A Neutrophil Phenotype Model for Extracorporeal Treatment of Sepsis
[['Sepsis , a systemic inflammatory response due to an infection , affects 900 , 000 Americans per year and its incidence is expected to increase over the next 10–20 years as the population ages [1] .', 'While it is acknowledged that sepsis is a growing problem , its associated mortality rate has remained persistently high for the last 20 years and is currently near 20% [1–4] .', 'Sepsis is now the leading cause of in-hospital death in the United States , yet there are no FDA approved specific treatments [5] .', 'While understanding of the underlying mechanisms in sepsis has been rapidly improving , translation to clinically effective treatments has proven very challenging [6 , 7] .', 'Much of this difficulty translating treatments may be the diversity and complexity of individual immune response and patient population [8 , 9] .', 'These complexities lend themselves well to computational modeling , which can help integrate these complexities into a unified pathophysiological framework and optimize potential treatments [10] .', 'Neutrophils are one of the first responders to sites of inflammation and play a critical role in the innate immune response .', 'When effective , neutrophils migrate from the bloodstream through endothelial walls to the site of inflammation by sensing gradients of chemokines , which bind to neutrophil cell surface receptors .', 'In early stages of sepsis neutrophils potentially play a duplicitous role , both actively fighting the invading pathogen but also contributing to undesirable systemic inflammation , which often leads to multiple organ dysfunction , immune paralysis , or death [11 , 12] .', 'Neutrophils’ roles in sepsis are well recognized but the dynamics of multiple phenotypes and their impact on treatments is not fully understood .', 'A key chemokine impacting neutrophil behavior and phenotype is interleukin-8 ( IL-8 ) .', 'IL-8 signals through functionally distinct surface receptors CXCR-1/2 , which are primarily expressed on neutrophils .', 'CXCR-1 is primarily responsible for activating phospholipase D [13] , which mediates respiratory burst and other pathogen killing functions .', 'CXCR-2 has been shown to stimulate migratory functions such as chemotaxis and diapedesis [14 , 15] .', 'The motivation of this work is to use computational modeling of CXCR-1/2 signaling , and the associated dynamics in neutrophil phenotype composition , to explore whether modifying this dynamic could be exploited to favorably impact outcome in sepsis .', 'A population based mechanistic computational model , which incorporates both receptor level dynamics and neutrophil response to pathogen , was developed to explore the mechanisms involved in sepsis progression and calibrated in septic baboons .', 'Furthermore , an experimental extracorporeal treatment which modulates CXCR-1/2 receptor levels was evaluated in silico using the model framework .', 'The computational model described in this manuscript provides a physiologic rationale for neutrophil’s CXCR-1/2 mediated activity in sepsis , delivers insight into the overriding mechanisms involved , and suggests that interventions aiming to modulate phenotypic composition are time sensitive .'], ['Of the 16 baboons subjected to bacterial infusion , 11 ( 69% ) died and 5 ( 31% ) survived , with death occurring within 6 days of bacterial infusion .', 'Based on these two systemic outcomes , a thorough investigation of the model ( see Methods section & Fig', '1 ) was completed to identify parameter regimes that explain the dynamics of each group of the responders .', 'The initial conditions for the state variables of the ODE were fixed to simulate experimental stimulation ( Table 1 ) .', 'Among the rate parameters , some were fixed to literature values .', 'These included pathogen growth and decay rates , basal decay rates of naïve neutrophils , CXCR-1/2 internalization and recycling rates and creatinine decay rate ( See fixed parameters in Tables 2 and 3 ) .', 'Remaining parameters were estimated by generating parameter ensembles using a Bayesian parallel tempering approach that fit our model to the survivor and non-survivor experimental data sets ( see Methods ) .', 'We conducted the parameter estimation process in two rounds .', 'In round one , the model was fitted to the two data sets separately .', 'By fitting to the two data sets separately , we were able to effectively show that the model was capable of replicating both lethal and non-lethal outcomes through only a change in few parameters .', 'In an attempt to classify the underlying differences , we identified the parameters that were most influential in determining the outcome ( survivor or non-survivor ) of an individual using stepwise logistic regression .', 'This resulted in a list of seven key parameters .', 'These parameters tend to control the rate at which neutrophils grow and how quickly they can change phenotypes , which play a critical role in determining how quickly and severely the animal will respond to the infection .', 'Once these differentiating parameters were identified , we put the model through a second round of estimation .', 'In the second