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PubMed2004

The Leksell gamma knife Model U versus Model C: a quantitative comparison of radiosurgical treatment parameters.

OBJECTIVE: We present a quantitative comparison of radiosurgery treatments for cavernous sinus tumors using the Leksell gamma knife Model U versus the Model C with automatic positioning system (APS) (Elekta Instruments, Norcross, GA). METHODS: At our medical center from August 1994 through May 2000, the Model U was used to treat 96 patients (37 men [39%] and 59 women [61%]; median age, 54.5 yr) with benign cavernous sinus tumors: 43 meningiomas (45%), 48 pituitary tumors (50%), and 5 others (5%). From June 2000 through April 2002, the Model C with APS treated 45 patients (20 men [44%] and 25 women [56%]; median age, 51.4 yr) with 15 meningiomas (33%), 29 pituitary tumors (65%), and 1 schwannoma (2%). The two groups had similar treated tumor volumes (Model U mean, 4.3 cm(3); Model C mean, 4.2 cm(3)), equivalent tumor distances from critical structures (optic nerve, chiasm, and pons), comparable distributions in Sekhar tumor grades, and the same median prescribed dose of 15 Gy to the 50% isodose line at the tumor periphery. All planning and treatments were performed by the same radiosurgery team to minimize dosage to adjacent critical tissues and to optimize conformity index. RESULTS: Analysis of multiple treatment parameters showed that the Model C plans were superior. Model C treatments had an improved conformity index (Model U mean, 1.7; Model C mean, 1.6; P < 0.02) and a lower underdosed tumor volume (Model U mean, 0.4 cm(3); Model C mean, 0.1 cm(3); P < 0.004). The total treated volume and the excess treated volume were similar. The Model C group had a reduction in optic chiasm dose (Model C mean dose, 3.8 Gy; Model U mean dose, 5.3 Gy; P < 0.0001). The average number of isocenters was slightly higher for the Model C group (6.7 versus 6 for the Model U), but with a lower mean number of collimator sizes (1 versus 2 for the Model U). Model C plans required a mean of 93 fewer plugs per treatment, thus contributing to an estimated 67.6 minutes saved per treatment session. CONCLUSION: Comparison of radiosurgery treatments using the Leksell gamma knife Model U versus the Model C with APS was performed by quantitative analysis of treatment parameters on a cohort of benign cavernous sinus tumors. Treatment plans using the Model C resulted in better tumor coverage (improved conformity, less underdosed tumor volume) and decreased optic chiasm dose. An estimated average of 1 hour was saved per treatment when using the Model C with APS.

Adolescent↗
PubMed2003

Model assessment and model building in fMRI.

Model quality is rarely assessed in fMRI data analyses and less often reported. This may have contributed to several shortcomings in the current fMRI data analyses, including: (1) Model mis-specification, leading to incorrect inference about the activation-maps, SPM[t] and SPM[F]; (2) Improper model selection based on the number of activated voxels, rather than on model quality; (3) Under-utilization of systematic model building, resulting in the common but suboptimal practice of using only a single, pre-specified, usually over-simplified model; (4) Spatially homogenous modeling, neglecting the spatial heterogeneity of fMRI signal fluctuations; and (5) Lack of standards for formal model comparison, contributing to the high variability of fMRI results across studies and centers. To overcome these shortcomings, it is essential to assess and report the quality of the models used in the analysis. In this study, we applied images of the Durbin-Watson statistic (DW-map) and the coefficient of multiple determination (R(2)-map) as complementary tools to assess the validity as well as goodness of fit, i.e., quality, of models in fMRI data analysis. Higher quality models were built upon reduced models using classic model building. While inclusion of an appropriate variable in the model improved the quality of the model, inclusion of an inappropriate variable, i.e., model mis-specification, adversely affected it. Higher quality models, however, occasionally decreased the number of activated voxels, whereas lower quality or inappropriate models occasionally increased the number of activated voxels, indicating that the conventional approach to fMRI data analysis may yield sub-optimal or incorrect results. We propose that model quality maps become part of a broader package of maps for quality assessment in fMRI, facilitating validation, optimization, and standardization of fMRI result across studies and centers. Hum. Brain Mapping 20:227-238, 2003.

