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PubMed2004

Scoliosis of the cranial base: radiological and mathematical analysis using finite elements system analysis (FESA) of a case.

INTRODUCTION AND PROPOSED STUDY: Numerous deforming syndromes of the craniofacial complex involve also the symmetry of the cranial base. This study considers a particular alteration, that of 'scoliosis', in which the line Nasion-Sella-Basion-Inion is not rectilinear but curved, due to a torsion of the cranial base in the horizontal plane. MATERIALS: Plagiocephaly was studied in one patient, which was probably caused by altered timing or mechanism of closure of the cranial sutures. METHODS: This study was carried out using CT images of the patient's craniofacial complex, using standard neuroradiological points. In order to study the forces that operated in the various complexes, a mathematical analysis was applied namely, a finite element system analysis (FESA). RESULTS: From this mathematical study, which has enabled us to evaluate the forces that operate in determining the deformity, it has been possible to locate two sites of force concentration. They were located at different levels and on opposite sides. CONCLUSION: This finding could explain why the middle and lower thirds of the face were also involved.

Biomechanical Phenomena↗
PubMed2005

Mathematical modeling of wire-duct single-stage electrostatic precipitators.

A two-dimensional mathematical model was developed to simulate the performance of wire-duct single-stage electrostatic precipitators (ESP). The model presented by Talaie et al. [M.R. Talaie, M. Taheri, J. Fathikaljahi, A new method to evaluate the voltage-current characteristics applicable for a single-stage electrostatic precipitator, J. Electrostat., 53 (3) (2001) 221-233] was used for prediction of electric field strength distribution and V-I characteristic for high-voltage wire-plate configuration. Simple Lagrangian approach was used to predict particle movement. Normal k-epsilon turbulent flow model with considering electrical body force due to ion and charged particle flow was used to evaluate gas velocity distribution. Ignoring the effect of particle movement and fluid flow, the results of electrical part of mathematical model are in good agreement with experimental data of Penny and Matick [G.W. Penny, R.E. Matrick, Potential in DC corona field, Trans. AIEE Part 1, 79 (1960) 91-99]. The prediction of corona sheath radius and its variation with particle loading and applied voltage is the main distinguishing feature of the present model. This fact was not included in the earlier models.

Filtration↗
PubMed2006

Mathematical simulation and long-term monitoring of leachate components from two different landfill cells.

In this study we monitored for 920 days the sulfate (SO(4)(2-)), chloride (Cl(-)), chemical oxygen demand (COD) and biological oxygen demand (BOD) parameters in leachate produced in two large-scale test cells at the Odayeri Sanitary Landfill, Istanbul, Turkey. We present a mathematical model of these parameter concentrations in leachates of two test cells with one being the control (C1) and the other (C2) leachate recirculation. The relationship between these parameters and refuse age is simulated by a mathematical formula. The unknown constants of the simulation formula are solved by the least squares method, which minimizes the squared total of deviation from the model of the actual data using a MATLAB computer program. A good fit was obtained between the measured data and model simulations. COD concentrations in leachate from C1 and C2 rapidly attained their maximum values of 75 and 70 g/l, respectively, after 1 month of landfilling. BOD to COD ratios are around 0.8 for both test cells during the acidogenic phase; this ratio then decreased to 0.06. A sharp decrease in the concentration of Cl(-) from 14 to 15 g/l was observed after approximately 2 months of operation, followed by a slow decrease. SO(4)(2-) concentrations rapidly reached a maximum value of 2000 mg/l within 45 days; development of anaerobic conditions caused a sharp decrease to around 75 mg/l for C2 and 450 mg/l for C1 after 5 months of operation. The results showed that there appeared to be little improvement in leachate quality by leachate recirculation in terms of COD and BOD values, however, it is determined that the pollution loads more rapidly reached minimum values within the C2 test cell.

Chlorides↗
PubMed2006

Mathematical modeling of copper(II) ion inhibition on COD removal in an activated sludge unit.

