Statistical methods in finite element analysis

Finite element analysis (FEA) is a commonly used tool within many areas of engineering and can provide useful information in structural analysis of mechanical systems. However, most analyses within the field of biomechanics usually take no account either of the wide variation in material properties and geometry that may occur in natural tissues or manufacturing imperfections in synthetic materials. This paper discusses two different methods of incorporating uncertainty in FE models. The first, Taguchi's robust parameter design, uses orthogonal matrices to determine how to vary the parameters in a series of FE models, and provides information on the sensitivity of a model to input parameters. The second, probabilistic analysis, enables the distribution of a response variable to be determined from the distributions of the input variables. The methods are demonstrated using a simple example of an FE model of a beam that is assigned material properties and geometry over a range similar to an orthopaedic fixation plate. In addition to showing how each method may be used on its own, we also show how computational effort may be minimised by first identifying the most important input variables before determining the effects of imprecision.     

生态产业共生系统仿真研究

通过ABM方法研究生态产业共生系统,利用STARLOGO软件平台,并结合案例分析生态产业共生系统的宏观规律。研究结果表明,(1)对于规模相当的不同的生态产业共生系统,在资源输入一定情况下,直接利用输入资源的企业总规模大于对系统内废弃物再利用的企业总规模是有利于系统稳定的:(2)对于特定的生态产业共生系统,系统稳定性对系统参数改变时的敏感性是不一样的,其中对污染物产出指标最敏感,对污染物产生量与系统产出的比例关系其次,对资源输入指标最不敏感;(3)系统时间序列稳定性的变化主要由节点处企业Ⅱ的不稳定性导致。     

The epidemiology of BSE in cattle herds in Great Britain. II. Model construction and analysis of transmission dynamics.

Mathematical model that describe the key processes determining the pattern of the bovine spongiform encephalopathy (BSE) epidemic in British cattle are derived that allow for infection from feed as well as maternal and direct horizontal transmission. Heterogeneous susceptibility classes are also incorporated into the analysis. Maximum likelihood methods are used to estimate parameters and to obtain confidence intervals from available experimental and epidemiological data. A comprehensive sensitivity analysis of all model parameters and distributional assumptions is presented. Additional validation is provided by fitting the model to independent data collected in Northern Ireland. Model estimates and predictions based on BSE case data for Great Britain and Northern Ireland, together with their implications, are reviewed, and future research priorities discussed.     

A methodology for performing global uncertainty and sensitivity analysis in systems biology

Accuracy of results from mathematical and computer models of biological systems is often complicated by the presence of uncertainties in experimental data that are used to estimate parameter values. Current mathematical modeling approaches typically use either single-parameter or local sensitivity analyses. However, these methods do not accurately assess uncertainty and sensitivity in the system as, by default, they hold all other parameters fixed at baseline values. Using techniques described within we demonstrate how a multi-dimensional parameter space can be studied globally so all uncertainties can be identified. Further, uncertainty and sensitivity analysis techniques can help to identify and ultimately control uncertainties. In this work we develop methods for applying existing analytical tools to perform analyses on a variety of mathematical and computer models. We compare two specific types of global sensitivity analysis indexes that have proven to be among the most robust and efficient. Through familiar and new examples of mathematical and computer models, we provide a complete methodology for performing these analyses, in both deterministic and stochastic settings, and propose novel techniques to handle problems encountered during these types of analyses.     

Sensitivity Analysis of an Individual-Based Model for Simulation of Influenza Epidemics

Individual-based epidemiology models are increasingly used in the study of influenza epidemics. Several studies on influenza dynamics and evaluation of intervention measures have used the same incubation and infectious period distribution parameters based on the natural history of influenza. A sensitivity analysis evaluating the influence of slight changes to these parameters (in addition to the transmissibility) would be useful for future studies and real-time modeling during an influenza pandemic.In this study, we examined individual and joint effects of parameters and ranked parameters based on their influence on the dynamics of simulated epidemics. We also compared the sensitivity of the model across synthetic social networks for Montgomery County in Virginia and New York City (and surrounding metropolitan regions) with demographic and rural-urban differences. In addition, we studied the effects of changing the mean infectious period on age-specific epidemics. The research was performed from a public health standpoint using three relevant measures: time to peak, peak infected proportion and total attack rate. We also used statistical methods in the design and analysis of the experiments.The results showed that: (i) minute changes in the transmissibility and mean infectious period significantly influenced the attack rate; (ii) the mean of the incubation period distribution appeared to be sufficient for determining its effects on the dynamics of epidemics; (iii) the infectious period distribution had the strongest influence on the structure of the epidemic curves; (iv) the sensitivity of the individual-based model was consistent across social networks investigated in this study and (v) age-specific epidemics were sensitive to changes in the mean infectious period irrespective of the susceptibility of the other age groups. These findings suggest that small changes in some of the disease model parameters can significantly influence the uncertainty observed in real-time forecasting and predicting of the characteristics of an epidemic.     

