Oscillations of NO synthase in the midgut of the Anopheles mosquito

The protocol included random 100 changes in head of bed(HOB) elevation (between 00 and 300) and mild hypo- andhyperventilation (achieved by changing the respiratory rate, RR).Each experimental session consisted of between 1 and 6 changes inHOB and/or RR over periods varying from 15 to 130 minutes.Multiple sessions were recorded for 6 patients. ICP and othersignals were recorded continuously, along with clinical annotationsto indicate the precise timing of the physiologic challenges. Datafrom early in single long session or from prior sessions were used toestimate patient-specific parameter values for a computer model ofICP dynamics that is similar to other models reported in theliterature. The parameter estimates were calculated using a curve-fitting optimization algorithm with the objective of minimizing thesquared error between the ICP calculated by the model and theactual ICP data. The resulting patient-specific models were thenused to predict the patient's ICP response to interventions atlater time periods, either later in the same session or duringsubsequent sessions.Results: Mean absolute error (MAE) between model-calculatedICP and the actual data averaged 1.9 mm Hg for full sessions and1.7 mm Hg for partial sessions. The average mean absolutedeviation (MAD) for these segments was 3.1 and 2.4 mm Hg,respectively. The MAE for the predictions was 4.0 mm Hg withinthe same session and 6.7 mm Hg across sessions.Conclusions: Despite the achievement of low model errors in thetraining segments, the error in predicted segments was too large forthe model to be useful clinically, that is to say, prediction is muchmore difficult than explanation. One implication for researchers isthat a degree of skepticism is warranted: the fact that a model can bemade to fit historical data does not mean that the model will be ableto predict anything. These results could be seen as tending tosupport the general lack of interest from clinicians regardingcomputer models of ICP dynamics.

doi:10.1016/j.jcrc.2007.10.022

Modeling bacterial clearance from the bloodstream usingcomputational fluid dynamics and Monte Carlo simulationDavid Lia, Danial Hohnea, David Bortzb, Joe Bulla, John YoungerbaDepartment of Emergency Medicine, University of MichiganbDepartment of Mathematics, University of Colorado-Boulder

Objectives: Removal of bacteria from the bloodstream is aprerequisite to survival during disseminated infection. The processis poorly understood and typically described as “filtration,”although the diameter of the filtering microvasculature may beseveral times larger than the diameter of the particle to be filtered.Our goal was to study the mechanics of bacterial motion as relatesto absorption, during transit, of the pathogen to the wall ofa capillary.Methods: Computational fluid dynamics and Monte Carlo (MC)simulations of bacterial random walks were used. Our model was a2-D rectangle bounded by capillary walls, the rear surface of aleading erythrocyte and the front surface of a lagging erythrocytewithin the vessel. We assumed Reynolds number ≪1 (modelingonly viscous forces) and a Péclet number for the bacterium of ≫1.Numerical solutions to the Stokes and vorticity equations wereobtained using finite differences and successive overrelaxation. Theflow field obtained was used in a series of MC random walksimulations to estimate the probability of capture by the endothelial

wall of bacteria given the axial and radial location of an organism asit entered the capillary.Results: Plasma flow within a capillary bounded by a forewordand rear erythrocyte was found to be toroidal, with a region ofhigh forward velocity at the vessel center surrounded by slowerrear-directed flow near the vessel wall. Simulated bacteria placedinto this system tended, over time, to be directed toward the rearwall of the leading erythrocyte and then to the vessel wall,facilitating contact between the bacteria and the endothelium.Accordingly, bacteria entering the modeled capillary near thevessel wall, the vessel centerline, or near the rear wall of theleading erythrocyte had the greatest probability of endothelialcontact during capillary transit.Conclusions: Our numerical model suggests a pattern of plasmaflow between red blood cells during capillary transit that promotescontact between bacteria and endothelial cells. This phenomenonmay be important not only for bacterial capture, but also for theefficient presentation of bacteria or bacterial elements to intravas-cular components of the immune system. Ongoing work is directedtoward use of this model as a low-order physical module of amultiscale model of bacterial clearance during disseminated life-threatening infection.

doi:10.1016/j.jcrc.2007.10.023

Oscillations of NO synthase in the midgut of the AnophelesmosquitoIan Pricea, Neil Parikha, Bard Ermentrouta, Yoram Vodovotzb,Shirley LuckhartcaDepartment of Mathematics, University of PittsburghbDepartment of Surgery, University of PittsburghcUniversity of California—Davis

