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PubMed2004

The impact of surface water exchange on the nutrient and particle dynamics in side-arms along the River Danube, Austria.

Results of two monitoring programs obtained in the free-flowing section of the Danube downstream of Vienna were used to evaluate the effects of river restoration designed to increase surface water inputs into side-arms. Functional descriptors like hydrochemical parameters and plankton react immediately to restored hydrological conditions and offer the opportunity to elucidate the hydrological control on organic processing as an important ecosystem function in fluvial landscapes. Two hydraulic parameters were estimated and linked to basic ecological properties. The level of hydrological connectivity was defined as the average annual duration (days per year) of upstream surface connection and can be used as a 'simple to estimate' parameter within the planning phase. Water age, an adapted measure of residence time based on more detailed information, allow description of the temporal development in side-arms. Greater hydrological connectivity leads to lower conductivity levels and increased nutrient concentrations due to the shift of the dominating source to river water. The contribution of river flow is indicated by higher suspended solid concentrations in side-arms than disconnected water bodies. The phytoplankton biomass shows the highest mean values at a duration of integration of 1 month a(-1) and decrease with increasing connectivity. The relationships point to a more 'main channel like' hydrochemical situation in the side-arms, with a medium level of phytoplankton biomass and increased autochthonous carbon export. No evidence of eutrophication was found due to the shift of the side-arm from an organic matter sink to a source. On a more detailed level, water age demonstrates the temporal patterns of riverine input, the development of plankton production and the shift between hydrological and biological control of phytoplankton vs. riverine flow in a side-arm. The hydrologic parameters were useful predictors for evaluating the effects of restoration measures in river floodplain systems.

Austria↗

PubMed2004

Why the lysogenic state of phage lambda is so stable: a mathematical modeling approach.

We develop a mathematical model of the phage lambda lysis/lysogeny switch, taking into account recent experimental evidence demonstrating enhanced cooperativity between the left and right operator regions. Model parameters are estimated from available experimental data. The model is shown to have a single stable steady state for these estimated parameter values, and this steady state corresponds to the lysogenic state. When the CI degradation rate (gammacI) is slightly increased from its normal value (gammacI approximately 0.0 min(-1)), two additional steady states appear (through a saddle-node bifurcation) in addition to the lysogenic state. One of these new steady states is stable and corresponds to the lytic state. The other steady state is an (unstable) saddle node. The coexistence these two globally stable steady states (the lytic and lysogenic states) is maintained with further increases of gammacI until gammacI approximately 0.35 min(-1), when the lysogenic steady state and the saddle node collide and vanish (through a reverse saddle node bifurcation) leaving only the lytic state surviving. These results allow us to understand the high degree of stability of the lysogenic state because, normally, it is the only steady state. Further implications of these results for the stability of the phage lambda switch are discussed, as well as possible experimental tests of the model.

Bacteriophage lambda↗

PubMed1989

Estimation of single channel kinetic parameters from data subject to limited time resolution.

The limited responsiveness of single-channel recording systems results in some brief events not being detected, and if this is ignored parameter estimation from the observed data will be biased. Statistical methods of correcting for this limited time resolution in a two-state Markov model have been proposed by Neher (1983. J. Physiol. (Lond.). 339:663-678) and by Colquhoun and Sigworth (1983. Single Channel Recording. 191-263). However, a numerical study by Blatz and Magleby (1986. Biophys. J. 49:967-980) indicated differences of 3-40% in the corrected values given by the two techniques. Here we explain why Neher's method produces biased results and the Colquhoun and Sigworth approach, which is no more difficult, provides reasonably accurate estimates.

Ion Channels↗

PubMed1999

Confined and unconfined stress relaxation of cartilage: appropriateness of a transversely isotropic analysis.

