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PubMed1980

A program library for computing the parameters of linear compartment models in pharmacokinetics.

A program library is presented with which explicit solutions of linear compartment models can be fitted to pharmacokinetic experimental data. Use is made of the fact that transport constants can be calculated from the numberical solution of such a problem without ambiguity. The non-linear regression is carried out using the Powell-method. A report of our experience with, e.g. choice of objective function, lag-time, accuracy of the numerical solution is included.

Computers↗

PubMed2003

Methods for quasi-linear viscoelastic modeling of soft tissue: application to incremental stress-relaxation experiments.

The quasi-linear viscoelastic (QLV) model was applied to incremental stress-relaxation tests and an expression for the stress was derived for each step. This expression was used to compare two methods for normalizing stress data prior to estimating QLV parameters. The first and commonly used normalization method was shown to be strain-dependent. Thus, a second normalization method was proposed and shown to be strain-independent and more sensitive to QLV time constants. These analytical results agreed with representative tendon data. Therefore, this method for normalizing stress data was proposed for future studies of incremental stress-relaxation, or whenever comparing stress-relaxation at different strains.

Animals↗

PubMed2002

Generalised linear accident models and goodness of fit testing.

This paper has two aims. The primary aim is to provide a practical resolution of the low mean value' problem, a barrier to goodness of fit testing for the commonly used generalised linear accident model. A secondary aim of the paper is to describe the underlying mechanism of these models, so making them fully accessible to the transport modeller.

Accidents, Traffic↗

PubMed1993

Late radiation induced laryngeal oedema in the treatment of vocal cord cancer: analysis using the linear quadratic model.

The incidence of late complications for different size of dose per fraction is analysed in 208 cases with squamous cell carcinoma of the vocal cord. The series comprised 156 cases with T1 and 52 cases with T2 lesions. Radical radiotherapy was given with three different regimens having dose per fraction as 3.33, 2.5 and 2.25 Gy. There were 46 cases with persisting radiation induced laryngeal oedema. Using two different statistical methods, an alpha/beta value of 2.38 Gy of linear quadratic model was estimated for late complications of vocal cord. The analysis indicate the increased incidence of late complications with size of dose per fraction. Relevance of linear quadratic model for the prediction of late complication is demonstrated in the present study.

Carcinoma, Squamous Cell↗

PubMed2005

Models to explain fatigue during prolonged endurance cycling.

Much of the previous research into understanding fatigue during prolonged cycling has found that cycling performance may be limited by numerous physiological, biomechanical, environmental, mechanical and psychological factors. From over 2000 manuscripts addressing the topic of fatigue, a number of diverse cause-and-effect models have been developed. These include the following models: (i) cardiovascular/anaerobic; (ii) energy supply/energy depletion; (iii) neuromuscular fatigue; (iv) muscle trauma; (v) biomechanical; (vi) thermoregulatory; (vii) psychological/motivational; and (viii) central governor. More recently, however, a complex systems model of fatigue has been proposed, whereby these aforementioned linear models provide afferent feedback that is integrated by a central governor into our unconscious perception of fatigue. This review outlines the more conventional linear models of fatigue and addresses specifically how these may influence the development of fatigue during cycling. The review concludes by showing how these linear models of fatigue might be integrated into a more recently proposed nonlinear complex systems model of exercise-induced fatigue.

Bicycling↗

PubMed2004

Application of the linear-quadratic model to combined modality radiotherapy.

PURPOSE: Methods of performing dosimetry for a combined modality radiotherapy (CMRT) consisting of a targeted radionuclide therapy (TRT) and separately delivered external beam therapy (EBT) have been established using the biologically effective dose (BED). However, a concurrent delivery of the two therapies may influence the radiobiologic effect of the treatment resulting from interaction between the therapies, and this situation has been modeled to assess the likely consequences of this regime. METHODS AND MATERIALS: A general form of the linear-quadratic model with a dose protraction factor was applied to concurrent delivery of EBT and TRT. Contributions to total BED from intra- and intermodality effects were calculated, and parameter values varied to determine conditions under which the intermodality contributions were likely to be most significant. A Poisson model of tumor control probability (TCP) was used to assess the predicted effect of concurrent delivery on treatment outcome. RESULTS: In general, over a wide range of parameter values, the effect of intermodality interactions in CMRT is small, increasing total BED delivered to tumor by approximately 1%, and producing a negligible increase in TCP. Synergistic effects could be greater in normal tissues if high doses were received from both therapies, with intermodality terms increasing total BED delivered by approximately 6% in the general case, and by approximately 18% for the case of slow repair in the spinal cord. A significant synergistic effect was predicted between EBT and I-125 seed therapy of the prostate when values of alpha/beta = 1.2 Gy, alpha = 0.026 Gy, mu = 0.36 h(-1) and N(0) = 138 clonogens were used, with TCP increasing from approximately 0.5 to 0.6. CONCLUSIONS: Under most clinical conditions, the relative temporal delivery of these two therapies is unlikely to significantly influence the overall radiobiologic effect to tumor at the cellular level. Synergistic effects may, however, be more significant in normal tissues and for tumors with low values of alpha/beta and alpha.

