Analysis and algorithmic generation of hepatic vascular systems

Approaches to vascular network, blood flow, and metabolite distribution modeling in brain tissue

The cardiovascular system plays a key role in the transport of nutrients, ensuring a continuous supply of all cells of the body with the metabolites necessary for life. The blood supply to the brain is carried out by the large arteries located on its surface, which branch into smaller arterioles that penetrate the cerebral cortex and feed the capillary bed, thereby forming an extensive branching network. The formation of blood vessels is carried out via vasculogenesis and angiogenesis, which play an important role in both embryo and adult life. The review presents approaches to modeling various aspects of both the formation of vascular networks and the construction of the formed arterial tree. In addition, a brief description of models that allows one to study the blood flow in various parts of the circulatory system and the spatiotemporal metabolite distribution in brain tissues is given. Experimental study of these issues is not always possible due to both the complexity of the cardiovascular system and the mechanisms through which the perfusion of all body cells is carried out. In this regard, mathematical models are a good tool for studying hemodynamics and can be used in clinical practice to diagnose vascular diseases and assess the need for treatment.

In silico simulation of hepatic arteries: An open-source algorithm for efficient synthetic data generation

BACKGROUND

In silico testing of novel image reconstruction and quantitative algorithms designed for interventional imaging requires realistic high-resolution modeling of arterial trees with contrast dynamics. Furthermore, data synthesis for training of deep learning algorithms requires that an arterial tree generation algorithm be computationally efficient and sufficiently random.

PURPOSE

The purpose of this paper is to provide a method for anatomically and physiologically motivated, computationally efficient, random hepatic arterial tree generation.

METHODS

The vessel generation algorithm uses a constrained constructive optimization approach with a volume minimization-based cost function. The optimization is constrained by the Couinaud liver classification system to assure a main feeding artery to each Couinaud segment. An intersection check is included to guarantee non-intersecting vasculature and cubic polynomial fits are used to optimize bifurcation angles and to generate smoothly curved segments. Furthermore, an approach to simulate contrast dynamics and respiratory and cardiac motion is also presented.

RESULTS

The proposed algorithm can generate a synthetic hepatic arterial tree with 40 000 branches in 11 s. The high-resolution arterial trees have realistic morphological features such as branching angles (MAD with Murray's law= 1.2 ± 1 . 2 o $ = \;1.2 \pm {1.2^o}$ ), radii (median Murray deviation= 0.08 $ = \;0.08$ ), and smoothly curved, non-intersecting vessels. Furthermore, the algorithm assures a main feeding artery to each Couinaud segment and is random (variability = 0.98 ± 0.01).

CONCLUSIONS

This method facilitates the generation of large datasets of high-resolution, unique hepatic angiograms for the training of deep learning algorithms and initial testing of novel 3D reconstruction and quantitative algorithms designed for interventional imaging.

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.

Rigorous mathematical optimization of synthetic hepatic vascular trees

In this paper, we introduce a new framework for generating synthetic vascular trees, based on rigorous model-based mathematical optimization. Our main contribution is the reformulation of finding the optimal global tree geometry into a nonlinear optimization problem (NLP). This rigorous mathematical formulation accommodates efficient solution algorithms such as the interior point method and allows us to easily change boundary conditions and constraints applied to the tree. Moreover, it creates trifurcations in addition to bifurcations. A second contribution is the addition of an optimization stage for the tree topology. Here, we combine constrained constructive optimization (CCO) with a heuristic approach to search among possible tree topologies. We combine the NLP formulation and the topology optimization into a single algorithmic approach. Finally, we attempt the validation of our new model-based optimization framework using a detailed corrosion cast of a human liver, which allows a quantitative comparison of the synthetic tree structure with the tree structure determined experimentally down to the fifth generation. The results show that our new framework is capable of generating asymmetric synthetic trees that match the available physiological corrosion cast data better than trees generated by the standard CCO approach.

