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PubMed1988

A comparison of mathematical models for regeneration in acutely responding tissues.

A mathematical model is presented to describe the regenerative response of mouse gut epithelal cells to radiation. The model, derived from radiobiological principles, predicts the cellular surviving fraction following any irradiation regimen. There are three basic elements to the model (a) a single dose survival curve, either the linear-quadratic or the two-component model, (b) a part to incorporate the regenerative response, either a Gompertzian or a logistic growth and (c) a part to accomodate the delayed onset of regeneration, including either a mitotic delay, a fixed time delay, both, or neither. The models are similar in spirit, but different in detail to the model proposed by Cohen. The various models are evaluated on three large datasets, where the response is cell survival in the jejunum or the colon measured using the crypt colony assay. The models were fit and the parameter estimates and standard errors were obtained from the raw observations using non-linear least squares. It is concluded that Gompertzian growth gives a better fit to the data than logistic growth; the delayed onset of regeneration in these tissues can be best accounted for by a mitotic delay or a mitotic delay plus a fixed time delay, and there is little to choose between the linear-quadratic and the two-component model. There was a strong relationship between the tissue cell cycle time and the regenerative response, the mitotic delay being longer and the rate of regeneration slower for the colon than for the jejunum.

Animals↗
PubMed1988

Mathematical and statistical strategies for biomarker research of aging.

The continuing revolution in personal computers has placed computing power rivaling that of some computational laboratories on the desktops of many investigators. Contained in this article are some suggestions for taking advantage of this enhanced computing power in analyzing data in which an investigator does not have control over his sample. Sample reuse methods, called the jackknife and the bootstrap, are discussed, along with possible applications of time-series methods. Some suggestions for getting help from mathematical scientists are also included.

Aging↗
PubMed1990

A mathematical model of erythropoiesis suggests an altered plasma volume control as cause for anemia in aged mice.

In order to evaluate whether the anemia observed in aged C57B1 and B6D2F1 mice reflects a defect in the control mechanisms regulating erythropoiesis a mathematical model of erythropoietic control is employed, validated previously. In the model it is hypothesized that the most important mechanism for compensating an actual demand of red blood cells is an increase in the mitotic amplification (number of mitoses) of erythroid progenitors (CFU-E, erythroblasts). The same sigmoidal dose-response-relationship between mitotic amplification and hematocrit (Hct) is proposed for young and aged mice. It is mediated by erythropoietin (EPO). Using this relationship one can demonstrate that the expansion of the plasma volume (PV) observed in aged mice is appropriately compensated by an increase in the mitotic amplification of CFU-E and erythroblasts. This implies that aged mice operate in a stimulated state of erythropoietic amplification which is closer to the maximum of the dose-response-relationship than the steady state in young mice. This explains the finding of a reduced proliferative reserve in aged mice following further erythropoietic stimulation. An additional analysis regarding the response of aged mice to bleeding anemia is consistent with the view that young and aged mice share the same dose-response-relationship but start from different steady states. These findings suggest that the control mechanisms regulating erythropoiesis in young and aged mice are similar and that the anemia is due to alterations in the PV control.

Animals↗
PubMedDate not supplied

Mathematical modelling of bacterial growth at subinhibitory levels of aminoglycosides.

The subinhibitory effect of antibiotics has often been studied without any clear theoretical framework; we have chosen to use mathematical bacterial growth modelling as a useful tool to analyse these biological states in a more rigorous manner. Since their mode of action and molecular target are relatively well known, aminoglycosides were well suited for this more sophisticated study of subinhibitory action. We have shown that two models (the Monod and the logistic models) regularly used in bacteriology, were adequate to describe these effects in a glucose-limited medium. A change of model, according to antibiotic concentration, revealed the existence of two separate actions. At lower concentrations, inhibition affected mainly glucose use, the substrate remained limiting and growth mode did not change. As soon as the concentration exceeded a threshold, growth was totally disturbed, probably through a physiological "catastrophe". This threshold can be used to estimate bacterial susceptibility to these antibiotics.

Aminoglycosides↗
PubMed1992

Verification of treatment plans by mathematical formulas for single catheter HDR brachytherapy.

In high dose-rate brachytherapy, 500 to 1000 cGy will be given in a matter of minutes. Therefore, careful treatment planning and accurate verification of the plan is critical. To expedite the plan verification procedure, simple mathematical formulas were derived in our previous paper for single catheter treatments on a Nucletron microSelectron system. In this paper, the usefulness and limitations of these formulas for the plan verification procedure are further discussed.

Adult↗
PubMed1995

A mathematical model of flow through the terminal lymphatics.