Brain↗
PubMed2005

Radionuclides in fruit systems: model-model intercomparison study.

Modeling is widely used to predict radionuclide distribution following accidental radionuclide releases. Modeling is crucial in emergency response planning and risk communication, and understanding model uncertainty is important not only in conducting analysis consistent with current regulatory guidance, but also in gaining stakeholder and decision-maker trust in the process and confidence in the results. However, while methods for dealing with parameter uncertainty are fairly well developed, an adequate representation of uncertainties associated with models remains rare. This paper addresses uncertainty about a model's structure (i.e., the relevance of simplifying assumptions and mathematical equations) that is seldom addressed in practical applications of environmental modeling. The use of several alternative models to derive a range of model outputs or risks is probably the only available technique to assess consistency in model prediction. Since each independent model requires significant resources for development and calibration, multiple models are not generally applied to the same problem. This study uses results from one such model intercomparison conducted by the Fruits Working Group, which was created under the International Atomic Energy Agency (IAEA) BIOMASS (BIOsphere Modelling and ASSessment) Program. Model-model intercomparisons presented in this study were conducted by the working group for two different scenarios (acute or continuous deposition), one radionuclide ((137)Cs), and three fruit-bearing crops (strawberries, apples, and blackcurrants). The differences between models were as great as five orders of magnitude for short-term predictions following acute radionuclide deposition. For long-term predictions and for the continuous deposition scenario, the differences between models were about two orders of magnitude. The difference between strawberry, apple, and blackcurrant contamination predicted by one model is far less than the difference in prediction of contamination for a single plant species given by different models. This study illustrates the importance of problem formulation and implementation of an analytic-deliberative process in risk characterization.

Cesium Radioisotopes↗
PubMed2001

Modeling of nitrogen in river water using a detailed and a simplified model.

To model catchment surface water quantity and quality, different model types are available. They vary from detailed physically based models to simplified conceptual and empirical models. The most appropriate model type for a certain application depends on the project objectives and the data availability. The detailed models are very useful for short-term simulations of representative events. They cannot be used for long-term statistical information or as a management tool. For those purposes, more simplified (conceptual or meta-) models must be used. In this study, nitrogen dynamics are modeled in a river in Flanders. Nitrogen sources from agricultural leaching and domestic point sources are considered. Based on this input, concentrations of ammonium (NH4-N) and nitrate (NO3-N) in the river water are modeled in MIKE 11 by taking into consideration advection and dispersion and the most important biological and chemical processes. Model calibration was done on the basis of available measured water quality data. To this detailed model, a more simplified model was calibrated with the objective to more easily yield long-term simulation results that can be used in a statistical analysis. The results show that the conceptual simplified model is 1800 times faster than the MIKE 11 model. Moreover the two models have almost the same accuracy. The detailed models are recommended for short-term simulations unless there are enough data for model input and model parameters. The conceptual simplified model is recommended for long-term simulations.

Agriculture↗
PubMed2006

Large-scale neural models and dynamic causal modelling.

Dynamic causal modelling (DCM) is a method for estimating and making inferences about the coupling among small numbers of brain areas, and the influence of experimental manipulations on that coupling [Friston, K.J., Harrison, L., Penny, W., 2003 Dynamic causal modelling. Neuroimage 19, 1273-1302]. Large-scale neural modelling aims to construct neurobiologically grounded computational models with emergent behaviours that inform our understanding of neuronal systems. One such model has been used to simulate region-specific BOLD time-series [Horwitz, B., Friston, K.J., Taylor, J.G., 2000. Neural modeling and functional brain imaging: an overview. Neural Netw. 13, 829-846]. DCM was used to make inferences about effective connectivity using data generated by a model implementing a visual delayed match-to-sample task [Tagamets, M.A., Horwitz, B., 1998. Integrating electrophysiological and anatomical experimental data to create a large-scale model that simulates a delayed match-to-sample human brain imaging study. Cereb. Cortex 8, 310-320]. The aim was to explore the validity of inferences made using DCM about the connectivity structure and task-dependent modulatory effects, in a system with a known connectivity structure. We also examined the effects of misspecifying regions of interest. Models with hierarchical connectivity and reciprocal connections were examined using DCM and Bayesian Model Comparison [Penny, W.D., Stephan, K.E., Mechelli, A., Friston, K.J., 2004. Comparing dynamic causal models. Neuroimage 22, 1157-1172]. This approach revealed strong evidence for those models with correctly specified anatomical connectivity. Furthermore, Bayesian model comparison favoured those models when bilinear effects corresponded to their implementation in the neural model. These findings generalised to an extended model with two additional areas and reentrant circuits. The conditional uncertainty of coupling parameter estimates increased in proportion to the number of incorrectly specified regions. These results highlight the role of neural models in establishing the validity of estimation and inference schemes. Specifically, Bayesian model comparison confirms the validity of DCM in relation to a well-characterised and comprehensive neuronal model.

