Mathematical model of liver regeneration in human live donors

Quantitative methods for optimizing patient outcomes in liver transplantation

Liver transplantation (LT) is a lifesaving yet complex intervention with considerable challenges impacting graft and patient outcomes. Despite best practices, 5-year graft survival is only 70%. Sophisticated quantitative techniques offer potential solutions by assimilating multifaceted data into insights exceeding human cognition. Optimizing donor-recipient matching and graft allocation presents additional intricacies, involving the integration of clinical and laboratory data to select the ideal donor and recipient pair. Allocation must balance physiological variables with geographical and logistical constraints and timing. Quantitative methods can integrate these complex factors to optimize graft utilization. Such methods can also aid in personalizing treatment regimens, drawing on both pretransplant and posttransplant data, possibly using continuous immunological monitoring to enable early detection of graft injury or infected states. Advanced analytics is thus poised to transform management in LT, maximizing graft and patient survival. In this review, we describe quantitative methods applied to organ transplantation, with a focus on LT. These include quantitative methods for (1) utilizing and allocating donor organs equitably and optimally, (2) improving surgical planning through preoperative imaging, (3) monitoring graft and immune status, (4) determining immunosuppressant doses, and (5) establishing and maintaining the health of graft and patient after LT.

Longitudinal ultrasound imaging and network modeling in rats reveal sex-dependent suppression of liver regeneration after resection in alcoholic liver disease

Liver resection is an important surgical technique in the treatment of cancers and transplantation. We used ultrasound imaging to study the dynamics of liver regeneration following two-thirds partial hepatectomy (PHx) in male and female rats fed via Lieber-deCarli liquid diet protocol of ethanol or isocaloric control or chow for 5–7 weeks. Ethanol-fed male rats did not recover liver volume to the pre-surgery levels over the course of 2 weeks after surgery. By contrast, ethanol-fed female rats as well as controls of both sexes showed normal volume recovery. Contrary to expectations, transient increases in both portal and hepatic artery blood flow rates were seen in most animals, with ethanol-fed males showing higher peak portal flow than any other experimental group. A computational model of liver regeneration was used to evaluate the contribution of physiological stimuli and estimate the animal-specific parameter intervals. The results implicate lower metabolic load, over a wide range of cell death sensitivity, in matching the model simulations to experimental data of ethanol-fed male rats. However, in the ethanol-fed female rats and controls of both sexes, metabolic load was higher and in combination with cell death sensitivity matched the observed volume recovery dynamics. We conclude that adaptation to chronic ethanol intake has a sex-dependent impact on liver volume recovery following liver resection, likely mediated by differences in the physiological stimuli or cell death responses that govern the regeneration process. Immunohistochemical analysis of pre- and post-resection liver tissue validated the results of computational modeling by associating lack of sensitivity to cell death with lower rates of cell death in ethanol-fed male rats. Our results illustrate the potential for non-invasive ultrasound imaging to assess liver volume recovery towards supporting development of clinically relevant computational models of liver regeneration.

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.

Predicting liver regeneration following major resection

Breakdown of synthesis, excretion and detoxification defines liver failure. Post-hepatectomy liver failure (PHLF) is specific for liver resection and a rightfully feared complication due to high lethality and limited therapeutic success. Individual cytokine and growth factor profiles may represent potent predictive markers for recovery of liver function. We aimed to investigate these profiles in post-hepatectomy regeneration. This study combined a time-dependent cytokine and growth factor profiling dataset of a training (30 patients) and a validation (14 patients) cohorts undergoing major liver resection with statistical and predictive models identifying individual pathway signatures. 2319 associations were tested. Primary hepatocytes isolated from patient tissue samples were stimulated and their proliferation was analysed through DNA content assay. Common expression trajectories of cytokines and growth factors with strong correlation to PHLF, morbidity and mortality were identified despite highly individual perioperative dynamics. Especially, dynamics of EGF, HGF, and PLGF were associated with mortality. PLGF was additionally associated with PHLF and complications. A global association-network was calculated and validated to investigate interdependence of cytokines and growth factors with clinical attributes. Preoperative cytokine and growth factor signatures were identified allowing prediction of mortality following major liver resection by regression modelling. Proliferation analysis of corresponding primary human hepatocytes showed associations of individual regenerative potential with clinical outcome. Prediction of PHLF was possible on as early as first postoperative day (POD1) with AUC above 0.75. Prediction of PHLF and mortality is possible on POD1 with liquid-biopsy based risk profiling. Further utilization of these models would allow tailoring of interventional strategies according to individual profiles.