Proper understanding of the mechanisms of fluid absorption and flow through the terminal lymphatics is essential for the control of several pathological conditions such as edema, bedsores and cancer. A mathematical model of the terminal lymphatics was developed using the principles of mechanics. Computer simulation results substantiate the hypothesis that fluid absorption and flow through the terminal lymphatics occur due to suction mechanisms of the adjacent contractile lymphatic segments and due to periodic fluctuations in the interstitial fluid pressure. In addition, the results suggested that increasing the length of a terminal lymphatic vessel beyond a certain limit does not cause further increase in fluid flow into the terminal lymphatic.

Biomedical Engineering↗
PubMed1995

A mathematical analysis of intestinal peristaltic waves.

Gut motility is usually investigated by introducing probes in the intestinal lumen. Image analysis could be used instead of intraluminal pressure measurements to avoid the inconvenience of this invasive procedure. The present study exposes the theoretical principles of intestinal peristalsis in terms of indirect intraluminal pressure and content velocity measurements. A geometrical model of intestinal contractions is mathematically described by using Stokes' equations in order to evaluate velocities and pressures in the equations established by quantitative analysis of cinematography pictures. The couple velocity-pressure is calculated at each point of the geometrical model for a viscous and non-compressible fluid. This fluid flows in a geometrical structure, the boundaries of which vary with time and behave in a periodic and regular way by simulating the movements of intestinal contractions. A comparison is made between experimental pressure recordings in isolated rat intestines and pressure values calculated by utilizing the geometrical model. Velocity values calculated at every grid node show positive and negative zones in the geometrical model output. The position of these zones vary from one geometrical model to another. Moreover, the calculated pressure and velocity values change according to the applied vector efforts. The similarity of the results obtained shows the efficiency of the finite element technique in the case of Stokes' equations.

Animals↗
PubMed1995

Maximum expiratory flow-volume curve: mathematical model and experimental results.

A mathematical simulation of the maximum expiratory flow-volume (MEFV) curve was developed using a lumped parameter model. The model uses a theoretical approximation of an activation function representing the lung's pressure-volume relationship during maximally forced expiration. The waveforms obtained by the model were compared to the flow-volume curves recorded from normal subjects and for patients with small airways disease, asthma, and emphysema. We were able to reproduce the flow-volume curves using the model and calculate new parameters that reflect the dependency of airways resistance on expired volume during FVS manoeuvre. These new parameters are based on the entire information presented in the flow-volume curve and on the reduction in flow at all lung volumes. We also calculated the mean slope of the resistance-expired volume curves obtained from the model by fitting a straight line to the curve. Using representative data for normal and COPD patients different mean slopes of 0.095, 0.13, 0.49 and 1.44 litre-1 were obtained for normal subject, small airways disease, asthma and emphysema patients, respectively. The model-based parameters may be applicable to human studies. However, further studies in large groups of patients are required to better define the true predictive value of the new indices described for the diagnosis of COPD.

Asthma↗
PubMed2006

Misuses of correlation and regression analyses in orthodontic research: the problem of mathematical coupling.

INTRODUCTION: The aim of this article was to encourage good practice in the statistical analyses of orthodontic research data. Our objective was to highlight the statistical problems caused by mathematical coupling (MC) in correlation and regression analyses. These statistical problems are among the most common pitfalls in orthodontic research when exploring associations among clinical variables. This article will show why these problems arise and how they can be avoided and overcome. METHODS: Four orthodontic journals were electronically and manually searched for articles that used correlation and regression analyses. Studies that seemed to suffer from MC in their statistical analyses were identified and carefully examined. RESULTS: Several examples from our search illustrate that MC in correlation and regression analyses can potentially cause misleading results. More appropriate statistical methods are available and should be used to eliminate confusing results and improve any subsequent interpretations. Because many clinical and radiographic variables used in orthodontic research are correlated due to direct or indirect MC, interpretation of studies in the literature needs to be cautious. CONCLUSIONS: Correlation and regression analyses are useful tools in orthodontic research when their assumptions and limitations are recognized. However, greater care is required in formulating research questions and experimental designs. It is prudent to seek statistical advice when orthodontic research involves complex data analyses.

Analysis of Variance↗
PubMed2006

Mathematics learning disability in girls with Turner syndrome or fragile X syndrome.

Two studies were carried out to examine the persistence (Study 1) and characteristics (Study 2) of mathematics learning disability (MLD) in girls with Turner syndrome or fragile X during the primary school years (ages 5-9 years). In Study 1, the rate of MLD for each syndrome group exceeded the rate observed in a grade-matched comparison group, although the likelihood of MLD persisting through the primary school years was comparable for all three groups. In Study 2, formal and informal math skills were compared across the syndrome groups, a normative group, and children from the normative group who had MLD. Few differences were observed between the Turner syndrome and normative groups. Despite having rote counting and number representation skills comparable to those in the normative group, girls with fragile X had difficulty with counting rules (e.g., cardinality, number constancy). However, this difficulty did not distingush them from the MLD group. Overall, counting skills appear to distinguish the Turner syndrome and fragile X groups, suggesting that the specificity of math deficits emerges earlier for fragile X than Turner syndrome.

