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A local mechanism generates saturation in an in silico model of in vitro multicellular tumor spheroid growth
Journal of Critical Care (2007) 22, 331–351
Abstracts for the 2007 International Conference on Complexity in Acute Illness (ICCAI) InvestigatorsT Abstracts A local mechanism generates saturation in an in silico model of in vitro multicellular tumor spheroid growth Jesse A. Engelberg, C. Anthony Hunt University of California, San Francisco The UCSF/UCB Joint Graduate Group in Bioengineering Objectives: In vitro multicellular tumor spheroids (MTSs) are a model of avascular tumor growth in vivo. The objective of this project was to describe, develop, and validate an axiom- and agentbased software analogue of MTS capable of representing key spatial, temporal, and morphological phenotypic attributes. Methods: The analogue uses grids to hold cells, which are represented by autonomous agents, as well as nutrients, which are represented as a numeric quantity. Events and processes that would be evident at a higher resolution are conflated into the essential axioms and components necessary to mimic the desired phenotypic attributes. Results: Simulation results mimic aspects of MTS growth, including its layered structure and growth patterns under different nutrient conditions. During each simulation cycle, in silico cells gain individual information through a local search of only their immediate neighborhood, similar to what occurs in vitro. They then use that information to select an axiom that determines the action to be taken, each cycle, when specific neighborhood preconditions are met. Growth curves in different conditions were tuned to match the corresponding in vitro growth curves. The model used cell death and randomized cell movement to generate volume loss. Conclusions: The in silico MTS is capable of reproducing both aspects of the morphology and growth curves of in vitro tumor spheroid systems. In addition, the results demonstrate that a necrotic inhibitor is not necessary to generate saturation within an in silico model, suggesting it may not be a key feature of the mechanisms by which in vitro systems reach saturation. doi:10.1016/j.jcrc.2007.10.002
A multiscale lung model of gas exchange under inflammatory stress Angela Reynolds a, G. Bard Ermentrout a,c, Gilles Clermont b,c a Department of Mathematics, University of Pittsburgh b Department of Critical Care Medicine, University of Pittsburgh c CIRM (Center for Inflammation and Regenerative Modeling) 0883-9441/$ – see front matter doi:10.1016/S0883-9441(07)00112-8
Objectives: The tissue barrier between air and blood swells during inflammation, which hinders the diffusion of oxygen and carbon dioxide. Severe swelling will cause the respiratory unit (RU) to close to incoming air (shunting). Global gas exchange in the lung is dependent on the combined output of multiple RUs under diverse physiologic conditions. To develop a multi-RU model, we first derived a model for oxygen and carbon dioxide exchange and inflammation on a single RU. The multi-RU model is used to simulate the impact of pulmonary inflammation of global gas exchange and resulting clinically relevant arterial PO2 and PCO2. Methods: We derived a model for gas exchange and inflammation on a single RU, which consist of 3 distinct compartments: air, tissue, and blood. This model includes partial differential equations for oxygen and carbon dioxide in all compartments, bicarbonate, and saturated hemoglobin in the blood. Immune variables include resting neutrophils in the blood and activated neutrophils and tumor necrosis factor (TNF) in both the blood and tissue. Inflammatory effects on gas exchange are implemented as changes in the compartments' volumes. Tissue volume increases cause decreases in both blood and alveolar air space volume, whereas RU volume is conserved. Blood output from multiple RUs are combined to evaluate overall effects of inflammation. Results: The reduced inflammatory subsystem implemented in this model has 2 possible outcomes: health, resting neutrophils return to background level and activated neutrophils and TNF are zero, and severe inflammation, activated neutrophils and TNF are elevated. Gas exchange in the absence of inflammation gives venous end PO2 and CO2 levels of approximately 100 and 40 mm Hg, respectively, as seen in a healthy lung. During severe inflammation, PO2 does not rise to 100 mm Hg as the blood transverses the capillary and hemoglobin does not fully saturate. The ability of the lung to eliminate PCO2 in the blood is also inhibited. In the multi-RU model, we assume a normal distribution of tidal volumes over the total number of RUs, with total tidal volume of the lung equal to 350 mL. This models RUs under various ventilation-perfusion ratios and allows us to evaluate the effects of inflammation and anatomical restrictions faced in the lung during gas exchange. During multi-RU simulations with severe inflammation, there is a gradual recruitment of shunted RUs. Shunt, rather than an increase barrier to diffusion, is the main mechanism of reduced arterial PO2. Conclusions: The single RU model with a distinct tissue compartment, which allowed the implementation of inflammation, was the first step in developing a useable multiscale model of the lung. With the multi-RU models, we have developed a method for combining the output of many RUs and introducing lung heterogeneity. The results of this multi-RU model are comparable
