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PubMed1992

Assessment of a model for overall left ventricular three-dimensional motion from MRI data.

In this paper we present a complete methodology to evaluate a model for overall three-dimensional (3D) motion of the human left ventricle (LV) from MRI data. The left ventricular motion is approximated by a linear model associated with an affine transformation to determine parameters for non-rigid motion of the LV. The proposed method has been applied to a normal patient and to a patient with cardiac disease. Results obtained show that the linear model provides a fairly good approximation of normal left ventricular motion, whereas serious cardiac disease produces abnormal motion, yielding altered model performances.

Heart Diseases↗
PubMedDate not supplied

Prediction of C60 solubilities from solvent molecular structures.

Models predicting fullerene solubility in 96 solvents at 298 K were developed using multiple linear regression and feed-forward computational neural networks (CNN). The data set consisted of a diverse set of solvents with solubilities ranging from -3.00 to 2.12 log (solubility) where solubility = (1 x 10(4))(mole fraction of C60 in saturated solution). Each solvent was represented by calculated molecular structure descriptors. A pool of the best linear models, as determined by rms error, was developed, and a CNN model was developed for each of the linear models. The best CNN model was chosen based on the lowest value of a specified cost function and had an architecture of 9-3-1. The 76-compound training set for this model had a root-mean-square error of 0.255 log solubility units, while the 10-compound cross-validation set had an rms error of 0.253. The 10-compound external prediction set had an rms error of 0.346 log solubility units.

Journal Article↗
PubMedDate not supplied

Nonlinear systems in medicine.

Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.

Cytokines↗
PubMed2004

A new approach to the solution of the linear mixing model for a single isotope: application to the case of an opportunistic predator.

Mixing models are used to determine diets where the number of prey items are greater than one, however, the limitation of the linear mixing method is the lack of a unique solution when the number of potential sources is greater than the number (n) of isotopic signatures +1. Using the IsoSource program all possible combinations of each source contribution (0-100%) in preselected small increments can be examined and a range of values produced for each sample analysed. We propose the use of a Moore Penrose (M-P) pseudoinverse, which involves the inverse of a 2x2 matrix. This is easily generalized to the case of a single isotope with (p) prey sources and produces a specific solution. The Antarctic leopard seal (Hydrurga leptonyx) was used as a model species to test this method. This seal is an opportunistic predator, which preys on a wide range of species including seals, penguins, fish and krill. The M-P method was used to determine the contribution to diet from each of the four prey types based on blood and fur samples collected over three consecutive austral summers. The advantage of the M-P method was the production of a vector of fractions f for each predator isotopic value, allowing us to identify the relative variation in dietary proportions. Comparison of the calculated fractions from this method with 'means' from IsoSource allowed confidence in the new approach for the case of a single isotope, N.

Animals↗
PubMed1994

Pulsatile growth pattern during catch-up growth in childhood coeliac disease.

Catch-up growth in coeliac disease was thought to be a continuous process and hence linear models have been proposed to interpret the pattern of catch-up growth. Observed longitudinal data do not fit a linear model adequately. The aim of this study is to clarify the pattern of short-term catch-up growth in coeliac patients. Twenty-one coeliac children (aged 6-24 months) entered the study and were monitored at short-time intervals. All showed a "pulsatile" pattern of growth velocity for height, weight, leg length, subscapular and triceps skinfolds. Peaks alternated with troughs at a mean time of 62 days for the whole set of measurements. The periodicity was remarkably stable. The size of the peaks decreased with time on a gluten-free diet. Catch-up growth is a discontinuous process made up of a sequence of bursts of growth followed by a resting phase. This provides strong evidence for the possibility that short-term growth may be pulsatile.

Body Height↗
PubMed1998

Trends in reported incidence of primary malignant brain tumors in children in the United States.

BACKGROUND: The reported incidence of primary malignant brain tumors among children in the United States increased by 35% during the period from 1973 through 1994. The purpose of our study was twofold: 1) to determine whether the reported incidence rates for this period are better represented by a linear increase over the entire period ("linear model") or, alternatively, by a step function, with a lower rate in the years preceding 1984-1985 and a constant higher rate afterward ("jump model"); and 2) to identify the specific brain regions and histologic subtypes that have increased in incidence. METHODS: Incidence data from the Surveillance, Epidemiology, and End Results Program of the National Cancer Institute for the period from 1973 through 1994 for primary malignant brain tumors in children were used to model the number of cases in a year as a random variable from a Poisson distribution by use of either a linear model or a jump model. RESULTS/CONCLUSIONS: The increase in reported incidence of childhood primary malignant brain tumors is best explained by the jump model, with a step increase in incidence occurring in the mid-1980s. The brain stem and the cerebrum are the primary sites for which an increase in tumor incidence has been reported. The increase in reported incidence of low-grade gliomas in the cerebrum and the brain stem (unaccompanied by an increase in mortality for these sites) supports the substantial contribution of low-grade gliomas to the overall increase in reported incidence for childhood brain tumors. IMPLICATIONS: The significantly better fit of the data to a jump model supports the hypothesis that the observed increase in incidence somehow resulted from changes in detection and/or reporting of childhood primary malignant brain tumors during the mid-1980s.

