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The effect of microwaves of 2355 MHz and 50 microW/cm2 on rat respiratory system has been investigated. On the basis of the experimental results and a priori suggestions a mathematical model has been developed to describe the process observed. Its structural and functional block-diagram is proposed permitting to define the mechanism of action of SHF field.
This approach uses a set of algebraic linear equations for reaction rates (the method of steady-state stoichiometric flux balance) to model the purposeful metabolism of the living self-reproducing biochemical system (i.e. cell), which persists in steady-state growth. Linear programming (SIMPLEX method) is used to derive the solution for the model equations set (determining reaction rates which provide flux balance at given conditions). Here, we demonstrate the approach through the mathematical modeling of steady-state metabolism in Saccharomyces cerevisiae mitochondria.
Motivated by the recent development of highly specific agents for brain tumours, we develop a mathematical model of the spatio-temporal dynamics of a brain tumour that receives an infusion of a highly specific cytotoxic agent (e.g. IL-4-PE, a cytotoxin comprised of IL-4 and a mutated form of Pseudomonas exotoxin). We derive an approximate but accurate mathematical formula for the tumour cure probability in terms of the tumour characteristics (size at time of detection, proliferation rate, diffusion coefficient), drug design (killing rate, loss rate and convection constants for tumour and tissue), and drug delivery (infusion rate, infusion duration). Our results suggest that high specificity is necessary but not sufficient to cure malignant gliomas; a nondispersed spatial profile of pretreatment tumour cells and/or good drug penetration are also required. The most important levers to improve tumour cure appear to be earlier detection, higher infusion rate, lower drug clearance rate and better convection into tumour, but not tissue. In contrast, the tumour cure probability is less sensitive to a longer infusion duration and enhancements in drug potency and drug specificity.
2-Fluoro-beta-alanine (FBAL) is the major metabolite of 5-fluorouracil (FUra), one of the most widely used anticancer drugs. It has been suggested previously that FBAL and/or its metabolites may have a role in the hepatotoxicity, neurotoxicity and cardiotoxicity resulting from FUra chemotherapy. Studies in patients and experimental animals have demonstrated that FBAL has a prolonged elimination compared with the parent drug, FUra. In the present manuscript, a mathematical model is developed for the kinetics and tissue distribution of FBAL. This model is based on recently published data from a study of the pharmacokinetics and disposition of FBAL in rats (Zhang et al., Drug Metab Dispos 20: 113-119, 1992). Satisfactory agreement was achieved between predicted and measured values, permitting an accurate evaluation of the kinetic and distribution parameters for FBAL. This model indicates that: (1) FBAL accumulates in several tissues including brain, heart, spleen, and enterohepatic system; and (2) enterohepatic circulation of FBAL and its bile acid conjugates has an important role in FBAL kinetics and distribution as demonstrated by a model in which enterohepatic circulation parameters were deleted.
T cell vaccination (TCV) is a method to induce resistance to autoimmune diseases by priming the immune system with autoreactive T cells. This priming evokes an anti-idiotypic regulatory T cell response to the receptors on the autoreactive T cells. Hence resistance is induced. To prevent the inoculated autoreactive cells from inducing autoimmunity, cells are given in a subpathogenic dose or in an attenuated form. We developed a mathematical model to study how the interactions between autoreactive T cells, self epitopes, and regulatory cells can explain TCV. The model is based on detailed data on experimental autoimmune encephalomyelitis, but can be generalized to other autoimmune diseases. We show that all of the phenomena collectively described as TCV occur quite naturally in systems where autoreactive T cells can be controlled by anti-idiotypic regulatory T cells. The essential assumption that we make is that TCV generally involves self epitopes for which T cell tolerance is incomplete. The model predicts a qualitative difference between the two vaccination methods: vaccination with normal autoreactive cells should give rise to a steady state of long lasting protection, whereas vaccination with attenuated cells should only confer transient resistance. Moreover, the model shows how autoimmune relapses can occur naturally without the involvement of T cells arising due to determinant spreading.
