Building a 3D Virtual Liver: Methods for Simulating Blood Flow and Hepatic Clearance on 3D Structures

Mechanobiological stimulation in organ-on-a-chip systems reduces hepatic drug metabolic capacity in favor of regenerative specialization

Hepatic physiology depends on the liver's complex structural composition which among others, provides high oxygen supply rates, locally differential oxygen tension, endothelial paracrine signaling, as well as residual hemodynamic shear stress to resident hepatocytes. While functional improvements were shown by implementing these factors into hepatic culture systems, direct cause-effect relationships are often not well characterized-obfuscating their individual contribution in more complex microphysiological systems. By comparing increasingly complex hepatic in vitro culture systems that gradually implement these parameters, we investigate the influence of the cellular microenvironment to overall hepatic functionality in pharmacological applications. Here, hepatocytes were modulated in terms of oxygen tension and supplementation, endothelial coculture, and exposure to fluid shear stress delineated from oxygen influx. Results from transcriptomic and metabolomic evaluation indicate that particularly oxygen supply rates are critical to enhance cellular functionality-with cellular drug metabolism remaining comparable to physiological conditions after prolonged static culture. Endothelial signaling was found to be a major contributor to differential phenotype formation known as metabolic zonation, indicated by WNT pathway activity. Lastly, oxygen-delineated shear stress was identified to direct cellular fate towards increased hepatic plasticity and regenerative phenotypes at the cost of drug metabolic functionality - in line with regenerative effects observed in vivo. With these results, we provide a systematic evaluation of critical parameters and their impact in hepatic systems. Given their adherence to physiological effects in vivo, this highlights the importance of their implementation in biomimetic devices, such as organ-on-a-chip systems. Considering recent advances in basic liver biology, direct translation of physiological structures into in vitro models is a promising strategy to expand the capabilities of pharmacological models.

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.

From Seeing to Simulating: A Survey of Imaging Techniques and Spatially-Resolved Data for Developing Multiscale Computational Models of Liver Regeneration

Liver regeneration, which leads to the re-establishment of organ mass, follows a specifically organized set of biological processes acting on various time and length scales. Computational models of liver regeneration largely focused on incorporating molecular and signaling detail have been developed by multiple research groups in the recent years. These modeling efforts have supported a synthesis of disparate experimental results at the molecular scale. Incorporation of tissue and organ scale data using noninvasive imaging methods can extend these computational models towards a comprehensive accounting of multiscale dynamics of liver regeneration. For instance, microscopy-based imaging methods provide detailed histological information at the tissue and cellular scales. Noninvasive imaging methods such as ultrasound, computed tomography and magnetic resonance imaging provide morphological and physiological features including volumetric measures over time. In this review, we discuss multiple imaging modalities capable of informing computational models of liver regeneration at the organ-, tissue- and cellular level. Additionally, we discuss available software and algorithms, which aid in the analysis and integration of imaging data into computational models. Such models can be generated or tuned for an individual patient with liver disease. Progress towards integrated multiscale models of liver regeneration can aid in prognostic tool development for treating liver disease.

Automated Detection of Portal Fields and Central Veins in Whole-Slide Images of Liver Tissue

Many physiological processes and pathological phenomena in the liver tissue are spatially heterogeneous. At a local scale, biomarkers can be quantified along the axis of the blood flow, from portal fields (PFs) to central veins (CVs), i.e., in zonated form. This requires detecting PFs and CVs. However, manually annotating these structures in multiple whole-slide images is a tedious task. We describe and evaluate a fully automated method, based on a convolutional neural network, for simultaneously detecting PFs and CVs in a single stained section. Trained on scans of hematoxylin and eosin-stained liver tissue, the detector performed well with an F1 score of 0.81 compared to annotation by a human expert. It does, however, not generalize well to previously unseen scans of steatotic liver tissue with an F1 score of 0.59. Automated PF and CV detection eliminates the bottleneck of manual annotation for subsequent automated analyses, as illustrated by two proof-of-concept applications: We computed lobulus sizes based on the detected PF and CV positions, where results agreed with published lobulus sizes. Moreover, we demonstrate the feasibility of zonated quantification of biomarkers detected in different stainings based on lobuli and zones obtained from the detected PF and CV positions. A negative control (hematoxylin and eosin) showed the expected homogeneity, a positive control (glutamine synthetase) was quantified to be strictly pericentral, and a plausible zonation for a heterogeneous F4/80 staining was obtained. Automated detection of PFs and CVs is one building block for automatically quantifying physiologically relevant heterogeneity of liver tissue biomarkers. Perspectively, a more robust and automated assessment of zonation from whole-slide images will be valuable for parameterizing spatially resolved models of liver metabolism and to provide diagnostic information.

