Modeling the Impact of Partial Hepatectomy on the Hepatic Hemodynamics Using a Rat Model

Liver fibrosis emulation: Impact of the vascular fibrotic alterations on hemodynamics

The liver circulatory system comprises two blood supply vascular trees (the hepatic artery and portal venous networks), microcirculation through the hepatic capillaries (the sinusoids), and a blood drainage vascular tree (the hepatic vein network). Vasculature changes due to fibrosis -located predominantly at the microcirculation level- lead to a marked increase in resistance to flow causing an increase in portal pressure (portal hypertension). Here, we present a liver fibrosis/cirrhosis model. We build on our 1D model of the healthy hepatic circulation, which considers the elasticity of the vessels walls and the pulsatile character of blood flow and pressure, and recreate the deteriorated liver vasculature due to fibrosis. We emulate altered sinusoids by fibrous tissue (stiffened, compressed and splitting) and propose boundary conditions to investigate the impact of fibrosis on hemodynamic variables within the organ. We obtain that the sinusoids stiffness leads to changes in the amplitude and shape of the blood flow and pressure waveforms but not in their mean value. For the compressed and splitting sinusoids, we observe significant increases in the mean value and amplitude of the pressure waveform in the altered sinusoids and in the portal venous network. In other words, we obtain the portal hypertension clinically observed in fibrotic/cirrhotic patients. We also study the extent of the spreading fibrosis by performing the structural fibrotic changes in an increasingly number of sinusoids. Finally, we calculate the portal pressure gradient (PPG) in the model and obtain values in agreement with those reported in the literature for fibrotic/cirrhotic patients.

1D-model of the human liver circulatory system

BACKGROUND AND OBJECTIVE

Blood flow rate and pressure can be measured in vivo by invasive and non-invasive techniques in the large vessels of the hepatic vasculature, but it is not possible to do so along the entire liver circulatory system. Here, we develop a novel 1D model of the liver circulatory system to obtain the hemodynamic signals from macrocirculation to microcirculation with a very low computational cost.

METHODS

The model considers structurally well-defined elements that constitute the entire hepatic circulatory system, the hemodynamics (the temporal-dependence of the blood flow rate and pressure), and the elasticity of the vessel walls.

RESULTS

Using flow rate signals from in vivo measurements as inputs in the model, we obtain pressure signals within their physiological range of values. Furthermore, the model allows to get and analyze the blood flow rate and pressure signals along any vessel of the hepatic vasculature. The impact of the elasticity of the different model components on the inlet pressures is also tested.

CONCLUSIONS

A 1D model of the entire blood vascular system of the human liver is presented for the first time. The model allows to obtain the hemodynamic signals along the hepatic vasculature at a low computational cost. The amplitude and shape of the flow and pressure signals has hardly been studied in the small liver vessels. In this sense, the proposed model is a useful non-invasive exploration tool of the characteristics of the hemodynamic signals. In contrast to models that partially address the hepatic vasculature or those using an electrical analogy, the model presented here is made entirely of structurally well-defined elements. Future works will allow to directly emulate structural vascular alterations due to hepatic diseases and studying their impact on pressure and blood flow signals at key locations of the vasculature.

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.

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.

Surgical Classification for Preclinical Rat Femoral Bone Defect Model: Standardization Based on Systematic Review, Anatomical Analysis and Virtual Surgery

Though surgical techniques profoundly influence in vivo experiments, significant heterogeneity exists in current surgeries for inducing rat femoral bone defects. Such variations reduce the reproducibility and comparability of preclinical studies, and are detrimental to clinical translation. The purposes of this study were: (1) to conduct a systematic review of rat femoral defect models, summarizing and analyzing the surgical techniques; (2) to analyze surgical design and potential pitfalls via 3D anatomy and virtual surgeries for fostering future precision research; and (3) to establish a surgical classification system, for improving the reproducibility and comparability among studies, avoiding unnecessary repetitive experiments. The online database PubMed was searched to identify studies from January 2000 to June 2022 using keywords, including rat, femur, bone defect. Eligible publications were included for a review of surgical methods. Anatomical analysis and virtual surgeries were conducted based on micro-CT reconstruction of the rat femur for further investigation and establishment of a classification system. A total of 545 publications were included, revealing marked heterogeneity in surgical methods. Four major surgical designs were reported for inducing defects from the proximal to distal femur: bone tunnel, cortical window, segmental defect, and wedge-shaped defect. Anatomical analysis revealed potential pitfalls hindering efficient clinical translation. A classification system was established according to the anatomical region, surgical design, and fixation devices. This systematic review in combination with 3D analysis and virtual surgery provides a general overview of current surgical approaches to inducing femoral defects in rats, and establishes a surgical classification facilitating preclinical research of quality and translational value.