round , the model was fit to both data sets simultaneously; allowing only the seven previously identified key parameters to vary between the survivor and non-survivor subpopulations ( see Table 3 ) .', 'Additionally , two fixed parameters were allowed to take different values across the two populations to maintain the appropriate initial conditions in creatinine and white blood cell count .', 'This step resulted in two new parameter ensembles that were identical in 28 parameters but varied in nine parameters .', 'This second step enabled us to better crystallize the differences between animals that survived and those that died .', 'These ensembles are biologically more relevant as we expect the animals’ immune responses to be highly similar , with small but important differences indicating susceptibility to a septic insult .', 'Resulting full marginal distributions for each of the 7 parameters were statistically different across survivor and non-survivor populations ( Fig 2 ) .', 'The final mean values and the standard deviation of all the estimated parameters are summarized in Tables 2 and 3 .', 'Until now , the focus was on deriving parametric ensembles explaining the mechanism of sepsis progression in each population .', 'In this section , the sensitivity of sepsis-mediated damage to different model parameters ( and hence different processes in the network ) was evaluated for each population .', 'Area under the damage curve ( AUCD ) was used as an output metric of cumulative damage from sepsis .', 'The analysis was done in two steps .', 'First the sensitive parameters affecting damage in each population was identified to check if similar parameters were responsible for modulating damage within each population .', 'Next , the two populations were combined to identify the parameters primarily responsible for a switch from a low to a high damage region .', 'Since the model is highly nonlinear , a global sensitivity analysis ( GSA ) based on variance decomposition was chosen .', 'This method decomposes the total variance in the output into variance and co-variance contributions from each rate parameter and its higher order combinations .', 'To reduce computational cost , a meta-model based approximation was done ( See Materials and Methods ) .', 'The meta-model method called Random Sampling High Dimensional Model Representation ( or RS-HDMR ) , decomposes the output function ( AUCD ) into a set of component functions that includes the mean followed by first order effects of each parameter and other higher order effects resulting from parameter combinations .', 'The degree of sensitivity of a parameter or its combination with other parameters ( as a set ) is captured by Sobol’ index which by definition is the fraction of the total output variance attributed to the selected parameter set .', 'To perform GSA , 4000 samples were generated from the parameter distributions of the two ensembles and the dynamics of the damage term was simulated for the survivors and the non-survivors .', 'Fig 6 ( A ) shows the AUCD distributions for each ensemble .', 'As expected , the survivors show lower levels of cumulative damage than the non-survivors .', 'The coefficient of variation was higher for the non-survivors ( CV = 1 . 98 ) as compared to the survivors ( CV = 0 . 32 ) .', 'When GSA was performed on the survivor and non-survivor samples separately and in combination , it was found that a third order RS-HDMR contributed close to 95% of the variance for both the populations .', 'However , most of the important contributions were from the parameters constituting highly ranked first order indices .', 'Fig 6B and 6C shows the first order and total Sobol’ indices for the first five most sensitive parameters of each population and Fig 6 ( E ) shows the results when both populations are combined .', 'Note that the total Sobol’ index for each parameter , is the sum of first order index and all higher order indices involving that parameter .', 'For GSA conducted separately on the survivor and non-survivor ensembles , it is found that damage is mainly determined by the decay rate of the killer neutrophils , kNK ( direction of influence shown in Fig ( 6D ) ) .', 'The decay rate of the killer neutrophil controls the rate at which killer neutrophils are removed from the system , and the faster these neutrophils are removed , the lesser the damage .', 'The next important term is the direct damaging effect of the killer neutrophils and this parameter has significant second order interactions with other parameters of the model as seen from the total sensitivity index .', 'The next set of parameters has secondary importance and these parameters are different for the two populations ( variance contributions of each parameter in this set is in the range , 1–10% ) .', 'In survivors , damage is more influenced by the production rate of basal neutrophils and IL-8 in presence of the pathogen .', 'In non-survivors , the effect is more pronounced for damage mediated IL-8 production ( a positive feedback component ) , damage recovery term and killer neutrophil production rate .', 'This indicates that overall damage in non-survivors is more sensitive to the parameters associated with