Global sensitivity analysis of a mathematical model of acute inflammation identifies nonlinear dependence of cumulative tissue damage on host interleukin-6 responses.

The precise inflammatory role of the cytokine interleukin (IL)-6 and its utility as a biomarker or therapeutic target have been the source of much debate, presumably due to the complex pro- and anti-inflammatory effects of this cytokine. We previously developed a nonlinear ordinary differential equation (ODE) model to explain the dynamics of endotoxin (lipopolysaccharide; LPS)-induced acute inflammation and associated whole-animal damage/dysfunction (a proxy for the health of the organism), along with the inflammatory mediators tumor necrosis factor (TNF)-α, IL-6, IL-10, and nitric oxide (NO). The model was partially calibrated using data from endotoxemic C57Bl/6 mice. Herein, we investigated the sensitivity of the area under the damage curve (AUCD) to the 51 rate parameters of the ODE model for different levels of simulated LPS challenges using a global sensitivity approach called Random Sampling High Dimensional Model Representation (RS-HDMR). We explored sufficient parametric Monte Carlo samples to generate the variance-based Sobol' global sensitivity indices, and found that inflammatory damage was highly sensitive to the parameters affecting the activity of IL-6 during the different stages of acute inflammation. The AUCIL6 showed a bimodal distribution, with the lower peak representing healthy response and the higher peak representing sustained inflammation. Damage was minimal at low AUCIL6, giving rise to a healthy response. In contrast, intermediate levels of AUCIL6 resulted in high damage, and this was due to the insufficiency of damage recovery driven by anti-inflammatory responses from IL-10 and the activation of positive feedback sustained by IL-6. At high AUCIL6, damage recovery was interestingly restored in some population of simulated animals due to the NO-mediated anti-inflammatory responses. These observations suggest that the host's health status during acute inflammation depends in a nonlinear fashion on the magnitude of the inflammatory stimulus, on the host's propensity to produce IL-6, and on NO-mediated downstream responses.

Combined in silico, in vivo, and in vitro studies shed insights into the acute inflammatory response in middle-aged mice.

We combined in silico, in vivo, and in vitro studies to gain insights into age-dependent changes in acute inflammation in response to bacterial endotoxin (LPS). Time-course cytokine, chemokine, and NO2 (-/)NO3 (-) data from "middle-aged" (6-8 months old) C57BL/6 mice were used to re-parameterize a mechanistic mathematical model of acute inflammation originally calibrated for "young" (2-3 months old) mice. These studies suggested that macrophages from middle-aged mice are more susceptible to cell death, as well as producing higher levels of pro-inflammatory cytokines, vs. macrophages from young mice. In support of the in silico-derived hypotheses, resident peritoneal cells from endotoxemic middle-aged mice exhibited reduced viability and produced elevated levels of TNF-α, IL-6, IL-10, and KC/CXCL1 as compared to cells from young mice. Our studies demonstrate the utility of a combined in silico, in vivo, and in vitro approach to the study of acute inflammation in shock states, and suggest hypotheses with regard to the changes in the cytokine milieu that accompany aging.

In Silico Augmentation of the Drug Development Pipeline: Examples from the study of Acute Inflammation.

The clinical translation of promising basic biomedical findings, whether derived from reductionist studies in academic laboratories or as the product of extensive high-throughput and -content screens in the biotechnology and pharmaceutical industries, has reached a period of stagnation in which ever higher research and development costs are yielding ever fewer new drugs. Systems biology and computational modeling have been touted as potential avenues by which to break through this logjam. However, few mechanistic computational approaches are utilized in a manner that is fully cognizant of the inherent clinical realities in which the drugs developed through this ostensibly rational process will be ultimately used. In this article, we present a Translational Systems Biology approach to inflammation. This approach is based on the use of mechanistic computational modeling centered on inherent clinical applicability, namely that a unified suite of models can be applied to generate in silico clinical trials, individualized computational models as tools for personalized medicine, and rational drug and device design based on disease mechanism.

Translational systems approaches to the biology of inflammation and healing.