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.

Hepatectomy-Induced Alterations in Hepatic Perfusion and Function - Toward Multi-Scale Computational Modeling for a Better Prediction of Post-hepatectomy Liver Function

Liver resection causes marked perfusion alterations in the liver remnant both on the organ scale (vascular anatomy) and on the microscale (sinusoidal blood flow on tissue level). These changes in perfusion affect hepatic functions via direct alterations in blood supply and drainage, followed by indirect changes of biomechanical tissue properties and cellular function. Changes in blood flow impose compression, tension and shear forces on the liver tissue. These forces are perceived by mechanosensors on parenchymal and non-parenchymal cells of the liver and regulate cell-cell and cell-matrix interactions as well as cellular signaling and metabolism. These interactions are key players in tissue growth and remodeling, a prerequisite to restore tissue function after PHx. Their dysregulation is associated with metabolic impairment of the liver eventually leading to liver failure, a serious post-hepatectomy complication with high morbidity and mortality. Though certain links are known, the overall functional change after liver surgery is not understood due to complex feedback loops, non-linearities, spatial heterogeneities and different time-scales of events. Computational modeling is a unique approach to gain a better understanding of complex biomedical systems. This approach allows (i) integration of heterogeneous data and knowledge on multiple scales into a consistent view of how perfusion is related to hepatic function; (ii) testing and generating hypotheses based on predictive models, which must be validated experimentally and clinically. In the long term, computational modeling will (iii) support surgical planning by predicting surgery-induced perfusion perturbations and their functional (metabolic) consequences; and thereby (iv) allow minimizing surgical risks for the individual patient. Here, we review the alterations of hepatic perfusion, biomechanical properties and function associated with hepatectomy. Specifically, we provide an overview over the clinical problem, preoperative diagnostics, functional imaging approaches, experimental approaches in animal models, mechanoperception in the liver and impact on cellular metabolism, omics approaches with a focus on transcriptomics, data integration and uncertainty analysis, and computational modeling on multiple scales. Finally, we provide a perspective on how multi-scale computational models, which couple perfusion changes to hepatic function, could become part of clinical workflows to predict and optimize patient outcome after complex liver surgery.

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).

Predicting the risk of post-hepatectomy portal hypertension using a digital twin: A clinical proof of concept

BACKGROUND & AIMS

Despite improvements in medical and surgical techniques, post-hepatectomy liver failure (PHLF) remains the leading cause of postoperative death. High postoperative portal vein pressure (P_PV) and portocaval gradient (PCG), which cannot be predicted by current tools, are the most important determinants of PHLF. Therefore, we aimed to evaluate a digital twin to predict the risk of postoperative portal hypertension (PHT).

METHODS

We prospectively included 47 patients undergoing major hepatectomy. A mathematical (0D) model of the entire blood circulation was assessed and automatically calibrated from patient characteristics. Hepatic flows were obtained from preoperative flow MRI (n = 9), intraoperative flowmetry (n = 16), or estimated from cardiac output (n = 47). Resection was then simulated in these 3 groups and the computed P_PV and PCG were compared to intraoperative data.

RESULTS

Simulated post-hepatectomy pressures did not differ between the 3 groups, comparing well with collected data (no significant differences). In the entire cohort, the correlation between measured and simulated P_PV values was good (r = 0.66, no adjustment to intraoperative events) or excellent (r = 0.75) after adjustment, as well as for PCG (respectively r = 0.59 and r = 0.80). The difference between simulated and measured post-hepatectomy PCG was ≤3 mmHg in 96% of cases. Four patients suffered from lethal PHLF for whom the model satisfactorily predicted their postoperative pressures.

CONCLUSIONS

We demonstrated that a 0D model could correctly anticipate postoperative PHT, even using estimated hepatic flow rates as input data. If this major conceptual step is confirmed, this algorithm could change our practice toward more tailor-made procedures, while ensuring satisfactory outcomes.

LAY SUMMARY

Post-hepatectomy portal hypertension is a major cause of liver failure and death, but no tool is available to accurately anticipate this potentially lethal complication for a given patient. Herein, we propose using a mathematical model to predict the portocaval gradient at the end of liver resection. We tested this model on a cohort of 47 patients undergoing major hepatectomy and demonstrated that it could modify current surgical decision-making algorithms.

