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PubMed2002

Modelling lung tumour risk in radon-exposed uranium miners using generalizations of the two-mutation model of Moolgavkar, Venzon and Knudson.

PURPOSES: To model radon-induced lung cancer in uranium miners using a quasi-biological model of carcinogenesis. MATERIALS AND METHODS: Fitting of generalizations of the stochastic two-mutation carcinogenesis model of Moolgavkar, Venzon and Knudson to a case-control dataset nested within the cohort and to the full cohort of lung cancer mortality in the Colorado Plateau uranium miners, taking account of exposure to cigarette smoke and to radon daughters. RESULTS: Models with three mutations gave adequate descriptions of the time and age patterns of radon-daughter-induced excess lung tumour mortality. The overall fit of the two-mutation model to the case-control data was somewhat worse than that of the three-mutation model. For both the optimal two- and three-mutation models radon daughters and cigarette smoke were assumed to act on the first mutation rate. In the optimal two-mutation model, radon daughters also modified the intermediate cell death or differentiation rate. In the optimal three-mutation model, radon daughters modified the second mutation rate. In all models, the action of radon daughters and cigarette smoke was markedly non-linear, particularly in their action on the mutation rates. The optimal two- and three-mutation models fitted to the cohort data were of slightly different form to those fitted to the case-control data. The model fits to the cohort data are preferred to those to the case-control data on grounds of plausibility. CONCLUSIONS: Quasi-biological carcinogenesis models with three mutations give adequate descriptions of the time and age patterns of radon-daughter-induced excess lung tumour mortality. The overall fit of the two-mutation model is somewhat worse than that of the three-mutation model.

Humans↗
PubMed2004

The utility of structure-activity relationship (SAR) models for prediction and covariate selection in developmental toxicity: comparative analysis of logistic regression and decision tree models.

Structure-activity relationship (SAR) models can be used to predict the biological activity of potential developmental toxicants whose adverse effects include death, structural abnormalities, altered growth and functional deficiencies in the developing organism. Physico-chemical descriptors of spatial, electronic and lipophilic properties were used to derive SAR models by two modeling approaches, logistic regression and Classification and Regression Tree (CART), using a new developmental database of 293 chemicals (FDA/TERIS). Both single models and ensembles of models (termed bagging) were derived to predict toxicity. Assessment of the empirical distributions of the prediction measures was performed by repeated random partitioning of the data set. Results showed that both the decision tree and logistic regression derived developmental SAR models exhibited modest prediction accuracy. Bagging tended to enhance the prediction accuracy and reduced the variability of prediction measures compared to the single model for CART-based models but not consistently for logistic-based models. Prediction accuracy of single logistic-based models was higher than single CART-based models but bagged CART-based models were more predictive. Descriptor selection in SAR for the understanding of the developmental mechanism was highly dependent on the modeling approach. Although prediction accuracy was similar in the two modeling approaches, there was inconsistency in the model descriptors.

Animals↗
PubMed1999

A Primer of Social Decision Scheme Theory: Models of Group Influence, Competitive Model-Testing, and Prospective Modeling.

The basic elements of social decision scheme (SDS) theory are individual preferences, group preference compositions (distinguishable distributions), patterns of group influence (decision schemes, social combination rules), and collective responses (group decisions, judgments, solutions, and the like). The theory provides a framework for addressing two fundamental questions in the study of group performance: How are individual resources combined to yield a group response (the individual-into-group problem)? What are the implications of empirical observations under one set of circumstances for other conditions where data do not exist (the sparse data problem)? Several prescriptions for how to conduct fruitful group research are contained in the SDS tradition: make precise theoretical statements, provide strong and competitive tests of theories, and interpret empirical findings in the context of robust process models. Copyright 1999 Academic Press.

Journal Article↗
PubMed2000

Predictive modeling of mixed microbial populations in food products: evaluation of two-species models.