Internal standard-based analysis of microarray data. Part 1: analysis of differential gene expressions

Genome-scale microarray experiments for comparative analysis of gene expressions produce massive amounts of information. Traditional statistical approaches fail to achieve the required accuracy in sensitivity and specificity of the analysis. Since the problem can be resolved neither by increasing the number of replicates nor by manipulating thresholds, one needs a novel approach to the analysis. This article describes methods to improve the power of microarray analyses by defining internal standards to characterize features of the biological system being studied and the technological processes underlying the microarray experiments. Applying these methods, internal standards are identified and then the obtained parameters are used to define (i) genes that are distinct in their expression from background; (ii) genes that are differentially expressed; and finally (iii) genes that have similar dynamical behavior.     

A numerical model of birch pollen emission and dispersion in the atmosphere. Model evaluation and sensitivity analysis

An evaluation of performance of the System for Integrated modeLling of Atmospheric coMposition (SILAM) in application to birch pollen dispersion is presented. The system is described in a companion paper whereas the current study evaluates the model sensitivity to details of the pollen emission module parameterisation and to the meteorological input data. The most important parameters are highlighted. The reference year considered for the analysis is 2006. It is shown that the model is capable of predicting about two-thirds of allergenic alerts, with the odds ratio exceeding 12 for the best setup. Several other statistics corroborate with these estimations. Low-pollen concentration days are also predicted correctly in more than two-thirds of cases. The model experiences certain difficulties only with intermediate pollen concentrations. It is demonstrated that the most important input parameter is the near-surface temperature, the bias of which can easily jeopardise the results. The model sensitivity to random fluctuations of temperature is much lower. Other parameters important at various stages of pollen development, release, and dispersion are precipitation and ambient humidity, as well as wind direction.     

Spectral analysis of electroencephalographic recordings of long duration by means of band-pass filters

A method is proposed for spectral analysis of EEG recordings of long duration, using a set of band-pass filters. The sensitivity of the filters varies continuously over their full range, and the input signal is sampled at every sensitivity level. The full spectrum is presented as an array of numbers where the columns are the frequencies and the rows the sensitivity levels, printed as a percentage of the total possible responses of the filter (percent of activity). The logarithm of the numbers expressing the activity of a filter are used for the calculation of the regression line. Thus, the activity in each frequency is characterized by two parameters, the slope and the ordinate at origin, the slope being the more interesting one.     

The analysis of hospital infection data using hidden Markov models

Surveillance data for communicable nosocomial pathogens usually consist of short time series of low-numbered counts of infected patients. These often show overdispersion and autocorrelation. To date, almost all analyses of such data have ignored the communicable nature of the organisms and have used methods appropriate only for independent outcomes. Inferences that depend on such analyses cannot be considered reliable when patient-to-patient transmission is important. We propose a new method for analysing these data based on a mechanistic model of the epidemic process. Since important nosocomial pathogens are often carried asymptomatically with overt infection developing in only a proportion of patients, the epidemic process is usually only partially observed by routine surveillance data. We therefore develop a 'structured' hidden Markov model where the underlying Markov chain is generated by a simple transmission model. We apply both structured and standard (unstructured) hidden Markov models to time series for three important pathogens. We find that both methods can offer marked improvements over currently used approaches when nosocomial spread is important. Compared to the standard hidden Markov model, the new approach is more parsimonious, is more biologically plausible, and allows key epidemiological parameters to be estimated.     

Critical thresholds in sea lice epidemics: evidence, sensitivity and subcritical estimation

Host density thresholds are a fundamental component of the population dynamics of pathogens, but empirical evidence and estimates are lacking. We studied host density thresholds in the dynamics of ectoparasitic sea lice (Lepeophtheirus salmonis) on salmon farms. Empirical examples include a 1994 epidemic in Atlantic Canada and a 2001 epidemic in Pacific Canada. A mathematical model suggests dynamics of lice are governed by a stable endemic equilibrium until the critical host density threshold drops owing to environmental change, or is exceeded by stocking, causing epidemics that require rapid harvest or treatment. Sensitivity analysis of the critical threshold suggests variation in dependence on biotic parameters and high sensitivity to temperature and salinity. We provide a method for estimating the critical threshold from parasite abundances at subcritical host densities and estimate the critical threshold and transmission coefficient for the two epidemics. Host density thresholds may be a fundamental component of disease dynamics in coastal seas where salmon farming occurs.     