Inflammation is a complex, non-linear process central to many of the diseases that affect both developed and emerging nations. A systems-based understanding of inflammation, coupled to translational applications, is therefore necessary for efficient development of drugs and devices, for streamlining analyses at the level of populations, and for the implementation of personalized medicine. We have carried out an iterative and ongoing program of literature analysis, generation of prospective data, data analysis, and computational modeling in various experimental and clinical inflammatory disease settings. These simulations have been used to gain basic insights into the inflammatory response under baseline, gene-knockout, and drug-treated experimental animals for in silico studies associated with the clinical settings of sepsis, trauma, acute liver failure, and wound healing to create patient-specific simulations in polytrauma, traumatic brain injury, and vocal fold inflammation; and to gain insight into host-pathogen interactions in malaria, necrotizing enterocolitis, and sepsis. These simulations have converged with other systems biology approaches (e.g., functional genomics) to aid in the design of new drugs or devices geared towards modulating inflammation. Since they include both circulating and tissue-level inflammatory mediators, these simulations transcend typical cytokine networks by associating inflammatory processes with tissue/organ impacts via tissue damage/dysfunction. This framework has now allowed us to suggest how to modulate acute inflammation in a rational, individually optimized fashion. This plethora of computational and intertwined experimental/engineering approaches is the cornerstone of Translational Systems Biology approaches for inflammatory diseases.

Mathematical modeling of posthemorrhage inflammation in mice: studies using a novel, computer-controlled, closed-loop hemorrhage apparatus.

Hemorrhagic shock (HS) elicits a global acute inflammatory response, organ dysfunction, and death. We have used mathematical modeling of inflammation and tissue damage/dysfunction to gain insight into this complex response in mice. We sought to increase the fidelity of our mathematical model and to establish a platform for testing predictions of this model. Accordingly, we constructed a computerized, closed-loop system for mouse HS. The intensity, duration, and time to achieve target MAP could all be controlled using a software. Fifty-four male C57/black mice either were untreated or underwent surgical cannulation. The cannulated mice were divided into 8 groups: (a) 1, 2, 3, or 4 h of surgical cannulation alone and b) 1, 2, 3, or 4 h of cannulation + HS (25 mmHg). MAP was sustained by the computer-controlled reinfusion and withdrawal of shed blood within +/-2 mmHg. Plasma was assayed for the cytokines TNF, IL-6, and IL-10 as well as the NO reaction products NO2-/NO3-. The cytokine and NO2-/NO3- data were compared with predictions from a mathematical model of post-hemorrhage inflammation, which was calibrated on different data. To varying degrees, the levels of TNF, IL-6, IL-10, and NO2/NO3 predicted by the mathematical model matched these data closely. In conclusion, we have established a hardware/software platform that allows for highly accurate, reproducible, and mathematically predictable HS in mice.

Translational systems biology of inflammation.

Inflammation is a complex, multi-scale biologic response to stress that is also required for repair and regeneration after injury. Despite the repository of detailed data about the cellular and molecular processes involved in inflammation, including some understanding of its pathophysiology, little progress has been made in treating the severe inflammatory syndrome of sepsis. To address the gap between basic science knowledge and therapy for sepsis, a community of biologists and physicians is using systems biology approaches in hopes of yielding basic insights into the biology of inflammation. "Systems biology" is a discipline that combines experimental discovery with mathematical modeling to aid in the understanding of the dynamic global organization and function of a biologic system (cell to organ to organism). We propose the term translational systems biology for the application of similar tools and engineering principles to biologic systems with the primary goal of optimizing clinical practice. We describe the efforts to use translational systems biology to develop an integrated framework to gain insight into the problem of acute inflammation. Progress in understanding inflammation using translational systems biology tools highlights the promise of this multidisciplinary field. Future advances in understanding complex medical problems are highly dependent on methodological advances and integration of the computational systems biology community with biologists and clinicians.

A mathematical simulation of the inflammatory response to anthrax infection.

Bacillus anthracis (anthrax) can trigger an acute inflammatory response that results in multisystem organ failure and death. Previously, we developed a mathematical model of acute inflammation after gram-negative infection that had been matched qualitatively to literature data. We modified the properties of the invading bacteria in that model to those specific to B. anthracis and simulated the host response to anthrax infection. We simulated treatment strategies against anthrax in a genetically diverse population including the following: (1) antibiotic treatment initiated at various time points, (2) antiprotective antigen vaccine, and (3) a combination of antibiotics and vaccine. In agreement with studies in mice, our simulations showed that antibiotics only improve survival if administered early in the course of anthrax infection. Vaccination that leads to the formation of antibodies to protective antigen is anti-inflammatory and beneficial in averting shock and improving survival. However, antibodies to protective antigen alone are predicted not to be universally protective against anthrax infection. Rather, our simulations suggest that an optimal strategy would require both vaccination and antibiotic administration.

Evidence-based modeling of critical illness: an initial consensus from the Society for Complexity in Acute Illness.

