Computational Modeling of Spatiotemporal Ca(2+) Signal Propagation Along Hepatocyte Cords

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.

A Spatial Model of Hepatic Calcium Signaling and Glucose Metabolism Under Autonomic Control Reveals Functional Consequences of Varying Liver Innervation Patterns Across Species

Rapid breakdown of hepatic glycogen stores into glucose plays an important role during intense physical exercise to maintain systemic euglycemia. Hepatic glycogenolysis is governed by several different liver-intrinsic and systemic factors such as hepatic zonation, circulating catecholamines, hepatocellular calcium signaling, hepatic neuroanatomy, and the central nervous system (CNS). Of the factors regulating hepatic glycogenolysis, the extent of lobular innervation varies significantly between humans and rodents. While rodents display very few autonomic nerve terminals in the liver, nearly every hepatic layer in the human liver receives neural input. In the present study, we developed a multi-scale, multi-organ model of hepatic metabolism incorporating liver zonation, lobular scale calcium signaling, hepatic innervation, and direct and peripheral organ-mediated communication between the liver and the CNS. We evaluated the effect of each of these governing factors on the total hepatic glucose output and zonal glycogenolytic patterns within liver lobules during simulated physical exercise. Our simulations revealed that direct neuronal stimulation of the liver and an increase in circulating catecholamines increases hepatic glucose output mediated by mobilization of intracellular calcium stores and lobular scale calcium waves. Comparing simulated glycogenolysis between human-like and rodent-like hepatic innervation patterns (extensive vs. minimal) suggested that propagation of calcium transients across liver lobules acts as a compensatory mechanism to improve hepatic glucose output in sparsely innervated livers. Interestingly, our simulations suggested that catecholamine-driven glycogenolysis is reduced under portal hypertension. However, increased innervation coupled with strong intercellular communication can improve the total hepatic glucose output under portal hypertension. In summary, our modeling and simulation study reveals a complex interplay of intercellular and multi-organ interactions that can lead to differing calcium dynamics and spatial distributions of glycogenolysis at the lobular scale in the liver.

Single-Cell Gene Expression Analysis Identifies Chronic Alcohol-Mediated Shift in Hepatocyte Molecular States After Partial Hepatectomy

The analysis of molecular states of individual cells, as defined by their mRNA expression profiles and protein composition, has gained widespread interest in studying biological phenomena ranging from embryonic development to homeostatic tissue function and genesis and evolution of cancers. Although the molecular content of individual cells in a tissue can vary widely, their molecular states tend to be constrained within a transcriptional landscape partly described by the canonical archetypes of a population of cells. In this study, we sought to characterize the effects of an acute (partial hepatectomy) and chronic (alcohol consumption) perturbation on the molecular states of individual hepatocytes during the onset and progression of liver regeneration. We analyzed the expression of 84 genes across 233 individual hepatocytes acquired using laser capture microdissection. Analysis of the single-cell data revealed that hepatocyte molecular states can be considered as distributed across a set of four states irrespective of perturbation, with the proportions of hepatocytes in these states being dependent on the perturbation. In addition to the quiescent, primed, and replicating hepatocytes, we identified a fourth molecular state lying between the primed and replicating subpopulations. Comparison of the proportions of hepatocytes from each experimental condition in these four molecular states suggested that, in addition to aberrant priming, a slower transition from primed to replication state could contribute toward ethanol-mediated suppression of liver regenerative response to partial hepatectomy.

Causality Analysis and Cell Network Modeling of Spatial Calcium Signaling Patterns in Liver Lobules

Dynamics as well as localization of Ca²⁺ transients plays a vital role in liver function under homeostatic conditions, repair, and disease. In response to circulating hormonal stimuli, hepatocytes exhibit intracellular Ca²⁺ responses that propagate through liver lobules in a wave-like fashion. Although intracellular processes that control cell autonomous Ca²⁺ spiking behavior have been studied extensively, the intra- and inter-cellular signaling factors that regulate lobular scale spatial patterns and wave-like propagation of Ca²⁺ remain to be determined. To address this need, we acquired images of cytosolic Ca²⁺ transients in 1300 hepatocytes situated across several mouse liver lobules over a period of 1600 s. We analyzed this time series data using correlation network analysis, causal network analysis, and computational modeling, to characterize the spatial distribution of heterogeneity in intracellular Ca²⁺ signaling components as well as intercellular interactions that control lobular scale Ca²⁺ waves. Our causal network analysis revealed that hepatocytes are causally linked to multiple other co-localized hepatocytes, but these influences are not necessarily aligned uni-directionally along the sinusoids. Our computational model-based analysis showed that spatial gradients of intracellular Ca²⁺ signaling components as well as intercellular molecular exchange are required for lobular scale propagation of Ca²⁺ waves. Additionally, our analysis suggested that causal influences of hepatocytes on Ca²⁺ responses of multiple neighbors lead to robustness of Ca²⁺ wave propagation through liver lobules.

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.