Hierarchical Modeling of the Liver Vascular System

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.

Lumped parameter liver simulation to predict acute haemodynamic alterations following partial resections

Partial liver resections are routinely performed in living donor liver transplantation and to debulk tumours in liver malignancies, but surgical decisions on vessel reconstruction for adequate inflow and outflow are challenging. Pre-operative evaluation is often limited to radiological imaging, which fails to account for post-resection haemodynamic alterations. Substantial evidence suggests post-surgical increase in local volume flow rate enhances shear stress, signalling hepatic regeneration, but excessive shear stress has been postulated to result in small for size syndrome and liver failure. Predicting haemodynamic alterations throughout the liver is particularly challenging due to the dendritic architecture of the vasculature, spanning several orders of magnitude in diameter. Therefore, we developed a mathematical lumped parameter model with realistic heterogeneities capturing inflow/outflow of the human liver to simulate acute perfusion alterations following surgical resection. Our model is parametrized using clinical measurements, relies on a single free parameter and accurately captures established perfusion characteristics. We quantify acute changes in volume flow rate, flow speed and wall shear stress following variable, realistic liver resections and make comparisons with the intact liver. Our numerical model runs in minutes and can be adapted to patient-specific anatomy, providing a novel computational tool aimed at assisting pre- and intra-operative surgical decisions for liver resections.

Assessing Enhanced Acoustic Absorption From Sonosensitive Perfluorocarbon Emulsion With Magnetic Resonance-Guided High-Intensity Focused Ultrasound and a Percolated Tissue-Mimicking Flow Phantom

OBJECTIVE

Sonosensitive high-boiling point perfluorocarbon F₈TAC₁₈-PFOB emulsions previously exhibited thermal enhancement during focused ultrasound heating in ex vivo pig livers, kidneys and a laminar flow phantom. The main objectives of this study were to evaluate heating under turbulent conditions, observe perfusion effects, quantify heating in terms of acoustic absorption and model the experimental data.

METHODS

In this study, similar perfluorocarbon emulsions were circulated at incremental concentrations of 0.07, 0.13, 0.19 and 0.25% v:v through a percolated turbulent flow phantom, more representative of the biological tissue than a laminar flow phantom. The concentrations represent the droplet content in only the perfused fluid, rather than the droplet concentration throughout the entire cross-section. The temperature was measured with magnetic resonance thermometry, during focused ultrasound sonications of 67 W, 95% duty cycle and 33 s duration. These were used in Bioheat equation simulations to investigate in silico the thermal phenomena. The temperature change was compared with the control condition by circulating de-gassed and de-ionized water through the flow phantom without droplets.

RESULTS

With these 1.24 µm diameter droplets at 0.25% v:v, the acoustic absorption coefficient increased from 0.93 ± 0.05 at 0.0% v:v to 1.82 ± 0.22 m^-1 at 0.25% v:v using a 0.1 mL s^-1 flow rate. Without perfusion at 0.25% v:v, an increase was observed from 1.23 ± 0.07 m^-1 at 0.0% v:v to 1.65 ± 0.17 m^-1.

CONCLUSION

The results further support previously reported thermal enhancement with F₈TAC₁₈-PFOB emulsion, quantified the increased absorption at small concentration intervals, illustrated that the effects can be observed in a variety of visceral tissue models and provided a method to simulate untested scenarios.

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.

Importance of Anatomical Variation of the Hepatic Artery for Complicated Liver and Pancreatic Surgeries: A Review Emphasizing Origin and Branching

Knowledge of anatomical variations of the hepatic artery from its origin to intrahepatic segmentation is of utmost importance for planning upper abdominal surgeries including liver transplantation, pancreatoduodenectomy, and biliary reconstruction. The origin and branching pattern of the hepatic artery was thoroughly described by the classification of Michels and Hiatt. Some rare variations of the hepatic artery were classified by Kobayashi and Koops. By the use of the multidetector computed tomography (MDCT) technique, the branching pattern of the hepatic artery can be visualized quite accurately. Unawareness of these arterial variations may lead to intraoperative injuries such as necrosis, abscess, and failure of the liver and pancreas. The origin and course of the aberrant hepatic arteries are crucial in the surgical planning of carcinoma of the head of the pancreas and hepatobiliary surgeries. In liver transplant surgeries, to minimize intraoperative bleeding complications and postoperative thrombosis, exact anatomy of the branching of the hepatic artery, its variations and intrahepatic course is of utmost importance. This review discusses variations in the anatomy of the hepatic artery from its origin to branching by the use of advanced imaging techniques and its effect on the liver, pancreatic, biliary and gastric surgeries.

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.

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

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