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At least 595 records · Page 33Linked to original sources
PubMed2002

A mathematical model that predicts the force-frequency relationship of human skeletal muscle.

In previous work we developed and validated a mathematical model that predicted force output from skeletal muscles subjected to six-pulse stimulation trains under isometric condition. The current study investigated the model's ability to predict force responses to longer stimulation trains under both nonfatigued and fatigued conditions. Using the six-pulse train model to predict the force produced by longer stimulation trains showed that the model was successful, but a modified parameter identification scheme was required. For most of the trains tested the model accounted for 95% of the variance in the experimental forces produced by stimulation trains, with mean frequencies from 12.5 to 100 HZ, train durations from 485 to 1000 ms, and number of pulses from 14 to 50 for both nonfatigued and fatigued muscles. The success of our mathematical model in predicting forces produced by stimulations with a wide range of frequencies, durations, and number of pulses implies great potential of the model for the identification of optimal activation patterns that should be used during functional electrical stimulation.

Actins↗
PubMedDate not supplied

Mathematical model of virus disease morbidity evolution in communities with several components.

Mathematical models previously developed for the evolution of virus disease morbidity in communities with a single component are generalized so as to be applied to the case of communities consisting of several coupled components. Epidemiological characteristics are discussed in the case of components linked by weak, strong or intermediate couplings. A detailed analysis is made of the cases when the different components are represented by; a) different geographical areas; b) different types of sources of infection; c) different age groups.

Age Factors↗
PubMedDate not supplied

[Mathematical model of stabilization of circadian rhythm in cell energy metabolism].

A mathematical model for circadian self-oscillation in the carbohydrate branch of energy metabolism (CEM) was analysed. The self-oscillations are due to the reciprocal regulation of the activities of 6-phosphofructokinase and fructose-1,6-bisphosphatase by fructose-1,6-bisphosphate. The circadian period was shown to be insensitive to metabolic disturbances because of the presence in CEM of negative feedback mechanisms regulating the activities of the key enzymes 6-phosphofructokinase, fructose-1,6-bisphosphatase, pyruvate kinase and phosphoenolpyruvate carboxykinase. It has been also shown that such mechanisms are largely synergistic in their action.

Adenylate Kinase↗
PubMed1976

A mathematical model of the acute myeloblastic leukemic state in man.

A dynamical mathematical model of the acute myeloblastic leukemic state is proposed in which normal neutrophils and their precursors, and leukemic myeloblasts, proliferate as distinct but interacting cell populations. Each population has a Go compartment, consisting of resting cells, that acts as a control center to determine the rate of proliferation. These rates are assumed to depend on the total number of cells in the combined populations. The presence of the leukemic population destabilizes the homeostatic state of the normal population, which is stable in the absence of leukemic cells, and drives the system to a new stable state consisting entirely of leukemic cells and no normal cells. Calculations based on the theory suggest that it is able to simulate the kinetic features of this disease state, at least in its typical manifestations.

Cell Division↗
PubMed1978

Transfer and dynamics of uric acid in the pregnant rhesus monkey. II. A mathematical model.

The objective of the present study was to develop a mathematical model of the dynamics of uric acid between fetal and maternal compartments in the term pregnant rhesus monkey. In 3 different animals 14C-labeled uric acid was injected into the fetal circulation, the amniotic fluid and the maternal circulation, respectively. In one experiment no uric acid was administered and the fetus was deliberately killed at the beginning of the experiment. Samples of fetal and maternal blood, maternal urine and amniotic fluid were collected at regular intervals. Semilogarithmic time-activity curves were constructed and time constants were determined. An open four-compartment model (fetal-placental plasma, fetal-placental interstitial space, amniotic fluid and maternal plasma) was applied to describe the intercompartmental dynamics of uric acid. Transplacental clearance was approx. 1 ml X min-1 in both directions, maternal renal clearance was about 17 ml X min-1. These results and the calculated values of the other intercompartmental clearances support earlier results, obtained with the steady infusion method. Uric acid concentrations in amniotic fluid and fetal plasma appeared to increase significantly during the experiments. The rise in amniotic fluid levels can only be explained by accepting a yet undefined compartment in which uric acid is produced and cleared directly into the amniotic cavity. It is speculated that this additional compartment could be the fetal lung.

