Inflammation is the body's initial response to acute biological stress such as bacterial infection or tissue trauma that involves both a simultaneous local reaction and a systemic response (1). This response, often termed the systemic inflammatory response syndrome (SIRS), involves a complex network of amplifying and downregulating signals mediated by a large array of cells and molecules that sense and control homeostatic perturbations. However, when this balance between proinflammatory and anti-inflammatory "forces" is lost, inflammation becomes prolonged, and sequelae of such immunologic dissonance include various chronic disease conditions and adverse outcomes (2). It is therefore a dysregulation of the inflammatory resolution that, in many cases, can turn what is normally a beneficial reparative process into a harmful state for the host.
Mechanisms regulating the inflammatory process involve an extensive network of multiscale interactions between the immune and the central nervous system (CNS) (3). The neuroimmune crosstalk is composed of a descending pathway that links CNS to peripheral immune tissues and a parallel afferent arm linking the immune system with the CNS. The integrity of this loop allows for communication between the CNS and the peripheral immune system, integrating neuronal and immune signals in the periphery as well as in the CNS. In particular, the hypothalamic-pituitary-adrenal axis (HPA) and the sympathetic nervous system (SNS) are the primary stress response pathways by which CNS regulates the immune response. Further, the parasympathetic division of the autonomic nervous system (ANS) also monitors and regulates inflammation (4). Such bidirectional communication pathways between the nervous, the endocrine, and the immune systems are essential components of the integrated homeostatic network of the primary host response, and, as such, a dysregulation of autonomic function may predisposes a host to excessive inflammatory responses (5).
The concept that sinus node pacemaker activity is under control of the ANS has promoted the use of heart rate variability to quantify the cardiac autonomic input and evaluate autonomic modulation of the sinus node (6). Normal heartbeats originate from the sinoatrial (SA) node, which is innervated by vagal (parasympathetic) and sympathetic fibers, and thus, ANS plays a pivotal role in heart rate regulation. Analysis of heart rate variation (HRV) has been widely used for assessing the activities of the ANS and as a marker of severity of illness across several clinical disease conditions (7). Heart rate variation is measured by assessing several expressions of electrocardiogram (R-R) interval variability, including both time-domain and various frequency-domain spectral analyses that may specifically reflect changes of sympathetic and vagal activities to the heart. For instance, time-domain parameters such as the percentage of adjacent normal heart beats that differ by more than 50 ms (PNN50) reflect parasympathetic influences on the heart. Such a statistical measure is strongly correlated to the high frequency component of HRV (∼0.15-0.4 Hz), which is also considered to be an index of vagal tone as well as to the SD of normal interbeat intervals (SDNN) that reflects overall heart rate variability (6). On the other hand, the low frequency range of HRV (0.04∼0.15 Hz) tends to reflect the combined effects of sympathetic and vagal controls.
These clinical measures of heart rate variability are noninvasive assessments that may reflect real-time alterations of physiological status. In general, autonomic dysregulation occurring in acute illnesses is manifested as parasympathetic attenuation and diminished physiological variability, as revealed by reduced PNN50 and SDNN indices, respectively, indicating a striking relationship of very early diminution in parameters of HRV to the later adverse outcome of critically ill patients (8). In addition to this, cardiovascular abnormalities in association with a hyperdynamic state characterized by increased cardiac index and heart rate (HR) have been also documented during the early flow phase of injury and infection.
The acute systemic inflammatory condition mediated by endotoxin (LPS) administration in healthy volunteers also elicits a hemodynamic response associated with increases in HR and a transient decrease in cardiac vagal tone (9). Endotoxin is one of the principal components of the outer membrane of gram-negative bacteria, and the inflammation caused by the activation of the innate immune system by this moiety alters manysystemic physiological processes in a qualitatively similar manner with acute illnesses (10). The responses following intravenous endotoxin administration in human subjects include core temperature, cardiac, vasomotor, hematologic, metabolic, hormonal, acute phase reactant, and cytokine components.
In an effort to establish quantifiable relationships among these various components, we have previously proposed in silico models of human endotoxemia as prototype models of acute inflammation in humans, of increasing complexity (11-13). Mathematical modeling is increasingly being used to address biological complexity, and we thereby developed semimechanistic-based host response models that integrate essential regulatory processes across the host linking the initiating signal (LPS) with transcriptional dynamics, signaling cascades, and physiological (hormonal) components. We are driven by the premise that such models can yield significant insights into how macroscopic phenotypic observations of a system emerge as the outcome of orchestrated interactions of critical network modules, thus advancing the translation of knowledge from basic research into an integrated framework sufficient to predict system behavior in the form of disturbances across an intricate web of interacting elements.