Predictive microbiology is an emerging research domain in which biological and mathematical knowledge is combined to develop models for the prediction of microbial proliferation in foods. To provide accurate predictions, models must incorporate essential factors controlling microbial growth. Current models often take into account environmental conditions such as temperature, pH and water activity. One factor which has not been included in many models is the influence of a background microflora, which brings along microbial interactions. The present research explores the potential of autonomous continuous-time/two-species models to describe mixed population growth in foods. A set of four basic requirements, which a model should satisfy to be of use for this particular application, is specified. Further, a number of models originating from research fields outside predictive microbiology, but all dealing with interacting species, are evaluated with respect to the formulated model requirements by means of both graphical and analytical techniques. The analysis reveals that of the investigated models, the classical Lotka-Volterra model for two species in competition and several extensions of this model fulfill three of the four requirements. However, none of the models is in agreement with all requirements. Moreover, from the analytical approach, it is clear that the development of a model satisfying all requirements, within a framework of two autonomous differential equations, is not straightforward. Therefore, a novel prototype model structure, extending the Lotka-Volterra model with two differential equations describing two additional state variables, is proposed to describe mixed microbial populations in foods.

Evaluation Studies as Topic↗
PubMed2006

Modeling motor vehicle crashes using Poisson-gamma models: examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter.

There has been considerable research conducted on the development of statistical models for predicting crashes on highway facilities. Despite numerous advancements made for improving the estimation tools of statistical models, the most common probabilistic structure used for modeling motor vehicle crashes remains the traditional Poisson and Poisson-gamma (or Negative Binomial) distribution; when crash data exhibit over-dispersion, the Poisson-gamma model is usually the model of choice most favored by transportation safety modelers. Crash data collected for safety studies often have the unusual attributes of being characterized by low sample mean values. Studies have shown that the goodness-of-fit of statistical models produced from such datasets can be significantly affected. This issue has been defined as the "low mean problem" (LMP). Despite recent developments on methods to circumvent the LMP and test the goodness-of-fit of models developed using such datasets, no work has so far examined how the LMP affects the fixed dispersion parameter of Poisson-gamma models used for modeling motor vehicle crashes. The dispersion parameter plays an important role in many types of safety studies and should, therefore, be reliably estimated. The primary objective of this research project was to verify whether the LMP affects the estimation of the dispersion parameter and, if it is, to determine the magnitude of the problem. The secondary objective consisted of determining the effects of an unreliably estimated dispersion parameter on common analyses performed in highway safety studies. To accomplish the objectives of the study, a series of Poisson-gamma distributions were simulated using different values describing the mean, the dispersion parameter, and the sample size. Three estimators commonly used by transportation safety modelers for estimating the dispersion parameter of Poisson-gamma models were evaluated: the method of moments, the weighted regression, and the maximum likelihood method. In an attempt to complement the outcome of the simulation study, Poisson-gamma models were fitted to crash data collected in Toronto, Ont. characterized by a low sample mean and small sample size. The study shows that a low sample mean combined with a small sample size can seriously affect the estimation of the dispersion parameter, no matter which estimator is used within the estimation process. The probability the dispersion parameter becomes unreliably estimated increases significantly as the sample mean and sample size decrease. Consequently, the results show that an unreliably estimated dispersion parameter can significantly undermine empirical Bayes (EB) estimates as well as the estimation of confidence intervals for the gamma mean and predicted response. The paper ends with recommendations about minimizing the likelihood of producing Poisson-gamma models with an unreliable dispersion parameter for modeling motor vehicle crashes.

Accidents, Traffic↗
PubMed2006

The effect of model structure and data in modeling land conditions in disturbed complex ecosystems.

Off-road vehicles increase soil erosion by reducing vegetation cover and other types of ground cover, and by changing the structure of soil. The investigation of the relationship between disturbance from off-road vehicles and the intensity of the activities that involve use of vehicles is essential for water and soil conservation and facility management. Models have been developed in a previous study to predict disturbance caused by off-road vehicles. However, the effect of data on model quality and model performance, and the appropriate structure of models have not been previously investigated. In order to improve the quality and performance of disturbance models, this study was designed to investigate the effects of model structure and data. The experiment considered and tested: (1) two measures of disturbance based on the Vegetation Cover Factor (C Factor) of the Revised Universal Soil Loss Equation (RUSLE) and Disturbance Intensity; (2) model structure using two modeling approaches; and (3) three subsets of data. The adjusted R-square and residuals from validation data are used to represent model quality and performance, respectively. Analysis of variance (ANOVA) is used to identify factors which have significant effects on model quality and performance. The results of the ANOVA show that subsets of data have significant effects on both model quality and performance for both measures of disturbance. The ANOVA also detected that the C Factor models have higher quality and performance than the Disturbance models. Although modeling approaches are not a significant factor based on the ANOVA tests, models containing interaction terms can increase the adjusted R-squares for nearly all tested conditions and the maximum improvement can reach 31%.