Amniotic Fluid↗
PubMed2000

Mathematical modeling for the prediction and optimization of laser hair removal.

BACKGROUND AND OBJECTIVE: The study of hair removal is a slow, tedious process. Efficacy evaluations require test-site observation for at least one complete hair cycle, a minimum of 6-8 months. In addition, tracking and counting individual hairs is extremely labor intensive. The objective of this study was to develop and evaluate a mathematical model for hair removal that could significantly speed the entire process. STUDY DESIGN/MATERIALS AND METHODS: Generally accepted kinetic and statistical modeling methods were used to develop a mathematical description of hair growth. The anagen and telogen percentages and decay times were the variables used to predict the kinetics of untreated hair. In the case that the follicles were treated, it was necessary to additionally consider the possible outcomes after treatment, making the calculations much too complicated for simple mathematical formulations. Therefore, a computerized statistical model was developed that considered the probabilities of no, partial, or complete follicular damage in addition to the untreated model variables. These models were then evaluated by comparing them to data derived from the literature and a study center. RESULTS: Values derived from the mathematical model were capable of closely approximating the experimental results of untreated (shaving) and treated (plucking, electrolysis, ruby laser, Q-switched Nd:YAG laser) hair growth kinetics. The model was also shown to be useful for optimizing the number and interval of Q-switched Nd:YAG laser treatments. CONCLUSIONS: A mathematical model can be used to reliably predict results from a variety of hair removal techniques. It also appears to be useful for optimizing a particular treatment protocol. In addition, the development of new hair removal products may be aided by using this method.

Computer Simulation↗
PubMed1979

A mathematical model for conduction of action potentials along bifurcating axons.

1. A mathematical model based on the Hodgkin-Huxley equations is derived to describe quantitatively the propagation of action potentials in a branching axon. 2. The model treats the case of a bifurcating axon with branches of different diameters. The solution takes into account the changes in space constant in the different regions. 3. The model allows for investigating parameters leading to preferential conduction of action potentials in one daughter branch as seen experimentally. 4. Assuming that the only difference between the various daughter branches is in their diameters, conduction blocks should occur simultaneously rather than differentially into all daughter branches when the geometrical ratio is greater than 10. 5. In order to obtain differential conduction into the two branches changes in ionic concentrations due to the repetitive action potentials had to be introduced into the equations. 6. We find that conditions which allow differential buildup of K concentration around the two branches, produce differential conduction block. These conditions may be different periaxonal spaces around the branches or different time constant for recovery processes that eliminate K from the periaxonal space. 7. The effects of an inexcitable branch on conduction of action potentials in the second branch are described. 8. We find that the membrane current which is associated with the action potential is much more sensitive than the action potential itself and shows more distinct changes near regions of inhomogeneity such as a branch point, a step increase in diameter or an inexcitable branch.

Action Potentials↗
PubMed1991

Mathematical model of cellular basis for the respiratory sinus arrhythmia.

The respiratory sinus arrhythmia (RSA) is a vagally mediated oscillation in cardiac cycle length at the frequency of breathing. We developed a mathematical model that predicted the temporal and frequency dependence of the RSA. We used the mathematical model to examine the underlying cellular basis for the RSA at the level of the sinus node. We alternated efferent vagal activity between a low and a high frequency at the frequency of breathing. This oscillation caused the rate of acetylcholine (ACh) release to oscillate between a low and a high rate at the frequency of breathing. ACh degradation followed linear pharmacokinetics for physiological concentrations of ACh. Therefore, the concentration of ACh in neuroeffector junctions of the sinus node oscillated at the frequency of breathing. Membrane potential responded rapidly to changes in the concentration of ACh relative to the rate of ACh degradation. Thus, the time course of the RSA depended on the rate of ACh degradation. Membrane potential oscillated at several integer multiples of frequency of breathing and at various higher frequencies, which were integer multiples of the frequency of breathing and the frequencies of firing of the sinus node. However, computing cardiac cycle length from membrane potential eliminated the higher frequencies. Therefore, cardiac cycle length oscillated at several integer multiples of the frequency of breathing, but not at these higher frequencies.

Acetylcholine↗
PubMed1978

[Role of computer technology and mathematical modelling in the treatment of patients after operations on the heart].

