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At least 1,729 records · Page 96Linked to original sources
PubMed2005

Mathematical modeling and optimization of drug delivery from intratumorally injected microspheres.

PURPOSE: Paclitaxel is a highly promising phase-sensitive antitumor drug that could conceivably be improved by extended lower dosing as opposed to intermittent higher dosing. Although intratumoral delivery of paclitaxel to the whole tumor at different loads and rates has already been achieved, determining an optimal release mode of paclitaxel for tumor eradication remains difficult. This study set out to rationally design such an optimal microsphere release mode based on mathematical modeling. EXPERIMENTAL DESIGN: A computational reaction-diffusion framework was used to model drug release from intratumorally injected microspheres, drug transport and binding in tumor interstitum, and drug clearance by microvasculature and intracellular uptake and binding. RESULTS: Numerical simulations suggest that interstitial drug concentration is characterized by a fast spatially inhomogeneous rise phase, during which interstitial and intracellular binding sites are saturated, followed by a slow spatially homogeneous phase that is governed by the rate of drug release from microspheres. For zero-order drug release, the slow phase corresponds to a plateau drug concentration that is proportional to the ratio of the rate of blood clearance of drug to the rate of drug release from microspheres. Consequently, increasing the duration of intratumoral drug release extends the duration of cell exposure to the drug but lowers the plateau drug concentration. This tradeoff implies that intratumoral drug release can be designed to optimize tumor cell kill. Synthesizing our modeling predictions with published dose-response data, we propose an optimal protocol for the delivery of paclitaxel-loaded microspheres to small solid tumors.

Animals↗
PubMed2002

Toxin-producing plankton may act as a biological control for planktonic blooms--field study and mathematical modelling.

Termination of planktonic blooms is of great importance to human health, ecosystem, environment, tourism and fisheries. Toxic substances released by plankton play an important role in this context. The effect of toxin-producing plankton (TPP) on zooplankton is observed from the field-collected samples and mathematical modelling. Information from both the studies led us to suggest that TPP may terminate the planktonic blooms by decreasing the grazing pressure of zooplankton and thus acts as a biological control.

Animals↗
PubMed1988

Effects of cocaine on release and uptake of dopamine in vivo: differentiation by mathematical modeling.

Although considerable effort has been invested trying to distinguish between the effects of cocaine on dopamine (DA) uptake and release in both in vitro and in vivo experiments, disagreement over the specific actions of cocaine remains. The results obtained by combining experimental extracellular DA data with a mathematical model of the dopaminergic neuron allow examination of the cocaine uptake inhibition/release question. The extracellular DA concentration profile observed following a 30 mg/kg IP cocaine injection can be modeled if both pre- and postsynaptic uptake are competitively inhibited by cocaine with or without an enhanced DA release effect. However, if cocaine elicits enhanced DA release, modeling predicts a 40% increase over basal levels of 3,4-dihydroxyphenylacetic acid (DOPAC) and a 30% increase in homovanillic acid (HVA) at 60 minutes following a 30 mg/kg IP cocaine injection. Reported DOPAC and HVA data for similar cocaine doses indicate little change in either DOPAC or HVA. These data agree best with modeled metabolite predictions for little or no cocaine-enhanced DA release.

Cocaine↗
PubMed2006

A stochastic mathematical model of methicillin resistant Staphylococcus aureus transmission in an intensive care unit: predicting the impact of interventions.

OBJECTIVES: To estimate the transmission rate of MRSA in an intensive care unit (ICU) in an 800 bed Australian teaching hospital and predict the impact of infection control interventions. METHODS: A mathematical model was developed which consisted of four compartments: colonised and uncolonised patients and contaminated and uncontaminated health-care workers (HCWs). Patient movements, MRSA acquisition and daily prevalence data were collected from an ICU over 939 days. Hand hygiene compliance and the probability of MRSA transmission from patient to HCW per discordant contact were measured during the study. Attack rate and reproduction ratio were estimated using Bayesian methods. The impact of a number of interventions on attack rate was estimated using both stochastic and deterministic versions of the model. RESULTS: The mean number of secondary cases arising from the ICU admission of colonised patients, also called the ward reproduction ratio, R(w), was estimated to be 0.50 (95% CI 0.39-0.62). The attack rate was one MRSA transmission per 160 (95% CI 130-210) uncolonised-patient days. Results were not sensitive to uncertainty in measured model parameters (hand hygiene rate and transmission probability per contact). Hand hygiene was predicted to be the most effective intervention. Decolonisation was predicted to be relatively ineffective. Increasing HCW numbers was predicted to increase MRSA transmission, in the absence of patient cohorting. The predictions of the stochastic model differed from those of the deterministic model, with lower levels of colonisation predicted by the stochastic model. CONCLUSIONS: The number of secondary cases of MRSA colonisation within the ICU in this study was below unity. Transmission of MRSA was sustained through admission of colonised patients. Stochastic model simulations give more realistic predictions in hospital ward settings than deterministic models. Increasing staff does not necessarily lead to reduced transmission of nosocomial pathogens.

