Mathematical modelling of microcirculation in a poroelastic model of the liver, and its application to the study of ascites

The liver performs many vital functions in the body and has a natural ability to regenerate itself, except in the case of repeated or severe damage often caused by liver diseases. Damage due to liver disease occurs in the form of scarring of healthy liver tissue, a process known as fibrosis. Chronic fibrosis can lead to liver cirrhosis, a condition that is irreversible and often requires liver transplantation. Cirrhosis manifests itself in the form of increased tissue stiffness and decreased tissue permeability, which then leads to a marked decrease in blood perfusion and functioning of the liver tissue. As a homeostatic response, hepatic portal blood pressure also increases, which then leads to an increased outflow of excess interstitial fluid across the surface of the liver and into the surrounding peritoneal cavity. The abnormal accumulation of fluid in the peritoneal cavity is known as ascites and is characterised by large abdominal girth, abdominal pain and discomfort. The aim of this thesis was to model the microcirculation of blood and interstitial fluid in the liver, so as to investigate the changes in vasculature that lead to impaired blood perfusion and the formation of ascites. To that end, we have developed a dual-porosity, dual-permeability deformable model of the liver tissue using the Biot theory of poroelasticity. We then used the model as part of a compartmental model of the peritoneal cavity and investigated the effect of liver disease (fibrosis/cirrhosis) on the accumulation of fluid in the peritoneal cavity. By varying the degree of liver tissue stiffness, we simulated and compared different stages of liver fibrosis, as well as predicted the severity of the resulting ascites. This makes our model an improvement on the current literature, with the aim of future use in informing and improving disease treatment strategies.Open Acces

Mathematical model of blood and interstitial flow and lymph production in the liver.

We present a mathematical model of blood and interstitial flow in the liver. The liver is treated as a lattice of hexagonal \u2018classic\u2019 lobules, which are assumed to be long enough that end effects may be neglected and a two-dimensional problem considered. Since sinusoids and lymphatic vessels are numerous and small compared to the lobule, we use a homogenized approach, describing the sinusoidal and interstitial spaces as porous media. We model plasma filtration from sinusoids to the interstitium, lymph uptake by lymphatic ducts, and lymph outflow from the liver surface. Our results show that the effect of the liver surface only penetrates a depth of a few lobules\u2019 thickness into the tissue. Thus, we separately consider a single lobule lying sufficiently far from all external boundaries that we may regard it as being in an infinite lattice, and also a model of the region near the liver surface. The model predicts that slightly more lymph is produced by interstitial fluid flowing through the liver surface than that taken up by the lymphatic vessels in the liver and that the on-peritonealized region of the surface of the liver results in the total lymph production (uptake by lymphatics plus fluid crossing surface) being about 5 % more than if the entire surface were covered by the Glisson\u2013peritoneal membrane. Estimates of lymph outflow through the surface of the liver are in good agreement with experimental data. We also study the effect of non-physiological values of the controlling parameters, particularly focusing on the conditions of portal hypertension and ascites. To our knowledge, this is the first attempt to model lymph production in the liver. The model provides clinically relevant information about lymph outflow pathways and predicts the systemic response to pathological variations

An Ultrasonically Actuated Needle Promotes the Transport of Nanoparticles and Fluids

Non-invasive therapeutic ultrasound methods, such as high-intensity focused ultrasound (HIFU), have limited access to tissue targets shadowed by bones or presence of gas. This study demonstrates that an ultrasonically actuated medical needle can be used to translate nanoparticles and fluids under the action of nonlinear phenomena, potentially overcoming some limitations of HIFU. A simulation study was first conducted to study the delivery of a tracer with an ultrasonically actuated needle (33 kHz) inside a porous medium acting as a model for soft tissue. The model was then validated experimentally in different concentrations of agarose gel showing a close match with the experimental results, when diluted soot nanoparticles (diameter < 150 nm) were employed as delivered entity. An additional simulation study demonstrated a threefold increase of the volume covered by the delivered agent in liver under a constant injection rate, when compared to without ultrasound. This method, if developed to its full potential, could serve as a cost effective way to improve safety and efficacy of drug therapies by maximizing the concentration of delivered entities within e.g. a small lesion, while minimizing exposure outside the lesion.Comment: 34 pages, 4 figures, under review in the Journal of the Acoustical Society of Americ

Design considerations and analysis of a bioreactor for application in a bio-artificial liver support system