Results of virological and serological studies of three influenza A Hong-Kong epidemics in Leningrad.

An analysis of morbidity of the population in the course of 3 influenza A/Hong-Kong epidemics showed a pronounced decrease in influenza affection of adult population in the last epidemic in 1971--1972. Comparative studies of the diagnostic value of CFR and HIT demonstrated identical sensitivity of CFR as a method of influenza diagnostics in both the epidemic and interepidemic periods. HIT was suitable for the detection of influenza only in the epidemic period. In the interepidemic period, the percentage of influenza infection diagnosed by means of HIT ammounted to only 23--24 of all serologically confirmed cases of influenza. The highest percentage of virus isolation was observed when material from patients with serologically confirmed influenza was used. All strains of influenza A virus isolated in 1969 and 1970 were similar in their sensitivity to inhibitors of animal sera. During the last influenza epidemic, 2 of the 136 isolated strains were found to be resistant to gamma inhibitors and highly sensitive to the inhibitors showed their close relationship to gamma inhibitors. Antigenic analysis of the influenza A strains isolated during the 3 influenza epidemics revealed changes in the antigenic structure of the agents of the influenza epidemic in Leningrad in comparison with the standard strain A/Hong-Kong/I/68 (H3N2).     

Characterisation of a blowfly male-specific neuron using behaviourally generated visual stimuli

The pursuit system controlling chasing behaviour in male blowflies has to cope with extremely fast and dynamically changing visual input. An identified male-specific visual neuron called Male Lobula Giant 1 (MLG1) is presumably one major element of this pursuit system. Previous behavioural and modelling analyses have indicated that angular target size, retinal target position and target velocity are relevant input variables of the pursuit system. To investigate whether MLG1 specifically represents any of these visual parameters we obtained in vivo intracellular recordings while replaying optical stimuli that simulate the visual signals received by a male fly during chasing manoeuvres. On the basis of these naturalistic stimuli we find that MLG1 shows distinct direction sensitivity and is depolarised if the target motion contains an upward component. The responses of MLG1 are jointly determined by the retinal position, the speed and direction, and the duration of target motimotion. Coherence analysis reveals that although retinal target size and position are in some way inherent in the responses of MLG1, we find no confirmation of the hypothesis that MLG1 encodes any of these parameters exclusively.     

On-line identification of sensory systems using pseudorandom binary noise perturbations.

A technique of on-line identification of linear system characteristics from sensory systems with spike train or analog voltage outputs was developed and applied to the semicircular canal. A pseudorandom binary white noise input was cross-correlated with the system's output to produce estimates of linear system unit impulse responses (UIRs), which were then corrected for response errors of the input transducers. The effects of variability in the system response characteristics and sensitivity were studied by employing the technique with known linear analog circuits. First-order unit afferent responses from the guitarfish horizontal semicircular canal were cross-correlated with white noise rotational acceleration inputs to produce non-parametric UIR models. In addition, the UIRs were fitted by nonlinear regression to truncated exponential series to produce parametric models in the form of low-order linear system equations. The experimental responses to the white noise input were then compared with those predicted from the UIR models linear convolution, and the differences were expressed as a percent mean-square-error (%MSE). The average difference found from a population of 62 semicircular canal afferents was relatively low mean and standard deviation of 10.2 +/- 5.9 SD%MSE, respectively. This suggests that relatively accurate inferences can be made concerning the physiology of the semicircular canal from the linear characteristics of afferent responses.     

Comprehensive,Population-Based Sensitivity Analysis of a Two-Mass Vocal Fold Model

Previous vocal fold modeling studies have generally focused on generating detailed data regarding a narrow subset of possible model configurations. These studies can be interpreted to be the investigation of a single subject under one or more vocal conditions. In this study, a broad population-based sensitivity analysis is employed to examine the behavior of a virtual population of subjects and to identify trends between virtual individuals as opposed to investigating a single subject or model instance. Four different sensitivity analysis techniques were used in accomplishing this task. Influential relationships between model input parameters and model outputs were identified, and an exploration of the model’s parameter space was conducted. Results indicate that the behavior of the selected two-mass model is largely dominated by complex interactions, and that few input-output pairs have a consistent effect on the model. Results from the analysis can be used to increase the efficiency of optimization routines of reduced-order models used to investigate voice abnormalities. Results also demonstrate the types of challenges and difficulties to be expected when applying sensitivity analyses to more complex vocal fold models. Such challenges are discussed and recommendations are made for future studies.     

Automated system for capture and detection of nucleic acids.