A mathematical model was developed to describe the Cu(II) ion inhibition on chemical oxygen demand (COD) removal from synthetic wastewater containing 15 mg l(-1) Cu(II) in an activated sludge unit. Experimental data obtained at different sludge ages (5-30 days) and hydraulic residence times (HRT) (5-25 h) were used to determine the kinetic, stoichiometric and inhibition constants for the COD removal rate in the presence and absence of Cu(II) ions. The inhibition pattern was identified as non-competitive, since Cu(II) ion inhibitions were observed both on maximum specific substrate removal rate (k) and on the saturation constant (Ks) with the inhibition constants of 97 and 18 mg l(-1), respectively, indicating more pronounced inhibition on Ks. The growth yield coefficient (Y) decreased and the death rate constant (b) increased in the presence of Cu(II) ions due to copper ion toxicity on microbial growth with inhibition constants of 29 and 200 mg l(-1), respectively indicating more effective inhibition on the growth yield coefficient or higher maintenance requirements. The mathematical model with the predetermined kinetic constants was able to predict the system performance reasonably well especially at high HRT operations.

Adsorption↗
PubMed2003

Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion.

Over the last 10 years increasingly complex mathematical models of cancerous growths have been developed, especially on solid tumors, in which growth primarily comes from cellular proliferation. The invasiveness of gliomas, however, requires a change in the concept to include cellular motility in addition to proliferative growth. In this article we review some of the recent developments in mathematical modeling of gliomas. We begin with a model of untreated gliomas and continue with models of polyclonal gliomas following chemotherapy or surgical resection. From relatively simple assumptions involving homogeneous brain tissue bounded by a few gross anatomical landmarks (ventricles and skull) the models have recently been expanded to include heterogeneous brain tissue with different motilities of glioma cells in grey and white matter on a geometrically complex brain domain, including sulcal boundaries, with a resolution of 1 mm(3) voxels. We conclude that the velocity of expansion is linear with time and varies about 10-fold, from about 4 mm/year for low-grade gliomas to about 3 mm/month for high-grade ones.

Brain Neoplasms↗
PubMed2005

The evolution of the human mind and logic--mathematics structures.

The evolution of the human mind is discussed based on: (i) the fact that living beings interchange matter, energy and information with their environment, (ii) an ontological interpretation of the "reality" of the quantum world, of which logic-mathematics structures are considered constitutive parts, (iii) recent theories according to which living beings are considered as dynamic complex systems organized by information, and (iv) the fact that the evolution of living beings is guided by information about the environment and by intrinsic information on living systems (auto-organization). Assuming the evolution of vision as a model we observe that the driving forces that directed the evolution of the eyes, as dynamic complex systems, are the information about the environment supplied by sunlight and the intrinsic information-gaining mechanism of living organisms. Thus, there exists a convergence toward a visual system with the greatest ability to obtain light information, like the human eye, and also a divergence that leads to the development of specific qualities in some species. As in the case of vision the evolution of the human mind-brain cannot be a consequence of factors unrelated to the object of its own functioning. The human mind was structured for the acquisition from reality of the logic-mathematics structures that underlie the whole universe and consequently of an internal representation of the external world and of its own self. Thus, these structures are, together with the intrinsic capacity for auto-organization of the human brain, the predominant driving force of the human mind evolution. Both factors are complementary.

Biological Evolution↗
PubMed2005

A mathematical model of hematopoiesis: II. Cyclical neutropenia.

Cyclical neutropenia is a dynamical disease of the hematopoietic system marked by an oscillation in circulating leukocyte (e.g. neutrophil) numbers to near zero levels and then back to normal. This oscillation is also mirrored in the platelets and reticulocytes which oscillate with the same period. Cyclical neutropenia has an animal counterpart in the grey collie. Using the mathematical model of the hematopoietic system of Colijn and Mackey [A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia. Companion paper to the present paper.] we have determined what parameters are necessary to mimic laboratory and clinical data on untreated grey collies and humans, and also what changes in these parameters are necessary to fit data during treatment with granulocyte colony stimulating factor (G-CSF). Compared to the normal steady-state values, we found that the major parameter changes that mimic untreated cyclical neutropenia correspond to a decreased amplification (increased apoptosis) within the proliferating neutrophil precursor compartment, and a decrease in the maximal rate of re-entry into the proliferative phase of the stem cell compartment. For the data obtained during G-CSF treatment, good fits were obtained only when parameters were altered that would imply that G-CSF led to higher amplification (lower rate of apoptosis) in the proliferating neutrophil precursors, and a elevated rate of differentiation into the neutrophil line.