Bayes Theorem↗
PubMedDate not supplied

Principles of good practice for decision analytic modeling in health-care evaluation: report of the ISPOR Task Force on Good Research Practices--Modeling Studies.

OBJECTIVES: Mathematical modeling is used widely in economic evaluations of pharmaceuticals and other health-care technologies. Users of models in government and the private sector need to be able to evaluate the quality of models according to scientific criteria of good practice. This report describes the consensus of a task force convened to provide modelers with guidelines for conducting and reporting modeling studies. METHODS: The task force was appointed with the advice and consent of the Board of Directors of ISPOR. Members were experienced developers or users of models, worked in academia and industry, and came from several countries in North America and Europe. The task force met on three occasions, conducted frequent correspondence and exchanges of drafts by electronic mail, and solicited comments on three drafts from a core group of external reviewers and more broadly from the membership of ISPOR. RESULTS: Criteria for assessing the quality of models fell into three areas: model structure, data used as inputs to models, and model validation. Several major themes cut across these areas. Models and their results should be represented as aids to decision making, not as statements of scientific fact; therefore, it is inappropriate to demand that models be validated prospectively before use. However, model assumptions regarding causal structure and parameter estimates should be continually assessed against data, and models should be revised accordingly. Structural assumptions and parameter estimates should be reported clearly and explicitly, and opportunities for users to appreciate the conditional relationship between inputs and outputs should be provided through sensitivity analyses. CONCLUSIONS: Model-based evaluations are a valuable resource for health-care decision makers. It is the responsibility of model developers to conduct modeling studies according to the best practicable standards of quality and to communicate results with adequate disclosure of assumptions and with the caveat that conclusions are conditional upon the assumptions and data on which the model is built.

Benchmarking↗
PubMed2005

Compartmental modeling of transdermal iontophoretic transport II: in vivo model derivation and application.

PURPOSE: This study was aimed to develop a family of compartmental models to describe in a strictly quantitative manner the transdermal iontophoretic transport of drugs in vivo. The new models are based on previously proposed compartmental models for the transport in vitro. METHODS: The novel in vivo model considers two separate models to describe the input into the systemic circulation: a) constant input and b) time-variant input. Analogous to the in vitro models, the in vivo models contain four parameters: 1) kinetic lag time (tL), 2) steady-state flux during iontophoresis (JSS), 3) skin release rate constant (KR), and 4) passive flux in the post-iontophoretic period (Jpas). The elimination from the systemic circulation is described by a) the one-compartment and b) the two-compartment pharmacokinetic models. The models were applied to characterize the observed plasma concentration vs. time data following single-dose iontophoretic delivery of growth hormone-releasing factor (GRF) and R-apomorphine. Moreover, the models were also used to simulate the observed plasma concentration vs. time profiles following a two-dose transdermal iontophoretic administration of alniditan. RESULTS: The time-variant input models were superior to the constant input models and appropriately converged to the observed data of GRF and R-apomorphine allowing the estimation of JSS, KR, and Jpas. In most cases, the values of tL were negligible. The estimated JSS and the in vivo flux profiles of GRF and R-apomorphine were similar to those obtained using the deconvolution method. The two-dose iontophoretic transport of alniditan was properly simulated using the proposed time-variant input model indicating the utility of the model to predict and to simulate the drug transport by a multiple-dose iontophoresis. Moreover, the use of the compartmental modeling approach to derive an in vitro-in vivo correlation for R-apomorphine was demonstrated. This approach was also used to identify the optimum in vitro model that closely mimics the in vivo iontophoretic transport of R-apomorphine. CONCLUSIONS: The developed in vivo models demonstrate their consistency and capability to describe the in vivo iontophoretic drug transport. This compartmental modeling approach provides a scientific basis to examine in vitro-in vivo correlations of drug transport by iontophoresis.