Previous studies have shown that stress relaxation behavior of calf ulnar growth plate and chondroepiphysis cartilage can be described by a linear transverse isotropic biphasic model. The model provides a good fit to the observed unconfined compression transients when the out-of-plane Poisson's ratio is set to zero. This assumption is based on the observation that the equilibrium stress in the axial direction (deltaz) is the same in confined and unconfined compression, which implies that the radial stress deltar = 0 in confined compression. In our study, we further investigated the ability of the transversely isotropic model to describe confined and unconfined stress relaxation behavior of calf cartilage. A series of confined and unconfined stress relaxation tests were performed on calf articular cartilage (4.5 mm diameter, approximately 3.3 mm height) in a displacement-controlled compression apparatus capable of measuring delta(z) and delta(r). In equilibrium, delta(r) > 0 and delta(z) in confined compression was greater than in unconfined compression. Transient data at each strain were fitted by the linear transversely isotropic biphasic model and the material parameters were estimated. Although the model could provide good fits to the unconfined transients, the estimated parameters overpredicted the measured delta(r). Conversely, if the model was constrained to match equilibrium delta(r), the fits were poor. These findings suggest that the linear transversely isotropic biphasic model could not simultaneously describe the observed stress relaxation and equilibrium behavior of calf cartilage.

Animals↗

PubMed1997

A mathematical model of breast and ovarian cancer treated with paclitaxel.

A mathematical model that describes the effects of cell-cycle-specific drugs on cancer and normal tissue is developed. The model takes into account the proliferating cells, which are sensitive to the treatment, and the quiescent cells, which are resistant to the treatment. With the use of information from the medical literature, model parameters are estimated for breast and ovarian cancer as well as for bone marrow. Then, with the use of the model and the estimated parameters, some acceptable treatment strategies are discussed in terms of treatment period, drug-infusion time, and proliferative fraction of cancer mass. Finally, these results are compared with current clinical practices for treatment with Taxol, and possible improvements on current treatment strategies are suggested.

Antineoplastic Agents, Phytogenic↗

PubMed2001

Characterization of preferential flow in undisturbed, structured soil columns using a vertical TDR probe.

Rapid movement of agricultural chemicals through soil to groundwater via preferential flow pathways is one cause of water contamination. Previous studies have shown that time domain reflectometry (TDR) could be used to characterize solute transport in soil. However, previous studies have only scarcely addressed preferential flow. This study presents an extended application of TDR for determining preferential flow properties. A TDR method was tested in carefully controlled laboratory experiments using 20-cm long and 12-cm diameter undisturbed, structured soil columns. The method used a vertically installed TDR probe and a short pulse of tracer application to obtain residual mass (RM) breakthrough curves (BTC). The RM BTC obtained from TDR were used to estimate mobile/immobile model (MIM) parameters that were compared to the parameter estimates from effluent data. A conventional inverse curve fitting method (CXTFIT) was used to estimate parameters. The TDR-determined parameters were then used to generate calculated effluent BTC for comparison with observed effluent BTC for the same soil columns. Time moments of the calculated and observed BTC were calculated to quantitatively evaluate the calculated BTC. Overall, the RM BTC obtained from TDR were similar to the RM BTC obtained from effluent data. The TDR-determined parameters corresponded well to the parameters obtained from the effluent data, although they were not within the 95% confidence intervals. Correlation coefficients between the parameters obtained from TDR and from effluent data for the immobile water fraction (theta im/theta), mass exchange coefficient (alpha), and dispersion coefficient (Dm) were 0.95, 0.95, and 0.99, respectively. For three of the four soil cores, theta im/theta ranged from 0.42 to 0.82, indicating considerable preferential flow. The TDR-calculated effluent BTC also were similar to the observed effluent BTC having an average coefficient of determination of 0.94. Time moments obtained from calculated BTC were representative of those obtained from observed BTC. The vertical TDR probe method was simple and minimally destructive and provided representative preferential flow properties that enabled the characterization of solute transport in soil.

Models, Theoretical↗

PubMed1996

Can the computerized physical examination differentiate normal subjects from abnormal subjects with benign mechanical low back pain?