Combined Modality Therapy↗

PubMed2006

A nanodosimetry-based linear-quadratic model of cell survival for mixed-LET radiations.

A new nanodosimetry-based linear-quadratic (LQ) model of cell survival for mixed-LET radiations has been developed. The new model employs three physical quantities and three biological quantities. The three physical quantities are related to energy depositions at two nanometre scales, 5 nm and 25 nm. The three biological quantities are related to the lesion production and interaction probabilities and the lesion repair rate. The coefficients alpha and beta of the LQ formula (alpha D + beta D(2)) are explicitly expressed in terms of the three physical quantities and the three biological quantities. The new model is shown to be consistent with the previously published cell survival curves of V-79 cells. The advantage of this new model is that it can be conveniently adopted to estimate the iso-effect for radiotherapies that involve ionizing radiation of mixed LET. An example is given to estimate the cell survival fractions for a high-dose-rate mixed neutron and gamma-ray field from a (252)Cf source.

Animals↗

PubMed1991

Multiple linear regression modeling of furosemide renal clearance and urinary excretion rate.

Multiple linear regression techniques were utilized to determine models for the renal clearance and urinary excretion rate of furosemide. Models for the renal clearance were formulated based on data collected from the literature. The best model predicted that the weight-normalized renal clearance was a function of the weight-normalized creatinine clearance, with coefficient values dependent on the presence or absence of heart, liver, and/or kidney failure. The predictive performance of this model was evaluated using a separate verification data set, and, prospectively, for a group of cardiac patients. The urinary excretion rate of furosemide is the primary determinate of response. Models for the furosemide excretion rate were formulated from data collected prospectively from a group of patients with cardiac disease. The best model predicted that the dose-normalized morning urinary excretion rate was a function of the blood urea nitrogen concentration (BUN), with modifications for the presence of liver failure and/or decompensated heart failure. The oral dosage required to produce a clinically optimal furosemide excretion rate in cardiac patients without liver disease was dose (mg) = 42.1/(0.925-0.0151 BUN).

Aged↗

PubMed1980

Estimation, resolution and solvability of linear compartmental models: cholesterol metabolism in man.

The paper presents a method to test metabolic linear multicompartment models for their mathematical solvability and their power of resolution with respect to individual parameters. The method can be seen as a means of predicting not only the model theoretical identifiability but also the expected quality of estimation before undertaking any actual serial experiments. The compartmental model of human cholesterol metabolism is taken as a demonstrative problem. The analysis shows that it is possible with tracer techniques to measure the cholesterol turnover, the cholesterol fluxes between exchangeable cholesterol pools, the cholesterol masses in individual pools, and the endogenous cholesterol synthesis in individual pools if certain conditions are met. In any complex kinetic situation, performance of a systematic model analysis is recommended before embarking on large-scale experimentation.

Body Fluid Compartments↗

PubMed2003

Linear Glauber model.

We study the time-dependent and the stationary properties of the linear Glauber model in a d-dimensional hypercubic lattice. This model is equivalent to the voter model with noise. By using the Green function method, we get exact results for the two-point correlations from which the critical behavior is obtained. For vanishing noise the model becomes critical with exponents beta=0, gamma=1, and nu=1/2 for d > or =2, with logarithmic corrections at the upper critical dimension d(c)=2, and beta=0, gamma=1/2, and nu=1/2 for d=1. We show that the model can be mapped into a particular reaction-diffusion model.

Journal Article↗

PubMed1997

Linear mixed models with heterogeneous within-cluster variances.

This paper describes an extension of linear mixed models to allow for heterogeneous within-cluster variances in the analysis of clustered data. Unbiased estimating equations based on quasilikelihood/pseudolikelihood and method of moments are introduced and are shown to give consistent estimators of the regression coefficients, variance components, and heterogeneity parameter under regularity conditions. Cluster-specific random effects and variances are predicted by the posterior modes. The method is illustrated through an analysis of menstrual diary data and its properties are evaluated in a simulation study.

Adolescent↗

PubMed1995

Cell loss factors and the linear-quadratic model.

A method is described for incorporating a variable cell loss factor (phi) within the linear-quadratic (LQ) model. By allowing for a progressive reduction in phi as treatment progresses, the revised model behaves in a way which is consistent with the apparent presence of accelerated tumour repopulation during fractionated radiotherapy. Predictions based on a slowing of the cell loss process, rather than a true increase in clonogen proliferation rate, are consistent with the phenomenon of 'unmasking' of potential doubling time described by Fowler (Fowler, J.F. Rapid repopulation in radiotherapy: a debate on mechanism. Radiother Oncol 24: 125, 1992). An optional time delay factor may be included, to allow for the fact that progressive reduction in cell loss may not begin until part of the treatment has been delivered. The model provides a description of the manner in which tumour control doses are likely to increase as overall treatment time is increased.