Simulation of a detoxifying organ function: Focus on hemodynamics modeling and convection-reaction numerical simulation in microcirculatory networks

When modeling a detoxifying organ function, an important component is the impact of flow on the metabolism of a compound of interest carried by the blood. We here study the effects of red blood cells (such as the Fahraeus-Lindqvist effect and plasma skimming) on blood flow in typical microcirculatory components such as tubes, bifurcations and entire networks, with particular emphasis on the liver as important representative of detoxifying organs. In one of the plasma skimming models, under certain conditions, oscillations between states are found and analyzed in a methodical study to identify their causes and influencing parameters. The flow solution obtained is then used to define the velocity at which a compound would be transported. A convection-reaction equation is studied to simulate the transport of a compound in blood and its uptake by the surrounding cells. Different types of signal sharpness have to be handled depending on the application to address different temporal compound concentration profiles. To permit executing the studied models numerically stable and accurate, we here extend existing transport schemes to handle converging bifurcations, and more generally multi-furcations. We study the accuracy of different numerical schemes as well as the effect of reactions and of the network itself on the bolus shape. Even though this study is guided by applications in liver micro-architecture, the proposed methodology is general and can readily be applied to other capillary network geometries, hence to other organs or to bioengineered network designs.

Modeling the hepatic arterial flow in living liver donor after left hepatectomy and postoperative boundary condition exploration

Preoperative and postoperative hepatic perfusion is modeled with one-dimensional (1-D) Navier-Stokes equations. Flow rates obtained from ultrasound (US) data and impedance resulted from structured trees are the inflow and outflow boundary condition (BC), respectively. Structured trees terminate at the size of the arterioles, which can enlarge their size after hepatectomy. In clinical studies, the resistance to pulsatile arterial flow caused by the microvascular bed can be reflected by the resistive index (RI), a frequently used index in assessing arterial resistance. This study uses the RI in a novel manner to conveniently obtain the postoperative outflow impedance from the preoperative impedance. The major emphasis of this study is to devise a model to capture the postoperative hepatic hemodynamics after left hepatectomy. To study this, we build a hepatic network model and analyze its behavior under four different outflow impedance: (a) the same as preoperative impedance; (b) evaluated using the RI and preoperative impedance; (c) computed from structured tree BC with increased radius of terminal vessels; and (d) evaluated using structured tree with both increased radius of root vessel, ie, the outlets of the postoperative hepatic artery, and increased radius of terminal vessels. Our results show that both impedance from (b) and (d) give a physiologically reasonable postoperative hepatic pressure range, while the RI in (b) allows for a fast approximation of postoperative impedance. Since hemodynamics after hepatectomy are not fully understood, the methods used in this study to explore postoperative outflow BC are informative for future models exploring hemodynamic effects of partial hepatectomy.

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.

Construction of sinusoid-scale microvessels in perfusion culture of a decellularized liver

There is a great deal of demand for the construction of transplantable liver grafts. Over the last decade, decellularization techniques have been developed to construct whole liver tissue grafts as potential biomaterials. However, the lack of intact vascular networks, especially sinusoids, in recellularized liver scaffolds leads to hemorrhage and thrombosis after transplantation, which is a major obstacle to the development of transplantable liver grafts. In the present study, we hypothesized that both mechanical (e.g., fluid shear stress) and chemical factors (e.g., fibronectin coating) can enhance the formation of hierarchical vascular networks including sinusoid-scale microvessels. We demonstrated that perfusion culture promoted formation of sinusoid-scale microvessels in recellularized liver scaffolds, which was not observed in static culture. In particular, perfusion culture at 4.7 ml/min promoted the formation of sinusoid-scale microvessels compared to perfusion culture at 2.4 and 9.4 ml/min. In addition, well-aligned endothelium was observed in perfusion culture, suggesting that endothelial cells sensed the flow-induced shear stress. Moreover, fibronectin coating of decellularized liver scaffolds enhanced the formation of sinusoid-scale microvessels in perfusion culture at 4.7 ml/min. This study represents a critical step in the development of functional recellularized liver scaffolds, which can be used not only for transplantation but also for drug screening and disease-modeling studies. STATEMENT OF SIGNIFICANCE: Decellularized liver scaffolds are promising biomaterials that allow production of large-scale tissue-engineered liver grafts. However, it is difficult to maintain recellularized liver grafts after transplantation due to hemorrhage and thrombosis. To overcome this obstacle, construction of an intact vascular network including sinusoid-scale microvessels is essential. In the present study, we succeeded in constructing sinusoid-scale microvessels in decellularized liver scaffolds via a combination of perfusion culture and surface coating. We further confirmed that endothelial cells in decellularized liver scaffolds responded to flow-derived mechanical stress by aligning actin filaments. Our strategy to construct sinusoid-scale microvessels is critical for the development of intact vascular networks, and addresses the limitations of recellularized liver scaffolds after transplantation.

