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At least 829 records · Page 46Linked to original sources
PubMed2006

Hydrogels in controlled release formulations: network design and mathematical modeling.

Over the past few decades, advances in hydrogel technologies have spurred development in many biomedical applications including controlled drug delivery. Many novel hydrogel-based delivery matrices have been designed and fabricated to fulfill the ever-increasing needs of the pharmaceutical and medical fields. Mathematical modeling plays an important role in facilitating hydrogel network design by identifying key parameters and molecule release mechanisms. The objective of this article is to review the fundamentals and recent advances in hydrogel network design as well as mathematical modeling approaches related to controlled molecule release from hydrogels. In the first section, the niche roles of hydrogels in controlled release, molecule release mechanisms, and hydrogel design criteria for controlled release applications are discussed. Novel hydrogel systems for drug delivery including biodegradable, smart, and biomimetic hydrogels are reviewed in the second section. Several mechanisms have been elucidated to describe molecule release from polymer hydrogel systems including diffusion, swelling, and chemically-controlled release. The focus of the final part of this article is discussion of emerging hydrogel delivery systems and challenges associated with modeling the performance of these devices.

Chemistry, Pharmaceutical↗
PubMed2006

Mathematical modeling of tumor therapy with oncolytic viruses: effects of parametric heterogeneity on cell dynamics.

BACKGROUND: One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical modeling of carcinogenesis that would account for parametric heterogeneity. RESULTS: Here we formulate a modeling approach that naturally takes stock of inherent cancer cell heterogeneity and illustrate it with a model of interaction between a tumor and an oncolytic virus. We show that several phenomena that are absent in homogeneous models, such as cancer recurrence, tumor dormancy, and others, appear in heterogeneous setting. We also demonstrate that, within the applied modeling framework, to overcome the adverse effect of tumor cell heterogeneity on the outcome of cancer treatment, a heterogeneous population of an oncolytic virus must be used. Heterogeneity in parameters of the model, such as tumor cell susceptibility to virus infection and the ability of an oncolytic virus to infect tumor cells, can lead to complex, irregular evolution of the tumor. Thus, quasi-chaotic behavior of the tumor-virus system can be caused not only by random perturbations but also by the heterogeneity of the tumor and the virus. CONCLUSION: The modeling approach described here reveals the importance of tumor cell and virus heterogeneity for the outcome of cancer therapy. It should be straightforward to apply these techniques to mathematical modeling of other types of anticancer therapy. REVIEWERS: Leonid Hanin (nominated by Arcady Mushegian), Natalia Komarova (nominated by Orly Alter), and David Krakauer.

Journal Article↗
PubMed2000

Mathematical modeling of controlled-release systems of herbicides using lignins as matrices. A review.

The herbicides applied in soils can be easily lost, owing to leaching, volatilization, and bio- and photodegradation. Controlled-release systems using polymeric matrices claim to solve these problems. The movement of the herbicides in the soil is also an important phenomenon to be studied in order to evaluate the loss processes. The development of mathematical models is a relevant requirement for simulation and optimization of such systems. This study reviews mathematical models as an initial step for modeling data obtained for controlled-release systems of herbicides (diuron, 2,4-dichlorophenoxyacetic acid, and ametryn) using sugarcane bagasse lignin as a polymeric matrix. The release kinetic studies were carried out using several acceptor systems including a water bath, soil, and soil-packed columns. Generally, these models take into account phenomena such as unsteady-state mass transfer by diffusion (Fick's law) and convection, consumption by several processes, and partitioning processes, resulting in partial differential equations with respect to time and space variables.

Delayed-Action Preparations↗
PubMedDate not supplied

Mathematical model for energy and protein balance simulation in broilers.

The authors used the empirical equations of mathematical modelling for the energy and protein balance simulation, with the view of calculating the body weight gain in broilers fed various diets. The results found by using the model were compared with the experimental data obtained by several authors. A standard deviation of +/- 1.20% and a mean error of +/- 0.28% and a mean error of +/- 0.28% which proved that the model average was a sufficient estimate of the experimental average were found. Furthermore, using the regression method, a significant correlation of variables was evidentiated.

Animal Feed↗
PubMed1997

Predictions of mathematical models of tissue oxygenation and generation of singlet oxygen during photodynamic therapy.