Child↗
PubMed2004

Dynamics of sulfur amino acids in mammalian brain: assessment of the astrocytic-neuronal cysteine interaction by a mathematical hybrid model.

A mathematically hybrid model was used to analyze three mechanisms by which cysteine could be produced in the brain to be used as preferential substrate in the synthesis of neuronal glutathione. In that way, the fluxes of sulfur-compounds at the brain-blood barrier were integrated with their transport in astrocytes and neurons, and with their metabolism in astrocytes. We concluded that cysteine, in contrast with its precursor cystine, would not be taken up from the blood at the blood-brain barrier, but instead it must be lost continuously from astrocytes. Cysteine efflux is produced because the uptake of cystine in astrocytes is much greater than their cysteine demand to synthesize glutathione, hypotaurine and taurine. Once in the interstitial parenchyma, cysteine would be taken for the neurons, as backwardly by the endothelial cells. Remarkably, a close sulfur-macro balance can be maintained only if the surplus of the produced cysteine is transferred from the endothelial cells to the blood together with significant amounts of other sulfur-compounds, probably taurine and hypotaurine. In addition, the results obtained shown that alternative mechanisms of cysteine generation (i.e., nonenzymatic-thiol-disulfide exchange reaction, enzymatic cleavage of the glutathione effluxed from astrocytes) are not quantitatively significant under physiological conditions, in situ.

Animals↗
PubMed2005

A mathematical model of fatty acid metabolism and VLDL assembly in human liver.

The lipid composition of very-low-density lipoprotein (VLDL) in plasma is crucial for human health. A pre-requisite for the alteration of VLDL composition is a co-ordinated understanding of the complex interactions in VLDL assembly. In order to determine the potential effects of changes in substrate availability on VLDL lipid composition, we constructed, parameterized and evaluated a mechanistic mathematical model of the biosynthesis of triglycerides, phospholipids, and cholesterol esters and the assembly of VLDL in human hepatocytes. Using published data on human liver metabolism, the model was also used to provide insight into the complex process of lipid metabolism and to estimate the affinities of different liver enzymes for different fatty acids (FA). For example, we found that Delta6-desaturase is 19 times more selective for C18:3n-3 than C18:2n-6, stearoyl-CoA-desaturase is 2.7 times more selective for C18:0 than C16:0, Delta5-desaturase desaturates C20:4n-3 preferentially over C20:3n-6 and FA elongase preferentially elongates C18:3n-6. The model was also used to predict the plasma free fatty acid (FFA) composition required to generate a prescribed change in plasma lipoprotein FA composition. Furthermore, the model was tested against a published human feeding trial that investigated the effect of changes in dietary FA composition on human plasma lipid FA composition. The model is a useful tool for predicting the effect of changes in plasma FFA composition on plasma lipoprotein lipid FA composition.

Dietary Fats↗
PubMed2004

Mathematical aspects of protein structure determination with NMR orientational restraints.

The field of structural biology is becoming increasingly important as new technological developments facilitate the collection of data on the atomic structures of proteins and nucleic acids. The solid-state NMR method is a relatively new biophysical technique that holds particular promise for determining the structures of peptides and proteins that are located within the cell membrane. This method provides information on the orientation of the peptide planes relative to an external magnetic field. In this article, we discuss some of the mathematical methods and tools that are useful in deriving the atomic structure from these orientational data. We first discuss how the data are viewed as tensors, and how these tensors can be used to construct an initial atomic model, assuming ideal stereochemistry. We then discuss methods for refining the models using global optimization, with stereochemistry constraints treated as penalty functions. These two processes, initial model building followed by refinement, are the two crucial steps between data collection and the final atomic model.

Magnetic Resonance Spectroscopy↗
PubMed2005

Evaluation of nonlinear chromatographic performance by frontal analysis using a simple multi-plate mathematical model.

A multi-plate (MP) mathematical model was proposed by frontal analysis to evaluate nonlinear chromatographic performance. One of its advantages is that the parameters may be easily calculated from experimental data. Moreover, there is a good correlation between it and the equilibrium-dispersive (E-D) or Thomas models. This shows that it can well accommodate both types of band broadening that is comprised of either diffusion-dominated processes or kinetic sorption processes. The MP model can well describe experimental breakthrough curves that were obtained from membrane affinity chromatography and column reversed-phase liquid chromatography. Furthermore, the coefficients of mass transfer may be calculated according to the relationship between the MP model and the E-D or Thomas models.

Chromatography↗
PubMed2005

A new mathematical procedure to evaluate peaks in complex chromatograms.