Objectives: Malaria affects 350 to 500 million and kills 2 millionpeople each year. Plasmodium falciparum, the most importanthuman malaria parasite, is transmitted by female Anophelesmosquitoes. Once the mosquito has ingested an infective blood-meal, the parasite invades the mosquito midgut, penetrates theepithelium into the circulatory system, and eventually enters thesalivary glands. The parasite is passed to the next host in the salivaof the feeding mosquito. The mosquito is not a neutral vector oftransmission but rather ingests blood components includingimmune-modulating factors from the infected mammalian host.One of these factors is the cytokine transforming growth factor β-1(TGF-β1), which is a central immune-modulating cytokine elevatedin malaria parasite-infected mammals. We have demonstratedpreviously that TGF-β1 induces the expression of Anophelesstephensi NO-synthase (AsNOS), which kills parasites through thegeneration of reactive NO species. High levels of NO also lead tothe activation of normally latent TGF-β1 in both mammals and A.stephensi, but in mammals, TGF-β1 suppresses the expression ofthe inducible nitric oxide synthase (iNOS). Successful modeling ofthis complex biology may allow for improved methods of malariacontrol and therapy.Methods: We created a mathematical model of the relevant NO-TGF-β1-parasite interactions that occur in the mosquito midgut,including (1) active and latent TGF-β1, (2) AsNOS, (3) an influencethat represses AsNOS expression, (4) a function that accounts forthe activation of latent TGF-β1, and (5) a function that accounts forthe combined suppression and activation of AsNOS depending on

344 Abstracts

http://dx.doi.org/YJCRC50293.21S0883-07)001331016/j.jcrc.2007.10.022Measuring the accuracy of predictions from patient-specific�models of intracranial pressure dynamicsWayneWakelandWayne Wakeland Portland State UniversityObjectives: To determine the degree to which patient-pecific computer simulation models of intracranial pressure (ICP) dynamics can predict patient response to interventions. Despite the availability of many treatment options for elevated intracranial pressure (ICP) after traumatic brain injury (TBI), outcomes remain mixed, and TBI remains the leading cause of death and disability in children. Research to address these challenges has been frequently reported, and a primary thread has been the development of sophisticated computer models to help explain the complex physiologic mechanisms that contribute to the prolonged ICP elevation. In some cases, the models have been calibrated using patient-pecific clinical data, but studies to measure the ability of these models to predict patient response to therapy have not been reported.Methods: Clinically annotated prospective data were collected according to a mild physiologic challenge protocol administered to patients with severe traumatic brain injury (9 patients, 24 sessions). The protocol included random 100 changes in head of bed (HOB)�elevation (between 00 and 300) and mild hypo-and hyperventilation (achieved by changing the respiratory rate, RR). Each experimental session consisted of between 1 and 6 changes in HOB and/or RR over periods varying from 15 to 130 minutes. Multiple sessions were recorded for 6 patients. ICP and other signals were recorded continuously, along with clinical annotations to indicate the precise timing of the physiologic challenges. Data from early in single long session or from prior sessions were used to estimate patient-pecific parameter values for a computer model of ICP dynamics that is similar to other models reported in the literature. The parameter estimates were calculated using a curveitting optimization algorithm with the objective of minimizing the squared error between the ICP calculated by the model and the actual ICP data. The resulting patient-pecific models were then used to predict the patient's ICP response to interventions at later�time periods, either later in the same session or during subsequent sessions.Results: Mean absolute error (MAE) between modelalculated ICP and the actual data averaged 1.9 mm Hg for full sessions and 1.7 mm Hg for partial sessions. The average mean absolute deviation (MAD) for these segments was 3.1 and 2.4 mm Hg, respectively. The MAE for the predictions was 4.0 mm Hg within the same session and 6.7 mm Hg across sessions.Conclusions: Despite the achievement of low model errors in the training segments, the error in predicted segments was too large for the model to be useful clinically, that is to say, prediction is much more difficult than explanation. One implication for researchers is that a degree of skepticism is warranted: the fact that a model can be made to fit historical data does not mean that the model will be able to predict anything. These results could be seen as tending to support the general lack of interest from clinicians regarding computer models of ICP dynamics.

