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This paper describes a mathematical method of the lap phases of Saccharomyces cerevisiae that incorporates the basic concepts previously presented in a two-stage deterministic model for the growth of this organism under conditions of oxygen excess with a sugar as the growth-limiting substrate. The model structure was suggested by an extensive investigation of the causes of the lap phases of S. cerevisiae which found that, in contrast to the traditionally accepted trends, the length of the lap phase was not inoculum-size dependent. This was consistent with other previously published work which suggested that a major factor in the length of the lag phases in S. cerevisiae was the need to synthesize adequate levels of glycolytic and respiratory enzymes. These suggestions were confirmed experimentally with lag-age data. Based on this conclusion a mathematical model was developed incorporating a description of the levels of glycolytic and respiratory enzymes and their effect on the growth rate and metabolism. This model was tested experimentally and the initial results indicate that many aspects of the lag phase of this organism may be described mathematically. The experimental findings further support the concept of primary regulatory control proposed by Bijkerk and Hall.
Clinical and research data indicate that active and passive changes in the mechanical environment of the heart are capable of influencing both the initiation and the spread of cardiac excitation via pathways that are intrinsic to the heart. This direction of the cross-talk between cardiac electrical and mechanical activity is referred to as mechano-electric feedback (MEF). MEF is thought to be involved in the adjustment of heart rate to changes in mechanical load and would help to explain the precise beat-to-beat regulation of cardiac performance as it occurs even in the recently transplanted (and, thus, denervated) heart. Furthermore, there is clinical evidence that MEF may be involved in mechanical initiation of arrhythmias and fibrillation, as well as in the re-setting of disturbed heart rhythm by 'mechanical' first aid procedures. This review will outline the clinical relevance of cardiac MEF, describe cellular correlates to the responses observed in situ, and discuss the role that quantitative mathematical models may play in identifying the involvement of cardiac MEF in the regulation of heart rate and rhythm.
Certain deep indentations observed in dry coatings are referred to as "craters". They are believed to arise from gradients in the coating surface tension. A mathematical model of surface-tension-gradient-driven flow, using the lubrication approximation for thin layers, is developed to study the formation of craters. The paint is modeled as consisting of an evaporating "solvent" part and a nonvolatile "resin" part. Surface tension gradients on the coating surface arise due to a nonuniform distribution of surfactant. Axisymmetric numerical simulations using the model are performed to explore two candidate crater production mechanisms: an initial release of concentrated surfactant and a steady surfactant source. The effects of changes in various properties, such as the paint drying rate, the surfactant diffusivity, and the viscosity increase during drying, are examined. The model produces craters with large diameters, pronounced rims, and central peaks, similar to those seen in practice. Drying rate has a large influence on crater diameter and depth, by limiting flow due to surface tension gradients within a given time. Reduction of the paint viscosity increase during drying causes increased flow rates, leading to larger craters. A preexisting layer of surfactant on the paint surface sharply reduces the extent of cratering. Surfactant diffusion also tends to reduce the severity of cratering by alleviating surface tension gradients. In some cases, a simplified form of the drying model may be used to quickly approximate the results of the full model. The model provides useful insights into the craters seen in industrial coating applications. Copyright 2000 Academic Press.
Influenza A virus and various single-stranded RNA viruses have been reported to be blocked by IFN-stimulated Mx protein. Here we present a mathematical model of regulation of mouse Mx1 protein induction and action under influenza infection. Parameter estimates are derived from published experimental data. Numerical solutions of the model equations completely correspond to experimental data. The model is used to analyse the role of virus- and interferon-mediated expression of Mx1 in maintenance of antiviral state. The study suggests that virus- and IFN-induced Mx1 proteins act on different stages of intracellular ontogenesis of influenza virus and these actions result in different efficacy of cell protection. The model demonstrates that the synergistic action of inteferon and virus in regulation of Mx1 gene expression is the important factor of antiviral resistance. The results of simulation permit to assume that the active form of Mx1 protein is trimer.