Techniques and Algorithms for Hepatic Vessel Skeletonization in Medical Images: A Survey

Hepatic vessel skeletonization serves as an important means of hepatic vascular analysis and vessel segmentation. This paper presents a survey of techniques and algorithms for hepatic vessel skeletonization in medical images. We summarized the latest developments and classical approaches in this field. These methods are classified into five categories according to their methodological characteristics. The overview and brief assessment of each category are provided in the corresponding chapters, respectively. We provide a comprehensive summary among the cited publications, image modalities and datasets from various aspects, which hope to reveal the pros and cons of every method, summarize its achievements and discuss the challenges and future trends.

Opposite response of blood vessels in the retina to 6° head-down tilt and long-duration microgravity

The Spaceflight Associated Neuro-ocular Syndrome (SANS), associated with the headward fluid shifts incurred in microgravity during long-duration missions, remains a high-priority health and performance risk for human space exploration. To help characterize the pathophysiology of SANS, NASA's VESsel GENeration Analysis (VESGEN) software was used to map and quantify vascular adaptations in the retina before and after 70 days of bed rest at 6-degree Head-Down Tilt (HDT), a well-studied microgravity analog. Results were compared to the retinal vascular response of astronauts following 6-month missions to the International Space Station (ISS). By mixed effects modeling, the trends of vascular response were opposite. Vascular density decreased significantly in the 16 retinas of eight astronauts and in contrast, increased slightly in the ten retinas of five subjects after HDT (although with limited significance). The one astronaut retina diagnosed with SANS displayed the greatest vascular loss. Results suggest that microgravity is a major variable in the retinal mediation of fluid shifts that is not reproduced in this HDT bed rest model.

Living Donor-Recipient Pair Matching for Liver Transplant via Ternary Tree Representation With Cascade Incremental Learning

Visual understanding of liver vessels anatomy between the living donor-recipient (LDR) pair can assist surgeons to optimize transplant planning by avoiding non-targeted arteries which can cause severe complications. We propose to visually analyze the anatomical variants of the liver vessels anatomy to maximize similarity for finding a suitable Living Donor-Recipient (LDR) pair. Liver vessels are segmented from computed tomography angiography (CTA) volumes by employing a cascade incremental learning (CIL) model. Our CIL architecture is able to find optimal solutions, which we use to update the model with liver vessel CTA images. A novel ternary tree based algorithm is proposed to map all the possible liver vessel variants into their respective tree topologies. The tree topologies of the recipient's and donor's liver vessels are then used for an appropriate matching. The proposed algorithm utilizes a set of defined vessel tree variants which are updated to maintain the maximum matching options by leveraging the accurate segmentation results of the vessels derived from the incremental learning ability of the CIL. We introduce a novel concept of in-order digital string based comparison to match the geometry of two anatomically varied trees. Experiments through visual illustrations and quantitative analysis demonstrated the effectiveness of our approach compared to state-of-the-art.

Decreased Vascular Patterning in the Retinas of Astronaut Crew Members as New Measure of Ocular Damage in Spaceflight-Associated Neuro-ocular Syndrome

Purpose

Ocular structural and functional changes, collectively termed spaceflight-associated neuro-ocular syndrome (SANS), have been described in astronauts undergoing long-duration missions in the microgravity environment of the International Space Station. We tested the hypothesis that retinal vascular remodeling, particularly by smaller vessels, mediates the chronic headward fluid shifts associated with SANS.

Methods

As a retrospective study, arterial and venous patterns extracted from 30° infrared Heidelberg Spectralis retinal images of eight crew members acquired before and after six-month missions were analyzed with NASA's recently released VESsel GENeration Analysis (VESGEN) software. Output parameters included the fractal dimension and overall vessel length density that was further classified into large and small vascular branching generations. Vascular results were compared with SANS-associated clinical ocular measures.

