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PubMed1980

An illness-death model for the study of the carcinogenic process using survival/sacrifice data.

A semi-Markov model for describing the development of a specific type of tumor which is followed by death from that tumor is proposed. This provides a method for investigating the observable phases of tumor development, when time to appearance of tumor in individual animals is not directly measurable. Parameters of the model are estimated by the method of maximum likelihood. The modeling and estimation procedures are illustrated with liver tumors induced by benzidine dihydrochloride in mice, and inferences with respect to strain, sex and dose differences are made.

Animals↗
PubMed2006

Modulation of brain and behavioural responses to cognitive visual stimuli with varying signal-to-noise ratios.

OBJECTIVE: To study behavioral and brain responses to variations in signal-to-noise ratio (SNR) of cognitive visual stimuli. METHODS: We presented meaningful words visually, embedded in varying amounts of dynamic noise, and utilized magnetoencephalography (MEG) to measure responses to the words. A multidipole model of the evoked fields was constructed to quantify the strengths and latencies of the neuronal sources at each noise level. The recognition rates of the words were measured in separate behavioral sessions. RESULTS: MEG revealed sequential activation of occipital and occipito-temporal areas (latencies 130-250 and 170-350 ms, respectively) followed by activity in superior temporal cortex (230-640 ms). The strengths and latencies of all identified sources followed functions similar to the SNR of the stimulus. The peak amplitudes and shortest latencies of all sources coincided with the maximum SNR of the stimulus. The occipito-temporal and temporal sources as well as the word recognition rate accurately followed the SNR of the stimulus whereas the early occipital source exhibited a more peaked dependence on the SNR. CONCLUSIONS: Evoked responses expectedly peaked at the maximum SNR of the stimulus. Interestingly, early visual responses showed sharper peaks than longer-latency sources as a function of the noise level. This can be understood as the higher-level processes analyzing the stimuli more holistically and thus being less sensitive to the salience of simple visual features. The similar noise-dependence of the longer-latency sources and the recognition rate provides new evidence for the relevance of these activations in the recognition of written words. SIGNIFICANCE: This study contributes to the understanding of brain activity evoked by degraded stimuli with cognitive content.

Adult↗
PubMed1997

A two-stage model for childhood acute lymphoblastic leukemia: application to hereditary and nonhereditary leukemogenesis.

A differential equation model is developed to represent a two-stage mutational process leading to childhood acute lymphoblastic leukemia (ALL). Leukemogenesis is modeled as transformation of target stem cells that initially grow rapidly in the embryo but plateau and then decline in postnatal childhood. Inheritance of the first of two leukemogenic mutations is allowed as a possibility in a small minority of leukemic patients who would characteristically develop leukemia at an early age. The model is shown to be capable of providing good fits to incidence data for childhood ALL; these fits allow estimation of some parameters of the model. The analysis shows that individuals inheriting one of the two mutations necessary for ALL would be likely to experience "multiclonal leukemogenesis"; that is, the parallel development of several leukemic clones arising from multiple independent leukemic events. The model suggests that between two and ten such clones would typically have developed in such individuals by the time of diagnosis. The main conclusions of the deterministic investigation were confirmed by stochastic modeling. The existence of multiclonal leukemogenesis is in principle testable by molecular biological methods (clonality analysis) that rely on the random inactivation of one of two X-chromosomes in normal female subjects. It is expected that the mathematical methods developed here will also be useful for more general (N-stage) models of malignant transformation of stem cell populations undergoing growth or decline.

Aging↗
PubMed1999

The molecular clock of HIV-1 unveiled through analysis of a known transmission history.

Detailed knowledge about the rate and mode of the genetic variation is vital for understanding how HIV-1 induces disease and develops resistance as well as for studies on the molecular epidemiology and origin of the virus. To unveil the molecular clock of HIV-1 we analyzed a unique set of viruses from a known transmission history with separation times between samples of up to 25 years. The env V3 and p17gag regions of the genome were sequenced, and genetic distances were estimated by using the true tree and a nucleotide substitution model based on a general reversible Markov process with a gamma distribution to account for differences in substitution rates among sites. Linear regression analysis showed that separation times were significantly correlated with synonymous as well as nonsynonymous nucleotide distances in both V3 and p17, giving strong support for the existence of a molecular clock. The estimated rate of nucleotide substitution was 6.7 +/- 2.1 x 10(-3) substitutions/site per year in V3 and 2.7 +/- 0.5 x 10(-3) in p17. Importantly, the regression analyses showed that there was a significant genetic distance at zero divergence times. This pretransmission interval exists because the ramifications in the phylogenetic trees do not correspond to time of transmission, but rather to the coalescence time of the most recent common ancestor of the viruses carried by the transmitter and the recipient. Simulation experiments showed that neither the V3 nor the p17 clocks were overdispersed, which indicates that the introduction of nucleotide substitutions can be described adequately by a simple stochastic Poisson process.