Ecosystem↗
PubMed2006

Modeling, identification, and validation of models for predictive ammonia control in a wastewater treatment plant--a case study.

The aim of this work is to develop the ammonia models that could be used for model predictive control (MPC) of nitrification process in a wastewater treatment plant. First, a reduced nonlinear model is presented, which is based on expression for nitrification reaction rate in activated sludge model No. 1 and modified for attached biomass processes, while second, a linear black-box model is shown. The data used for model identification were collected during several weeks of experiments on a real plant so that good identification data were obtained. The designed models were validated based on open loop simulations and predictions. Validation results show that the reduced nonlinear model performs better compared to the linear model, however, both models show relatively large errors compared to the real plant data. Hence, a closed loop simulation study was performed to see the differences between the performance of model predictive controller using previously estimated linear and nonlinear models and a standard proportional integral (PI) controller. From the simulation study results it was seen that in spite of relatively large model errors the MPC algorithms give better results in terms of ammonia removal compared to the PI controller, while MPC with the nonlinear model shows additional improvements over the MPC with the linear model.

Ammonia↗
PubMed2003

Reduction and lumping of physiologically based pharmacokinetic models: prediction of the disposition of fentanyl and pethidine in humans by successively simplified models.

Physiologically based pharmacokinetic (PBPK) models can be used to predict drug disposition in humans from animal data and the influence of disease or other changes in physiology on the pharmacokinetics of a drug. The potential usefulness of a PBPK model must however be balanced against the considerable effort needed for its development. Proposed methods to simplify PBPK modeling include predicting the necessary tissue:blood partition coefficients (kp) from physicochemical data on the drug instead of determining them in vivo, formal lumping of model compartments, and replacing the various kp values of the organs and tissues by only two values, for "fat" and "lean" tissues, respectively. The aim of this study was to investigate the effects of simplifying complex PBPK models on their ability to predict drug disposition in humans. Arterial plasma concentration curves of fentanyl and pethidine were simulated by means of a number of successively reduced models. Median absolute prediction errors were used to evaluate the performance of each model, in relation to arterial plasma concentration data from clinical studies, and the Wilcoxon matched pairs test was used for comparison of predictions. An originally diffusion-limited model for fentanyl was simplified to perfusion-limitation, and this model was either lumped, reducing 11 organ/tissue compartments to six, or changed to a model based on only two kp values, those of fat (used for fat and lungs) and muscle (used for all other tissues). None of these simplifications appreciably changed the predictions of arterial drug concentrations in the 10 patients. Perfusion-limited models for pethidine were set up using either experimentally determined [Gabrielsson et al. 1986] or theoretically calculated [Davis and Mapleson 1993] kp values, and predictions using the former were found to be significantly better. Lumping of the models did not appreciably change the predictions; however, going from a full set of kp values to only two ("fat" and "lean") had an adverse effect. Using a kp for lungs determined either in rats or indirectly in humans [Persson et al. 1988], i.e., a total of three kp values, improved these predictions. In conclusion, this study strongly suggested that complex PBPK models for lipophilic basic drugs may be considerably reduced with marginal loss of power to predict standard plasma pharmacokinetics in humans. Determination of only two or three kp values instead of a "full" set can mean an important reduction of experimental work to define a basic model. Organs of particular pharmacological or toxicological interest should of course be investigated separately as needed. This study also suggests and applies a simple method for statistical evaluation of the predictions of PBPK models.

Adult↗
PubMed2006

On the use of zero-inflated and hurdle models for modeling vaccine adverse event count data.