The present study describes a continuation of this effort, with the attempt to quantify essential aspects of the autonomic control of HR regulation. During the progression of endotoxin-induced inflammation, disruptions in autonomic cardiac control are reflected by alterations in the joint activity of sympathetic and parasympathetic arms of ANS, which thereby influence the intrinsic pacemaker activity (HR). Predicated upon this, the proposed model intends to describe changes in HR response to the prototypical inflammatory stimulus (endotoxin) as a result of altered autonomic activity, incorporating explicitly the relative contribution of efferent branches of the ANS (sympathetic/parasympathetic outflow). Specifically, we expanded our prior modeling work to include physicochemical interactions related to the release, binding, and degradation of cardiac neurotransmitters occurring at the systemic level of the sinus node of the heart. Of particular relevance to this study are human data associated with a constrained cardiovascular response to the endotoxin paradigm including vital signs such as HR measurements and parameters of HR variability, namely, PNN50. Such response is phenotypically expressed as tachycardia that resolves within 24 h and is simulated as a result of increased efferent sympathetic activity and reduced parasympathetic response.
The dynamics of the system are characterized by 26 variables, and the validity of the proposed physiology-based human inflammation model is demonstrated through its potential to reproduce biologically relevant situations described as the following scenarios: (i) a self-limited inflammatory response evoked by low-dose endotoxin corresponding to successful resolution of all clinical manifestations within 24 h after LPS exposure; (ii) cardiovascular implications of antecedent stress (i.e., acute epinephrine [EPI] infusion) upon the systemic inflammatory manifestations of human endotoxemia. Prior experimental studies demonstrate that catecholamine excess, as produced by 3-h infusion before LPS challenge, attenuates not only the proinflammatory manifestations of human endotoxemia but also the vagus nerve activity followed by tachycardia (14); (iii) dose-dependent effects of acute endotoxin injury on the neuroendocrine immune axis; and finally (iv) scenarios associated with systematic perturbations that modulate the host dynamics toward either an irreversible response or in favor of a balanced immune response depending on the anti-inflammatory "reservoir" of the host relative to the intense (pro)inflammatory response elicited under high doses of LPS. Such scenarios explore the importance of dynamic anti-inflammation during the course of unremitting inflammation in balancing neuroimmunologic dissonance promoting inflammatory resolution manifested by cardiovascular homeostasis. Hence, we opt to assess the qualitative behavior of our model by simulating a series of nonlinear host responses to endotoxin injury that could potentially provide invaluable insights into the complex relationship between injury and cardiac dysfunction within the context of antecedent stresses occurring during critical illnesses.
It is the goal of this study to demonstrate the feasibility of a semimechanistic and physiology-based model of human inflammation that captures essential features of the multiscale nature of the response. Such a modeling approach integrates central influences between autonomic control systems and physiological inflammatory components, making it a critical enabler for clarifying how cellular events and inflammatory processes mediate the links between patterns of autonomic activities and adverse clinical outcomes, thereby advancing the translational potential of systems modeling in clinical research.
MATERIALS AND METHODS
Experimental models of human endotoxemia and data collection
A great deal about the initial human inflammatory response to infectious challenges has been learned from the elective administration of endotoxin (9). Using the human endotoxin challenge model (CC-RE, lot 2 at a dose of 2 ng/kg body weight [BW]), vital signs including HR and parameters of HRV, namely, pNN50, were recorded (14, 15). Specifically, HR was recorded every 30 min from the arterial monitoring system for the first 6 h after endotoxin challenge and at 24 h after LPS administration. The determination of HRV indices was obtained using a continuous electrocardiography technique.
In a continuous electrocardiography record, each QRS complex (resulting from sinus node depolarization) was detected, and one of the time-domain measures, which were analyzed in this study, included the percentage of interval differences of successive interbeat intervals greater than 50 ms (pNN50). This time-domain statistic reflects the occurrence of large changes between adjacent heartbeats, and it serves as surrogate for parasympathetic influences on the heart (vagal function) (7). In addition to time-domain analyses, spectral methods have also been used to describe parasympathetic modulation of the sinus node. For instance, high frequency variability (0.15-0.4 Hz), the usual statistic for assessing respiratory sinus arrhythmia, correlates with parasympathetic and vagal tone. However, respiration rate, oftentimes, falls outside the high frequency range during the post-LPS administration, and pNN50 can be used as an alternative method for assessing parasympathetic efferent activity. Thus, in this study, among the various HRV indices, the time-domain measure pNN50 was used to assess vagus nerve activity and parasympathetic influences on the sinus node pacemaker activity.