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.

A methodology for numerically analysing the hepatic artery haemodynamics during B-TACE: a proof of concept

Balloon-occluded transarterial chemoembolisation (B-TACE) is an intraarterial transcatheter treatment for liver cancer. In B-TACE, an artery-occluding microballoon catheter occludes an artery and promotes collateral circulation for drug delivery to tumours. This paper presents a methodology for analysing the haemodynamics during B-TACE, by combining zero-dimensional and three-dimensional modelling tools. As a proof of concept, we apply the methodology to a patient-specific hepatic artery geometry and analyse two catheter locations. Results show that the blood flow redistribution can be predicted in this proof-of-concept study, suggesting that this approach could potentially be used to optimise catheter location.

Quantitative analysis of hepatic macro- and microvascular alterations during cirrhogenesis in the rat

Cirrhosis represents the end-stage of any persistent chronically active liver disease. It is characterized by the complete replacement of normal liver tissue by fibrosis, regenerative nodules, and complete fibrotic vascularized septa. The resulting angioarchitectural distortion contributes to an increasing intrahepatic vascular resistance, impeding liver perfusion and leading to portal hypertension. To date, knowledge on the dynamically evolving pathological changes of the hepatic vasculature during cirrhogenesis remains limited. More specifically, detailed anatomical data on the vascular adaptations during disease development is lacking. To address this need, we studied the 3D architecture of the hepatic vasculature during induction of cirrhogenesis in a rat model. Cirrhosis was chemically induced with thioacetamide (TAA). At predefined time points, the hepatic vasculature was fixed and visualized using a combination of vascular corrosion casting and deep tissue microscopy. Three-dimensional reconstruction and data-fitting enabled cirrhogenic features to extracted at multiple scales, portraying the impact of cirrhosis on the hepatic vasculature. At the macrolevel, we noticed that regenerative nodules severely compressed pliant venous vessels from 12 weeks of TAA intoxication onwards. Especially hepatic veins were highly affected by this compression, with collapsed vessel segments severely reducing perfusion capabilities. At the microlevel, we discovered zone-specific sinusoidal degeneration, with sinusoids located near the surface being more affected than those in the middle of a liver lobe. Our data shed light on and quantify the evolving angioarchitecture during cirrhogenesis. These findings may prove helpful for future targeted invasive interventions.

Effects of splanchnic vasoconstrictors on liver regeneration and survival after 90% rat hepatectomy

Purpose

Posthepatectomy liver failure is a serious complication and considered to be caused by increased portal pressure and flow. Splanchnic vasoactive agents and propranolol are known to decrease portal pressure. The aim of this study was to identify optimal candidates with potential for clinical use among somatostatin, terlipressin, and propranolol using rats with 90% hepatectomy.

Methods

Rats were divided into 5 groups: sham operation (n = 6), control (n = 20), propranolol (n = 20), somatostatin (n = 20), and terlipressin group (n = 20). Seven-day survival rates and portal pressure change were measured, and biochemical, histologic, and molecular analyses were performed.

Results

Portal pressure was significantly decreased in all 3 treatment groups compared to control. All treatment groups showed a tendency of decreased liver injury markers, and somatostatin showed the most prominent effect at 24 hours postoperatively. Histologic liver injury at 24 hours was significantly decreased in propranolol and terlipressin groups (P = 0.016, respectively) and somatostatin group showed borderline significance (P = 0.056). Hepatocyte proliferation was significantly increased after 24 hours in all treatment groups. Median survival was significantly increased in terlipressin group compared to control group (P < 0.01).

Conclusion

Terlipressin is considered as the best candidate, while somatostatin has good potential for clinical use, considering their effects on portal pressure and subsequent decrease in liver injury and increase in liver regeneration.

