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PubMed1988

A comparison of mathematical models for regeneration in acutely responding tissues.

A mathematical model is presented to describe the regenerative response of mouse gut epithelal cells to radiation. The model, derived from radiobiological principles, predicts the cellular surviving fraction following any irradiation regimen. There are three basic elements to the model (a) a single dose survival curve, either the linear-quadratic or the two-component model, (b) a part to incorporate the regenerative response, either a Gompertzian or a logistic growth and (c) a part to accomodate the delayed onset of regeneration, including either a mitotic delay, a fixed time delay, both, or neither. The models are similar in spirit, but different in detail to the model proposed by Cohen. The various models are evaluated on three large datasets, where the response is cell survival in the jejunum or the colon measured using the crypt colony assay. The models were fit and the parameter estimates and standard errors were obtained from the raw observations using non-linear least squares. It is concluded that Gompertzian growth gives a better fit to the data than logistic growth; the delayed onset of regeneration in these tissues can be best accounted for by a mitotic delay or a mitotic delay plus a fixed time delay, and there is little to choose between the linear-quadratic and the two-component model. There was a strong relationship between the tissue cell cycle time and the regenerative response, the mitotic delay being longer and the rate of regeneration slower for the colon than for the jejunum.

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↗
PubMedDate not supplied

[Programmed complex for planning fractionated regimens of malignant tumor irradiation by local adjustment of mathematical model parameters].

The accuracy of planning the fractionated radiation regimens may be enhanced by the proposed method of local adjustment of its parameters. For planning the fractionated radiation regimens in practical radiology, TDF was used to design a programmed complex (PC) which defines the main radiological parameters of a radiation plan as a system of interchangeable values in remote, contact, and combined radiation therapy for uniform and nonuniform dose fractionation regimens. PC allows a radiologist to actively use his clinical observation for local adjustment of mathematical model parameters and for planning the fractionated radiation regimens. The method of local adjustment of mathematical model parameters for dose fractionation is applicable to lung tissue radiation. Its advantage is that it permits one to consider the complexity of the organism exposed to radiation and, to a definite extent, to minimize the possible inadequacy of the used mathematical model of dose fractionation.

Dose Fractionation, Radiation↗
PubMed1990

Percutaneous absorption of benzoic acid across human skin. I. In vitro experiments and mathematical modeling.

The percutaneous absorption of benzoic acid across human skin in vitro was experimentally and mathematically modeled. Skin partition coefficients were measured over a range of benzoic acid concentrations in both saline and distilled water. The permeation of benzoic acid was measured across isolated stratum corneum, stratum corneum and epidermis, and split-thickness skin. These experiments demonstrated that the stratum corneum was the rate-limiting barrier and that the flux is proportional to the concentration of the undissociated species. The permeation data were analyzed with a comprehensive non-steady-state mathematical model of diffusion across skin. Two adjustable parameters, the effective skin thickness and diffusivity, were fit to the permeation data by nonlinear regression.

Benzoates↗
PubMedDate not supplied

Use of mathematical models for the evaluation of two- and three-drug combination chemotherapy in murine tumor models.

In parallel with an ongoing clinical trial in patients with metastatic mammary carcinoma, we compared the three-drug combination of cyclophosphamide, tegafur, and methotrexate with the two-drug combination of cyclophosphamide and tegafur in the murine L1210 leukemia and B16 melanoma models. The obtained data based on a central composite design were calculated by mathematical models, which estimate optimum dose combinations for survival by restricting side effect constraints (loss of weight, leukopenia). The main results were as follows: (a) long-term survival can be reached only by accepting a relatively high toxicity in each case, and (b) in the L1210 model the three-drug combination was superior to the two-drug combination, while in the B16 melanoma cyclophosphamide as a single agent offered the best results. The experimental yields are in accordance with preliminary results of the clinical trial. The mathematical model used offers the possibility of comparing drug combinations in a relatively economic way.

Animals↗
PubMed2003

Mathematical modelling for the study of respiratory mechanics.