Photodynamic therapy (PDT) is a relatively new protocol for cancer treatment which has recently been approved for limited clinical use. Traditionally, the success of treatment with PDT has been compared on the basis of total light delivery. Using the mathematical model of Henning et al. (Radiat. Res. 142, 221-226, 1995), we have determined that when oxygen is not depleted from the tissue, the concentration of singlet oxygen that is generated is directly proportional to the product of the light fluence rate (phi) and the concentration of the photosensitizer (Cs). Therefore, phiCs is an appropriate parameter for comparing the potential success of PDT protocols under these conditions. For a treatment of time t, the observed photodynamic effect resulting from singlet oxygen exposure should be directly related to phiCst. For high phiCs, the model predicts that oxygen depletion occurs within the tumor tissue. As a result, the photodynamic effect is no longer proportional to phiCst. We have expanded the model of Henning et al. to include the changes in oxygen concentration which occur within the capillary as blood flows through the tissue. Our new predictions with the mathematical model for optimal PDT treatment conditions are significantly different from those predicted by the previous models. Predictions of the model are given using parameters relevant for treatment of solid tumors with Photofrin.

Dihematoporphyrin Ether↗
PubMed2006

A mathematical model of twin-twin transfusion syndrome with pulsatile arterial circulations.

The twin-twin transfusion syndrome (TTTS) is a severe complication of monochorionic twin pregnancies caused by a net transfusion of blood from one twin (the donor) to the other (the recipient) through placental anastomoses. To examine the pathophysiology of TTTS evolving through clinical stages I to IV, we extended our mathematical model to include pulsating circulations propagating along the arterial tree as well as placental and cerebral vascular resistances, and arterial wall thickness and stiffness. The model demonstrates that abnormal umbilical arterial flow (TTTS stage III) in the donor twin results from increased placental resistance as well as reduced resistance in the cerebral arteries. In contrast, recipient twin abnormal umbilical arterial flow requires a significantly greater increase in placental resistance, resulting from the compressive effects of high amniotic fluid pressure. Thus simulated abnormalities of donor umbilical arterial pulsations occur in the donor more commonly and earlier than in the recipient. The "normal" staging sequence (I, II, III, IV) correlates with the presence of compensating placental anastomoses, constituting the majority of monochorionic twin placentas. However, TTTS stage III may occur before manifestations of stage II (lack of donor bladder filling), in our model correlating with severe TTTS from a single arteriovenous anastomosis, an infrequent occurring placental angioarchitecture. In conclusion, this mathematical model describes the onset and development of the four stages of TTTS, reproduces a variety of clinical manifestations, and may contribute to identifying the underlying pathophysiology of the staging sequence in TTTS.

Chorion↗
PubMed2003

Mathematical model for predicting biliary therapeutic endoscopic retrograde pancreatography (ERCP).

INTRODUCTION: Magnetic resonance cholangiopancreatography is as sensitive as endoscopic retrograde pancreatography in the evaluation of biliary tract diseases but does not offer therapeutic options. The aim of the present study was to develop a mathematical model to predict 'therapeutic endoscopic retrograde pancreatography' using clinical variables so that patients with low probability could be more appropriately investigated by magnetic resonance cholangiopancreatography in future. METHODS: Endoscopic retrograde pancreatography cases between January 1996 to December 1997 were retrospectively reviewed (before introduction of magnetic resonance cholangiopancreatography). Clinical, biochemical and radiological variables were analysed and a model was developed using multiple logistic regression. RESULTS: Case notes for 573 patients were successfully reviewed. A total of 330 patients underwent therapeutic endoscopic retrograde pancreatography (sphincterotomy or stent insertion). Clinical indications of obstructive jaundice and cholangitis, ultrasonographic findings of dilated common bile duct, and raised liver function tests (two or more elevated parameters) were each found to be predictive for 'therapeutic' endoscopic retrograde pancreatography. Using these variables, the mathematical model in the present study has specificity of 77% and sensitivity of 75% at the probability level of 50% or higher. This model has been tested in a separate group of endoscopic retrograde pancreatography cases carried out in 1998 and was found to have sensitivity 77.6%, specificity 80.3%, positive predictive value 68.5% and negative predictive value 86.6%. CONCLUSIONS: The model reported in the present study can help clinicians to identify cases for therapeutic endoscopic retrograde pancreatography and diagnostic magnetic resonance cholangiopancreatography.

Adolescent↗
PubMedDate not supplied

[Mathematical modeling of the dynamics of the intestinal epithelium in non-irradiated and irradiated mammals].

A mathematical model has been developed to describe the dynamics of the crypt-villus system of the small intestine epithelium in nonirradiated and chronically irradiated mammals. The model involves the chalone mechanism of regulation of crypt cell reproduction and represents a system of nonlinear differentiation equations. The model presents the dynamics of the small intestine epithelium in nonirradiated animals, including stable fluctuations of the concentrations of crypt and villus cells (the limited cycle), and simulates quantitatively the impairment of the intestinal epithelium in small laboratory animals subjected to long-term irradiation.

Animals↗
PubMedDate not supplied

[Mathematical model of transitional processes in the chemostat culture of microorganisms].