Results

Significant postflight decreases in Df, Lv, and in smaller but not larger vessels were quantified in 11 of 16 retinas for arteries and veins (P value for Df, Lv, and smaller vessels in all 16 retinas were ≤0.033). The greatest vascular decreases occurred in the only retina displaying clinical evidence of SANS by choroidal folds and optic disc edema. In the remaining 15 retinas, decreases in vascular density from Df and Lv ranged from minimal to high by a custom Subclinical Vascular Pathology Index.

Conclusions

Together with VESGEN, the Subclinical Vascular Pathology Index may represent a new, useful SANS biomarker for advancing the understanding of SANS etiology and developing successful countermeasures for long duration space exploration in microgravity, although further research is required to better characterize retinal microvascular adaptations.

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.

An in silico pipeline for subject-specific hemodynamics analysis in liver surgery planning

The progresses in fast simulations of the hepatic flow in subject-specific vascular tree have created new toolkits for pre-surgical planning. The aim of this short communication is to introduce a computational pipeline that integrates several recently developed in silico liver models and algorithms. Firstly, a semi-automatic segmentation pipeline is used to digitise hepatic vessels. Then, a constructive constraint optimisation (CCO) algorithm is used to extend the digitised vascular tree, and also to compute the blood pressure and flow velocity in the tree. Couinaud segments are simulated from the diffusion zones of the portal venous tree. The constructed surgical planning model is then deployed cross-platform for use in various scenarios.

Anatomically based simulation of hepatic perfusion in the human liver

Liver structures of a healthy subject are digitised and segmented from computed tomography (CT) images, and hepatic perfusion is modelled in the hepatic artery and portal vein of the healthy subject with structured tree-based outflow boundary conditions. This self-similar structured tree is widely used in the literature, eg, blood flow simulation in larger systemic arteries and cerebral circulation, and is used in this study to model the effect of the smaller hepatic arteries and arterioles, as well as the smaller hepatic portal veins and portal venules. Physiologically reasonable results are obtained. Since the structured tree terminates at the size of the microvasculature system in liver lobules, the structured tree boundary condition will enable the proposed organ-level model of hepatic arterial flow to be easily connected to tissue-level models of liver lobules. Blood flow in the hepatic vein is also modelled in this subject with three-element Windkessel model as outflow boundary conditions. The benefit of integrating the perfusion in all hepatic vascular vessels is that it helps us analyse some complicated clinical phenomenon more efficiently, eg, one possible application is to obtain the portal pressure gradient (PPG) to help examine the reliability of hepatic venous pressure gradient (HVPG) as an indirect measure of portal pressure. Moreover, since four to six generations of hepatic vessels, which are sufficient for liver classification analysis, were employed in the model, this study is setting the computational foundation of a potentially handy surgical tool.

Fundamental constraints of vessels network architecture properties revealed by reconstruction of a rat brain vasculature

The studies of mammalian vasculature are an essential part of biomedical research, enabling the development of physiological understanding and forming the background of medical techniques and therapy. Despite the fact that the basic principles of vessel network description were established in the first quarter of the twentieth century, a digital model describing the vasculature in full accordance with experimental data has not yet been created. In the present study, we combine the determined structure design of basic arterial vessels with the stochastic creation of small vessel networks. By the example of rat brain arterial network model it was shown that the arterial blood volume and the magnitude of the blood flow impose a limitation on the network architecture. In particular, the bifurcation exponent (γ) should not be less than 2.7, and the optimal value of this parameter lies in the range of 2.9-3.0. Although the networks with a low γ appear as branched and complex, they do not fill out the phantom properly. Thus, the architecture of the vasculature is fundamentally determined by topological geometrical parameters.