The target of this study was the development of mathematical models that best describe the behaviour of respiratory parameters. First of all, we studied lung volume in relation to time both for normal and maximal inspiration/expiration by developing mathematical models. For the construction of these equations the exponential model was used. Then we tried to study the flow-volume of a typical spirometer curve by dividing it into two parts: the first part reaches the Peak Expiratory Flow (PEF) point and the second follows until the volume reaches Vital Capacity (VC). For the first part we built an exponential equation; for the second part a number of existing prediction equations for the flow in various points of VC were used. For the volume-pressure diagram, we built exponential equations that describe the volume-pressure relation below Vo (Vo: lung volume where pressure is zero). The equations were coupled for expiration and inspiration. The modeling of respiratory mechanics led us to the conclusion that the developed models could offer new potentials in the description of other respiratory parameters as well.

Adult↗
PubMed1995

A mathematical model explaining the molecular weights and distribution of very long chain dicarboxylic acids formed during the adaptive response of Sarcina ventriculi.

A simple mathematical model is presented to explain a recent new discovery of an unusual membrane adaptive response in Sarcina ventriculi. In this response, this organism synthesizes very long chain alpha, omega-dicarboxylic acids ranging from 28 to 36 carbon atoms in length. The distribution of chain lengths of the new fatty acid species is not consistent with de novo synthesis but suggests elaboration from the existing regular-chain fatty acids by a coupling process. Here, we demonstrate, using a mathematical model, that if the molecular weights and relative abundances of regular chain fatty acids are known, the molecular weights and relative abundances of the new, very long chain dicarboxylic fatty acid species can be predicted using a model based on the random, pairwise combination of regular chain species. This combination takes place across the bilayer leaflet to form transmembrane fatty acids. It is proposed that this coupling phenomenon is regulated by the motional dynamics of the membrane.

Cell Membrane↗
PubMed1999

Mathematical modeling of the retention and clearance of low-toxicity particles in the lung.

A mathematical model has been formulated to describe the mechanisms that determine the retention or clearance of insoluble inhaled particles in the rat lung. The hypotheses underlying the model are described-for example, the phagocytosis of free particles by macrophages, the transport of particles in macrophages from the alveolar region, the effect of the life cycle of macrophages leading to the eventual release of phagocytosed particles, the effect of lung burden on the macrophage activity, the transport of particles into the interstitium, the role of interstitial macrophages, the formation of granulomata, and transport of interstitialized particles to the thoracic lymph nodes. With these hypotheses, the fate of particles is described mechanistically via the cellular response of the lung. The mathematical model expresses these particle transitions as differential equations quantifying the transport of particles from one compartment to another, where the compartments represent the alveolar surface, the alveolar macrophages, overloaded alveolar macrophages, the interstitium, interstitial macrophages, and the thoracic lymph nodes. A companion article describes the application of the model to a data set from rats exposed to a low-toxicity dust at several concentrations and for a range of exposure times.

Algorithms↗
PubMed1992

[The quantization of regional blood flow and volume with contrast echography: a mathematical model].

In this paper is described a new mathematical model for the study of regional blood flow in organs accessible to ultrasonic imaging. A prerequisite for the correct application of this model is the utilization of an echocontrast agent presenting with the same microrheology as red blood cells. This model is derived from an implementation of the indicator-dilution theory and is specifically designed to calculate relative changes in blood flow and volume in neighboring segments within the same organ. With this model is not required the acquisition of an input function, that is one of the major shortcomings affecting the classical theory. The applicability of quantitative contrast ultrasonography in humans may have a significant impact on our understanding of the pathophysiology of cardiovascular diseases.

Algorithms↗
PubMed2006

Mathematical model of phosphatidylinositol-4,5-bisphosphate hydrolysis mediated by epidermal growth factor receptor generating diacylglycerol.

