. To protect public health it is necessary to quantitatively estimate the risk of long-term low dose exposure to environmental pollutants. Animal testing is the primary tool for extrapolating human risk but it is fraught with uncertainty, necessitating novel alternative approaches. Our goal is to integrate in vitro liver experiments with agent-based cellular models to simulate a spatially extended hepatic lobule. Here we describe a graphical model of the sinusoidal network that efficiently simulates portal to centrilobular mass transfer in the hepatic lobule. We analyzed the effects of vascular topology and metabolism on the cell-level distribution following oral exposure to chemicals. The spatial distribution of metabolically inactive chemicals was similar across different vascular networks and a baseline well-mixed compartment. When chemicals were rapidly metabolized, concentration heterogeneity of the parent compound increased across the vascular network. As a result, our spatially extended lobule generated greater variability in dose-dependent cellular responses, in this case apoptosis, than were observed in the classical well-mixed liver or in a parallel tubes model. The mass-balanced graphical approach to modeling the hepatic lobule is computationally efficient for simulating long-term exposure, modular for incorporating complex cellular interactions, and flexible for dealing with evolving tissues.

Virtual tissues are emerging as a powerful tool for computational biology. By encoding known biology into a simulation of tissue function, gaps in knowledge can be identified. As a simulation of tissue function, in silico experiments can be performed inexpensively and rapidly. There are over 6000 chemicals produced in large quantities that may be present in our environment, many of which have not been thoroughly examined for human toxicity. Traditional toxicity testing is expensive, lengthy, and relies heavily upon the use of animals. For this reason in vitro toxicity testing techniques are being developed. However, techniques are needed to relate in vitro results to in vivo conditions. The liver is often the first tissue to show signs of toxicity and therefore a predictive liver toxicity simulator would be a powerful tool to reduce the financial and animal cost of toxicity testing. As a first step, we have developed a model for relating environmental exposure to cell-level concentrations; a model for virtual tissue microdosimetry. We identify regimes in which this approach is equivalent to previous techniques, as well as regimes where large cell-to-cell variability exists. This variability should have consequences both for normal liver function and the onset of injury.

Hepatic stem cells and liver development

The liver consists of many cell types with specialized functions. Hepatocytes are one of the main players in the organ and therefore are the most vulnerable cells to damage. Since they are not everlasting cells, they need to be replenished throughout life. Although the capacity of hepatocytes to contribute to their own maintenance has long been recognized, recent studies have indicated the presence of both intrahepatic and extrahepatic stem/progenitor cell populations that serve to maintain the normal organ and to regenerate damaged parenchyma in response to a variety of insults.The intrahepatic compartment most likely derives primarily from the biliary tree, particularly the most proximal branches, i.e. the canals of Hering and smallest ductules. The extrahepatic compartment is at least in part derived from diverse populations of cells from the bone marrow. Embryonic stem cells (ES's) are considered as a part of the extrahepatic compartment. Due to their pluripotent capabilities, ES cell-derived cells form a potential future source of hepatocytes, to replace or restore hepatic tissues that have been damaged by disease or injury. Progressing knowledge about stem cells in the liver would allow a better understanding of the mechanisms of hepatic homeostasis and regeneration. Although a human stem cell-derived cell type equivalent to primary hepatocytes does not yet exist, the promising results obtained with extrahepatic stem cells would open the way to cell-based therapy for liver diseases.