Monte Carlo uncertainty analysis of dose estimates in radiochromic film dosimetry with single-channel and multichannel algorithms

PurposeTo provide a multi-stage model to calculate uncertainty in radiochromic film dosimetry with Monte-Carlo techniques. This new approach is applied to single-channel and multichannel algorithms.Material and methodsTwo lots of Gafchromic EBT3 are exposed in two different Varian linacs. They are read with an EPSON V800 flatbed scanner. The Monte-Carlo techniques in uncertainty analysis provide a numerical representation of the probability density functions of the output magnitudes. From this numerical representation, traditional parameters of uncertainty analysis as the standard deviations and bias are calculated. Moreover, these numerical representations are used to investigate the shape of the probability density functions of the output magnitudes. Also, another calibration film is read in four EPSON scanners (two V800 and two 10000XL) and the uncertainty analysis is carried out with the four images.ResultsThe dose estimates of single-channel and multichannel algorithms show a Gaussian behavior and low bias. The multichannel algorithms lead to less uncertainty in the final dose estimates when the EPSON V800 is employed as reading device. In the case of the EPSON 10000XL, the single-channel algorithms provide less uncertainty in the dose estimates for doses higher than four Gy.ConclusionA multi-stage model has been presented. With the aid of this model and the use of the Monte-Carlo techniques, the uncertainty of dose estimates for single-channel and multichannel algorithms are estimated. The application of the model together with Monte-Carlo techniques leads to a complete characterization of the uncertainties in radiochromic film dosimetry.     

From spiking neuron models to linear-nonlinear models

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.     

Pulse pressure variation tracking using sequential Monte Carlo methods

The pulse pressure variation (PPV) is a measure of the respiratory effect on the variation of systemic arterial blood pressure (ABP) in patients receiving full mechanical ventilation. It is a promising predictor of increases in cardiac output due to an infusion of fluid. We describe a novel automatic algorithm to estimate the PPV of ABP signals recorded under full respiratory support. The algorithm utilizes our recently developed sequential Monte Carlo method (SMCM), which is called a maximum a-posteriori adaptive marginalized particle filter (MAM-PF). MAM-PF estimates the state-space model parameters of the ABP signal continuously and its upper and lower envelopes are derived as a combination of those parameter estimates. Then, the continuous PPV values can be easily obtained based on those estimated envelopes. We report the assessment results of the proposed algorithm on real ABP signals.     

A model of copepod population dynamics in the southern Benguela upwelling region

A simple population dynamics model was constructed to simulate temporal variability in the biomass of a dominant copepod Calanoides carinatus (Copepoda: Calanoida) along the West Coast region of South Africa. Calanoides carinatus is extensively preyed upon by the commercially important anchovy Engraulis capensis, thus variability in zooplankton production may serve as a useful predictor of variability in anchovy recruitment levels. The model developed here circumvents the need to include a large number of parameters because it uses satellite-derived estimates of chlorophyll a concentration and sea surface temperature as primary inputs. Abundance estimates necessary to initialize the model are readily obtainable from biannual research cruises. The model successfully simulates observed features of a copepod population's response to pulses of upwelling and is robust with respect to most of its parameters because minor changes in their values result in predictable changes in model output. The model showed greatest sensitivity to parameters that are difficult to determine empirically, such as predator-induced mortality rates. Gaps in our present understanding of the nature and scale of processes affecting copepod egg abundance, survival and viability in the southern Benguela system were identified as the dominant impediment to simulating copepod population dynamics in the region.      

