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At least 613 records · Page 34Linked to original sources
PubMedDate not supplied

Mathematical model of chloride concentration in human blood.

This paper deals with mathematical modelling of blood chloride concentration. The main features of the model are that it reveals mathematically the physiological relationship between blood chloride and other electrolytes and serves as an accurate indirect method for chloride measurements with accuracy fulfilling clinical requirements. The main advantages of the method based on this model are that it is more comfortable than traditional methods and clinically less harmful for the patient under study. Experimental verification of the developed model ensures that the results of chloride measurements obtained using this model are significantly correlated with the results for the blood samples obtained from standard chloride analysers.

Algorithms↗
PubMedDate not supplied

[Mathematical modelling and the prognosis of treatment efficacy in papillomavirus infection of the cervix uteri].

In this paper, consideration is given to the problem of mathematical modelling, diagnosis and effects of treatment options on the condition of a patient exposed to papillomavirus infection. The problem is tackled of identifying the most prominent signs of degree of severity of the disease course and of therapy efficiency on the basis of parameters characterizing the immunologic vigor with making use of the covariation matrix eigenvalues algorithm, namely the modelling manifolds algorithm. Such an approach allows the central problem of classification of indices for the immunologic vigor to be settled. A mathematical model as discrimination surface to be used for prediction of results of the treatments administered is constructed.

Algorithms↗
PubMedDate not supplied

Automated rescreening in cervical cytology. Mathematical models for evaluating overall process sensitivity, specificity and cost.

OBJECTIVE: To develop mathematical models to assist decision makers with the difficult task of evaluating the use of automated rescreening in the process of screening cervical smears. STUDY DESIGN: Using assumptions about incidence, per smear screening costs, and the sensitivity and specificity of cytotechnologists, pathologists and the rescreening device, basic probability models were developed to describe the overall sensitivity, specificity and cost of the screening process. RESULTS: The optimal screening policy is highly dependent on assumptions, and an automated system can significantly affect the overall system cost and accuracy. CONCLUSION: Mathematical planning models are valuable tools to assist decision makers in the design of a screening process for cervical smears.

Automation↗
PubMed1988

A mathematical model for the freezing process in biological tissue.

A mathematical model has been developed to study the process of freezing in biological organs. The model consists of a repetitive unit structure comprising a cylinder of tissue with an axial blood vessel (Krogh cylinder) and it is analysed by the methods of irreversible thermodynamics. The mathematical simulation of the freezing process in liver tissue compares remarkably well with experimental data on the structure of tissue frozen under controlled thermal conditions and the response of liver cells to changes in cooling rate. The study also supports the proposal that the damage mechanism responsible for the lack of success in attempts to preserve tissue in a frozen state, under conditions in which cells in suspension survive freezing, is direct mechanical damage caused by the formation of ice in the vascular system.

Animals↗
PubMed1992

Hematotoxic effects of benzene analyzed by mathematical modeling.

The hematopoietic cell response to benzene intoxication in mice (during and after long-term inhalation) was analyzed by a mathematical model of murine hematopoiesis. Two complementary methods, Time-Curve and Steady-State Analysis, were developed to identify target cells for benzene toxicity and to quantify the extent of damage in different stages of development of these target cells. We found that (i) erythropoietic cells were the most sensitive; (ii) granulopoietic cells were about half as sensitive as erythropoietic and (iii) hematopoietic stem cells exhibited a sensitivity that ranged between that of erythropoietic and granulopoietic cells. A dose-response relationship between benzene levels and damage in target cells (valid from 1 to more than 900 ppm) was derived that was linear for doses up to 300 ppm and plateaued thereafter. This relationship indicated that benzene-induced hematotoxicity is subject to a saturable process. Recovery of hematopoiesis following chronic benzene intoxication was simulated for different doses and preceding exposure periods. The impaired recovery following exposure periods greater than 8 weeks could be explained by a severe reduction in the maximum self-maintenance of stem cells. This study indicates that the present mathematical model represents a useful approach to investigate alternate hypotheses for the action of hematotoxic agents.

Animals↗
PubMed2006

Multipolar radiofrequency ablation with internally cooled electrodes: experimental study in ex vivo bovine liver with mathematic modeling.