Multiscale physicochemical models of systemic inflammation in humans
The administration of a low dose of endotoxin (LPS) to human subjects elicits significant dynamic transcriptional changes as well as hemodynamic and neuroendocrine responses that mimic those observed in acute injury and early sepsis (10). In an effort to establish quantifiable relationships among these components, a multiscale physicochemical host response model is developed (11-13) that addresses the following unique aspects: (i) identification of the essential responses characterizing the cellular (leukocyte) transcriptional dynamics in response to endotoxin administration; (ii) reverse engineering of connectivity and interaction dynamics of these elements exploring the concept of physicochemical and (iii) indirect response (IDR) modeling that connect extracellular signals and intracellular signaling cascades leading to the emergent transcriptional dynamics; and finally (iv) multiscale, physiology-based modeling that quantifies critical aspects of the neuroendocrine-immune crosstalk and assesses systemic disruptions manifested by diminished physiological variability (HRV). All the interacting components and the associated equations defining the dynamics of the host are succinctly presented in Equations (1) to (7).
The propagation of LPS signaling mediated by the activation of endotoxin signaling receptor and elementary proinflammatory pathways (i.e., NF-κB signaling module) is described by Equations (1) to (4). Furthermore, Equations (5) and (6) quantify the release of endocrine stress hormones (cortisol, EPI) from neuroendocrine axis (HPA, SNS) coupled with their anti-inflammatory influence on the host, and finally, Equation (7) integrates systemic-level responses associated with the physiological status of the host. In addition to endotoxin-induced reduced HRV, endotoxin challenge also elicits tachycardia in association with a hyperdynamic cardiovascular response that mimics acute critical illness (16).
Although the terms increased HR and reduced HRV are, oftentimes, used interchangeably in the literature, several lines of evidence indicate examples in which concomitant changes in mean HR might complicate the interpretation of overall HRV. This applies particularly to studies evaluating drugs that may have direct effects on sinus node pacemaker activity (6). For instance, experimental observations, at least in a context of self-limited systemic inflammatory response (14), show that HRV indices, including pNN50 (vagal activity), and HR dynamics may be significantly modulated because of adrenergic infusion without reflecting any change in overall system's adaptability as assessed by SDNN parameter. In the following section, we discuss the potential of a physiology-based model of autonomic control of HR response to endotoxin, to capture the cardiovascular effect of agents (i.e., catecholamines) that affect sinus pacemaker activity.
Developing a semimechanistic model for the autonomic control of HR in acute human inflammation
Among the many interesting correlates for human infectious pathology arising from the human models of endotoxemia is the documentation that low-dose LPS (2-4 ng/kg BW) induces an increase in cardiac index and HR (17). Overall variations in HR being largely dependent on autonomic modulation, an increased HR has been considered to reflect a diminished parasympathetic (vagal) tone and an increased sympathetic modulation of the sinus node. Such interpretation lies in agreement not only with experimental evidence indicating sympathetic activity excess (and/or parasympathetic attenuation) but also with the findings that reductions in implied vagal nerve activity are associated with increased morbidity in critically ill patients (10). Although the mechanism for this systemic "decomplexification" is unknown, it is likely that altered central autonomic (ANS) activity and disruptions in efferent sympathetic and parasympathetic signaling are contributory.
The effect on HR of combined modulation of sympathetic and parasympathetic (vagal) nerves has been described in a quantitative fashion since the 1960s. Warner and Cox (18) developed a mathematical model (Warner model) to simulate the dynamics of SA node in response to vagal and sympathetic stimulations. Because this model forms the foundation of this study, we briefly summarize the key elements and the associated interactions. The relationship, for instance, between stimulation of sympathetic nerve to the heart and the HR is illustrated in Figure 1.
Specifically, at the level of sympathetic nerve activity, the instantaneous neural activity is described by a sinusoidal function (f1) that serves as the input of the model stimulating the release of sympathetic neurotransmitters at the nerve ending (A1). However, the cardiac neurotransmitter release (A1) is not limited to centrally mediated neural traffic but may be also triggered in response to neurotransmitters from peripheral tissues such as blood (Ao). On the active site (SA node), an effective concentration of catecholamine (A2) is derived from a set of first-order kinetic equations that reacts with substance (B) forming the signal (AB) to produce a change in HR when only sympathetic activity is present.