The retina is one of the best examples of modular organisation in neural circuitry. This modular structure enables it to perform parallel processing. A mathematical model of the retina has been set up, focusing on mechanical features of retinal neurons and on the interaction and dendritic overlapping among retinal cells. The model focuses on the actions of local mechanical forces on the neuron's cytoskeleton. The cytoskeleton is regarded as a structure in which elastic and rigid elements are combined according to the tensegrity concept. We have assumed that dendritic overlap takes place in such a way as to favour uniform retinal neurons' distribution and that dendritic overlap is the only cause of neuron's motion on the retinal surface. This overlap depends on the growth of the dendrites due to the cytoskeletic deformation. The results obtained are in agreement with experimental results that support the notion that local mechanical interaction and dendritic overlapping are capable to transform random cell distributions into regular mosaics.
The current study was undertaken to characterize the East and West Ponds and develop a mathematical model of the effects of nutrient and BOD loading on dissolved oxygen (DO) concentrations in these ponds. The model predicted that both ponds will recover adequately given the average expected range of nutrient and BOD loading due to waste from surface runoff and migratory birds. The predicted dissolved oxygen levels in both ponds were greater than 5.0 mg/L, and were supported by DO levels in the field which were typically above 5.0 mg/L during the period of this study. The model predicted a steady-state NBOD concentration of 12.0-14.0 mg/L in the East Pond, compared to an average measured value of 3.73 mg/L in 1994 and an average measured value of 12.51 mg/L in a 1996-97 study. The model predicted that the NBOD concentration in the West Pond would be under 3.0 mg/L compared to the average measured values of 7.50 mg/L in 1997, and 8.51 mg/L in 1994. The model predicted that phosphorus (as PO4(3-)) concentration in the East Pond will approach 4.2 mg/L in 4 months, compared to measured average value of 2.01 mg/L in a 1994 study. The model predicted that phosphorus concentration in the West Pond will approach 1.00 mg/L, compared to a measured average phosphorus (as PO4(3-)) concentration of 1.57 mg/L in a 1994 study.
The mechanical properties of lung tissue are important determinants of the overall mechanical behaviour of the lung itself. Our understanding of lung tissue mechanics is embodied in various mathematical models, that relate measurements of transpulmonary pressure to lung volume and flow. The purpose of this paper is to review the most basic and important of these models. Firstly, the single-compartment linear model of lung tissue is invoked to explain measurements of transpulmonary pressure and volume under quasi-static conditions, when volume excursions are modest. The exponential nonlinear extension of this model may be used to account for measurements made when volume approaches total lung capacity. Secondly, the Kelvin body as a model of the viscoelastic properties of lung tissue is considered, as a means for accounting for tissue stress adaptation and the frequency dependencies of tissue resistance and elastance. The Prandtl body is also invoked to explain tissue plastoelasticity, manifest in quasi-static hysteresis between transpulmonary pressure and volume. Finally, some more complicated and intricate extensions of these models are considered.
The appearance rate of insulin (calculated insulin secretion rate) in the circulating blood after subcutaneous injection was estimated in diabetic dogs from serial measurements of immunoreactive insulin concentrations using a simple mathematical model based on the insulin half-life and the distribution space. In the case of highly purified monocomponent porcine insulin, maximum concentrations occurred after 30-60 min. The duration of insulin appearance was dose-dependent and the rate of appearance could be described by a bi-exponential function. It was linearly dose-dependent but the effect on glycaemia showed saturation kinetics. The action of the injected dose on the fasting glycaemia diminished when the appearance rate became less than 0.3 mU X kg-1 X min-1. Fractional dose recovery was between 70% and 90% and was not different between depot and regular insulin. Appearance kinetics were not significantly affected by the initial glycaemia. The model presented provides a means for quantitative characterization of different insulin preparations.
