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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↗
PubMed1988

The ability of a mathematical model to evaluate the effects of two pain modulating procedures on pulpal pain in man.

The ability of a mathematical model to evaluate the effects of two different pain modulating procedures (partial nerve block and vibration) on acute experimental pulpal pain was studied. The results were also compared with placebo procedures and it was shown that the model could accurately quantify the parameters that determine the pain response following cold-induced intradental nerve impulse activity (INA). The most effective pain relieving method was found to be partial nerve block which induced significant parameter alterations reflecting decreased pain sensation and increased reaction time. Thus, it was shown that the present mathematical model is a useful tool enabling detailed analysis of differences in pain relieving procedures on human pulpal pain mediated by nerves of the A type.

Adult↗
PubMed1988

Research needs and advances in inhalation dosimetry identified through the use of mathematical dosimetry models of ozone.

Knowledge of the quantitative relationship between exposure concentration and delivered dose (i.e., dosimetry) is a fundamental starting point in the evaluation of the toxicity of chemicals, not only for intra- and interspecies comparisons but also for designing experiments that elucidate mechanisms of action and that identify issues or research areas for further study. To these ends a mathematical, lower respiratory tract dosimetry model for gases has been developed which, when linked to experimentally determined upper respiratory tract removal of a gas, can be used for dosimetric extrapolations between one test condition to a theoretical condition (e.g., animal-to-man, child-to-adult, high-to-low dose). This paper, using the ozone (O3) dosimetry model as an example, describes (1) the results of sensitivity analyses that have identified variables that can significantly influence the precision of model predicted doses, (2) research progress in improving the precision of those highly sensitive variables, and (3) approaches being used to validate the model. Results from studies of upper respiratory tract removal of O3 in animals and human are used as inputs into the mathematical model of the lower respiratory tract to illustrate applications of dosimetric extrapolations.

Administration, Inhalation↗
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↗
PubMed2005

Quantitative mathematical expressions for accurate in vivo assessment of cytosolic [ADP] and DeltaG of ATP hydrolysis in the human brain and skeletal muscle.

Magnetic Resonance Spectroscopy affords the possibility of assessing in vivo the thermodynamic status of living tissues. The main thermodynamic variables relevant for the knowledge of the health of living tissues are: DeltaG of ATP hydrolysis and cytosolic [ADP], the latter as calculated from the apparent equilibrium constant of the creatine kinase reaction. In this study we assessed the stoichiometric equilibrium constant of the creatine kinase reaction by in vitro (31)P NMR measurements and computer calculations resulting to be: logK(CK)=8.00+/-0.07 at T=310 K and ionic strength I=0.25 M. This value refers to the equilibrium: PCr(2-)+ADP(3-)+ H(+)=Cr+ATP(4-). We also assessed by computer calculation the stoichiometric equilibrium constant of ATP hydrolysis obtaining the value: logK(ATP-hyd)=-12.45 at T=310 K and ionic strength I=0.25 M, which refers to the equilibrium: ATP(4-)+H(2)O=ADP(3-)+PO(4)(3-)+2H(+). Finally, we formulated novel quantitative mathematical expressions of DeltaG of ATP hydrolysis and of the apparent equilibrium constant of the creatine kinase reaction as a function of total [PCr], pH and pMg, all quantities measurable by in vivo (31)P MRS. Our novel mathematical expressions allow the in vivo assessment of cytosolic [ADP] and DeltaG of ATP hydrolysis in the human brain and skeletal muscle taking into account pH and pMg changes occurring in living tissues both in physiological and pathological conditions.

Adenosine Diphosphate↗
PubMed2005

A mathematical model of combination therapy using the EGFR signaling network.