Neutropenia, frequently a side effect of chemo- and radiotherapy, increases susceptibility to microbial infections and is a life-threatening condition. For realistically predicting drug treatment effects on granulopoiesis, we have constructed a new mathematical model of granulopoiesis in the bone marrow and in the peripheral blood, featuring cell cycle phase transition and detailed granulocyte-colony stimulating factor (G-CSF) pharmacokinetics (PK) and pharmacodynamics (PD), including intracellular second messenger. Using this model, in conjunction with clinical results, we evaluated the system parameters, implemented those in the model and successfully retrieved the results of several independent clinical experiments under a wide range of G-CSF regimens. Our results show that the introduction of G-CSF-controlled intracellular second messenger is indispensable for precise retrieval of the clinical results, and suggest that the half-life of this messenger varies between a single and multiple G-CSF administration schedules. In addition, our model provided reliable steady-state, as well as dynamic, estimations of human granulopoiesis parameters. These included an estimation of apoptosis index in the post-mitotic compartment, which corroborates previous results. At present the model is used for suggesting improved drug regimens.
Complex hepatitis B (HBV) epidemiology makes it difficult to evaluate and compare effectiveness of different immunization policies. A method for doing so is presented using a mathematical model of HBV transmission dynamics which can represent universal infant and adolescent vaccination strategies and those targeted at genito-urinary (GU) clinic attenders and infants born to infectious mothers. Model structure, epidemiological underpinning, and parameterization, are described. Data from the UK National Survey of Sexual Attitudes and Lifestyles is used to define patterns of sexual activity and GU clinic attendance; data deficiencies are discussed, in particular that of UK seroprevalence of HBV markers stratified by age, sex, and risk factors. General model predictions of endemic HBV marker prevalence in homosexual and heterosexual populations seem consistent with published UK data. The simulations exhibit non-linearities in the impact of different vaccination strategies. Estimated number of carriers prevented per vaccine dose for each strategy provides a measure of costs and benefits, varying temporally over the course of a programme, and with level of vaccine coverage. Screening before vaccination markedly increases payback per dose in homosexuals but not in heterosexuals; mass infant vaccination gives the poorest effectiveness ratio and vaccination of infants after antenatal screening the best; in general, increasing vaccine coverage yields lower pay-back per dose. The model provides a useful framework for evaluating costs and benefits of immunization programmes, but for precise quantitative comparison more UK epidemiological data is urgently needed.
Social importance of skin emphasizes an importance of quality of methods of planning for reconstructive and plastic surgery. With modern technical improvement the usage of complex mathematical model based on biomechanical characteristics of tissue is possible. Two- and three-dimensional model, expert systems and mechanical analysis are used. In this work we tested the system for mechanical analysis in preoperative planning of a simple procedure of the Z-plastic, named the finite-element method. Computer model simulates tissue coverages. With geometrical data some physical characteristics are added. Complex surface of skin is marked by the grid divided in quadrangular elements. Mechanical consequences and definitive results of surgical procedure are analysed during the computer simulation of the action of tension of skin and suture material. In our analysis we found the finite-element method of great usefulness and noticed that "surgery simulators" might be an efficient way to speed-up learning curve in reconstructive surgery.
A mathematical model of the response of cytotoxic T lymphocytes (CTL) to the nonexponential growth of an immunogenic tumour is presented. The model describes satisfactorily the kinetics of growth and regression of the B lymphoma BCL1 in the spleen of mice chimeric with respect to the major histocompatibility complex (H-2b----H-2d). Numerical estimations of the parameters describing processes that cannot be measured in vivo have been derived. It is predicted that the development of the tumour and its clinical manifestation have a recurrent profile with a cycle of three to four months. According to the model the limited growth of the BCL1 tumour and its transition into the dormant state are associated with a high rate of accumulation of CTL in the tumour, rapid lysis of lymphoma cells, and the inability of tumour cells to suppress the affector functions of cytotoxic lymphocytes. The model is also capable of representing the phenomenon of tumours 'sneaking through' and the immunostimulation of tumour growth.