Partial hepatectomy hemodynamics changes: Experimental data explained by closed-loop lumped modeling

The liver function may be degraded after partial liver ablation surgery. Adverse liver hemodynamics have been shown to be associated to liver failure. The link between these hemodynamics changes and ablation size is however poorly understood. This article proposes to explain with a closed-loop lumped model the hemodynamics changes observed during twelve surgeries in pigs. The portal venous tree is modeled with a pressure-dependent variable resistor. The variables measured, before liver ablation, are used to tune the model parameters. Then, the liver partial ablation is simulated with the model and the simulated pressures and flows are compared with post-operative measurements. Fluid infusion and blood losses occur during the surgery. The closed-loop model presented accounts for these blood volume changes. Moreover, the impact of blood volume changes and the liver lobe mass estimations on the simulated variables is studied. The typical increase of portal pressure, increase of liver pressure loss, slight decrease of portal flow and major decrease in arterial flow are quantitatively captured by the model for a 75% hepatectomy. It appears that the 75% decrease in hepatic arterial flow can be explained by the resistance increase induced by the surgery, and that no hepatic arterial buffer response (HABR) mechanism is needed to account for this change. The different post-operative states, observed in experiments, are reproduced with the proposed model. Thus, an explanation for inter-subjects post-operative variability is proposed. The presented framework can easily be adapted to other species circulations and to different pathologies for clinical hepatic applications.

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.

Multiscale computational model of fluid flow and matrix deformation in decellularized liver

Currently little is known about the biomechanical environment in decellularized tissue. The goal of this research is to quantify the mechanical microenvironment in decellularized liver, for varying organ-scale perfusion conditions, using a combined experimental/computational approach. Needle-guided ultra-miniature pressure sensors were inserted into liver tissue to measure parenchymal fluid pressure ex-situ in portal vein-perfused native (n=5) and decellularized (n=7) ferret liver, for flow rates from 3-12mL/min. Pressures were also recorded at the inlet near the portal vein cannula to estimate total vascular resistance of the specimens. Experimental results were fit to a multiscale computational model to simulate perfusion conditions inside native versus decellularized livers for four experimental flow rates. The multiscale model consists of two parts: an organ-scale electrical analog model of liver hemodynamics and a tissue-scale model that predicts pore fluid pressure, pore fluid velocity, and solid matrix stress and deformation throughout the 3D hepatic lobule. Distinct models were created for native versus decellularized liver. Results show that vascular resistance decreases by 82% as a result of decellularization. The hydraulic conductivity of the decellularized liver lobule, a measure of tissue permeability, was 5.6 times that of native liver. For the four flow rates studied, mean fluid pressures in the decellularized lobule were 0.6-2.4mmHg, mean fluid velocities were 211-767μm/s, and average solid matrix principal strains were 1.7-6.1%. In the future this modeling platform can be used to guide the optimization of perfusion seeding and conditioning strategies for decellularized scaffolds in liver bioengineering.

Engineering point of view on liver transplantation strategies: multi-level modeling of hepatic perfusion

BACKGROUND

Hepatic perfusion plays a crucial role in liver transplantation strategies, for example, when preserving procured organs with the use of machine perfusion preservation (MP) and in the case of living donor liver transplantation (LDLT). Liver hemodynamics are not yet fully understood because of insufficient knowledge on the hepatic vascular morphology and its perfusion characteristics, hampering the optimization of liver transplantation procedures. To this end, we developed computer models to simulate the complex blood circulation through the liver from the macro-scale down to the terminal micro-scale level.

METHODS

A combination of state-of-the-art techniques (vascular corrosion casting, micro-CT scanning up to a 2.6-μm resolution, and image processing) led to 3D visualizations and detailed geometrical analyses of the complex architecture of the liver's 3 vascular trees, ranging from the largest vessels (macrocirculation) down to the sinusoids (microcirculation).

RESULTS

On the basis of these data, we developed various computational models (electrical analog models and 3D computational fluid dynamics models) to study the blood flow-induced forces acting on the hepatic blood vessels. The latter was done for physiological blood flow through the liver as well as for livers undergoing MP or LDLT procedures. Hereby, several scenarios were simulated to study the behavior of livers in different hemodynamic circumstances.

CONCLUSIONS

A novel, multi-level modeling framework was developed to simulate hepatic perfusion in support of liver transplantation strategies. We obtained unique anatomical data on the vascular architecture of both human and rat livers. These data formed the building blocks of electrical analog models of hepatic perfusion and numerical models of the liver microcirculation. The results revealed novel insights into the hemodynamic impact of liver MP and LDLT procedures as well as into the microcirculatory perfusion characteristics. The presented methodology is also applicable to other tree-like structures (eg, the biliary tree) or organs (eg, kidneys, lungs).

