Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Mathematical Model”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,261 records · Page 70Linked to original sources
PubMed1998

A mathematical model of growth of population of fish in the larval stage: density-dependence effects.

A mathematical model for the growth of a population of fish in the larval stage is proposed. The emphasis is put on the first part of the larval stage, when the larvae are still passive. It is assumed that during this stage, the larvae move with the phytoplankton on which they feed and share their food equally, leading to ratio-dependence. The other stages of the life cycle are modeled using simple demographic mechanisms. A distinguishing feature of the model is that the exit from the early larval stage as well as from the active one is determined in terms of a threshold to be reached by the larvae. Simplifying the model further on, the whole dynamics is reduced to a two dimensional system of state-dependent delay equations. The model is put in perspective with some of the main hypotheses proposed in the literature as an explanation to the massive destruction which occurs between the egg stage and the adult stage.

Animals↗
PubMed1998

A three-dimensional mathematical model for predicting spinal joint force distribution during manual liftings.

OBJECTIVE: A three-dimensional dynamic mathematical model was developed to discover what loads are imposed on the lumbar structures by performance of asymmetric manual liftings. DESIGN: An external model was used to estimate the intersegmental resultant forces and moments at the L(5)/S(1) joint in this dynamic biomechanical model. Using an optimization algorithm, an internal model then distributed the intersegmental resultants to forces of muscle, disc, facet joints, and ligaments. BACKGROUND: To study the relation between large loads and low-back disorders, many biomechanical models have been developed. Most of the models were two-dimensional models discussed with symmetric activities. Some three-dimensional biomechanical models were static models or only included limited elements of the disc and muscles in the model. METHODS: A healthy young male subject was asked to perform asymmetric lift with bent knees. Dynamic data of body motion and ground reaction forces were monitored, and the EMG of six muscles were recorded simultaneously. A Newtonian equation was used to calculate the joint intersegmental resultant forces and moments. In the internal model, three components of the disc force, eight muscle forces, two ligament forces and two facet joint forces were computed. RESULTS: The correlation between the reaction moments from the upper and lower models of the external part were generally above 0.94, and the root mean square differences were below 19 Nm. In this internal model, the maximal disc compression was close to the data showed on the literature, and the estimation of muscle forces corresponded to the EMG activities. CONCLUSIONS: A three-dimensional biomechanical model has been developed and evaluated to estimate the spinal joint force distribution during asymmetric manual lifting activities.

Journal Article↗
PubMed2000

Predictions of the emergence of vaccine-resistant hepatitis B in The Gambia using a mathematical model.

Vaccine escape variants of hepatitis B virus (HBV) have been identified world-wide. A mathematical model of HBV transmission is used to investigate the potential pattern of emergence of such variants. Attention is focused on The Gambia as a country with high quality epidemiological data, universal infant immunization and in which escape mutants after childhood infections have been observed. We predict that a variant cannot become dominant for at least 20 years from the start of vaccination, even when using a vaccine which affords no cross protection. The dominant factor responsible for this long time scale is the low rate of infectious contacts between infected and susceptible individuals (we estimate the basic reproduction number of hepatitis B in The Gambia to be 1.7). A variant strain that achieves high prevalence will also take many years to control, and it is questionable whether emergence will be identifiable by sero-surveillance until of high prevalence. The sensitivity of the model predictions to epidemiological and demographic factors is explored.

Adolescent↗
PubMed2003

Emergent oscillations in a mathematical model of the human menstrual cycle.

BACKGROUND: The aim of this study was to develop a mathematical model of the hypothalamo-pituitary-gonadal axis that would reflect available data in humans. METHODS: A model of hormonal relationships at the early follicular and midluteal phases of the human menstrual cycle is proposed. FINDINGS: Two distinct temporal patterns of oscillatory behavior have been demonstrated for both pituitary and gonadal steroids in the early follicular phase: first, rapid oscillations in gonadotropin releasing hormone, follicle stimulating hormone and luteinizing hormone (Q approximate to 1 hour) that were an immediate consequence of the programmed equations. Second, there were slower, undulating, emergent rhythms in luteinizing hormone and follicle stimulating hormone, and also in estrogen, having oscillatory periods of 2-12 hours. There was also a longer-period (Q2-3 days) emergent rhythm in progesterone. In the mid-luteal phase, estrogen and progesterone rhythms were correlated, and all hormones showed an approximately 6-hour periodicity. CONCLUSIONS: To our knowledge, the oscillatory behavior of peripheral sex steroids in the follicular phase has not been previously noted.