Among clinical users of the registration of distortion product otoacoustic emissions (DPOAE), the understanding of the basic causality and interpretation of the phenomenon is not yet widely spread, nor is the expected influence of the middle ear and ear canal clear. On the other side, the effort in mathematical modeling of middle and inner ear structures is driven very far by now. We are convinced, though, that the essentials of an effect as DPOAE generation must be understandable from quite simple models. In a first step de Boer's one-dimensional model was adopted and expanded by a weak frictional and a weak elastic nonlinearity, respectively. By means of perturbation theory the weakly nonlinear problem is converted in an approximation series of linear problems. So it is solvable by the common methods of linear differential equations (DEs), above all the superposition principle can be used. At the same time a structure of causality is introduced: Sources for outgoing waves are in first order approximation formed by incoming waves, and so they can be localized. The calculations show clearly that of all six cubic distortions only the 2f(1) - f(2) term does have a source in its 'allowed' region and so can travel outward. We can use the calculated DPOAE to study the influence of middle ear, external ear canal and probe plug. Some problems remain: the weakly nonlinear model in first order does not give account for proper L(dp) = f(L(1), L(2)) and L(dp) = f(f(2)/f(1)) dependency, nor does it deliver additional sources or the effect of additional suppressor tones. In a second step, therefore, we replace de Boer's simple model basilar membrane (BM) by a doubly resonant, coupled tectorial/basilar membrane (TM/BM) system. By feedback now we introduce a strong nonlinearity, which we can mathematically care for by an iterative feedback loop. The algorithm shapes the incoming waves according to strong compressive nonlinearity. More relastic incoming waves yield better source terms, and after optimization of the mistuning function between TM and BM the model now is able to deliver qualitatively correct L(dp) (L(1),L(2)) and L(dp)(f(2)/f(1)) dependencies.
A mathematic algorithm was developed to calculate mandibular repositioning resulting from occlusal equilibration. A formula to determine the amount of tooth reduction necessary for the adjustment also was derived.
The possibility of describing cestode infection dynamics in various host groups (e.g in birds, fishes and copepods) by trigonometric and parabolic polynomials is examined. The necessity of observing certain requirements during data collection for the correct application of the examined models is shown; the possibility of applying a parabolic polynomial in case of non-observing of some of these requirements has been found. The mathematical models obtained are of prognostic value and may serve as a measure of the uniformity and validity of the empirical data.
Proficiency testing (PT) programs may fail to establish a range of acceptable performance in a challenge when an insufficient number of participants use a particular method. In this study I analyzed a mathematical approach to establish acceptable performance in alanine aminotransferase (ALT; EC 2.6.1.2) PT challenges. This approach was derived from the mathematical model used in establishing a nationwide ALT standardization system for blood-collection facilities in 1988. A ratio of results was derived between each method in the PT program and an arbitrarily chosen "standard" method. The intent of this approach was to transform a target value for a challenge as determined in the "standard" method to units applicable to methods utilized less often. However, the high degree of variability over time in the ratios for some methods precluded general application of this approach. Therefore, although this simple mathematical method was successful in implementing an ALT standardization system across different methods, a derivation of this approach did not afford comparison of results in PT challenges.