An increasing awareness of the significance of abnormal signal transduction in tumors and the concomitant development of target-based drugs to selectively modulate aberrantly-activated signaling pathways has given rise to a variety of promising new strategies in cancer treatment. This paper uses mathematical modeling to investigate a novel type of combination therapy in which multiple nodes in a signaling cascade are targeted simultaneously with selective inhibitors, pursuing the hypothesis that such an approach may induce the desired signal attenuation with lower doses of the necessary agents than when one node is targeted in isolation. A mathematical model is presented which builds upon previous theoretical work on EGFR signaling, simulating the effect of administering multiple kinase inhibitors in various combinations. The model demonstrates that attenuation of biochemical signals is significantly enhanced when multiple upstream processes are inhibited, in comparison with the inhibition of a single upstream process. Moreover, this enhanced attenuation is most pronounced in signals downstream of serially-connected target points. In addition, the inhibition of serially-connected processes appears to have a supra-additive (synergistic) effect on the attenuation of downstream signals, owing to the highly non-linear relationships between network parameters and signals.

Animals↗
PubMed2004

A simple mathematical model of cooperativity in receptor mosaics based on the "symmetry rule".

The phenomenon of receptor-receptor interactions was hypothesized about 20 years ago. It has been demonstrated by now that receptor-receptor interactions between G-protein coupled receptors (GPCRs) occur at plasma membrane level and result in the reciprocal modulation of their binding characteristics (i.e., cooperativity). One of the most important feature of this phenomenon is the concept of cluster of receptors, or receptor mosaic (RM). However, no proper mathematical approach has still been available to characterize RMs as far as their receptor composition, receptor topography and order of receptor activation inside the RM. This paper tries to fill the gap. A simple mathematical approach to the cooperativity in RMs formed by dimers of identical receptors and/or by iso-receptors is proposed. To this aim the so-called "symmetry rule" has been considered. This approach allows to describe by means of a simple energy function the effects of receptor composition (number of dimers), spatial organisation (respective location of the dimers) and order of activation (order according to which the single receptors are ligated) on the integrative cooperativity (index) of the RMs.

Binding Sites↗
PubMed2004

Sensitivity analysis of a novel mathematical model identifies factors determining bone resorption rates.

The development of pharmaceutical treatments for bone disease can be enhanced by computational models that predict their effects on resorption and rates of remodeling. Therefore, a simple mathematical model was formulated to simulate erosion depth and duration of resorption, using Michaelis-Menten (M-M) equations to describe changing rates of cellular activity during the two phases of bone resorption. The model was based on histomorphometric data and cellular interactions that occur in the bone microenvironment cited from the literature. Availability of bone substrate for osteoclastic activity during Phase I was assumed to be limited by the ratio of RANKL (ligand for receptor activator for nuclear factor kappaB) to osteoprotegerin (OPG) ('effective RANKL'). The required presence of marrow stromal cell produced macrophage-colony stimulating factor (M-CSF) for osteoclast action was represented as a factor equal to 1 for healthy bone. Growth factors released from the matrix during Phase I were assumed to cause two negative feedback effects: (1) the inhibitory effect of transforming growth factor-beta1 (TGFbeta1)-induced production of OPG by marrow osteoblast stromal cells, reducing effective RANKL; (2) the apoptosis of osteoclast nuclei assumed to occur at high concentrations of TGFbeta. This signaled the end of Phase I. During Phase II, cellular activity to remove the collagen fibrils left behind by osteoclasts was also simulated by Michaelis-Menten kinetic equations. Results of sensitivity analysis revealed variation in resorption depth and duration to fluctuate within 6% and 7% of the baseline value for changes in most input parameters. However, resorption depth was reduced and the duration of resorption lengthened by both a decrease in matrix TGFbeta and an increase the apoptotic threshold. Furthermore, the duration of resorption, but not erosion depth, was sensitive to changes in the maximum rate of cellular activity during removal of collagen fibrils. This mathematical model, which simulates the changing rates of cellular activity, has identified factors that reduce the duration and depth of resorption. It also suggests new targets for modeling therapeutic intervention to slow the rate of bone remodeling.