Administration, Cutaneous↗
PubMed2002

Using Monte Carlo techniques to judge model prediction accuracy: validation of the pesticide root zone model 3.12.

Individuals from the Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA) Environmental Model Validation Task Force (FEMVTF) Statistics Committee periodically met to discuss the mechanism for conducting an uncertainty analysis of Version 3.12 of the pesticide root zone model (PRZM 3.12) and to identify those model input parameters that most contribute to model prediction error. This activity was part of a larger project evaluating PRZM 3.12. The goal of the uncertainty analysis was to compare site-specific model predictions and field measurements using the variability in each as a basis of comparison. Monte Carlo analysis was used as an integral tool for judging the model's ability to predict accurately. The model was judged on how well it predicts measured values, taking into account the uncertainty in the model predictions. Monte Carlo analysis provides the tool for inferring model prediction uncertainty. We argue that this is a fairer test of the model than a simple one-to-one comparison between predictions and measurements. Because models are known to be imperfect predictors prior to running the model, the inaccuracy in model predictions should be considered when models are judged for their predictive ability. Otherwise, complex models can easily fail a validation test. Few complex models, such as PRZM 3.12, would pass a typical model validation exercise. This paper describes the approaches to the validation of PRZM 3.12 used by the committee and discusses issues in sampling distribution selection and appropriate statistics for interpreting the model validation results.

Forecasting↗
PubMed2004

An extended aqueous solvation model based on atom-weighted solvent accessible surface areas: SAWSA v2.0 model.

A new method is proposed for calculating aqueous solvation free energy based on atom-weighted solvent accessible surface areas. The method, SAWSA v2.0, gives the aqueous solvation free energy by summing the contributions of component atoms and a correction factor. We applied two different sets of atom typing rules and fitting processes for small organic molecules and proteins, respectively. For small organic molecules, the model classified the atoms in organic molecules into 65 basic types and additionally. For small organic molecules we proposed a correction factor of "hydrophobic carbon" to account for the aggregation of hydrocarbons and compounds with long hydrophobic aliphatic chains. The contributions for each atom type and correction factor were derived by multivariate regression analysis of 379 neutral molecules and 39 ions with known experimental aqueous solvation free energies. Based on the new atom typing rules, the correlation coefficient (r) for fitting the whole neutral organic molecules is 0.984, and the absolute mean error is 0.40 kcal mol(-1), which is much better than those of the model proposed by Wang et al. and the SAWSA model previously proposed by us. Furthermore, the SAWSA v2.0 model was compared with the simple atom-additive model based on the number of atom types (NA). The calculated results show that for small organic molecules, the predictions from the SAWSA v2.0 model are slightly better than those from the atom-additive model based on NA. However, for macromolecules such as proteins, due to the connection between their molecular conformation and their molecular surface area, the atom-additive model based on the number of atom types has little predictive power. In order to investigate the predictive power of our model, a systematic comparison was performed on seven solvation models including SAWSA v2.0, GB/SA_1, GB/SA_2, PB/SA_1, PB/SA_2, AM1/SM5.2R and SM5.0R. The results showed that for organic molecules the SAWSA v2.0 model is better than the other six solvation models. For proteins, the model classified the atoms into 20 basic types and the predicted aqueous free energies of solvation by PB/SA were used for fitting. The solvation model based on the new parameters was employed to predict the solvation free energies of 38 proteins. The predicted values from our model were in good agreement with those from the PB/SA model and were much better than those given by the other four models developed for proteins.