Bayes Theorem↗
PubMed2006

Mathematical modelling: a tool for hospital infection control.

Health-care-associated infections caused by antibiotic-resistant pathogens have become a menace in hospitals worldwide and infection control measures have lead to vastly different outcomes in different countries. During the past 6 years, a theoretical framework based on mathematical models has emerged that provides solid and testable hypotheses and opens the road to a quantitative assessment of the main obstructions that undermine current efforts to control the spread of health-care-associated infections in hospitals and communities. We aim to explain to a broader audience of professionals in health care, infection control, and health systems administration some of these models that can improve the understanding of the hidden dynamics of health-care-associated infections. We also appraise their usefulness and limitations as an innovative research and decision tool for control purposes.

Cross Infection↗
PubMedDate not supplied

An analysis of hypoxia in sheep brain using a mathematical model.

Cerebral blood flow (CBF) increases as arterial oxygen content falls with hypoxic (low PO2), anemic (low hemoglobin) and carbon monoxide (CO) (high carboxyhemoglobin) hypoxia. Despite a higher arterial PO2, CO hypoxia provokes a greater increase in CBF than hypoxic hypoxia. We analyzed published data using a compartmental mathematical model to test the hypothesis that differences in PO2 in tissue, or a closely related vascular compartment, account for the greater response to CO hypoxia. Calculations showed that tissue, but not arteriolar, PO2 was lower in CO hypoxia because of the increased oxyhemoglobin affinity with CO hypoxia. Analysis of studies in which oxyhemoglobin affinity was changed independently of CO supports the conclusion that changes in tissue PO2 (or closely related capillary or venular PO2) are predictive of alterations in CBF. We then sought to determine the role of tissue PO2 in anemic hypoxia, with no change in arterial and little, if any, change in venous PO2. Calculations predict a small fall in tissue PO2 as hematocrit decreases from 55% to 20%. However, calculations show that changes in blood viscosity can account for the increase in CBF in anemic hypoxia over this range of hematocrits.

Algorithms↗
PubMed2002

Edema-induced increase in tumour cell survival for 125I and 103Pd prostate permanent seed implants--a bio-mathematical model.

Edema caused by the surgical procedure of prostate seed implantation expands the source-to-point distances within the prostate and hence decreases the dose coverage. The decrease of dose coverage results in an increase in tumour cell survival. To investigate the effects of edema on tumour cell survival, a bio-mathematical model of edema and the corresponding cell killing by continuous low dose rate irradiation (CLDRI) was developed so that tumour cell surviving fractions can be estimated in an edematous prostate for both 125I and 103Pd seed implants. The dynamic nature of edema and its resolution were modelled with an exponential function V(T) = V(p)(1 + M exp(-0.693T/ T(e))) where V(p) is the prostate volume before implantation, M is the edema magnitude and T(e) is edema half-life (EHL). The dose rate of a radioactive seed was calculated according to AAPM TG43, i.e. D = SkAg(r)phi(an)/r2, where r is the distance between a seed and a given point. The distance r is now a function of time because of edema. The g(r) was approximated as 1/r(0,4) and 1/r(0.8) for 125I and 103Pd, respectively. By expanding the mathematical expression of the resultant dose rate in a Taylor series of exponential functions of time, the dose rate was made equivalent to that produced from multiple fictitious radionuclides of different decay constants and strengths. The biologically effective dose (BED) for an edematous prostate implant was then calculated using a generalized Dale equation. The cell surviving fraction was computed as exp(-alphaBED), where alpha is the linear coefficient of the survival curve. The tumour cell survival was calculated for both 125I and 103Pd seed implants and for different tumour potential doubling time (TPDT) (from 5 days to 30 days) and for edemas of different magnitudes (from 0% to 95%) and edema half-lives (from 4 days to 30 days). Tumour cell survival increased with the increase of edema magnitude and EHL. For a typical edema of a half-life of 10 days and a magnitude of 50%. the edema increased tumour cell survival by about 1 and 2 orders of magnitude for 125I and 103Pd seed implants respectively. At the extreme (95% edema magnitude and an edema half-life of 30 days), the increase was more than 3 and 5 orders of magnitude for 125I and I03Pd seed implants respectively. The absolute increases were almost independent of TPDT and the prostate edema did not significantly change the effective treatment time. Tumour cell survival for prostate undergoing CLDRI using 125I or 103Pd seeds may be increased substantially due to the presence of edema caused by surgical trauma. This effect appears to be more pronounced for 103Pd than 125I because of the shorter half-life of 103Pd. If significant edema is observed post implantation, then a boost to the prostate using external beam radiotherapy may be considered as a part of the treatment strategy.