PURPOSE: To evaluate the size and geometry of thermally induced coagulation by using multipolar radiofrequency (RF) ablation and to determine a mathematic model to predict coagulation volume. MATERIALS AND METHODS: Multipolar RF ablations (n = 80) were performed in ex vivo bovine livers by using three internally cooled bipolar applicators with two electrodes on the same shaft. Applicators were placed in a triangular array (spacing, 2-5 cm) and were activated in multipolar mode (power output, 75-225 W). The size and geometry of the coagulation zone, together with ablation time, were assessed. Mathematic functions were fitted, and the goodness of fit was assessed by using r(2). RESULTS: Coagulation volume, short-axis diameter, and ablation time were dependent on power output and applicator distance. The maximum zone of coagulation (volume, 324 cm(3); short-axis diameter, 8.4 cm; ablation time, 193 min) was induced with a power output of 75 W at an applicator distance of 5 cm. Coagulation volume and ablation time decreased as power output increased. Power outputs of 100-125 W at applicator distances of 2-4 cm led to a reasonable compromise between coagulation volume and ablation time. At 2 cm (100 W), coagulation volume, short-axis diameter, and ablation time were 66 cm(3), 4.5 cm, and 19 min, respectively; at 3 cm (100 W), 90 cm(3), 5.2 cm, and 22 min, respectively; at 4 cm (100 W), 132 cm(3), 6.1 cm, and 27 min, respectively; at 2 cm (125 W), 56 cm(3), 4.2 cm, and 9 min, respectively; at 3 cm (125 W), 73 cm(3), 4.9 cm, and 12 min, respectively; and at 4 cm (125 W), 103 cm(3), 5.5 cm, and 16 min, respectively. At applicator distances of 4 cm (>125 W) and 5 cm (>100 W), the zones of coagulation were not confluent. Coagulation volume (r(2) = 0.80) and RF ablation time (r(2) = 0.93) were determined by using the mathematic model. CONCLUSION: Multipolar RF ablation with three bipolar applicators may produce large volumes of confluent coagulation ex vivo. A compromise is necessary between prolonged RF ablations at lower power outputs, which produce larger volumes of coagulation, and faster RF ablations at higher power outputs, which produce smaller volumes of coagulation.

Animals↗
PubMed2000

Mathematical modeling of epidermal growth factor receptor signaling through the phospholipase C pathway: mechanistic insights and predictions for molecular interventions.

Combining engineering analyses and mathematical modeling with intervention and detection methodologies at the molecular level will allow manipulation of intracellular signal transduction pathways, and therefore rational control of functional processes central to medicine and biotechnology. We have formulated a simple mathematical model of a key signaling pathway required for regulated migration of fibroblasts and other cell types: activation of the intracellular enzyme phospholipase C (PLC) mediated by epidermal growth factor receptor (EGFR) and a multitude of other transmembrane receptors. One of the interesting features of this pathway is that the substrate of PLC, the lipid phosphatidylinositol (4,5)-bisphosphate (PIP(2)), is turned over quite rapidly and must be constantly resupplied to the plasma membrane by a known transfer mechanism. The model, which accounts for regulation of PIP(2) concentration, is sufficiently detailed to explain unique quantitative features of recent experimental data. We find that competitive pathways that deplete PIP(2) from the membrane, as well as receptor-mediated enhancement of PIP(2) supply, must be significant for agreement between model and experiment. Importantly, the mechanistic nature of the model also allowed us to predict the efficacy of various molecular intervention strategies, including overexpression of wild-type and variant proteins in the pathway as well as treatment with specific drug inhibitors. For many parameter conditions the intuitive strategy of targeting the enzyme itself is actually predicted to be relatively inefficient, with a novel and potentially useful alternative being disruption of the reactant supply mechanism.

ErbB Receptors↗
PubMed2002

Mathematical models of the balance between apoptosis and proliferation.

As our understanding of cellular behaviour grows, and we identify more and more genes involved in the control of such basic processes as cell division and programmed cell death, it becomes increasingly difficult to integrate such detailed knowledge into a meaningful whole. This is an area where mathematical modelling can complement experimental approaches, and even simple mathematical models can yield useful biological insights. This review presents examples of this in the context of understanding the combined effects of different levels of cell death and cell division in a number of biological systems including tumour growth, the homeostasis of immune memory and pre-implantation embryo development. The models we describe, although simplistic, yield insight into several phenomena that are difficult to understand using a purely experimental approach. This includes the different roles played by the apoptosis of stem cells and differentiated cells in determining whether or not a tumour can grow; the way in which a density dependent rate of apoptosis (for instance mediated by cell-cell contact or cytokine signalling) can lead to homeostasis; and the effect of stochastic fluctuations when the number of cells involved is small. We also highlight how models can maximize the amount of information that can be extracted from limited experimental data. The review concludes by summarizing the various mathematical frameworks that can be used to develop new models and the type of biological information that is required to do this.

Apoptosis↗
PubMed2006

Mathematical models for predicting the epidemiologic and economic impact of vaccination against human papillomavirus infection and disease.