A mathematical model of the growth of the cell culture was developed. The model takes into account changes of the levels of the enzymes which define the metabolism rate, transport of the substrate into the cell, regeneration of the donors of energy. The model is based on the proposition that the rate of overall protein synthesis in the cell is defined by the concentration of a few aminoacids limiting the growth. The chemostat culture of the methanol-assimilating yeast was used as the object of modelling. The model allows to explain the experimental kinetics of alterations in cell number (biomass) and other measurable characteristics of the culture during the transient process when the dilution rate was changed.

Culture Media↗
PubMed1996

Mathematical modeling of helper T lymphocyte/antigen-presenting cell interactions: analysis of methods for modifying antigen processing and presentation.

Helper T lymphocytes (Th cells) are activated by contact with antigen-presenting cells (APCs) that have processed and presented the appropriate MHC-peptide complexes. Two experimental methods for modifying antigen processing and presentation include altering the properties of the antigen and altering the method of antigen uptake. Mathematical modeling was used to investigate the effects of these two methods on the Th cell response. Two mathematical models were used, one for relating the external antigen concentration to the number of MHC-peptide complexes to the number of bound T cell receptors (TCRs) on the Th cell. Large values of MHC/peptide affinity were predicted to compensate for small values of TCR/MHC-peptide affinity in particular parameter ranges. Similarly, large values of antigen receptor number were predicted to compensate for small values of antigen receptor affinity in particular parameter ranges. Results were shown to agree with a variety of experimental data. In addition, model predictions suggest that knowledge of MHC/peptide, TCR/MHC-peptide, and receptor/antigen affinities is not sufficient to accurately describe an experimental system; the kinetic rate constants can dramatically affect antigen processing and presentation, the Th-APC interaction, and the Th cell response. This theoretical approach is useful not only for interpreting experimental data but also for guiding future experiments aimed at manipulating the Th cell response.

Antigen Presentation↗
PubMed1985

A mathematical model to study short-term regulation of mitochondrial energy transduction.

A mathematical model is presented which includes the following elementary process of mitochondrial energy transduction: hydrogen supply, proton translocation by the respiratory chain, proton-driven ATP synthesis by the F0F1-ATPase, passive back-flow of protons (leak) and carrier-mediated exchange of adenine nucleotides and phosphate. For these processes empirical rate laws are used. The model is applied to calculate time-dependent states of energy transduction in isolated rat liver mitochondria. From the general agreement of the computational results with experimental data (Ogawa, S. and Lee, T.M. (1984) J. Biol. Chem. 259, 10004-10011) the following conclusions can be drawn. (1) The length of the time interval during which mitochondria are able to maintain a relatively high and constant delta pH in the absence of oxygen (anaerobiosis) is limited by the availability of intramitochondrial ATP. (2) The overshoot kinetics of delta pH which appear when reoxigenating mitochondria after a preceeding anaerobiosis might be due to a lag phase kinetics of the F0F1-ATPase. (3) In phosphorylating mitochondria the homeostasis of delta pH is brought about by a high sensitivity of the respiration rate and the rate of the F0F1-ATPase as to changes of delta pH. (4) Analysis of the mean transient times shows that the rate of ATP synthesis in State 3 is controlled to almost the same extent by the hydrogen supply, the respiratory chain, the adenine nucleotide translocator and the proton leak.

Adenine Nucleotides↗
PubMed1985

[Mathematical model of the combined effects of ionizing radiation and hyperthermia on mammalian cells].

A previously proposed mathematical model for the depiction of the effects of combined ionizing radiation and hyperthermia on yeast cells of different species was applied to the description of experimental data on mammalian cells. The model suggests that the synergistic effect of combined ionizing radiation and hyperthermia is caused by additional lethal damages arising from the interaction of "sublesions" induced by both agents. These "sublesions" are not lethal after the action of these agents, each taken alone. It has been shown that the thermal enhancement ratios are strongly determined by the ratios of radiation and hyperthermia-induced lethal damages. The model predicts that the maximal synergistic effect after a separate action of these modalities will be achieved if the former agent induces a greater part of lethal damages as compared to the latter one. It has been shown that the model depicts quantitatively the synergism of the simultaneous action of the agents used for Chinese hamster cells and predicts the maximal value of the synergistic effect, conditions under which it can be achieved and the dependence of the synergistic effect on the do se rate.

Animals↗
PubMed1980

[Mathematical model for carbohydrate energy metabolism. Mechanism of the Pasteur effect].