INTRODUCTION: Given the complexity of biological systems, understanding their dynamic behaviors, such as the Acute Inflammatory Response (AIR), requires a formal synthetic process. Dynamic Mathematical Modeling (DMM) represents a suite of methods intended for inclusion within the required synthetic framework. The DMM, however, is a relatively novel approach in the practice of biomedical research. The Society for Complexity in Acute Illness (SCAI) was formed in 2004 from the leading research groups using DMM in the study of acute inflammation. This society believes that it is important to offer guidelines for the design, development, and use of DMM in the setting of AIR research to avoid the "garbage in, garbage out" problem. Accordingly, SCAI identified a need for and carried out a critical appraisal of DMM as currently used in the setting of acute illness. METHODS: The SCAI annual meeting in 2005, the Fourth International Conference on Complexity in Acute Illness (Cologne, Germany), was structured with the intent of developing a consensus statement on the methods and execution of DMM in AIR research. The conference was organized to include a series of interactive breakout sessions that included thought leaders from both the DMM and acute illness fields, the results of which were then presented in summary form to the entire group for discussion and consensus. The information in this article represents the concatenation of those presentations. RESULTS: The output from the Fourth International Conference on Complexity in Acute Illness involved consensus statements for the following topics: (1) the need for DMM; (2) a suggested approach for the process of establishing a modeling project; (3) the type of "wet" laboratory experiments and data needed to establish a modeling project; (4) general quality measures for data to be input to a modeling project; and (5) a descriptive list of several types of DMM to provide guidance in selection of a method for a project. CONCLUSION: We believe that the complexity of biological systems requires that DMM needs to be among the methods used to improve understanding and make progress with attempts to characterize and manipulate the AIR. We believe that this consensus statement will help guide the integration, rational implementation, and standardization of DMM into general biomedical research.

The role of initial trauma in the host's response to injury and hemorrhage: insights from a correlation of mathematical simulations and hepatic transcriptomic analysis.

Trauma and hemorrhagic shock (HS) elicit severe physiological disturbances that predispose the victims to subsequent organ dysfunction and death. The general lack of effective therapeutic options for these patients is mainly due to the complex interplay of interacting inflammatory and physiological elements working at multiple levels. Systems biology has emerged as a new paradigm that allows the study of large portions of physiological networks simultaneously. Seeking a better understanding of the interplay among known inflammatory pathways, we constructed a mathematical model encompassing the dynamics of the acute inflammatory response that incorporates the intertwined effects of inflammation and global tissue damage. The model was calibrated using data from C57Bl/6 mice subjected to endotoxemia, sham operation (i.e., surgical trauma induced by cannulation [ST]) or ST + HS+ resuscitation (ST-HS-R). An in silico simulation, made at whole-organism level, suggested that similar pathways of different magnitudes were operant as the degree of total body damage increased. We sought to validate this hypothesis by subjecting mice to HS and comparing the models predictions to circulating markers of inflammation and tissue injury as well as the global transcriptomic response of the liver. C57Bl/6 mice were subjected to ST or ST-HS (without resuscitation). Liver gene expression was assessed using an Affymetrix DNA microarray (GeneChip Mouse Expression Set 430A, Affymetrix, Santa Clara, CA), which contains 22,621 probe sets and effectively interrogates 12,341 mouse genes. The microarray data sets were subjected to hierarchical clustering and pathway analysis. In agreement with model predictions, circulating levels of inflammation/tissue injury markers and the microarray analysis both demonstrated that ST alone accounts for a substantial proportion of the observed phenotypic and genetic/molecular changes versus untreated animals. The addition of HS further increased the magnitude of gene expression, but relatively few additional genes were recruited. Mathematical simulations and DNA microarrays, both systems biology tools, may provide valuable insight into the complex global physiological interactions that occur in response to trauma and hemorrhagic shock.

In silico and in vivo approach to elucidate the inflammatory complexity of CD14-deficient mice.

The inflammatory phenotype of genetically modified mice is complex, and the role of Gram-negative lipopolysaccharide (LPS) in acute inflammation induced by surgical cannulation trauma, alone or in combination with hemorrhage and resuscitation ("hemorrhagic shock"), is both complex and controversial. We sought to determine if a mathematical model of acute inflammation could elucidate both the phenotype of CD14-deficient (CD14(-/-)) mice--following LPS, cannulation, or hemorrhagic shock--and the role of LPS in trauma/hemorrhage-induced inflammation. A mathematical model of inflammation initially calibrated in wild-type (C57Bl/6) mice subjected to LPS, cannulation, and hemorrhagic shock was recalibrated in CD14(-/-) mice subjected to the same insults, yielding an ensemble of models that suggested specific differences at the cellular and molecular levels (for example, 43-fold lower activation of leukocytes by LPS). The CD14(-/-)-specific model ensemble could account for complex changes in inflammatory analytes in these mice following LPS treatment. Model prediction of similar organ damage in CD14(-/-) and wild-type mice subjected to cannulation alone or with hemorrhagic shock was verified in vivo (similar ALT levels). These studies suggest that LPS-CD14 responses do not cause inflammation in surgical trauma/hemorrhagic shock and demonstrate a novel use of combined in silico and in vivo methods to elucidate the complex inflammatory phenotype of genetically modified animals.

