An individual-based model to explore the impact of psychological stress on immune infiltration into tumour spheroids.

In recentin vitroexperiments on co-culture between breast tumour spheroids and activated immune cells, it was observed that the introduction of the stress hormone cortisol resulted in a decreased immune cell infiltration into the spheroids. Moreover, the presence of cortisol deregulated the normal levels of the pro- and anti-inflammatory cytokines IFN-γand IL-10. We present an individual-based model to explore the interaction dynamics between tumour and immune cells under psychological stress conditions. With our model, we explore the processes underlying the emergence of different levels of immune infiltration, with particular focus on the biological mechanisms regulated by IFN-γand IL-10. The set-up of numerical simulations is defined to mimic the scenarios considered in the experimental study. Similarly to the experimental quantitative analysis, we compute a score that quantifies the level of immune cell infiltration into the tumour. The results of numerical simulations indicate that the motility of immune cells, their capability to infiltrate through tumour cells, their growth rate and the interplay between these cell parameters can affect the level of immune cell infiltration in different ways. Ultimately, numerical simulations of this model support a deeper understanding of the impact of biological stress-induced mechanisms on immune infiltration.

Mathematical modeling of adipocyte size distributions: Identifiability and parameter estimation from rat data.

Fat cells, called adipocytes, are designed to regulate energy homeostasis by storing energy in the form of lipids. Adipocyte size distribution is assumed to play a role in the development of obesity-related diseases. These cells that do not have a characteristic size, indeed a bimodal size distribution is observed in adipose tissue. We propose a model based on a partial differential equation to describe adipocyte size distribution. The model includes a description of the lipid fluxes and the cell size fluctuations and using a formulation of a stationary solution fast computation of bimodal distribution is achieved. We investigate the parameter identifiability and estimate parameter values with CMA-ES algorithm. We first validate the procedure on synthetic data, then we estimate parameter values with experimental data of 32 rats. We discuss the estimated parameter values and their variability within the population, as well as the relation between estimated values and their biological significance. Finally, a sensitivity analysis is performed to specify the influence of parameters on cell size distribution and explain the differences between the model and the measurements. The proposed framework enables the characterization of adipocyte size distribution with four parameters and can be easily adapted to measurements of cell size distribution in different health conditions.

Discrete and continuum models for the coevolutionary dynamics between CD8+ cytotoxic T lymphocytes and tumour cells.

We present an individual-based model for the coevolutionary dynamics between CD8+ cytotoxic T lymphocytes (CTLs) and tumour cells. In this model, every cell is viewed as an individual agent whose phenotypic state is modelled by a discrete variable. For tumour cells, this variable represents a parameterization of the antigen expression profiles, while for CTLs it represents a parameterization of the target antigens of T-cell receptors (TCRs). We formally derive the deterministic continuum limit of this individual-based model, which comprises a non-local partial differential equation for the phenotype distribution of tumour cells coupled with an integro-differential equation for the phenotype distribution of CTLs. The biologically relevant homogeneous steady-state solutions of the continuum model equations are found. The linear-stability analysis of these steady-state solutions is then carried out in order to identify possible conditions on the model parameters that may lead to different outcomes of immune competition and to the emergence of patterns of phenotypic coevolution between tumour cells and CTLs. We report on computational results of the individual-based model, and show that there is a good agreement between them and analytical and numerical results of the continuum model. These results shed light on the way in which different parameters affect the coevolutionary dynamics between tumour cells and CTLs. Moreover, they support the idea that TCR-tumour antigen binding affinity may be a good intervention target for immunotherapy and offer a theoretical basis for the development of anti-cancer therapy aiming at engineering TCRs so as to shape their affinity for cancer targets.

A Hybrid Discrete-Continuum Modelling Approach to Explore the Impact of T-Cell Infiltration on Anti-tumour Immune Response.

We present a spatial hybrid discrete-continuum modelling framework for the interaction dynamics between tumour cells and cytotoxic T cells, which play a pivotal role in the immune response against tumours. In this framework, tumour cells and T cells are modelled as individual agents while chemokines that drive the chemotactic movement of T cells towards the tumour are modelled as a continuum. We formally derive the continuum counterpart of this model, which is given by a coupled system that comprises an integro-differential equation for the density of tumour cells, a partial differential equation for the density of T cells and a partial differential equation for the concentration of chemokines. We report on computational results of the hybrid model and show that there is an excellent quantitative agreement between them and numerical solutions of the corresponding continuum model. These results shed light on the mechanisms that underlie the emergence of different levels of infiltration of T cells into the tumour and elucidate how T-cell infiltration shapes anti-tumour immune response. Moreover, to present a proof of concept for the idea that, exploiting the computational efficiency of the continuum model, extensive numerical simulations could be carried out, we investigate the impact of T-cell infiltration on the response of tumour cells to different types of anti-cancer immunotherapy.