Inconsistencies among physicians in the evaluation of benign low back conditions make standardization desirable. A computerized physical examination device was used to evaluate low back pain patients and compare their results with a normative database obtained from a selection of healthy subjects. A high-resolution motion analysis system tracked the movement of skin markers placed on the midline and pelvis. Surface electromyography electrodes placed above L(5) collected data from multifidus. From the kinematics of skin markers during flexion extension with lifts up to 32 kg, and lateral bending with lifts up to 4.6 kg, the following parameters were estimated: lumbosacral angle and elongation, contribution of each lumbar segment to the lordosis reduction, relative pelvic/spine motion and trunk velocity. First, the average normal value for each estimated parameter was determined using 40 normal subjects. For each subject, the difference between his parameter and the normal was processed by an expert system generating a normality index varying from zero (perfect abnormal) to one (perfect normal). To develop the expert system's rules, a preliminary group of 20 very abnormal subjects were used, such that the normality index separated them from the normals. For validation, a set of 29 WCB sprain patients and another set of 42 discogram positive were selected. Each subject was tested and his computerized normality index calculated without any clinicians' input. The computerized normality index was compared with the clinicians' evaluation which was taken to be the gold standard. The Receiver Operating Characteristic technique was used to quantify the discrepancies. Results show that the expert system can detect clinically abnormal subjects with accuracy (sensitivity 83-91% and specificity >/=90%) while providing quantitative information on workers' functional capacities.

Journal Article↗

PubMed2003

Mixed discrete and continuous Cox regression model.

The Cox (1972) regression model is extended to include discrete and mixed continuous/discrete failure time data by retaining the multiplicative hazard rate form of the absolutely continuous model. Application of martingale arguments to the regression parameter estimating function show the Breslow(1974) estimator to be consistent and asymptotically Gaussian under this model. A computationally convenient estimator of the variance of the score function can be developed, again using martingale arguments. This estimator reduces to the usual hypergeometric form in the special case of testing equality of several survival curves, and it leads more generally to a convenient consistent variance estimator for the regression parameter. A small simulation study is carried out to study the regression parameter estimator and its variance estimator under the discrete Cox model special case and an application to a bladder cancer recurrence dataset is provided.

Analysis of Variance↗

PubMed1989

Deoxyglucose kinetics in a rat brain tumor.

Accurate quantitation of local glucose metabolic rates (LMRglc) of abnormal tissues such as brain tumors with the 2-deoxyglucose (DG) method requires knowledge of the tissue rate constants and lumped constant. The deoxyglucose rate constants were measured in an experimental intracerebral glioma in 24 awake rats with a dual tracer [(3H)-DG and (14C)-DG] method. Tissue time points were obtained at 2, 5, 10, 18, 30, 60, 90, and 180 min after injection by decapitation and liquid scintillation counting. Blood samples were obtained at 1 min intervals initially and at longer intervals later. The rate constants were estimated with parameter estimation. LMRglc was calculated from the rate constants, assuming a lumped constant of 0.5. K1 for normal cerebrum was found to be 0.258 ml/g/min, and k2-k4 were 0.406, 0.075, and 0.0103 min-1; LMRglc = 65.1 mumol/100 g/min. The corresponding values for the glioma were 0.108, 0.126, 0.040, and 0.0019 with LMRglc = 41.7. The considerably lower k4 in the glioma was reflected in persistent higher activity in the glioma at longer times. Thus, tissue activity alone cannot be used to assess relative glucose metabolic rates in abnormal tissues such as gliomas, particularly at late times after injection.

Animals↗

PubMed2002

Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography.

A method for inverting measurements made on the surfaces of tissues for recovery of interior optical property maps is demonstrated for sparse near-infrared (NIR) fluorescence measurement sets on large tissue-simulating volumes with highly variable signal-to-noise ratio. A Bayesian minimum-variance reconstruction algorithm compensates for the spatial variability in signal-to-noise ratio that must be expected to occur in actual NIR contrast-enhanced diagnostic medical imaging. Image reconstruction is demonstrated by using frequency-domain photon migration measurements on 256-cm(3) tissue-mimicking phantoms containing none, one, or two 1-cm(3) heterogeneities with 50- to 100-fold greater concentration of Indocyanine Green dye over background levels. The spatial parameter estimate of absorption owing to the dye was reconstructed from only 160 to 296 surface measurements of emission light at 830 nm in response to incident 785-nm excitation light modulated at 100 MHz. Measurement error of acquired fluence at fluorescent emission wavelengths is shown to be highly variable. Convergence and quality of image reconstructions are improved by Bayesian conditioning incorporating (i) experimentally determined measurement error variance, (ii) recursively updated estimates of parameter uncertainty, and (iii) dynamic zonation. The results demonstrate that, to employ NIR fluorescence-enhanced optical imaging for large volumes, reconstruction approaches must account for the large range of signal-to-noise ratio associated with the measurements.