Adolescent↗
PubMed1994

Application of the linear-quadratic model to radioimmunotherapy: further support for the advantage of longer-lived radionuclides.

UNLABELLED: Radioimmunotherapy (RIT), as it is currently practiced, delivers low doses to tumors primarily because of dose-limiting bone marrow toxicity. The biologic effectiveness of RIT depends on the total dose, dose rate and the fractionation schedule of the radiolabeled antibodies administered. METHODS: An approach based on the linear-quadratic (LQ) model, which is currently used in conventional radiotherapy, is advanced for treatment planning in RIT. This approach incorporates repair rates, radiosensitivity of the tissues, biologic half-lives of the antibodies, physical half-lives of the radionuclides, dose rates and total doses needed for a given biologically effective dose. The concept of a relative advantage factor (RAF) is introduced to quantify the therapeutic gain that can be realized by using longer-lived radionuclides instead of the shorter-lived counterparts currently in use. RESULTS: RAFs are calculated for different biologic and physical half-lives, and values as high as 3 to 5 can be attained when longer-lived radionuclides are used. The RAFs predicted by the LQ model reaffirm the authors' earlier conclusion based on the time-dose-fractionation approach that relatively long-lived radionuclides coupled to monoclonal antibodies are indeed more likely to deliver therapeutically effective doses to tumors. Several radionuclides are evaluated in this context. CONCLUSION: The authors maintain that 32P is the most promising isotope and the optimal physical half-life is about two to three times the biologic clearance half-life of the antibodies in the tumor.

Brachytherapy↗
PubMed2006

In vitro biosorption of ochratoxin A on the yeast industry by-products: comparison of isotherm models.

Biosorption of ochratoxin A (OA) onto yeast biomass appears to be a reasonably low cost decontamination method. In vitro adsorption of OA onto three yeast industry by-products: a vinasse containing yeast cell walls (EX16), a purified yeast beta-glucan (BETA) and a yeast cell wall fraction (LEC) was examined at 25 degrees C. Seven classical adsorption models were tested to provide the best description of toxin adsorption. A comparison of these models was performed using the magnitude of the coefficient of determination R(2) for the linear models and the value of the sum of normalised errors (SNE) for linear and non-linear models. Based on the R(2) and the SNE values, Hill, Freundlich and Brunauer-Emmett-Teller equations produced the best models for OA biosorption onto respectively, EX16, BETA and LEC. For these best models, the values of isotherm constants were consistent when measured using both linear and non-linear calculations. The SNE calculation procedure presented in this paper in association with the linear equation analysis method is an appropriate approach for designing a better adsorption isothermal model.

Adsorption↗
PubMed2006

Case-parent triads: estimating single- and double-dose effects of fetal and maternal disease gene haplotypes.

Case-parent triad data are considered a robust basis for studying association between variants of a gene and a disease. Methods evaluating statistical significance of association, like the TDT-test and its extensions, are frequently used. When there are prior hypotheses of a causal effect of the gene under study, however, methods measuring penetrance of alleles or haplotypes as relative risks will be more informative. Log-linear models have been proposed as a flexible tool for such relative risk estimation. We demonstrate an extension of the log-linear model to a natural framework for also estimating effects of multiple alleles or haplotypes, incorporating both single- and double-dose effects. The model also incorporates effects of single- and double-dose maternal haplotypes on a fetus during pregnancy. Unknown phase of haplotypes as well as missing parents are accounted for by the EM algorithm. A number of numerical improvements to maximum likelihood estimation are also implemented to facilitate a larger number of haplotypes. Software for these analyses, HAPLIN, is publicly available through our web site. As an illustration we have re-analyzed data on the MSX1 homeobox-gene on chromosome 4 to show how haplotypes may influence the risk of oral clefts.

Cleft Lip↗
PubMed2003

Evaluating dissolution profiles of an anti-HIV agent using ANOVA and non-linear regression models in JMP software.