In silico models of acute inflammation in animals.

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 model's 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.

Computer simulations help determine safe vertical boom speeds for roof bolting in underground coal mines.

PROBLEM: Incident investigation reports do not usually contain enough information to aid in studying boom arm vertical speed for roof bolting machines to determine the impact that appendage speed had on an operator's risk of experiencing a contact. Laboratory experiments with human subjects are also not feasible because of safety and ethical issues. METHOD: Researchers successfully developed a three-dimensional computer model that uses virtual human simulation software as the primary means to gather contact data when the boom arm touches the operator's hand, arm, head, or leg. RESULTS: Data analysis of roof bolter simulations shows that the speed of the boom arm is the most important factor in determining the risk of an operator making contact. Regardless of other variables, contact incidents were always greater when the bolter arm was moving up, greater on the hand, and greater for the boom arm part of the machine. The reason why the subject experiences more contacts when the boom arm is moving up rather than down is that more risky behaviors occur during drilling and bolting when the boom arm is ascending. Based on the data collected, boom speeds greater than 13 in/sec result in a substantial increase in risk to the roof bolter operator of making contact. Speeds less than or equal to 13 in/sec are associated with a more modest relative risk of making contact, which represents a decrease in potential hazard. IMPACT ON INDUSTRY: The use of such information can be quite helpful in making recommendations to machine design and task procedures to reduce the likelihood that roof bolter operators will experience injury due to contact with a moving roof bolting machine's boom arm.

The acute inflammatory response in diverse shock states.

A poorly controlled acute inflammatory response can lead to organ dysfunction and death. Severe systemic inflammation can be induced and perpetuated by diverse insults such as the administration of toxic bacterial products (e.g., endotoxin), traumatic injury, and hemorrhage. Here, we probe whether these varied shock states can be explained by a universal inflammatory system that is initiated through different means and, once initiated, follows a course specified by the cellular and molecular mechanisms of the immune and endocrine systems. To examine this question, we developed a mathematical model incorporating major elements of the acute inflammatory response in C57Bl/6 mice, using input from experimental data. We found that a single model with different initiators including the autonomic system could describe the response to various insults. This model was able to predict a dose range of endotoxin at which mice would die despite having been calibrated only in nonlethal inflammatory paradigms. These results show that the complex biology of inflammation can be modeled and supports the hypothesis that shock states induced by a range of physiologic challenges could arise from a universal response that is differently initiated and modulated.

In silico design of clinical trials: a method coming of age.

OBJECTIVE: To determine the feasibility and potential usefulness of mathematical models in evaluating immunomodulatory strategies in clinical trials of severe sepsis. DESIGN: Mathematical modeling of immunomodulation in simulated patients. SETTING: Computer laboratory. MEASUREMENTS AND MAIN RESULTS: We introduce and evaluate the concept of conducting a randomized clinical trial in silico based on simulated patients generated from a mechanistic mathematical model of bacterial infection, the acute inflammatory response, global tissue dysfunction, and a therapeutic intervention. Trial populations are constructed to reflect heterogeneity in bacterial load and virulence as well as propensity to mount and modulate an inflammatory response. We constructed a cohort of 1,000 trial patients submitted to therapy with one of three different doses of a neutralizing antibody directed against tumor necrosis factor (anti-TNF) for 6, 24, or 48 hrs. We present cytokine profiles over time and expected outcome for each cohort. We identify subgroups with high propensity for being helped or harmed by the proposed intervention and identify early serum markers for each of those subgroups. The mathematical simulation confirms the inability of simple markers to predict outcome of sepsis. The simulation clearly separates cases with favorable and unfavorable outcome on the basis of global tissue dysfunction. Control survival was 62.9% at 1 wk. Depending on dose and duration of treatment, survival ranged from 57.1% to 80.8%. Higher doses of anti-TNF, although effective, also result in considerable harm to patients. A statistical analysis based on a simulated cohort identified markers of favorable or adverse response to anti-TNF treatment. CONCLUSIONS: A mathematical simulation of anti-TNF therapy identified clear windows of opportunity for this intervention as well as populations that can be harmed by anti-TNF therapy. The construction of an in silico clinical trial could provide profound insight into the design of clinical trials of immunomodulatory therapies, ranging from optimal patient selection to individualized dosage and duration of proposed therapeutic interventions.