Brachytherapy↗
PubMed1997

Progression rate of radiation damage to the mouse kidney: a quantitative analysis of experimental data using a simple mathematical model of the nephron.

Mouse kidneys were irradiated bilaterally with a range of single or fractionated X-ray doses. After an interval of 2 weeks or 26 weeks, the animals were reirradiated with a range of single X-ray doses. The rate of development of functional kidney damage was assessed repeatedly by the 51Cr-EDTA clearance assay. The rate at which the damage is expressed was found to depend on the primary dose, on the interval between primary treatment and retreatment, and on the retreatment dose. A subset of the data was analysed using a mathematical model of nephron function. In the model, the residual activity of 51Cr-EDTA depends on the glomerular filtration rate (GFR). The GFR is related to the cellularities of three target cell populations. The filtration capacity of the glomerulus is assumed to depend on the numbers of glomerular endothelial cells and mesangial cells. The reabsorption capacity of the tubule is related to the number of tubular epithelial cells. The impact of tubulo-glomerular feedback and the reserve capacity of the kidney on residual activity is considered. The target cell populations are assumed to be of a flexible type, i.e. to consist of cells which are all both functional and self-renewing. Free parameters of the model were optimized by minimizing the residual sum of squares. With the optimized parameter values, the measured and the model-predicted rates of progression of the functional damage correspond well for a wide range of irradiation schedules. The model analysis suggests a pronounced role of tubulo-glomerular feedback in the development of functional injury in the kidney. It is concluded that the model represents a good starting point for quantitative studies of the cellular basis of radiation nephropathy.

Animals↗
PubMed2006

QxDB: a generic database to support mathematical modelling in biology.

QxDB (quantitative x-modelling database) is a web-based generic database package designed especially to house quantitative and structural information. Its development was motivated by the need for centralized access to such results for development of mathematical models, but its usefulness extends to the general research community of both modellers and experimentalists. Written in PHP (Hyper Preprocessor) and MYSQL, the database is easily adapted to new fields of research and ported to Apache-based web servers. Unlike most existing databases, experimental and observational results curated in QxDB are supplemented by comments from the experts who contribute input to the database, giving their evaluations of experimental techniques, breadth of validity of results, experimental conditions, and the like, thus providing the visitor with a basis for gauging the quality (or appropriateness) of each item for his/her needs. QxDB can be easily customized by adapting the contents of the database table containing the descriptors that characterize each data record according to an informal ontology of the research domain. We will illustrate this adaptability of QxDB by presenting two examples, the first dealing with modelling in oncology and the second with mechanical properties of cells and tissues.

Biology↗
PubMed2001

A mathematical model for hydrodynamic and size exclusion chromatography of polymers on porous particles.

When packed columns filled with porous particles are used for the separation of macromolecules, either size exclusion chromatography (SEC), hydrodynamic chromatography (HDC), or a combination of both determine the macromolecule retention mechanism. This paper develops a simple mathematical model to describe a molecular weight calibration graph, which includes both HDC and SEC. There is a transition between the HDC calibration region at higher molecular weights to an SEC region at lower molecular weights. The degree to which SEC and HDC are mixed depends on the particle diameter, the relative size of the pores, and the macromolecule size. In addition, using fractal considerations, the fractal character of the apparent selectivity between two adjacent peaks on the chromatogram is shown. This model constitutes an attractive tool to enhance the expansion of these two chromatographic techniques for the separation of biological or synthetical macromolecules.

Journal Article↗
PubMed2001

Territorial intrusion risk and antipredator behaviour: a mathematical model.

