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

An adaptive numerical method for multi-cellular simulations of tissue development and maintenance

In recent years, multi-cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi-cellular modelling tools and to demonstrate which numerical methods are appropriate for simulations of tissue and organ development, maintenance, and disease. The second aim is to introduce an adaptive time-stepping algorithm and to demonstrate it's efficiency and accuracy. We focus on off-lattice, mechanics based, models where cell movement is defined by a series of first order ordinary differential equations, derived by assuming over-damped motion and balancing forces. We see that many numerical methods have been used, ranging from simple Forward Euler approaches through to higher order single-step methods like Runge-Kutta 4 and multi-step methods like Adams-Bashforth 2. Through a series of exemplar multi-cellular simulations, we see that if: care is taken to have events (births deaths and re-meshing/re-arrangements) occur on common time-steps; and boundaries are imposed on all sub-steps of numerical methods or implemented using forces, then all numerical methods can converge with the correct order. We introduce an adaptive time-stepping method and demonstrate that the best compromise between L∞ error and run-time is to use Runge-Kutta 4 with an increased time-step and moderate adaptivity. We see that a judicious choice of numerical method can speed the simulation up by a factor of 10-60 from the Forward Euler methods seen in Osborne et al. (2017), and a further speed up by a factor of 4 can be achieved by using an adaptive time-step.

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.

In vitro to in vivo acetaminophen hepatotoxicity extrapolation using classical schemes, pharmacodynamic models and a multiscale spatial-temporal liver twin

In vitro to in vivo extrapolation represents a critical challenge in toxicology. In this paper we explore extrapolation strategies for acetaminophen (APAP) based on mechanistic models, comparing classical (CL) homogeneous compartment pharmacodynamic (PD) models and a spatial-temporal (ST), multiscale digital twin model resolving liver microarchitecture at cellular resolution. The models integrate consensus detoxification reactions in each individual hepatocyte. We study the consequences of the two model types on the extrapolation and show in which cases these models perform better than the classical extrapolation strategy that is based either on the maximal drug concentration (Cmax) or the area under the pharmacokinetic curve (AUC) of the drug blood concentration. We find that an CL-model based on a well-mixed blood compartment is sufficient to correctly predict the in vivo toxicity from in vitro data. However, the ST-model that integrates more experimental information requires a change of at least one parameter to obtain the same prediction, indicating that spatial compartmentalization may indeed be an important factor.

Digital twin demonstrates significance of biomechanical growth control in liver regeneration after partial hepatectomy

Partial liver removal is an important therapy option for liver cancer. In most patients within a few weeks, the liver is able to fully regenerate. In some patients, however, regeneration fails with often severe consequences. To better understand the control mechanisms of liver regeneration, experiments in mice were performed, guiding the creation of a spatiotemporal 3D model of the regenerating liver. The model represents cells and blood vessels within an entire liver lobe, a macroscopic liver subunit. The model could reproduce the experimental data only if a biomechanical growth control (BGC)-mechanism, inhibiting cell cycle entrance at high compression, was taken into account and predicted that BGC may act as a short-range growth inhibitor minimizing the number of proliferating neighbor cells of a proliferating cell, generating a checkerboard-like proliferation pattern. Model-predicted cell proliferation patterns in pigs and mice were found experimentally. The results underpin the importance of biomechanical aspects in liver growth control.

A Novel Mouse Model of Nonalcoholic Steatohepatitis Suggests that Liver Fibrosis Initiates around Lipid-Laden Macrophages