A powerful statistical method was designed using JMP software to detect factors contributing to differences in the dissolution process of an antiviral drug delivered in an oral dosage form. Due to the large number of dissolution media available for solid dosage forms, a statistical method to choose the appropriate medium is critical for testing solid dosage forms. We have developed an analysis of variance model to analyze the overall dissolution profile obtained from the various media. In vitro tests were performed using a standard USP basket apparatus (Vankel Inc., Cary, NC), and the analysis used the restricted/residual maximum likelihood method (JMP software) to partition the variance due to media (pH 1.2 and 6.8, +SDS, water alone and at pH 1.2 with pepsin), time (repeated measure) and capsule (random effect). This allowed correct standard error estimates to be used to compare dissolution in different media using planned linear contrasts. The model provided us with statistically powerful criteria to identify significant differences in capsule dissolution across time and to quantify capsule-to-capsule population variance estimate. The time specific linear contrasts showed the largest sum of square values (SS) occurred at 180 min (SS=0.268) for the simulated SIF (pH 6.8) versus SGF (pH 1.2) comparison (DF=166, MSE=3.92 x 10(-3)). The dissolution processes were further characterized using a non-linear regression fit of a power law function to the data for each capsule. This resulted in a method to statistically differentiate between the dissolution processes of the capsules in different media.

Analysis of Variance↗
PubMedDate not supplied

[Use of regression analysis in the study of the association between different mercury exposure routes and some functional variables].

AIMS: The "Mercury Multicentric Project" data-set was analysed with the aim to identify a group of biological variables associated with different types of Hg exposure (occupational exposure, fish dietary intake, exposure due to amalgam restorations). The distribution of socio-demographic, biological and surrogate outcome variables was rather different among the collaborating Units. METHODS: Mixed linear models (MLM) were used to overcome the problems related to the heterogeneity of variances among Units. MLM are a generalization of the standard linear models, the generalization being that the data are permitted to exhibit correlation and non constant variability. MLM therefore provide with the flexibility of modelling not only the means of the dependent variable, but also their variances and co-variances as well. This allows to represent the total variability of the dependent variable as a sum of two components: the first attributable to the Units and the other one to the random error. RESULTS AND CONCLUSIONS: A set of biological variables significantly associated with at least one of the Hg exposure variables or with the HgU/creatinine ratio (as surrogate variable for Hg exposure) was identified by means of MLM. This set includes beta 2-MG, sIL8, CD4+, sPRL, FT dominant, BAMT, and some variables related to neurological behaviour. An extension of this analysis will be performed with a structural equations approach in order to study the dose-response relationships among the various variables according to a hierarchical path defined on biological basis. One of the possible simplified general models including all the selected variables is described.

Adult↗
PubMed2003

Volume and flow dependence of respiratory mechanics in mechanically ventilated COPD patients.

Volume and flow dependencies of respiratory mechanics are examined in 10 COPD patients under mechanical ventilation (MV) at 3 levels of externally applied PEEP (PEEPe). Airways pressure (Paw), flow (V') and volume (V) data are analyzed according to (1) the linear and (2) a non-linear model, accounting for volume dependence of elastance and for flow and volume dependence of resistance. The models' fitness to data is assessed by the regression errors. Non-linear modelling fits significantly better to data, while the difference of fitness decreases with PEEPe. Linear mechanics are not significantly different between the 3 levels of PEEPe. A positive volume dependence of elastance observed at 0, decreases at 5 and increases again at 10 hPa of PEEPe. A seriously negative volume dependence of resistance at 0 turned to positive with PEEPe. These dependencies of respiratory mechanics during COPD under MV, show that the present non-linear respiratory mechanical monitoring may help for better and less risky adjustment of PEEPe.

Female↗
PubMed2000

Standardized mortality ratio and life expectancy: a comparative study of Chinese mortality.

BACKGROUND: Various models have been proposed for rapid conversion of the standardized mortality ratio (SMR) to life expectancy using data from developed countries. METHODS: We compared two methods for converting the SMR to life expectancy using mortality data from the largest developing country, China. RESULTS: The first model, using the Gompertz function, does not provide a good fit to the life expectancy and SMR of China. The regression lines derived from the second, a log-linear model using parameters estimated from the US white population are not a good fit to Chinese males and older females. However, if the parameters in the log-linear model are estimated using Chinese mortality data, the resultant regression lines fit the data reasonably well. CONCLUSION: The relationship between life expectancy and SMR based on mortality data from developed countries may not be valid for developing countries. Based on our empirical study, separate estimates of the coefficients of the model are required for developing countries.

Adult↗
PubMedDate not supplied

Concussions in college football. A multivariate analysis.

