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PubMedDate not supplied

Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization.

We have developed a mathematical model of the human atria myocyte based on averaged voltage-clamp data recorded from isolated single myocytes. Our model consists of a Hodgkin-Huxley-type equivalent circuit for the sarcolemma, coupled with a fluid compartment model, which accounts for changes in ionic concentrations in the cytoplasm as well as in the sarcoplasmic reticulum. This formulation can reconstruct action potential data that are representative of recordings from a majority of human atrial cells in our laboratory and therefore provides a biophysically based account of the underlying ionic currents. This work is based in part on a previous model of the rabbit atrial myocyte published by our group and was motivated by differences in some of the repolarizing currents between human and rabbit atrium. We have therefore given particular attention to the sustained outward K+ current (I[sus]), which putatively has a prominent role in determining the duration of the human atrial action potential. Our results demonstrate that the action potential shape during the peak and plateau phases is determined primarily by transient outward K+ current, I(sus) and L-type Ca2+ current (I[Ca,L]) and that the role of I(sus) in the human atrial action potential can be modulated by the baseline sizes of I(Ca,L), I(sus) and the rapid delayed rectifier K+ current. As a result, our simulations suggest that the functional role of I(sus) can depend on the physiological/disease state of the cell.

Action Potentials↗
PubMedDate not supplied

[Mathematical model of proliferative activity in epidermis of the normal skin and of the skin afflicted by psoriasis].

A mathematical model of the mitotic activity of epidermis in norm and psoriasis is presented, which consists of a system of two autonomous nonlinear differential equations. A qualitative analysis of the model was done, and numerical solutions at the parameter values corresponding to these state were obtained. It was shown that, in norm, the system can exist only in one stationary equilibrium state of the "focus" type, and in psoriasis, due to an increase in the growing fraction, hyperproliferation, and enhanced migration of keratinocytes, a stable limiting cycle arises from the state of an unstable focus. The existence of two stable states (focus and the limiting cycle) is regulated by a parameter that describes the inhibition of division of maturing cells of suprabasal epidermal layers by the intrinsic tissue-specific transmitters of mitosis of G1-keilon type. The model is consistent with experimental data on the kinetics of cell proliferation in the epidermis in norm and psoriasis and the clinical course of the disease.

Algorithms↗
PubMedDate not supplied

[Mathematical model of the mechanical properties of skeletal muscle fibres taking into account compliance of the actin filaments].

A mathematical model describing mechanical transients induced by the step length changes in skeletal muscle fibres is suggested. The model takes into account compliance of actin filaments and the cross-bridge mechanics. Two different approaches were used for modeling of the cross-bridges: the Huxley-Simmons (1971) model and a new nonlinear viscoelasic model. From a comparison of the results of computer simulation with experimental data we conclude that the best fitting is achieved by using a combined model where both Huxley-Simmons mechanism and cross-bridges viscoelastisity are represented.

Actins↗
PubMed1989

A mathematical model of the gate control theory of pain.

The first test which any theory of pain must pass is that it must be able to explain the phenomena observed in acute pain in humans. This criterion is used to test the major theory of pain at present, the gate control theory of Melzack & Wall (1965, 1982). The theory is explicit enough to be cast in mathematical terms, and the mathematical model is shown to explain the observations considered. It also points up a common misconception on the consequences of the theory, and thus demolishes an argument which has been used against it. A hypothesis of the origin of rhythmic pain is then made, and consequent testable predictions given. This is the first time that the gate control theory has been used to explain any quality of pain. It has important consequences for the treatment of such pain. Finally, the applicability of the gate control theory as an explanation for chronic pain is discussed.

Humans↗
PubMed1975

A mathematical model of pattern formation by swimming microorganisms.

Bioconvection in suspensions of Tetrahymena pyriformis and Crypthecodinium cohnii is described and 2 new patterns, the toroid and the cat's-eye, which appear in shallow suspensions of C. cohnii, are reported. Except in very dense cultures, bioconvection does not arise unless the depth of the suspensions or the mean concentration exceed certain critical values, other things being equal. A mathematical model describing the hydrodynamics of suspension of negatively geotactic microorganisms is described which predicts the existence of critical depths and concentrations. The equations presented admit solutions describing the "polka-dot" patterns seen at low organism concentration in suspensions slightly deeper than the critical value. The discussion here is limited to the case of fairly dilute suspensions, but the basic approach can be applied also to richer cultures.