Chemistry, Organic↗
PubMed2005

Sources of uncertainty in model predictions: lessons learned from the IAEA Forest and Fruit Working Group model intercomparisons.

The International Atomic Energy Agency (IAEA), through the BIOMASS program, has provided a unique international forum for assessing the relative contribution of different sources of uncertainty associated with environmental modeling. The methodology and guidance for dealing with parameter uncertainty have been fairly well developed and quantitative tools such as Monte-Carlo modeling are often recommended. The issue of model uncertainty is still rarely addressed in practical applications and the use of several alternative models to derive a range of model outputs (similar to what was done in IAEA model intercomparisons) is one of a few available techniques. This paper addresses the often overlooked issue of what we call 'modeler uncertainty,' i.e., differences in problem formulation, model implementation and parameter selection originating from subjective interpretation of the problem at hand. This study uses results from the Fruit and Forest Working Groups created under the BIOMASS program (BIOsphere Modeling and ASSessment). The greatest uncertainty was found to result from modelers' interpretation of scenarios and approximations made by modelers. In scenarios that were unclear for modelers, the initial differences in model predictions were as high as seven orders of magnitude. Only after several meetings and discussions about specific assumptions did the differences in predictions by various models merge. Our study shows that the parameter uncertainty (as evaluated by a probabilistic Monte-Carlo assessment) may have contributed over one order of magnitude to the overall modeling uncertainty. The final model predictions ranged between one and three orders of magnitude, depending on the specific scenario. This study illustrates the importance of problem formulation and implementation of an analytic-deliberative process in fate and transport modeling and risk characterization.

Fruit↗
PubMed2006

Complex hybrid models combining deterministic and machine learning components for numerical climate modeling and weather prediction.

A new practical application of neural network (NN) techniques to environmental numerical modeling has been developed. Namely, a new type of numerical model, a complex hybrid environmental model based on a synergetic combination of deterministic and machine learning model components, has been introduced. Conceptual and practical possibilities of developing hybrid models are discussed in this paper for applications to climate modeling and weather prediction. The approach presented here uses NN as a statistical or machine learning technique to develop highly accurate and fast emulations for time consuming model physics components (model physics parameterizations). The NN emulations of the most time consuming model physics components, short and long wave radiation parameterizations or full model radiation, presented in this paper are combined with the remaining deterministic components (like model dynamics) of the original complex environmental model--a general circulation model or global climate model (GCM)--to constitute a hybrid GCM (HGCM). The parallel GCM and HGCM simulations produce very similar results but HGCM is significantly faster. The speed-up of model calculations opens the opportunity for model improvement. Examples of developed HGCMs illustrate the feasibility and efficiency of the new approach for modeling complex multidimensional interdisciplinary systems.

Artificial Intelligence↗
PubMedDate not supplied

The site-scale saturated zone flow model for Yucca Mountain: calibration of different conceptual models and their impact on flow paths.

This paper presents several different conceptual models of the Large Hydraulic Gradient (LHG) region north of Yucca Mountain and describes the impact of those models on groundwater flow near the potential high-level repository site. The results are based on a numerical model of site-scale saturated zone beneath Yucca Mountain. This model is used for performance assessment predictions of radionuclide transport and to guide future data collection and modeling activities. The numerical model is calibrated by matching available water level measurements using parameter estimation techniques, along with more informal comparisons of the model to hydrologic and geochemical information. The model software (hydrologic simulation code FEHM and parameter estimation software PEST) and model setup allows for efficient calibration of multiple conceptual models. Until now, the Large Hydraulic Gradient has been simulated using a low-permeability, east-west oriented feature, even though direct evidence for this feature is lacking. In addition to this model, we investigate and calibrate three additional conceptual models of the Large Hydraulic Gradient, all of which are based on a presumed zone of hydrothermal chemical alteration north of Yucca Mountain. After examining the heads and permeabilities obtained from the calibrated models, we present particle pathways from the potential repository that record differences in the predicted groundwater flow regime. The results show that Large Hydraulic Gradient can be represented with the alternate conceptual models that include the hydrothermally altered zone. The predicted pathways are mildly sensitive to the choice of the conceptual model and more sensitive to the quality of calibration in the vicinity on the repository. These differences are most likely due to different degrees of fit of model to data, and do not represent important differences in hydrologic conditions for the different conceptual models.