OBJECTIVE: One of the main difficulties in electrical compound action potential (ECAP) recordings is to reduce the stimulus artifact due to electrical stimulation. The neural response telemetry (NRT) system of the Nucleus 24 cochlear implant extracts the ECAP response using a forward-masking (standard) subtraction technique. However, it has been shown that this subtraction technique may distort the ECAP responses in certain situations. In order to improve ECAP recordings, a modified forward-masking subtraction technique was recently proposed (Ear Hear. 21 (2000) 280). This modified subtraction technique can be applied to recovery function measurement. The objective of this study is to compare results obtained with the modified method to those obtained using the standard method. METHODS: ECAP responses were recorded in 4 adult patients using a Nucleus 24 cochlear implant. Data were collected for the 20 active electrodes. For each electrode, measurements consisted of the recovery function recording using 16 different Masker-Probe intervals. The modified method was then applied and the results compared with the standard method. RESULTS: Comparison between the two methods revealed that results were different when using the standard or modified method. Using the modified method, more ECAP responses were obtained (61.8 vs. 44.2%), but the P1 peak was sometimes attenuated; when using the standard method, N1 peak was missing in many cases. A mathematical model has been established and the mathematical simulation confirms the results obtained in patients. CONCLUSIONS: The results suggest that both methods have limitations and advantages. The modified subtraction method seems to be better for analyzing ECAP recordings in recovery function measurement because of the higher number of responses obtained compared to the standard method.
Rapid and simple calculations make it possible to get precise data for requirements estimate of medical supplies, including opportune replacement of medicaments and other disposables which have a reduced period of storage, etc. The calculations of weight and volume of medical supplies give the possibility to evaluate transport and depot requirements. This mathematical model is destined for projection of automatic information systems in the interests of medical supplies.
The evolution of Lactobacillus spp. during the curing process of dry fermented sausage (Chorizo), has been studied under natural climatic conditions and in a controlled drying chamber, with regulated temperature and relative humidity. In order to fully understand the development of the microorganisms in each of these two cases, it applied a mathematical model based on a modified Gompertz equation. The proposed mathematical function is easy to use and statistically appropriate. Furthermore, it allows the distinction to be made between the four phases which characterise the behaviour of these microorganisms during the curing of the sausage (a) latency from an initial threshold level; (b) exponential growth; (c) stationary state; (d) depletion to a residual level. The mathematical analysis of this function has highlighted certain differences in the behaviour of the microbial flora depending on the technological conditions to which the drying of the sausages is subjected. Under the climatically controlled conditions of the drying process, a better development of the lactobacillus spp. is observed, but conversely the final stage of the exponential growth is brought forward, the length of the stationary phase is shortened and is reached before the end of the drying period, at which point the marginal decline of the microorganisms becomes ever more reduced.
Arch length analysis should consider discrepancies not only within the sagittal plane but also within the vertical and transverse planes. The vertical deviation of the occlusal plane from a flat plane is known as the curve of Spee. The purpose of this study was to produce a mathematical model of the mandibular arch form in three planes of space and to determine the effect that the curve of Spee has on arch circumference. Two mandibular arch forms, the catenary and the Bonwill-Hawley, were examined. The curve of Spee was modeled as a cylinder perpendicular to the midsagittal plane centered on the arch anteroposteriorly. A mathematical distance formula was used to calculate arch circumferences from the central fossa of the first molars for 10 arches with curves of Spee ranging from 0 to 10 mm. This procedure was repeated for arch circumferences extending from the central fossa of the second molars. Plots for the difference in arch circumferences verses depth of the curve of Spee showed that the relationship between these two variables is not linear and is less than one to one. This model showed that clinical practice of allowing 1 mm of arch circumference for leveling each millimeter of curve of Spee overestimates the amount of arch circumference needed to flatten the curve of Spee.
The amino acid composition of blood serum was studied in patients with duodenal ulcers, with this parameter characterizing protein metabolism most delicately. Essential changes were established in the amino acid composition as dependent on a number of factors: disease standing, complications and their duration, acid-forming function of the stomach. Based on the mechanism established, a mathematical model was simulated of protein metabolism impairment associated with peptic ulcer. The use of the model permits making an early diagnosis and correction of the abnormalities described.
Experimental data of the radial incorporation of labeled cholesterol [14C-4] into the artery wall is regressed against a mathematical model that predicts macromolecular transport in this biological system. Data is obtained using excised canine carotid arteries that are perfused in vitro under pulsatile hemodynamic conditions for 2 hr. Vessels are exposed to either normotensive hemodynamics, hypertensive hemodynamics, or simulations in which the rate of flow or vessel compliance is deliberately altered. Several arteries are studied under normotensive conditions following balloon catheter deendothelialization. Transmural concentration profiles of [14C-4] activity are determined by microcryotomy of longitudinal sections of perfused vessels. Nonlinear Marquardt regression on 12 experimental cases yields parameter estimates of effective diffusivity, D and solute filtration velocity, V. Results of this experimental investigation support our hypothesis that hemodynamics and the endothelial lining influence wall flux in intact vessels. Exposure to altered (vs normotensive) hemodynamics is associated with increased incorporation of labeled cholesterol. A similar observation is made for deendothelialized vessels (e.g. a greater accumulation of label and a rise in convective flux). Based upon our companion measurements of vessel wall forces and endothelial cellular morphology accompanying hemodynamic simulations, we suggest that hemodynamically induced alterations to endothelial structures lead to the increased permeability, convection and incorporation that we observe in this work.