Hierarchical Modeling of the Liver Vascular System

The liver plays a key role in the metabolic homeostasis of the whole organism. To carry out its functions, it is endowed with a peculiar circulatory system, made of three main dendritic flow structures and lobules. Understanding the vascular anatomy of the liver is clinically relevant since various liver pathologies are related to vascular disorders. Here, we develop a novel liver circulation model with a deterministic architecture based on the constructal law of design over the entire scale range (from macrocirculation to microcirculation). In this framework, the liver vascular structure is a combination of superimposed tree-shaped networks and porous system, where the main geometrical features of the dendritic fluid networks and the permeability of the porous medium, are defined from the constructal viewpoint. With this model, we are able to emulate physiological scenarios and to predict changes in blood pressure and flow rates throughout the hepatic vasculature due to resection or thrombosis in certain portions of the organ, simulated as deliberate blockages in the blood supply to these sections. This work sheds light on the critical impact of the vascular network on mechanics-related processes occurring in hepatic diseases, healing and regeneration that involve blood flow redistribution and are at the core of liver resilience.

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.

A Negative Feedback Loop and Transcription Factor Cooperation Regulate Zonal Gene Induction by 2, 3, 7, 8-Tetrachlorodibenzo-p-Dioxin in the Mouse Liver

The cytochrome P450 (Cyp) proteins Cyp1A1 and Cyp1A2 are strongly induced in the mouse liver by the potent environmental toxicant 2, 3, 7, 8‐tetrachlorodibenzo‐p‐dioxin (TCDD), acting through the aryl hydrocarbon receptor (AHR). The induction of Cyp1A1 is localized within the centrilobular regions of the mouse liver at low doses of TCDD, progressing to pan‐lobular induction at higher doses. Even without chemical perturbation, metabolic functions and associated genes are basally zonated in the liver lobule along the central‐to‐portal axis. To investigate the mechanistic basis of spatially restricted gene induction by TCDD, we have developed a multiscale computational model of the mouse liver lobule with single‐cell resolution. The spatial location of individual hepatocytes in the model was calibrated from previously published high‐resolution images. A systems biology model of the network of biochemical signaling pathways underlying Cyp1A1 and Cyp1A2 induction was then incorporated into each hepatocyte in the model. Model simulations showed that a negative feedback loop formed by binding of the induced Cyp1A2 protein to TCDD, together with cooperative gene induction by the β‐catenin/AHR/TCDD transcription factor complex and β‐catenin, help produce the spatially localized induction pattern of Cyp1A1. Although endogenous WNT regulates the metabolic zonation of many genes, it was not a driver of zonal Cyp1A1 induction in our model. Conclusion: In this work, we used data‐driven computational modeling to identify the mechanistic basis of zonally restricted gene expression induced by the potent and persistent environmental pollutant TCDD. The multiscale model and derived results clarify the mechanisms of dose‐dependent hepatic gene induction responses to TCDD. Additionally, this work contributes to our broader understanding of spatial gene regulation along the liver lobule.