Modeling sphere dynamics in blood vessels for SIRT pre-planning - To fathom the potential and limitations

For selective internal radiation therapy (SIRT) the calculation of the 3D distribution of spheres based on individual blood flow properties is still an open and relevant research question. The purpose of this work is to develop and analyze a new treatment planning method for SIRT to calculate the absorbed dose distribution. For this intention, flow dynamics of the SIRT-spheres inside the blood vessels was simulated. The challenge is treatment planning solely using high-resolution imaging data available before treatment. The resolution required to reliably predict the sphere distribution and hence the dose was investigated. For this purpose, arteries of the liver were segmented from a contrast-enhanced angiographic CT. Due to the limited resolution of the given CT, smaller vessels were generated via a vessel model. A combined 1D/3D-flow simulation model was implemented to simulate the final 3D distribution of spheres and dose. Results were evaluated against experimental data from Y90-PET. Analysis showed that the resolution of the vessels within the angiographic CT of about 0.5mm should be improved to a limit of about 150μm to reach a reliable prediction.

Modeling of the contrast-enhanced perfusion test in liver based on the multi-compartment flow in porous media

The paper deals with modeling the liver perfusion intended to improve quantitative analysis of the tissue scans provided by the contrast-enhanced computed tomography (CT). For this purpose, we developed a model of dynamic transport of the contrast fluid through the hierarchies of the perfusion trees. Conceptually, computed time-space distributions of the so-called tissue density can be compared with the measured data obtained from CT; such a modeling feedback can be used for model parameter identification. The blood flow is characterized at several scales for which different models are used. Flows in upper hierarchies represented by larger branching vessels are described using simple 1D models based on the Bernoulli equation extended by correction terms to respect the local pressure losses. To describe flows in smaller vessels and in the tissue parenchyma, we propose a 3D continuum model of porous medium defined in terms of hierarchically matched compartments characterized by hydraulic permeabilities. The 1D models corresponding to the portal and hepatic veins are coupled with the 3D model through point sources, or sinks. The contrast fluid saturation is governed by transport equations adapted for the 1D and 3D flow models. The complex perfusion model has been implemented using the finite element and finite volume methods. We report numerical examples computed for anatomically relevant geometries of the liver organ and of the principal vascular trees. The simulated tissue density corresponding to the CT examination output reflects a pathology modeled as a localized permeability deficiency.

Computational modelling of the cerebral cortical microvasculature: effect of x-ray microbeams versus broad beam irradiation

Microbeam Radiation Therapy is an innovative pre-clinical strategy which uses arrays of parallel, tens of micrometres wide kilo-voltage photon beams to treat tumours. These x-ray beams are typically generated on a synchrotron source. It was shown that these beam geometries allow exceptional normal tissue sparing from radiation damage while still being effective in tumour ablation. A final biological explanation for this enhanced therapeutic ratio has still not been found, some experimental data support an important role of the vasculature. In this work, the effect of microbeams on a normal microvascular network of the cerebral cortex was assessed in computer simulations and compared to the effect of homogeneous, seamless exposures at equal energy absorption. The anatomy of a cerebral microvascular network and the inflicted radiation damage were simulated to closely mimic experimental data using a novel probabilistic model of radiation damage to blood vessels. It was found that the spatial dose fractionation by microbeam arrays significantly decreased the vascular damage. The higher the peak-to-valley dose ratio, the more pronounced the sparing effect. Simulations of the radiation damage as a function of morphological parameters of the vascular network demonstrated that the distribution of blood vessel radii is a key parameter determining both the overall radiation damage of the vasculature and the dose-dependent differential effect of microbeam irradiation.

A multilevel framework to reconstruct anatomical 3D models of the hepatic vasculature in rat livers