In territorial animals that hide to avoid predators, a predatory attack creates a conflict because a hiding animal cannot defend its territory from conspecific intruders. When intruders are persistent, a past conspecific intrusion informs a territorial resident that future intrusions by the same animal are likely. Using a mathematical model, I examine the effects that past territorial intrusions can have on antipredator behaviour. Past territorial intrusions rarely affect a resident animal's time to hide (the optimal behaviour is to hide as soon as the predator initiates its attack). In contrast, past intrusions should shorten the length of time during which territory holders remain in hiding, with the magnitude of this effect depending on the time of the predator's attack, the re-intruder's pattern of return, and the intrusion rates of other conspecifics. The results of the model show that we need more information on patterns of re-intruders' behaviour, and emphasize that a similar functional explanation could underlie other behavioural changes following territorial and/or aggressive encounters (such as winner/loser effects or changes in display frequency and territorial vigilance). Differences between my findings and those from previous studies suggest that the trade-off between antipredator behaviour and territorial defence can involve different costs from the trade-off between antipredator behaviour and foraging.

Animals↗
PubMed1996

Mathematical models for determining metabolic fluxes through the citric acid and the glyoxylate cycles in Saccharomyces cerevisiae by 13C-NMR spectroscopy.

We propose, first, a practical method for studying the isotopic transformation of glutamate or any other metabolite isotopomers in the citric acid and the glyoxylate cycles; second, two mathematical models, one for evaluating the flux through the citric acid cycle and the other for evaluating the flux through the latter coupled to the glyoxylate cycle in yeast. These models are based on the analysis of 13C-NMR spectra of glutamate obtained from Saccharomyces cerevisiae, NCYC strain, fed with 100% enriched [2-13C]acetate. The population of each glutamate isotopomer, the change in intensity of each multiplet component or the enrichment of any glutamate carbon is expressed by a specific analytical equation from which the flux in the citric acid and the glyoxylate cycles can be deduced. The aerobic metabolism of 100% [2-13C]acetate in acetate-grown S. cerevisiae cells was studied as a function of time using 13C-NMR. 1H-NMR and biochemical techniques. The C1 and C6 doublet and singlet of labeled trehalose increase continuously with time indicating that there is no isotopic transformation between trehalose isotopomers even though the corresponding formation rates are different. By contrast, the glutamate C4 singlet increases then decreases with time. The C4 doublet, which is lower than the singlet for t < 60 min, increases continuously and becomes higher than the singlet for t > 90 min. A similar observation was made for the C2 resonance singlet and doublet. In addition, the glutamate C2 multiplet consists of only seven instead of nine peaks as in random labeling. These results agree well with our models and demonstrate that, in the presence of acetate, anaplerotic carbon sources involved in the synthesis of acetyl-CoA are negligible in yeast. The flux in the citric acid cycle was deduced from a plot of the C4 area versus incubation time, while the flux within the glyoxylate cycle was determined from the relative intensity of the glutamate C4 doublet and singlet. The fluxes in the citric acid and the glyoxylate cycles were found to be comparable. The proportion of glutamate in isotopic exchange with the citric acid cycle is about 2.5% min1 in yeast.

Acetates↗
PubMed2000

Cerebral hemodynamics during arterial and CO(2) pressure changes: in vivo prediction by a mathematical model.

The aim of this work was to analyze changes in cerebral hemodynamics and intracranial pressure (ICP) evoked by mean systemic arterial pressure (SAP) and arterial CO(2) pressure (Pa(CO(2))) challenges in patients with acute brain damage. The study was performed by means of a new simple mathematical model of intracranial hemodynamics, particularly aimed at routine clinical investigation. The model was validated by comparing its results with data from transcranial Doppler velocity in the middle cerebral artery (V(MCA)) and ICP measured in 44 tracings on 13 different patients during mean SAP and Pa(CO(2)) challenges. The validation consisted of individual identification of 6 parameters in all 44 tracings by means of a best fitting algorithm. The parameters chosen for the identification summarize the main aspects of intracranial dynamics, i.e., cerebrospinal fluid circulation, intracranial elastance, and cerebrovascular control. The results suggest that the model is able to reproduce the measured time patterns of V(MCA) and ICP in all 44 tracings by using values for the parameters that lie within the ranges reported in the pathophysiological literature. The meaning of parameter estimates is discussed, and comments on the main virtues and limitations of the present approach are offered.

Adolescent↗
PubMedDate not supplied

Evaluation of fractionation regimens in stereotactic radiotherapy using a mathematical model of repopulation and reoxygenation.

PURPOSE: Various forms of stereotactic fractionation regimens have been used in the clinic. The purpose of this article is to evaluate the influence of the number of fractions on tumor control in stereotactic radiotherapy. METHODS: The 50% curative dose (D50) is calculated using a mathematical model of reoxygenation and repopulation. A review of the literature of stereotactic fractionation regimens is also presented. RESULTS: The number of fractions required to achieve the best therapeutic ratio is strongly influenced by the pattern of reoxygenation and the potential doubling time of the tumor. In the case of rapid repopulation, well-oxygenated clonogenic cells present a greater danger than hypoxic cells in a prolonged fractionated treatment schedule. In a slowly growing tumor, repopulation is relatively unimportant and the response is dominated by the pattern of reoxygenation. For a small number of large dose fractions, the potential doubling time and the time interval between fractions have a negligible effect on the D50 values. CONCLUSION: If a small number of large dose fractions is used in stereotactic radiotherapy and if reoxygenation occurs more efficiently with the passage of time, the therapeutic ratio can be enlarged by a sufficient time interval between fractions.