The purpose of this investigation was to examine risk patterns of concussion in college football. Multivariate models were used to interpret the data. Specifically, log-linear modeling and analysis techniques were incorporated into the investigation. An average of 49 college teams were studied over the 8 year period 1975 to 1982. This represented over 36,000 athlete-seasons and 395 team-seasons. The data selected were limited to 1,005 game-related concussions. The general hypotheses tested were the null hypothesis that the variables of team (offense and defense), player position, situation (rushing and passing), and activity (block and tackle) had no effect on the occurrence of these game-related concussions. It was found that concussions were a persistent and regular but relatively infrequent type of injury in college football. Concussions accounted for 75% of the total number of injuries on or about the head. The injuries were examined relative to player position, situation, and activity using a log-linear modeling technique, with interactions among the variables also established. The contribution of each variable was not always equal or completely interactive. Generally, the highest risk of concussion was associated with offensive and defensive players involved in a block on a rushing play. Specifically, running backs demonstrated the highest risk of concussion, regardless of activity. The lowest risk was for offensive linemen and quarterbacks while blocking on any type of play. On defense, the secondary exhibited the highest risk of concussion while being blocked on a running play. Similarly, linemen experienced their greatest risk while being blocked on plays run inside the tackle.(ABSTRACT TRUNCATED AT 250 WORDS)

Analysis of Variance↗
PubMed2002

Linear mechanistic models for the dorsal lateral geniculate nucleus of cat probed using drifting-grating stimuli.

Experiments with sinusoidal visual stimuli in the early visual pathway have traditionally been interpreted in terms of descriptive filter models. We present an alternative mechanistic approach for interpretation of this type of data recorded from X cells in the dorsal lateral geniculate nucleus (dLGN) of cat. A general, linear, rate-based mathematical expression for the geniculate transfer ratio, i.e. the ratio between the first-harmonic components of the output of a geniculate relay cell and its retinal input, is derived. In linear theory this ratio is independent of the signal processing occurring at the retinal level. Further, the ratio is straightforwardly accessible in experiments due to the presence of S-potentials, representing the retinal input, in extracellular recordings from dLGN. The expression accounts for feedforward inputs from retina and intrageniculate interneurons as well as feedback inputs from cortex and the thalamic reticular nucleus and can be used to experimentally test different mechanistic models for the geniculate circuitry. Two examples of this are considered: a purely feedforward model incorporating relay cell inputs from retinal ganglion cells and interneurons, and a model including cortical feedback inhibition of relay cells via intrageniculate interneurons.

Animals↗
PubMed2003

X-linked and lineage-dependent inheritance of coping responses to stress.

Coping-or how one routinely deals with stress-is a complex behavioral trait with bearing on chronic disease and susceptibility to psychiatric disorders. This complexity is a result of not only underlying multigenic factors, but also important non-genetic ones. The defensive burying (DB) test, although originally developed as a test of anxiety, can accurately measure differences in coping strategies by assaying an animal's behavioral response to an immediate threat with ethological validity. Using offspring derived from reciprocal crosses of two inbred rat strains differing in DB behaviors, we provide convergent phenotypic and genotypic evidence that coping styles are inherited in an X-linked fashion. We find that first-generation (F(1)) males, but not females, show maternally derived coping styles, and second-generation (F(2)) females, but not males, show significant differences in coping styles when separated by grandmaternal lineage. By using a linear modeling approach to account for covariate effects (sex and lineage) in QTL analysis, we map three quantitative trait loci (QTL) on the X Chromosome (Chr) ( Coping-1, Approach-1, and Approach-2) associated with coping behaviors in the DB paradigm. Distinct loci were associated with different aspects of coping, and their effects were modulated by both the sex and lineage of the animals, demonstrating the power of the general linear modeling approach and the important interplay of allelic and non-allelic factors in the inheritance of coping behaviors.

Adaptation, Psychological↗
PubMed2004

Microemulsion electrokinetic chromatography of drugs varying in charge and hydrophobicity: I. Impact of parameters on separation performance evaluated by multiple linear regression models.

The separation of anionic, cationic and neutral drugs in microemulsion electrokinetic chromatography (MEEKC) was studied with a statistical experimental design. The concentration of sodium dodecyl sulfate (SDS, surfactant), 1-butanol (co-surfactant) and borate buffer and the factors Brij 35 (surfactant), 2-propanol (organic solvent) and cassette temperature were varied simultaneously, while the parameters pH (9.2), the concentration of octane (oil, 0.8% w/w), the voltage (10 kV) and the dimension of the fused-silica capillary, were kept constant. Eight different model substances were chosen with different hydrophobicities. Two of the analytes were positively charged, two were negatively charged, and the remaining four were neutral or close to neutral at the pH explored. The importance of each parameter on the separation window, the plate height and the retention factor for each of the analytes was studied by means of multiple linear regression (MLR) models. A new response was evaluated for anions, the quotient between the effective mobility in the microemulsion and the effective mobility in the corresponding buffer. Factors affecting selectivity changes were also explored, and it was found that SDS and 2-propanol had the largest effect on selectivity.

2-Propanol↗