On the basis of ten-year experience in theoretical studies and experimental tests mathematical models of hemodynamics were built for the follow-up of parameters of the cardiovascular system which cannot be determined by means of any other modern methods. Three years of clinical studies of the Hewlett-Pachard monitoring computer system and its modification helped to elaborate the mathematical backing, a bank of mathematical models, original automatic programs for measuring the cardiac index, the index of myocardial viability, etc. The automatic system provides for an individual approach in assessing the patient's condition in actual time and for control of the treatment.

Cardiac Surgical Procedures↗
PubMed1984

Estimation of mean age at first marriage: use of a simple mathematical model.

"The present paper is an attempt to introduce a simple mathematical model to describe the age pattern of proportion never married women. The underlying model was found to give fairly close fit to an observed set of data of some 17 WFS [World Fertility Survey] countries. A mathematical formulation was then suggested in terms of the parameters in the model to estimate the mean age at first marriage. The mean ages obtained under the approach agreed quite closely with those obtained by Hajnal's method. The agreement between the estimates of ever married proportions obtained by the suggested model and...Coale's nuptiality model appeared also to be satisfactory."

Age Distribution↗
PubMed1998

Feto-maternal circulation: mathematical model and comparison with Doppler measurements.

OBJECTIVES: Clinicians are more and more frequently studying fetal blood flow velocity curves recorded by Doppler ultrasound in vital organs such as the placenta and fetal brain to evaluate fetal well-being. We have therefore developed a mathematical model of the utero-placental and fetal circulations which could be used for teaching and for a better understanding of regulatory mechanisms. METHODS: The model is based on two basic elements-an arterial segment and a bifurcation-and we have reproduced the major arteries of the feto-maternal circulation combining these basic elements. The mathematical model of the system is based on the Navier-Stokes equations. The peripheral areas such as the brain, kidneys and placenta are modeled by a simple Windkessel model and the model computes instantaneous flow and pressure at any point in the fetal arterial tree and the uterine arteries. RESULTS: We have compared the computed instantaneous flow curves and pressure with in vivo data and our results agree with the findings in physiological situations and in gravidic hypertension. CONCLUSIONS: Our model provides new interesting insights into fetal hemodynamics such as a better understanding of the mismatch impedance phenomena and is a promising model for the study of blood redistribution mechanisms in hypoxic situations.

Blood Vessels↗
PubMed2005

A mathematical model quantifying the impact of antibiotic exposure and other interventions on the endemic prevalence of vancomycin-resistant enterococci.

BACKGROUND: Mathematical modeling can be used to describe the interdependent and dynamic interactions that contribute to the transmission dynamics of vancomycin-resistant enterococci (VRE). A model was developed to quantify the contribution of antibiotic exposure and of other modifiable factors to the dissemination of VRE in the hospital setting. METHODS: The model consists of 4 compartments: patients colonized with VRE receiving and not receiving antibiotics and uncolonized patients receiving and not receiving antibiotics. A series of differential equations describe the movement between these compartments. Baseline parameter estimates were obtained from pharmacy, infection-control, and clinical databases. RESULTS: The main predictions of this model are that (1) preventing the initiation or enhancing the discontinuation of unnecessary antimicrobial therapy will have a greater impact if it is targeted to patients who are not colonized with VRE; (2) increasing the number of patients harboring VRE at the time of hospital admission substantially increases the endemic prevalence of VRE; and (3) eliminating the influx of VRE results in the eradication of this pathogen from the hospital. A decrease in the endemic prevalence of VRE also occurs with a decrease in the length of hospital stay of colonized patients, increased hand hygiene compliance, and a lower ratio of health-care workers : patients. CONCLUSION: This mathematical model provides a framework to assist in targeting necessary interventions aimed at limiting the spread of VRE.

Anti-Bacterial Agents↗
PubMed2004

[A mathematical model of determining the knee joint injury].

A mathematical model of determining the injury of human knee joint was established by using structural dynamics method. The results showvered the corresponding shearing displacement and bending angle of the knee joint on the occasion of ligament avulsion, and the shearing force and bending moment which caused tibial condylar fractures under purest shearing and bending condition. The calculated results consisted with the experimental results greatly, suggesting that using mathematical method to determine the injury is feasible and this kind of method can do good to lots of subjects, such as pedestrian protection, athletic medicine and rehabilitation engineering.

