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 1,045 records · Page 58Linked to original sources
PubMed2005

A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. I. Formulation and base-case results.

We have developed a highly detailed mathematical model for the urine concentrating mechanism (UCM) of the rat kidney outer medulla (OM). The model simulates preferential interactions among tubules and vessels by representing four concentric regions that are centered on a vascular bundle; tubules and vessels, or fractions thereof, are assigned to anatomically appropriate regions. Model parameters, which are based on the experimental literature, include transepithelial transport properties of short descending limbs inferred from immunohistochemical localization studies. The model equations, which are based on conservation of solutes and water and on standard expressions for transmural transport, were solved to steady state. Model simulations predict significantly differing interstitial NaCl and urea concentrations in adjoining regions. Active NaCl transport from thick ascending limbs (TALs), at rates inferred from the physiological literature, resulted in model osmolality profiles along the OM that are consistent with tissue slice experiments. TAL luminal NaCl concentrations at the corticomedullary boundary are consistent with tubuloglomerular feedback function. The model exhibited solute exchange, cycling, and sequestration patterns (in tubules, vessels, and regions) that are generally consistent with predictions in the physiological literature, including significant urea addition from long ascending vasa recta to inner-stripe short descending limbs. In a companion study (Layton AT and Layton HE. Am J Physiol Renal Physiol 289: F1367-F1381, 2005), the impact of model assumptions, medullary anatomy, and tubular segmentation on the UCM was investigated by means of extensive parameter studies.

Animals↗
PubMed1991

On the dynamic organization of memory. A mathematical model of associative free recall.

The interaction of memory structures and retrieval dynamics is discussed. A mathematical model for associative free recall is presented to support the view that the organization of simple processing units plays an important role in the retrieval of memory traces. Computer simulations show that "flexibility" and "fidelity" of the dynamics strongly depend on the network structure, the amplification and decay parameters, and the noise term.

Association Learning↗
PubMed2005

A mathematical model for regulating monomer composition of the microbially synthesized polyhydroxyalkanoate copolymers.

A mathematical model is proposed for predicting the copolymer composition of the microbially synthesized polyhydroxyalkanoate (PHA) copolymers. Based on the biochemical reactions involved in the precursor formation and polymerization pathways, the model correlates the copolymer composition with the cultivation conditions, the enzyme levels and selectivity, and the metabolic pathways. It suggests the following points: (1) in the case of a sole carbon source, the copolymer composition depends mainly on the topology of the metabolic pathways and the selectivity of both the enzymes involved in the precursor formation and the polymerization route; (2) the copolymer composition can be varied in a wide range via alteration of the flux ratio of different types of monomers channeled from two or more independent and simultaneous pathways; (3) the enzymes which should be over-expressed or inhibited to obtain the desired copolymer composition can be predicted. For example, inhibition of the beta-oxidation pathway will increase the content of the monomer units with longer chain length. To test the model, various experiments were envisaged by varying cultivation time, concentration and chain length of the sole carbon source, and molar ratio of the cosubstrates. The predictions from the model agree well with the experimental results. Therefore, the proposed model will be useful in predicting the PHA copolymer composition under different biochemical reaction conditions. In other words, it can provide a guide for the synthesis of desired PHA copolymers.

Computer Simulation↗
PubMed1995

A mathematical model for biopanning (affinity selection) using peptide libraries on filamentous phage.

A mathematical model is presented for the process of selection of peptides for binding to a target. The affinity enrichment process commonly known as biopanning relies on subjecting a library of peptides on filamentous phage to a selection for binding to the target immobilized on solid support or in solution. The model is an implementation of the mass-action law to the diverse population of macromolecular assemblies. An analytical solution is presented for the enrichment process. Most parameters in the enrichment formula can be easily determined experimentally. Two examples corresponding to biopanning with epitope libraries and antibody libraries are given. The model allows for an estimation of the contribution of equilibrium and dissociative biopanning to the overall enrichment. The model can be a tool in the evaluation of the role of different biopanning parameters. Its implementation in a spreadsheet makes it possible to perform a computer simulation of a biopanning experiment.