In this study, the kinetic part of the sympathetic site of the Warner model is used as a template for producing the concentrations of neurotransmitters in response to the related autonomic activities in human endotoxemia. Embedding the structure of Figure 1 in the dynamics of our human endotoxin model, we assume that the released neurotransmitters from SNS nerve are triggered by the increased circulating levels of catecholamines evoked by endotoxin, Equation (8), and thereby influencing the effective neurotransmitter concentration on the sinus node of the heart, Equation (9).
Specifically, the release of sympathetic neurotransmitters from the SNS nerve ending (A1) is quantified by first-order kinetics (K1 and K2), Equation (8). The reuptake process of the SNS neurotransmitter from the sinus node to the nerve ending is described by the term K2(A2 − A1), whereas the effective concentration of the neurotransmitter at the active site of the heart (A2) is influenced by the rate of sympathetic nerve traffic (A1), Equation (9). We recognize that in the kinetic part of the Warner model sinusoidal functions were also used as input signals to sympathetic nerve stimulation. Because these functions represent the frequency stimulus that was experimentally performed in the nerves of anesthetized animals, such neural patterns are not considered in our model. Alternatively, for purposes of our model, plasma concentration of EPI serves as the primary "input" signal to the efferent sympathetic site, which in line with evidence (19) high plasma catecholamine concentrations is associated with high rate of sympathetic nerve traffic.
As it previously mentioned, the formed signal (AB) represents the sympathetically mediated active signal that affects pacemaker activity, and here, this mediator serves as a surrogate for the overall sympathetic response (Tsym). Regarding the dynamics of the vagal site, although the relationship between the two major autonomic divisions may be highly complex, it is believed that changes in HR are brought about by simultaneous reciprocal changes in the autonomic influences on the heart (20). Such mutual antagonism between the efferent sympathetic and parasympathetic branches of the (ANS) is further considered and quantified in Equations (10) and (11).
Assuming that the two major autonomic control systems act as endogenous neuronal antagonists (21), such dynamic interaction is described by the kinetic parameters (kTsym,Tpar, kTpar,Tsym), Equation (10). Thus, the kinetics of the Warner model are extended by incorporating the stimulatory function (1 + kTsym,TparTpar) that inhibits the first-order kinetic rate (K3) of sympathetic activity and represents the antagonism of parasympathetic response (Tpar). Similarly, the inhibitory effect of sympathetic response (Tsym) to vagal function is represented by the linear function (1 + kTpar,TsymTsym), whereas the dynamics that define the substance (B) are the same as in the original Warner model, Equation (11).
In an effort to quantify the overall dynamics of the parasympathetic reflex activity (Tpar), the principles of IDR modeling are used as previously explored (12). The underlying assumption is that the baseline of parasympathetic tone is produced in a zero-order kinetics (Kin,Tpar) and removed in a first-order kinetics described by a constant rate (Kout,Tpar). In our endotoxin injury model, a dynamic change in vagal function (Tpar) is simulated because of an increase in sympathetic outflow (Tsym), which is evoked by neuroendocrine stress hormones (i.e., EPI) coupled with the activation of other sympathetically mediated physiological processes (i.e., blood pressure) (22) that might contribute to further modulation of vagal function and are represented by (A1) signaling mediator. The potential of the IDR modeling in simulating physiological variables including autonomic reflex activity has been effectively demonstrated in Perlstein et al. (23), and here, this modeling concept is also explored to quantify HR dynamics as follows:
The basal HR response is assumed to be maintained by the balance of relevant neurotransmitters that are given by a constant rate of synthesis (Kin,HR) and a first-order degradation rate (Kout,HR) (see Appendix Table 1, Supplemental Digital Content 1, at http://links.lww.com/SHK/A66). It is well recognized that the HR increases when sympathetic stimulation increases and that it decelerates upon increased parasympathetic response (20). Hence, the effect of sympathetic and parasympathetic activities on the HR is quantified by (kHR,Tsym) and (kHR,Tpar), respectively. Specifically, in this model, the vagus nerve mediates deceleration of HR by stimulating the degradation rate of HR response (Kout,HR). Taken together, in our endotoxin injury model, cardiac acceleration is induced by the antagonistic interplay of autonomic activities on the heart manifested as prevalence (increase) of efferent sympathetic activity (Tsym) and attenuation of parasympathetic nervous system function (Tpar).