The intricate (micro)vascular architecture of the liver has not yet been fully unravelled. Although current models are often idealized simplifications of the complex anatomical reality, correct morphological information is instrumental for scientific and clinical purposes. Previously, both vascular corrosion casting (VCC) and immunohistochemistry (IHC) have been separately used to study the hepatic vasculature. Nevertheless, these techniques still face a number of challenges such as dual casting in VCC and limited imaging depths for IHC. We have optimized both techniques and combined their complementary strengths to develop a framework for multilevel reconstruction of the hepatic circulation in the rat. The VCC and micro-CT scanning protocol was improved by enabling dual casting, optimizing the contrast agent concentration, and adjusting the viscosity of the resin (PU4ii). IHC was improved with an optimized clearing technique (CUBIC) that extended the imaging depth for confocal microscopy more than five-fold. Using in-house developed software (DeLiver), the vascular network - in both VCC and IHC datasets - was automatically segmented and/or morphologically analysed. Our methodological framework allows 3D reconstruction and quantification of the hepatic circulation, ranging from the major blood vessels down to the intertwined and interconnected sinusoids. We believe that the presented framework will have value beyond studies of the liver, and will facilitate a better understanding of various parenchymal organs in general, in physiological and pathological circumstances.

Roadmap for cardiovascular circulation model

Computational models of many aspects of the mammalian cardiovascular circulation have been developed. Indeed, along with orthopaedics, this area of physiology is one that has attracted much interest from engineers, presumably because the equations governing blood flow in the vascular system are well understood and can be solved with well-established numerical techniques. Unfortunately, there have been only a few attempts to create a comprehensive public domain resource for cardiovascular researchers. In this paper we propose a roadmap for developing an open source cardiovascular circulation model. The model should be registered to the musculo-skeletal system. The computational infrastructure for the cardiovascular model should provide for near real-time computation of blood flow and pressure in all parts of the body. The model should deal with vascular beds in all tissues, and the computational infrastructure for the model should provide links into CellML models of cell function and tissue function. In this work we review the literature associated with 1D blood flow modelling in the cardiovascular system, discuss model encoding standards, software and a model repository. We then describe the coordinate systems used to define the vascular geometry, derive the equations and discuss the implementation of these coupled equations in the open source computational software OpenCMISS. Finally, some preliminary results are presented and plans outlined for the next steps in the development of the model, the computational software and the graphical user interface for accessing the model.

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

In this paper, we develop a spatio-temporal modeling approach to describe blood and drug flow, as well as drug uptake and elimination, on an approximation of the liver. Extending on previously developed computational approaches, we generate an approximation of a liver, which consists of a portal and hepatic vein vasculature structure, embedded in the surrounding liver tissue. The vasculature is generated via constrained constructive optimization, and then converted to a spatial grid of a selected grid size. Estimates for surrounding upscaled lobule tissue properties are then presented appropriate to the same grid size. Simulation of fluid flow and drug metabolism (hepatic clearance) are completed using discretized forms of the relevant convective-diffusive-reactive partial differential equations for these processes. This results in a single stage, uniformly consistent method to simulate equations for blood and drug flow, as well as drug metabolism, on a 3D structure representative of a liver.

Quantification of Hepatic Vascular and Parenchymal Regeneration in Mice

BACKGROUND

Liver regeneration consists of cellular proliferation leading to parenchymal and vascular growth. This study complements previous studies on cellular proliferation and weight recovery by (1) quantitatively describing parenchymal and vascular regeneration, and (2) determining their relationship. Both together are needed to (3) characterize the underlying growth pattern.

METHODS

Specimens were created by injecting a polymerizing contrast agent in either portal or hepatic vein in normal or regenerating livers after 70% partial hepatectomy. 3D image data were obtained through micro-CT scanning. Parenchymal growth was assessed by determining weight and volume of the regenerating liver. Vascular growth was described by manually determined circumscribed parameters (maximal vessel length and radius of right inferior portal/hepatic vein), automatically determined cumulative parameters (total edge length and total vascular volume), and parameters describing vascular density (total edge length/volume, vascular volume fraction). The growth pattern was explored by comparing the relative increase of these parameters to the increase expected in case of isotropic expansion.