Antibodies↗
PubMed1990

Mathematical model for the computation of alveolar partial pressure of carbon monoxide.

A mathematical model is formulated for computing alveolar partial pressure of carbon monoxide (PACO) from that in the atmospheric air. The model takes into account parameters like inspired/expired air flow rates, diffusion capacity of the lung, concentration of CO in the atmospheric air, blood flow rate and the non-linear CO dissociation curve. The effect due to the presence of O2 in the blood on CO dissociation curve is also incorporated. It is shown that for a given atmospheric CO concentration, PACO increases exponentialy with time and attains asymptotic value. Alveolar PCO increases further with the increase in the atmospheric CO concentration. The model can also be used to compute carboxyhaemoglobin levels in the blood as a function of exposure time and the results are comparable with the CFK equation and the values measured experimentally.

Carbon Monoxide↗
PubMed1990

A mathematical model for scheduling screening tests for progressive diseases.

In this paper, a mathematical model describing the stochastic process underlying the etiology of noncontagious, curable, progressive diseases is developed. In our previous study of progressive diseases, the reliabilities of screening tests were assumed to be constants, independent of how long the individual has had the disease. The purpose of this study is to develop more insight into modeling the disease process, and the interaction of screening tests with the natural behavior of the disease. To accomplish this task, more realistic screening parameters are selected, and optimum policies for mass screening programs under different reliabilities of screening tests are developed. These modifications make the model general enough to be applicable to a larger class of progressive diseases that includes breast cancer. Solutions to two simplified versions of the model for childhood neuroblastoma illustrate the use of our proposed procedure.

Catastrophic Illness↗
PubMed1984

A mathematical model for lambda dv plasmid replication: analysis of copy number mutants.

A mathematical model based on the molecular control mechanisms for lambda dv plasmid replication in a single Escherichia coli cell has been applied to simulate replication of mutant lambda dv plasmids. Model simulations of changes in repressor level and copy number resulting from mutations in the promoter-operator PROR region are consistent with experimental data. Calculated effects on lambda dv plasmid copy number of oligomer formation and of alternations in termination efficiency at tR1 also agree with experiment. The model has been employed to simulate the influence of cro mutants and of cro and tR1 double mutants on copy number and stable maintenance of lambda dv plasmid copy number. The genetic structure included in formulation of the replicon model provides a framework for relating changes in specific genetic loci on the plasmid with resulting alterations in host-plasmid system function.

Base Sequence↗
PubMed1988

An improved calibration procedure for computer-based quantitative autoradiography utilizing a mathematical model for the non-linear response of camera and film.

A mathematical model which accounts for the non-linear response of both the camera and film in computer-aided quantitative autoradiography is derived. This model and the algorithm to fit the data for radioactive standards by a non-linear least-squares procedure to this model are described. The usefulness of this technique is demonstrated by employing it to analyze a set of 14C-labeled brain paste standards which were exposed to Ultrofilm in such a way that the full response range of the film was used. This technique can be readily implemented on most commercially available image analysis systems and is compatible with most types of video cameras.

Algorithms↗
PubMed1981

Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes.

A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.

Journal Article↗
PubMed2005

Response to continuous and pulsatile PTH dosing: a mathematical model for parathyroid hormone receptor kinetics.

In this paper, we propose a mathematical model for parathyroid hormone receptor (PTH1R) kinetics, focusing on the receptor's response to PTH dosing to discern bone formation responses from bone resorption. The PTH1R is a major target for new osteoporosis treatments, as pulsatile PTH dosing has been shown to induce net bone formation in both animals and humans, and PTH(1-34) was recently FDA approved for the treatment of post-menopausal osteoporosis. PTH has also been shown to cause net bone loss when given continuously, so that the net action of PTH on bone is dependent on the dosing pattern. We have developed a simplified two-state receptor kinetics model for the PTH1R, based on the concepts of Segel et al., to distinguish the activity of active and inactive receptor and receptor-ligand complexes. The goal is to develop a plausible model of the minimal essential biological relationships necessary for understanding the responses to PTH dosing. A two-state model is able to effectively discriminate between continuous and pulsatile PTH dosing using the active species as surrogates for the downstream anabolic response. For continuous PTH dosing, the model predicts a desensitized system dominated by the inactive receptor and complex, consistent with downstream net bone loss that has been demonstrated experimentally. Using pulsatile PTH dosing, the model system predicts a highly sensitized state dominated by the active receptor and complex, corresponding to net bone formation. These results are consistent with the hypothesis that the kinetics of the receptor plays a critical role in the downstream effects of PTH dosing. Moreover, these results indicate that within a range of biologically relevant PTH doses, the two-state model is able to capture the differential behavior of the system for both continuous and pulsatile PTH dosing. The development of such a model provides a rational basis for developing more biologically extensive models that may support the design of optimal dosing strategies for PTH-based anti-osteoporosis treatments. Moreover, this model provides a unique starting point from which to design experiments investigating PTH receptor biology.

