Charlotte Debbaut

From Vascular Corrosion Cast to Electrical Analog Model for the Study of Human Liver Hemodynamics and Perfusion

Hypothermic machine perfusion (HMP) is experiencing a revival in organ preservation due to the limitations of static cold storage and the need for better preservation of expanded criteria donor organs. For livers, perfusion protocols are still poorly defined, and damage of sinusoidal endothelial cells and heterogeneous perfusion are concerns. In this study, an electrical model of the human liver blood circulation is developed to enlighten internal pressure and flow distributions during HMP. Detailed vascular data on two human livers, obtained by combining vascular corrosion casting, micro-CT-imaging and image processing, were used to set up the electrical model. Anatomical data could be measured up to 5-6 vessel generations in each tree and showed exponential trend lines, used to predict data for higher generations. Simulated flow and pressure were in accordance with literature data. The model was able to simulate effects of pressure-driven HMP on liver hemodynamics and reproduced observations such as flow competition between the hepatic artery and portal vein. Our simulations further indicate that, from a pure biomechanical (shear stress) standpoint, HMP with low pressures should not result in organ damage, and that fluid viscosity has no effect on the shear stress experienced by the liver microcirculation in pressure-driven HMP.

Perfusion characteristics of the human hepatic microcirculation based on three-dimensional reconstructions and computational fluid dynamic analysis

The perfusion of the liver microcirculation is often analyzed in terms of idealized functional units (hexagonal liver lobules) based on a porous medium approach. More elaborate research is essential to assess the validity of this approach and to provide a more adequate and quantitative characterization of the liver microcirculation. To this end, we modeled the perfusion of the liver microcirculation using an image-based three-dimensional (3D) reconstruction of human liver sinusoids and computational fluid dynamics techniques. After vascular corrosion casting, a microvascular sample (±0.134 mm(3)) representing three liver lobules, was dissected from a human liver vascular replica and scanned using a high resolution (2.6 μm) micro-CT scanner. Following image processing, a cube (0.15 × 0.15 × 0.15 mm(3)) representing a sample of intertwined and interconnected sinusoids, was isolated from the 3D reconstructed dataset to define the fluid domain. Three models were studied to simulate flow along three orthogonal directions (i.e., parallel to the central vein and in the radial and circumferential directions of the lobule). Inflow and outflow guidances were added to facilitate solution convergence, and good quality volume meshes were obtained using approximately 9 × 10(6) tetrahedral cells. Subsequently, three computational fluid dynamics models were generated and solved assuming Newtonian liquid properties (viscosity 3.5 mPa s). Post-processing allowed to visualize and quantify the microvascular flow characteristics, to calculate the permeability tensor and corresponding principal permeability axes, as well as the 3D porosity. The computational fluid dynamics simulations provided data on pressure differences, preferential flow pathways and wall shear stresses. Notably, the pressure difference resulting from the flow simulation parallel to the central vein (0-100 Pa) was clearly smaller than the difference from the radial (0-170 Pa) and circumferential (0-180 Pa) flow directions. This resulted in a higher permeability along the central vein direction (k(d,33) = 3.64 × 10(-14) m(2)) in comparison with the radial (k(d,11) = 1.56 × 10(-14) m(2)) and circumferential (k(d,22) = 1.75 × 10(-14) m(2)) permeabilities which were approximately equal. The mean 3D porosity was 14.3. Our data indicate that the human hepatic microcirculation is characterized by a higher permeability along the central vein direction, and an about two times lower permeability along the radial and circumferential directions of a lobule. Since the permeability coefficients depend on the flow direction, (porous medium) liver microcirculation models should take into account sinusoidal anisotropy.

Preserving the morphology and evaluating the quality of liver grafts by hypothermic machine perfusion: a proof-of-concept study using discarded human livers.

The wider use of livers from expanded criteria donors and donation after circulatory death donors may help to improve access to liver transplantation. A prerequisite for safely using these higher risk livers is the development of objective criteria for assessing their condition before transplantation. Compared to simple cold storage, hypothermic machine perfusion (HMP) provides a unique window for evaluating liver grafts between procurement and transplantation. In this proof‐of‐concept study, we tested basic parameters during HMP that may reflect the condition of human liver grafts, and we assessed their morphology after prolonged HMP. Seventeen discarded human livers were machine‐perfused. Eleven livers were nontransplantable (major absolute contraindications and severe macrovesicular steatosis in the majority of the cases). Six livers were found in retrospect to be transplantable but could not be allocated and served as controls. Metabolic parameters (pH, lactate, partial pressure of oxygen, and partial pressure of carbon dioxide), enzyme release in the perfusate [aspartate aminotransferase (AST) and lactate dehydrogenase (LDH)], and arterial/portal resistances were monitored during HMP. Nontransplantable livers released more AST and LDH than transplantable livers. In contrast, arterial/portal vascular resistances and metabolic profiles did not differ between the 2 groups. Morphologically, transplantable livers remained well preserved after 24 hours of HMP. In conclusion, HMP preserves the morphology of human livers for prolonged periods. A biochemical analysis of the perfusate provides information reflecting the extent of the injury endured. Liver Transpl, 2012.

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).

A 3D porous media liver lobule model: the importance of vascular septa and anisotropic permeability for homogeneous perfusion

The hepatic blood circulation is complex, particularly at the microcirculatory level. Previously, 2D liver lobule models using porous media and a 3D model using real sinusoidal geometries have been developed. We extended these models to investigate the role of vascular septa (VS) and anisotropic permeability. The lobule was modelled as a hexagonal prism (with or without VS) and the tissue was treated as a porous medium (isotropic or anisotropic permeability). Models were solved using computational fluid dynamics. VS inclusion resulted in more spatially homogeneous perfusion. Anisotropic permeability resulted in a larger axial velocity component than isotropic permeability. A parameter study revealed that results are most sensitive to the lobule size and radial pressure drop. Our model provides insight into hepatic microhaemodynamics, and suggests that inclusion of VS in the model leads to perfusion patterns that are likely to reflect physiological reality. The model has potential for applications to unphysiological and pathological conditions.