Automatic peak evaluation in chromatograms and subsequent quantification of compound concentrations is still a challenge in the analysis of complex samples containing hundreds or thousands of compounds. Although a number of software packages for peak evaluation exist, baseline definition and overlapping peaks of different shapes are the main reasons which prevent reliable automatic analysis of complex chromatograms. A new mathematical procedure is presented which uses peak shapes extracted from the chromatogram itself and modified by nonlinear (in fact, hyperbolic) stretching of the peak head and tail. With this approach, the peak parameters are position, height, scale of front, scale of tail, and smoothness of transition from front to tail scaling. This approach is found to give a substantially better fit than traditional analytically defined peak shapes. Together with a good peak finding heuristic and nonlinear optimization of parameters this allows a reliable automatic analysis of chromatograms with a large number of peaks, even with large groups of overlapping peaks. The analysis matches the quality of standard interactive methods, but still permits interactive refinement. This approach has been implemented and tested on a large set of data from chromatography of hydrocarbons in ambient air samples.

Chromatography↗
PubMed2005

Effect of gravitational force on type-J counter-current chromatography by mathematical analysis.

The gravitational force exerts an important effect on the counter-current chromatography (CCC) and has been used to retain the stationary phase and improve the efficiency in the various CCC separations. This paper deals with the effect of gravitational force on type-J CCC, one of the most popular CCC methods by the mathematical analysis for the first time. The theoretical analyses reveal a close relationship between the effect of gravitational force, the placed orientation of type-J CCC apparatus, and the revolutional speed. Two placed orientations are more suitable for preparative CCC separation: one is common horizontal, and the other upright. Thus, there are three optimum conditions for type-J CCC separation, the first using horizontal apparatus at very low revolutional speed around 10rpm in the gravitational filed, the second by use of upright apparatus at moderate revolutional speed around 100rpm in the three-dimensional complex force field composed of centrifugal and orthogonal gravitational force, and the third employing the apparatus placed at any orientation including horizontal and upright CCC apparatus at high revolutional speed above 300rpm in the centrifugal force field. Therefore, we should consider the effect of gravitation force on CCC at the selection of proper operational conditions according to properties of two immiscible phases, the desired revolutional speed and the parameters of apparatus in order to utilize efficiently the effect of gravitational force. These analyses and results will benefit to improve the efficiency of CCC separation, especially large-scale industrial preparation.

Countercurrent Distribution↗
PubMed2006

The role of language in mathematical development: evidence from children with specific language impairments.

A sample (n=48) of eight-year-olds with specific language impairments is compared with age-matched (n=55) and language matched controls (n=55) on a range of tasks designed to test the interdependence of language and mathematical development. Performance across tasks varies substantially in the SLI group, showing profound deficits in production of the count word sequence and basic calculation and significant deficits in understanding of the place-value principle in Hindu-Arabic notation. Only in understanding of arithmetic principles does SLI performance approximate that of age-matched-controls, indicating that principled understanding can develop even where number sequence production and other aspects of number processing are severely compromised.

Child↗
PubMed2007

A mathematical analysis of SELEX.

Systematic evolution of ligands by exponential enrichment (SELEX) is a procedure by which a mixture of nucleic acids that vary in sequence can be separated into pure components with the goal of isolating those with specific biochemical activities. The basic idea is to combine the mixture with a specific target molecule and then separate the target-NA complex from the resulting reaction. The target-NA complex is then separated by mechanical means (for example by filtration), the NA is then eluted from the complex, amplified by polymerase chain reaction (PCR) and the process repeated. After several rounds, one should be left with a pool of [NA] that consists mostly of the species in the original pool that best binds to the target. In Irvine et al. [Irvine, D., Tuerk, C., Gold, L., 1991. SELEXION, systematic evolution of nucleic acids by exponential enrichment with integrated optimization by non-linear analysis. J. Mol. Biol. 222, 739-761] a mathematical analysis of this process was given. In this paper we revisit Irvine et al. [Ibid]. By rewriting the equations for the SELEX process, we considerably reduce the labor of computing the round to round distribution of nucleic acid fractions. We also establish necessary and sufficient conditions for the SELEX process to converge to a pool consisting solely of the best binding nucleic acid to a fixed target in a manner that maximizes the percentage of bound target. The assumption is that there is a single nucleic acid binding site on the target that permits occupation by not more than one nucleic acid. We analyze the case for which there is no background loss (no support losses and no free [NA] left on the support). We then examine the case in which such there are such losses. The significance of the analysis is that it suggests an experimental approach for the SELEX process as defined in Irvine et al. [Ibid] to converge to a pool consisting of a single best binding nucleic acid without recourse to any a priori information about the nature of the binding constants or the distribution of the individual nucleic acid fragments.

Ligands↗