Vessel network extraction and analysis of mouse pulmonary vasculature via X-ray micro-computed tomographic imaging

In this work, non-invasive high-spatial resolution three-dimensional (3D) X-ray micro-computed tomography (μCT) of healthy mouse lung vasculature is performed. Methodologies are presented for filtering, segmenting, and skeletonizing the collected 3D images. Novel methods for the removal of spurious branch artefacts from the skeletonized 3D image are introduced, and these novel methods involve a combination of distance transform gradients, diameter-length ratios, and the fast marching method (FMM). These new techniques of spurious branch removal result in the consistent removal of spurious branches without compromising the connectivity of the pulmonary circuit. Analysis of the filtered, skeletonized, and segmented 3D images is performed using a newly developed Vessel Network Extraction algorithm to fully characterize the morphology of the mouse pulmonary circuit. The removal of spurious branches from the skeletonized image results in an accurate representation of the pulmonary circuit with significantly less variability in vessel diameter and vessel length in each generation. The branching morphology of a full pulmonary circuit is characterized by the mean diameter per generation and number of vessels per generation. The methods presented in this paper lead to a significant improvement in the characterization of 3D vasculature imaging, allow for automatic separation of arteries and veins, and for the characterization of generations containing capillaries and intrapulmonary arteriovenous anastomoses (IPAVA).

Impact of tumor-parenchyma biomechanics on liver metastatic progression: a multi-model approach

Colorectal cancer and other cancers often metastasize to the liver in later stages of the disease, contributing significantly to patient death. While the biomechanical properties of the liver parenchyma (normal liver tissue) are known to affect tumor cell behavior in primary and metastatic tumors, the role of these properties in driving or inhibiting metastatic inception remains poorly understood, as are the longer-term multicellular dynamics. This study adopts a multi-model approach to study the dynamics of tumor-parenchyma biomechanical interactions during metastatic seeding and growth. We employ a detailed poroviscoelastic model of a liver lobule to study how micrometastases disrupt flow and pressure on short time scales. Results from short-time simulations in detailed single hepatic lobules motivate constitutive relations and biological hypotheses for a minimal agent-based model of metastatic growth in centimeter-scale tissue over months-long time scales. After a parameter space investigation, we find that the balance of basic tumor-parenchyma biomechanical interactions on shorter time scales (adhesion, repulsion, and elastic tissue deformation over minutes) and longer time scales (plastic tissue relaxation over hours) can explain a broad range of behaviors of micrometastases, without the need for complex molecular-scale signaling. These interactions may arrest the growth of micrometastases in a dormant state and prevent newly arriving cancer cells from establishing successful metastatic foci. Moreover, the simulations indicate ways in which dormant tumors could "reawaken" after changes in parenchymal tissue mechanical properties, as may arise during aging or following acute liver illness or injury. We conclude that the proposed modeling approach yields insight into the role of tumor-parenchyma biomechanics in promoting liver metastatic growth, and advances the longer term goal of identifying conditions to clinically arrest and reverse the course of late-stage cancer.

The liver, a functionalized vascular structure

The liver is not only the largest organ in the body but also the one playing one of the most important role in the human metabolism as it is in charge of transforming toxic substances in the body. Understanding the way its blood vasculature works is key. In this work we show that the challenge of predicting the hepatic multi-scale vascular network can be met thanks to the constructal law of design evolution. The work unveils the structure of the liver blood flow architecture as a combination of superimposed tree-shaped networks and porous system. We demonstrate that the dendritic nature of the hepatic artery, portal vein and hepatic vein can be predicted, together with their geometrical features (diameter ratio, duct length ratio) as the entire blood flow architectures follow the principle of equipartition of imperfections. At the smallest scale, the shape of the liver elemental systems-the lobules-is discovered, while their permeability is also predicted. The theory is compared with good agreement to anatomical data from the literature.

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.

An image-based geometric model for numerical simulation of blood perfusion within the liver lobules

An image-based numerical algorithm is presented for simulating blood flow through the liver tissue. First, a geometric model is constructed by applying image processing techniques on a real microscopic image of a liver tissue. Then, incompressible blood flow through liver lobules is simulated. Effects of tissue heterogeneity and deformity, presence/absence of the second central vein in a particular lobule, and apparent sinusoids density in the liver cross section on the blood flow are investigated. Numerical results indicate that the existence of thick low permeability vascular septum, high permeability sinusoids, and lobule tissue heterogeneity can considerably affect interlobular and intralobular blood flow.