We compared several modeling strategies for vaccine adverse event count data in which the data are characterized by excess zeroes and heteroskedasticity. Count data are routinely modeled using Poisson and Negative Binomial (NB) regression but zero-inflated and hurdle models may be advantageous in this setting. Here we compared the fit of the Poisson, Negative Binomial (NB), zero-inflated Poisson (ZIP), zero-inflated Negative Binomial (ZINB), Poisson Hurdle (PH), and Negative Binomial Hurdle (NBH) models. In general, for public health studies, we may conceptualize zero-inflated models as allowing zeroes to arise from at-risk and not-at-risk populations. In contrast, hurdle models may be conceptualized as having zeroes only from an at-risk population. Our results illustrate, for our data, that the ZINB and NBH models are preferred but these models are indistinguishable with respect to fit. Choosing between the zero-inflated and hurdle modeling framework, assuming Poisson and NB models are inadequate because of excess zeroes, should generally be based on the study design and purpose. If the study's purpose is inference then modeling framework should be considered. For example, if the study design leads to count endpoints with both structural and sample zeroes then generally the zero-inflated modeling framework is more appropriate, while in contrast, if the endpoint of interest, by design, only exhibits sample zeroes (e.g., at-risk participants) then the hurdle model framework is generally preferred. Conversely, if the study's primary purpose it is to develop a prediction model then both the zero-inflated and hurdle modeling frameworks should be adequate.

Adolescent↗
PubMed2003

Finite-element modeling of needle electrodes in tissue from the perspective of frequent model computation.

Information about electric field distribution in tissue is very important for effective electropermeabilization. In heterogeneous tissues with complex geometry, finite-element (FE) models provide one of alternative sources of such information. In the present study, modeling of needle electrode geometry in the FE model was investigated in order to determine the most appropriate geometry by considering the need for frequent FE model computation present in electroporation models. The 8-faceted needle electrode geometry proposed--determined on a model with a single needle electrode pair by means of criteria function--consisted of the weighted sum of relative difference between measured and computed total current, the relative difference in CPU time spent on solving model, and the relative difference in cross section surface of electrodes. Such electrode geometry was further evaluated on physical models with needle arrays by comparison of computed total current and measured current. The agreement between modeled and measured current was good (within 9% of measurement), except in cases with very thin gel. For voltage above 50 V, a linear relationship between current and voltage was observed in measurements. But at lower voltages, a nonlinear behavior was detected resulting from side (electrochemical) effects at electrode-gel interface. This effect was incorporated in the model by introducing a 50-V shift which reduced the difference between the model and the measurement to less than 3%. As long as material properties and geometry are well described by FE model, current-based validation can be used for a rough model validation. That is a routine assay compared with imaging of electric field, which is otherwise employed for model validation. Additionally, current estimated by model, can be preset as maximum in electroporator in order to protect tissue against damage.

Animals↗
PubMed1994

Comparison of the predicted impact of a screwworm fly outbreak in Australia using a growth index model and a life-cycle model.

The spatial population dynamics of an Old World screwworm fly, Chrysomya bezziana Villeneuve (OWS), outbreak in Australia have been modelled in two ways. The first model uses weekly growth indices derived from climatic data to predict the adult female population. The second is a detailed cohort life-cycle model. Due to technical and time constraints, the growth index model is preferred as the biological component of a much larger bioeconomic model because of its smaller program size and faster execution. In deciding whether adoption of the growth index model would be at the expense of scientific accuracy, the life-cycle model was developed as a yardstick. We showed that the growth index model was a practical and adequate substitution for the OWS life-cycle model and a novel spatial/temporal modelling approach with generic qualities. We elaborate on the previously reported growth index model, describe the life-cycle model and compare the results of both models. In the event of an OWS incursion in northern or eastern Australia, given average climatic conditions, both models predict that most of the suitable range (some 2.3M km2) will be colonized within 4-5 years if an eradication campaign is not attempted. Much of its permanent range would be in tropical and subtropical extensive grazing regions. Where computer or funding resources are restrictive, models incorporating growth indices may prove adequate for spatial population studies of some species.

Animals↗
PubMed1974

A kinetic description for sodium and potassium effects on (Na+ plus K+)-adenosine triphosphatase: a model for a two-nonequivalent site potassium activation and an analysis of multiequivalent site models for sodium activation.