Abstracts for the 2007 International Conference on Complexity in Acute Illness (ICCAI) InvestigatorsT Abstracts A local mechanism generates saturation in an in silico model of in vitro multicellular tumor spheroid growth Jesse A. Engelberg, C. Anthony Hunt University of California, San Francisco The UCSF/UCB Joint Graduate Group in Bioengineering Objectives: In vitro multicellular tumor spheroids (MTSs) are a model of avascular tumor growth in vivo. The objective of this project was to describe, develop, and validate an axiom- and agentbased software analogue of MTS capable of representing key spatial, temporal, and morphological phenotypic attributes. Methods: The analogue uses grids to hold cells, which are represented by autonomous agents, as well as nutrients, which are represented as a numeric quantity. Events and processes that would be evident at a higher resolution are conflated into the essential axioms and components necessary to mimic the desired phenotypic attributes. Results: Simulation results mimic aspects of MTS growth, including its layered structure and growth patterns under different nutrient conditions. During each simulation cycle, in silico cells gain individual information through a local search of only their immediate neighborhood, similar to what occurs in vitro. They then use that information to select an axiom that determines the action to be taken, each cycle, when specific neighborhood preconditions are met. Growth curves in different conditions were tuned to match the corresponding in vitro growth curves. The model used cell death and randomized cell movement to generate volume loss. Conclusions: The in silico MTS is capable of reproducing both aspects of the morphology and growth curves of in vitro tumor spheroid systems. In addition, the results demonstrate that a necrotic inhibitor is not necessary to generate saturation within an in silico model, suggesting it may not be a key feature of the mechanisms by which in vitro systems reach saturation. doi:10.1016/j.jcrc.2007.10.002
A multiscale lung model of gas exchange under inflammatory stress Angela Reynolds a, G. Bard Ermentrout a,c, Gilles Clermont b,c a Department of Mathematics, University of Pittsburgh b Department of Critical Care Medicine, University of Pittsburgh c CIRM (Center for Inflammation and Regenerative Modeling) 0883-9441/$ – see front matter doi:10.1016/S0883-9441(07)00112-8
Objectives: The tissue barrier between air and blood swells during inflammation, which hinders the diffusion of oxygen and carbon dioxide. Severe swelling will cause the respiratory unit (RU) to close to incoming air (shunting). Global gas exchange in the lung is dependent on the combined output of multiple RUs under diverse physiologic conditions. To develop a multi-RU model, we first derived a model for oxygen and carbon dioxide exchange and inflammation on a single RU. The multi-RU model is used to simulate the impact of pulmonary inflammation of global gas exchange and resulting clinically relevant arterial PO2 and PCO2. Methods: We derived a model for gas exchange and inflammation on a single RU, which consist of 3 distinct compartments: air, tissue, and blood. This model includes partial differential equations for oxygen and carbon dioxide in all compartments, bicarbonate, and saturated hemoglobin in the blood. Immune variables include resting neutrophils in the blood and activated neutrophils and tumor necrosis factor (TNF) in both the blood and tissue. Inflammatory effects on gas exchange are implemented as changes in the compartments' volumes. Tissue volume increases cause decreases in both blood and alveolar air space volume, whereas RU volume is conserved. Blood output from multiple RUs are combined to evaluate overall effects of inflammation. Results: The reduced inflammatory subsystem implemented in this model has 2 possible outcomes: health, resting neutrophils return to background level and activated neutrophils and TNF are zero, and severe inflammation, activated neutrophils and TNF are elevated. Gas exchange in the absence of inflammation gives venous end PO2 and CO2 levels of approximately 100 and 40 mm Hg, respectively, as seen in a healthy lung. During severe inflammation, PO2 does not rise to 100 mm Hg as the blood transverses the capillary and hemoglobin does not fully saturate. The ability of the lung to eliminate PCO2 in the blood is also inhibited. In the multi-RU model, we assume a normal distribution of tidal volumes over the total number of RUs, with total tidal volume of the lung equal to 350 mL. This models RUs under various ventilation-perfusion ratios and allows us to evaluate the effects of inflammation and anatomical restrictions faced in the lung during gas exchange. During multi-RU simulations with severe inflammation, there is a gradual recruitment of shunted RUs. Shunt, rather than an increase barrier to diffusion, is the main mechanism of reduced arterial PO2. Conclusions: The single RU model with a distinct tissue compartment, which allowed the implementation of inflammation, was the first step in developing a useable multiscale model of the lung. With the multi-RU models, we have developed a method for combining the output of many RUs and introducing lung heterogeneity. The results of this multi-RU model are comparable