We developed an algorithm, using recursive partitioning, that utilized information from a computerized, diagnostic database to predict the diagnosis of osteoarthritis as determined by medical record review. The complete (inpatient and outpatient) medical records for a random sample of 400 Olmsted County, Minnesota residents with a database diagnosis consistent with osteoarthritis were reviewed, and confirmation or rejection of the diagnosis was accomplished. Of the 387 patients in our sample, only 232 (a positive predictive value of 60%) fulfilled diagnostic criteria for osteoarthritis following medical record review. A classification tree was created that used information from the diagnostic database to partition the study population according to the proportion of individuals with a "true" diagnosis of osteoarthritis (based on medical record review). The receiver-operating characteristic curve generated from these data illustrated that the algorithm substantially improved the validity of the database diagnosis, yielding a positive predictive value of 89% and a negative predictive value of 70% (sensitivity of 75% and specificity of 86%) at a selected cutoff point. This model also provides the capability of selecting the cutoff point to favor either specificity or sensitivity. These data demonstrate that a mathematical model can substantially improve the validity of computerized diagnostic databases in osteoarthritis.
Potential mechanisms of immunoregulation have been investigated for the capacity to generate heterogeneity in the outcome of infection with helminth parasites. We have developed a mathematical model of the interaction between T cell and parasite populations, based on the assumption that activation of a Th1 CD4+ T cell response is required for host resistance. Antigen dose-dependent inhibition of Th1 cell proliferation generates heterogeneity in the outcome of host response to infection, with relatively low levels of exposure inducing resistance, and high levels of exposure associated with host susceptibility. Heterogeneity is additionally predicted in the duration of infection before individuals of the resistant class clear infection, with infection becoming more prolonged as the level of exposure rises. Similar categories of response are predicted if an alternative regulatory mechanism, that of interferon gamma-regulated control of Th1 cell differentiation, is substituted into the model. However, the relationship between level of exposure and duration of infection is reversed. Results are discussed in the context of how these simple models of parasite-immune system interactions might be used to make predictions concerning specific examples of parasitic infection.
A mathematical model is described that predicts the effect of altered nuclear/cell division kinetics and cytotoxicity on micronucleus expression in vitro when the micronucleus assay is performed without discriminating between cells that have divided once and cells that have not divided after genotoxic insult. The model is based on the probabilities of: (i) a viable cell completing nuclear division; (ii) micronucleus expression in a cell that completes nuclear division after genotoxic insult; (iii) a cell not dividing and surviving as a mononuclear cell; (iv) a cell dying by necrosis or apoptosis. The model predicts: (i) false negative results for relatively weak chromosome damaging agents that also inhibit nuclear division, if micronuclei are scored in mononucleated cells without discriminating between divided and non-divided cells; (ii) this tendency for a false negative result when scoring micronuclei without discriminating between non-divided and once-divided mononuclear cells increases with cell lines and culture conditions that do not result in optimal rates of nuclear division (i.e. >90% of dividing cells); (iii) the absolute increment in micronucleus frequency in binucleated cells is at least 2-fold greater than that observed in mononucleated cells when nuclear division is not inhibited and this difference increases with increasing nuclear inhibition. The number of dead cells does not influence the micronucleus frequency if only viable cells are considered when determining the micronucleus frequency ratio. The results from this model suggest that the micronucleus assay when performed by scoring mononucleated cells, without restricting the score to those cells that have divided once after genotoxic insult, is prone to produce false negative results and, therefore, cannot be considered reliable or conclusive. Scoring of micronuclei in cytokinesis-blocked binucleated cells is predicted by the model to provide consistent results under all culture conditions and based on these theoretical results should be considered the preferred choice.