Calibration↗
PubMed2004

Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy.

We demonstrate that single-variable integrate-and-fire models can quantitatively capture the dynamics of a physiologically detailed model for fast-spiking cortical neurons. Through a systematic set of approximations, we reduce the conductance-based model to 2 variants of integrate-and-fire models. In the first variant (nonlinear integrate-and-fire model), parameters depend on the instantaneous membrane potential, whereas in the second variant, they depend on the time elapsed since the last spike [Spike Response Model (SRM)]. The direct reduction links features of the simple models to biophysical features of the full conductance-based model. To quantitatively test the predictive power of the SRM and of the nonlinear integrate-and-fire model, we compare spike trains in the simple models to those in the full conductance-based model when the models are subjected to identical randomly fluctuating input. For random current input, the simple models reproduce 70-80 percent of the spikes in the full model (with temporal precision of +/-2 ms) over a wide range of firing frequencies. For random conductance injection, up to 73 percent of spikes are coincident. We also present a technique for numerically optimizing parameters in the SRM and the nonlinear integrate-and-fire model based on spike trains in the full conductance-based model. This technique can be used to tune simple models to reproduce spike trains of real neurons.

Action Potentials↗
PubMed1992

Numerical comparisons of two formulations of the logistic regressive models with the mixed model in segregation analysis of discrete traits.

Segregation analysis of discrete traits can be conducted by the classical mixed model and the recently introduced regressive models. The mixed model assumes an underlying liability to the disease, to which a major gene, a multifactorial component, and random environment contribute independently. Affected persons have a liability exceeding a threshold. The regressive logistic models assume that the logarithm of the odds of being affected is a linear function of major genotype effects, the phenotypes of older relatives, and other covariates. A formulation of the regressive models, based on an underlying liability model, has been recently proposed. The regression coefficients on antecedents are expressed in terms of the relevant familial correlations and a one-to-one correspondence with the parameters of the mixed model can thus be established. Computer simulations are conducted to evaluate the fit of the two formulations of the regressive models to the mixed model on nuclear families. The two forms of the class D regressive model provide a good fit to a generated mixed model, in terms of both hypothesis testing and parameter estimation. The simpler class A regressive model, which assumes that the outcomes of children depend solely on the outcomes of parents, is not robust against a sib-sib correlation exceeding that specified by the model, emphasizing testing class A against class D. The studies reported here show that if the true state of nature is that described by the mixed model, then a regressive model will do just as well. Moreover, the regressive models, allowing for more patterns of family dependence, provide a flexible framework to understand gene-environment interactions in complex diseases.

Computer Simulation↗
PubMed1988

Light adaptation in the turtle retina: embedding a parametric family of linear models in a single nonlinear model.

A method for constructing nonlinear models for light adaptation in the retina is introduced. The components of the models are linear filters and static (instantaneous) nonlinear elements configured in a feedback arrangement. The signals in the models are combined through algebraic addition or multiplication. We apply the method to model light adaptation measured in turtle horizontal cells. Given a particular wiring diagram for the components, the functional forms of the static nonlinearities and frequency responses of the linear filters are determined by constraining the model to give temporal frequency responses (linear regime behavior) consistent with a family of linear feedback models which has been shown to provide a good description of adaptation in these cells. Two particular models, quite different in structure, are presented. Each model responds to perturbations around a mean light level as a feedback circuit in which the gain (strength) of feedback is adjusted to be proportional to the mean light level, but neither model has a separate pathway for measuring the mean light level. Thus, each of these nonlinear models embeds an entire family of linear models parametric in mean light level. Harmonic distortion in the responses of these models to sinusoidal input is found to be qualitatively consistent with physiological data. An alternative class of nonlinear models in which feedback gain is set by a separate slow pathway which tracks the mean light level is ruled out on the basis of its incorrect steady-state input-output behavior. The methods presented can be used to develop specific physical models for light adaptation based on the chemical kinetics of phototransduction or on nonlinear neural feedback. The relevance of the nonlinear models and construction techniques to modeling phototransduction is discussed.