The simple mathematical model based on the stoichiometric structure of carbohydrate metabolism and the only allosteric regulation presented, i. e. activation of phosphofructokinase by AMP, was used to study the mechanism of the Pasteur effect, e. g. interrelationship of glycolysis, the Krebs cycle and H-transporting shuttles at varying rates of oxidative phosphorylation and ATPase load. It was shown that the mechanism of the Pasteur effect is based on the presence of two negative feed-back mechanisms in carbohydrate metabolism, namely by the level of ATP in glycolysis and by the level of mitochondrial NADH in the Krebs cycle and H-transporting shuttles. It was also shown that the value and sign of the Pasteur effect depend on the level of ATPase load. The role of this phenomenon in stabilization of ATP in the cell is discussed. The effects of changes in the allosteric properties of phosphofructokinase and low activity of H-transporting shuttles on the Pasteur effect was studied. It was shown that the low values of the pasteur effect in tumour tissues are mainly determined by an insufficient activity of oxidative phosphorylation.

Adenosine Triphosphatases↗
PubMedDate not supplied

[Mathematical model of intracranial blood-cerebrospinal fluid dynamics system applied to the study of extreme conditions].

A mathematical model of cerebral blood and lymph circulation that can be used to study various effects (simulated space flight factors, functional loads) on the human body was developed. Biophysical patterns that determine relationships between cerebral blood and lymph circulation as well as between fluid volumes and pressures (P and V) are discussed. Involvement of the mechanism of brain circulation autoregulation in cerebral blood and lymph circulation is considered. The model was applied to study responses of cerebral blood and lymph circulation to various exposures such as orthostatic and antiorthostatic tests and provocative tests which led to intracranial pressure shifts and modified the ratio between volumes and pressures in different hydrodynamic systems. The modelling data were consistent with clinical, physiological and experimental observations which demonstrate an adequacy of the above model.

Aerospace Medicine↗
PubMedDate not supplied

[Mathematical model of protoplasm flow in a viscous-elastic active strand of a myxomycete plasmodium].

A mathematical model is plotted of protoplasmic flow in long strands of Myxomycete plasmodium. An analytical relationship was obtained between the characteristics of protoplasmic flow: amplitude and contour of velocity in the strand channel with the amplitude and wave length of pressure developed by contractile filaments of the strand cortical layer. The model permitted a comparison to be made between the experimental data of protoplasmic flow obtained by optical methods and the evidence on contractile apparatus obtained by tensiometric measurements. A conclusion is drawn on the consistency of the basic hypothesis concerning an autowave pattern of the motive force of the cortical layer filaments.

Elasticity↗
PubMedDate not supplied

[Mathematic model of the cupuloendolymphatic system for various densities of cupula and endolymph].

This paper presents a mathematical model of time-course variations of the cupulo-endolymphatic system which can be described by the Steinhauzen phenomenological equation for the case of a unidimensional toroid, assuming that the densities of the cupula and endolymph are identical. If the densities are different, the time-course variations of the cupuloendolymphatic system may aggravate and manifest at the powered stages of space flight.

Acceleration↗
PubMed1980

A mathematical model of canine granulocytopoiesis.

The granulocyte cell renewal system of the dog is represented by a mathematical model consisting of the following compartments: The pool of pluripotential stem cells, the committed stem cell pool, divided into a blood and a bone marrow compartment, the proliferation pool, the maturation pool, the reserve pool and the blood pool of functional granulocytes. This chain of compartments is described by a system of non-linear differential equations. Cell losses anyplace in the system provoke increased production in all pools containing cells capable to divide. A reduced number of granulocytes in the blood pool stimulates production of a "granulocyte releasing factor" which mobilizes a rising number of cells to transit from the marrow reserve into the blood pool. The model was simulated on a digital computer. It was found to be capable to reproduce the steady state conditions and it also fits the data of two distinct experimental perturbations of the system both equally well. These perturbations are a loss of proliferating cells as it occurs after the administration of cytostatic drugs and losses of functional cells as they are induced by leukapheresis experiments of differing leukapheresis rates.

Animals↗
PubMed1992

The epidemiology of varicella-zoster virus infections: a mathematical model.

Herpes-zoster is caused by the reactivation of varicella-zoster virus (VZV). In this paper different hypotheses of how this re-emergence of virus comes about are reviewed and discussed. From these hypotheses, and epidemiological data describing the initial transmission of the virus, a mathematical model of primary disease (varicella) and reactivated disease (zoster) in developed countries is derived. The steady-state age distributions of zoster cases predicted by this model are compared with the observed distribution, derived from a review and analysis of published epidemiological data. The model allows differentiation between published hypotheses in which age of host may or may not influence the probability of viral reactivation. The results indicate that the probability of reactivation must increase with age to allow the observed pattern of zoster cases. The basic mathematical model presented provides a conceptual framework, which may be extended to assess possible control programmes.

Adolescent↗