RESULTS

Liver volume recovery paralleled weight recovery and reached 90% of the original liver volume within 7 days. Comparing radius-related vascular parameters immediately after surgical resection and after virtual resection in-silico revealed a slight increase, possibly reflecting the effect of resection-induced portal hyperperfusion. Comparing length-related parameters between post-operative day 7 and after virtual resection showed similar vascular growth in both vascular systems investigated. In contrast, radius-related parameters increased slightly more in the portal vein. Despite the seemingly homogeneous 3D growth, the observed vascular parameters were not compatible with the hypothesis of isotropic expansion of liver parenchyma and vascular structures.

CONCLUSION

We present an approach for the quantitative analysis of the vascular systems of regenerating mouse livers. We applied this technique for assessing the hepatic growth pattern. Prospectively, this approach can be used to investigate hepatic vascular regeneration under different conditions.

Cholestasis-induced adaptive remodeling of interlobular bile ducts

Cholestasis is a common complication in liver diseases that triggers a proliferative response of the biliary tree. Bile duct ligation (BDL) is a frequently used model of cholestasis in rodents. To determine which changes occur in the three-dimensional (3D) architecture of the interlobular bile duct during cholestasis, we used 3D confocal imaging, surface reconstructions, and automated image quantification covering a period up to 28 days after BDL. We show a highly reproducible sequence of interlobular duct remodeling, where cholangiocyte proliferation initially causes corrugation of the luminal duct surface, leading to an approximately five-fold increase in surface area. This is analogous to the function of villi in the intestine or sulci in the brain, where an expansion of area is achieved within a restricted volume. The increase in surface area is further enhanced by duct branching, branch elongation, and loop formation through self-joining, whereby an initially relatively sparse mesh surrounding the portal vein becomes five-fold denser through elongation, corrugation, and ramification. The number of connections between the bile duct and the lobular bile canalicular network by the canals of Hering decreases proportionally to the increase in bile duct length, suggesting that no novel connections are established. The diameter of the interlobular bile duct remains constant after BDL, a response that is qualitatively distinct from that of large bile ducts, which tend to enlarge their diameters. Therefore, volume enhancement is only due to net elongation of the ducts. Because curvature and tortuosity of the bile duct are unaltered, this enlargement of the biliary tree is caused by branching and not by convolution.

CONCLUSION

BDL causes adaptive remodeling that aims at optimizing the intraluminal surface area by way of corrugation and branching.

Living Donor Liver Transplantation in Children: Surgical and Immunological Results in 250 Recipients at Université Catholique de Louvain

OBJECTIVES

To evaluate the outcome of pediatric living donor liver transplantation (LDLT) regarding portal vein (PV) reconstruction, ABO compatibility, and impact of maternal donation on graft acceptance.

BACKGROUND

LDLT and ABO-mismatched transplantation constitute feasible options to alleviate organ shortage in children. Vascular complications of portal hypoplasia in biliary atresia (BA) and acute rejection (AR) are still major concerns in this field.

METHODS

Data from 250 pediatric LDLT recipients, performed at Cliniques Universitaires Saint-Luc between July 1993 and June 2012, were collected retrospectively. Results were analyzed according to ABO matching and PV complications. Uni- and multivariate analyses were performed to study the impact of immunosuppression, sex matching, and maternal donation on AR rate.

RESULTS

Overall, the 10-year patient survival rate was 93.2%. Neither patient or graft loss nor vascular rejection, nor hemolysis, was encountered in the ABO nonidentical patients (n = 58), provided pretransplant levels of relevant isoagglutinins were below 1/16. In BA recipients, the rate of PV complications was lower after portoplasty (4.6%) than after truncal PV anastomosis (9.8%) and to jump graft interposition (26.9%; P = 0.027). In parental donation, maternal grafts were associated with higher 1-year AR-free survival (55.2%) than paternal grafts (39.8%; P = 0.041), but only in BA patients.

CONCLUSIONS

LDLT, including ABO-mismatched transplantation, constitutes a safe and efficient therapy for liver failure in children. In BA patients with PV hypoplasia, portoplasty seems to constitute the best technique for PV reconstruction. Maternal donation might be a protective factor for AR.