While the interaction of cells such as macrophages and hepatic stellate cells is known to be involved in the generation of fibrosis in nonalcoholic steatohepatitis (NASH), the mechanism remains unclear. This study employed a high-fat/cholesterol/cholate (HFCC) diet to generate a model of NASH-related fibrosis to investigate the pathogenesis of fibrosis. Two mouse strains: C57BL/6J, the one susceptible to obesity, and A/J, the one relatively resistant to obesity, developed hepatic histologic features of NASH, including fat deposition, intralobular inflammation, hepatocyte ballooning, and fibrosis, after 9 weeks of HFCC diet. The severity of hepatic inflammation and fibrosis was greater in A/J mice than in the C57BL/6J mice. A/J mice fed HFCC diet exhibited characteristic CD204-positive lipid-laden macrophage aggregation in hepatic parenchyma. Polarized light was used to visualize the Maltese cross, cholesterol crystals within the aggregated macrophages. Fibrosis developed in a ring shape from the periphery of the aggregated macrophages such that the starting point of fibrosis could be visualized histologically. Matrix-assisted laser desorption/ionization mass spectrometry imaging analysis detected a molecule at m/z 772.462, which corresponds to the protonated ion of phosphatidylcholine [P-18:1 (11Z)/18:0] and phosphatidylethanolamine [18:0/20:2 (11Z, 14Z)], in aggregated macrophages adjacent to the fibrotic lesions. In conclusion, the HFCC diet-fed A/J model provides an ideal tool to study fibrogenesis and enables novel insights into the pathophysiology of NASH-related fibrosis.

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.

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.

A quantitative high-resolution computational mechanics cell model for growing and regenerating tissues

Mathematical models are increasingly designed to guide experiments in biology, biotechnology, as well as to assist in medical decision making. They are in particular important to understand emergent collective cell behavior. For this purpose, the models, despite still abstractions of reality, need to be quantitative in all aspects relevant for the question of interest. This paper considers as showcase example the regeneration of liver after drug-induced depletion of hepatocytes, in which the surviving and dividing hepatocytes must squeeze in between the blood vessels of a network to refill the emerged lesions. Here, the cells' response to mechanical stress might significantly impact the regeneration process. We present a 3D high-resolution cell-based model integrating information from measurements in order to obtain a refined and quantitative understanding of the impact of cell-biomechanical effects on the closure of drug-induced lesions in liver. Our model represents each cell individually and is constructed by a discrete, physically scalable network of viscoelastic elements, capable of mimicking realistic cell deformation and supplying information at subcellular scales. The cells have the capability to migrate, grow, and divide, and the nature and parameters of their mechanical elements can be inferred from comparisons with optical stretcher experiments. Due to triangulation of the cell surface, interactions of cells with arbitrarily shaped (triangulated) structures such as blood vessels can be captured naturally. Comparing our simulations with those of so-called center-based models, in which cells have a largely rigid shape and forces are exerted between cell centers, we find that the migration forces a cell needs to exert on its environment to close a tissue lesion, is much smaller than predicted by center-based models. To stress generality of the approach, the liver simulations were complemented by monolayer and multicellular spheroid growth simulations. In summary, our model can give quantitative insight in many tissue organization processes, permits hypothesis testing in silico, and guide experiments in situations in which cell mechanics is considered important.

Effects of a high protein diet and liver disease in an in silico model of human ammonia metabolism

BACKGROUND

After proteolysis, the majority of released amino acids from dietary protein are transported to the liver for gluconeogenesis or to peripheral tissues where they are used for protein synthesis and eventually catabolized, producing ammonia as a byproduct. High ammonia levels in the brain are a major contributor to the decreased neural function that occurs in several pathological conditions such as hepatic encephalopathy when liver urea cycle function is compromised. Therefore, it is important to gain a deeper understanding of human ammonia metabolism. The objective of this study was to predict changes in blood ammonia levels resulting from alterations in dietary protein intake, from liver disease, or from partial loss of urea cycle function.

METHODS

A simple mathematical model was created using MATLAB SimBiology and data from published studies. Simulations were performed and results analyzed to determine steady state changes in ammonia levels resulting from varying dietary protein intake and varying liver enzyme activity levels to simulate liver disease. As a toxicity reference, viability was measured in SH-SY5Y neuroblastoma cells following differentiation and ammonium chloride treatment.

RESULTS

Results from control simulations yielded steady state blood ammonia levels within normal physiological limits. Increasing dietary protein intake by 72% resulted in a 59% increase in blood ammonia levels. Simulations of liver cirrhosis increased blood ammonia levels by 41 to 130% depending upon the level of dietary protein intake. Simulations of heterozygous individuals carrying a loss of function allele of the urea cycle carbamoyl phosphate synthetase I (CPS1) gene resulted in more than a tripling of blood ammonia levels (from roughly 18 to 60 μM depending on dietary protein intake). The viability of differentiated SH-SY5Y cells was decreased by 14% by the addition of a slightly higher amount of ammonium chloride (90 μM).

