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At least 1,135 records · Page 63Linked to original sources
PubMed1998

Mathematical models of purine metabolism in man.

Experimental and clinical data on purine metabolism are collated and analyzed with three mathematical models. The first model is the result of an attempt to construct a traditional kinetic model based on Michaelis-Menten rate laws. This attempt is only partially successful, since kinetic information, while extensive, is not complete, and since qualitative information is difficult to incorporate into this type of model. The data gaps necessitate the complementation of the Michaelis-Menten model with other functional forms that can incorporate different types of data. The most convenient and established representations for this purpose are rate laws formulated as power-law functions, and these are used to construct a Complemented Michaelis-Menten (CMM) model. The other two models are pure power-law-representations, one in the form of a Generalized Mass Action (GMA) system, and the other one in the form of an S-system. The first part of the paper contains a compendium of experimental data necessary for any model of purine metabolism. This is followed by the formulation of the three models and a comparative analysis. For physiological and moderately pathological perturbations in metabolites or enzymes, the results of the three models are very similar and consistent with clinical findings. This is an encouraging result since the three models have different structures and data requirements and are based on different mathematical assumptions. Significant enzyme deficiencies are not so well modeled by the S-system model. The CMM model captures the dynamics better, but judging by comparisons with clinical observations, the best model in this case is the GMA model. The model results are discussed in some detail, along with advantages and disadvantages of each modeling strategy.

Animals↗
PubMed1984

A mathematical model that applies to protein degradation and post-translational processing of proteins and to analogous processes for other molecules in non-growing and exponentially growing cells.

A mathematical model is presented that describes first order degradation and post-translational processing of proteins in non-growing and exponentially growing cells. The model applies to proteins that are substrates or products of processing. General equations are presented that can be applied to many different experimental protocols. Application of the model to pulse-chase and continuous labeling experiments is illustrated. The mathematical expressions apply to any cellular component that is synthesized in proportion to cellular mass and is degraded or processed by reactions that follow first order kinetics. However, in this paper, the model is discussed solely as it applies to protein metabolism.

Amino Acids↗
PubMedDate not supplied

A mathematical model for evaluating the reaction of paraoxon with human serum cholinesterase and with polymorphic forms of paraoxonase.

The inhibition of cholinesterase of human serum by paraoxon can be predicted by a mathematical model which considers two competing reactions for paraoxon: one, the direct interaction with cholinesterase, and the other, enzymatic hydrolysis by paraoxonase. On the basis of the residual cholinesterase activity at various times during the incubation with paraoxon, it is possible to determine the rate constants for the reaction of paraoxon with cholinesterase (k1), and the reaction with paraoxonase (k2), the latter being directly proportional to paraoxonase activity. The percentage of initial activity remaining as residual cholinesterase depends primarily upon the paraoxonase level; it is influenced only slightly by variations in initial cholinesterase levels within the normal range. From these results, we conclude that the residual cholinesterase activity test is, in fact, an indirect measure of serum paraoxonase activity; it has the same limitations and is no more reliable a means of differentiating individual paraoxonase genotypes than measuring the level of serum paraoxonase activity directly. Our model suggests that there are conditions where paraoxonase genotype may alter the clearance of paraoxon and in turn the reaction of paraoxon with target sites. Whether similar results would be obtained in vivo is unknown. Since this model predicts the degradation of paraoxon well in vitro, it may be possible to extend the model and predict the effect of paraoxonase genotype on the clearance of paraoxon in vivo.

Aryldialkylphosphatase↗
PubMed1984

A mathematical model of aortic valve vibration.

It has been shown experimentally that the second heart sound is produced by diastolic vibrations of the closed aortic valve. In the present paper a mathematical model of this vibration is developed from first principles. The model assumes a one dimensional but non-linear fluid behavior. The problem is coupled through a non-linear, planar valve. A solution is obtained using the method of characteristics developed in finite difference form. The resulting valve frequency and amplitude are in good agreement with patient data. The model predicts a strong dependency of response on the valve forcing function and valve stiffness; and a weaker dependency of response on valve mass.