killer cells , IL-8 and damage .', 'For GSA conducted on the combined population , the decay rate of killer neutrophils remains the most important parameter .', 'Interestingly , the sensitivity value and ranking of three parameters increase relative to the case where the populations are analyzed separately .', 'Among these , the transition rate of naïve neutrophils to the killer phenotype via CXCR1 ( kNK−IL8 ) is the most important parameter .', 'The next two parameters include the decay rate in filter Eq ( 7 ) ( which determines the delay between pathogen generation and resulting neutrophil entry into circulation during sepsis ) followed by the parameter controlling transition rate of killer neutrophil to the dual phenotype by CXCR2 .', 'Functional dependence of damage on these three parameters shows that they could be responsible for shift in the population from a low to a high damage region .', 'For example , Fig 6 ( F ) shows the dependence of AUCD on parameter kNK−IL8 .', 'Within each population , no particular trend is visible , but relative increase in the transition rate in the non-survivors correlates well with increased damage .', 'Results in Fig 2 showed that the ranges of two of the parameters , kNK−IL8 and kfilter_off were significantly different for the survivors and non-survivors .', 'Results from sensitivity analysis support this prediction and further show that the parameter values correlate well with the transition in observed damage .', 'Extracorporeal devices are emerging as promising therapies for treatment of sepsis[16–19] .', 'In this instance we propose extracorporeal treatment which directly modulates CXCR-1/2 levels using a bioactive surface which interacts with unbound neutrophil surface receptors upon contact .', 'Such a device , which is currently under development at the University of Pittsburgh , generates targeted and controlled downregulation of neutrophil surface receptors .', 'The dynamics of this device can be analyzed within the framework of the generated computational model to determine its proof of principle in silico and help optimize treatment parameters .', 'The proposed treatment implementation is shown in Fig 7 .', 'Specifically , the receptors are allowed to go to a trapped state and become unavailable for activation by IL-8 for the indicated time of treatment .', 'To evaluate the potential of such an immunomodulatory treatment , we next performed an in silico trial by varying ( 1 ) the time when the treatment is introduced and removed and ( 2 ) the strength of interaction between the trapping device and the unbound neutrophil surface receptors .'], ['This manuscript discusses the development of a mechanistic computational model of IL-8 mediated activation of CXCR-1/2 receptors in baboons which were administered intravenous E . coli .', 'Neutrophil phenotypes , which dictate neutrophil functional response , were generated in silico based on CXCR-1/2 surface receptor levels , linking receptor level dynamics with neutrophil functional response .', 'Parameter ensembles were generated for survivor and non-survivor populations , allowing for in silico observation of sepsis progression .', 'Additionally , an extracorporeal treatment which modulates CXCR-1/2 levels on neutrophils was introduced in silico .', 'This proof of concept evaluation allowed for preliminary device evaluation and optimization of treatment parameters .', 'To our knowledge , this is the first model describing dynamic interactions of neutrophils which specifically takes into account information sharing between the systemic variables and the receptor levels .', 'The receptor level dynamics of the model function on a rapid time scale , adjusting to systemic IL-8 levels in a matter of minutes .', 'These changes in receptor signaling dictate changes in neutrophil phenotype , which dictates neutrophil function and hence mortality .', 'This link thus provides a valuable mechanistic framework that can be subjected to clinically relevant treatment scenarios .', 'For example , the experimental treatment could be implemented purely on the receptor level .', 'Alternatively , systemic variables such as IL-8 levels or neutrophil phenotype could be modulated to evaluate performance of hemoadsorption or neutrophil sequestration extracorporeal devices .', 'Application of parallel tempering approach for parameter estimation allowed for the efficient generation of ensembles of parameters and resulted in a model that could fit experimental data well [20] , allowing reasonably accurate simulations of the system without making strong claims about the values of single parameters which are notoriously difficult to measure and are likely to vary between individuals .', 'This allows for robust , population-level predictions rather than point predictions of model parameters and model behavior .', 'However , the computed multi-dimensional posterior distribution in parameter space reflects constraints imposed by empirical data , as well as data sparsity and uncertainty .', 'These constraints impose a covariance structure in the posterior distribution such that there is robustness in model behavior , despite large uncertainties in individual parameter values .', 'Learning