Animals↗
PubMed1996

Predicting discharge destination of stroke patients using a mathematical model based on six items from the Functional Independence Measure.

OBJECTIVE: A mathematical model using selected items from the Functional Independence Measure (FIM) was developed to predict disposition of stroke patients from an acute care hospital. DESIGN: Case series of 279 acute stroke patients admitted to the hospital from 4/91 through 12/93. Data collection remains ongoing; a second series of patients will be analyzed to validate results and determine if the same 6 FIM items are significant. SETTING: Tertiary care center, general acute care community hospital. PATIENTS: Diagnosis of acute stroke; 298 patients whose attending physician referred the patient to the rehabilitation team. An 18-item FIM was administered within 3 days of admission and 24 hours of discharge. MAIN OUTCOME MEASURE: FIM scores were analyzed to determine if the initial score could be used to predict disposition. Discriminant analysis identified 6 items as being statistically significant in predicting discharge to home, rehabilitation facility, or nursing home. Patient's actual discharge location was compared with the location predicted by the model developed using the FIM. RESULTS: Bathing, bowel, toileting, social interaction, dressing lower body, and eating were the selected initial FIM items that predicted disposition with 70% accuracy in our patient series. CONCLUSION: The FIM is effective in the acute care setting to help determine appropriate discharge status, with certain variables being more predictive than others.

Activities of Daily Living↗
PubMed1991

A mathematical model and computer simulation study of insulin sensitive glucose transporter regulation.

A mathematical model of insulin sensitive glucose transporter regulation is developed. Model structure is based on experimental evidence from adipocytes and myocytes. Model parameters correspond with known cellular processes. As an example, computer simulation results are compared with data from rat adipocytes. Cellular processes explicitly represented in the model include state-dependent glucose transporter synthesis and degradation rates, insulin sensitive glucose transporter translocation rates, and a glucose transporter endocytosis rate. Most of these processes are represented as first-order events. Using more complex representations of the model structure (e.g. higher order rate constants or saturable pathways) or alternative structures did not result in qualitatively better results. The model is able to accurately simulate the insulin sensitive, insulin concentration dependent, reversible translocation of glucose transporters observed in normal adipocytes. The model is also able to accurately simulate the changes in regulation of glucose transporter translocation observed with increases in cell surface area. Finally, the model can simulate pathogenic states which induce impairment of glucose transporter regulation (e.g. altered glucose transporter regulation in adipocytes from rats on high fat diets, rats with streptozotocin induced diabetes, and fasted rats). Since the structure of our model is sufficient to explain glucose transporter regulation in both normal and pathological states, it may aid in understanding the post-receptor components of insulin resistance (decreased sensitivity or responsiveness to insulin) seen in pathological states such as obesity and diabetes mellitus.

Adipose Tissue↗
PubMed2001

Mathematical modeling of response of ecosystems with different structure to external impact.

A mathematical model was used to study the response of ecosystems of different structures to external impact. The response was measured as a sensitivity coefficient: the magnitude of the system's response vs. the change of the factor in the inflow. The formula has been obtained to calculate the sensitivity coefficient for ecosystems containing different numbers of trophic links. The derived sensitivity coefficients demonstrate that the degree of compensation for the external impact can differ depending on the type of system regulation and the length of the trophic chain. E. g. the sensitivity coefficient decreases with complexity of trophic links in an ecosystem for top-down controlled systems and impact of degree of openness on sensitivity e.g. closed ecosystems show higher sensitivity then fully open ecosystem to impacts also bottom-up control system show less sensitivity then top-down. Grant numbers: N99-04-96017, N25.