Disease Transmission, Infectious↗
PubMed2002

Optimal solution, quantitative performance estimation, and robust tuning of the simplifying controller.

Recently, a simplifying controller has been proposed based on the principal of simplification of the control system transfer functions, which offers improved control for processes with a large time delay. It is the purpose of this complementary paper to give a comprehensive analysis on the scheme. First, the relationship among the simplifying controller, the Smith predictor, and the internal model control are discussed. Second, an analytical design procedure is developed based on internal model control (IMC) and optimal solution is derived. Third, the problem of estimating the time domain performance of the closed loop system, quantitatively, is discussed. Fourth, a simple robust tuning procedure is presented. Numerical examples are provided to illustrate the proposed method.

Computer Simulation↗
PubMed2005

Integrate-and-fire neurons with threshold noise: a tractable model of how interspike interval correlations affect neuronal signal transmission.

Many neurons exhibit interval correlations in the absence of input signals. We study the influence of these intrinsic interval correlations of model neurons on their signal transmission properties. For this purpose, we employ two simple firing models, one of which generates a renewal process, while the other leads to a nonrenewal process with negative interval correlations. Different methods to solve for spectral statistics in the presence of a weak stimulus (spike train power spectra, cross spectra, and coherence functions) are presented, and their range of validity is discussed. Using these analytical results, we explore a lower bound on the mutual information rate between output spike train and input stimulus as a function of the system's parameters. We demonstrate that negative correlations in the baseline activity can lead to enhanced information transfer of a weak signal by means of noise shaping of the background noise spectrum. We also show that an enhancement is not compulsory--for a stimulus with power exclusively at high frequencies, the renewal model can transfer more information than the nonrenewal model does. We discuss the application of our analytical results to other problems in neuroscience. Our results are also relevant to the general problem of how a signal affects the power spectrum of a nonlinear stochastic system.

Action Potentials↗
PubMed2005

Modelling antigenic drift in weekly flu incidence.

Since influenza in humans is a major public health threat, the understanding of its dynamics and evolution, and improved prediction of its epidemics are important aims. Underlying its multi-strain structure is the evolutionary process of antigenic drift whereby epitope mutations give mutant virions a selective advantage. While there is substantial understanding of the molecular mechanisms of antigenic drift, until now there has been no quantitative analysis of this process at the population level. The aim of this study is to develop a predictive model that is of a modest-enough structure to be fitted to time series data on weekly flu incidence. We observe that the rate of antigenic drift is highly non-uniform and identify several years where there have been antigenic surges where a new strain substantially increases infective pressure. The SIR-S approach adopted here can also be shown to improve forecasting in comparison to conventional methods.

Antigenic Variation↗
PubMed2003

Discovering local structure in gene expression data: the order-preserving submatrix problem.

This paper concerns the discovery of patterns in gene expression matrices, in which each element gives the expression level of a given gene in a given experiment. Most existing methods for pattern discovery in such matrices are based on clustering genes by comparing their expression levels in all experiments, or clustering experiments by comparing their expression levels for all genes. Our work goes beyond such global approaches by looking for local patterns that manifest themselves when we focus simultaneously on a subset G of the genes and a subset T of the experiments. Specifically, we look for order-preserving submatrices (OPSMs), in which the expression levels of all genes induce the same linear ordering of the experiments (we show that the OPSM search problem is NP-hard in the worst case). Such a pattern might arise, for example, if the experiments in T represent distinct stages in the progress of a disease or in a cellular process and the expression levels of all genes in G vary across the stages in the same way. We define a probabilistic model in which an OPSM is hidden within an otherwise random matrix. Guided by this model, we develop an efficient algorithm for finding the hidden OPSM in the random matrix. In data generated according to the model, the algorithm recovers the hidden OPSM with a very high success rate. Application of the methods to breast cancer data seem to reveal significant local patterns.

Algorithms↗
PubMed2003

High resolution processing techniques for ultrasound doppler velocimetry in the presence of colored noise. Part I: Nonstationary methods.

Real-time flow velocity measurement is a practical issue in industrial and biomedical applications. Because their good frequency resolution, parametric methods such as autoregressive (AR) modeling and time-frequency distributions (TFD) are generally preferred to Fourier analysis. However, these methods become highly inaccurate in the presence of colored noise. We review here the principal parametric and nonparametric techniques and show their limitations in the estimation of Doppler frequency in the presence of strong colored noise. Different solutions to overcome these limitations are then proposed and compared using synthetic Doppler signals with colored noise.