Aortic Valve↗
PubMed1993

The epidemiology of neural tube defects. A mathematical model.

The incidence of neural tube defects (NTDs) shows a seasonal variation; and incidence as well as female/male ratio show a relation with latitude. The interrelation of these phenomena is presented as a mathematical model, which has a 'predictive' value, and is an instrument in estimating the local gene frequency. The model offers a simple explanation of the conundrum why the double X-chromosome has a variable influence on the sex ratio. UV light and the herpes virus fit in this model as related causative factors of NTDs.

Epidemiologic Factors↗
PubMed1984

Determining "safe" levels of exposure: safety factors or mathematical models?

The object of regulatory toxicology is to determine "safe" levels of human exposure to toxicants present in the environment. The traditional safety factor approach is compared to more recent mathematical modeling techniques, outlining the underlying assumptions and statistical properties of each procedure. Several linear extrapolation procedures are examined in detail using computer simulation, along with the impact of nonlinear kinetics on the extrapolation process.

Biotransformation↗
PubMed1975

[Mathematical modeling of the relationship between the cytogenetic effect and the concentration of the mutagen].

The effect of different concentrations of thiophosphamide on the culture of human leucocytes was investigated. Three mathematical models were studied, one of which, being satisfactory for describing the experimental data, was chosen. According to this model a quantity of aberrant cells changes with the concentration of thiophosphamide non-linearly and can be described according to the equation A=exp[-(KC+alpha)2], where A is a portion of normal cells, C - a concentration of a mutagen, K and alpha - the coefficients, while exp[-alpha2] is the control level of normal metaphases. The quantity of chromosome breaks per cell is described according to the equation X= exp [KC + +alpha)2]-1. The general view of the equation is constant for different phases of the cell cycle. It follows from the suggested model that the action of two molecules of an alkylating agent is necessary for the formation of a chromosome break. This is indicative of double-stranded structure of a chromosome in its section. It also follows from the suggested model that the action of thiophosphamide has no cut-off. Thiophosphamide induced chromatid aberrations during the G2 phase, therefore it is not a mutagen of the check action.

Cells, Cultured↗
PubMed1981

The electric potential across the erythrocyte membrane: a mathematical model.

The space-dependent electric potential of erythrocyte membranes is determined on the basis of a mathematical model which takes into account the membrane surface charges of glycophorine A, spectrin and phosphatidyl serine. The calculations are performed by numerical integration of the nonlinear Poisson-Boltzmann-equation.

Erythrocyte Membrane↗
PubMed2005

Detection of different shapes of lactation curve for milk yield in dairy cattle by empirical mathematical models.

The study of relationships between mathematical properties of functions used to model lactation curves is usually limited to the evaluation of the goodness of fit. Problems related to the existence of different lactation curve shapes are usually neglected or solved drastically by considering shapes markedly different from the standard as biologically atypical. A deeper investigation could yield useful indications for developing technical tools aimed at modifying the lactation curve in a desirable fashion. Relationships between mathematical properties and lactation curve shapes were analyzed by fitting several common functions (Wood incomplete gamma, Wilmink's exponential, Ali and Schaeffer's polynomial regression, and fifth-order Legendre polynomials) to 229,518 test-day records belonging to 27,837 lactations of Italian Simmental cows. Among the best fits (adjusted r(2) higher than 0.75), the 3-parameter models (Wood and Wilmink) were able to detect 2 main groups of curve shape: standard and atypical. Five-parameter models (Ali and Schaeffer function and the Legendre polynomials) were able to recognize a larger number of curve shapes. The higher flexibility of 5-parameter models was accompanied by increased sensitivity to local random variation as evidenced by the bias in estimated test-day yields at the beginning and end of lactation (border effect). Meaning of parameters, range of their values and of their (co) variances are clearly different among groups of curves. Our results suggest that analysis based on comparisons between parameter values and (co)variances should be done carefully. Comparisons among parameter values and (co)variances could yield more robust, reliable, and easy to interpret results if performed within groups based on curve shape.

Animals↗
PubMedDate not supplied

A mathematical model of coagulation factor VIII kinetics.