CONCLUSIONS

Data from the model suggest decreasing protein consumption may be one simple strategy to decrease blood ammonia levels and minimize the risk of developing hepatic encephalopathy for many liver disease patients. In addition, the model suggests subjects who are known carriers of disease-causing CPS1 alleles may benefit from monitoring blood ammonia levels and limiting the level of protein intake if ammonia levels are high.

Hemodynamic changes in hepatic sinusoids of hepatic steatosis mice

BACKGROUND

Fatty liver (FL) is now a worldwide disease. For decades, researchers have been kept trying to elucidate the mechanism of FL at the molecular level, but rarely involve the study of morphology and medical physics. Traditionally, it was believed that hemodynamic changes occur only when fibrosis occurs, but it has been proved that these changes already show in steatosis stage, which may help to reveal the pathogenesis and its progress. Because the pseudolobules are not formed during the steatosis stage, this phenomenon may be caused by the compression of the liver microcirculation and changes in the hemodynamics.

AIM

To understand the pathogenesis of hepatic steatosis and to study the hemodynamic changes associated with hepatic steatosis.

METHODS

Eight-week-old male C57BL/6 mice were divided into three groups randomly (control group, 2-wk group, and 4-wk group), with 16 mice per group. A hepatic steatosis model was established by subcutaneous injection of carbon tetrachloride in mice. After establishing the model, liver tissue from mice was stained with hematoxylin and eosin (HE), and oil red O stains. Blood was collected from the angular vein, and hemorheological parameters were estimated. A two-photon fluorescence microscope was used to examine the flow properties of red blood cells in the hepatic sinusoids.

RESULTS

Oil red O staining indicated lipid accumulation in the liver after CCl₄ treatment. HE staining indicated narrowing of the hepatic sinusoidal vessels. No significant difference was observed between the 2-wk and 4-wk groups of mice on morphological examination. Hemorheological tests included whole blood viscosity (mPas, γ = 10 s-¹/γ = 100 s^-1) (8.83 ± 2.22/4.69 ± 1.16, 7.73 ± 2.46/4.22 ± 1.32, and 8.06 ± 2.88/4.22 ± 1.50), red blood cell volume (%) (51.00 ± 4.00, 42.00 ± 5.00, and 40.00 ± 3.00), the content of plasma fibrinase (g/L) (3.80 ± 0.50, 2.90 ± 0.80, and 2.30 ± 0.70), erythrocyte deformation index (%) (44.49 ± 5.81, 48.00 ± 15.29, and 44.36 ± 15.01), erythrocyte electrophoresis rate (mm/s per V/m) (0.55 ± 0.11, 0.50 ± 0.11, and 0.60 ± 0.20), revealing pathological changes in plasma components and red blood cells of hepatic steatosis. Assessment of blood flow velocity in the hepatic sinusoids with a laser Doppler flowmeter (mL/min per 100 g) (94.43 ± 14.64, 80.00 ± 12.12, and 67.26 ± 5.92) and two-photon laser scanning microscope (μm/s) (325.68 ± 112.66, 213.53 ± 65.33, and 173.26 ± 44.02) revealed that as the modeling time increased, the blood flow velocity in the hepatic sinusoids decreased gradually, and the diameter of the hepatic sinusoids became smaller (μm) (10.28 ± 1.40, 6.84 ± 0.93, and 5.82 ± 0.79).

CONCLUSION

The inner diameter of the hepatic sinusoids decreases along with the decrease in the blood flow velocity within the sinusoids and the changes in the systemic hemorheology.

Quantitative cell-based model predicts mechanical stress response of growing tumor spheroids over various growth conditions and cell lines

Model simulations indicate that the response of growing cell populations on mechanical stress follows the same functional relationship and is predictable over different cell lines and growth conditions despite experimental response curves look largely different. We develop a hybrid model strategy in which cells are represented by coarse-grained individual units calibrated with a high resolution cell model and parameterized by measurable biophysical and cell-biological parameters. Cell cycle progression in our model is controlled by volumetric strain, the latter being derived from a bio-mechanical relation between applied pressure and cell compressibility. After parameter calibration from experiments with mouse colon carcinoma cells growing against the resistance of an elastic alginate capsule, the model adequately predicts the growth curve in i) soft and rigid capsules, ii) in different experimental conditions where the mechanical stress is generated by osmosis via a high molecular weight dextran solution, and iii) for other cell types with different growth kinetics from the growth kinetics in absence of external stress. Our model simulation results suggest a generic, even quantitatively same, growth response of cell populations upon externally applied mechanical stress, as it can be quantitatively predicted using the same growth progression function.

