Examining the controllability of sepsis using genetic algorithms on an agent-based model of systemic inflammation

Abstract

Sepsis, a manifestation of the body's inflammatory response to injury and infection, has a mortality rate of between 28%-50% and affects approximately 1 million patients annually in the United States. Currently, there are no therapies targeting the cellular/molecular processes driving sepsis that have demonstrated the ability to control this disease process in the clinical setting. We propose that this is in great part due to the considerable heterogeneity of the clinical trajectories that constitute clinical "sepsis," and that determining how this system can be controlled back into a state of health requires the application of concepts drawn from the field of dynamical systems. In this work, we consider the human immune system to be a random dynamical system, and investigate its potential controllability using an agent-based model of the innate immune response (the Innate Immune Response ABM or IIRABM) as a surrogate, proxy system. Simulation experiments with the IIRABM provide an explanation as to why single/limited cytokine perturbations at a single, or small number of, time points is unlikely to significantly improve the mortality rate of sepsis. We then use genetic algorithms (GA) to explore and characterize multi-targeted control strategies for the random dynamical immune system that guide it from a persistent, non-recovering inflammatory state (functionally equivalent to the clinical states of systemic inflammatory response syndrome (SIRS) or sepsis) to a state of health. We train the GA on a single parameter set with multiple stochastic replicates, and show that while the calculated results show good generalizability, more advanced strategies are needed to achieve the goal of adaptive personalized medicine. This work evaluating the extent of interventions needed to control a simplified surrogate model of sepsis provides insight into the scope of the clinical challenge, and can serve as a guide on the path towards true "precision control" of sepsis.

Fig 1. IIRABM schematic diagram.

This is a high-level overview of the signaling rules incorporated into the IIRABM. Rules represented include cytokine up-regulation/down-regulation, cell activation, and cellular differentiation.

Fig 2. Representation of computed intervention.

This figure contains 8 bar graphs, each of which represents a single stage of the 8-stage intervention. The cytokines operated on are shown on the x-axes and the base-2 logarithm of the augmentation or inhibition strength is shown on the y-axes. This sequence of interventions lowered the probability of death from 68% to 12% for the patient upon which the GA was trained; the probability of death was lowered from 82% to 16% for the general population using an identical parameter set.

Fig 3. Examination of generalizability of computed intervention.

In panel A, the mortality rate distribution for the parameter sets that generate between 1 and 99% mortality rate (MR) is presented with the mortality rate on the x-axis and the number of parameter sets that generate that mortality rate (with 100 stochastic replicates) is on the y-axis. Panel B shows the MR distribution for a set of simulations with parameterizations identical to those in panel A, however they have been treated with the calculated intervention. Panel C shows the post intervention MR for those simulations in panel A which have a base MR between 20% and 30%; Panel D: 40% and 50%; Panel E: 60% and 70%; Panel F: 70% and 80%; Panel G: 80% and 90%. In Panel H, we plot the base MR against the post treatment MR for all clinically relevant parameter sets. Those points which lie below the black diagonal line represent parameter sets for which this treatment was beneficial.

Fig 4. Non-responder system dynamics.

Panel A displays the oxygen deficit (an inverse measure of the system’s health) for an intervention non-responder (red) compared to the average oxygen deficit for intervention responders (blue) over time. Panel B displays the total GCSF for the non-responder and the responder average; panel C displays the total neutrophil population for an individual non-responder and the responder average. In this case, the non-responder does not end up healing due to a hyper-productive response to GCSF pathway stimulation, which leads to a surplus neutrophil population; this patient ultimately dies due to inflammation, which is exacerbated by the applied intervention.

Fig 5. Intervention comparison for responders and non-responder.

The set of bar graphs on the left shows the final 5 interventions in a sequence of 8 that showed the greatest success in healing the most in silico patients. The set of bar graphs on the right shows an alternate intervention sequence that was generated by training the genetic algorithm on a patient who was non-responsive to the original intervention. The cytokines operated on are shown on the x-axes and the base-2 logarithm of the augmentation or inhibition strength is shown on the y-axes. The in silico patients received identical interventions for the first three time points. At time point 3, a significant deviation from expected behavior is noted in the non-responder. At this time point, the simulation is halted and used to populate the sample set for a new run of the genetic algorithm. When given the original intervention, this patient has a 75% chance of death at 60 hrs post-injury; the alternate intervention lowers this chance to 8%.

Fig 6. Stochastic trajectory example.

Panel A displays 100 stochastic trajectories generated by the IIRABM for a specific parameter set (Invasiveness = 2; Host Resilience = 0.1; Toxigenesis = 5; Environmental Toxicity = 2) with an injury with a radius of 33 cells. The total systemic oxygen deficit, an inverse measure of the in silico patient’s health (y-axis) is presented as a function of time (x-axis). 82% of the simulated patients (red) end in death, while 18% heal completely (blue). The trajectories shown in panel B use the same parameter set as in panel A, however the run is started with a specific random number generator seed; the random number generator is re-seeded at 12 hrs post injury. At 1-day post injury, this specific patient has a 68% chance of death.