http://dx.doi.org/YJCRC50293.22S0883-07)001341016/j.jcrc.2007.10.023Modeling bacterial clearance from the bloodstream using computational fluid dynamics and Monte Carlo simulationDavidLiaDanialHohneaDavidBortzbJoeBullaJohnYoungerbaDepartment of Emergency Medicine, University of MichiganbDepartment of Mathematics, University of Colorado-oulderObjectives: Removal of bacteria from the bloodstream is a prerequisite to survival during disseminated infection. The process is poorly understood and typically described as �filtration,� although the diameter of the filtering microvasculature may be several times larger than the diameter of the particle to be filtered. Our goal was to study the mechanics of bacterial motion as relates to absorption, during transit, of the pathogen to the wall of a�capillary.Methods: Computational fluid dynamics and Monte Carlo (MC) simulations of bacterial random walks were used. Our model was a 2- rectangle bounded by capillary walls, the rear surface of a leading erythrocyte and the front surface of a lagging erythrocyte within the vessel. We assumed Reynolds number j1 (modeling only viscous forces) and a P�clet number for the bacterium of k1. Numerical solutions to the Stokes and vorticity equations were obtained using finite differences and successive overrelaxation. The flow field obtained was used in a series of MC random walk simulations to estimate the probability of capture by the endothelial wall of bacteria given the axial and radial location of an organism as it entered the capillary.Results: Plasma flow within a capillary bounded by a foreword and rear erythrocyte was found to be toroidal, with a region of high forward velocity at the vessel center surrounded by slower rearirected flow near the vessel wall. Simulated bacteria placed into this system tended, over time, to be directed toward the rear wall of the leading erythrocyte and then to the vessel wall, facilitating contact between the bacteria and the endothelium. Accordingly, bacteria entering the modeled capillary near the vessel wall, the vessel centerline, or near the rear wall of the leading erythrocyte had the greatest probability of endothelial contact during capillary transit.Conclusions: Our numerical model suggests a pattern of plasma flow between red blood cells during capillary transit that promotes contact between bacteria and endothelial cells. This phenomenon may be important not only for bacterial capture, but also for the efficient presentation of bacteria or bacterial elements to intravascular components of the immune system. Ongoing work is directed toward use of this model as a lowrder physical module of a multiscale model of bacterial clearance during disseminated life-hreatening infection.</ce:sections>

the repressing influence and TGF-β1. We made certain simplifyingassumptions regarding latent and active TGF-β1 to examine themodel in 2 variables. Because AsNOS gene expression is known tooscillate with time post-bloodfeeding in experimental systems, wecalibrated model parameters to induce such oscillations.Results: The resulting simplified model depicts the oscillatinglevels of AsNOS expression found in our experimental data for acertain period of time. Varying parameters yields either a systemwithout oscillations, or a system with oscillations that do notdecay sufficiently quickly outside our given period of time.Further, the simplified model does not vary as desired with theinitial amounts of TGF-β1. However, the simplified model doesdemonstrate oscillations that are primarily dependent on initialexpression of AsNOS.Conclusions: Varying the initial level of AsNOS, assumingconstant levels of TGF-β1, and truncating the time frame ofoscillations to the period of our experimental data, the simplifiedmodel gives a good approximation of the oscillating behavior ofAsNOS in the mosquito midgut. However, the model is over-activated, and the oscillations do not decay as seen in ourexperimental data. We hypothesize this overactivation arises fromour simplifying assumption that TGF-β1 does not decay in the timeframe of our interest. We see from the simplified model theAndronov-Hopf bifurcation that induces the oscillations, and inferthe existence of a similar bifurcation in the larger model. Furtheranalysis of the larger model may yield a better match to our data.

doi:10.1016/j.jcrc.2007.10.024

Parameter identifiability in a model of the acuteinflammatory responseSilvia Dauna,b, Robert Parkerc, Anirban Royc, Jonathan Rubina,Gilles ClermontbaDepartment of Mathematics, University of PittsburghbDepartment of Critical Care, University of PittsburghcDepartment of Chemical and Petroleum Engineering,University of Pittsburgh

Objectives: Mechanistic models often include a large number ofparameters. The ensuing inverse problem of calibrating the model toexperimental data is therefore ill-posed. We want to reduce thenumber of parameters to facilitate the computations required toidentify an ensemble parameter set that is representative of thesystem and experimental design.Methods: We developed an 8-state (8-D) differential equationmodel of the acute inflammatory response system to endotoxinchallenge seeking to include a number of physiologic mechanisms.The model was calibrated from cytokine data (IL-6, TNFα andIL-10) obtained from series of rats challenged by endotoxin dosesof 3 and 12 mg/kg. For each rat, seven time points were observed.Model validation was performed by comparing the modelpredictions to an endotoxin challenge of 6 mg/kg with correspond-ing experimental data. We performed an identifiability analysis bycalculating the correlation matrix of the parameters, making use ofthe sensitivity equations based on Jacquez and Greif (1985).Results: The model successfully captured the cytokine dynamicsafter perturbation with endotoxin at various challenge levels. 2 pairsof parameters displayed perfect correlation (+1 or −1 off thediagonal of the correlation matrix), meaning that these parametersare not locally identifiable, or are a priori unidentifiable. Of the