Phosphatidylinositol-4,5-bisphosphate (PIP2) is hydrolyzed in response to the tyrosine phosphorylation of the epidermal growth factor receptor (EGFR) and plays an important role in regulating cell proliferation and differentiation through the generation of second messengers diacylglycerol (DAG) and trisphosphate inositol (IP3) which lead to the activation of protein kinase C (PKC) and increased levels of intracellular calcium, respectively. In the paper, a mathematical model was established to simulate the accumulation of DAG due to PIP2 hydrolysis mediated by EGFR. Molecular mechanisms between DAG, PIP2, EGFR and phosphatidylinositol transfer protein (PITP) were explained successfully, and positive cooperativity which existed between phospholipase C-gamma1 (PLC-gamma1) and PIP2 was also explained. In the model the effects of parameters on simulation of PIP2 hydrolysis were analyzed and the efficacies of some molecular intervention strategies were predicted. To test the coherence between the model and the biological response to epidermal growth factor (EGF) in cells, the levels of DAG and the tyrosine phosphorylation-EGFRs in NIH3T3 mouse embryonic fibroblast (MEF) were determined by biochemical experiments which showed that the accumulation of DAG was a sigmoidal function of phosphorylation-EGFR concentration, and the consistency between the mathematical model and experimental results was confirmed. In brief, this mathematical model provided a new idea for the further study of the dynamic change of biological characteristics in inositol phospholipid hydrolysis, predicting the efficacy of molecular intervention and the relationship between the metabolisms of inositol phospholipid and other signal transduction pathways.

Animals↗
PubMed2004

Mathematical modelling of skeletal repair.

Tissue engineering offers significant promise as a viable alternative to current clinical strategies for replacement of damaged tissue as a consequence of disease or trauma. Since mathematical modelling is a valuable tool in the analysis of complex systems, appropriate use of mathematical models has tremendous potential for advancing the understanding of the physical processes involved in such tissue reconstruction. In this review, the potential benefits, and limitations, of theoretical modelling in tissue engineering applications are examined with specific emphasis on tissue engineering of bone. A central tissue engineering approach is the in vivo implantation of a biomimetic scaffold seeded with an appropriate population of stem or progenitor cells. This review will therefore consider the theory behind a number of key factors affecting the success of such a strategy including: stem cell or progenitor population expansion and differentiation ex vivo; cell adhesion and migration, and the effective design of scaffolds; and delivery of nutrient to avascular structures. The focus will be on current work in this area, as well as on highlighting limitations and suggesting possible directions for future work to advance health-care for all.

Animals↗
PubMed1991

A physiologically based mathematical model for the human inhalation pharmacokinetics of 1,1,2-trichloro-1,2,2-trifluoroethane.

A physiologically based mathematical model is described for the human inhalation pharmacokinetics of 1,1,2-trichloro-1,2,2-trifluoroethane (FC113). Physiological parameters for the model are derived from the scientific literature. Partition coefficients are determined from in vitro measurements. Predictions of the resulting model for breath and blood concentrations compare well with results of a human volunteer study described in a companion paper (Woollen et al. 1990). Using this data some alternative models are also examined with different choices of physiological parameters and partition coefficients. The mathematical model is used to examine the consequences of metabolic elimination of FC113. A value for metabolic clearance is estimated using the during-exposure breath concentration data; however, the concentrations of FC113 in breath or blood during and after exposure are shown to be insensitive to metabolic clearance. Consequently, no firm conclusion can yet be drawn as to whether FC113 is metabolised by man.

Air Pollutants, Occupational↗
PubMedDate not supplied

Analytical approach to mathematical modelling of the isometric contraction of the hypertrophied myocardium.

It is attempted on the basis of the Hill two-element model to simulate mathematically the rising phase of the isometric mechanogram in the pressure-hypertrophied rat myocardium (Goldblatt II). The evaluation is based on the experimentally determined force-velocity relation as well as on the characteristic of the series-elastic stiffness. The changes in the isometric mechanogram of the hypertrophied heart muscle observed in the experiment can be mathematically predicted solely by means of the alterations in the force-velocity relationships induced by the hypertrophy, whereby the characteristic of the series-elastic stiffness is considered to be unchanged.

Cardiomegaly↗
PubMed1986

A limit cycle mathematical model of the REM sleep oscillator system.

