Anatomically based simulation of hepatic perfusion in the human liver

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.

Modelling the liver region as porous media to noninvasively measure portal vein pressure gradient (PPG) with numerical methods

Portal hypertension is the initial and main consequence of liver cirrhosis. Currently the diagnosis relies on invasive and complex operation. This study proposed a new computational method in computational fluid dynamics (CFD) analysis to noninvasively measure the portal pressure gradient (PPG) by considering the liver region as porous media to account for the patient-specific liver resistance. Patient-specific computational models based on the CT scan images and the ultrasound (US) velocity measurement was established. The results show that the PPG derived from CFD analysis is in great agreement with clinical measured data (23.93 mmHg vs 23 mmHg). Validation of the numerical method and was performed by post-TIPS PPG measurement (10.69 mmHg vs 11 mmHg). Then the range of porous media parameters is investigated in a validation group of three patients. The computational method proposed in this study is promising in more accurately measuring the PPG noninvasively.

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.

Emulating clinical pressure waveforms in cell culture using an Arduino-controlled millifluidic 3D-printed platform for 96-well plates

High blood pressure is the primary risk factor for heart disease, the leading cause of death globally. Despite this, current methods to replicate physiological pressures in vitro remain limited in sophistication and throughput. Single-chamber exposure systems allow for only one pressure condition to be studied at a time and the application of dynamic pressure waveforms is currently limited to simple sine, triangular, or square waves. Here, we introduce a high-throughput hydrostatic pressure exposure system for 96-well plates. The platform can deliver a fully-customizable pressure waveform to each column of the plate, for a total of 12 simultaneous conditions. Using clinical waveform data, we are able to replicate real patients' blood pressures as well as other medically-relevant pressures within the body and have assembled a small patient-derived waveform library of some key physiological locations. As a proof of concept, human umbilical vein endothelial cells (HUVECs) survived and proliferated for 3 days under a wide range of static and dynamic physiologic pressures ranging from 10 mm Hg to 400 mm Hg. Interestingly, pathologic and supraphysiologic pressure exposures did not inhibit cell proliferation. By integrating with, rather than replacing, ubiquitous lab cultureware it is our hope that this device will facilitate the incorporation of hydrostatic pressure into standard cell culture practice.

The Influence of Interdisciplinary Work towards Advancing Knowledge on Human Liver Physiology

The knowledge accumulated throughout the years about liver regeneration has allowed a better understanding of normal liver physiology, by reconstructing the sequence of steps that this organ follows when it must rebuild itself after being injured. The scientific community has used several interdisciplinary approaches searching to improve liver regeneration and, therefore, human health. Here, we provide a brief history of the milestones that have advanced liver surgery, and review some of the new insights offered by the interdisciplinary work using animals, in vitro models, tissue engineering, or mathematical models to help advance the knowledge on liver regeneration. We also present several of the main approaches currently available aiming at providing liver support and overcoming organ shortage and we conclude with some of the challenges found in clinical practice and the ethical issues that have concomitantly emerged with the use of those approaches.

Noninvasive imaging of hepatic dysfunction: A state-of-the-art review

Hepatic dysfunction represents a wide spectrum of pathological changes, which can be frequently found in hepatitis, cholestasis, metabolic diseases, and focal liver lesions. As hepatic dysfunction is often clinically silent until advanced stages, there remains an unmet need to identify affected patients at early stages to enable individualized intervention which can improve prognosis. Passive liver function tests include biochemical parameters and clinical grading systems (e.g., the Child-Pugh score and Model for End-Stage Liver Disease score). Despite widely used and readily available, these approaches provide indirect and limited information regarding hepatic function. Dynamic quantitative tests of liver function are based on clearance capacity tests such as the indocyanine green (ICG) clearance test. However, controversial results have been reported for the ICG clearance test in relation with clinical outcome and the accuracy is easily affected by various factors. Imaging techniques, including ultrasound, computed tomography, and magnetic resonance imaging, allow morphological and functional assessment of the entire hepatobiliary system, hence demonstrating great potential in evaluating hepatic dysfunction noninvasively. In this article, we provide a state-of-the-art summary of noninvasive imaging modalities for hepatic dysfunction assessment along the pathophysiological track, with special emphasis on the imaging modality comparison and selection for each clinical scenario.

Anatomically- and physiologically-informed computational model of hepatic contrast perfusion for virtual imaging trials

PURPOSE

Virtual (in silico) imaging trials (VITs), involving computerized phantoms and models of the imaging process, provide a modern alternative to clinical imaging trials. VITs are faster, safer, and enable otherwise-impossible investigations. Current phantoms used in VITs are limited in their ability to model functional behavior such as contrast perfusion which is an important determinant of dose and image quality in CT imaging. In our prior work with the XCAT computational phantoms, we determined and modeled inter-organ (organ to organ) intravenous contrast concentration as a function of time from injection. However, intra-organ concentration, heterogeneous distribution within a given organ, was not pursued. We extend our methods in this work to model intra-organ concentration within the XCAT phantom with a specific focus on the liver.

METHODS

Intra-organ contrast perfusion depends on the organ's vessel network. We modeled the intricate vascular structures of the liver, informed by empirical and theoretical observations of anatomy and physiology. The developed vessel generation algorithm modeled a dual-input-single-output vascular network as a series of bifurcating surfaces to optimally deliver flow within the bounding surface of a given XCAT liver. Using this network, contrast perfusion was simulated within voxelized versions of the phantom by using knowledge of the blood velocities in each vascular structure, vessel diameters and length, and the time since the contrast entered the hepatic artery. The utility of the enhanced phantom was demonstrated through a simulation study with the phantom voxelized prior to CT simulation with the relevant liver vasculature prepared to represent blood and iodinated contrast media. The spatial extent of the blood-contrast mixture was compared to clinical data.