Humans↗
PubMed1975

Hepatic albumin and urea synthesis: The mathematical modelling of the dynamics of [14C]carbonate-derived guanidine-labelled arginine in the isolated perfused rat liver.

A mathematical model was constructed to define the dynamics of incorporation of radioactivity into urea carbon and the guanidine carbon of arginine in plasma albumin after the rapid intraportal-venous administration of Na214CO3 in the isolated perfused rat liver. 2. The model was formulated in terms of compartmental analysis and additional experiments were designed to provide further information on subsystem dynamics and to discriminate between alternative model structures. 3. Evidence for the rapid-time-constant of labelling of intracellular arginine was provided by precursor-product analysis of precursor [14C]carboante and product [14C]urea in the perfusate. 4. Compartmental analysis of the dynamics of newly synthesized urea was based on the fate of exogenous [13C]urea, endogenous [14C]urea and the accumulation of [12C]urea in perfusate water, confirming the early completion of urea carbon labelling, the absence of continuing synthesis of labelled urea, and the presence of a small intrahepatic urea-delay pool. 5. Analysis of the perfusate dynamics of endogenously synthesized and exogenously administered [6-14C]arginine indicated that although the capacity for extrahepatic formation of [14C]-urea exists, little or no arginine formed within the intrahepatic urea cycle was transported out of the liver. However, the presence of a rapidly turning-over intrahepatic arginine pool was confirmed. 6. On the basis of these subsystem analyses it was possible to offer feasible estimations for the parameters of the mathematical model. However, it was not possible to stimulate the form and magnitude of the dynamics of newly synthesized labelled urea and albumin which were simultaneously observed after administration of [14C]carbonate on the basis of a preliminary model which postulated that both products were derived from a single hepatic pool of [16-14C]arginine. On the other hand these observed dynamics could be satisfied to a two-compartment arginine model, which also provided an explanation for discrepancies observed between albumin synthesis measured radioisotopically and immunologically. This was based on a relative overestimation of [14C]urea specific radioactivity resulting from the rapid dynamics of [14C]carbonate and the [14C]urea subsystem relative to the labelled albumin subsystem. The effects of arginine compartmentalization could be minimized in the model by minor slowing of the rate of [14C]carbonate turnover or by constant infusion of [14C]carbonate, both of which permitted valid determination of albumin-synthesis rates.

Animals↗
PubMed2004

Sensitivity analysis of a novel mathematical model identifies factors determining bone resorption rates.

The development of pharmaceutical treatments for bone disease can be enhanced by computational models that predict their effects on resorption and rates of remodeling. Therefore, a simple mathematical model was formulated to simulate erosion depth and duration of resorption, using Michaelis-Menten (M-M) equations to describe changing rates of cellular activity during the two phases of bone resorption. The model was based on histomorphometric data and cellular interactions that occur in the bone microenvironment cited from the literature. Availability of bone substrate for osteoclastic activity during Phase I was assumed to be limited by the ratio of RANKL (ligand for receptor activator for nuclear factor kappaB) to osteoprotegerin (OPG) ('effective RANKL'). The required presence of marrow stromal cell produced macrophage-colony stimulating factor (M-CSF) for osteoclast action was represented as a factor equal to 1 for healthy bone. Growth factors released from the matrix during Phase I were assumed to cause two negative feedback effects: (1) the inhibitory effect of transforming growth factor-beta1 (TGFbeta1)-induced production of OPG by marrow osteoblast stromal cells, reducing effective RANKL; (2) the apoptosis of osteoclast nuclei assumed to occur at high concentrations of TGFbeta. This signaled the end of Phase I. During Phase II, cellular activity to remove the collagen fibrils left behind by osteoclasts was also simulated by Michaelis-Menten kinetic equations. Results of sensitivity analysis revealed variation in resorption depth and duration to fluctuate within 6% and 7% of the baseline value for changes in most input parameters. However, resorption depth was reduced and the duration of resorption lengthened by both a decrease in matrix TGFbeta and an increase the apoptotic threshold. Furthermore, the duration of resorption, but not erosion depth, was sensitive to changes in the maximum rate of cellular activity during removal of collagen fibrils. This mathematical model, which simulates the changing rates of cellular activity, has identified factors that reduce the duration and depth of resorption. It also suggests new targets for modeling therapeutic intervention to slow the rate of bone remodeling.