Algorithms↗
PubMed1994

Noise and signal decoupling in maximum-likelihood reconstructions and Metz filters for PET brain images.

Images reconstructed with the maximum-likelihood-by-expectation-maximization (ML) algorithm have lower noise in some regions, particularly low count areas, compared with images reconstructed with filtered backprojection (FBP). The use of statistically correct noise model coupled with the positivity constraint in the ML algorithm provides this noise improvement, but whether this model confers a general advantage for ML over FBP with no noise model and any reconstruction filter, is unclear. We have studied the quantitative impact of the correct noise model in the ML algorithm applied to simulated and real PET fluoro-deoxyglucose (FDG) brain images, given a simplified but accurate reconstruction model with spatially invariant resolution. For FBP reconstruction, several Metz filters were chosen and images with different resolution were obtained depending on the order (1-400) of the Metz filters. Comparisons were made based on the mean Fourier spectra of the projection amplitudes, the noise-power spectra, and the mean region-of-interest signal and noise behaviour in the images. For images with resolution recovery beyond the intrinsic detector resolution, the noise increased significantly for FBP compared with ML. This indicates that in the process of signal recovery using ML, the noise is decoupled from the signal. Such noise decoupling is not possible for FBP. However, for image resolution equivalent to or less than the intrinsic detector resolution, FBP with Metz filters of various orders can achieve a performance similar to ML. The significance of the noise decoupling advantage in ML is dependent on the reconstructed image resolution required for specific imaging tasks.

Algorithms↗
PubMedDate not supplied

Electrocochleography potentials evoked by condensation and rarefaction clicks independently derived by a new numerical filtering approach.

The cochlear microphonic potential (CM) and the compound action potential (CAP) cannot be measured separately but only in combination. In the literature their individual estimates are conventionally recovered by the so-called CM cancellation technique. This method averages the potential obtained in response to rarefaction and condensation clicks under the assumption that changing the polarity of the clicks only affects the CM sign and does not alter the CAP in any way. However, both theory and evidence suggest that these hypotheses can be critical. In addition, recent contributions in the electrocochleography (ECochG) literature suggested that assessing the influence of stimulus polarity on the evoked CAP may constitute an indicator of clinical usefulness which the CM cancellation method cannot supply. In this work we propose a new algorithm to estimate the cochlear potentials evoked from positive clicks, CAP+ and CM+, and those evoked from negative clicks, CAP- and CM-, by processing the same kind and amount of data employed in the CM cancellation method. The application to real data taken from 3 subjects exhibiting quantitatively and qualitatively different ECochG responses at various levels of stimulation intensity is presented. In addition, simulated problems where the true CAP and CM are known are studied to permit a fair assessment of the proposed technique. Results suggest that the new algorithm is potentially able to point out small differences between CAP+ and CAP-. This encourages its further employment on a larger scale.

Audiometry, Evoked Response↗
PubMedDate not supplied

Diffusion processes, Feller semigroups and Wentzell boundary conditions.

Different approaches to the study of many diffusion processes in Genetics involve Probability, Functional Analysis and Partial Differential Equations, as in the case of changes in gene frequency due only to random sampling or under random fluctuation of selective advantages. In the one-dimensional case, a unified treatment of them was given by Feller. For particular classes of Markov processes, Taira showed that these different approaches are equivalent even in the N-dimensional case. It follows that the generator of a Feller semigroup on the space of real-valued continuous functions C(D), where D is a bounded domain of RN with smooth boundary, can be identified with a particular Markov transition function. Under suitable assumptions, Taira, Favini and the author proved that some classes of degenerate elliptic operators with Wentzell boundary condition generate Feller semigroups on C(D), in such a way that the diffusion phenomenon of viscosity occurs at each point of the boundary.

Gene Frequency↗
PubMedDate not supplied

Strategies for analysing ecological health data: models of the biological risk of individuals.

Frequently, the analysis of environmental health hazards using ecological data does not involve explicit recognition of the difficulties in translating health effects expressed in the aggregate to the health risks of individuals. We discuss these difficulties and suggest the need for the appropriate conceptualization of risk mechanisms at the individual level and of the population processes that determine the form in which these risk mechanisms are expressed in aggregate data. To illustrate the implications of these concepts we develop a biologically motivated model of lung cancer risk and apply it to both national and county data. In addition, to measure the total health effects of the long term elevation or depression of lung cancer incidence rates, we calculate prevalence distributions from the time series analysis of incidence patterns in county data.