Population modeling for a captive squirrel monkey colony

Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was approached with the use of two different mathematical modeling techniques. Deterministic modeling was used initially on a spreadsheet to estimate future census figures for animals in various age/sex classes. Historical data were taken as input parameters for the model, combined with harvesting policies to calculate future population figures in the colony. This was followed by a more sophisticated stochastic model that is capable of accommodating random variations in biological phenomena, as well as smoothing out measurement errors. Point estimates (means) for input parameters used in the deterministic model are replaced by probability distributions fitted into historical data from colony records. With the use of Crystal Ball (Decisioneering, Inc., Denver, CO) software, user-selected distributions are embedded in appropriate cells in the spreadsheet model. A Monte Carlo simulation scheme running within the spreadsheet draws (on each cycle) random values for input parameters from the distribution embedded in each relevant cell, and thus generates output values for forecast variables. After several thousand runs, a distribution is formed at the output end representing estimates for population figures (forecast variables) in the form of probability distributions. Such distributions provide the decision-maker with a mathematical habitat for statistical analysis in a stochastic setting. In addition to providing standard statistical measures (e.g., mean, variance, and range) that describe the location and shape of the distribution, this approach offers the potential for investigating crucial issues such as conditions surrounding the plausibility of extinction.     

Parameter estimation and sensitivity analysis of a nonlinearly elastic static lung model

A model for the static pressure-volume behavior of the lung parenchyma based on a pseudo-elastic strain energy function was tested. Values of the model parameters and their variances were estimated by an optimal least-squares fit of the model-predicted pressures to the corresponding data from excised, saline-filled dog lungs. Although the model fit data from twelve lungs very well, the coefficients of variation for parameter values differed greatly. To analyze the sensitivity of the model output to its parameters, we examined an approximate Hessian, H, of the least-squares objective function. Based on the determinant and condition number of H, we were able to set formal criteria for choosing the most reliable estimates of parameter values and their variances. This in turn allowed us to specify a normal range of parameter values for these dog lungs. Thus the model not only describes static pressure-volume data, but also uses the data to estimate parameters from a fundamental constitutive equation. The optimal parameter estimation and sensitivity analysis developed here can be widely applied to other physiologic systems.     

Fitting a Structured Juvenile–Adult Model for Green Tree Frogs to Population Estimates from Capture–Mark–Recapture Field Data

We derive point and interval estimates for an urban population of green tree frogs (Hyla cinerea) from capture–mark–recapture field data obtained during the years 2006–2009. We present an infinite-dimensional least-squares approach which compares a mathematical population model to the statistical population estimates obtained from the field data. The model is composed of nonlinear first-order hyperbolic equations describing the dynamics of the amphibian population where individuals are divided into juveniles (tadpoles) and adults (frogs). To solve the least-squares problem, an explicit finite difference approximation is developed. Convergence results for the computed parameters are presented. Parameter estimates for the vital rates of juveniles and adults are obtained, and standard deviations for these estimates are computed. Numerical results for the model sensitivity with respect to these parameters are given. Finally, the above-mentioned parameter estimates are used to illustrate the long-time behavior of the population under investigation.     

Respirometric assay for biofilm kinetics estimation: parameter identifiability and retrievability

Currently, no fast and accurate methods exist for measuring extant biokinetic parameters for biofilm systems. This article presents a new approach to measure extant biokinetic parameters of biofilms and examines the numerical feasibility of such a method. A completely mixed attached growth bioreactor is subjected to a pulse of substrate, and oxygen consumption is monitored by on-line measurement of dissolved oxygen concentration in the bulk liquid. The oxygen concentration profile is then fit with a mechanistic mathematical model for the biofilm to estimate biokinetic parameters. In this study a transient biofilm model is developed and solved to generate dissolved oxygen profiles in the bulk liquid. Sensitivity analysis of the model reveals that the dissolved oxygen profiles are sufficiently sensitive to the biokinetic parameters-the maximum specific growth rate coefficient (insertion markμ) and the half-saturation coefficient (Ks)-to support parameter estimation if accurate estimates of other model parameters can be obtained. Monte Carlo simulations are conducted with the model to add typical measurement error to the generated dissolved oxygen profiles. Even with measurement error in the dissolved oxygen profile, a pair of biokinetic parameters is always retrievable. The geometric mean of the parameter estimates from the Monte Carlo simulations prove to be an accurate estimator for the true biokinetic values. Higher precision is obtained for insertion markμ estimates than for Ks estimates. In summary, this theoretical analysis reveals that an on-line respirometric assay holds promise for measuring extant biofilm kinetic parameters. Copyright 1998 John Wiley & Sons, Inc.     