Bipolar Disorder↗
PubMed2000

Mathematic modeling of forces associated with shoulder dystocia: a comparison of endogenous and exogenous sources.

OBJECTIVE: A mathematic model was developed to estimate the compressive pressure on the fetal neck overlying the roots of the brachial plexus by the symphysis pubis during a shoulder dystocia event. The induced pressure was calculated for both exogenous (clinician applied) and endogenous (maternal and uterine) forces during the second stage of labor. STUDY DESIGN: Intrauterine pressure and clinician-applied force data were taken from the existing literature. A free-body diagram was generated and equilibrium equations were used to calculate the contact pressure between the base of the fetal neck and the symphysis pubis during a shoulder dystocia event. RESULTS: Clinician-applied traction to the fetal head (exogenous force) led to an estimated contact pressure of 22.9 kPa between the fetal neck and the symphysis pubis. In contrast, uterine and maternal expulsive efforts (endogenous forces) resulted in contact pressures that ranged from 91.1 to 202.5 kPa. The estimated pressures resulting from endogenous forces are 4 to 9 times greater than the value calculated for clinician-applied forces. CONCLUSION: Neonatal brachial plexus injury is not a priori explained by iatrogenically induced excessive traction. Spontaneous endogenous forces may contribute substantially to this type of neonatal trauma.

Brachial Plexus↗
PubMed2001

Mathematical modelling of responses of cerebral blood vessels to changing intraluminal pressure.

The authors have designed a mathematical model to investigate the influences of the physical and chemical properties of the cerebral blood vessel resistance on vessel diameter. The model is based on the way the total tension within the blood vessel walls varies due to specific ions interacting and affecting the vascular smooth muscle cells and the vascular walls. In particular, we shall model a series of calcium sites and derive a generalized equation of the diameter as a function of pressure. The model includes the action of the vascular smooth muscle cells and the elasticity of the vascular walls, the pressure exerted on the walls by the blood and the effect of alterations to their properties within the blood vessel. They are formulated in terms of three parameters: the diameter at zero pressure, the myogenic response as the pressure tends to zero and a term associated with the myogenic tone. All three parameters may be reliably extracted from diameter-pressure measurements. The model was successfully used in quantifying diameter oscillations and dynamic myogenic responses that are frequently observed both in vivo and in vitro. Finally, we tested the model on experimental data obtained from the resistance of cerebral vessels that have been isolated from rats. In particular, we have first shown that the blood vessel characteristics are such that the diameter change due to calcium ion variations is at a maximum value. Second, we have shown that blood flow affects the myogenic response and third, we can explain the affect of ATP on the vessel diameter.

Adenosine Triphosphate↗
PubMed1991

A mathematical model for the computation of carboxyhaemoglobin in human blood as a function of exposure time.

A mathematical model is developed for the carbon monoxide (CO) uptake by the blood by taking into account the molecular diffusion, convection, facilitated diffusion and the non-equilibrium kinetics of CO with haemoglobin. The overall rate for the combination of CO with haemoglobin is derived by including the dissociation of CO from carboxyhaemoglobin (COHb). The resulting coupled system of nonlinear partial differential equation with physiologically relevant initial, entrance and boundary conditions is solved numerically. A fixed point iterative technique is used to deal with nonlinearities. The concentration of COHb in the blood is computed as a function of exposure time and ambient CO concentration. The COHb levels computed from our model are in good agreement with those measured experimentally. Also, results computed from our model give better approximation to the experimental values compared with the results from other models. The time taken by the blood COHb to attain 95% of its equilibrium value is computed. The COHb concentration in the blood increases with the increase in ventilation rate, association rate coefficient of CO with haemoglobin and total haemoglobin content in the blood, and with the decrease in dissociation rate coefficient of CO with haemoglobin and mean capillary blood PO2. It is found that the COHb level in the blood is not affected significantly because of endogenous production of CO in the body under normal condition. However, the effect may be significant in the patients with haemolytic anaemia.

Capillaries↗
PubMed2004

Opioid-induced respiratory depression: a mathematical model for fentanyl.

