(431a) Game Theoretic Approach to Multiple Organ Dysfunction Syndrome

Every year an estimated 5 million people die due to sepsis-induced multiple organ dysfunction syndrome (MODS).¹ Due to the variety of pathophysiological mechanisms that can initiate organ failure, it can be difficult to determine an appropriate course of treatment. This work develops a mathematical model that integrates physiological dynamics essential to organ and system function with a game theoretic component that accounts for inter-organ interactions through a shared environment. The model supports the expansion of game theory concepts from their current uses in ecology to human physiology, through its ability to provide insight into critical parameters that maintain or lead to the loss of homeostasis during MODS.

Methods

The physiological component of the model includes a simplified set of organs focused on the trafficking and local regulation of resources and organ-specific waste. Our initial model utilizes mass balance derived ordinary differential equations (ODEs) to describe lung and liver function, by tracking the concentration of oxygen (resource) and bilirubin (waste) through time. Within the lung compartment, the pulmonary capillaries are modeled as three reactors in series to capture both the spatial and temporal dynamics of oxygen uptake. Oxygen uptake is regulated through changes in the ventilation and perfusion rate in response to deviations from steady state arterial oxygen content. The ventilation rate is adjusted through a static gain proportional controller with a low pass filter, while perfusion is dependent on localized oxygen content. Within the liver compartment the clearance rate of bilirubin is dependent on the localized oxygen content and bilirubin concentration.

The physiological portion of the model relates the lung and liver through the liver’s dependence on oxygen. In response to reduced oxygen availability, the liver will not only have reduced energy production potential, but some hepatocytes will begin to enter a state of lower energy utilization. To model the ability for cells to shut down in response to stressors, we have integrated into the model the game theoretic structure of replicator dynamics with environmental feedback. This game is governed by a set of ODEs that define the internal interactions between cells as having two strategic choices, cooperation (x₁) and defection (x₂). Each combination of choices has a corresponding payoff function in the payoff matrix, A(n), which in turn determines the frequency of cells pursuing each strategy. The system contains two feedback loops: (i) at the organ level, the concentration of resources alters the payoff functions found in A(n); (ii) the condition of the local environment (n) is then used to calculate the payoff for each of the possible strategies an organ can follow. Then the cells within an organ can make an informed decision dependent on the amount of resources available and the payoff for each strategy. In turn, the selected strategy feeds back into the physiological model and influences the function of the organ. By developing this system of ODEs we are providing hepatocytes strategic options, to cooperate or defect. Furthermore, we have developed a set of payoff matrices that produce a series of stable equilibria at varying frequencies of each strategy and corresponding blood oxygen levels. This allows the model to produce stable states of reduced oxygen content, where the oxygen content level is dependent on the severity of the disturbance applied to the model.

Results

We analyzed the effectiveness of the model in its ability to accurately predict the onset of reduced liver function in response to graded hypoxia. Initially, as expected, a small hypoxic disturbance shows little effect due to the physiologically-available oxygen reserve that can offset small magnitude and short duration decreases in arterial oxygen content. As hypoxia exposure (magnitude * duration) was increased, ventilation rate increased (due to physiologically-motivated feedback) until saturation, at which point the body had reached maximal oxygen uptake. Once oxygen uptake could no longer be increased, further increases in hypoxia significantly reduced the arterial oxygen content. The simulated reduction in oxygen content was consistent with experimental data of the change in arterial oxygen content in response to reduced inspired oxygen.² This decrease in oxygen availability results in a decrease in bilirubin clearance and reduced liver function as hepatocytes begin to defect. The subsequent increase in plasma bilirubin concentration had a similar trajectory to experimental data of bilirubin concentration during hypoxia of a perfused rat liver.³

Summary

Through the integration of replicator dynamics and physiology, we have constructed an initial description of homeostatic failure in the game theory framework. The model structure provided a simplified method to analyze organ response to resource stress, and the concomitant loss of organ function consistent with early-phase organ failure. We continue to build on the interorgan interaction effects, both in terms of waste impact on remote tissues (e.g., liver effect on lung function) and the potential to include other key organs prone to failure in MODS (e.g., kidney). The ultimate outcome of this work could provide clinicians with a framework in which to characterize patients suffering from organ failure as well as organ support treatment decisions that avoid multi-organ failure.

References

1. Fleischmann, C.; Scherag, A.; Adhikari, N. K.; Hartog, C. S.; Tsaganos, T.; Schlattmann, P.; Angus, D. C.; Reinhart, K.; International Forum of Acute Care, T., Assessment of Global Incidence and Mortality of Hospital-treated Sepsis. Current Estimates and Limitations. Am J Respir Crit Care Med 2016, 193 (3), 259-72.
2. Hall, J. E.; Hall, M. E., Guyton and Hall textbook of medical physiology. 2021.
3. Angus, P. W.; Mihaly, G. W.; Morgan, D. J.; Smallwood, R. A., Hypoxia impairs conjugation and elimination of harmol in the isolated perfused rat liver. Journal of Pharmacology and Experimental Therapeutics 1987, 240, 931-936.