Estimating the parameters in the two-component model for cell survival from experimental quantal response data

A statistical technique is given which can be used to estimate the parameters of the two-component model for cell survival from quantal response multifraction data. The method is a nonlinear logistic regression and relies on a mild assumption relating the probability of death to cell survival level. The method is demonstrated on mouse colon data, where more efficient estimates of the parameters are known, and the agreement is good. Also for some mouse lung LD50 data we obtain estimates of the parameters, and the fit to the data is shown to be better than that of linear-quadratic model.     

Estimation of cardiac output by analysis of respiratory gas exchange.

Cardiac output is estimated by least squares fitting of a model of pulmonary gas exchange to measurements of respiratory gas composition obtained with a mass spectrometer during a rebreathing maneuver. This new technique estimates cardiac output on spontaneously breathing subjects at rest and requires neither central venous nor arterial blood samples. Principal features of the technique are the use of multiple gases simultaneously in the analysis, the use of a mathematical model for breath-to-breath evaluation of gas exchange, and simultaneous estimation of gas exchange and alveolar gas tensions with the same instrumentation. The technique is compared with thermal dilution estimates in dogs before and during hemorrhagic shock. Two-thirds of these estimates were within 20% of one another. The standard deviation of replication was 15%. Shortcomings, possibilities for improvement, and possible applications are discussed.     

The probabilistic economic injury level: incorporating uncertainty into pest management decision-making

Despite the recognition that the economic injury level (EIL) is determined by dynamic biological and economic parameters, which can be highly variable and uncertain, there has been little effort to quantify uncertainty and to use estimates of uncertainty in the determination of EILs. In this paper, we define the probabilistic EIL (PEIL) and develop PEILs for two insect pest scenarios: alfalfa weevil larvae, Hypera postica (Gyllenhal), on early bud-stage alfalfa, and bean leaf beetle adults, Cerotoma trifurcata (Forster), on V1-stage soybean. The PEIL is an EIL that reflects its probability of occurrence. The probability of occurrence is determined by incorporating the uncertainty associated with the input variables used to calculate the EIL. We used Monte Carlo simulation, a random sampling technique in which each input variable in the model was sampled repeatedly from a range of possible values based on probability distributions. Each input variable's probability distribution was sampled such that the distribution's shape was reproduced. Then, the variability for each input was propagated into the output of the model so that the model output reflected the probability of values that could occur. This represents the first use of the Monte Carlo technique to determine EILs.     

Sensitivity analysis of an energetic muscle model applied at whole body level in recumbent pedalling

Musculoskeletal models are used in order to describe and analyse the mechanics of human movement. In order to get a complete evaluation of the human movement, energetic muscle models were developed and were shown to be promising. The aim of this work is to determine the sensitivity of muscle mechanical and energetic model estimates to changes in parameters during recumbent pedalling. Inputs of the model were electromyography and joint angles, collected experimentally on one participant. The sensitivity analysis was performed on muscle-specific tension, physiological cross-sectional area, muscle maximal force, tendon rest length and percentage of fast-twitch fibres using an integrated sensitivity ratio. Soleus, gastrocnemius, vasti, gluteus and medial hamstrings were selected for the analyses. The energetic model was found to be always less sensitive to parameter changes than the mechanical model. Tendon slack length was found to be the most critical parameter for both energetic and mechanical models even if the effect on the energetic output was smaller than on muscle force and joint moments.     

Selection of optimal model for the DNA histogram by analysis of error of estimated parameters.

The ability of four different mathematical models of the DNA histogram to give accurate estimates for the fractions of cells in G1, S, and G2 + M has been investigated. The models studied differ in the form and number of parameters of the function used to represent cells in S-phase. Results obtained from simulated DNA histograms suggest that the standard deviations of the model parameters increase exponentially with the width of the G1 and G2 + M peaks of the histogram. Error analysis is presented as a method to select a model of optimal complexity in relation to the resolution provided by the data in a given set of DNA histograms. Introduction of additional parameters improves the agreement between model and data but may result in a less well-posed model. A model with an optimal number of parameters can therefore be found that will yield parameter estimates with the smallest possible standard deviations.     