A fully automated nucleic acid analysis system is described, which offers positive sample identification, improved sensitivity and reduced user interaction compared to conventional techniques. The system relies on the sequence-specific capture of DNA onto solid-phase particles, confirming product identity without the problems of interpretation and lack of sequence information inherent in gel-based analyses. The system can be used for sequence confirmation, mutation analysis and semiquantitative detection of PCR products.     

Determination of beta-D-glucose using flow injection analysis and composite-type amperometric tubular biosensors

An amperometric tubular cell involving composite biosensors for the determination of beta-d-glucose in a flow injection analysis (FIA) system is proposed. Diverse configurations and parameters are evaluated to improve the system's response. The configuration producing less noise resulted when the biosensor was located closer to the auxiliary electrode, which also required coupling both electrodes within the system under a continuous flow regime. Further, we report on the influence of the active area of the biosensor and of the flow rate used. Statistical analyses of the data revealed two regions with a linear response range for the determination of beta-d-glucose, with a detection limit of 4.7 x 10(-4) M and in the low concentration region a sensitivity of 17.46 +/- 0.12 microAM(-1). At the beta-d-glucose concentrations studied there was no evidence of enzymatic saturation. An increment on the ionic strength of the sample and carrier passing through the analysis system decreases its sensitivity. The reproducibility of the analytical system in terms of its standard deviation was 2.9% with a 95% confidence level, having a lifetime that lasted at least 100 days. beta-d-Glucose was determined in different commercial medical glucose-containing solutions, the experimental results are in good agreement with those reported by the manufacturer.     

Evaluating the Use of Global Sensitivity Analysis in Dynamic MFA

Dynamic material flow analysis (MFA) provides information about material usage over time and consequent changes in material stocks and flows. In order to understand the effect of limited data quality and model assumptions on MFA results, the use of sensitivity analysis methods in dynamic MFA studies has been on the increase. So far, sensitivity analysis in dynamic MFA has been conducted by means of a one‐at‐a‐time method, which tests parameter perturbations individually and observes the outcomes on output. In contrast to that, variance‐based global sensitivity analysis decomposes the variance of the model output into fractions caused by the uncertainty or variability of input parameters. The present study investigates interaction and time‐delay effects of uncertain parameters on the output of an archetypal input‐driven dynamic material flow model using variance‐based global sensitivity analysis. The results show that determining the main (first‐order) effects of parameter variations is often sufficient in dynamic MFA because substantial effects attributed to the simultaneous variation of several parameters (higher‐order effects) do not appear for classical setups of dynamic material flow models. For models with time‐varying parameters, time‐delay effects of parameter variation on model outputs need to be considered, potentially boosting the computational cost of global sensitivity analysis. Finally, the implications of exploring the sensitivities of model outputs with respect to parameter variations in the archetypical model are used to derive model‐ and goal‐specific recommendations on choosing appropriate sensitivity analysis methods in dynamic MFA.     

Effect of a pedicle-screw-based motion preservation system on lumbar spine biomechanics: A probabilistic finite element study with subsequent sensitivity analysis

Pedicle-screw-based motion preservation systems are often used to support a slightly degenerated disc. Such implants are intended to reduce intradiscal pressure and facet joints forces, while having a minimal effect on the motion patterns.In a probabilistic finite element study with subsequent sensitivity analysis, the effects of 10 input parameters, such as elastic modulus and diameter of the elastic rod, distraction of the segment, level of bridged segments, etc. on the output parameters intervertebral rotations, intradiscal pressures, and facet joint forces were determined. A validated finite element model of the lumbar spine was employed. Probabilistic studies were performed for seven loading cases: upright standing, flexion, extension, left and right lateral bending and left and right axial rotation.The simulations show that intervertebral rotation angles, intradiscal pressures and facet joint forces are in most cases reduced by a motion preservation system. The influence on intradiscal pressure is small, except in extension. For many input parameter combinations, the values for intervertebral rotations and facet joint forces are very low, which indicates that the implant is too stiff in these cases. The output parameters are affected most by the following input parameters: loading case, elastic modulus and diameter of the elastic rod, distraction of the segment, and angular rigidity of the connection between screws and rod.The designated functions of a motion preservation system can best be achieved when the longitudinal rod has a low stiffness, and when the connection between rod and pedicle screws is rigid.     

Sensitivity of muscle force estimations to changes in muscle input parameters using nonlinear optimization approaches.

The purpose of this study was to analyze the sensitivity of muscle force calculations to changes in muscle input parameters. Force sharing between two synergistic muscles was derived analytically for a one-degree-of-freedom system using three nonlinear optimization approaches. Changes in input parameters that are within normal anatomical variations often caused changes in muscular forces exceeding 100 percent. These results indicate that errors in muscle force calculations may depend as much on inadequate muscle input parameters as they may on the choice of the objective and constraint functions of the optimization approach.