1. Dissociation constants for sodium and potassium of a site that modulates the rate of ouabain-(Na(+)+K(+))-ATPase interaction were applied to models for potassium activation of (Na(+)+K(+))-ATPase. The constants for potassium (0.213 mM) and for sodium (13.7 mM) were defined, respectively, as activation constant, K(a) and inhibitory constant, K(i).2. Tests of the one- and the two-equivalent site models, that describe sodium and potassium competition, revealed that neither model adequately predicts the activation effects of potassium in the presence of 100 or 200 mM sodium.3. The potassium-activation data, obtained at low potassium and high sodium, were explained by a two-nonequivalent site model where the dissociation constants of the first site are 0.213 mM for potassium and 13.7 mM for sodium. The second site was characterized by dissociation constants of 0.091 mM for potassium and 74.1 mM for sodium.4. The two-nonequivalent site model adequately predicted the responses to concentrations of potassium between 0.25 and 5 mM in the presence of 100-500 mM sodium. At lower sodium concentrations the predicted responses formed an upper limit for the function of observed activities. This limit was reached at lower concentrations of potassium and higher concentrations of sodium, which inferred saturation of the sodium-activation sites with sodium.5. Sodium-activation data were corrected for sodium interaction with potassium-activation sites by use of the two-nonequivalent site model for potassium activation. Tests of equivalent site models suggested that the corrected data for sodium activation may be most consistent with a model that has three-equivalent sites. Other multiequivalent site models (n = 2, 4, 5 or 6), however, cannot be statistically eliminated as possibilities. The three-equivalent site activation model was characterized by dissociation constants of 1.39 mM for sodium and 11.7 mM for potassium. The system theoretically would be half-maximally activated by 5.35 mM sodium in the absence of potassium.6. Derivation of the model for sodium activation assumed that the affinities of these sites for sodium and potassium are independent of cation interactions with the potassium-activation sites. Therefore, the kinetic descriptions for sodium and potassium effects form a composite model that is consistent with simultaneous transport of sodium and potassium.7. Predictions of the composite equation are in reasonable agreement with data obtained by variation of sodium (potassium = 10 mM), variation of potassium (sodium = 100 mM) and by simultaneous variation of sodium and potassium (sodium:potassium = 10). Sodium-activation data (2.5-20 mM sodium) also agree with predictions of the model in the presence of potassium concentrations which are thought to be present at the sodium-activation sites in vivo.8. The kinetic description for sodium (three-equivalent sites) and potassium (two-nonequivalent sites) activation of the transport-ATPase is in accord with the probable stoichiometric requirements of the sodium pump. The model is also in general agreement with other studies on intact transporting systems and (Na(+)+K(+))-ATPase in fragmented membrane preparations with respect to potassium activation, although there is a quantitative disagreement. The model for sodium activation, though consistent with data obtained by other studies on fragmented (Na(+)+K(+))-ATPase preparations, is in apparent variance with much of the data obtained for intact transporting systems. The description for potassium activation suggests that the rates of ouabain binding to (Na(+)+K(+))-ATPase are modulated by competition between sodium and potassium for one of the two potassium-activation sites.

Adenosine Triphosphatases↗
PubMed1997

Modeling neural mechanisms for genesis of respiratory rhythm and pattern. III. Comparison of model performances during afferent nerve stimulation.

The goal of the present study was to evaluate the relative plausibility of the models of the central respiratory pattern generator (CRPG) proposed in our previous paper. To test the models, we compared changes in generated patterns with the experimentally observed alterations of the respiratory pattern induced by various stimuli applied to superior laryngeal (SLN), vagus and carotid sinus (CS) nerves. In all models, short-duration SLN simulation caused phase-resetting behavior consistent with experimental data. Relatively weak sustained SLN stimulation elicited a two-phase rhythm comprising inspiration and postinspiration whereas a stronger stimulation stopped oscillations in the postinspiratory phase ("postinspiratory apnea"). In all models, sustained vagus nerve stimulation produced postinspiratory apnea. A short vagal stimulus delivered during inspiration terminated this phase. The threshold for inspiratory termination decreased during the course of the inspiratory phase. The effects of short-duration vagal stimulation applied during expiration were different in different models. In model 1, stimuli delivered in the postinspiratory phase prolonged expiration whereas the late expiratory phase was insensitive to vagal stimulation. No insensitive period was found in model 2 because vagal stimuli delivered at any time during expiration prolonged this phase. Model 3 demonstrated a short period insensitive to vagal stimulation at the very end of expiration. When phasic CS nerve stimulation was applied during inspiration or the first half of expiration, the performances of all models were similar and consistent with experimental data: stimuli delivered at the beginning inspiration shortened this phase whereas stimuli applied in the middle or at the end of inspiration prolonged it and stimuli delivered in the first half of expiration prolonged the expiratory interval. Behavior of the models were different when CS stimuli were delivered during the late expiratory phase. In model 1, these stimuli were ineffective or shortened expiration initiating the next inspiration. Alternatively, in models 2 and 3, they caused a prolongation of expiration. Although all CRPG models demonstrated a number of plausible alterations in the respiratory pattern elicited by afferent nerve stimulation, the behavior of model 1 was most consistent with experimental data. Taking into account differences in the model architectures and employed neural mechanisms, we suggest that the concept of respiratory rhythmogenesis based on the essential role of postinspiratory neurons is more plausible than the concept employing specific functional properties of decrementing expiratory (dec-E) neurons and that the ramp firing pattern of the late expiratory neuron is more likely to reflect intrinsic properties than disinhibition from the dec-E neurons.