Prediction of Liver Weight Recovery by an Integrated Metabolomics and Machine Learning Approach After 2/3 Partial Hepatectomy

Liver has an ability to regenerate itself in mammals, whereas the mechanism has not been fully explained. Here we used a GC/MS-based metabolomic method to profile the dynamic endogenous metabolic change in the serum of C57BL/6J mice at different times after 2/3 partial hepatectomy (PHx), and nine machine learning methods including Least Absolute Shrinkage and Selection Operator Regression (LASSO), Partial Least Squares Regression (PLS), Principal Components Regression (PCR), k-Nearest Neighbors (KNN), Support Vector Machines (SVM), Random Forest (RF), eXtreme Gradient Boosting (xgbDART), Neural Network (NNET) and Bayesian Regularized Neural Network (BRNN) were used for regression between the liver index and metabolomic data at different stages of liver regeneration. We found a tree-based random forest method that had the minimum average Mean Absolute Error (MAE), Root Mean Squared Error (RMSE) and the maximum R square (R²) and is time-saving. Furthermore, variable of importance in the project (VIP) analysis of RF method was performed and metabolites with VIP ranked top 20 were selected as the most critical metabolites contributing to the model. Ornithine, phenylalanine, 2-hydroxybutyric acid, lysine, etc. were chosen as the most important metabolites which had strong correlations with the liver index. Further pathway analysis found Arginine biosynthesis, Pantothenate and CoA biosynthesis, Galactose metabolism, Valine, leucine and isoleucine degradation were the most influenced pathways. In summary, several amino acid metabolic pathways and glucose metabolism pathway were dynamically changed during liver regeneration. The RF method showed advantages for predicting the liver index after PHx over other machine learning methods used and a metabolic clock containing four metabolites is established to predict the liver index during liver regeneration.

Hepatectomy-Induced Alterations in Hepatic Perfusion and Function - Toward Multi-Scale Computational Modeling for a Better Prediction of Post-hepatectomy Liver Function

Liver resection causes marked perfusion alterations in the liver remnant both on the organ scale (vascular anatomy) and on the microscale (sinusoidal blood flow on tissue level). These changes in perfusion affect hepatic functions via direct alterations in blood supply and drainage, followed by indirect changes of biomechanical tissue properties and cellular function. Changes in blood flow impose compression, tension and shear forces on the liver tissue. These forces are perceived by mechanosensors on parenchymal and non-parenchymal cells of the liver and regulate cell-cell and cell-matrix interactions as well as cellular signaling and metabolism. These interactions are key players in tissue growth and remodeling, a prerequisite to restore tissue function after PHx. Their dysregulation is associated with metabolic impairment of the liver eventually leading to liver failure, a serious post-hepatectomy complication with high morbidity and mortality. Though certain links are known, the overall functional change after liver surgery is not understood due to complex feedback loops, non-linearities, spatial heterogeneities and different time-scales of events. Computational modeling is a unique approach to gain a better understanding of complex biomedical systems. This approach allows (i) integration of heterogeneous data and knowledge on multiple scales into a consistent view of how perfusion is related to hepatic function; (ii) testing and generating hypotheses based on predictive models, which must be validated experimentally and clinically. In the long term, computational modeling will (iii) support surgical planning by predicting surgery-induced perfusion perturbations and their functional (metabolic) consequences; and thereby (iv) allow minimizing surgical risks for the individual patient. Here, we review the alterations of hepatic perfusion, biomechanical properties and function associated with hepatectomy. Specifically, we provide an overview over the clinical problem, preoperative diagnostics, functional imaging approaches, experimental approaches in animal models, mechanoperception in the liver and impact on cellular metabolism, omics approaches with a focus on transcriptomics, data integration and uncertainty analysis, and computational modeling on multiple scales. Finally, we provide a perspective on how multi-scale computational models, which couple perfusion changes to hepatic function, could become part of clinical workflows to predict and optimize patient outcome after complex liver surgery.