Geometrical force constraint method for vessel and x-ray angiogram simulation

This study proposes a novel geometrical force constraint method for 3-D vasculature modeling and angiographic image simulation. For this method, space filling force, gravitational force, and topological preserving force are proposed and combined for the optimization of the topology of the vascular structure. The surface covering force and surface adhesion force are constructed to drive the growth of the vasculature on any surface. According to the combination effects of the topological and surface adhering forces, a realistic vasculature can be effectively simulated on any surface. The image projection of the generated 3-D vascular structures is simulated according to the perspective projection and energy attenuation principles of X-rays. Finally, the simulated projection vasculature is fused with a predefined angiographic mask image to generate a realistic angiogram. The proposed method is evaluated on a CT image and three generally utilized surfaces. The results fully demonstrate the effectiveness and robustness of the proposed method.

Representative Sinusoids for Hepatic Four-Scale Pharmacokinetics Simulations

The mammalian liver plays a key role for metabolism and detoxification of xenobiotics in the body. The corresponding biochemical processes are typically subject to spatial variations at different length scales. Zonal enzyme expression along sinusoids leads to zonated metabolization already in the healthy state. Pathological states of the liver may involve liver cells affected in a zonated manner or heterogeneously across the whole organ. This spatial heterogeneity, however, cannot be described by most computational models which usually consider the liver as a homogeneous, well-stirred organ.

The goal of this article is to present a methodology to extend whole-body pharmacokinetics models by a detailed liver model, combining different modeling approaches from the literature. This approach results in an integrated four-scale model, from single cells via sinusoids and the organ to the whole organism, capable of mechanistically representing metabolization inhomogeneity in livers at different spatial scales. Moreover, the model shows circulatory mixing effects due to a delayed recirculation through the surrounding organism.

To show that this approach is generally applicable for different physiological processes, we show three applications as proofs of concept, covering a range of species, compounds, and diseased states: clearance of midazolam in steatotic human livers, clearance of caffeine in mouse livers regenerating from necrosis, and a parameter study on the impact of different cell entities on insulin uptake in mouse livers.

The examples illustrate how variations only discernible at the local scale influence substance distribution in the plasma at the whole-body level. In particular, our results show that simultaneously considering variations at all relevant spatial scales may be necessary to understand their impact on observations at the organism scale.

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.

Spatio-temporal simulation of first pass drug perfusion in the liver

The liver is the central organ for detoxification of xenobiotics in the body. In pharmacokinetic modeling, hepatic metabolization capacity is typically quantified as hepatic clearance computed as degradation in well-stirred compartments. This is an accurate mechanistic description once a quasi-equilibrium between blood and surrounding tissue is established. However, this model structure cannot be used to simulate spatio-temporal distribution during the first instants after drug injection. In this paper, we introduce a new spatially resolved model to simulate first pass perfusion of compounds within the naive liver. The model is based on vascular structures obtained from computed tomography as well as physiologically based mass transfer descriptions obtained from pharmacokinetic modeling. The physiological architecture of hepatic tissue in our model is governed by both vascular geometry and the composition of the connecting hepatic tissue. In particular, we here consider locally distributed mass flow in liver tissue instead of considering well-stirred compartments. Experimentally, the model structure corresponds to an isolated perfused liver and provides an ideal platform to address first pass effects and questions of hepatic heterogeneity. The model was evaluated for three exemplary compounds covering key aspects of perfusion, distribution and metabolization within the liver. As pathophysiological states we considered the influence of steatosis and carbon tetrachloride-induced liver necrosis on total hepatic distribution and metabolic capacity. Notably, we found that our computational predictions are in qualitative agreement with previously published experimental data. The simulation results provide an unprecedented level of detail in compound concentration profiles during first pass perfusion, both spatio-temporally in liver tissue itself and temporally in the outflowing blood. We expect our model to be the foundation of further spatially resolved models of the liver in the future.