Afferent Pathways↗
PubMed2002

Pharmacokinetic-pharmacodynamic modelling of insulin: comparison of indirect pharmacodynamic response with effect-compartment link models.

The pharmacokinetic and pharmacodynamic modelling of insulin has been reported using a combined pharmacokinetic/pharmacodynamic (PK/PD) model, in which a hypothetical effect compartment is linked to a pharmacokinetic compartment. Review of the literature, however, indicated that the recently developed PK/PD models have consisted of an indirect pharmacodynamic response component, but none of them has been applied to the modelling of insulin. To study the relative relevance of the indirect pharmacodynamic response model and the effect-compartment link model in modelling the pharmacokinetics and pharmacodynamics of insulin, regular human insulin was administered intravenously at a dose of 0.1 IU kg(-1) to healthy Yucatan minipigs (after an overnight fasting). The plasma concentrations of insulin were measured by radioimmunoassay at predetermined time intervals, while blood glucose levels were monitored continuously using a glucose monitor. Analysis of the plasma insulin and the blood glucose profiles was performed by fitting with various PK/PD models and the results indicated that all of the 12 sets of plasma insulin data (after normalizing by the basal levels) have been adequately fitted to the two-compartment open pharmacokinetic model (a mean+/-s.e. correlation coefficient of 0.996+/-0.001 was obtained). The mean+/-s.e. correlation coefficient, the weighted residuals sum of squares (WRSS), and the Akaike's information criterion (AIC) were found, respectively, to be 0.935+/-0.008, 624+/-67, and 522+/-9 for the inhibitory indirect pharmacodynamic response model and 0.941+/-0.010, 547+/-63 and 513+/-9 for the stimulatory indirect pharmacodynamic response model, as compared with 0.725+/-0.041, 2309+/-276 and 628+/-10 for the effect-compartment link model. Based on these results, one may conclude that the indirect pharmacodynamic response model is a more appropriate approach for modelling the PK/PD of insulin than the effect-compartment link model.

Animals↗
PubMed2005

Genetic evaluation of dairy cattle with test-day models with autoregressive covariance structures and with a 305-d model.

This study compared genetic evaluations from 3 test-day (TD) models with different assumptions about the environmental covariance structure for TD records and genetic evaluations from 305-d lactation records for dairy cows. Estimates of genetic values of 12,071 first-lactation Holstein cows were obtained with the 3 TD models using 106,472 TD records. The compound symmetry (CS) model was a simple test-day repeatability animal model with compound symmetry covariance structure for TD environmental effects. The ARs and ARe models also used TD records but with a first-order autoregressive covariance structure among short-term environmental effects or residuals, respectively. Estimates of genetic values with the TD models were also compared with those from a model using 305-d lactation records. Animals were genetically evaluated for milk, fat, and protein yields, and somatic cell score (SCS). The largest average estimates of accuracy of predicted breeding values were obtained with the ARs model and the smallest were with the 305-d model. The 305-d model resulted in smaller estimates of correlations between average predicted breeding values of the parents and lactation records of their daughters for milk and protein yields and SCS than did the CS and ARe models. Predicted breeding values with the 3 TD models were highly correlated (0.98 to 1.00). Predicted breeding values with 305-d lactation records were moderately correlated with those with TD models (0.71 to 0.87 for sires and 0.80 to 0.87 for cows). More genetic improvement can be achieved by using TD models to select for animals for higher milk, fat, and protein yields, and lower SCS than by using models with 305-d lactation records.

Analysis of Variance↗
PubMed2005

Improving pharmacokinetic-pharmacodynamic models of muscle relaxants using potentiation modelling.