Bone Resorption↗
PubMed2005

A mathematical model to determine molecular kinetic rate constants under non-steady state conditions using fluorescence recovery after photobleaching (FRAP).

Fluorescence recovery after photobleaching (FRAP) analyses of binding and unbinding of molecules that interact with insoluble scaffolds, such as the cytoskeleton and nuclear matrix, in living cells commonly assume that this process is at equilibrium over the time scale of fluorescence recovery. This assumption breaks down for relatively fast intracellular processes like focal adhesion assembly at the leading edge of a migrating cell, or changes of transcriptional activation in the nucleus, that can occur in a matter of a few minutes. In this paper, we formulate a mathematical model that permits FRAP to be used to determine kinetic rate constants of molecules that interact with insoluble cellular structures under non-steady state conditions. We show that unlike steady state FRAP, fluorescence recovery time scales under these unsteady conditions are determined not only by unbinding rates, but also by the overall assembly and disassembly dynamics of the structural scaffold which supports these binding interactions. Experimental data from FRAP analysis and quantification of scaffold assembly dynamics may be combined and used with our mathematical model to estimate kinetic rate constants, as well as the apparent rate constant of scaffold assembly and disassembly.

Fluorescence Recovery After Photobleaching↗
PubMed2004

The use of mathematical models to evaluate pelvic masses; can they beat an expert operator?

The pre-operative characterization of ovarian cysts remains a major challenge. Functional cysts and some other benign cysts should be managed conservatively, whereas persistent tumours may need removal. It is crucial to distinguish between malignant tumours, which are better treated by a gynaecological oncologist, and benign tumours, which may be suitable for minimal-access surgery. Over the past decade several ultrasound-based morphological scoring systems, colour Doppler parameters, logistic regression models and artificial neural networks have been proposed and tested in order to try to predict the histology of ovarian tumours. On prospective testing none of the current models can beat an expert sonologist. Signs of malignancy include the presence of papillary structures, irregular solid areas, septa and a strong vascularization at colour Doppler imaging. Further refinement of mathematical models and the results of multicentre trials need to be reviewed before the clinical use of mathematical models can be advocated.

Biomarkers, Tumor↗
PubMed2005

Mathematical models for the Aedes aegypti dispersal dynamics: travelling waves by wing and wind.

Biological invasion is an important area of research in mathematical biology and more so if it concerns species which are vectors for diseases threatening the public health of large populations. That is certainly the case for Aedes aegypti and the dengue epidemics in South America. Without the prospect of an effective and cheap vaccine in the near future, any feasible public policy for controlling the dengue epidemics in tropical climates must necessarily include appropriate strategies for minimizing the mosquito population factor. The present paper discusses some mathematical models designed to describe A. aegypti's vital and dispersal dynamics, aiming to highlight practical procedures for the minimization of its impact as a dengue vector. A continuous model including diffusion and advection shows the existence of a stable travelling wave in many situations and a numerical study relates the wavefront speed to a few crucial parameters. Strategies for invasion containment and its prediction based on measurable parameters are analysed.

Aedes↗
PubMed2005

Mathematical model for optimal control in wastewater discharges: the global performance.

In this work we show how mathematical models and optimal control techniques can help us to solve some problems of environmental engineering, more precisely, water pollution problems arising from wastewater discharges into coastal areas or rivers. We deal with a complete two-dimensional mathematical model for the evolution of pollutant concentration in a shallow water domain. By integrating this model we obtain a zero-dimensional one and we use it to study the global performance of the system in a realistic situation. Finally, by using the two-dimensional model, we recall two optimal control problems related to the wastewater disposal problem.

Models, Theoretical↗
PubMed2004

Mathematical analysis of tooth and restoration contour using image analysis.