A mathematical model to study the impact of intra-tumour heterogeneity on anti-tumour CD8+ T cell immune response.

Intra-tumour heterogeneity (ITH) has a strong impact on the efficacy of the immune response against solid tumours. The number of sub-populations of cancer cells expressing different antigens and the percentage of immunogenic cells (i.e. tumour cells that are effectively targeted by immune cells) in a tumour are both expressions of ITH. Here, we present a spatially explicit stochastic individual-based model of the interaction dynamics between tumour cells and CD8+ T cells, which makes it possible to dissect out the specific impact of these two expressions of ITH on anti-tumour immune response. The set-up of numerical simulations of the model is defined so as to mimic scenarios considered in previous experimental studies. Moreover, the ability of the model to qualitatively reproduce experimental observations of successful and unsuccessful immune surveillance is demonstrated. First, the results of numerical simulations of this model indicate that the presence of a larger number of sub-populations of tumour cells that express different antigens is associated with a reduced ability of CD8+ T cells to mount an effective anti-tumour immune response. Secondly, the presence of a larger percentage of tumour cells that are not effectively targeted by CD8+ T cells may reduce the effectiveness of anti-tumour immunity. Ultimately, the mathematical model presented in this paper may provide a framework to help biologists and clinicians to better understand the mechanisms that are responsible for the emergence of different outcomes of immunotherapy.

Modeling and characterization of inter-individual variability in CD8 T cell responses in mice.

To develop vaccines it is mandatory yet challenging to account for inter-individual variability during immune responses. Even in laboratory mice, T cell responses of single individuals exhibit a high heterogeneity that may come from genetic backgrounds, intra-specific processes (e.g. antigen-processing and presentation) and immunization protocols.To account for inter-individual variability in CD8 T cell responses in mice, we propose a dynamical model coupled to a statistical, nonlinear mixed effects model. Average and individual dynamics during a CD8 T cell response are characterized in different immunization contexts (vaccinia virus and tumor). On one hand, we identify biological processes that generate inter-individual variability (activation rate of naive cells, the mortality rate of effector cells, and dynamics of the immunogen). On the other hand, introducing categorical covariates to analyze two different immunization regimens, we highlight the steps of the response impacted by immunogens (priming, differentiation of naive cells, expansion of effector cells and generation of memory cells). The robustness of the model is assessed by confrontation to new experimental data.Our approach allows to investigate immune responses in various immunization contexts, when measurements are scarce or missing, and contributes to a better understanding of inter-individual variability in CD8 T cell immune responses.

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 (PPV) 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 PPV 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 PPV 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.

Kinetics of Hepatic Volume Evolution and Architectural Changes after Major Resection in a Porcine Model.

BACKGROUND: The hepatic volume gain following resection is essential for clinical recovery. Previous studies have focused on cellular regeneration. This study aims to explore the rate of hepatic regeneration of the porcine liver following major resection, highlighting estimates of the early microarchitectural changes that occur during the cellular regeneration. METHODS: Nineteen large white pigs had 75% resection with serial measurements of the hepatic volume, density, blood flow, and architectural changes. RESULTS: The growth rate initially was 45% per day, then rapidly decreased and was accompanied by a similar pattern of hepatic fat deposition. The architectural changes showed a significant increase in the Ki67 expression (p < 0.0001) in the days following resection with a peak on the 2nd day and nearly normalized on day 7. The expression of CD31 increased significantly on the 2nd and 3rd days compared to the pre-resection samples (p = 0.03). Hepatic artery flow per liver volume remained at baseline ranges during regeneration. Portal flow per liver volume increased after liver resection (p < 0.001), was still elevated on the 1st postoperative day, then decreased. Correlations were significantly negative between the hepatic volume increase on day 3 and the hepatic oxygen consumption and the net lactate production at the end of the procedure (r = -0.82, p = 0.01, and r = -0.70, p = 0.03). CONCLUSION: The volume increase in the first days - a fast process - is not explained by cellular proliferation alone. The liver/body weight ratio is back to 50% of the preoperative value after 3 days to close to 100% volume regain on days 10-15.

Transit time ultrasound perivascular flow probe technology is superior to MR imaging on hepatic blood flow measurement in a porcine model.