In this paper, respiratory depressant effects of fentanyl are described quantitatively by a mathematical model. The model is an extension of a previous one, which reproduces the human ventilatory control system on a physiological basis. It includes the following: three compartments for gas storage and exchange (lungs, body tissue, and brain tissue); the main mechanisms involved in ventilation control (peripheral chemoreceptors, central chemoreceptors, and the central hypoxic depression); and local blood flow regulation. The effects of fentanyl on the respiratory system include a decrease in peripheral and central chemoreceptor gains on ventilation and a direct inhibition of respiratory neural activity. All parameters in the model were chosen according to the literature. The model is able to reproduce the ventilatory effects of fentanyl in several conditions: 1) constant levels of fentanyl; 2) after a bolus injection; 3) at fixed levels of P(ETCO2); and 4) after artificial ventilation. According to the model, in spontaneously breathing subjects, minute ventilation depends on two opposing actions: fentanyl inhibitory influences, which depress ventilation, reducing oxygen tension and increasing CO2 tension, and the consequent activation of chemoreceptors, which stimulates ventilation. Simulations of anesthetized patients resuming spontaneous breathing after artificial ventilation demonstrate the risk of prolonged apnea and tissue hypoxemia. A safe transition can be achieved by increasing patient PCO2 toward the end of artificial ventilation, because an advanced chemoreceptor stimulation is produced, which promptly counteracts fentanyl-induced inhibition at cessation of artificial ventilation.

Adaptation, Physiological↗
PubMed1998

Mathematical model of vertebrate gap junctions derived from electrical measurements on homotypic and heterotypic channels.

1. A mathematical model has been developed which describes the conductive and kinetic properties of homotypic and heterotypic gap junction channels of vertebrates. 2. The model consists of two submodels connected in series. Each submodel simulates a hemichannel and consists of two conductances corresponding to a high (H) and low (L) conductance state and a switch, which simulates the voltage-dependent channel gating. 3. It has been assumed that the conductances of the high state and low state vary exponentially with the voltage across the hemichannel. 4. The parameters of the exponentials can be derived from data of heterotypic or homotypic channels. As a result, the behaviour of heterotypic channels can be predicted from homotypic channel data and vice versa. 5. The two switches of a channel are governed by the voltage drop across the respective hemichannel. The switches of a channel work independently, thus giving rise to four conformational states, i.e. HH, LH, HL and LL. 6. The computations show that the dogma of a constant conductance for homotypic channels results from the limited physiological range of transjunctional voltages (Vj) and the kinetic properties of the channel, so a new fitting procedure is presented. 7. Simulation of the kinetic properties at the multichannel level revealed current time courses which are consistent with a contingent gating. 8. The calculations have also shown that the channel state LL is rare and of short duration, and hence easy to miss experimentally. 9. The design of the model has been kept flexible. It can be easily expanded to include additional features, such as channel substates or a closed state.

Animals↗
PubMed1995

Mathematical modeling of noninvasive blood pressure estimation techniques--Part I: Pressure transmission across the arm tissue.

A mathematical model of the arm tissue mechanical behavior under the effect of external pressure loads is presented. The model has been used to study stress and strain distribution across the tissue, and pressure transmission to the brachial artery, when the arm is compressed by two adjacent cuffs independently inflated. Using this configuration, the tissue elastic parameters (Young modulus and Poisson ratio) can be individually identified using a simple and noninvasive experimental procedure. Model validation has been achieved by comparing its results with data obtained experimentally on 10 subjects. These comparisons demonstrate that the proposed model may constitute a simple but valid new tool able to describe tissue behavior, subjected to external pressures, with sufficient accuracy. Joined with a model of brachial hemodynamics, it might contribute to improve our understanding of noninvasive blood pressure estimation techniques.

Arm↗
PubMed1999

A mathematical model for human brain cooling during cold-water near-drowning.

A two-dimensional mathematical model was developed to estimate the contributions of different mechanisms of brain cooling during cold-water near-drowning. Mechanisms include 1) conductive heat loss through tissue to the water at the head surface and in the upper airway and 2) circulatory cooling to aspirated water via the lung and via venous return from the scalp. The model accounts for changes in boundary conditions, blood circulation, respiratory ventilation of water, and head size. Results indicate that conductive heat loss through the skull surface or the upper airways is minimal, although a small child-sized head will conductively cool faster than a large adult-sized head. However, ventilation of cold water may provide substantial brain cooling through circulatory cooling. Although it seems that water breathing is required for rapid "whole" brain cooling, it is possible that conductive cooling may provide some advantage by cooling the brain cortex peripherally and the brain stem centrally via the upper airway.

Algorithms↗
PubMed1993

A general mathematical model for respiratory dynamics relevant to the clinical setting.

We have developed and validated a general mathematical model for the dynamic behavior of the single-compartment respiratory system in response to an arbitrary waveform of applied inspiratory pressure. Our general model for ventilation applies to all integrable functions of applied pressure, and it enables computation of most ventilation and pressure variables of clinical interest from clinician-selected and impedance-determined inputs readily measured or estimated at the bedside. Interactions between both phases of the ventilatory cycle are considered by assuming that deflation occurs passively from a unicompartment lung. Because this flexible model appears both capable of accurate prediction and robust to major violations of its underlying linear assumptions, it may prove to be of value in a variety of scientific, educational, and clinical settings.