Analysis of Variance↗

PubMed2001

A dynamic model to analyse intravenous glucose and insulin tolerance tests performed on dairy cows.

A dynamic model was developed to assess insulin sensitivity and pancreatic response in lactating dairy cows. The model is based on a simultaneous analysis of insulin and glucose intravenous tolerance tests. It comprises five compartments corresponding to insulin in portal-hepatic plasma, and insulin or glucose in both systemic plasma and in interstitial fluid. Insulin secretion rate is a sigmoidal function of glucose in plasma. Insulin is cleared from hepatic plasma and from the interstitial fluid. The glucose entry rate is constant and glucose utilization rate is a sigmoidal function of insulin in the interstitial fluid. Six parameters were estimated: two for insulin secretion rate, two for insulin clearance, one for glucose entry rate and one for glucose utilization rate. After integration of the functions, the model yielded a relative estimate of the quantities of insulin secreted and cleared, as well as the glucose entering and utilized during each test. Using an experimental dataset composed of ten pairs of tolerance tests, the explained variations for plasma insulin and glucose concentrations were 96.0 and 98.3 % and standard errors of estimates were 0.032 nmol/l and 0.14 mmol/l respectively. Except in the early stages after injection, residual errors were low. A Jackknife analysis showed that the estimated parameters exhibited low statistical bias. This model simplifies the interpretation of both tests through a simulation based on six common parameters. Compared to a classical analysis of tolerance tests, it may improve the analysis of modifications in the key functions regulating glucose homeostasis in ruminants.

Animals↗

PubMed1988

A mark-recapture method for ecological studies of schistosomiasis vector snail populations.

Mark-recapture methods have been used only sporadically in studies of the population biology of the snail vectors of schistosomiasis, yet mark-recapture has potential advantages for obtaining estimates of absolute abundance and recruitment and loss rates for snail populations in the field. A case study is described that uses Bailey's triple catch design to estimate these parameters for Bulinus globosus and Biomphalaria pfeifferi in a small river in Zimbabwe. The assumptions inherent in the design and tests of these assumptions are described. The parameter estimates obtained are biologically plausible, suggesting significant recruitment into the population at the time of the study and a life expectancy for B. globosus of about three weeks. The major drawback is the lack of precision of these estimates. Means of improving precision are discussed, and mark-recapture is evaluated as a research tool for the study of vector snail population biology.

Animals↗

PubMed2005

The sensitivity and specificity of markers for event times.

The statistical literature on assessing the accuracy of risk factors or disease markers as diagnostic tests deals almost exclusively with settings where the test, Y, is measured concurrently with disease status D. In practice, however, disease status may vary over time and there is often a time lag between when the marker is measured and the occurrence of disease. One example concerns the Framingham risk score (FR-score) as a marker for the future risk of cardiovascular events, events that occur after the score is ascertained. To evaluate such a marker, one needs to take the time lag into account since the predictive accuracy may be higher when the marker is measured closer to the time of disease occurrence. We therefore consider inference for sensitivity and specificity functions that are defined as functions of time. Semiparametric regression models are proposed. Data from a cohort study are used to estimate model parameters. One issue that arises in practice is that event times may be censored. In this research, we extend in several respects the work by Leisenring et al. (1997) that dealt only with parametric models for binary tests and uncensored data. We propose semiparametric models that accommodate continuous tests and censoring. Asymptotic distribution theory for parameter estimates is developed and procedures for making statistical inference are evaluated with simulation studies. We illustrate our methods with data from the Cardiovascular Health Study, relating the FR-score measured at enrollment to subsequent risk of cardiovascular events.

Aged↗

PubMed2003

New explicit expressions for relative frequencies of single-nucleotide polymorphisms with application to statistical inference on population growth.

We present new methodology for calculating sampling distributions of single-nucleotide polymorphism (SNP) frequencies in populations with time-varying size. Our approach is based on deriving analytical expressions for frequencies of SNPs. Analytical expressions allow for computations that are faster and more accurate than Monte Carlo simulations. In contrast to other articles showing analytical formulas for frequencies of SNPs, we derive expressions that contain coefficients that do not explode when the genealogy size increases. We also provide analytical formulas to describe the way in which the ascertainment procedure modifies SNP distributions. Using our methods, we study the power to test the hypothesis of exponential population expansion vs. the hypothesis of evolution with constant population size. We also analyze some of the available SNP data and we compare our results of demographic parameters estimation to those obtained in previous studies in population genetics. The analyzed data seem consistent with the hypothesis of past population growth of modern humans. The analysis of the data also shows a very strong sensitivity of estimated demographic parameters to changes of the model of the ascertainment procedure.