Adult↗
PubMed1985

Neural modeling and model identification.

The complexity of the nervous system poses challenging experimental and theoretical problems to the investigator. While experimental studies have provided a broad understanding of the physiological and anatomical role of neural elements, a comprehensive description of how the nervous system acquires and processes information is still lacking. Neural modeling addresses itself to the quantitative interpretation of neurophysiological experiments, to the assimilation of diverse experimental results into unified theories, and to the investigation of mechanisms of information-processing units, codes, and networks and their relation to capabilities of living systems. This review will emphasize neural models which can be tested by physiological or psychophysical experiments and will include the identification of model parameters based on experimental measurements. An overview of neural firing models, neural interaction models, neural variability and coding, design of input-output experiments for model identification, and description of small network interactions through multiunit and gross potential recording will be included.

Action Potentials↗
PubMed1999

Strength of a weak bond connecting flexible polymer chains.

Bond dissociation under steadily rising force occurs most frequently at a time governed by the rate of loading (Evans and Ritchie, 1997 Biophys. J. 72:1541-1555). Multiplied by the loading rate, the breakage time specifies the force for most frequent failure (called bond strength) that obeys the same dependence on loading rate. The spectrum of bond strength versus log(loading rate) provides an image of the energy landscape traversed in the course of unbonding. However, when a weak bond is connected to very compliant elements like long polymers, the load applied to the bond does not rise steadily under constant pulling speed. Because of nonsteady loading, the most frequent breakage force can differ significantly from that of a bond loaded at constant rate through stiff linkages. Using generic models for wormlike and freely jointed chains, we have analyzed the kinetic process of failure for a bond loaded by pulling the polymer linkages at constant speed. We find that when linked by either type of polymer chain, a bond is likely to fail at lower force under steady separation than through stiff linkages. Quite unexpectedly, a discontinuous jump can occur in bond strength at slow separation speed in the case of long polymer linkages. We demonstrate that the predictions of strength versus log(loading rate) can rationalize conflicting results obtained recently for unfolding Ig domains along muscle titin with different force techniques.

Animals↗
PubMed2006

Modelling SARS data using threshold geometric process.

During the outbreak of an epidemic disease, for example, the severe acute respiratory syndrome (SARS), the number of daily infected cases often exhibit multiple trends: monotone increasing during the growing stage, stationary during the stabilized stage and then decreasing during the declining stage. Lam first proposed modelling a monotone trend by a geometric process (GP) [X(i), i=1,2,...] directly such that [a(i-1)X(i), i=1,2,...] forms a renewal process for some ratio a>0 which measures the direction and strength of the trend. Parameters can be conveniently estimated using the LSE methods. Previous GP models limit to data with only a single trend. For data with multiple trends, we propose a moving window technique to locate the turning point(s). The threshold GP model is fitted to the SARS data from four regions in 2003.

Data Interpretation, Statistical↗
PubMed2006

Selective effects of external noise on Ca2+ signal in mesoscopic scale biochemical cell systems.

We have investigated how the external noise would influence the intracellular calcium signaling processes due to the existence of internal noise in small systems. Using chemical Langevin equations, we demonstrate numerically that the behavior of 'system size bi-resonance' induced by internal noise will change with the external noise intensity in different regions, indicating the occurrence of selective effects of external noise. Meanwhile, cell system may also automatically select an optimal cell size to obtain the best performance in the presence of external noise. These results may imply that such selective-effect phenomenon should have some inherent relevance with the distinct deterministic bifurcation features of the system.

Animals↗
PubMed2005

Mass balance modelling of contaminants in river basins: a flexible matrix approach.

A novel and flexible approach is described for simulating the behaviour of chemicals in river basins. A number (n) of river reaches are defined and their connectivity is described by entries in an n x n matrix. Changes in segmentation can be readily accommodated by altering the matrix entries, without the need for model revision. Two models are described. The simpler QMX-R model only considers advection and an overall loss due to the combined processes of volatilization, net transfer to sediment and degradation. The rate constant for the overall loss is derived from fugacity calculations for a single segment system. The more rigorous QMX-F model performs fugacity calculations for each segment and explicitly includes the processes of advection, evaporation, water-sediment exchange and degradation in both water and sediment. In this way chemical exposure in all compartments (including equilibrium concentrations in biota) can be estimated. Both models are designed to serve as intermediate-complexity exposure assessment tools for river basins with relatively low data requirements. By considering the spatially explicit nature of emission sources and the changes in concentration which occur with transport in the channel system, the approach offers significant advantages over simple one-segment simulations while being more readily applicable than more sophisticated, highly segmented, GIS-based models.

Environmental Monitoring↗