Liver Regeneration: Different Sub-Populations of Parenchymal Cells at Play Choreographed by an Injury-Specific Microenvironment

Liver regeneration is crucial for the maintenance of liver functional mass during homeostasis and diseases. In a disease context-dependent manner, liver regeneration is contributed to by hepatocytes or progenitor cells. As long as they are replicatively competent, hepatocytes are the main cell type responsible for supporting liver size homeostasisand regeneration. The concept that all hepatocytes within the lobule have the same proliferative capacity but are differentially recruited according to the localization of the wound, or whether a yet to be defined sub-population of hepatocytes supports regeneration is still debated. In a chronically or severely injured liver, hepatocytes may enter a state of replicative senescence. In such conditions, small biliary cells activate and expand, a process called ductular reaction (DR). Work in the last few decades has demonstrated that DR cells can differentiate into hepatocytes and thereby contribute to parenchymal reconstitution. In this study we will review the molecular mechanisms supporting these two processes to determine potential targets that would be amenable for therapeutic manipulation to enhance liver regeneration.

Model Prediction and Validation of an Order Mechanism Controlling the Spatiotemporal Phenotype of Early Hepatocellular Carcinoma

Recently, hepatocyte-sinusoid alignment (HSA) has been identified as a mechanism that supports the coordination of hepatocytes during liver regeneration to reestablish a functional micro-architecture (Hoehme et al. in Proc Natl Acad Sci 107(23):10371-10376, 2010). HSA means that hepatocytes preferentially align along the closest micro-vessels. Here, we studied whether this mechanism is still active in early hepatocellular tumors. The same agent-based spatiotemporal model that previously correctly predicted HSA in liver regeneration was further developed to simulate scenarios in early tumor development, when individual initiated hepatocytes gain increased proliferation capacity. The model simulations were performed under conditions of realistic liver micro-architectures obtained from 3D reconstructions of confocal laser scanning micrographs. Interestingly, the established model predicted that initiated hepatocytes at first arrange in elongated patterns. Only when the tumor progresses to cell numbers of approximately 4000, does it adopt spherical structures. This prediction may have relevant consequences, since elongated tumors may reach critical structures faster, such as larger vessels, compared to a spherical tumor of similar cell number. Interestingly, this model prediction was confirmed by analysis of the spatial organization of initiated hepatocytes in a rat liver tumor initiation study using single doses of 250 mg/kg of the genotoxic carcinogen N-nitrosomorpholine (NNM). Indeed, small clusters of GST-P positive cells induced by NNM were elongated, almost columnar, while larger GDT-P positive foci of approximately the size of liver lobuli adopted spherical shapes. From simulations testing numerous possible mechanisms, only HSA could explain the experimentally observed initial deviation from spherical shape. The present study demonstrates that the architecture of small cell clusters of hepatocytes early after initiation is still controlled by physiological mechanisms. However, this coordinating influence is lost when the tumor grows to approximately 4000 cells, leading to further growth in spherical shape. Our findings stress the potential importance of organ micro-architecture in understanding tumor phenotypes.

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.

The balancing act of the liver: tissue regeneration versus fibrosis

Epithelial cell loss alters a tissue's optimal function and awakens evolutionarily adapted healing mechanisms to reestablish homeostasis. Although adult mammalian organs have a limited regeneration potential, the liver stands out as one remarkable exception. Following injury, the liver mounts a dynamic multicellular response wherein stromal cells are activated in situ and/or recruited from the bloodstream, the extracellular matrix (ECM) is remodeled, and epithelial cells expand to replenish their lost numbers. Chronic damage makes this response persistent instead of transient, tipping the system into an abnormal steady state known as fibrosis, in which ECM accumulates excessively and tissue function degenerates. Here we explore the cellular and molecular switches that balance hepatic regeneration and fibrosis, with a focus on uncovering avenues of disease modeling and therapeutic intervention.