this structure is likely crucial in building predictive model [21 , 22] .', 'Yet , the method is making no claim that individual parameter sets in the ensemble represent individuals in a population .', 'At best , an individual could be represented by a smaller ensemble , reflecting uncertainty relating to this particular individual .', 'Yet , it is fair to say that the ensemble is meant to represent uncertainly about a population of individuals , so that simulating the ensemble will provide expected behaviors across a population of individuals , as long as such behaviors are compatible with the empirical data used to generate the ensemble .', 'One trend that arose in the estimated parameter ensembles was a large difference in the magnitudes of different rate constants , sometimes spanning many orders of magnitude .', 'This is not surprising , due to the inclusion of biological events spanning many time scales , ranging from fast molecular events to cell phenotype transitions and finally to the full duration of infections lasting for days .', 'This suggests that future iterations of the model would benefit from a multiscale approach optimized towards handling these different time scales .', 'Previous efforts [23–25] have worked out approaches that allow for efficient deterministic simulation of fast-scale molecular events , combined with more accurate stochastic simulation of slow-scale or rare events , and such techniques have resulted in impressive results [26 , 27] .', 'Sensitivity analysis on the parametric ensembles enabled identification of the relative importance of the model parameters to state variables of the model .', 'In general , sensitivity analysis is an important step in systems biology workflows and provides valuable information on model characteristics [28 , 29] .', 'Most models in the literature resort to a local analysis which is sufficient if the parameters are well defined .', 'For nonlinear dynamic models based on sparse experimental data and for systems which have inherently high parametric uncertainty , a global analysis needs to be done .', 'Global techniques perform combinatorial perturbations of the parameters utilizing samples from the high-dimensional space .', 'Application of meta-modeling approximations via RS-HDMR as was done in this work can significantly reduce the computational cost of sampling requirements for global methods .', 'Additionally , if the sampling process takes into account parameter covariance computed from an ensemble model , biologically relevant sensitivity indices can be obtained .', 'The systematic integration of ensemble modeling and global sensitivity analysis in this work allowed for identification of the parameters that control biological outcomes like sepsis induced tissue damage .', 'In addition to parameter fits , the behavior of the non-fitted state variables were inspected to check for features relevant to a clinical prognosis .', 'Sepsis progression was analyzed by comparing differences between survivor and non-survivor populations .', 'Neutrophil phenotypes in particular give insight into the differences between survivors and non-survivors .', 'Of importance is the killer neutrophil population , which is highly elevated in the non-survivor population ( see Figs 4 & 5 ) .', 'This neutrophil phenotype is associated with neutrophil induced tissue damage in the model .', 'With support from sensitivity analysis , killer neutrophil decay rate , which sets the levels and dynamics of NK , was found to be the most important contributor to total damage in both the populations .', 'Multiple studies support this finding , indicating that non-survivors or those with more severe sepsis experience increased levels of neutrophil induced tissue damage and MPO generation [11 , 30–33] .', 'Furthermore , the importance of this term is supported by studies on neutrophil apoptosis and lifespan .', 'Research by Taneja [34] and Fialkow [35] determined that neutrophil apoptosis was reduced in cases of severe sepsis , leading to increased lifespan of primed and activated neutrophils .', 'Damage caused by these neutrophils was partially responsible for the progression of sepsis in these severe cases .', 'Upon completion of the combined GSA , kNK−IL8 was also found to be a significant contributor to total damage .', 'Increase of this term leads to preferential generation of the NK neutrophil phenotype , which directly contributes to tissue damage .', 'On the other hand neutrophils in the migratory phenotype were similar in survivor and non-survivor populations .', 'These findings agree with the data from Cummings et al [32] which found neutrophil’s harvested from septic and non-septic patients migrated to IL-8 at similar levels .', 'Interestingly , survivors and non-survivors had similar levels of neutrophil kill/migrate phenotype , indicating that both ensembles had adequate neutrophil populations to eliminate the source pathogen .', 'Therefore , the additional damage in non-survivors was neutrophil induced resulting from elevated neutrophil killer phenotype levels .', 'The IL-8 mediated killing functions of neutrophils are primarily triggered through CXCR-1 rather than CXCR-2 .', 'Modulation of CXCR-1 