Animals↗
PubMed2002

The role of mathematical modelling in the control of the 2001 FMD epidemic in the UK.

Mathematical models played an important role in guiding the development of the control policies in the 2001 foot-and-mouth disease epidemic in the UK. The variety of approaches that helped to guide the policy can sometimes be confusing. Here, the different modelling exercises that were developed over the course of the epidemic are reviewed, describing the difficulties in interpreting the available data and the appropriateness of the various assumptions.

Animals↗
PubMed2003

A mathematical model for the transmission of Plasmodium vivax malaria.

We have proposed a mathematical model for the transmission of Plasmodium vivax malaria quantitatively, which is adjusted to the infected region, Guadalcanal, in the Solomon Islands. The simulation of a transmission model will be instrumental in planning the malaria control strategy. A characteristic of the life cycle of P. vivax is that a sporozoite injected into the blood stream by a mosquito bite may sometimes stay in a hepatocyte as a hypnozoite. Therefore, we have incorporated a phenomenon of renewed infections caused by a relapse into the transmission model. Also through the simulations we have attempted to evaluate the decline in prevalence caused by the programs of selective mass drug administration (MDA) and vector control such as the distribution of permethrin-treated bednets. The simulations have indicated that the concentrated repetition of MDA at 1-week intervals would reduce the prevalence of vivax malaria swiftly in the beginning and would keep the parasite rate below 1% for a few years but the prevalence would increase thereafter. In contrast, the parasite rate would remain below 1% for a long time if a trial of 1 or 2 times MDA is accompanied with some reduction of the vectorial capacity by the enforcement of vector control. In any case, it is important to beware of relapse cases because even after the execution of MDA it takes a long time to decrease the proportion of hypnozoite carriers.

Age Distribution↗
PubMed1983

Mathematical model of synaptic facilitation and depression during and following repetitive stimulation.

A mathematical model of facilitation and depression of postsynaptic potential amplitude (PSP) during and following repetitive stimulation is proposed. The model uses first-degree linear equations to simulate the interactions of different presynaptic physiological mechanisms that may influence and control the amount of transmitters liberated outside the nerve terminal. These mechanisms are: (1) vesicle movement toward the presynaptic membrane, (2) transmitter release, (3) vesicle recycling within the synapse, and (4) transmitter synthesis. When submitted to the same frequencies and durations of stimulation as used in a variety of electrophysiological studies of synaptic facilitation and depression, the model successfully reproduces all the variations of PSP amplitude obtained in these studies. The analysis of the internal functioning of the model during the process of simulation also allows a better understanding of the dynamics of diverse phenomena characterizing facilitation and depression during and following the administration of a tetanus. The main conclusion of this study is that both facilitation and depression may be explained in terms of the dynamics of a single synaptic system.

Computers↗
PubMed1978

Mathematical modeling of rewarming after cold therapy.

Statistical methods are presented for fitting mathematical models to skin temperature data. Three types of regression curves, namely, linear regression (Y = A + BX), second-degree regression (Y = A + BX + CX2), and asymptotic regression (Y = alpha + betapx), are discussed as possible models for the rewarming process following cold therapy. The data for fitting the curves consists of back surface temperature (degrees C) corresponding to various times after cold pack treatment (19 degrees C, administered for 20 minutes) was terminated.

Cryotherapy↗
PubMed1998

A mathematical model for the assessment of hemodynamic parameters using quantitative contrast echocardiography.

A mathematical model for the assessment of hemodynamic parameters using quantitative echocardiography is presented. The method involves the intravenous injection of an ultrasonic echo contrast agent. The relative enhancement of the backscattered ultrasound intensity is measured as a function of time (the time-intensity curve). From this measurement, the volume flow rate (cardiac output) and the mixing volume are calculated. Relevant acoustic properties of the ultrasound contrast agent are discussed. An in vitro experiment is performed to corroborate the theory presented.

Calibration↗