A limit cycle mathematical model of the rapid-eye-movement (REM) sleep oscillator system has been developed from a structural model of interaction of populations of REM-on and REM-off neurons. The marked differences in latency, amplitude, and duration of the first REM sleep period seen with circadian variation and depressive pathology are modeled by beginning the REM oscillation at different initial points relative to the final position in the limit cycle. Beginning from a point that is graphically interior to the limit cycle produces a long-latency, short-duration, and less intense first REM period. Beginning from a point graphically exterior to the limit cycle produces a short-latency, long-duration, and more intense first REM period. In the model the determinant of whether the oscillation begins exterior or interior to the limit cycle is the time course of decay of the REM-off population discharge activity at sleep onset. When this time course is made to depend on circadian phase, the model produces a very close match to the empirically observed large shifts between the first and second REM periods in duration (often a 50% change) and intensity and also closely mimics the empirically observed shifts in REM latency as human sleep begins at different circadian phases. Although this variation in limit cycle entry accounts for the major changes in REM sleep over the night, the model also postulates a continuous but small circadian variation (of the order of +/- 5% change in REM parameters) acting throughout the course of a night's sleep. Because the model is derived from actual physiological data, rather than being a purely ad hoc or phenomenological construct, it offers the possibility of direct tests of its postulates through neurobiological studies in animals, by circadian phase-related manipulations of the sleep cycle, and through perturbations of the system in humans by the use of drugs. Indeed, an explicit phase-response curve of the system to cholinergic agonists has been developed; this will permit experimental tests of the model in both animals and humans.

Animals↗
PubMed1983

Mathematical model of the human ankle joint.

It has been suspected that the mechanical environment in which a particular joint functions has an effect on the initiation or progression of degenerative joint disease. The objective of this study is to define the mechanical environment of the ankle joint, specifically, the contact areas and pressure distributions, through the development and analysis of a simplified mathematical model. Since the state of pressure across articular surfaces during function is influenced by joint incongruity, cartilage thickness profile and the geometry of the opposing surfaces, these factors have been incorporated into the model formulation. Mathematical analysis of the model has resulted in pressure distributions in both the anterior-posterior and medial-lateral directions and contact area growth plots which correlate well with observed ankle contact patterns obtained from in vitro investigations. The significance of joint incongruity to these pressure distributions and to the relative immunity of the ankle joint to primary osteoarthritis is discussed.

Ankle Joint↗
PubMed1990

A mathematical model of atrioventricular conduction block using the excitability recovery curve of the myocardial cell.

A simple mathematical model of AV conduction block was constructed on the basis of single-cell electrophysiological experiments concerning the rate-dependent property of excitability of the AV nodal cells (the excitability recovery curve, ERC). This ERC was analogous to the phase response curve (PRC) of cardiac pacemaker cells, which the authors had previously used to construct a model of modulated parasystole. Computer simulation was used to reproduce the ERC. The single-cell ERC was then extended to the entire AV node, and this curve was used to formulate a mathematical model of AV conduction block as a nonlinear, first-order difference equation of the successive PR intervals of the ECG. This model predicted a variety of ECG patterns of AV conduction block: normal rhythm, first-degree block, and several second-degree blocks of complex Wenckebach periodicity in relation to the sinus rate and the shape of the ERC. By assuming this model it was possible to identify the underlying ERC of actual ECGs with complex Wenckebach periodicity.

Animals↗
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↗
PubMed1991

A mathematical model of some aspects of jet nebuliser performance.

A simple mathematical model describing the performance of an Acorn jet nebuliser system (Medic-Aid Ltd) has been developed in which nebuliser efficiency E, defined as the volume fraction of solution (water) released as an aerosol or lost by evaporation, and nebulisation time T, are given as functions of the initial volume of solution. The model identifies an initial phase during which the nebuliser output is at a constant, continuous rate of 0.007 ml s-1. This is followed by an intermittent phase of operation during which output is estimated to occur for 0.25 of the total duration of the phase and results from solution deposited on the walls being recycled. The model indicates that increasing the flow of solution to the nebulisation region in the nebuliser or decreasing the fraction of aerosol intercepted by the baffle, will decrease T whilst leaving E unaffected. Two residence times tau 1, tau 2 which are a measure of the time that solution droplets adhere to the inner walls of the nebuliser are also identified; tau 1 (= 1.6 s) is the residence time associated with the rapid recycling of the majority (a fraction eta 1 = 0.992) of the aerosol while tau 2 (= 200 s) the residence time associated with the remaining fraction 1 - eta 1. Increasing eta 1 will increase E for constant tau 1, tau 2 while increasing tau 1, tau 2 will decrease E, T remaining essentially unchanged. It is proposed that the model may be applicable to other jet nebulisers.

Aerosols↗