BACKGROUND: The hepatic hemodynamics is an essential parameter in surgical planning as well as in various disease processes. The transit time ultrasound (TTUS) perivascular flow probe technology is widely used in clinical practice to evaluate the hepatic inflow, yet invasive. The phase-contrast-MRI (PC-MRI) is not invasive and potentially applicable in assessing the hepatic blood flow. In the present study, we compared the hepatic inflow rates using the PC-MRI and the TTUS probe, and evaluated their predictive value of post-hepatectomy adverse events. METHODS: Eighteen large white pigs were anaesthetized for PC-MRI and approximately 75% hepatic resection was performed under a unified protocol. The blood flow was measured in the hepatic artery (Qha), the portal vein (Qpv), and the aorta above the celiac trunk (Qca) using PC-MRI, and was compared to the TTUS probe. The Bland-Altman method was conducted and a partial least squares regression (PLS) model was implemented. RESULTS: The mean Qpv measured in PC-MRI was 0.55 ±â€¯0.12 L/min, and in the TTUS probe was 0.74 ±â€¯0.17 L/min. Qca was 1.40 ±â€¯0.47 L/min in the PC-MRI and 2.00 ±â€¯0.60 L/min in the TTUS probe. Qha was 0.17 ±â€¯0.10 L/min in the PC-MRI, and 0.13 ±â€¯0.06 L/min in the TTUS probe. The Bland-Altman method revealed that the estimated bias of Qca in the PC-MRI was 32% (95% CI: -49% to 15%); Qha 17% (95% CI: -15% to 51%); and Qpv 40% (95% CI: -62% to 18%). The TTUS probe had a higher weight in predicting adverse outcomes after 75% resection compared to the PC-MRI (ß= 0.35 and 0.43 vs ß = 0.22 and 0.07, for tissue changes and premature death, respectively). CONCLUSIONS: There is a tendency of the PC-MRI to underestimate the flow measured by the TTUS probes. The TTUS probe measures are more predictive of relevant post-hepatectomy outcomes.

Closed-Loop Lumped Parameter Modeling of Hemodynamics During Cirrhogenesis in Rats.

OBJECTIVE: Cirrhosis is the common end stage of any given chronic liver disease, developing after persistent destruction and regeneration of parenchymal liver cells. The associated architectural distortion increases the intrahepatic vascular resistance, leading to portal hypertension and systemic circulatory disorders. This study investigates the impact of the changing vascular resistances on the hepatic and global circulation hemodynamics during cirrhogenesis. METHODS: Cirrhogenesis was revisited using the thioacetamide rat model (N = 20). Rats were sacrificed at weeks 0, 6, 12, and 18. For each time-point, three-dimensional vascular geometries were created by combining hepatic vascular corrosion casting with µCT imaging. Morphological quantification of the trees branching topology provided the input for a lobe-specific lumped parameter model of the liver that was coupled to a closed-loop model of the entire circulation of the rat. Hemodynamics was simulated in physiological and pathological circumstances. RESULTS: The simulations showed the effect of the liver vascular resistances (driven by the hepatic venous resistance increase) on liver hemodynamics with portal hypertension observed after 12 weeks. The closed-loop model was further adapted to account for systemic circulatory compensation mechanisms and disorders frequently observed in cirrhosis and simulated their impact on the hepatic, systemic, and pulmonary hemodynamics. CONCLUSION: The simulations explain how vascular changes due to cirrhosis severely disrupt both hepatic and global hemodynamics. SIGNIFICANCE: This study is a priori the first to model the rat's entire blood circulation during cirrhogenesis. Since it is able to simulate cirrhosis main characteristics, the model may be translated to humans for the assessment of liver interventions.

Model and methods to assess hepatic function from indocyanine green fluorescence dynamical measurements of liver tissue.

The indocyanine green (ICG) clearance, presented as plasma disappearance rate is, presently, a reliable method to estimate the hepatic "function". However, this technique is not instantaneously available and thus cannot been used intra-operatively (during liver surgery). Near-infrared spectroscopy enables to assess hepatic ICG concentration over time in the liver tissue. This article proposes to extract more information from the liver intensity dynamics by interpreting it through a dedicated pharmacokinetics model. In order to account for the different exchanges between the liver tissues, the proposed model includes three compartments for the liver model (sinusoids, hepatocytes and bile canaliculi). The model output dependency to parameters is studied with sensitivity analysis and solving an inverse problem on synthetic data. The estimation of model parameters is then performed with in-vivo measurements in rabbits (El-Desoky et al. 1999). Parameters for different liver states are estimated, and their link with liver function is investigated. A non-linear (Michaelis-Menten type) excretion rate from the hepatocytes to the bile canaliculi was necessary to reproduce the measurements for different liver conditions. In case of bile duct ligation, the model suggests that this rate is reduced, and that the ICG is stored in the hepatocytes. Moreover, the level of ICG remains high in the blood following the ligation of the bile duct. The percentage of retention of indocyanine green in blood, which is a common test for hepatic function estimation, is also investigated with the model. The impact of bile duct ligation and reduced liver inflow on the percentage of ICG retention in blood is studied. The estimation of the pharmacokinetics model parameters may lead to an evaluation of different liver functions.