We hypothesized that during high-frequency oscillatory ventilation (HFOV), a reduction of peak-to-peak oscillatory pressure along the endotracheal tube is maximal when respiratory system compliance is maximal. We made a mathematical model of the endotracheal tube and the respiratory system of a neonate suffering from idiopathic respiratory distress syndrome (IRDS). The model consisted of linear viscous and inertive elements, a non-linear endotracheal tube resistance, and a non-linear compliance allowing for alveolar recruitment and overdistention. Respiratory compliance was maximal at the transition between maximal recruitment and minimal overdistention. A new variable, the oscillatory pressure ratio (OPR), was defined as the ratio between peak-to-peak oscillatory pressures at the distal end and the proximal opening of the endotracheal tube, respectively. The respiratory variables of four patients were fed into the model, and the relationship between respiratory system compliance and OPR was determined. OPR decreased as compliance increased, except for very low compliances below where 0.08 mL. cm H2O(-1), and OPR increased with increasing compliance. The relationship between mean airway pressure P(aw) and OPR revealed that the minimal OPR (range, 0.37-0.78) and maximal respiratory compliance coincided at the same P(aw). However, the relationship did depend on oscillation frequency, applied oscillatory pressure, and endotracheal tube resistance, parameters that may change during clinical application of HFOV. When 81 permutations of nominal and extreme respiratory variables were used in the model, the minimum OPR (0.60 +/- 0.23) and maximum compliance coincided in all cases. These model experiments support our hypothesis. The results indicate that the OPR may be a useful index to optimize lung expansion, where lung recruitment is maximal and overdistention minimal. In vivo tests will be needed to reveal the feasibility and reliability of such an index for biomedical and clinical application.
An alternative way to estimate the endemic level of malaria amongst Brazilian indians is proposed. This is achieved by estimating the age-related 'force of infection' of malaria (the effective inoculation rate), applying a mathematical model, described elsewhere, to serological data. In addition we present a way to estimate the Basic Reproductive Rate of malaria in the same area. The results have shown a good degree of accuracy in describing the endemic pattern of malaria in the area, and also indicate some relevant aspects of its age distribution related to the design of control strategies.
Using average number of patients expected in a year, average length of stay and a target occupancy level to calculate the number of critical care beds needed is mathematically incorrect because of nonlinearity and variability in the factors that control length of stay. For a target occupancy in excess of 80%, this simple calculation will typically underestimate the number of beds required. More seriously, it provides no quantitative guidance information about other aspects of critical care demand such as the numbers of emergency patients transferred, deferral rates for elective patients and overall utilisation. The combination of appropriately analysing raw data and detailed mathematical modelling provides a much better method for estimating numbers of beds required. We describe this modelling approach together with evidence of its performance.
This paper attempts to obtain a better understanding of the oxygen supply to tissue cells of the optic nerve head by describing all phases of the release, diffusion and consumption process by means of a mathematical model. As a result the oxygen partial pressure reduction induced by intraocular pressure elevation--as it occurs in glaucoma--seems to be mainly influenced by a pressure-induced lowering of the average blood velocity in the retinal capillaries. A reduction of this velocity to a fourth of its normal value even makes the oxygen partial pressure at the venous capillary wall drop below the critical level necessary for maintaining cell activity. Furthermore our calculations allow us to conclude that an involvement of the retinal capillary network supplied by the central retinal artery should not be neglected in glaucoma.
In the proximal tubule in vivo, glomerulotubular balance requires that tubule epithelial cells accommodate a twofold variation in Na+ reabsorption through the Na+/H+ exchanger of the luminal membrane. In a mathematical model of proximal tubule, in which permeability coefficients are fixed, doubling flux through the Na+/H+ antiporter produces a substantial increase in cell volume and cytosolic HCO3-. In this model, it is possible to vary peritubular K+ permeability with changes in luminal Na+ entry, so that cell volume is constrained to be constant. In these calculations, the model predicts that peritubular hyperpolarization and nearly constant cytosolic HCO3- will accompany increases in luminal Na+ entry. Realistic models of variable peritubular K+ permeability might include a functional dependence on flux through the Na(+)-K(+)-adenosinetriphosphatase, cytosolic pH, or cell volume. When K+ permeability is represented as a function of any of these variables, homeostatic control of cell volume and pH can be obtained over a physiological variation of Na+/H+ flux. However, when luminal Na+ entry is via Na(+)-glucose cotransport, volume homeostasis is best when peritubular K+ permeability depends on the rate of active Na+ transport. For any modulator of K+ permeability, realistic constraints on the value of this parameter suggest that peritubular K+ permeability is, by itself, not sufficient to maintain cell volume within narrow limits. Parallel activation of another exit pathway, such as peritubular Na(+)-3 HCO3- cotransport, may be required to achieve the necessary homeostasis.