RESULTS AND DISCUSSION
Elements of the physiology-based model of human endotoxin-induced inflammation
We have previously demonstrated the feasibility of a multiscale physicochemical host response model that integrates essential regulatory processes across the host linking the initiating signal (LPS) with transcriptional (cellular) dynamics, signaling cascades, and hormonal (physiological) components. Specifically, elementary proinflammatory pathways (i.e., NF-κB signaling module) triggered by the recognition process of LPS from its signaling receptor (i.e., R, TLR4) propagate the acute inflammatory reaction at the transcriptional response level (P, A, E). Essential aspects associated with the neuroendocrine immune crosstalk and systemic "decomplexification" are also considered. In an effort to assess autonomic modulation of the sinus node of the heart, we attempted to describe the effect on HR of simultaneous sympathetic and vagal controls as illustrated in Figure 2. Specifically, at the systemic level of the sinus node, physicochemical interactions related to the release, binding, and degradation of cardiac (SNS) neurotransmitters (A1, A2) are incorporated. Such interactions are stimulated by the neuroendocrine axis and particularly by circulating levels of EPI released upon endotoxin from activation of SNS pathway. During the progression of endotoxin-induced inflammation, disruptions in autonomic cardiac control are evaluated by alterations in the joint activity of sympathetic (Tsym) and parasympathetic (Tpar) arms of the ANS, which thereby influence the intrinsic pacemaker activity (HR). Thus, the proposed model intends to associate disordered neuroendocrine function with concomitant dysfunctional adrenergic modulation at the SA node (cardiac pacemaker).
Model calibration and validation
The appropriateness of the assumptions invoked in the construction of the proposed model is demonstrated in the following three stages including: (i) calibration of the model using human experimental data associated with HR measurements and time-domain measures of HRV, namely, pNN50, after exposure to low-dose of LPS; (ii) model verification using experimental data that have not been used as a training data set. These data refer to human subjects who received either low-dose (2 ng/kg BW) LPS or an infusion of EPI for 3 h before LPS administration and continued until 6 h after endotoxin administration. Hence, we opt to assess the validity of our model by assessing the cardiovascular implications of acute EPI infusion on the host; and finally (iii) further qualitative model validation simulating a series of biological implications of the host response to endotoxin that can be equated with the (complex) nonlinear dynamics of severe inflammation in the critical care setting. Such scenarios refer to systematic perturbations that modulate the dynamics toward either an irreversible response or in favor of a balanced immune response depending on the anti-inflammatory "reservoir" of the host relative to the intense (pro)inflammatory response.
Model kinetic parameters involved in the autonomic control of HR are estimated by minimizing the discrepancy (error) between model predictions and the experimental data, as depicted in Table 1. Relevant experimental data are normalized by taking the ratio of the measured response at each time point of the study period with respect to the control time point (t = 0 h). Thus, the associated model variables represent dimensionless entities and are considered to quantify the response of the immune function. The parameter estimation (optimization) problem consists of a nonlinear performance criterion (sum of square of errors) and is solved using MATLAB (R2008b) nonlinear optimization solvers such as fmincon (24). All the other parameters related to the propagation of LPS signaling on the transcriptional level and to the neuroendocrine immune system interactions are maintained to agree with those presented in Foteinou et al. (13) (see Appendix Table 3, Supplemental Digital Content 1, at http://links.lww.com/SHK/A66). The differential equations are solved using MATLAB's solver ode15 s, which is a variable-order, variable-step solver for stiff ordinary differential equations.
The performance of the model in reconstructing the clinical manifestations of human endotoxemia is presented in Figure 3. In essence, a self-limited inflammatory response, as previously simulated (11-13), involves the successful elimination of the inflammatory stimulus (endotoxin) within 2 h after endotoxin administration followed by subsequent resolution of all inflammatory manifestations (i.e., transcriptional responses, hormonal concentrations) within 24 h. Here, at the level of autonomic cardiovascular control, intravenous administration of endotoxin elicits tachycardia (elevated HR) as a result of cardiac autonomic imbalance, reflected by increased sympathetic activity (Tsym) and reduced parasympathetic response (Tpar). An increase in sympathetic activity followed by reductions in implied vagal nerve activity has now been noted during inflammatory conditions associated with human endotoxemia (10). In our computational model, such dysregulation is mediated by an acute neuroendocrine stress response evoked by endotoxin and specifically by increased circulating levels of EPI, which gives rise to a high rate of efferent sympathetic nerve traffic. Such stimulation is manifested as upregulation in the concentration of cardiac sympathetic neurotransmitters (A1, A2) that participate in the sympathetic control of HR.
