By Austin Baird, Matthew McDaniel, and Jonathan Keller
Sepsis is a debilitating condition with a high mortality rate that greatly strains hospital resources. Here, we present a mathematical model of sepsis and the associated acute inflammatory patient response (AIR)—implemented in the BioGears physiology engine—to explore the underlying biological mechanisms and patient phenotypes that contribute to variability in septic patient outcomes. In addition, one could potentially use this model to design in silico clinical trials that determine optimal patient treatments.
Sepsis represents an array of dysregulated physiologic reactions from the body in response to suspected or confirmed infection. The physiologic changes are often overwhelming, can result in severe tissue damage, and are potentially life threatening. Large cohort studies indicate that sepsis is a leading contributor to hospital mortality [3], and patients who acquire sepsis in the hospital have a mortality rate of 25 percent [7]. Outcomes for septic patients will not improve until doctors attain a better understanding of the disease and its treatment. To that end, mathematical modeling can provide significant insight and momentum towards this goal. While models cannot replace clinical trials, they can drive hypothesis development, narrow the focus of research, and complement medical education.
Figure 1. Overview of the whole-body model of sepsis. The green circles indicate the acute inflammatory response model. Arrows depict the way in which this model impacts other downstream models in the BioGears physiology engine. Solid lines designate up-regulation (or positive effects) and dashed lines designate inhibition (or negative effects). Figure courtesy of [6].
Model Design
We designed our AIR model in the BioGears physiology engine by extending a previous diverse shock model [2] (see Figure 1). Though it is optimized with murine data, this model considers a wide range of pro- and anti-inflammatory mediators—such as tumor necrosis factor alpha and interleukins 6 and 10 (IL-6, IL-10)—that are implicated in human models of inflammation [8]. Consideration of these factors, in conjunction with the activation of macrophages and neutrophils, increases the variability in virtual patient outcomes that the model supports. Furthermore, the diverse shock model explores the role of nitric oxide in blood pressure homeostasis — a pathway of great interest in septic shock research. We have already used this framework to implement a model of burn-induced systemic inflammation in BioGears [1, 5]. A full description of the model is available in [6].
Figure 2. The virtual patient subsets that are generated by varying acute inflammatory response model parameters in the set {kPTMT, k6M, x66}. A moderate level of BioGears infection action is applied. In the nominal case (black), the pathogen is eliminated. Here, green is “susceptible,” orange is “hyperinflammatory,” and purple represents an “immunosuppressed” patient. Figure courtesy of [6].
To properly design a trail of interest, sufficient variability should exist within a given patient population for treatments and outcomes that are related to a similar injury type. We specify two ways to include such variability using our model and the BioGears physiology engine. The first is to randomize the initial patient parameters, such as height, weight, gender,
and others. The second is to configure three subpopulations of potential interest, which we compared to the nominal model response (see Figure 2). We can configure the model in three distinct ways, the first of which we call the “susceptible” population. We characterize this patient group by rapid bacteremia and sepsis onset when presented with a moderate level of infection, and we effected this response by decreasing the rate of phagocytosis by tissue macrophages. The other two subpopulations are derived from aberrant IL-6 activity, as dictated by the parameters that determine IL-6 recruitment by macrophages and IL-6 self-inhibition. Decreasing either (or both) of these parameters produces an “immuno-suppressed” state, in which relatively low levels of blood bacteria remain. Finally, we construct a “hyperinflammatory” state in which the bacteria are eradicated but the body incurs significant tissue damage due to prolonged and inadequately balanced pro-inflammation. For these model configurations, we demonstrate that one can generate distinct inflammatory response trajectories from the same level of infection by varying a small subset of model parameters (see Figure 2).
REFRESH Study Results
Figure 3. The progression of treatment and reassessment metrics in simulations following the REFRESH control (green) and experimental (orange) treatment protocols. We denote time \(= 0 \; \rm{hr}\) as the start of REFRESH protocol; time \(< 0\) corresponds to the period of initial fluid challenge and observation. Figure courtesy of [6].
We conducted all treatment scenarios using virtual patient states that were generated from the nominal BioGears severe infection action, and we modeled our treatment protocols after an existing study [4]. This pilot program, called the “REstricted Fluid REsuscitation in Sepsis-associated Hypotension” (REFRESH) study, sought to determine whether limiting fluid administration and initiating early vasopressor therapy improves septic patient mortality when compared to standard of care. Patients who qualified for enrollment in REFRESH (due to a suspected infection accompanied by persistent systolic blood pressure < 100 mmHg after fluid challenge) were randomly assigned to either a “standard” treatment group or a reduced fluids and early pressor treatment group.