Resilience of three-dimensional sinusoidal networks in liver tissue

Can three-dimensional, microvasculature networks still ensure blood supply if individual links fail? We address this question in the sinusoidal network, a plexus-like microvasculature network, which transports nutrient-rich blood to every hepatocyte in liver tissue, by building on recent advances in high-resolution imaging and digital reconstruction of adult mice liver tissue. We find that the topology of the three-dimensional sinusoidal network reflects its two design requirements of a space-filling network that connects all hepatocytes, while using shortest transport routes: sinusoidal networks are sub-graphs of the Delaunay graph of their set of branching points, and also contain the corresponding minimum spanning tree, both to good approximation. To overcome the spatial limitations of experimental samples and generate arbitrarily-sized networks, we developed a network generation algorithm that reproduces the statistical features of 0.3-mm-sized samples of sinusoidal networks, using multi-objective optimization for node degree and edge length distribution. Nematic order in these simulated networks implies anisotropic transport properties, characterized by an empirical linear relation between a nematic order parameter and the anisotropy of the permeability tensor. Under the assumption that all sinusoid tubes have a constant and equal flow resistance, we predict that the distribution of currents in the network is very inhomogeneous, with a small number of edges carrying a substantial part of the flow-a feature known for hierarchical networks, but unexpected for plexus-like networks. We quantify network resilience in terms of a permeability-at-risk, i.e., permeability as function of the fraction of removed edges. We find that sinusoidal networks are resilient to random removal of edges, but vulnerable to the removal of high-current edges. Our findings suggest the existence of a mechanism counteracting flow inhomogeneity to balance metabolic load on the liver.

Liver Bioreactor Design Issues of Fluid Flow and Zonation, Fibrosis, and Mechanics: A Computational Perspective

Tissue engineering, with the goal of repairing or replacing damaged tissue and organs, has continued to make dramatic science-based advances since its origins in the late 1980’s and early 1990’s. Such advances are always multi-disciplinary in nature, from basic biology and chemistry through physics and mathematics to various engineering and computer fields. This review will focus its attention on two topics critical for tissue engineering liver development: (a) fluid flow, zonation, and drug screening, and (b) biomechanics, tissue stiffness, and fibrosis, all within the context of 3D structures. First, a general overview of various bioreactor designs developed to investigate fluid transport and tissue biomechanics is given. This includes a mention of computational fluid dynamic methods used to optimize and validate these designs. Thereafter, the perspective provided by computer simulations of flow, reactive transport, and biomechanics responses at the scale of the liver lobule and liver tissue is outlined, in addition to how bioreactor-measured properties can be utilized in these models. Here, the fundamental issues of tortuosity and upscaling are highlighted, as well as the role of disease and fibrosis in these issues. Some idealized simulations of the effects of fibrosis on lobule drug transport and mechanics responses are provided to further illustrate these concepts. This review concludes with an outline of some practical applications of tissue engineering advances and how efficient computational upscaling techniques, such as dual continuum modeling, might be used to quantify the transition of bioreactor results to the full liver scale.

Current knowledge in pathophysiology and management of Budd-Chiari syndrome and non-cirrhotic non-tumoral splanchnic vein thrombosis

Budd-Chiari syndrome and non-cirrhotic non-tumoral portal vein thrombosis are 2 rare disorders, with several similarities that are categorized under the term splanchnic vein thrombosis. Both disorders are frequently associated with an underlying prothrombotic disorder. They can cause severe portal hypertension and usually affect young patients, negatively influencing life expectancy when the diagnosis and treatment are not performed at an early stage. Yet, they have specific features that require individual consideration. The current review will focus on the available knowledge on pathophysiology, diagnosis and management of both entities.