Influence of cytokines, circulating markers and growth factors on liver regeneration and post-hepatectomy liver failure: a systematic review and meta-analysis

The pathophysiology of post-hepatectomy liver failure is not entirely understood but is rooted in the disruption of normal hepatocyte regeneration and homeostasis. Current investigations of post-hepatectomy liver failure and regeneration are focused on evaluation of circulating hepatic function parameters (transaminases, cholestasis, and coagulation parameters), volumetry and hepatic hemodynamics. However, identification of biochemical factors associated with regeneration and post hepatectomy liver failure is crucial for understanding the pathophysiology and identification of patients at risk. The objective of the present systematic review was to identify circulating factors associated with liver regeneration and post hepatectomy liver failure in patients undergoing hepatectomy. The quantitative analysis was intended if studies provided sufficient data. Electronic databases (MEDLINE via PubMed, Web of Knowledge, Cochrane Library and WHO International Clinical Trials Registry Platform) were searched for publications on cell signaling factors in liver regeneration and post-hepatectomy liver failure following liver resection in clinical setting. No date restriction was given. No language restriction was used. Studies were assessed using MINORS. This study was registered at PROSPERO (CRD42020165384) prior to data extraction. In total 1953 publications were evaluated for titles and abstracts after exclusion of duplicates. Full texts of 167 studies were further evaluated for inclusion. 26 articles were included in the review and 6 publications were included in the meta-analyses. High levels of serum hyaluronic acid even preoperatively are associated with PHLF but especially increased levels early after resection are predictive of PHLF with high sensitivity and specificity. Postoperative elevation of HA to levels between 100 and 500 ng/ml is increased the risk for PHLF ([OR] = 246.28, 95% [CI]: 11.82 to 5131.83; p = 0.0004) Inteleukin-6 levels show contradicting result in association with organ dysfunction. HGF positively correlates with liver regeneration. Overall, due to heterogeneity, scarcity, observational study design and largely retrospective analysis, the certainty of evidence, assessed with GRADE, is very low. High levels of serum hyaluronic acid show a strong association with PHLF and increased levels after resection are predictive of PHLF with high sensitivity and specificity, even on POD1. Interleukin-6 levels need to be studied further due to contradictive results in association with organ dysfunction. For HGF, no quantitative analysis could be made. Yet, most studies find positive correlation between high HGF levels and regeneration. Prospective studies investigating HGF and other growth factors, hyaluronic acid and interleukins 1 and 6 in correlation with liver regeneration measured sequentially through e.g. volumetry, and liver function parameters, preferably expanding the analysis to include dynamic liver function tests, are needed to sufficiently illustrate the connection between biomolecule levels and clinical outcomes.

Model-based virtual patient analysis of human liver regeneration predicts critical perioperative factors controlling the dynamic mode of response to resection

BACKGROUND

Liver has the unique ability to regenerate following injury, with a wide range of variability of the regenerative response across individuals. Existing computational models of the liver regeneration are largely tuned based on rodent data and hence it is not clear how well these models capture the dynamics of human liver regeneration. Recent availability of human liver volumetry time series data has enabled new opportunities to tune the computational models for human-relevant time scales, and to predict factors that can significantly alter the dynamics of liver regeneration following a resection.

METHODS

We utilized a mathematical model that integrates signaling mechanisms and cellular functional state transitions. We tuned the model parameters to match the time scale of human liver regeneration using an elastic net based regularization approach for identifying optimal parameter values. We initially examined the effect of each parameter individually on the response mode (normal, suppressed, failure) and extent of recovery to identify critical parameters. We employed phase plane analysis to compute the threshold of resection. We mapped the distribution of the response modes and threshold of resection in a virtual patient cohort generated in silico via simultaneous variations in two most critical parameters.

RESULTS

Analysis of the responses to resection with individual parameter variations showed that the response mode and extent of recovery following resection were most sensitive to variations in two perioperative factors, metabolic load and cell death post partial hepatectomy. Phase plane analysis identified two steady states corresponding to recovery and failure, with a threshold of resection separating the two basins of attraction. The size of the basin of attraction for the recovery mode varied as a function of metabolic load and cell death sensitivity, leading to a change in the multiplicity of the system in response to changes in these two parameters.

CONCLUSIONS

Our results suggest that the response mode and threshold of failure are critically dependent on the metabolic load and cell death sensitivity parameters that are likely to be patient-specific. Interventions that modulate these critical perioperative factors may be helpful to drive the liver regenerative response process towards a complete recovery mode.