Infection with human papillomavirus (HPV) is the primary cause of cervical cancer, other anogenital cancers, genital warts, and recurrent respiratory papillomatosis. Clinical studies have demonstrated that a prophylactic HPV vaccine can prevent infection, genital warts, and the precancerous lesions that lead to cervical cancer. Given the absence of data on the long-term effectiveness of HPV vaccination, a number of mathematical models have been developed to provide insight to policy makers by projecting the long-term epidemiologic and economic consequences of vaccination and evaluate alternative vaccination policies. This paper reviews the state of these models. Three types of HPV mathematical models have been reported in the literature: cohort, population dynamic, and hybrid. All have demonstrated that vaccination can significantly reduce the incidence of cervical cancer in the long term. However, only the cohort and hybrid models have evaluated the cost-effectiveness of vaccination strategies for preventing cervical cancer. These models have generally shown that vaccinating females can be cost-effective. None has accounted for the potential benefits of vaccinating the population to reduce the burden of recurrent respiratory papillomatosis and cancers of the vagina, vulva, anus, penis, and head/neck. Given that only the population dynamic model can account for both the direct and indirect (i.e., herd immunity effects) benefits of vaccination in the population, future research should focus on further development of dynamic models by expanding the range of epidemiologic outcomes tracked and including the ability to assess the cost-effectiveness of alternative vaccination policies.

Cost-Benefit Analysis↗
PubMed2025

Mathematical modeling suggests 14-3-3 proteins modulate RAF paradoxical activation.

RAF inhibitor "paradoxical activation" (PA) is a phenomenon where RAF kinase inhibitors increase RAF kinase signaling. Through mathematical modeling and experimental data analysis, we recently demonstrated that the combination of conformational autoinhibition (CA) with the disruption of CA by RAF inhibitors plays an important role in PA. 14-3-3 proteins are known to modulate RAF CA and RAF dimerization. We here extend our mathematical model to include both roles of 14-3-3 proteins, and we derive rigorous analytical expressions of RAF signal regulation as modulated by 14-3-3 proteins. We then use the model to investigate how 14-3-3 proteins may modulate PA. We mathematically show 14-3-3 protein stabilization of the autoinhibited form of RAF should potentiate PA, while 14-3-3 protein stabilization of the active RAF dimer should reduce PA. Our analysis suggests that the net-effect will often be a potentiation of PA, and that 14-3-3 proteins may be capable of inducing PA for RAF inhibitors that normally show little to no PA. We test model-based insights experimentally with two different approaches: forced increases in 14-3-3 expression (which we find amplifies PA) and evolved resistance assays (which suggest increased 14-3-3 expression may contribute to resistance to RAF inhibitors). Overall, this work supports a role for 14-3-3 in modulating RAF-inhibitor mediated paradoxical activation.

14-3-3 Proteins↗
PubMedDate not supplied

[Mathematic modeling of the processes of water and salt metabolism].

This paper describes mathematical modeling of fluid-electrolyte metabolism and fluid homeostasis in real and simulated microgravity. At the first stage physiological reactions to provocative tests were simulated. The assumptions made yielded satisfactory results, particularly with respect to the excretion of the most important electrolytes in different time intervals of bed rest and recovery. The development of models of fluid homeostasis, taking into consideration tissue elasticity and plasticity and fluid buffering capacity, is discussed.

Blood Physiological Phenomena↗
PubMedDate not supplied

Mathematical modelling of stimulus-secretion coupling in the pancreatic B-cell. V. Threshold phenomenon for the response to cyclic AMP.

Recent experimental data suggest that a rise in cyclic AMP content of pancreatic islet cells may have little effect upon cytosolic Ca2+ activity. Hence, a mathematical model for stimulus-secretion coupling was designed in which cyclic AMP fails to affect Ca2+ movements in the islet cells, but augments the responsiveness to cytosolic Ca2+ of the effector system for insulin release. Provided that the latter effect of cyclic AMP becomes operative only when the nucleotide concentration exceeds a critical threshold value, the mathematical model was found suitable to predict the dynamics of both insulin release and 45Ca fluxes in islets deprived of or exposed to D-glucose, Ca2+ and a phosphodiesterase inhibitor.

Animals↗
PubMed1990

Mathematical modelling of energy and redox metabolism of G6PD-deficient erythrocytes.

A mathematical model aimed at the study of erythrocyte metabolism under normal conditions and under glucose 6-phosphate dehydrogenase (G6PD) deficiency has been developed. The degree of deficiency as predicted by the model on the basis of calculated upper limits of oxidative load as well as of maximal methylene blue stimulation correlates with the individual clinical manifestation of the metabolic disease. Therefore, the model permits to judge the degree of metabolic disorder in the presence of G6PD enzymopathies if the kinetic properties of the defect enzyme are known. Experimentally accessible parameters for an assessment of the oxidative load capacity of cells in vivo are proposed. Furthermore, the model predicts that the threshold of tolerance as to energetic load is drastically reduced in the case of severe G6PD deficiency.

Energy Metabolism↗
PubMedDate not supplied

[Mathematical model of a simultaneous combined effect of ionizing radiation and hyperthermia].