Acute Liver Failure (ALF) is a devastating ailment with a high mortality rate and limited treatment alternatives. This study presents a methodology for the design and development of a bio-artificial bioreactor to be used in a Bio-Artificial Liver Support System. The system will ultimately be used either to bridge a patient to orthotopic liver transplant (OLT), the only current cure for end stage ALF, or spontaneous recovery. Methods to optimize and visualize the flow and related mass transfer in the BR are presented. The use of magnetic resonance imaging (MRI), scanning electron microscopy (SEM) and simple testing methodology is applied with emphasis on modeling the flow conditions in the BR. The bioreactor (BR) used in the Bio-Artificial Liver Support System (BALSS), currently under-going animal trials at the University of Pretoria, was modeled and simulated for the flow conditions in the device. Two different perfusion steps were modeled including the seeding of hepatocyte cells and later the clinical perfusion step. It was found that the BR geometry was not optimal with “dead spots” and regions of retarded flow. This would restrict the effective transport of nutrients and oxygen to the cells. The different perfusion rates for the seeding and clinical perfusion steps allowed for different velocity contours with cells seeing inconsistent flow patterns and mass transfer gradients. An optimized BR design is suggested and simulated, that effectively reduces the areas of retarded flow (dead spots) and increases the flow speed uniformly through the BR to an order of magnitude similar to that found in the sinusoidal range. The scaffolding volume was also decreased to allow a larger local cell density promoting cell-cell interaction. Finally a summarized design table for the design of a hepatic BR is presented.Dissertation (MEng (Mechanical))--University of Pretoria, 2008.Mechanical and Aeronautical Engineeringunrestricte

Investigation of Heat Therapies using Multi-Scale Models and Statistical Methods

Ph.DDOCTOR OF PHILOSOPH

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

International audienceWhen 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

Engineering oxygen transport for improving cell performance in hepatic devices

The bioartificial liver (BAL) advancing medical technology aims to provide temporary liver substitution for patients in dire need of liver transplants and also for drug development. Yet despite nearly fifty years of development, the approval for this medical device from U.S. regulatory agencies (e.g., Food and Drug Administration) is still pending. The reasons for this have both clinical and fundamental aspects. Current clinical trial data does not convincingly demonstrate a higher survival rate of patients that received BAL treatment than non-BAL treated control. This issue may be attributed to the fundamental fact that, as a medical bioreactor, BALs still lack the effectiveness at the level of the natural liver. As oxygen (O2) is a key substance to determine efficiency of the hepatocytes housed in the BAL, intensifying the O2 conditions within the BAL cellular space will elevate overall BAL performance. This proposition has been substantiated by several studies. With higher efficiency the BAL may increase the liver patients' survival rate, benefit new drug development, and may ultimately attain the government approval in the U.S. The work of this doctoral study focuses on methods of enhancing O 2 transport into three-dimensional (3D) customized hepatic devices. Firstly, enriched O2 conditions were established within customized hepatic systems by applying an inert organic compound - perfluorocarbon (PFC). The PFC-treated hepatic cells demonstrated high cytochrome P450 (CYP 450) function performance especially when 3D gelatin sponge were used as the scaffold. They also exhibited less glucose consumption. Next the 3D iv gelatin sponge scaffold was then characterized in a computational fluid dynamics (CFD)-based simulation to clarify the reasons for the performance improvement. The results of this simulation also suggest that using the new 3D cellular scaffold is an effective method for addressing the O2 delivery problem previously reported for a novel BAL design, the four quadrant bioreactor (4QB) when using the 4QB for the support of larger cell numbers. Lastly, the effects of a previously custom designed flow device and the gelatin sponge scaffold, on the drug metabolism of rat primary hepatocytes (RPHs) were evaluated. The key results from the drug metabolism tests were confirmation of the benefits of combining the 3D gelatin sponge scaffold and flow condition in increasing the hepatocytes drug metabolism enzyme performance. Surprisingly, the results also demonstrated the suppression of the RPHs drug metabolizing ability in flow devices and relevant analysis to this phenomenon was also conducted. This doctoral study has thus provided valuable information on experimental and numerical approaches for improving the fundamental performance of future BAL designs. It mainly highlights that in BALs, the 3D cell cultures and efficient flow perfusion are key to O2 delivery for the scaffold interstitial region (extracellular space). The work thus helps moving toward their development one step closer to establish the future clinical trial and industrial application of BAL devices

Three-dimensional Numerical Modeling and Computational Fluid Dynamics Simulations to Analyze and Improve Oxygen Availability in the AMC Bioartificial Liver

A numerical model to investigate fluid flow and oxygen (O(2)) transport and consumption in the AMC-Bioartificial Liver (AMC-BAL) was developed and applied to two representative micro models of the AMC-BAL with two different gas capillary patterns, each combined with two proposed hepatocyte distributions. Parameter studies were performed on each configuration to gain insight in fluid flow, shear stress distribution and oxygen availability in the AMC-BAL. We assessed the function of the internal oxygenator, the effect of changes in hepatocyte oxygen consumption parameters in time and the effect of the change from an experimental to a clinical setting. In addition, different methodologies were studied to improve cellular oxygen availability, i.e. external oxygenation of culture medium, culture medium flow rate, culture gas oxygen content (pO(2)) and the number of oxygenation capillaries. Standard operating conditions did not adequately provide all hepatocytes in the AMC-BAL with sufficient oxygen to maintain O(2) consumption at minimally 90% of maximal uptake rate. Cellular oxygen availability was optimized by increasing the number of gas capillaries and pO(2) of the oxygenation gas by a factor two. Pressure drop over the AMC-BAL and maximal shear stresses were low and not considered to be harmful. This information can be used to increase cellular efficiency and may ultimately lead to a more productive AMC-BAL