Adult↗
PubMed2005

Pest control through viral disease: mathematical modeling and analysis.

This paper deals with the mathematical modeling of pest management under viral infection (i.e. using viral pesticide) and analysis of its essential mathematical features. As the viral infection induces host lysis which releases more virus into the environment, on the average 'kappa' viruses per host, kappain(1,infinity), the 'virus replication parameter' is chosen as the main parameter on which the dynamics of the infection depends. We prove that there exists a threshold value kappa(0) beyond which the endemic equilibrium bifurcates from the free disease one. Still for increasing kappa values, the endemic equilibrium bifurcates towards a periodic solution. We further analyse the orbital stability of the periodic orbits arising from bifurcation by applying Poor's condition. A concluding discussion with numerical simulation of the model is then presented.

Agriculture↗
PubMed2005

Cost-effective G-CSF therapy strategies for cyclical neutropenia: mathematical modelling based hypotheses.

Using computer simulations of a mathematical model for the regulation of stem cell and neutrophil production in dogs, we have studied the efficacy of four different treatment protocols for cyclical neutropenia involving granulocyte colony stimulating factor (G-CSF). The first treatment scheme is based on the bifurcation analysis of the mathematical model and proposes a daily, phase-dependent, protocol. The second involves alternate day administration of G-CSF. The third triggers G-CSF administration whenever neutrophil levels fall below a predetermined level, and the fourth one follows a random administration protocol. The computer simulations predict that clinically desirable results can be achieved with the three last methods, using far less G-CSF than would be needed with the standard daily treatment. If the results of this modelling are borne out clinically, they will entail a considerable financial savings for patients.

Animals↗
PubMed2005

Mathematical modeling of the course and prognosis of factitious disorders: a game-theoretic approach.

A mathematical model using simple concepts of repeated games is proposed to model the course and prognosis of factitious disorders. Although simple, the model seems capable of explaining the yet unknown mechanisms underlying the variable course of factitious disorders. One of the notable results of this study is the significant effect of involved physicians in the treatment process on the course of the disease. Particularly, the doctor's error rate in realizing whether the symptoms are real or factitious can considerably affect the course of the disease. This is the first paper to apply a mathematical model to factitious disorders.

Factitious Disorders↗
PubMed2006

Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies.

Angiogenesis, the growth of a network of blood vessels, is a crucial component of solid tumour growth, linking the relatively harmless avascular growth phase and the potentially fatal vascular growth phase. As a process, angiogenesis is a well-orchestrated sequence of events involving endothelial cell migration, proliferation; degradation of tissue; new capillary vessel (sprout) formation; loop formation (anastomosis) and, crucially, blood flow through the network. Once there is blood flow associated with the nascent network, the subsequent growth of the network evolves both temporally and spatially in response to the combined effects of angiogenic factors, migratory cues via the extracellular matrix and perfusion-related haemodynamic forces in a manner that may be described as both adaptive and dynamic. In this paper we present a mathematical model which simultaneously couples vessel growth with blood flow through the vessels--dynamic adaptive tumour-induced angiogenesis (DATIA). This new mathematical model presents a theoretical and computational investigation of the process and highlights a number of important new targets for therapeutic intervention. In contrast to earlier flow models, where the effects of perfusion (blood flow) were essentially evaluated a posteriori, i.e. after generating a hollow network, blood flow in the model described in this paper has a direct impact during capillary growth, with radial adaptations and network remodelling occurring as immediate consequences of primary anastomoses. Capillary network architectures resulting from the dynamically adaptive model are found to differ radically from those obtained using earlier models. The DATIA model is used to examine the effects of changing various physical and biological model parameters on the developing vascular architecture and the delivery of chemotherapeutic drugs to the tumour. Subsequent simulations of chemotherapeutic treatments under different parameter regimes lead to the identification of a number of new therapeutic targets for tumour management.