A mathematical model has been proposed suggesting that the synergistic action of a combination of ionizing radiation and hyperthermia is conditioned by additional lethal damages arising from the interaction of "sub-lesions" induced by both agents. The model describes quantitatively the synergism of the combined action of the agents used and predicts the maximal value of the synergistic effect and conditions in which it can be achieved.

Cell Survival↗
PubMed1998

Genetically structured mathematical modeling of trp attenuator mechanism.

A genetically structured mathematical model of the trp attenuator in Escherichia coli based on known coupling mechanisms of the transcription of the trp leader region and translation of the trp leader peptide region is proposed. The model simulates, both qualitatively and quantitatively, the effects of tryptophan on the repression of cloned gene products. It shows that repression by attenuation mechanism alone operates over a narrow trp concentration range of 1 to 5 microM compared with 1 to 100 microM for trp repressor mechanism. This implies that attenuation by transcription termination is not relaxed until tryptophan starvation is severe. Simulation results show that the attenuator starts to derepress when the repressor is about 40% repressed, and becomes significantly derepressed only when the repressor repression decreased to about 20%. Unlike the case of repressor-operator interaction, the operating range of tryptophan concentration in the attenuator mechanism is not sensitive to plasmid copy number.

Amino Acid Sequence↗
PubMed1998

Mathematical models for motile bacterial transport in cylindrical tubes.

Mathematical models considering motile bacterial transport within a geometrically restrictive cylindrical tube were developed. Two macroscopic transport parameters, the random motility coefficient as a self-diffusion coefficient of the cell population and the chemotactic velocity as a chemical-induced velocity, were derived. The three-dimensional cell balance equation was reduced to forms similar to Segel's one-dimensional phenomenological cell balance equations with additional modifications for bacteria-wall interactions. Two conceptually different approaches accounting for such interactions were presented. The first approach parallels treatments in the gas kinetic theory by viewing bacterial interactions with walls as collisions and subsequent diffusive/specular reflections, which led to the Bosanquet formula for the bacterial diffusion coefficient. Based on the experimental observation that bacterial swimming motion is guided by a straight tube, the second approach considered modifications in the bacterial swimming orientation as a consequence of various long-range interactions with the tube surface. A phenomenological turning model capable of aligning bacterial motion along a tube axis was proposed. The model predicts that under the geometrical restriction of a small cylindrical tube, the macroscopic bacterial transport resulting from the proposed turning model can exhibit behavior that ranges from dimensionally reduced diffusion to pure wave propagation, depending on the influence of the tube diameter on the reversal probability in the bacterial swimming motion. Our theoretical model provides explicit equations that explain how such a transition can occur. The predicted results were then qualitatively compared with experimental data from the literature. As a preliminary comparison, we concluded that bacterial transport in cylindrical tubes of diameter 10 micrometers remains in the mode of a dimensionally reduced diffusion, and shifts to a wave motion when the tube diameter decreases to 6 micrometers.

Bacterial Physiological Phenomena↗
PubMed1983

Analysis of the interrelationships of non-nutrient blood flow, oxygen delivery, oxygen consumption, and the ratio of oxygen delivery/oxygen consumption based on a mathematical model of non-nutrient blood flow.

A mathematical model for total body non-nutrient blood flow has been presented. This is a gross model that will show effective non-nutrient blood flow. It shows how NNBF can occur in the setting of decreased oxygen delivery. The implications of this model on the interrelationships of oxygen delivery, oxygen consumption, the ratio of oxygen delivery/oxygen consumption, and NNBF are discussed.

Acidosis↗
PubMed1993

A mathematical model for fluoride uptake by the skeleton.

A mathematical model was developed that predicts fluoride accumulation and clearance from the skeleton based upon fluoride bioavailability, bone remodeling rate, and the fluoride binding characteristics of bone. It was assumed that fluoride binds to bone in a nonlinear fashion such that a smaller percentage of fluoride is bound to bone if fluoride intake is increased to high levels. Bone resorption rate was assumed to be proportional to the solubility of hydroxyfluoroapatite which is inversely related to bone fluoride content. The predictions made by the model compared favorably with experimental results from fluoride uptake and clearance studies. Parametric studies done using the model showed the following: (1) fluoride can be cleared from the skeleton by bone remodeling, but fluoride clearance takes over four times longer than does fluoride uptake; and (2) fluoride uptake by the skeleton was positively associated with bone remodeling rate. However, the concentration of fluoride in newly formed bone does not decrease with reduced remodeling rates and surpasses 10,000 ppm for intakes of fluoride greater than 9 mg/day. For osteoporosis, daily dose and duration of fluoride treatment should be selected to avoid reaching a toxic cumulative bone fluoride content.

Apatites↗