Implications of acute EPI infusion on the host response to endotoxin
Catecholamines, the main neurotransmitters of the SNS pathway, exert anti-inflammatory and vasoactive properties affecting both immune cell activation and cardiovascular function (25). At the cellular (immune) level, we have previously simulated the effect of EPI on attenuating the proinflammatory manifestations of human endotoxemia via a cyclic adenosine monophosphate-dependent mechanism (13). Although the immunosuppressive effects of antecedent periods of catecholamine excess following the systemic inflammatory manifestations of human endotoxemia have been well described, their effect on HR parameters induced by endotoxin is not well understood.
Predicated upon this, the influence of EPI infusion initiated 3 h before the intravenous administration of endotoxin and continued until 6 h after LPS exposure is simulated at various doses in Figure 4. We specifically sought to simulate whether there exists a particular dose of exogenously induced catecholamine excess (defined in our model by the parameter, Rin,EPI) that describes significantly the relevant experimental data. Thus, increasing the parameter (Rin,EPI) at various values, the total concentration of EPI, represented by dashed and dotted lines (Fig. 4A), increases in a dose-dependent manner, which subsequently potentiates the cardiac sympathetic activity (Tsym; Fig. 4B) relative to the response invoked by the administration of the inflammatory stimulus (- lines). Such increase in efferent sympathetic outflow further diminishes the parasympathetic (vagal) function (Tpar) and thereby affects the intrinsic pacemaker activity as assessed by increased HR. Experimentally, such modulation in parasympathetic and HR response to endotoxin under conditions of prior EPI infusions is demonstrated in Jan et al. (14). Regarding the experimental study, antecedent EPI infusion mediated a decrease in parasympathetic function, which was significantly different from the effect induced by LPS (Fig. 5C), and a significantly higher HR response (HR) (Fig. 5D). It is important to emphasize that the aforementioned experimental data represent the dynamics of the host under conditions of a particular dose of EPI and are used to test the validity of our model in predicting inflammatory relevant responses in situations on which it has not been trained. Although plasma concentrations of EPI are not available under conditions of prior EPI infusion, our simulations indicate that there exists a value of the model parameter (Rin,EPI) that captures the vagolytic influence of exogenously induced catecholamine excess as assessed by an average correlation coefficient that approximates the value of 0.8 between relevant experimental data and model output (see Appendix Table 4, Supplemental Digital Content 1, at http://links.lww.com/SHK/A66).
Dose-dependent effects of acute endotoxin injury on the neuroendocrine-immune axis
The dose-dependent LPS inflammatory effects on immune-endocrine host responses are reported by relevant human studies (26). Specifically, in this study, increasing the concentration of LPS leads to differential peak responses of the human host response as assessed by immune-neuroendocrine parameters including cytokines and stress hormones (i.e., cortisol) and physiological responses (i.e., HR) after the administration of low doses of endotoxin (i.e., 0.4 ng/kg) in healthy human subjects. On the other hand, high doses of endotoxin can be responsible for a dysregulation in the host defense intrinsic dynamics, although this bacterial byproduct does not proliferate as a gram-negative bacteria (27). Regarding endotoxin administration and mortality, it is generally accepted that the maximum dose of LPS that can be safely administered to humans is 4 ng/kg BW. In the following, we demonstrate the ability of our model to enable such "predictions," providing further evidence of the validity of the assumptions invoked in the development of our model.
In an effort to simulate proper responses to survivable and lethal endotoxin doses, we simply vary the concentration of LPS at time zero (LPS [t = 0 h]), carrying out simulations with low (i.e., LPS [t = 0 h] = 0.4 ng/kg) and high LPS doses (i.e., 8 ng/kg-four times greater than the nominal value [2 ng/kg BW] used to calibrate the model) (Figs. 6 and 7). We observe that when the concentration of LPS exceeds a critical threshold, the inflammatory response does not abate, as was seen in solid lines, where lower doses of LPS were simulated. This response is characterized by the uncontrolled secretion of endocrine hormones (cortisol, EPI) that are not adequate to balance (control) the overall immune response, thereby giving rise to a cytokine "burst" (Fig. 6). Such dysregulation is further accompanied by impaired autonomic function and cardiac instability manifested as sustained elevations in HR response (Fig. 7). Prolonged HR elevations are particularly simulated because of a persistent diminished vagus nerve activity (Tpar) and/or sympathetic (Tsym) overshooting that occur under conditions of severe endotoxin injury. In acute critical illness, comparable to the overwhelming immune response, adrenergic stress may also be uncontrolled and cause adverse effects.