A Liver-Centric Multiscale Modeling Framework for Xenobiotics

We describe a multi-scale, liver-centric in silico modeling framework for acetaminophen pharmacology and metabolism. We focus on a computational model to characterize whole body uptake and clearance, liver transport and phase I and phase II metabolism. We do this by incorporating sub-models that span three scales; Physiologically Based Pharmacokinetic (PBPK) modeling of acetaminophen uptake and distribution at the whole body level, cell and blood flow modeling at the tissue/organ level and metabolism at the sub-cellular level. We have used standard modeling modalities at each of the three scales. In particular, we have used the Systems Biology Markup Language (SBML) to create both the whole-body and sub-cellular scales. Our modeling approach allows us to run the individual sub-models separately and allows us to easily exchange models at a particular scale without the need to extensively rework the sub-models at other scales. In addition, the use of SBML greatly facilitates the inclusion of biological annotations directly in the model code. The model was calibrated using human in vivo data for acetaminophen and its sulfate and glucuronate metabolites. We then carried out extensive parameter sensitivity studies including the pairwise interaction of parameters. We also simulated population variation of exposure and sensitivity to acetaminophen. Our modeling framework can be extended to the prediction of liver toxicity following acetaminophen overdose, or used as a general purpose pharmacokinetic model for xenobiotics.

Multiscale modelling approaches for assessing cosmetic ingredients safety

The European Union's ban on animal testing for cosmetic ingredients and products has generated a strong momentum for the development of in silico and in vitro alternative methods. One of the focus of the COSMOS project was ab initio prediction of kinetics and toxic effects through multiscale pharmacokinetic modeling and in vitro data integration. In our experience, mathematical or computer modeling and in vitro experiments are complementary. We present here a summary of the main models and results obtained within the framework of the project on these topics. A first section presents our work at the organelle and cellular level. We then go toward modeling cell levels effects (monitored continuously), multiscale physiologically based pharmacokinetic and effect models, and route to route extrapolation. We follow with a short presentation of the automated KNIME workflows developed for dissemination and easy use of the models. We end with a discussion of two challenges to the field: our limited ability to deal with massive data and complex computations.

Computational Modeling of Spatiotemporal Ca(2+) Signal Propagation Along Hepatocyte Cords

OBJECTIVE

The purpose of this study is to model the dynamics of lobular Ca(2+) wave propagation induced by an extracellular stimulus, and to analyze the effect of spatially systematic variations in cell-intrinsic signaling parameters on sinusoidal Ca(2+) response.

METHODS

We developed a computational model of lobular scale Ca(2+) signaling that accounts for receptor- mediated initiation of cell-intrinsic Ca(2+) signal in hepatocytes and its propagation to neighboring hepatocytes through gap junction-mediated molecular exchange.

RESULTS

Analysis of the simulations showed that a pericentral-to-periportal spatial gradient in hormone sensitivity and/or rates of IP3 synthesis underlies the Ca(2+) wave propagation. We simulated specific cases corresponding to localized disruptions in the graded pattern of these parameters along a hepatic sinusoid. Simulations incorporating locally altered parameters exhibited Ca(2+) waves that do not propagate throughout the hepatic plate. Increased gap junction coupling restored normal Ca(2+) wave propagation when hepatocytes with low Ca(2+) signaling ability were localized in the midlobular or the pericentral region.

CONCLUSION

Multiple spatial patterns in intracellular signaling parameters can lead to Ca(2+) wave propagation that is consistent with the experimentally observed spatial patterns of Ca(2+) dynamics. Based on simulations and analysis, we predict that increased gap junction-mediated intercellular coupling can induce robust Ca(2+) signals in otherwise poorly responsive hepatocytes, at least partly restoring the sinusoidally oriented Ca (2+) waves.

SIGNIFICANCE

Our bottom-up model of agonist-evoked spatial Ca(2+) patterns can be integrated with detailed descriptions of liver histology to study Ca(2+) regulation at the tissue level.

Model-guided identification of a therapeutic strategy to reduce hyperammonemia in liver diseases

BACKGROUND & AIMS

Recently, spatial-temporal/metabolic mathematical models have been established that allow the simulation of metabolic processes in tissues. We applied these models to decipher ammonia detoxification mechanisms in the liver.