Modulating Portal Hemodynamics With Vascular Ring Allows Efficient Regeneration After Partial Hepatectomy in a Porcine Model.

OBJECTIVE: To investigate safety and efficacy of temporary portal hemodynamics modulation with a novel percutaneously adjustable vascular ring (MID-AVR) onto a porcine model of 75% hepatectomy. BACKGROUND: Postoperative liver failure is a leading cause of mortality after major hepatectomy. Portal flow modulation is an increasingly accepted concept to prevent postoperative liver failure. Nonetheless, the current strategies have shortcomings. METHODS: Resection was performed under hemodynamic monitoring in 17 large, white pigs allocated into 2 groups. Eight pigs had ring around the portal vein for 3 days with the aim of reducing changes in hemodynamics due to hepatectomy. Analysis of hemodynamics, laboratory, and histopathological parameters was performed. RESULTS: Percutaneous inflation, deflation, and removal of the MID-AVR were safe. Two (25%) pigs in the MID-AVR group and 4 (45%) controls died before day 3 (P = NS). A moderate increase of portal flow rate per liver mass after resection was associated with better survival (P = 0.017). The portocaval pressure gradient was lower after hepatectomy in the MID-AVR group (P = 0.001). Postoperative serum bilirubin levels were lower in the MID-AVR group (P = 0.007 at day 5). In the MID-AVR group, the Ki67 index was significantly higher on day 3 (P = 0.043) and the architectural derangement was lower (P < 0.05). Morphometric quantification of the bile canaliculi revealed a significantly lower number of intersection branches (P < 0.05) and intersection nodes (P < 0.001) on day 7 compared with the preoperative specimen, in the control group. These differences were not found in the ring group. CONCLUSIONS: MID-AVR is safe for portal hemodynamics modulation. It might improve liver regeneration by protecting liver microarchitecture.

Simplified technique for 75% and 90% hepatic resection with hemodynamic monitoring in a large white swine model.

BACKGROUND: Accurate measuring of the hepatic hemodynamic parameters in humans is inconvenient. Swine has been a favorite surgical model for the study of liver conditions due to many similarities with human livers. However, pigs cannot tolerate pedicle clamping and to reduce bleeding during resection a simplified technique is required. The aim of this study is to present a simplified technique for different percentages of hepatic resection in a porcine model. METHODS: Twenty-two consecutive large white pigs were operated with 75% and 90% liver resection. Computarized tomography liver volumetry is performed before and after surgery. In both types of surgery, hemodynamic monitoring was performed using a specialized apparatus. RESULTS: Resections were performed in both groups successfully. The residual volume in the planned 75% was 235 ± 77 mL and 118 ± 119 mL in the planned 90% resection. For 75% resection, the portal flow was reduced after resection by 8.13 ± 28%, which might be part of systemic circulatory depression. However, the portal pressure increased by 20.1 ± 51%. The hepatic artery flow decreased by 63.86 ± 26.3% as well as the pressure by 5 ± 28%. The central venous pressure at the start of surgery was 3.34 ± 1.9 mm Hg and 2.8 ± 2.2 mm Hg at the end of surgery. The portacaval pressure gradient was 4.4 ± 2.9 mm Hg at the beginning of surgery and was 5.9 ± 2.8 mm Hg at the end of surgery. For 90% resection, the portal flow decreased by 33.6 ± 12.6% and the pressure increased by 104 ± 58%. The hepatic artery flow decreased by 88 ± 7%, and the pressure decreased by 5 ± 14.8%. The central venous pressure was 3.5 ± 1.7 mm Hg before resection and 3 ± 2.5 mm Hg after resection. The portacaval pressure gradient was 3.8 ± 1.1 mm Hg before resection and 8 ± 3.7 mm Hg after resection. The mean anesthesia time was 6.6 ± 1.05 h and 6.9 ± 0.5 h for 75% and 90% resection, respectively. The mean operative time was 4.6 ± 0.9 h and 5 ± 0.7 h for 75% and 90% resections, respectively. The mean time for hepatectomy was 1.23 ± 0.76 h and 2.4 ± 0.1 h for 75% and 90% resection, respectively. The mean time consumed in the measurements was 2.28 ± 1.4 h and 1.1 ± 0.3 h for 75% and 90% resections, respectively. The mean volume of aspirated fluid and blood in the 75% resection was 1062 ± 512 mL, while it was 1050 ± 354 mL in 90% resections. CONCLUSIONS: The hereby described technique is simple and easily applicable for major liver resection in a porcine model. Portal flow decreases after 90% resection more than in 75% due to the relative reduction of remnant hepatic mass. There was a larger increase in portal pressure following 90% compared to 75% resection. The hepatic artery flow decreases more in 90% than in 75% resections.

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.