Modeling Dynamics and Function of Bone Marrow Cells in Mouse Liver Regeneration

In rodents and humans, the liver can efficiently restore its mass after hepatectomy. This is largely attributed to the proliferation and cell cycle re-entry of hepatocytes. On the other hand, bone marrow cells (BMCs) migrate into the liver after resection. Here, we find that a block of BMC recruitment into the liver severely impairs its regeneration after the surgery. Mobilized hematopoietic stem and progenitor cells (HSPCs) in the resected liver can fuse with hepatocytes, and the hybrids proliferate earlier than the hepatocytes. Genetic ablation of the hybrids severely impairs hepatocyte proliferation and liver mass regeneration. Mathematical modeling reveals a key role of bone marrow (BM)-derived hybrids to drive proliferation in the regeneration process, and predicts regeneration efficiency in experimentally non-testable conditions. In conclusion, BM-derived hybrids are essential to trigger efficient liver regeneration after hepatectomy.

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Bone marrow cell migration after liver hepatectomy is key for liver regeneration

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Migrated bone marrow cells fuse with hepatocytes

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Hybrids are essential for liver regeneration

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Mathematical modeling unveils the hybrid function for liver regeneration

Computational Modeling in Liver Surgery

The need for extended liver resection is increasing due to the growing incidence of liver tumors in aging societies. Individualized surgical planning is the key for identifying the optimal resection strategy and to minimize the risk of postoperative liver failure and tumor recurrence. Current computational tools provide virtual planning of liver resection by taking into account the spatial relationship between the tumor and the hepatic vascular trees, as well as the size of the future liver remnant. However, size and function of the liver are not necessarily equivalent. Hence, determining the future liver volume might misestimate the future liver function, especially in cases of hepatic comorbidities such as hepatic steatosis. A systems medicine approach could be applied, including biological, medical, and surgical aspects, by integrating all available anatomical and functional information of the individual patient. Such an approach holds promise for better prediction of postoperative liver function and hence improved risk assessment. This review provides an overview of mathematical models related to the liver and its function and explores their potential relevance for computational liver surgery. We first summarize key facts of hepatic anatomy, physiology, and pathology relevant for hepatic surgery, followed by a description of the computational tools currently used in liver surgical planning. Then we present selected state-of-the-art computational liver models potentially useful to support liver surgery. Finally, we discuss the main challenges that will need to be addressed when developing advanced computational planning tools in the context of liver surgery.

Prediction of postoperative liver regeneration from clinical information using a data-led mathematical model

Although the capacity of the liver to recover its size after resection has enabled extensive liver resection, post-hepatectomy liver failure remains one of the most lethal complications of liver resection. Therefore, it is clinically important to discover reliable predictive factors after resection. In this study, we established a novel mathematical framework which described post-hepatectomy liver regeneration in each patient by incorporating quantitative clinical data. Using the model fitting to the liver volumes in series of computed tomography of 123 patients, we estimated liver regeneration rates. From the estimation, we found patients were divided into two groups: i) patients restored the liver to its original size (Group 1, n = 99); and ii) patients experienced a significant reduction in size (Group 2, n = 24). From discriminant analysis in 103 patients with full clinical variables, the prognosis of patients in terms of liver recovery was successfully predicted in 85-90% of patients. We further validated the accuracy of our model prediction using a validation cohort (prediction = 84-87%, n = 39). Our interdisciplinary approach provides qualitative and quantitative insights into the dynamics of liver regeneration. A key strength is to provide better prediction in patients who had been judged as acceptable for resection by current pragmatic criteria.

Metabolic scaling predicts posthepatectomy liver regeneration after accounting for hepatocyte hypertrophy

We adapted a mathematical model of posthepatectomy liver regeneration using data from a subset of patients in the Adult-to-Adult Living Donor Liver Transplantation Cohort Study. The original model addressed changes in the number of quiescent, primed, and proliferating cells. Our adapted model takes into account hypertrophy of primed and replicating cells, and it is better able to predict liver volume. In addition, by building off the hypothesis that cell cycle parameters are approximately the same across all mammals, we found that changing only a single parameter characterizing metabolic load could model liver regeneration in 5 species of mammals. In conclusion, we improved a mathematical model of liver regeneration, predicted mammalian liver regeneration based on metabolism, and found correlations between model parameters and physiological measurements from liver donors.