OBJECTIVES: The aim of this study was to develop a methodology for comparison of the contour of artificial crowns in the mid bucco-lingual plane with their equivalent natural teeth on the opposing side of the same arch (antimeres) using a novel application of image analysis software. The objective was to determine whether artificial crowns were overcontoured. METHODS: Specimens consisted of thin sections of silicone putty impressions of the buccal and lingual surfaces of 55 full crown restorations and their natural antimeric teeth. A thin slice of the putty was obtained in the mid-tooth bucco-lingual plane and a digital image was captured and this was analysed to produce a data set (x, y) representing the curvature of the tooth surface. Further analysis was performed in order to describe the profile in optimum mathematical terms. RESULTS: The curves were best represented by three equations: y = a + bx(0.5), ln(y) = a + bx2, and y2 = a + bx. In all equations parameter (b), which expresses the contour curvature, was used as a deciding factor in comparing the degree of contour of the crown restorations with their natural antimeres. Most artificial crowns were found to be either similarly or undercontoured when compared with their natural antimeres. When overcontouring was present in the artificial crowns this tended to occur on the lingual aspects of anterior and posterior crowns. SIGNIFICANCE: Simplifying tooth contour into a mathematical model can be useful in determining whether restorations are overcontoured. Clinically, particular attention should be directed towards the lingual aspects of restorations which were more likely to be overcontoured.

Crowns↗
PubMed2005

A mathematical model for evaluation of maternal cell contamination in cultured cells from spontaneous abortions: significance for cytogenetic analysis of prenatal selection factors.

OBJECTIVE: To develop a mathematical model for more precise estimation of the incidence of chromosomal abnormalities and the sex ratio among spontaneous abortions masked by maternal cell contamination. DESIGN: Retrospective analysis. SETTING: Academic medical center. PATIENT(S): One hundred twelve samples of spontaneous abortion with a "46,XX" karyotype and 97 parents with aborted embryos. INTERVENTION(S): The presence of Y chromosome DNA in native tissues of "46,XX" spontaneous abortions was detected by amelogenin locus analysis. Detection of aneuploidies in noncultured tissues of "46,XX" abortions was performed by microsatellite DNA analysis and confirmed by fluorescence in situ hybridization. MAIN OUTCOME MEASURE(S): Accuracy of cytogenetic evaluation of spontaneous abortions. RESULT(S): Y chromosome DNA was revealed in 16% of the embryos with a "46,XX" karyotype. According to the mathematical model proposed, the frequency of chromosomal abnormalities in a sample of 478 abortions increased from 54.6% to 60.3%, and the sex ratio in embryos with normal karyotype changed from 0.66 to 1.02. The experimental validation of the model has shown that the observed and expected incidences of chromosomal abnormalities in "46,XX" abortions were in good agreement. CONCLUSION(S): Maternal cell contamination clearly affects the incidence of registered chromosomal abnormalities and the sex ratio in spontaneous abortions. Correction for maternal cell contamination should be taken into account before invoking biological explanations of sex ratio bias and might be useful to include in diagnostic reporting.

Abortion, Spontaneous↗
PubMed2005

Some mathematical problems in the DNA identification of victims in the 2004 tsunami and similar mass fatalities.

DNA is a major and essential identification tool for mass fatality incidents including the hundreds of thousands of victims of the 2004 Indian Ocean tsunami. Mathematical complications characteristic of this sort of mass fatality include prevalence of related victims, the many races represented among the victims, and various identification modalities in tandem with DNA. Four mathematical problems of interest are discussed in this paper. (1) Other quantifiable factors (i.e. geography) can be formally accounted for by including a likelihood ratio that can be thought of as reducing the "effective number of victims." (2) When a victim is found and tentatively identified as V, but then it comes to light that the victim has a relative W who is also missing, confidence in the identity is depressed. To account for the existence of W, increment the effective number of victims by the likelihood ratio supporting W as the identity of the victim. (3) When several apparently related victims are found, their mutual identities should be calculated simultaneously. Compared to one-at-a-time, serial identifications, this is both logical and may lead to much more confidence in the identities. (4) Although there may be many different population groups represented among the missing, it is generally sufficient to consider population statistics for only a few of them in deciding whether to declare an identification.