levels in particular may reduce the killing neutrophil phenotype and reduce neutrophil induced organ damage .', 'A number of experimental treatments for sepsis and other acute inflammatory diseases have targeted the CXCR-1 receptor with success in animal models [36–38] .', 'However , translation to humans has been difficult for two main reasons [6] .', 'First are inherent species dependent differences between human and animal immune systems that must be recognized and accounted for in pre-clinical studies .', 'Second is the misuse of animal models and misinterpretation of pre-clinical data [39] .', 'The recent debate on the translational fidelity of critical disease mouse models is a prime example where two separate comparisons of the human versus mouse genomic leukocyte responses using the same database resulted in two contradictory conclusions [40 , 41] .', 'In the case of IL-8 signaling , which is not present in murine models , homologous cytokines and their associated surface receptors must be examined in IL-8’s place [42] .', 'In this context , in silico modeling is an attractive alternative given that it allows preliminary evaluation of experimental human treatments at minimal costs .', 'Multiple extracorporeal sepsis treatments are currently under investigation with promising results .', 'Blood purification techniques such as hemoadsorption [16 , 17 , 43–45] allow for cytokines and other detrimental proteins to be removed directly from the blood during the cytokine storm , curbing the patient’s immune response .', 'Another approach called activated neutrophil sequestration [19 , 46] , selectively removes harmful neutrophil phenotypes from circulation .', 'In this instance we propose extracorporeal treatment which directly modulates CXCR-1/2 levels using a bioactive surface which interacts with unbound neutrophil surface receptors upon contact , resulting in CXCR-1/2 downregulation .', 'This approach is advantageous because no components of blood are removed from circulation , allowing for a healthy immune response after appropriate modulation of neutrophil surface receptors .', 'In addition , all necessary cell-cell interactions are allowed to occur within well-controlled microcirculation of the device .', 'Such a setup also allows treatment to be easily titrated or halted by adjusting blood flow through the device .', 'The dynamics of such a device were analyzed within the framework of the generated ensemble model to determine its proof of principle in silico and to evaluate its benefits in rescuing individuals marked as non-survivors by the parameter ensembles .', 'When evaluated in silico the proposed extracorporeal CXCR-1/2 modulation device improved mortality from 31% to above 80% when deployed under certain ranges of conditions .', 'This substantial improvement in survival supports the hypothesis that a CXCR-1/2 modulatory device may improve patient outcomes .', 'However , time and length of treatment implementation are critical parameters tied to this success .', 'The importance of quickly beginning sepsis treatment has been well established [47] , particularly for antibiotic administration .', 'Our simulations showed a well-defined optimal time for the initiation of treatment , between 3 and 6 hours after the onset of severe infection .', 'Treatment , if started within this time frame , had a high degree of success over a large range of treatment durations and strengths .', 'This window is specific to the animal model under study and will not directly translate to a clinical setting for two main reasons .', 'First , the model was calibrated with experimental data obtained from baboons , and differences between the baboon and human immune systems must be considered .', 'Second , the baboons were exposed to a well-controlled bacterial infusion at a known time point , followed by a predictably quick and strong immune response .', 'In this instance the pathogen load is well controlled and a large portion of the ensemble can therefore be addressed by a single treatment setting .', 'In clinical practice , patients present with varied pathogen loads and they may be in different stages of infection and immune response .', 'So , future experiments will need to combine clinical knowledge with additional data gathering and simulation to obtain treatment timing relevant for human patients .', 'Clinicians are actively searching for biomarkers to track sepsis disease progression and prescribe treatment [48–50] .', 'Neutrophil phenotype may be a valuable indicator of disease state and individual patient response , but this information is difficult to collect in the clinic .', 'Currently neutrophil phenotype can be evaluated either through functional testing or flow cytometry analysis of critical neutrophil surface receptors .', 'In addition to CXCR-1/2 which are the focus of this model , CD11b , CD88 , and CD62L all have roles in dictating neutrophil phenotype [51] and surface receptor expressions vary depending on severity of the inflammatory response .', 'To more readily exploit phenotype data it may be possible to map neutrophil function to easily measurable biomarkers .', 'Using these indirect measures of neutrophil phenotype can guide clinicians