Data Interpretation, Statistical↗

PubMed1992

Poisson sampling-based inference for single ion channel data with time interval omission.

Patch-clamp recording allows investigations of the gating kinetics of single ion channels. Statistical analysis of kinetic data can enhance our understanding of channel gating at a molecular level. Experimental channel records suffer from time interval omission, i.e. failure to detect brief channel openings and closings. It is important to incorporate this phenomenon into statistical analyses of ion channel data. When time interval omission is ignored, the method of maximum likelihood can usually be used to estimate gating parameters from a single channel record. However, it is far more difficult to apply this method when time interval omission is incorporated. We present an alternative approach to parameter estimation based on Poisson sampling. A simulated homogeneous Poisson process is superimposed onto the channel record and inference is based on the numbers of points in successive open and closed sojourns, rather than on the sojourn times themselves. We describe the method for the two-state Markov model C<-->O, although it is applicable to more general models. Computer-simulated data are used to demonstrate the efficacy of the method. Modifications of the method are discussed briefly.

Animals↗

PubMed1989

Modified asymmetric T-tube model to infer arterial wave reflection at the aortic root.

A modified version of the T-tube model was constructed to represent the systemic arterial loading system as "seen" by the left ventricle (LV). This model consisted of two uniform tubes connected in parallel. It differs from the original T-tube model in that the transmission paths have no frictional losses and are terminated with complex impedances, rather than simple resistors. To estimate model parameters (load and tube compliances, tube inertances, characteristic impedances, and peripheral resistances) we measured ascending aortic pressure and flow in a group of five open-chest, anesthetized dogs. Parameter estimates were obtained by fitting experimental pressure to the pressure predicted by the model from experimental flow. To check the reliability of the model, an additional experiment was performed where flow in the upper descending thoracic aorta was measured in addition to ascending aorta pressure and flow. The fit between the experiment and model predicted ascending aortic pressure was satisfactory in all six dogs. This pressure was always characterized by the presence of a prominent diastolic oscillation. Our model showed that this oscillation is due to reflections from the lower body, the effective reflection site being most probably located at the level of middle to low abdominal aorta. The effective reflection site located in the upper body is closer to the heart. The related reflected wave affects pressure in late systole.

Analog-Digital Conversion↗

PubMed2001

Tissue characterization using the continuous wavelet transform. Part I: Decomposition method.

In this paper, a novel decomposition of the RF ultrasound signal into its coherent and diffused components is proposed. This decomposition is based on thresholding the energy of the continuous wavelet transform of the RF signal using appropriate wavelets. The two components are modeled separately, and the model parameters are estimated. Previous work [1] required assumptions about the periodicity of the coherent scatterers in the tissue. These assumptions are not necessary in this work. The decomposition algorithm is tested on simulated RF images. The accuracy of the estimated parameters is presented as well as the performance of the algorithm in low coherent-to-diffuse components' energy ratios (SNR).

Algorithms↗

PubMed2003

A unifying framework for partial volume segmentation of brain MR images.

Accurate brain tissue segmentation by intensity-based voxel classification of magnetic resonance (MR) images is complicated by partial volume (PV) voxels that contain a mixture of two or more tissue types. In this paper, we present a statistical framework for PV segmentation that encompasses and extends existing techniques. We start from a commonly used parametric statistical image model in which each voxel belongs to one single tissue type, and introduce an additional downsampling step that causes partial voluming along the borders between tissues. An expectation-maximization approach is used to simultaneously estimate the parameters of the resulting model and perform a PV classification. We present results on well-chosen simulated images and on real MR images of the brain, and demonstrate that the use of appropriate spatial prior knowledge not only improves the classifications, but is often indispensable for robust parameter estimation as well. We conclude that general robust PV segmentation of MR brain images requires statistical models that describe the spatial distribution of brain tissues more accurately than currently available models.

Algorithms↗