A Multilevel Modeling Framework to Study Hepatic Perfusion Characteristics in Case of Liver Cirrhosis

Liver cirrhosis represents the end-stage of different liver disorders, progressively affecting hepatic architecture, hemodynamics, and function. Morphologically, cirrhosis is characterized by diffuse fibrosis, the conversion of normal liver architecture into structurally abnormal regenerative nodules and the formation of an abundant vascular network. To date, the vascular remodeling and altered hemodynamics due to cirrhosis are still poorly understood, even though they seem to play a pivotal role in cirrhogenesis. This study aims to determine the perfusion characteristics of the cirrhotic circulation using a multilevel modeling approach including computational fluid dynamics (CFD) simulations. Vascular corrosion casting and multilevel micro-CT imaging of a single human cirrhotic liver generated detailed datasets of the hepatic circulation, including typical pathological characteristics of cirrhosis such as shunt vessels and dilated sinusoids. Image processing resulted in anatomically correct 3D reconstructions of the microvasculature up to a diameter of about 500 μm. Subsequently, two cubic samples (150 × 150 × 150 μm3) were virtually dissected from vascularized zones in between regenerative nodules and applied for CFD simulations to study the altered cirrhotic microperfusion and permeability. Additionally, a conceptual 3D model of the cirrhotic macrocirculation was developed to reveal the hemodynamic impact of regenerative nodules. Our results illustrate that the cirrhotic microcirculation is characterized by an anisotropic permeability showing the highest value in the direction parallel to the central vein (kd,zz = 1.68 × 10−13 m2 and kd,zz = 7.79 × 10−13 m2 for sample 1 and 2, respectively) and lower values in the circumferential (kd,ϑϑ = 5.78 × 10−14 m2 and kd,ϑϑ = 5.65 × 10−13 m2 for sample 1 and 2, respectively) and radial (kd,rr = 9.87 × 10−14 m2 and kd,rr = 5.13 × 10−13 m2 for sample 1 and 2, respectively) direction. Overall, the observed permeabilities are markedly higher compared to a normal liver, implying a locally decreased intrahepatic vascular resistance (IVR) probably due to local compensation mechanisms (dilated sinusoids and shunt vessels). These counteract the IVR increase caused by the presence of regenerative nodules and dynamic contraction mechanisms (e.g., stellate cells, NO-concentration, etc.). Our conceptual 3D model of the cirrhotic macrocirculation indicates that regenerative nodules severely increase the IVR beyond about 65 vol. % of regenerative nodules. Numerical modeling allows quantifying perfusion characteristics of the cirrhotic macro- and microcirculation, i.e., the effect of regenerative nodules and compensation mechanisms such as dilated sinusoids and shunt vessels. Future research will focus on the development of models to study time-dependent degenerative adaptation of the cirrhotic macro- and microcirculation.

Analyzing the human liver vascular architecture by combining vascular corrosion casting and micro-CT scanning: a feasibility study

Although a full understanding of the hepatic circulation is one of the keys to successfully perform liver surgery and to elucidate liver pathology, relatively little is known about the functional organization of the liver vasculature. Therefore, we materialized and visualized the human hepatic vasculature at different scales, and performed a morphological analysis by combining vascular corrosion casting with novel micro-computer tomography (CT) and image analysis techniques. A human liver vascular corrosion cast was obtained by simultaneous resin injection in the hepatic artery (HA) and portal vein (PV). A high resolution (110 μm) micro-CT scan of the total cast allowed gathering detailed macrovascular data. Subsequently, a mesocirculation sample (starting at generation 5; 88 × 68 × 80 mm³) and a microcirculation sample (terminal vessels including sinusoids; 2.0 × 1.5 × 1.7 mm³) were dissected and imaged at a 71-μm and 2.6-μm resolution, respectively. Segmentations and 3D reconstructions allowed quantifying the macro- and mesoscale branching topology, and geometrical features of HA, PV and hepatic venous trees up to 13 generations (radii ranging from 13.2 mm to 80 μm; lengths from 74.4 mm to 0.74 mm), as well as microvascular characteristics (mean sinusoidal radius of 6.63 μm). Combining corrosion casting and micro-CT imaging allows quantifying the branching topology and geometrical features of hepatic trees using a multiscale approach from the macro- down to the microcirculation. This may lead to novel insights into liver circulation, such as internal blood flow distributions and anatomical consequences of pathologies (e.g. cirrhosis).