to ideal treatment regimens .', 'In conclusion , the ensemble model presented in this report provided key insights into the progression and mechanisms involved in progression of sepsis .', 'We underline the role of relative abundance of killer , migratory and dual neutrophil phenotypes in deciding survivorship in an animal model .', 'In addition , an in silico extracorporeal treatment which modulates CXCR-1/2 neutrophil surface receptors showed promising results .', 'Further study and collection of experimental data will help further refine both the model and experimental device .', 'Incorporation of data from a diverse patient population and expansion of current ensembles would increase the model’s generalizability , improving the potential for translation .', 'Additional model parameters related to the device such as flow rate , surface area , and form factor could be included , allowing the model to streamline device development .'], ['After general anesthesia , instrumentation and a 30 minute stabilization period , sixteen baboons ( Papio ursinus ) weighing between 19 and 32 kg were infused with 2 x 109 CFU Escherichia coli per kg over a two-hour period as described previously [52] .', 'Thereafter , antibiotic therapy was delivered ( gentamycin 4mg/kg twice a day ) .', 'Eight animals were placed in an acute study lasting 6 days , while another eight were placed in the chronic study intended to last 28 days .', 'All animals were observed for a 4-hour period after bacteria infusion then 11 , 23 , 35 , 47 , 72 hour and 6 days after infusion .', 'Pathogen counts in blood , IL-8 , creatinine , white blood cell , neutrophil elastase / α1-PI complex , and other physiologic parameters and biomarkers were gathered at multiple time point .', 'For animals in the chronic study an additional time point was collected at 28 days .', 'At the end of the study period , the baboons were again anesthetized for measurements and thereafter sacrificed with an overdose of pentobarbital .', 'This study was approved by the Institutional Animal Care and Use Committee at Biocon Research Institute and animals were treated according to NIH guidelines .', 'A simplified mechanistic model of IL-8 mediated activation of CXCR-1/2 receptors and neutrophil response to a pathogen was developed based on available literature information and general knowledge of acute inflammatory response .', 'Receptor level dynamics and systemic parameters were coupled with multiple neutrophil phenotypes to generate dynamic populations of activated neutrophils which reduce pathogen load , and/or primed neutrophils which cause adverse tissue damage when misdirected .', 'Mathematical representation of the interactions detailed in Fig 1 were generated using ordinary differential equation ( ODE ) framework with the rate of interactions described by mass action kinetics or Hill type kinetics [53 , 54] .', 'The interactions included in the model gives rise to 16 ODE state variables and 43 rate parameters .', 'In brief , the model is initiated by a pathogen load , which represents a bacterial inoculation .', 'Presence of pathogen leads to continued growth as well as IL-8 and fMLP cytokine production .', 'IL-8 is generated indirectly from pathogen generation from responding phagocytic mononuclear cells [55] .', 'IL-8 initiates CXCR-1/2 activation in the receptor level , which in turn generates neutrophil phenotype change .', 'Depending on phenotype , neutrophils may cause either pathogen elimination or misdirected tissue damage .', 'A systemic damage indicator represents overall patient health .', 'Increased systemic damage results in further IL-8 generation [56 , 57] , resulting in a positive feedback loop .', 'This simplified system captures the basic functionality of acute IL-8 mediated immune response to pathogen and is capable providing valuable feedback on potential therapeutic treatments modulating these mechanisms .', 'A more detailed description of model equations follows .', 'The model contains 38 parameters , 13 of which are fixed based on literature data ( Table 1 ) .', 'Parameter values were inferred using a Bayesian parallel tempering approach [22 , 67] , which utilizes traditional Markov Chain Monte Carlo ( MCMC ) methods to sample the Bayesian posterior distribution P ( p|y ) , the probability of parameter set p given data y , given by the Bayes formula', 'P ( p|y ) =L ( y|p ) θ ( p ) ∫L ( Y|p ) θ ( p )', 'where L ( y|p ) is the likelihood of observing y for a model with parameters p , θ ( p ) is the prior distribution , and ∫L ( Y | p ) θ ( p ) is the normalizing constant .', 'Additional sampling efficiency is gained by running multiple parallel chains evolving at different temperatures .', 'Higher temperature increases the likelihood of acceptance of proposed steps .', 'This allows the high temperature chains to move more freely through the parameter space , avoiding getting stuck in local minima .', 'This results in more efficient exploration of parameter space [20 , 68] a method we have applied extensively in parameter estimation of practically unidentifiable complex non-linear models [10 , 69 , 70] .', 'This resulted in the creation of parameter ensembles , where each parameter