We recognize that we have previously simulated the dose dependence of LPS effects on the cellular host response level (11, 12). However, the proposed model allows us to simulate concomitant dysfunctional adrenergic modulation of the heart and peripheral blood leukocytes during the progression of severe human injury. Specifically, impaired neuroendocrine regulation during SIRS contributes to disruptions in cardiovascular homeostasis phenotypically expressed as persistent elevations in HR that are, in many cases, associated with increased morbidity and mortality (28). Having established these nonlinear responses, we now consider scenarios that involve possible reversibility in the dynamics of unremitting inflammation in response to a dynamic anti-inflammatory intervention strategy.
Evaluation of hormone replacement "therapy" in modulating severe acute inflammation
A fundamental assumption of our model is the existence of 2 relevant asymptotically stable steady states, which depending on the anti-inflammatory capacity of the host can represent either "recovery/self-limited" or "uncontrolled/sustained tachyarrhythmias" that might account for the transient clinical phenotype of severely stressed patients. To illustrate such scenarios, we consider the trajectory of an unconstrained response, simulated as high concentration of the initial stimulus (LPS), to serve as a surrogate for the high-risk profile of severely stressed patients. Predicated upon the fact that antecedent stress hormone excess abrogates several features of human endotoxemia (29), anti-inflammatory intervention strategies will involve pre-exposure of the host into either exogenously induced catecholamine excess (Fig. 8) or hypercortisolemia (Fig. 9).
Catecholamines, as potent anti-inflammatory and vasoactive agents, have received increased recognition as part of "replacement" therapy in the critical care setting (30). To capture such situation, antecedent periods of EPI infusion following high inflammatory challenge (t = 0 h) are simulated in Figure 8. We observe that acute pre-exposure of the host to catecholamine excess reverses the dynamics of the intense inflammatory reaction toward homeostasis-"recovery phase"-manifested as autonomic restoration and control of cardiovascular instability. Such reversibility in the transient inflammatory phenotype of severe injury annotates the impact of dynamic anti-inflammation on compromising outcome. It is worth mentioning that the sympathomimetic properties of EPI prevail, during the first hours of stress hormone (EPI) infusion, i.e., 3 h before LPS, against its anti-inflammatory effect. This prevalence is illustrated by diminished vagal function (Tpar) and/or increased sympathetic control of HR as shown by solid lines relative to the effect invoked by LPS administration (dashed representation). However, in our model, as the inflammatory response evolves, the dynamic anti-inflammatory mechanism (A) mediated by EPI signaling becomes activated and attenuates the build-up of proinflammation (P), mitigating the subsequent protracted stimulation of neuroendocrine axis and the HR response. Such dynamics indicate the careful use of catecholamine vasopressors in the critically ill to an extent where beneficial effects still prevail without putting an excessive adrenergic stress on the heart (31).
During the progression of sustained tachycardia (dashed lines in Fig. 8F) attained by an irreversible disturbance (i.e., high LPS concentration), the HR response (HR) settles to an "unhealthy" steady state, which approximates the value of 1.68 or else 107 beats/min. Such simulations associate adverse stress (adrenergic) outcomes with severe cardiovascular complications manifested as persistent tachycardia at a high rate. As reviewed by Dunser and Hasibeder (32), among the several hemodynamic parameters, HR greater than 106 beats/min was linked to mortality in patients with septic shock. Such strong association between increased HR and cardiovascular mortality has resurged interest in treatments that compromise HR control and reduce excessive adrenergic stress including hydrocortisone infusion, as simulated in Figure 9.
Prior studies evaluating human responses to infectious challenge (endotoxin) within the context of antecedent stress hormone excess have shown that glucocorticoid excess, as produced by 6-h infusion before LPS challenge, abrogates much of the clinical responses to endotoxin including HR (29). It also attenuates the production of circulating proinflammatory cytokines through an increase in plasma IL-10 concentrations. In our prior models, we simulated the immunosuppressive effects of low-dose hydrocortisone infusion upon the proinflammatory manifestations of human endotoxemia (13). The aim of the present study, however, was to associate the anti-inflammatory effects of glucocorticoids, during the progression of uncontrolled inflammation, with the abrogation of prolonged and intense adrenergic stress that mitigates the subsequent amplified inflammatory response.