METHODS

An integrated metabolic-spatial-temporal model was used to generate hypotheses of ammonia metabolism. Predicted mechanisms were validated using time-resolved analyses of nitrogen metabolism, activity analyses, immunostaining and gene expression after induction of liver damage in mice. Moreover, blood from the portal vein, liver vein and mixed venous blood was analyzed in a time dependent manner.

RESULTS

Modeling revealed an underestimation of ammonia consumption after liver damage when only the currently established mechanisms of ammonia detoxification were simulated. By iterative cycles of modeling and experiments, the reductive amidation of alpha-ketoglutarate (α-KG) via glutamate dehydrogenase (GDH) was identified as the lacking component. GDH is released from damaged hepatocytes into the blood where it consumes ammonia to generate glutamate, thereby providing systemic protection against hyperammonemia. This mechanism was exploited therapeutically in a mouse model of hyperammonemia by injecting GDH together with optimized doses of cofactors. Intravenous injection of GDH (720 U/kg), α-KG (280 mg/kg) and NADPH (180 mg/kg) reduced the elevated blood ammonia concentrations (>200 μM) to levels close to normal within only 15 min.

CONCLUSION

If successfully translated to patients the GDH-based therapy might provide a less aggressive therapeutic alternative for patients with severe hyperammonemia.

A physiologically-based flow network model for hepatic drug elimination III: 2D/3D DLA lobule models

Background

One of the major issues in current pharmaceutical development is potential hepatotoxicity and drug-induced liver damage. This is due to the unique metabolic processes performed in the liver to prevent accumulation of a wide range of chemicals in the blood. Recently, we developed a physiologically-based lattice model to address the transport and metabolism of drugs in the liver lobule (liver functional unit).

Method

In this paper, we extend our idealized model to consider structural and spatial variability in two and three dimensions. We introduce a hexagonal-based model with one input (portal vein) and six outputs (hepatic veins) to represent a typical liver lobule. To capture even more realistic structures, we implement a novel sequential diffusion-limited aggregation (DLA) method to construct a morphological sinusoid network in the lobule. A 3D model constructed with stacks of multiple 2D sinusoid realizations is explored to study the effects of 3D structural variations. The role of liver zonation on drug metabolism in the lobule is also addressed, based on flow-based predicted steady-state O₂ profiles used as a zonation indicator.

Results

With this model, we analyze predicted drug concentration levels observed exiting the lobule with their detailed distribution inside the lobule, and compare with our earlier idealized models. In 2D, due to randomness of the sinusoidal structure, individual hepatic veins respond differently (i.e. at different times) to injected drug. In 3D, however, the variation of response to the injected drug is observed to be less extreme. Also, the production curves show more diffusive behavior in 3D than in 2D.

Conclusion

Although, the individual producing ports respond differently, the average lobule production summed over all hepatic veins is more diffuse. Thus the net effect of all these variations makes the overall response smoother. We also show that, in 3D, the effect of zonation on drug production characteristics appears quite small. Our new biophysical structural analysis of a physiologically-based 3D lobule can therefore form the basis for a quantitative assessment of liver function and performance both in health and disease

Electronic supplementary material

The online version of this article (doi:10.1186/s12976-016-0034-5) contains supplementary material, which is available to authorized users.

Inferring Growth Control Mechanisms in Growing Multi-cellular Spheroids of NSCLC Cells from Spatial-Temporal Image Data