Animals↗
PubMed2006

Mathematical modeling of humoral immune response suppression by passively administered antibodies in mice.

Although passively administered antibodies are known to suppress the humoral immune response, the mechanism is not fully understood. Here, we developed a mathematical model to better understand the suppression phenomena in mice. Using this model, we tested the generally accepted but difficult to prove "epitope masking hypothesis." To simulate the hypothesis and clearly observe masking of epitopes, we modeled epitope-antibody and epitope-B-cell receptor interactions at the epitope level. To validate this model, we simulated the effect of the antibody affinity and quantity as well as the timing of administration on the suppression, and we compared the results with experimental observations reported in the literature. We then developed a simulation to determine whether the epitope-masking hypothesis alone can explain known immune suppression phenomena, especially the conflicting results on F(ab')2 fragment-induced suppression, which has been shown to be no suppression, or similar to or up to 1000-fold weaker than the suppression by intact antibody. We found that suppression was caused by a synergistic effect of both epitope masking and rapid antigen clearance. Although the latter hypothesis has lost support because FcgammaRI/III mutant mice show antibody-mediated suppression, our simulations predict that, even in FcgammaRI/III mutant mice, the immune response can be suppressed according to the antibody affinity. Our model also effectively reproduced the conflicting results obtained using F(ab')2 fragments. Thus, in contrast to the idea that the F(ab')2 results prove the FcgammaRIIb involvement in suppression, our mathematical model suggests that the epitope-masking hypothesis together with rapid antigen clearance explains the conflicting results.

Animals↗
PubMed2006

Mathematical modeling of ovarian cancer treatments: sequencing of surgery and chemotherapy.

Ovarian cancer has long been one of the most common forms of cancer in women. The main treatment for ovarian cancer comprises a combination of surgery and chemotherapy. In an effort to improve treatment strategies, a variety of mathematical models have been developed in the literature. In this paper, we consider a simple mathematical model that incorporates tumor growth as well as the effects of chemotherapeutic and surgical treatments in ovarian cancer. We consider several growth models and combine them with different cell-kill hypotheses. Surgery is assumed to eliminate a fixed fraction of tumor cells instantaneously. We discuss how different models predict the optimal sequencing of chemotherapeutic and surgical treatments. This work has been carried out in the context of ovarian cancer; however, the results may also be useful for other kind of cancers.

Antineoplastic Agents↗
PubMed2006

An integrated agent-mathematical model of the effect of intercellular signalling via the epidermal growth factor receptor on cell proliferation.

We have previously developed Epitheliome, a software agent representation of the growth and repair characteristics of epithelial cell populations, where cell behaviour is governed by a number of simple rules. In this paper, we describe how this model has been extended to incorporate an example of a molecular 'mechanism' behind a rule-in this case, how signalling by both endogenous and exogenous ligands of the epidermal growth factor receptor (EGFR) can impact on the proliferation of cell agents. We have developed a mathematical model representing release of endogenous ligand by cells, three-dimensional diffusion of the secreted molecules through a volume of cell culture medium, ligand-receptor binding, and bound receptor internalization and trafficking. Information relating to quantities of molecular species associated with each cell agent is frequently exchanged between the agent and signalling models, and the ratio of bound to free receptors determines cell cycle progression and hence the proliferative behaviour of the cell agents. We have applied this integrated model to examine the effect of plating density on tissue growth via autocrine/paracrine signalling. This predicts that cell growth is dependent on the concentration of exogenous ligand, but where this is limited, then growth becomes dependent on cell density and the availability of endogenous ligand. We have further modified the calcium concentration of the medium to modulate the formation of intercellular bonds between cells and shown that the increased propensity for cells to form colonies in physiological calcium does not result in significantly different patterns of receptor occupancy. In conclusion, our approach demonstrates that by combining agent-based and mathematical modelling paradigms, it is possible to probe the complex feedback relationship between the behaviour of individual cells and their interaction with one another and their environment.

