Judy Day

Modeling the immune rheostat of macrophages in the lung in response to infection

In the lung, alternatively activated macrophages (AAM) form the first line of defense against microbial infection. Due to the highly regulated nature of AAM, the lung can be considered as an immunosuppressive organ for respiratory pathogens. However, as infection progresses in the lung, another population of macrophages, known as classically activated macrophages (CAM) enters; these cells are typically activated by IFN-γ. CAM are far more effective than AAM in clearing the microbial load, producing proinflammatory cytokines and antimicrobial defense mechanisms necessary to mount an adequate immune response. Here, we are concerned with determining the first time when the population of CAM becomes more dominant than the population of AAM. This proposed “switching time” is explored in the context of Mycobacterium tuberculosis (MTb) infection. We have developed a mathematical model that describes the interactions among cells, bacteria, and cytokines involved in the activation of both AAM and CAM. The model, based on a system of differential equations, represents a useful tool to analyze strategies for reducing the switching time, and to generate hypotheses for experimental testing.

IN SILICO MODELS OF ACUTE INFLAMMATION IN ANIMALS

ABSTRACT Trauma and hemorrhagic shock elicit an acute inflammatory response, predisposing patients to sepsis, organ dysfunction, and death. Few approved therapies exist for these acute inflammatory states, mainly due to the complex interplay of interacting inflammatory and physiological elements working at multiple levels. Various animal models have been used to simulate these phenomena, but these models often do not replicate the clinical setting of multiple overlapping insults. Mathematical modeling of complex systems is an approach for understanding the interplay among biological interactions. We constructed a mathematical model using ordinary differential equations that encompass the dynamics of cells and cytokines of the acute inflammatory response, as well as global tissue dysfunction. The model was calibrated in C57Bl/6 mice subjected to (1) various doses of lipopolysaccharide (LPS) alone, (2) surgical trauma, and (3) surgery + hemorrhagic shock. We tested the models predictive ability in scenarios on which it had not been trained, namely, (1) surgery ± hemorrhagic shock + LPS given at times after the beginning of surgical instrumentation, and (2) surgery + hemorrhagic shock + bilateral femoral fracture. Software was created that facilitated fitting of the mathematical model to experimental data, as well as for simulation of experiments with various inflammatory challenges and associated variations (gene knockouts, inhibition of specific cytokines, etc.). Using this software, the C57Bl/6-specific model was recalibrated for inflammatory analyte data in CD14−/− mice and was used to elucidate altered features of inflammation in these animals. In other experiments, rats were subjected to surgical trauma ± LPS or to bacterial infection via fibrin clots impregnated with various inocula of Escherichia coli. Mathematical modeling may provide insights into the complex dynamics of acute inflammation in a manner that can be tested in vivo using many fewer animals than has been possible previously.

Insights into the Role of Chemokines, Damage-Associated Molecular Patterns, and Lymphocyte-Derived Mediators from Computational Models of Trauma-Induced Inflammation

SIGNIFICANCE Traumatic injury elicits a complex, dynamic, multidimensional inflammatory response that is intertwined with complications such as multiple organ dysfunction and nosocomial infection. The complex interplay between inflammation and physiology in critical illness remains a challenge for translational research, including the extrapolation to human disease from animal models. RECENT ADVANCES Over the past decade, we and others have attempted to decipher the biocomplexity of inflammation in these settings of acute illness, using computational models to improve clinical translation. In silico modeling has been suggested as a computationally based framework for integrating data derived from basic biology experiments as well as preclinical and clinical studies. CRITICAL ISSUES Extensive studies in cells, mice, and human blunt trauma patients have led us to suggest (i) that while an adequate level of inflammation is required for healing post-trauma, inflammation can be harmful when it becomes self-sustaining via a damage-associated molecular pattern/Toll-like receptor-driven feed-forward circuit; (ii) that chemokines play a central regulatory role in driving either self-resolving or self-maintaining inflammation that drives the early activation of both classical innate and more recently recognized lymphoid pathways; and (iii) the presence of multiple thresholds and feedback loops, which could significantly affect the propagation of inflammation across multiple body compartments. FUTURE DIRECTIONS These insights from data-driven models into the primary drivers and interconnected networks of inflammation have been used to generate mechanistic computational models. Together, these models may be used to gain basic insights as well as serving to help define novel biomarkers and therapeutic targets.