Bone Resorption↗
PubMed1994

Mathematical model of antiviral immune response. III. Influenza A virus infection.

We present an approach to studying theoretically the regularities and the kinetic characteristics of influenza A virus (IAV) infection in man. The estimates of the "numbers" (Zinkernagel et al., 1985) characterizing evolutionary established interferon and immune responses in uncomplicated IAV infection are explored by developing a multiparameter mathematical model which allows direct quantitative references to the biological reality. The system of equations of the mathematical model of antiviral immune response, applied earlier to acute hepatitis B virus infection (Marchuk et al., 1991a, b), is modified and extended to describe the joint reaction of the interferon and immune systems in IAV infection. Macrophages infiltrating the airway's epithelium are considered to be the principal source of interferon that induces antiviral resistance in lung epithelial cells. The model is formulated as a delay-differential system with about 60 parameters characterizing the rates of various processes contributing to the typical course of IAV infection. The key aspect of the adjustment between the model and various data on the immunity to influenza is the derivation of a consistent data set--the generalized picture of uncomplicated IAV infection. It serves as a consistent theoretical definition of the structure of the normal course of the infection and the antiviral immune response suitable for model fitting. The parameter estimates for the processes considered in the model are carefully discussed. The quantitative model is used to study the organization and dynamic properties of the processes contributing to IAV infection. The threshold condition for immune protection of virus-free host to infection with IAV is analyzed. The relative roles of humoral, cellular and interferon reactions for the kinetics of the uncomplicated IAV infection are studied. The contribution of parameters of virus-sensitive tissue, interferon and IAV-specific immune processes to the variations of duration and severity of the infection is quantitatively estimated by sensitivity studies. It is shown that the variations in the parameters of a virus-epithelial cell system are more influential on the severity of the infection rather than that of the antiviral immune response. The need for fine co-ordination of the kinetics of the non-specific interferon response and the adaptive antigen-specific immune reactions to provide recovery from the infection is illustrated.

Humans↗
PubMedDate not supplied

A mathematical model of the regulation of the G1 phase of Rb+/+ and Rb-/- mouse embryonic fibroblasts and an osteosarcoma cell line.

A mathematical model integrating the roles of cyclin D, cdk4, cyclin E, cdk2, E2F and RB in control of the G1 phase of the cell cycle is described. Experimental results described with murine embryo fibroblasts (MEFs), either Rb+/+ or Rb-/-, and with the RB-deficient osteosarcoma cell line, Saos-2, served as the basis for the formulation of this mathematical model. A model employing the known interactions of these six proteins does not reproduce the experimental observations described in the MEFs. The appropriate modelling of G1 requires the inclusion of a sensing mechanism which adjusts the activity of cyclin E/cdk2 in response to both RB concentration and growth factors. Incorporation of this sensing mechanism into the model allows it to reproduce most of the experimental results observed in Saos-2 cells, Rb-/- MEFS, and Rb+/+ MEFs. The model also makes specific predictions which have not been tested experimentally.

Animals↗
PubMed1999

[Mathematical model of micturition allowing a detailed analysis of free urine flowmetry].

A mathematical model of micturition allowing precise analysis of uroflowmetry curves (VBN method) is described together with some of its applications. The physiology of micturition and possible diagnostic hypotheses able to explain the shape of the uroflowmetry curve can be expressed by a series of differential equations. Integration of the system allows the validity of these hypotheses to be tested by simulation. A theoretical uroflowmetry is calculated in less than 1 second and analysis of a dysuric uroflowmetry takes about 5 minutes. The efficacy of the model is due to its rapidity and the precision of the comparisons between measured and predicted values. The method has been applied to almost one thousand curves. The uroflowmetries of normal subjects are restored without adjustment with a quadratic error of less than 1%, while those of dysuric patients require identification of one or two adaptive parameters characteristic of the underlying disease. These parameters remain constant during the same session, but vary with the disease and/or the treatment. This model could become a tool for noninvasive urodynamic studies.

Diagnostic Techniques, Urological↗