Flow competition between hepatic arterial and portal venous flow during hypothermic machine perfusion preservation of porcine livers.

Hypothermic machine perfusion (HMP) is regarded as a better preservation method for donor livers than cold storage. During HMP, livers are perfused through the inlet blood vessels, namely the hepatic artery (HA) and the portal vein (PV). In previous HMP feasibility studies of porcine and human livers, we observed that the PV flow decreased while the HA flow increased. This flow competition restored either spontaneously or by lowering the HA pressure (PHA). Since this phenomenon had never been observed before and because it affects the HMP stability, it is essential to gain more insight into the determinants of flow competition. To this end, we investigated the influence of the HMP boundary conditions on liver flows during controlled experiments. This paper presents the flow effects induced by increasing PHA and by obstructing the outlet blood vessel, which is the vena cava inferior (VCI). Flow competition was evoked by increasing PHA to 55–70 mmHg, as well as by obstructing the VCI. Remarkably, a severe obstruction resulted in a repetitive and alternating tradeoff between the HA and PV flows. These phenomena could be related to intra-sinusoidal pressure alterations. Consequently, a higher PHA is most likely transmitted to the sinusoidal level. This increased sinusoidal pressure reduces the pressure drop between the PV and the sinusoids, leading to a decreased PV perfusion. Flow competition has not been encountered or evoked under physiological conditions and should be taken into account for the design of liver HMP protocols. Nevertheless, more research is necessary to determine the optimal parameters for stable HMP.

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

Due to the growing shortage of donor livers, more patients are waiting for transplantation. Living donor liver transplantation may help expanding the donor pool, but is often confronted with the small-for-size syndrome. Since the hemodynamic effects of partial hepatectomy are not fully understood, we developed an electrical rat liver model to compare normal with resected liver hemodynamics. Detailed geometrical data and 3-D reconstructions of the liver vasculature of two rats were gathered by combining vascular corrosion casting, micro-CT scanning, and image processing. Data extrapolations allowed obtaining a total liver pressure- and flow-driven electrical analog. Subsequently, virtual resections led to 70%, 80%, or 90% partial hepatectomy models. Results demonstrated hyperperfusion effects such as portal hypertension and elevated lobe-specific portal venous flows (11, 12, and 24 mmHg, and 1.0-3.0, 1.8-3.5, and 7.4 ml/min for 70%, 80%, and 90% hepatectomy, respectively). Comparison of two 90% resection techniques demonstrated different total arterial flows (0.28 ml/min versus 0.61 ml/min), portal (24 mmHg versus 21 mmHg), and sinusoidal pressures (14 mmHg versus 9.5-12 mmHg), probably leading to better survival for lower portal and sinusoidal pressures. Toward the future, the models may be extrapolated to human livers and help us to optimize hepatectomy planning.

Mathematical modeling of intraperitoneal drug delivery: simulation of drug distribution in a single tumor nodule

Abstract The intraperitoneal (IP) administration of chemotherapy is an alternative treatment for peritoneal carcinomatosis, allowing for higher intratumor concentrations of the cytotoxic agent compared to intravenous administration. Nevertheless, drug penetration depths are still limited to a few millimeters. It is thus necessary to better understand the limiting factors behind this poor penetration in order to improve IP chemotherapy delivery. By developing a three-dimensional computational fluid dynamics (CFD) model for drug penetration in a tumor nodule, we investigated the impact of a number of key parameters on the drug transport and penetration depth during IP chemotherapy. Overall, smaller tumors showed better penetration than larger ones, which could be attributed to the lower IFP in smaller tumors. Furthermore, the model demonstrated large improvements in penetration depth by subjecting the tumor nodules to vascular normalization therapy, and illustrated the importance of the drug that is used for therapy. Explicitly modeling the necrotic core had a limited effect on the simulated penetration. Similarly, the penetration depth remained virtually constant when the Darcy permeability of the tissue changed. Our findings illustrate that the developed parametrical CFD model is a powerful tool providing more insight in the drug transport and penetration during IP chemotherapy.

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.

Validation and calibration of an electrical analog model of human liver perfusion based on hypothermic machine perfusion experiments

Purpose Hypothermic machine perfusion (HMP) is reviving as a better preservation method for donor livers than the golden standard of cold storage, but still faces challenges such as the risk for endothelial damage and flow competition between the arterial and portal venous inflow. Therefore, we previously developed an electrical analog model to investigate the effect of HMP settings on the human liver hemodynamics. While the model provided plausible results, it is based on a number of assumptions and its performance was never subjected to experimental validation. To this end, we present a new methodology to validate and calibrate this model to a specific liver. Methods and Results HMP experiments were performed to capture the perfusion behavior of a human liver during varying perfusion settings. Simultaneous pressure and flow signals were acquired at the hepatic artery, portal vein, and vena cava inferior. The calculation of hydraulic input impedances enabled reduced Windkessel models to be fitted to the global hepatic perfusion properties as an intermediate step. Based on these Windkessel models, the extended electrical analog model was calibrated to the specific available liver. Results revealed that literature values of one of the critical model parameters (wall viscoelasticity) are a few orders of magnitude off, having important consequences for simulated (pulsatile) hemodynamic variables. Conclusions A novel methodology, based on HMP experiments, signal processing and unconstrained nonlinear optimization was developed to validate and calibrate the liver-specific extended electrical model. Future research may focus on extending this approach to other applications (e.g. liver pathologies such as cirrhosis).