Exogenously induced hypercortisolemia initiated 6 h before the LPS challenge potentiates total cortisol levels (solid lines in Fig. 9A), which accounts for alterations in the observed adrenergic stress signaling (Fig. 9B). Such dynamic changes are simulated by reductions in circulating levels of EPI that mediate further attenuation in the efferent sympathetic activity, whereas the latter gives rise to increased parasympathetic function (Tpar) when compared with the dynamics elicited upon the manifestation of severe endotoxin injury. Such altered adaptability in neuroendocrine and autonomic function under conditions of acute hypercortisolemia results in improved autonomic HR regulation as assessed by reversibility in sustained tachyarrhythmias toward homeostasis. Qualitatively, such dynamics might reflect the transient clinical improvement (i.e., "survivors") noted to critically ill patients that respond to a treatment. For example, in an observational study (33), the impact of low-dose hydrocortisone infusion on modulating the course of the SIRS is manifested by reduced HR, inflammatory markers, and eventual recovery from stress-induced implications. However, we would like to emphasize that it is not the purpose of this study to make direct comparisons between our model predictions and clinical observations. Instead, the overall goal of this study was to develop a semimechanistic model of human endotoxemia as a prototype model of acute human inflammation that would potentially allow us to evaluate antecedent stresses upon the systemic inflammatory manifestations of acute infectious illnesses.
A key assumption of the present study is the association between increased circulating levels of EPI and a high rate of sympathetic nerve traffic (outflow to the sinus node). From a modeling standpoint, any modulation in the plasma concentration of EPI to drive subsequent changes in the cardiac sympathetic nerve activity accompanied by further changes in the autonomic HR dynamics is expected. We note, however, that such relationship is not simple, given that a modulation in the plasma concentration of catecholamines does not necessarily indicate a change in the rate of sympathetic nerve traffic (34). Recently, exogenously induced hypercortisolemia within the context of human endotoxemia modulated inflammatory responses to low-dose endotoxin without affecting any autonomic relevant parameter including HR (15). In this experimental study, the implied discordance between acute hypercortisolemia and no modulation of adrenergic stress response to endotoxin as previously shown (29) raises questions related to a possible nonlinear relationship between glucocorticoid activity and these inflammatory parameters. As new mechanisms become established and their role demonstrated reproducibly, these other mechanisms can be integrated, leading to more complete in silico representations.
In summary, a semimechanistic, physiology-based model of human endotoxemia is developed, as a prototype model of acute inflammation in humans that quantifies essential aspects of the autonomic HR regulation. We expanded our prior mathematical modeling work to include systemic-level interactions associated with the dynamic interplay of sympathetic and parasympathetic nerves to the heart. Such physicochemical interactions are related to the release, binding, and degradation of cardiac neurotransmitters that allow us to associate endogenous neuroendocrine stress responses with centrally altered autonomic activities that give rise to HR changes. Kinetic parameters are estimated by reconstructing human relevant experimental data associated with a constrained hyperdynamic cardiovascular response to the endotoxin paradigm. Such response is phenotypically expressed as tachycardia, which resolves within 24 h, and is simulated as a result of increased efferent sympathetic activity and reduced parasympathetic response.
Despite suffering from various limitations (i.e., calibration to limited data), the proposed model can simulate the cardiovascular implications of acute EPI infusion on the host as well as a series of systematic perturbations that qualitatively can be equated with the (complex) nonlinear dynamics of severe acute inflammation. Such scenarios explore the importance of dynamic anti-inflammation during the course of unremitting inflammation in balancing neuroimmunologic dissonance, promoting inflammatory resolution and thereby cardiovascular homeostasis. Although the present article describes a continuation of our prior work, we plan in future studies to concatenate processes involved in the autonomic regulation of HR with diminished physiological variability (HRV). It is therefore our future goal to further describe changes in HRV by taking the mean HR into account, assessing the contribution of efferent branches of the ANS to changes in overall system adaptability. Developing more mechanistic-based and physiological relevant in silico models of inflammation can yield significant insights into the complex relationship between injury and cardiac dysfunction in severely stressed patients, thereby advancing the translational potential of systems modeling in clinical research.
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Mathematical modeling; infection; humans; inflammation; autonomic nervous system; heart
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