It appears that the binding of coagulation factor VIII to von Willebrand factor in plasma stabilizes the otherwise highly labile factor VIII. A mathematical model of factor VIII kinetics has been developed based upon this proposed effect of factor VIII binding. The model's kinetic parameter values have been estimated by fitting the model to data available in the medical literature. The model gives accurate quantitative predictions of the elevated steady-state concentrations of factor VIII in clinical conditions associated with the acute phase reaction and in pregnancy, the decreased steady-state concentrations of factor VIII in females heterozygous for hemophilia, the decreased steady-state concentrations of factor VIII in patients with type 1 (heterozygous) and type 3 (homozygous) von Willebrand disease, and the variable half-life of factor VIII in factor replacement therapy for hemophilia and von Willebrand disease.

Computer Simulation↗
PubMed2001

Mathematical modeling of controlled-release kinetics of herbicides in a dynamic-water-bath system.

Release of herbicides from lignin-based formulations follows a diffusion-controlled mechanism. For mathematical modeling of diffusive transport, the conventional approach is to assume sink conditions at both surfaces of polymeric matrix. This boundary condition proved to be inadequate to describe experimental data obtained in a water dynamic bath system. However, satisfactory descriptions for this system were obtained when a stagnant unstirred layer of herbicide solution was used as the boundary condition. The adequacy of the model incorporating this new boundary condition was statistically tested using the Fisher test at a confidence level of 95% and plotting the residual distribution.

Biomass↗
PubMed1993

A mathematical model for cell killing by heat applied to a C3H mammary carcinoma in vivo.

Jung (1986) has proposed a mathematical model for cell killing by hyperthermia which assumes that heat killing involves two steps: the production (p) of non-lethal lesions at random and a subsequent conversion (c) into lethal lesions. The p & c model has been shown to predict the survival of CHO cells heated in vitro even when complicated biological phenomena such as thermotolerance and step-down heating (SDH) are involved (Jung 1986, 1991). In the present study the objective was to test the p & c model's ability to describe the effect of single heating and SDH in an experimental tumour in vivo. The endpoint was tumour growth delay (GD). The doubling times (DT) for untreated and heated tumours were similar, and the surviving fraction (SF) could therefore be estimated using: SF = -in(2).GD/DT. SF was fitted to the model by non-linear regression. The p & c model adequately described the GD obtained by SDH (39-44.5 degrees C) and single heating above 42.5 degrees C. Multiple linear regression showed that the residuals for single heating and SDH were independent of both heating time and temperature. However, the residuals for single heating (41-44.5 degrees C) were significantly correlated to heating time when analysed separately. The GD obtained by the use of extended single heating times at or below 42.5 degrees C was therefore overestimated by the model. Development of chronic thermotolerance during heating may account for the observed divergence. The Arrhenius plots for both p and c were log-linear with activation energies of 678 and 311 kJ/mol, respectively. Jung (1986) has previously reported similar p and c activation energies above 42.5 degrees C for CHO cells in vitro.

Animals↗
PubMed1999

A mathematical model of an aqueous-organic partition-based controlled release system using microporous membranes.

A mathematical model with an exact solution is presented for the membrane-controlled release of small molecules such as nicotine, caffeine, and benzoic acid initially present in solution in the reservoir of the device. Both hollow fiber and flat membrane device geometries are considered. The reservoir is bounded by a microporous membrane, the pores of which are filled with a pore liquid immiscible with the reservoir phase liquid. At the interface between the reservoir and the pore, the solute partitions between the reservoir and the pore liquid phases, before diffusing outward through the membrane pore. The model results compare well with experimental data. Parametric studies reveal the interaction between system parameters and the controlled release behavior. A high partition coefficient of the solute between the reservoir and pore phases is found to effect pseudo-zero order release for an extended time. Similarly, when the ratio of time constants for transport of the solute through the reservoir and membrane regions is small, a constant release rate is achieved for an extended time.

Benzoic Acid↗
PubMed1998

[Mathematical model for the predictive value of a test in critically ill patients studies according to APACHE II score and pathology at admission].