DNA↗
PubMed2006

A mathematical program to predict survival and to support initial therapeutic decisions for trauma patients with long-bone and pelvic fractures.

AIM: To test a mathematical program to monitor early haemodynamic patterns of patients with fractures, predict survival and support initial therapeutic decisions. METHODS: A mathematical search and display program based on non-invasive haemodynamic monitoring was used to study 430 consecutively monitored patients with fractures during the first 48 h after admission to the emergency department of an inner city public hospital. We studied four types of fractures: simple extremity fractures, long-bone fractures, pelvic fractures and fractures incidental to severe trauma. The program continuously displayed haemodynamic patterns and predicted survival probability (SP), which was evaluated by the actual outcome at hospital discharge. The program also assessed the effectiveness of therapies according to haemodynamic responses. RESULTS: The cardiac index, heart rate, mean arterial pressure, arterial saturation and transcutaneous oxygen tensions at the initial resuscitation were significantly higher in survivors than in non-survivors. After the first 48 h, the haemodynamic patterns were more influenced by fever, sepsis, complications and organ failures. The calculated survival probability averaged 81%+/-18% in the first 48 h for survivors and 72%+/-20% for non-survivors. CONCLUSION: Early continuous non-invasive haemodynamic monitoring using the proposed information system is helpful in predicting outcome and guiding therapy for patients with fractures.

Adult↗
PubMed2004

A mathematical model for the laser treatment of heart disease.

Transmyocardial laser revascularisation (TMLR) is used to treat patients with severe coronary artery disease. A laser is used to create narrow tunnels within ischemic heart muscle in an attempt to reperfuse the area with oxygenated blood directly from the left-ventricular chamber. It has been hypothesised that initially blood flow through the patent tunnels plays an important role in the efficacy of the treatment (J. Am. College Cordiol. 25(1) (1995) 258) and Waters (J. Fluid Mech. 433 (2001) 193) developed a simple mathematical model to show that this blood flow enhances the quantity of oxygenated blood drawn into the tunnel and the subsequent delivery of oxygen to the tissue. To date, however, the optimum parameter values for this clinical technique have not been determined, e.g. the radius of the laser-drilled tunnels and their relative spacing. We present a mathematical model to determine the distribution of oxygen for a wide range of the governing parameters. Our results indicate that the tunnel radius has a significant effect on the degree of tissue reperfusion and predictions for the optimum tunnel spacing are made.

Animals↗
PubMed2005

Mathematical and numerical models for transfer of low-density lipoproteins through the arterial walls: a new methodology for the model set up with applications to the study of disturbed lumenal flow.

In this work we introduce and discuss several mathematical models, based on partial differential equations, devised to study the coupled transport of macromolecules as low-density lipoproteins in the blood stream and in the arterial walls. These models are accurate provided that a suitable set of physical parameters characterizing the physical properties of the molecules and of the wall layers are available. Here we turn our attention on this aspect, and propose a new methodology to compute the physical parameters needed for the model set up, starting from available in vivo measurements. Then, we focus on the study of the accumulation of low-density lipoproteins in vascular districts featuring a highly disturbed flow. Our results demonstrate that mathematical models whose set up procedure benefits from an experimental feedback provide reliable information not only qualitatively, but also quantitatively. Their application to geometrically perturbed vascular districts (as for example a severe stenosis) shows that geometrical parameters such as curvature and variations of the lumenal section strongly influence the accumulation of low-density lipoproteins within the wall. For instance, in a stenotic segment with 75% area constriction, the LDL concentration at the lumenal side of the wall is about 10% higher than for the undisturbed segment.

Arterial Occlusive Diseases↗