We develop a quantitative single cell-based mathematical model for multi-cellular tumor spheroids (MCTS) of SK-MES-1 cells, a non-small cell lung cancer (NSCLC) cell line, growing under various nutrient conditions: we confront the simulations performed with this model with data on the growth kinetics and spatial labeling patterns for cell proliferation, extracellular matrix (ECM), cell distribution and cell death. We start with a simple model capturing part of the experimental observations. We then show, by performing a sensitivity analysis at each development stage of the model that its complexity needs to be stepwise increased to account for further experimental growth conditions. We thus ultimately arrive at a model that mimics the MCTS growth under multiple conditions to a great extent. Interestingly, the final model, is a minimal model capable of explaining all data simultaneously in the sense, that the number of mechanisms it contains is sufficient to explain the data and missing out any of its mechanisms did not permit fit between all data and the model within physiological parameter ranges. Nevertheless, compared to earlier models it is quite complex i.e., it includes a wide range of mechanisms discussed in biological literature. In this model, the cells lacking oxygen switch from aerobe to anaerobe glycolysis and produce lactate. Too high concentrations of lactate or too low concentrations of ATP promote cell death. Only if the extracellular matrix density overcomes a certain threshold, cells are able to enter the cell cycle. Dying cells produce a diffusive growth inhibitor. Missing out the spatial information would not permit to infer the mechanisms at work. Our findings suggest that this iterative data integration together with intermediate model sensitivity analysis at each model development stage, provide a promising strategy to infer predictive yet minimal (in the above sense) quantitative models of tumor growth, as prospectively of other tissue organization processes. Importantly, calibrating the model with two nutriment-rich growth conditions, the outcome for two nutriment-poor growth conditions could be predicted. As the final model is however quite complex, incorporating many mechanisms, space, time, and stochastic processes, parameter identification is a challenge. This calls for more efficient strategies of imaging and image analysis, as well as of parameter identification in stochastic agent-based simulations.

We here present how to parameterize a mathematical agent-based model of growing MCTS almost completely from experimental data. MCTS show a similar establishment of pathophysiological gradients and concentric arrangement of heterogeneous cell populations as found in avascular tumor nodules. We build a process chain of imaging, image processing and analysis, and mathematical modeling. In this model, each individual cell is represented by an agent populating one site of a three dimensional un-structured lattice. The spatio-temporal multi-cellular behavior, including migration, growth, division, death of each cell, is considered by a stochastic process, simulated numerically by the Gillespie algorithm. Processes on the molecular scale are described by deterministic partial differential equations for molecular concentrations, coupled to intracellular and cellular decision processes. The parameters of the multi-scale model are inferred from comparisons to the growth kinetics and from image analysis of spheroid cryosections stained for cell death, proliferation and collagen IV. Our final model assumes ATP to be the critical resource that cells try to keep constant over a wide range of oxygen and glucose medium concentrations, by switching between aerobic and anaerobic metabolism. Besides ATP, lactate is shown to be a possible explanation for the control of the necrotic core size. Direct confrontation of the model simulation results with image data on the spatial profiles of cell proliferation, ECM distribution and cell death, indicates that in addition, the effects of ECM and waste factors have to be added to explain the data. Hence the model is a tool to identify likely mechanisms at work that may subsequently be studied experimentally, proposing a model-guided experimental strategy.

Natural Killer Cells and Liver Fibrosis

In the 40 years since the discovery of natural killer (NK) cells, it has been well established that these innate lymphocytes are important for early and effective immune responses against transformed cells and infections with different pathogens. In addition to these classical functions of NK cells, we now know that they are part of a larger family of innate lymphoid cells and that they can even mediate memory-like responses. Additionally, tissue-resident NK cells with distinct phenotypical and functional characteristics have been identified. Here, we focus on the phenotype of different NK cell subpopulations that can be found in the liver and summarize the current knowledge about the functional role of these cells with a special emphasis on liver fibrosis. NK cell cytotoxicity can contribute to liver damage in different forms of liver disease. However, NK cells can limit liver fibrosis by killing hepatic stellate cell-derived myofibroblasts, which play a key role in this pathogenic process. Therefore, liver NK cells need to be tightly regulated in order to balance these beneficial and pathological effects.

Unraveling liver complexity from molecular to organ level: challenges and perspectives

Biological responses are determined by information processing at multiple and highly interconnected scales. Within a tissue the individual cells respond to extracellular stimuli by regulating intracellular signaling pathways that in turn determine cell fate decisions and influence the behavior of neighboring cells. As a consequence the cellular responses critically impact tissue composition and architecture. Understanding the regulation of these mechanisms at different scales is key to unravel the emergent properties of biological systems. In this perspective, a multidisciplinary approach combining experimental data with mathematical modeling is introduced. We report the approach applied within the Virtual Liver Network to analyze processes that regulate liver functions from single cell responses to the organ level using a number of examples. By facilitating interdisciplinary collaborations, the Virtual Liver Network studies liver regeneration and inflammatory processes as well as liver metabolic functions at multiple scales, and thus provides a suitable example to identify challenges and point out potential future application of multi-scale systems biology.