Cell Death↗

PubMed1990

The analysis of assortative mating: a LISREL model.

The use of linear models to discriminate between primary and secondary assortative mating has allowed a significant advance in our understanding of the mate selection process. We describe how these methods may be implemented in the LISREL and COSAN packages and illustrate the method with data on cognitive ability, education, and personality reported by Phillips et al. (Behav. Genet. 18:347-356, 1988). Issues discussed include the interface between path diagrams and computer program specification, the near-independence of parameters for within-person correlations from parameters for marital correlations, and the fact that almost all of marital resemblance for IQ seems to be due to assortative mating for educational level.

Analysis of Variance↗

PubMed2001

Hysteresivity of the lung and tissue strip in the normal rat: effects of heterogeneities.

We measured lung impedance in rats in closed chest (CC), open chest (OC), and isolated lungs (IL) at four transpulmonary pressures with a optimal ventilator waveform. Data were analyzed with an homogeneous linear or an inhomogeneous linear model. Both models include tissue damping and elastance and airway inertance. The homogeneous linear model includes airway resistance (Raw), whereas the inhomogeneous linear model has a continuous distribution of Raw characterized by the mean Raw and the standard deviation of Raw (SDR). Lung mechanics were compared with tissue strip mechanics at frequencies and operating stresses comparable to those during lung impedance measurements. The hysteresivity (eta) was calculated as tissue damping/elastance. We found that 1) airway and tissue parameters were different in the IL than in the CC and OC conditions; 2) SDR was lowest in the IL; and 3) eta in IL at low transpulmonary pressure was similar to eta in the tissue strip. We conclude that eta is primarily determined by lung connective tissue, and its elevated estimates from impedance data in the CC and OC conditions are a consequence of compartment-like heterogeneity being greater in CC and OC conditions than in the IL.

Airway Resistance↗

PubMed2001

A noninvasive estimation of hypernasality using a linear predictive model.

The pronunciation of a speaker with a defective soft palate is marked by hypernasality and an operation may be necessary to repair the defective soft palate to reduce this hypernasality. An assessment of hypernasality is necessary to quantify the effect of the surgery. The current clinical methods for assessing hypernasality are uncomfortable or require expensive equipment. In this paper, a new quantitative method is proposed to estimate hypernasality. This method requires only a microphone and a personal computer equipped with a sound card. Zeros in the frequency response of the vocal tract system are one of the major characteristics of hypernasality. The proposed method made use of the fact that a linear predictive model with a typical order for the human vocal tract system is not accurate when the vocal tract system has zeros in its frequency response. Hypernasality was estimated by comparing the distance between the sequences of linear predictive cepstrum of low- and high-order linear predictive models. The proposed method provides a better correlation (0.58) with nasalance measured by a nasometer than Teager method (0.44) for all the data. Furthermore, the proposed method showed higher correlation of 0.84 than 0.71 of the Teager method for data with a nasalance higher than 35%. Since the proposed method needs only digitized speech data, it is much less invasive and provides an easy and cost-effective evaluation of hypernasality.

Biomedical Engineering↗

PubMed2004

Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency.

Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often called the anomalous attenuation. In this study, a linear integro-differential equation wave model was developed for the anomalous attenuation by using the space-fractional Laplacian operation, and the strategy is then extended to the nonlinear Burgers equation. A new definition of the fractional Laplacian is also introduced which naturally includes the boundary conditions and has inherent regularization to ease the hypersingularity in the conventional fractional Laplacian. Under the Szabo's smallness approximation, where attenuation is assumed to be much smaller than the wave number, the linear model is found consistent with arbitrary frequency power-law dependency.

Acoustics↗

PubMed2001

Meta-analysis using linear mixed models.

Psychologists often use special computer programs to perform meta-analysis. Until recently, this had been necessary because standard statistical packages did not provide procedures for such analysis. This paper introduces linear mixed models as a framework for meta-analysis in psychological research, using a popular general purpose statistical package, SAS. The approach is illustrated with three examples, using SAS PROC MIXED.

Humans↗

PubMed1998

Marginal versus conditional versus 'structural source' models: a rationale for an alternative to log-linear methods for capture-recapture estimates.

Log-linear models for capture-recapture type data are widely used for estimating sizes of populations. Log-linear methods model conditional interactions between the sources. Often, however, the marginal associations are more appropriate and easier for the practitioner to conceptualize. Analyses here of previously published data on cases of spina bifida in upstate New York are used to show how the assumption that sources are conditionally independent can give biased estimates if in fact the sources are marginally independent. A plausible model for the structural sources of interactions between the sources of information about spina bifida cases is developed which implies marginal independence of two of the sources rather than conditional independence. Estimates of the population total based on marginal independence are derived and give larger estimates of the population total than those derived based upon conditional dependence. When investigators can in fact model the likely underlying relationships of the sources in the population, we suggest considering modelling the potential interdependencies of the sources, which we term 'structural source modeling'.

Birth Certificates↗