Modeling the host response to inhalation anthrax.

Inhalation anthrax, an often fatal infection, is initiated by endospores of the bacterium Bacillus anthracis, which are introduced into the lung. To better understand the pathogenesis of an inhalation anthrax infection, we propose a two-compartment mathematical model that takes into account the documented early events of such an infection. Anthrax spores, once inhaled, are readily taken up by alveolar phagocytes, which then migrate rather quickly out of the lung and into the thoracic/mediastinal lymph nodes. En route, these spores germinate to become vegetative bacteria. In the lymph nodes, the bacteria kill the host cells and are released into the extracellular environment where they can be disseminated into the blood stream and grow to a very high level, often resulting in the death of the infected person. Using this framework as the basis of our model, we explore the probability of survival of an infected individual. This is dependent on several factors, such as the rate of migration and germination events and treatment with antibiotics.

Model-free immune therapy: A control approach to acute inflammation

Control of an inflammatory immune response is still an ongoing research. Here, a strategy consisting of manipulating a pro and anti-inflammatory mediator is considered. Already existing and promising model-based techniques suffer unfortunately from a most difficult calibration. This is due to the different types of inflammations and to the strong parameter variation between patients. This communication explores another route via the new model-free control and its corresponding “intelligent” controllers. A “virtual” patient, i.e., a mathematical model, is only employed for digital simulations. A most interesting feature of our control strategy is the fact that the two outputs which must be driven are sensorless. This difficulty is overcome by assigning suitable reference trajectories to two other outputs with sensors. Several most encouraging computer simulations, corresponding to different drug treatment strategies, are displayed and discussed.

Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen.

The inflammatory response aims to restore homeostasis by means of removing a biological stress, such as an invading bacterial pathogen. In cases of acute systemic inflammation, the possibility of collateral tissue damage arises, which leads to a necessary down-regulation of the response. A reduced ordinary differential equations (ODE) model of acute inflammation was presented and investigated in [10]. That system contains multiple positive and negative feedback loops and is a highly coupled and nonlinear ODE. The implementation of nonlinear model predictive control (NMPC) as a methodology for determining proper therapeutic intervention for in silico patients displaying complex inflammatory states was initially explored in [5]. Since direct measurements of the bacterial population and the magnitude of tissue damage/dysfunction are not readily available or biologically feasible, the need for robust state estimation was evident. In this present work, we present results on the nonlinear reachability of the underlying model, and then focus our attention on improving the predictability of the underlying model by coupling the NMPC with a particle filter. The results, though comparable to the initial exploratory study, show that robust state estimation of this highly nonlinear model can provide an alternative to prior updating strategies used when only partial access to the unmeasurable states of the system are available.

Nonlinear state estimation for complex immune responses

The inflammatory response is a complex, highly nonlinear biological process, for which complete measurements of all variables are not usually available. Since it is desirable to find therapeutic inputs that enable the response to be controlled toward a favorable outcome, it is crucial to estimate the states that are impossible to measure, and use them for the appropriate control strategy. This article begins with a study of nonlinear observability of a reduced mathematical model of the acute inflammatory response. This will provide theoretical support for employing various state estimation approaches, including the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and the particle filter (PF). A comparison of these techniques is presented with respect to the reduced model of inflammation and the performance of each filter is evaluated in terms of accuracy and consistency.

Optimal control of an inflammatory immune response model

A reduced model of an acute inflammatory response to severe infection is considered. Regulation of the inflammatory response is crucial for restoring the patient to a healthy state. Therefore, an optimal control strategy given by a pro-inflammatory and anti-inflammatory drug treatment are derived. A study of controllability is also presented and the existence result is established. The optimality system composed of four differential equation and their corresponding adjoint equations are solved numerically. Simulation results are presented and different drug treatment strategies are discussed.

Mathematical modeling of early cellular innate and adaptive immune responses to ischemia/reperfusion injury and solid organ allotransplantation

A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient’s (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression.

Immune therapy using optimal control with L1 type objective

Treatment of pathogenic infection is formulated as an optimal control problem with an L1 type objective. Being unable to regulate the resulting inflammatory response can be detrimental for the affected patient. A strategy given by a pro-inflammatory and anti-inflammatory mediator drug treatment is derived. We apply maximum principle and the optimality system composed of four differential equation and their corresponding adjoint equations are solved numerically. Simulation results are discussed for two commun critical cases.