A fully coupled porous media and channels flow approach for simulation of blood and bile flow through the liver lobules

Two dimensional, steady state, and incompressible blood and bile flows through the liver lobules are numerically simulated. Two different geometric models A and B are proposed to study the effects of lobule structure on the fluid flow behaviour. In Model A, the lobule tissue is represented as a hexagonal shape porous medium with a set of flow channels at its vertices accounting for the hepatic artery, portal and central veins along with bile ductules. Model B is a channelized porous medium constructed by adding a set of flow channels, representing the bile canaliculies and lobule sinusoids, to Model A. The bile and blood flow through the lobule is simulated by the finite element approach, based on the Darcy/Brinkman equations in the lobule tissue and the Navier-Stokes (or Stokes) equations in the flow channels. In Model B, a transmission factor on the boundaries of the bile canaliculies is introduced to connect the bile and blood flows. First, a single regular lobule is utilized to exhibit the fluid flow pattern through the liver lobule represented by proposed geometric models. Then, the model is extended to a group of liver lobules to demonstrate the flow through a liver slice represented by irregular lobules. Numerical results indicate that the Darcy and Brinkman equations provide nearly the same solutions for Model A and similar solutions with a little difference for Model B. It is shown that the existence of sinusoids and bile canaliculies inside the liver lobules has noticeable effects on its fluid flow pattern, in terms of pressure and velocity fields.

Better prediction of the local concentration-effect relationship: the role of physiologically based pharmacokinetics and quantitative systems pharmacology and toxicology in the evolution of model-informed drug discovery and development

Model-informed drug discovery and development (MID3) is an umbrella term under which sit several computational approaches: quantitative systems pharmacology (QSP), quantitative systems toxicology (QST) and physiologically based pharmacokinetics (PBPK). QSP models are built using mechanistic knowledge of the pharmacological pathway focusing on the putative mechanism of drug efficacy; whereas QST models focus on safety and toxicity issues and the molecular pathways and networks that drive these adverse effects. These can be mediated through exaggerated on-target or off-target pharmacology, immunogenicity or the physiochemical nature of the compound. PBPK models provide a mechanistic description of individual organs and tissues to allow the prediction of the intra- and extra-cellular concentration of the parent drug and metabolites under different conditions. Information on biophase concentration enables the prediction of a drug effect in different organs and assessment of the potential for drug-drug interactions. Together, these modelling approaches can inform the exposure-response relationship and hence support hypothesis generation and testing, compound selection, hazard identification and risk assessment through to clinical proof of concept (POC) and beyond to the market.

Scaling behavior of drug transport and absorption in in silico cerebral capillary networks

Drug delivery to the brain is challenging due to the presence of the blood-brain barrier. Mathematical modeling and simulation are essential tools for the deeper understanding of transport processes in the blood, across the blood-brain barrier and within the tissue. Here we present a mathematical model for drug delivery through capillary networks with increasingly complex topologies with the goal to understand the scaling behavior of model predictions on a coarse-to-fine sequence of grids. We apply our model to the delivery of L-Dopa, the primary drug used in the therapy of Parkinson’s Disease. Our model replicates observed blood flow rates and ratios between plasma and tissue concentrations. We propose an optimal network grain size for the simulation of tissue volumes of 1 cm³ that allows to make reliable predictions with reasonable computational costs.

Targeting Ligand Specificity Linked to Tumor Tissue Topological Heterogeneity via Single-Cell Micro-Pharmacological Modeling

Targeted therapy has held promise to be a successful anticancer treatment due to its specificity towards tumor cells that express the target receptors. However, not all targeting drugs used in the clinic are equally effective in tumor eradication. To examine which biochemical and biophysical properties of targeted agents are pivotal for their effective distribution inside the tumor and their efficient cellular uptake, we combine mathematical micro-pharmacological modeling with in vivo imaging of targeted human xenograft tumors in SCID mice. The mathematical model calibrated to experimental data was used to explore properties of the targeting ligand (diffusion and affinity) and ligand release schemes (rates and concentrations) with a goal to identify the properties of cells and ligands that enable high receptor saturation. By accounting for heterogeneities typical of in vivo tumors, our model was able to identify cell- and tissue-level barriers to efficient drug uptake. This work provides a base for utilizing experimentally measurable properties of a ligand-targeted agent and patient-specific attributes of the tumor tissue to support the development of novel targeted imaging agents and for improvement in their delivery to individual tumor cells.