Systems analysis of non-parenchymal cell modulation of liver repair across multiple regeneration modes

Background

A hallmark of chronic liver disease is the impairment of the liver’s innate regenerative ability. In this work we use a computational approach to unravel the principles underlying control of liver repair following an acute physiological challenge.

Methods

We used a mathematical model of inter- and intra-cellular interactions during liver regeneration to infer key molecular factors underlying the dysregulation of multiple regeneration modes, including delayed, suppressed, and enhanced regeneration. We used model analysis techniques to identify organizational principles governing the cellular regulation of liver regeneration. We fit our model to several published data sets of deficient regeneration in rats and healthy regeneration in humans, rats, and mice to predict differences in molecular regulation in disease states and across species. 

Results

Analysis of the computational model pointed to an important balance involving inflammatory signals and growth factors, largely produced by Kupffer cells and hepatic stellate cells, respectively. Our model analysis results also indicated an organizational principle of molecular regulation whereby production rate of molecules acted to induce coarse-grained control of signaling levels while degradation rate acted to induce fine-tuning control. We used this computational framework to investigate hypotheses concerning molecular regulation of regeneration across species and in several chronic disease states in rats, including fructose-induced steatohepatitis, alcoholic steatohepatitis, toxin-induced cirrhosis, and toxin-induced diabetes. Our results indicate that altered non-parenchymal cell activation is sufficient to explain deficient regeneration caused by multiple disease states. We also investigated liver regeneration across mammalian species. Our results suggest that non-invasive measures of liver regeneration taken at 30 days following resection could differentiate between several hypotheses about how human liver regeneration differs from rat regeneration.

Conclusions

Overall, our results provide a new computational platform integrating a wide range of experimental information, with broader utility in exploring the dynamic patterns of liver regeneration across species and over multiple chronic diseases.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0220-9) contains supplementary material, which is available to authorized users.

Microarray-based characterization of differential gene expression during vocal fold wound healing in rats

The vocal fold (VF) mucosa confers elegant biomechanical function for voice production but is susceptible to scar formation following injury. Current understanding of VF wound healing is hindered by a paucity of data and is therefore often generalized from research conducted in skin and other mucosal systems. Here, using a previously validated rat injury model, expression microarray technology and an empirical Bayes analysis approach, we generated a VF-specific transcriptome dataset to better capture the system-level complexity of wound healing in this specialized tissue. We measured differential gene expression at 3, 14 and 60 days post-injury compared to experimentally naïve controls, pursued functional enrichment analyses to refine and add greater biological definition to the previously proposed temporal phases of VF wound healing, and validated the expression and localization of a subset of previously unidentified repair- and regeneration-related genes at the protein level. Our microarray dataset is a resource for the wider research community and has the potential to stimulate new hypotheses and avenues of investigation, improve biological and mechanistic insight, and accelerate the identification of novel therapeutic targets.

Rodent models and imaging techniques to study liver regeneration

The liver has the unique capability of regeneration from various injuries. Different animal models and in vitro methods are used for studying the processes and mechanisms of liver regeneration. Animal models were established either by administration of hepatotoxic chemicals or by surgical approach. The administration of hepatotoxic chemicals results in the death of liver cells and in subsequent hepatic regeneration and tissue repair. Surgery includes partial hepatectomy and portal vein occlusion or diversion: hepatectomy leads to compensatory regeneration of the remnant liver lobe, whereas portal vein occlusion leads to atrophy of the ipsilateral lobe and to compensatory regeneration of the contralateral lobe. Adaptation of modern radiological imaging technologies to the small size of rodents made the visualization of rodent intrahepatic vascular anatomy possible. Advanced knowledge of the detailed intrahepatic 3D anatomy enabled the establishment of refined surgical techniques. The same technology allows the visualization of hepatic vascular regeneration. The development of modern histological image analysis tools improved the quantitative assessment of hepatic regeneration. Novel image analysis tools enable us to quantify reliably and reproducibly the proliferative rate of hepatocytes using whole-slide scans, thus reducing the sampling error. In this review, the refined rodent models and the newly developed imaging technology to study liver regeneration are summarized. This summary helps to integrate the current knowledge of liver regeneration and promises an enormous increase in hepatological knowledge in the near future.