is represented by a posterior distribution , rather than a single value .', 'Free parameters were fit separately to the survivor and non-survivor experimental data sets , resulting in two parameter ensembles representing surviving and non-surviving animals .', 'In order to better capture the underlying biological differences between animals that survive and those that die following the same challenge we attempted to identify the most important parameters in determining animal fate .', 'After computing ensembles for survivors and non-survivors , we performed regularized logistic regression , forward conditional stepwise logistic regression , and backward conditional logistic regression to identify a subset of parameters that are most indicative of outcome .', 'Predictors consisted of all estimated parameters of both ensembles , and the indicator variable was the source ( survivor or non-survivor ) of the ensemble .', 'Parameters were selected that were considered significant by all three methods , leaving a set of seven key parameters .', 'Global Sensitivity analysis was done to determine the independent and correlated contributions of rate parameters on cumulative damage .', 'Area under the damage curve was chosen as the system output .', 'To reduce the computational cost of GSA , Random Sampling High Dimensional Model Representation ( RS-HDMR ) approac
['Introduction', 'Results', 'Discussion', 'Methods']
['Neutrophils play a central role in eliminating bacterial pathogens , but may also contribute to end-organ damage in sepsis .', 'Interleukin-8 ( IL-8 ) , a key modulator of neutrophil function , signals through neutrophil specific surface receptors CXCR-1 and CXCR-2 .', 'In this study a mechanistic computational model was used to evaluate and deploy an extracorporeal sepsis treatment which modulates CXCR-1/2 levels .', 'First , a simplified mechanistic computational model of IL-8 mediated activation of CXCR-1/2 receptors was developed , containing 16 ODEs and 43 parameters .', 'Receptor level dynamics and systemic parameters were coupled with multiple neutrophil phenotypes to generate dynamic populations of activated neutrophils which reduce pathogen load , and/or primed neutrophils which cause adverse tissue damage when misdirected .', 'The mathematical model was calibrated using experimental data from baboons administered a two-hour infusion of E coli and followed for a maximum of 28 days .', 'Ensembles of parameters were generated using a Bayesian parallel tempering approach to produce model fits that could recreate experimental outcomes .', 'Stepwise logistic regression identified seven model parameters as key determinants of mortality .', 'Sensitivity analysis showed that parameters controlling the level of killer cell neutrophils affected the overall systemic damage of individuals .', 'To evaluate rescue strategies and provide probabilistic predictions of their impact on mortality , time of onset , duration , and capture efficacy of an extracorporeal device that modulated neutrophil phenotype were explored .', 'Our findings suggest that interventions aiming to modulate phenotypic composition are time sensitive .', 'When introduced between 3–6 hours of infection for a 72 hour duration , the survivor population increased from 31% to 40–80% .', 'Treatment efficacy quickly diminishes if not introduced within 15 hours of infection .', 'Significant harm is possible with treatment durations ranging from 5–24 hours , which may reduce survival to 13% .', 'In severe sepsis , an extracorporeal treatment which modulates CXCR-1/2 levels has therapeutic potential , but also potential for harm .', 'Further development of the computational model will help guide optimal device development and determine which patient populations should be targeted by treatment .']
['Sepsis occurs when a patient develops a whole body immune response due to infection .', 'In this condition , white blood cells called neutrophils circulate in an active state , seeking and eliminating invading bacteria .', 'However , when neutrophils are activated , healthy tissue is inadvertently targeted , leading to organ damage and potentially death .', 'Even though sepsis kills millions worldwide , there are still no specific treatments approved in the United States .', 'This may be due to the complexity and diversity of the body’s immune response , which can be managed well using computational modeling .', 'We have developed a computational model to predict how different levels of neutrophil activation impact survival in an overactive inflammatory conditions .', 'The model was utilized to assess the effectiveness of a simulated experimental sepsis treatment which modulates neutrophil populations and activity .', 'This evaluation determined that treatment timing plays a critical role in therapeutic effectiveness .', 'When utilized properly the treatment drastically improves survival , but there is also risk of causing patient harm when introduced at the wrong time .', 'We intend for this computational model to support and guide further development of sepsis treatments and help translate these preliminary results from bench to bedside .']
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