Repeated motor nerve stimulation performed during neuromuscular monitoring enhances the evoked mechanical response of the corresponding muscle resulting in an increased twitch response. This is known as twitch potentiation or the staircase phenomenon. For neuromuscular modelling research twitch stabilisation techniques are often used to reduce the visible effect of potentiation, but such techniques are not always effective. Our objective was to model pharmacokinetic-pharmacodynamic (PK-PD) and twitch potentiation and to estimate neuromuscular block (NMB) in the presence of twitch potentiation. We combined a standard PK-PD model with a model describing the degree of twitch potentiation. The combined model was used to predict mechanomyographic twitch measurements and estimate NMB and twitch potentiation during muscle relaxation monitoring. Model parameters and prediction accuracy were compared to the standard PK-PD model with and without linear baseline correction. The PK-PD-potentiation model allows NMB to be estimated in the presence of twitch potentiation. It also accurately predicts data from twitch stabilisation, which is ignored with the standard PK-PD model. Compared to the standard PK-PD model, estimated PD parameters ec50 and gamma were found to be higher using the PK-PD-potentiation model. Compared to linear baseline correction, estimated PD parameters ke0 and ec50 were found to be higher. A PK-PD-potentiation model can estimate the degree of twitch potentiation and the degree of NMB during neuromuscular monitoring. This model leads to different PD parameter estimations than the standard PK-PD model however the differences are small enough to be unlikely to cause great concern among researchers.

Algorithms↗
PubMed2000

Analyzing sensitivity to model form assumptions of infection transmission system models.

PURPOSE: Transmission system models make restrictive assumptions that might distort the conclusions of model analyses. We propose methods to progressively relax the following assumptions of classical deterministic compartmental models: 1) that the population has an effectively infinite size 2) that contact is instantaneous with no duration, 3) that mixing in this large population is instantaneously thorough after contact.METHODS: Analyses of contact patterns between high and low risk groups on gonorrhea transmission were performed. Initial models were similar to those analyzed by Hethcote and Yorke with compartments corresponding to sets of individuals. The instantaneous contact assumption in these models was relaxed by using continuous deterministic pairing models in the style of models presented by Dietz and Hadelar. That model makes restrictive assumptions about concurrent contacts, population sizes, and instantaneously random mixing. To relax these assumptions, we simulated our GERMS model of discrete individuals forming pairings and transmitting infection in continuous time.RESULTS: Relaxing the instantaneous contact assumption demonstrated a progressively decreased effect of mixing between high and low risk groups as the duration of contact was increased. The GERMS model simulations were shown to effectively reproduce pairing model behavior given the same restrictive assumptions as the pairing model. Further GERMS model analysis then demonstrated that concurrency assumptions alter the effects of contact rates between risk groups in ways that are dependent upon contact parameters. Finally GERMS models were used to structure mixing into four local areas. This affected the dynamics of reaching equilibrium but not the equilibrium value.CONCLUSIONS: Assessing the effects of assumptions in continuous compartmental models of transmission systems is feasible and important.

Journal Article↗
PubMed1991

The Hodgkin-Huxley Na+ channel model versus the five-state Markovian model.

In describing the Na+ channel-gating kinetics, it is generally believed the Hodgkin-Huxley model is inadequate and other types of Markovian models are more appropriate. In this paper, we perform detailed kinetic analyses to find out whether the Hodgkin-Huxley model is really unacceptable. Specifically, we consider two models for the analyses: A five-state Markovian model that allows inactivation to take place before opening and a Hodgkin-Huxley eight-state model. The criteria used to check the goodness of the two models are (a) Akaike's information criterion; (b) chi 2 tests on the waiting-time, open-time, and closed-time distributions, and the number of openings per record; and (c) comparison between all latency distributions and the probability of the open state predicted from the two models. In order to do this, we first develop a method of constructing probability density histograms of a specified event (e.g., waiting time, closed time, open time, number of openings per patch) from the multichannel patch-clamp recordings. The goodness of our method is checked by simulating multichannel patch recordings using a multinomial random number generator. Our kinetic analysis on the single Na+ channel recordings from the cardiac cells revealed that (a) on the basis of Akaike's information criterion, the Hodgkin-Huxley model is definitely a better model than the five-state model, but (b) on the basis of chi 2 tests on the probability density functions, the latter model is slightly better than the former. We find no evidence that the Hodgkin-Huxley model is inferior to the five-state model for this cell type.

Ion Channel Gating↗