Animals↗
PubMed2006

A mathematical model for the evaluation of amplitude of hemoglobin fluctuations in elderly anemic patients affected by myelodysplastic syndromes: correlation with quality of life and fatigue.

Therapy with RBC transfusions and rHuEPO for management of anemia in patients with myelodysplastic syndromes causes recurrent fluctuations in hemoglobin levels. The purpose of this study was to elaborate a mathematical model for the interpretation of hemoglobin fluctuations and to correlate the resulting numerical parameter (Variaglobin Index) with quality of life and fatigue. In 32 myelodysplastic patients, lower amplitude of the Variaglobin Index was found significantly correlated with a better quality of life and less fatigue. The mathematical model proposed here makes it easy to monitor anemia in myelodysplastic patients and to adjust therapy accordingly.

Aged↗
PubMed2004

Mathematical modeling confirms the length-dependency of telomere shortening.

Telomeres, the ends of chromosomes, shorten with each cell division in human somatic cells, because of the end-replication problem, C-strand processing and oxidative damage. On the other hand, the reverse transcriptase telomerase can add back telomeric repeats at the telomere ends. It has been suggested that once telomeres have reached a critical length, cells cease proliferation, also known as senescence. Evidence is accumulating that telomere shortening and subsequent senescence might play a crucial role in life-threatening diseases. So far, mathematical models described telomere shortening as an autonomous process, where the loss per cell division does not depend on the telomere length itself. In this study, published measurements of telomere distributions in human fibroblasts and human endothelial cells were used to show that telomeres shorten in a length-dependent fashion. Thereafter, a mathematical model of telomere attrition was composed, in which a shortening factor and an autonomous loss were incorporated. It was assumed that the percentage of senescence was related to the percentage of telomeres below a critical length. The model was compared with published data of telomere length and senescence of human endothelial cells using the maximum likelihood method. This enabled the estimation of physiologically important parameters and confirmed the length-dependency of telomere shortening.

Aging↗
PubMed2005

Mathematical modeling of cancer radiovirotherapy.

Cancer virotherapy represents a dynamical system that requires mathematical modeling for complete understanding of the outcomes. The combination of virotherapy with radiation (radiovirotherapy) has been recently shown to successfully eliminate tumors when virotherapy alone failed. However, it introduces a new level of complexity. We have developed a mathematical model, based on population dynamics, that captures the essential elements of radiovirotherapy. The existence of corresponding equilibrium points related to complete cure, partial cure, and therapy failure is proved and discussed. The parameters of the model were estimated by fitting to experimental data. By using simulations we analyzed the influence of parameters that describe the interaction between virus and tumor cell on the outcome of the therapy. Furthermore, we evaluated relevant therapeutic scenarios for radiovirotherapy, and offered elements for optimization.

Algorithms↗
PubMed2006

A mathematical model to study the effects of drugs administration on tumor growth dynamics.

A mathematical model for describing the cancer growth dynamics in response to anticancer agents administration in xenograft models is discussed. The model consists of a system of ordinary differential equations involving five parameters (three for describing the untreated growth and two for describing the drug action). Tumor growth in untreated animals is modelled by an exponential growth followed by a linear growth. In treated animals, tumor growth rate is decreased by an additional factor proportional to both drug concentration and proliferating cells. The mathematical analysis conducted in this paper highlights several interesting properties of this tumor growth model. It suggests also effective strategies to design in vivo experiments in animals with potential saving of time and resources. For example, the drug concentration threshold for the tumor eradication, the delay between drug administration and tumor regression, and a time index that measures the efficacy of a treatment are derived and discussed. The model has already been employed in several drug discovery projects. Its application on a data set coming from one of these projects is discussed in this paper.

Animals↗