OBJECTIVE: To find a predictive model for mortality at four different days from the admission for critically ill patients. DESIGN: Retrospective study on two consecutive series of critically ill patients admitted in ICU. SUBJECTS: 1254 critically ill patients, subdivided into two series of 813 (561 survivors and 252 non survivors) and 441 patients (291 survivors and 150 non survivors), respectively. INTERVENTIONS: None. MEASUREMENTS: All patients had APACHE II calculated within the first 24 hours from the admission in ICU and, if the patient was still in ICU, also at the 5th, 10th and 15th day from the admission. Casistics was subdivided into two unequal series, ratio 2:1, with a random selection made on each of the 6 considered years. On the 1st series, in 1st, 5th, 10th and 15th day, for mathematical predictive models were made, using stepwise logistic regression (BMDP, Los Angeles). In the 1st day the following independent variables were utilized: APACHE II score, the specific diagnosis at admission, fitted following Knaus' diagnostic criteria, united in 6 principal categories, while for the other 3 days the variation % of APACE II score as regards the previous day. RESULTS: For each of the considered day four mathematical models have been made. These models have been validated in both series in calibration from the Hosmer-Lemeshow Goodness-of-fit test and in discrimination from the ROC curves. For each day Y (Prob.% to die) = eLogit/1 + eLogit, where Logit = beta 0 (constant) + beta 1*APACHE II + beta 2*Variat.%APACE II (difference between actual APACHE II - APACHE II of the previous day/actual APACHE II) + beta k, (coefficient pertinent to pathology). CONCLUSIONS: The mathematical model, as other models do, stratifies enough the casistics according to the risk of death. Waiting for further studies to make more precise prognostic mathematical models, this one and others can help the clinical assessment in single patient evaluation.

APACHE↗
PubMed1975

[Use of a mathematical model to assess cutaneous blood flow and heat loss during a thermoregulatory reaction].

The general blood flow and heat loss were determined in the rabbit ear with the aid of a mathematical model and on the basis of measurements of ambient, hypothalamic, and the ear temperatures, while the ambient temperature changed from--10 degrees C to + 40 degrees C. A static dependence of ear's heat loss on the blood flow intensity at different ambient temperatures, was quantitatively determined.

Animals↗
PubMed1979

A non-linear mathematical model for the in vivo determination of Kupffer cells number and rate of phagocytosis of radiocolloids in rats.

In order to perform a quantification of the hepatic RES function, a mathematical model of the colloids phagocytosis was constructed and validated in normal and partially hepatectomised rats. The experimental design consisted of the collection of successive blood samples for the measurement of radiocolloids time courses after the injection of different doses of gelatin colloids (0.075--5 mg of gelatin/100 g body wt). The unknown parameters were estimated by method of maximum likelihood using a second order algorithm. A good fit between experimental and simulated data was obtained for a large range of injected doses using a single set of parameters. Comparisons of parameters values between normal and hepatectomised rats were found to be -onsistent with the hepatectomy ratio. This computerised estimation of parameters provides a determination of both the total number of Kupffer cells and the mean time of a complete phagocytosis cycle which cannot be obtained by classical approaches.

Animals↗
PubMed1985

A mathematical model for the quantitative study of left to right cardiac shunt.

Non-invasive radioisotope cardiographic techniques have become a useful tool for studying the anatomy and function of the heart. The mathematical model described justifies the phenomenological analysis of pulmonary time-activity histograms and was invented for quantitative study of left to right cardiac shunt. The model also gives a theoretical insight into such an empirically proposed diagnostic method and represents an adequate framework for the understanding of other possible approaches to the problem of left to right shunt.

Blood Circulation↗
PubMedDate not supplied

Computer analysis of external counterpulsation by use of a nonlinear mathematical model of the cardiovascular system.

A pressure system externally applied to the limbs of a patient has been proven effective in assisting circulation in animal and clinical studies. In this study a nonlinear mathematical model of the cardiovascular system is utilized to determine the effectiveness of high-frequency components in the external pressure waveform. The development of the model, the method of analysis, and the results acquired with the model are presented in this report, demonstrating its suitability for the study of external counterpulsation.

Animals↗