Brain Neoplasms↗
PubMedDate not supplied

[Experimental and mathematical modeling of population dynamics of rhizospheric bacteria under conditions of cadmium stress].

The method of membrane filters was used to study the population dynamics of bacteria belonging to the genera Arthrobacter, Flavobacterium, and Klebsiella in barley (Hordeum vulgare) rhizosphere under conditions of cadmium stress (5-15 mg Cd/g soil). Mathematical modeling allowed us to demonstrate that the phytoprotective effect is implemented via the following succession of events: the bacteria synthesize phytohormones (IAA and ethylene)-->root excretory activity increases-->the number of the bacteria in the rhizoplane grows-->the flux of bacteria migrating from the rhizoplane to the rhizosphere increases-->the number of bacteria binding cadmium ions in the rhizosphere grows-->the amount of free ions entering the plant decreases. Among the bacteria studied, K. mobilis 880 displayed the highest migration and immobilization activity and the best survival rate under conditions of cadmium stress. Consequently, K. mobilis 880 is recommended for use in biopreparations for stimulating plant growth under conditions of heavy metal pollution.

Agriculture↗
PubMed2006

The pier abutment: a review of the literature and a suggested mathematical model.

Many clinicians consider the prosthetic restoration of missing posterior teeth by means of a 5-unit fixed partial denture with a pier abutment a non-favorable situation. The present article assesses the validity of the pier abutment by means of a critical review of the literature and mathematical analysis of the forces generated within a fixed partial denture of this design. Few studies are available, and none substantiate the theory that the pier abutment serves as a fulcrum. A mathematical model suggests that debonding may occur in the anterior abutment, but not due to the teetering of the fixed partial denture around the pier abutment.

Algorithms↗
PubMed2003

Balance of cell proliferation and death among dynamic populations: a mathematical model.

Developmental changes in cell numbers represent the dynamic balance between cell proliferation and death. One obstacle to assessing this balance is an inability to quantify the total amount of cell death, i.e., with a positive indicator such as terminal dUTP nick end labeling (TUNEL) or caspase activity. A novel mathematical model is described wherein data on daily cell growth (the change in cell number) and cell cycle kinetics can be used to determine the total amount of cell death. Two sets of data from previously published studies were tested in this model; primary cultured cortical neurons and B104 neuroblastoma cells. These two preparations have contrasting features: neuronal cultures are heterogeneous and have relatively few cells that are actively cycling (i.e., the growth fraction for these cells is low), whereas B104 cells are relatively homogeneous cultures in which the growth fraction is high. In primary cortical cultures, there was a balance in cell production and death. Treatment with a potent anti-mitogen, ethanol (400 mg/dl), affected this balance principally by reducing cell production, although the rate of cell death was also increased. In untreated B104 cells, there was eight-fold more cell production than cell death. Growth factors such as platelet-derived growth factor BB doubled cell production. Ethanol reduced cell production by >60%, and it eliminated growth factor-mediated cell production. All of these changes occurred in the absence of an effect on the amount of cell death. Thus, the model is ideal for predicting the effects of an epigenetic factor (e.g., a growth factor, toxin, or pharmacological agent) on cell development and can be useful in determining the consequences of a genetic manipulation as well.

Animals↗
PubMed1997

A phosphorylation cascade in the basal ganglia of the mammalian brain: regulation by the D-1 dopamine receptor. A mathematical model of known biochemical reactions.

Stimulation of the dopamine D-1 receptor in the corpus striatum initiates a cascade of biochemical events. These events include: activation of adenylate cyclase, stimulation of cAMP-dependent protein kinase, protein phosphorylation and inhibition of phosphoprotein phosphotase-1. This article presents and discusses a mathematical model of these biochemical events (and their dependence upon the concentration of cytosolic calcium). According to this model, the activity of calcineurin (which is regulated by the concentration of cytosolic calcium ions) counterbalances the activity of the "D-1 cascade". The combined activity of the "D-1 cascade" and calcineurin can regulate the activity of calcium- and calmodulin-dependent protein kinase II.

Adenylyl Cyclases↗