1035 pairs of parameters, 163 and 388 exhibited an absolute valueof the correlation coefficient N0.99 and N0.95, respectively. Theabsolute value of the correlation coefficient was b0.5 in 91 pairs ofparameters and less than 0.1 for 2 parameters.Conclusions: The calibrated model captures data well in both thecalibration and validation series. The identifiability analysisindicates that it is possible to reduce the number of parameters inthe model. The reduction will be accomplished by an iterativeprocess consisting of calculating the correlation matrix of theparameters, removing one unidentifiable parameter, recalculatingthe correlation matrix, removing another unidentifiable parameter,and so on, until no more unidentifiable or almost perfectlycorrelated parameters remain. For this iterative process a cut-offlimit for identifiability has to be defined.

doi:10.1016/j.jcrc.2007.10.025

Poincare plot analysis for assessment of injury severity inprehospital trauma patientsJose Salinasa, Andriy Batchinskya, Leopoldo Cancioa,William Cookeb, Victor Convertinoa, Steven Wolf a, John HolcombaaU.S. Army Institute of Surgical Research, Fort Sam Houston,TX, USAbUniversity of Texas at San Antonio, San Antonio, TX, USA

Objectives: Previous studies have shown that standard vital signssuch as heart rate and blood pressure are poor predictors of outcomein prehospital trauma patients. Linear and non linear analyses of Rto R intervals (RRI) of the electrocardiogram (ECG) have been usedto provide a more accurate and earlier indication of impendingcardiovascular collapse and death. These approaches however,require an ideal ECG waveform free of mechanical and organicartifacts. Poincare plot analysis has been shown to provide somenoise and artifact tolerance and thus may be useful for processing ofreal life noisy waveform data. The purpose of this study was toevaluate the utility of Poincare plot descriptors (transversal mean,longitudinal mean, transversal/longitudinal mean [TLM], SD1,SD2, and SD2/SD1) derived from ECG of prehospital patients asindicators of patient outcome.Methods: A random cohort of 30 trauma patients transported viahelicopter service was identified from a retrospective database. Thecohort was divided into 2 equal groups of 15 patients each whoeither lived or died. All patients were transported to one of 2 level Iurban trauma centers. Primary outcome was mortality. All patientelectronic vital signs and results of physical exams were recordedand analyzed. Age, sex, Glasgow Coma Scale score (GCS), bloodpressure, pulse pressure, pulse, SpO2 were recorded. Vital signswere composed of both numeric values (heart rate [HR], systolicblood pressure [SBP], SpO2), and ECG recorded at 375 Hz.Derived vital signs for shock index (SI) and pulse pressure (PP)were also computed. RRI intervals were identified from the firstavailable 5-minute sections through an automated R wave detector.Univariate analysis was performed on the Poincare plot descriptorsto determine differences between groups.Results: Injury severity (ISS) scores were not statistically differentbetween the 2 groups. GCS scores were significantly lower inpatients that died (4.7 ± 3.77 vs 11.69 ± 5.0, P = .001). Both SD1and SD2 were also significantly higher in the group that died (SD1:96.6 ± 113.3 vs 20.7 ± 23.5, P = .02, SD2: 129.4 ± 144.4 vs 46.5 ±33.1, P = .05). SD2/SD1 was significantly lower in the patients that