RESULTS

The vascular structures of the liver were generated with size and orientation which resulted in minimal energy expenditure required to maintain blood flow. Intravenous contrast was simulated as having known concentration and known total volume in the liver as calibrated from time-concentration curves (TCC). Measurements of simulated CT ROIs were found to agree with clinically-observed values of early arterial phase contrast enhancement of the parenchyma (∼5 HU). Similarly, early enhancement in the hepatic artery was found to agree with average clinical enhancement (180 HU).

CONCLUSIONS

The computational methods presented here furthered the development of the XCAT phantoms allowing for multi-timepoint contrast perfusion simulations, enabling more anthropomorphic virtual clinical trials intended for optimization of current clinical imaging technologies and applications. This article is protected by copyright. All rights reserved.

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.

Application of Magnetic Resonance Imaging in Liver Biomechanics: A Systematic Review

MRI-based biomechanical studies can provide a deep understanding of the mechanisms governing liver function, its mechanical performance but also liver diseases. In addition, comprehensive modeling of the liver can help improve liver disease treatment. Furthermore, such studies demonstrate the beginning of an engineering-level approach to how the liver disease affects material properties and liver function. Aimed at researchers in the field of MRI-based liver simulation, research articles pertinent to MRI-based liver modeling were identified, reviewed, and summarized systematically. Various MRI applications for liver biomechanics are highlighted, and the limitations of different viscoelastic models used in magnetic resonance elastography are addressed. The clinical application of the simulations and the diseases studied are also discussed. Based on the developed questionnaire, the papers' quality was assessed, and of the 46 reviewed papers, 32 papers were determined to be of high-quality. Due to the lack of the suitable material models for different liver diseases studied by magnetic resonance elastography, researchers may consider the effect of liver diseases on constitutive models. In the future, research groups may incorporate various aspects of machine learning (ML) into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification.

Thermomechanical Modeling of Laser Ablation Therapy of Tumors: Sensitivity Analysis and Optimization of Influential Variables

In cancer treatment, laser ablation is a promising technique used to induce localized thermal damage. Different variables influence the temperature distribution in the tissue and the resulting therapy efficacy; thus, the optimal therapy settings are required for obtaining the desired clinical outcome. In this work, thermomechanical modeling of contactless laser ablation was implemented to analyze the sensitivity of independent variables on the optimal treatment conditions. The Finite Element Method was utilized to solve the governing equations, i.e., the bioheat, mechanical deformation, and the Navier-Stokes equations. Validation of the model was evaluated by comparing experimental and simulated temperatures, which indicated high accuracy for estimating temperature. In particular, the results showed that the model is capable of estimating temperature with a good correlation factor (R=0.98) and low Mean Absolute Error (3.9 C). A sensitivity analysis based on laser irradiation time, power, beam distribution, and the blood vessel depth on temperature distribution and fraction of necrotic tissue was performed. Based on the most significant variables i.e., laser irradiation time and power, an optimization process was performed. This resulted into an indication of the optimal therapy settings for achieving maximum procedure efficiency i.e., the required fraction of necrotic tissue within the target volume, constituted by tumor and safety margins around it.

A highly parallel simulation of patient-specific hepatic flows

Computational hemodynamics is being developed as an alternative approach for assisting clinical diagnosis and treatment planning for liver diseases. The technology is non-invasive, but the computational time could be high when the full geometry of the blood vessels is taken into account. Existing approaches use either one-dimensional model of the artery or simplified three-dimensional tubular geometry in order to reduce the computational time, but the accuracy is sometime compromised, for example, when simulating blood flows in arteries with plaque. In this work, we study a highly parallel method for the transient incompressible Navier-Stokes equations for the simulation of the blood flows in the full three-dimensional patient-specific hepatic artery, portal vein and hepatic vein. As applications, we also simulate the flow in a patient with hepatectomy and calculate the S (PPG). One of the advantages of simulating blood flows in all hepatic vessels is that it provides a direct estimate of the PPG, which is a gold standard value to assess the portal hypertension. Moreover, the robustness and scalability of the algorithm are also investigated. A 83% parallel efficiency is achieved for solving a problem with 7 million elements on a supercomputer with more than 1000 processor cores.

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.

Structural and hemodynamic properties of murine pulmonary arterial networks under hypoxia-induced pulmonary hypertension

Detection and monitoring of patients with pulmonary hypertension, defined as a mean blood pressure in the main pulmonary artery above 25 mmHg, requires a combination of imaging and hemodynamic measurements. This study demonstrates how to combine imaging data from microcomputed tomography images with hemodynamic pressure and flow waveforms from control and hypertensive mice. Specific attention is devoted to developing a tool that processes computed tomography images, generating subject-specific arterial networks in which one-dimensional fluid dynamics modeling is used to predict blood pressure and flow. Each arterial network is modeled as a directed graph representing vessels along the principal pathway to ensure perfusion of all lobes. The one-dimensional model couples these networks with structured tree boundary conditions representing the small arteries and arterioles. Fluid dynamics equations are solved in this network and compared to measurements of pressure in the main pulmonary artery. Analysis of microcomputed tomography images reveals that the branching ratio is the same in the control and hypertensive animals, but that the vessel length-to-radius ratio is significantly lower in the hypertensive animals. Fluid dynamics predictions show that in addition to changed network geometry, vessel stiffness is higher in the hypertensive animal models than in the control models.