Non-Invasive Sampling of Schistosomes from Humans Requires Correcting for Family Structure

For ethical and logistical reasons, population-genetic studies of parasites often rely on the non-invasive sampling of offspring shed from their definitive hosts. However, if the sampled offspring are naturally derived from a small number of parents, then the strong family structure can result in biased population-level estimates of genetic parameters, particularly if reproductive output is skewed. Here, we document and correct for the strong family structure present within schistosome offspring (miracidia) that were collected non-invasively from humans in western Kenya. By genotyping 2,424 miracidia from 12 patients at 12 microsatellite loci and using a sibship clustering program, we found that the samples contained large numbers of siblings. Furthermore, reproductive success of the breeding schistosomes was skewed, creating differential representation of each family in the offspring pool. After removing the family structure with an iterative jacknifing procedure, we demonstrated that the presence of relatives led to inflated estimates of genetic differentiation and linkage disequilibrium, and downwardly-biased estimates of inbreeding coefficients (F_IS). For example, correcting for family structure yielded estimates of F_ST among patients that were 27 times lower than estimates from the uncorrected samples. These biased estimates would cause one to draw false conclusions regarding these parameters in the adult population. We also found from our analyses that estimates of the number of full sibling families and other genetic parameters of samples of miracidia were highly intercorrelated but are not correlated with estimates of worm burden obtained via egg counting (Kato-Katz). Whether genetic methods or the traditional Kato-Katz estimator provide a better estimate of actual number of adult worms remains to be seen. This study illustrates that family structure must be explicitly accounted for when using offspring samples to estimate the genetic parameters of adult parasite populations.     

Testing marker-based estimates of heritability in the wild

Marker-based estimates of heritability are an attractive alternative to pedigree-based methods for estimating quantitative genetic parameters in field studies where it is difficult or impossible to determine relationships and pedigrees. Here I test the ability of the marker-based method to estimate heritability of a suite of traits in a wild population of bighorn sheep (Ovis canadensis) using marker data from 32 microsatellite loci. I compared marker-based estimates with estimates obtained using a pedigree and the animal model. Marker-based estimates of heritability were imprecise and downwardly biased. The high degree of uncertainty in marker-based estimates suggests that the method may be sufficient to detect the presence of genetic variance for highly heritable traits, but not sufficiently reliable to estimate genetic parameters.     

A Monte Carlo analysis of muscle force estimation sensitivity to muscle-tendon properties using a Hill-based muscle model

Surface electromyography driven models are desirable for estimating subject-specific muscle forces. However, these models include parameters that come from an array of sources, thus creating uncertainty in the model-estimated force. In this study, we used Monte-Carlo simulations to evaluate the sensitivity of Hill-based model muscle forces to changes in 11 parameters in the muscle-tendon unit morphological properties and in the model force-length and force-velocity relationships. We decomposed the force variability and ranked the sensitivity of the model to the underlying parameters using the Variogram Analysis of Response Surfaces. For the analyzed running experiments and the adopted Hill model structure, our results show that the parameters are separable into four groups, where the parameters in each group have a synergistic contribution to the model global sensitivity. The first group consists of the maximum isometric force and the pennation angle. The second group contains the optimal fiber length, the tendon slack length, the tendon reference strain and the tendon shape factor. The third group contains the width and shape at the extremities of the active contractile element, along with the maximum contraction velocity and the curvature constant in the force-velocity curve. The fourth group consisted only of the force enhancement during eccentric contraction. The first two groups revealed the largest influence on the output force sensitivity. As many input parameters are difficult to measure and impact estimated forces, we propose that model estimates be presented with confidence intervals as well as inter-parameter relationships, to encourage users to explicitly consider the model uncertainty.     

Individualized performance prediction of sleep-deprived individuals with the two-process model.