345Abstracts

http://dx.doi.org/YJCRC50293.23S0883-07)001351016/j.jcrc.2007.10.024Oscillations of NO synthase in the midgut of the Anopheles mosquitoIanPriceaNeilParikhaBardErmentroutaYoramVodovotzbShirleyLuckhartcaDepartment of Mathematics, University of PittsburghbDepartment of Surgery, University of PittsburghcUniversity of California�DavisObjectives: Malaria affects 350 to 500 million and kills 2 million people each year. Plasmodium falciparum, the most important human malaria parasite, is transmitted by female Anopheles mosquitoes. Once the mosquito has ingested an infective bloodmeal, the parasite invades the mosquito midgut, penetrates the epithelium into the circulatory system, and eventually enters the salivary glands. The parasite is passed to the next host in the saliva of the feeding mosquito. The mosquito is not a neutral vector of transmission but rather ingests blood components including immuneodulating factors from the infected mammalian host. One of these factors is the cytokine transforming growth factor �-TGF-1), which is a central immuneodulating cytokine elevated in malaria parasitenfected mammals. We have demonstrated previously that TGF-1 induces the expression of Anopheles stephensi NO-ynthase (AsNOS), which kills parasites through the generation of reactive NO species. High levels of NO also lead to the activation of normally latent TGF-1 in both mammals and A. stephensi, but in mammals, TGF-1 suppresses the expression of the inducible nitric oxide synthase (iNOS). Successful modeling of this complex biology may allow for improved methods of malaria control and therapy.Methods: We created a mathematical model of the relevant NO-GF-1-rasite interactions that occur in the mosquito midgut, including (1) active and latent TGF-1, (2) AsNOS, (3) an influence that represses AsNOS expression, (4) a function that accounts for the activation of latent TGF-1, and (5) a function that accounts for the combined suppression and activation of AsNOS depending on the repressing influence and TGF-1. We made certain simplifying assumptions regarding latent and active TGF-1 to examine the model in 2 variables. Because AsNOS gene expression is known to oscillate with time postloodfeeding in experimental systems, we calibrated model parameters to induce such oscillations.Results: The resulting simplified model depicts the oscillating levels of AsNOS expression found in our experimental data for a certain period of time. Varying parameters yields either a system without oscillations, or a system with oscillations that do not decay sufficiently quickly outside our given period of time. Further, the simplified model does not vary as desired with the initial amounts of TGF-1. However, the simplified model does demonstrate oscillations that are primarily dependent on initial expression of AsNOS.Conclusions: Varying the initial level of AsNOS, assuming constant levels of TGF-1, and truncating the time frame of oscillations to the period of our experimental data, the simplified model gives a good approximation of the oscillating behavior of AsNOS in the mosquito midgut. However, the model is overactivated, and the oscillations do not decay as seen in our experimental data. We hypothesize this overactivation arises from our simplifying assumption that TGF-1 does not decay in the time frame of our interest. We see from the simplified model the Andronov-opf bifurcation that induces the oscillations, and infer the existence of a similar bifurcation in the larger model. Further analysis of the larger model may yield a better match to our data.

http://dx.doi.org/YJCRC50293.24S0883-07)001361016/j.jcrc.2007.10.025Parameter identifiability in a model of the acute inflammatory�responseSilviaDaunabRobertParkercAnirbanRoycJonathanRubinaGillesClermontbaDepartment of Mathematics, University of PittsburghbDepartment of Critical Care, University of PittsburghcDepartment of Chemical and Petroleum Engineering, University�of PittsburghObjectives: Mechanistic models often include a large number of parameters. The ensuing inverse problem of calibrating the model to experimental data is therefore ill-sed. We want to reduce the number of parameters to facilitate the computations required to identify an ensemble parameter set that is representative of the system and experimental design.Methods: We developed an 8-tate (8-) differential equation model of the acute inflammatory response system to endotoxin challenge seeking to include a number of physiologic mechanisms. The model was calibrated from cytokine data (IL-NF� and IL-10) obtained from series of rats challenged by endotoxin doses of 3 and 12 mg/kg. For each rat, seven time points were observed. Model validation was performed by comparing the model predictions to an endotoxin challenge of 6 mg/kg with corresponding experimental data. We performed an identifiability analysis by calculating the correlation matrix of the parameters, making use of the sensitivity equations based on Jacquez and Greif (1985).Results: The model successfully captured the cytokine dynamics after perturbation with endotoxin at various challenge levels. 2 pairs of parameters displayed perfect correlation (r �1 off the diagonal of the correlation matrix), meaning that these parameters are not locally identifiable, or are a priori unidentifiable. Of the 1035 pairs of parameters, 163 and 388 exhibited an absolute value of the correlation coefficient >0.99 and >0.95, respectively. The absolute value of the correlation coefficient was <0.5 in 91 pairs of parameters and less than 0.1 for 2 parameters.Conclusions: The calibrated model captures data well in both the calibration and validation series. The identifiability analysis indicates that it is possible to reduce the number of parameters in the model. The reduction will be accomplished by an iterative process consisting of calculating the correlation matrix of the parameters, removing one unidentifiable parameter, recalculating the correlation matrix, removing another unidentifiable parameter, and so on, until no more unidentifiable or almost perfectly correlated parameters remain. For this iterative process a cutff limit for identifiability has to be defined.

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Oscillations of NO synthase in the midgut of the Anopheles mosquito