Humans↗
PubMedDate not supplied

[Mathematical model of microorganism biomass growth in the absence of a limiting substrate and inhibiting agents].

A mathematical model for the growth of microbial cells upon submerged cultivation was constructed. The model describes the growth phases of the biomass of microorganisms in the absence of inhibiting agents and limitation by substrate in the medium. At the basis of model is the requirement that cells should not be in physical contact during some time in order that they can divide. The model involves the known concepts of statistical physics. The consequences of the model are discussed.

Biomass↗
PubMed2002

[A mathematical model of water stress and light condition effects on cotton dry matter and yield formation].

A mathematical model was developed to analyze the effects of water stress and light condition on crop dry matter accumulation and yield formation based on canopy carbon net assimilation rate. The function leaf water potential (psi l) indicating the water status of canopy was incorporated into this model, according to the assumption that the canopy resistance (Rc) was increased under the conditions of water stress and low light density. Psi l was estimated by a simplified regression equation, in which, the independent variables were relative soil moisture (Aw), ambient temperature (Ta), and vapor pressure deficit (VPD). The aerodynamic resistance (Ra) in the model was defined as a function of wind speed (u), and the yield was calculated by a linear increase in harvest index (hi) with time. The modeled data agreed well with the data observed from pot experiment. Sensitivity analysis and simulation results suggested that the model could be useful in identifying environment factors, especially soil water content and light density effects on crop growth and yield formation.

Bombax↗
PubMed1995

Mathematical models for tumour angiogenesis: numerical simulations and nonlinear wave solutions.

To ensure its sustained growth, a tumour may secrete chemical compounds which cause neighbouring capillaries to form sprouts which then migrate towards it, furnishing the tumour with an increased supply of nutrients. In this paper a mathematical model is presented which describes the migration of capillary sprouts in response to a chemoattractant field set up by a tumour-released angiogenic factor, sometimes termed a tumour angiogenesis factor (TAF). The resulting model admits travelling wave solutions which correspond either to successful neovascularization of the tumour or failure of the tumour to secure a vascular network, and which exhibit many of the characteristic features of angiogenesis. For example, the increasing speed of the vascular front, and the evolution of an increasingly developed vascular network behind the leading capillary tip front (the brush-border effect) are both discernible from the numerical simulations. Through the development and analysis of a simplified caricature model, valuable insight is gained into how the balance between chemotaxis, tip proliferation and tip death affects the tumour's ability to induce a vascular response from neighbouring blood vessels. In particular, it is possible to define the success of angiogenesis in terms of known parameters, thereby providing a potential framework for assessing the viability of tumour neovascularization in terms of measurable quantities.

Animals↗
PubMed1998

Mathematical modelling of morphogenesis in fungi: spatial organization of the gravitropic response in the mushroom stem of Coprinus cinereus.

The purpose of this work was to establish how the distribution of local curvatures changed during the mushroom stem gravitropic reaction and to suggest a suitable mathematical model based on these new data. The gravitropic bending of base- and apex-pinned Coprinus cinereus (Fries) S. F. Gray stems was recorded on videotapes. The images were captured from the tapes after each 10 min, rotated by 45 degrees and transformed into tables of changing co-ordinates of points for each stem. The non-linear regression of these points was performed using Legendre polynomials. From the resulting equations the patterns of changing local curvature for 50 subsections per stem during 400 min of gravitropic reaction were calculated. It was observed that base-pinned stems first bent from the apex, but later the curvature of this part decreased, and in the late stages the apex became nearly completely straight again. Subsections, located about one third of stem length from the base determined the main part of the final curvature. The free basal part of the apex-pinned stems bent upward and after a certain bending time also began to straighten. However, this process started significantly later and was weaker. Bending of the subsections close to the pinned apex did not stop when they reached the vertical position, and the final angle of gravitropic curvature could exceed 180 degrees. Plotting various functions of local bending speed and its derivatives against each other and against local angle indicated that, if the hypothetical signal about reorientation arises in the apex, its propagation towards the base did not follow simple wave or simple diffusion laws. The importance of the local angle of all subsections both for signal origin and transmission was established and a signal transmission equation, involving local angle of each subsection, was derived. After creating a suitable program this partial differential equation was solved numerically. The generated shapes of the bending stem coincided in high degree with experimentally observed images.

Computer Simulation↗