We present a new method for developing individualized biomathematical models that predict performance impairment for individuals restricted to total sleep loss. The underlying formulation is based on the two-process model of sleep regulation, which has been extensively used to develop group-average models. However, in the proposed method, the parameters of the two-process model are systematically adjusted to account for an individual's uncertain initial state and unknown trait characteristics, resulting in individual-specific performance prediction models. The method establishes the initial estimates of the model parameters using a set of past performance observations, after which the parameters are adjusted as each new observation becomes available. Moreover, by transforming the nonlinear optimization problem of finding the best estimates of the two-process model parameters into a set of linear optimization problems, the proposed method yields unique parameter estimates. Two distinct data sets are used to evaluate the proposed method. Results of simulated data (with superimposed noise) show that the model parameters asymptotically converge to their true values and the model prediction accuracy improves as the number of performance observations increases and the amount of noise in the data decreases. Results of a laboratory study (82 h of total sleep loss), for three sleep-loss phenotypes, suggest that individualized models are consistently more accurate than group-average models, yielding as much as a threefold reduction in prediction errors. In addition, we show that the two-process model of sleep regulation is capable of representing performance data only when the proposed individualized model is used.     

An Approximate EM Algorithm for Nonlinear Mixed Effects Models

In this article, we construct an approximate EM algorithm to estimate the parameters of a nonlinear mixed effects model. The iterative procedure can be viewed as an iterative method of moments procedure for estimating the variance components and an iterative reweighted least squares estimates for estimating the fixed effects. Therefore, it is valid without the normality assumptions on the random components. A computationally simple method of moments estimates of the model parameters are used as the starting values for our iterative procedure. A simulation study was conducted to compare the performances of the proposed procedure with the procedure proposed by Lindstrom and Bates (1990) for some normal models and nonnormal models.     

Sensitivity analysis of an energetic muscle model applied at whole body level in recumbent pedalling

Musculoskeletal models are used in order to describe and analyse the mechanics of human movement. In order to get a complete evaluation of the human movement, energetic muscle models were developed and were shown to be promising.

The aim of this work is to determine the sensitivity of muscle mechanical and energetic model estimates to changes in parameters during recumbent pedalling.

Inputs of the model were electromyography and joint angles, collected experimentally on one participant. The sensitivity analysis was performed on muscle-specific tension, physiological cross-sectional area, muscle maximal force, tendon rest length and percentage of fast-twitch fibres using an integrated sensitivity ratio. Soleus, gastrocnemius, vasti, gluteus and medial hamstrings were selected for the analyses.

The energetic model was found to be always less sensitive to parameter changes than the mechanical model. Tendon slack length was found to be the most critical parameter for both energetic and mechanical models even if the effect on the energetic output was smaller than on muscle force and joint moments.     

METHODS FOR JOINT INFERENCE FROM MULTIPLE DATA SOURCES FOR IMPROVED ESTIMATES OF POPULATION SIZE AND SURVIVAL RATES

Critical conservation decisions often hinge on estimates of population size, population growth rate, and survival rates, but as a practical matter it is difficult to obtain enough data to provide precise estimates. Here we discuss Bayesian methods for simultaneously drawing on the information content from multiple sorts of data to get as much precision as possible for the estimates. The basic idea is that an underlying population model can connect the various sorts of observations, so this can be elaborated into a joint likelihood function for joint estimation of the respective parameters. The potential for improved estimates derives from the potentially greater effective sample size of the aggregate of data, even though some of the data types may only bear directly on a subset of the parameters. The achieved improvement depends on specifics of the interactions among parameters in the underlying model, and on the actual content of the data. Assuming the respective data sets are unbiased, notwithstanding the fact that they may be noisy, we may gauge the average improvement in the estimates of the parameters of interest from the reduction, if any, in the standard deviations of their posterior marginal distributions. Prospective designs may be evaluated from analysis of simulated data. Here this approach is illustrated with an assessment of the potential value in various ways of merging mark-resight and carcass-survey data for the Florida manatee, as could be made possible by various modifications in the data collection protocols in both programs.