Our simulation of the two REFRESH protocols produced patients who differed in volume and blood pressure status after multiple hours of treatment (see Figure 3). From these results, we observe that the smaller fluid boluses that were administered in the experimental case helped the patient avoid the more drastic shifts in blood pressure that the control group experienced. We also note that the smaller fluid boluses kept the experimental patient in a hypovolemic state longer than the control patient, thus potentially mitigating the positive effects of curtailing blood pressure fluctuations. In addition, the larger volume of administered fluid and the expanded extravascular volume could put the control patient at increased risk for reperfusion injury when compared to the experimental patient.
Ultimately, we present a model—designed in the BioGears physiology engine—that displays proper variability and possesses sufficient treatment models for the design and execution of in silico clinical trials. In the future, we aim to apply our model to large population studies of sepsis progression and treatment protocol design to hopefully better understand this complicated condition.
Austin Baird presented this research during a minisymposium at the 2021 SIAM Conference on Applications of Dynamical Systems, which took place virtually in May 2021.
References
[1] Baird, A., Serio-Melvin, M., Hackett, M., Clover, M., McDaniel, M., Rowland, M., ..., Wilson, B. (2020). BurnCare tablet trainer to enhance burn injury care and treatment. BMC Emerg. Med., 20(1), 1-10.
[2] Chow, C.C., Clermont, G., Kumar, R., Lagoa, C., Tawadrous, Z., Gallo, D., ..., Vodovotz, Y. (2005). The acute inflammatory response in diverse shock states. Shock, 24(1), 74-84.
[3] Liu, V., Escobar, G.J., Greene, J.D., Soule, J., Whippy, A., Angus, D.C., & Iwashyna, T.J. (2014). Hospital deaths in patients with sepsis from 2 independent cohorts. Jama, 312(1), 90-92.
[4] Macdonald, S.P., Taylor, D.M., Keijzers, G., Arendts, G., Fatovich, D.M., Kinnear, F.B., ..., Wibrow, B. (2017). REstricted Fluid REsuscitation in Sepsis-associated Hypotension (REFRESH): Study protocol for a pilot randomised controlled trial. Trials, 18(1), 1-15.
[5] McDaniel, M., & Baird, A. (2019, July). A full-body model of burn pathophysiology and treatment using the BioGears engine. In 2019 41st annual international conference of the IEEE engineering in medicine and biology society (EMBC) (pp. 261-264). Berlin, Germany: IEEE.
[6] McDaniel, M., Keller, J.M., White, S., & Baird, A. (2019). A whole-body mathematical model of sepsis progression and treatment designed in the BioGears physiology engine. Front. Physiol., 10, 1321.
[7] Rhee, C., Dantes, R., Epstein, L., Murphy, D.J., Seymour, C.W., Iwashyna, T.J., ..., CDC Prevention Epicenter Program. (2017). Incidence and trends of sepsis in US hospitals using clinical vs claims data, 2009-2014. Jama, 318(13), 1241-1249.
[8] Zhang, J.M., & An, J. (2007). Cytokines, inflammation and pain. Internat. Anesth. Clinics, 45(2), 27.
Austin Baird holds a Ph.D. in applied mathematics for biomedical applications. His research focuses on mathematical modeling of biological systems, specifically fluid-structure interaction, mathematical models in patient physiology, and healthcare simulation applications. At Applied Research Associates, Baird is the principal investigator of the BioGears open-source human physiology engine, which is funded by the U.S. Department of Defense. Matthew McDaniel applies his professional knowledge of engineering, biochemistry, and mathematics to the computational biology field. His initial work in this area focused on systems pharmacology and development of physiologically-based pharmacokinetic/pharmacodynamic (PBPK/PD) models. He is currently an embedded systems engineer at Raytheon. Jonathan Keller, MD, is a pulmonologist and critical care physician. He is a clinical instructor in the Division of Pulmonary, Critical Care, and Sleep Medicine at the University of Washington’s School of Medicine, where he completed his Fellowship in Pulmonary and Critical Care Medicine. Keller also completed his residency, served as Chief Resident in Internal Medicine, and received his MD at the UW School of Medicine.