Adaptation, Ocular↗
PubMed2005

Evolutionary models for insertions and deletions in a probabilistic modeling framework.

BACKGROUND: Probabilistic models for sequence comparison (such as hidden Markov models and pair hidden Markov models for proteins and mRNAs, or their context-free grammar counterparts for structural RNAs) often assume a fixed degree of divergence. Ideally we would like these models to be conditional on evolutionary divergence time. Probabilistic models of substitution events are well established, but there has not been a completely satisfactory theoretical framework for modeling insertion and deletion events. RESULTS: I have developed a method for extending standard Markov substitution models to include gap characters, and another method for the evolution of state transition probabilities in a probabilistic model. These methods use instantaneous rate matrices in a way that is more general than those used for substitution processes, and are sufficient to provide time-dependent models for standard linear and affine gap penalties, respectively. Given a probabilistic model, we can make all of its emission probabilities (including gap characters) and all its transition probabilities conditional on a chosen divergence time. To do this, we only need to know the parameters of the model at one particular divergence time instance, as well as the parameters of the model at the two extremes of zero and infinite divergence. I have implemented these methods in a new generation of the RNA genefinder QRNA (eQRNA). CONCLUSION: These methods can be applied to incorporate evolutionary models of insertions and deletions into any hidden Markov model or stochastic context-free grammar, in a pair or profile form, for sequence modeling.

Algorithms↗
PubMed1998

Physiologically relevant one-compartment pharmacokinetic models for skin. 1. Development of models.

Many studies have used pharmacokinetic (compartment) models for skin to predict or analyze absorption of chemicals through skin. In these studies, several different definitions of the rate constants were used. The purpose of this study was to develop a general procedure for relating compartment model rate constants to dermal absorption parameters, such as permeability and partition coefficients, and to assess whether different definitions of the rate constants produce different results. Rate constant expressions were developed by requiring a one-compartment model to match a one-membrane model at specific conditions. Because a membrane model contains more information than a compartment model, a compartment model cannot match the membrane model in all respects. Consequently, many compartment models (i.e., different definitions of the rate constants) can be developed which match the membrane model for different conditions. Using this procedure, 11 different compartment models were developed and compared to the membrane model for four different dermal absorption scenarios. The compartment model that most closely matches the membrane model depends on the specific exposure scenario and what is to be predicted. One of the new compartment models agrees reasonably well with the membrane model, for the cases considered.

Models, Biological↗
PubMed2006

Using nonlinear models in fMRI data analysis: model selection and activation detection.

There is an increasing interest in using physiologically plausible models in fMRI analysis. These models do raise new mathematical problems in terms of parameter estimation and interpretation of the measured data. In this paper, we show how to use physiological models to map and analyze brain activity from fMRI data. We describe a maximum likelihood parameter estimation algorithm and a statistical test that allow the following two actions: selecting the most statistically significant hemodynamic model for the measured data and deriving activation maps based on such model. Furthermore, as parameter estimation may leave much incertitude on the exact values of parameters, model identifiability characterization is a particular focus of our work. We applied these methods to different variations of the Balloon Model (Buxton, R.B., Wang, E.C., and Frank, L.R. 1998. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 39: 855-864; Buxton, R.B., Uludağ, K., Dubowitz, D.J., and Liu, T.T. 2004. Modelling the hemodynamic response to brain activation. NeuroImage 23: 220-233; Friston, K. J., Mechelli, A., Turner, R., and Price, C. J. 2000. Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12: 466-477) in a visual perception checkerboard experiment. Our model selection proved that hemodynamic models better explain the BOLD response than linear convolution, in particular because they are able to capture some features like poststimulus undershoot or nonlinear effects. On the other hand, nonlinear and linear models are comparable when signals get noisier, which explains that activation maps obtained in both frameworks are comparable. The tools we have developed prove that statistical inference methods used in the framework of the General Linear Model might be generalized to nonlinear models.

Adult↗