Dinoflagellida↗
PubMed1992

Mathematical models of wound healing in embryonic and adult epidermis.

Epidermal wound healing occurs by quite different mechanisms in embryos and adults. In the latter case, it has long been known that cells crawl inwards via lamellipodia to close the defect. In the embryonic system, recent evidence suggests that healing may be caused by a quite different mechanism, namely the contraction of a cable of filamentous actin at the wound edge. The authors use mathematical modelling to investigate both systems. A mechanical model for the initial formation of the actin cable in embryonic epidermal wounds is presented, which incorporates the important phenomenon of stress-induced microfilament alignment. Also discussed is a reaction-diffusion model for the healing of adult wounds subject to autoregulation of cell division. In both cases, the results suggest possible biological mechanisms for key aspects of the healing process.

Actins↗
PubMed1994

Quantitative structure-activity relationship (QSAR) studies in genetic toxicology: mathematical models and the "biological activity" term of the relationship.

At first sight, the QSAR issue might appear to be a mere pattern recognition problem; however, a purely "surface" approach to QSAR as a pattern recognition problem, not involving the profound plausibility of the solutions, has often been demonstrated to be devoid of scientific value and of predictive strength. The requirement for such a lateral validation should imply the recognition of the basic differences between the two terms of the QSAR issue: biology and chemistry. In particular, the difficulty to derive strong quantitative theories for the biological aspect of QSAR procedures should be taken into serious consideration. Within this conceptual framework, this paper examines the different families of mathematical models (classical regression, multivariate methods, neural networks) used in the QSAR research.

Mathematics↗
PubMed1979

Cross-sectional echocardiography. I. Analysis of mathematic models for quantifying mass of the left ventricle in dogs.

Cross-sectional echocardiography was used to quantify left ventricular mass noninvasively in 21 dogs. Short- and long-axis cross-sectional images of the left ventricle were reproducibly traced at endocardial and epicardial borders during stop-motion video-tape replay. We used area, length and diameter measurements to calculate left ventricular mass by seven mathematic models, including the standard formulas used with M-mode echocardiography and cineangiography. Calculated mass was compared with excised weight of the left ventricle by regression and percent error analyses. Formulas using short-axis areas and long-axis length resulted in higher correlation coefficients (0.94--0.95) and lower mean errors (6--7%) than for standard formulas. Since short-axis areas account for regional left ventricular irregularities, noninvasive quantification of left ventricular mass by cross-sectional echocardiography in dogs is most accurate with formulas using short-axis areas.

Animals↗
PubMed1988

Mathematical modelling of oxygen supply and oxygenation in tumor tissues: prognostic, therapeutic, and experimental implications.

Radiation response of some tumors is dependent on the oxygenation of the tumor tissue. To improve tissue oxygenation, attempts to increase a reduced hemoglobin concentration or to shift the dissociation curve of hemoglobin have been made. The aim of this paper is to estimate the influence of such measures on the volume of radiobiologically hypoxic tissue by means of a mathematical model. In addition, the influence of blood velocity and metabolic status of tumor tissues on tissue oxygenation is evaluated. The calculations show a strong influence on hypoxic tissue volume over a modest range of variation of physiological parameters, especially when interactions of several parameters may occur.

Hematocrit↗
PubMed2001

Mathematical models of cognitive recovery.

Longitudinal psychological test results are used as dependent variables to explore the complex relationship between length of coma, time of testing on the recovery curve, and corresponding cognitive status after traumatic brain injury (TBI). A database containing 319 TBI patients with a broad spectrum of coma duration was used. Statistical analysis of mixed effects modelling was applied to longitudinal WAIS-R (Wechsler Adult Intelligence Scale-Revised) scores to construct two mathematical models (verbal IQ and performance IQ). The models predict the course of recovery (initial cognitive level post-coma, eventual recovery level, and level of cognitive functioning at any point on the recovery curve) when the duration of coma is known. Performance IQ was found to recover at a rate that is almost four times slower than verbal IQ. The results have important clinical rehabilitation implications. This statistical modelling technique also enables the medical researcher to investigate disease progression or recovery using structured assessments, which would normally be part of the routine medical monitoring.

Adult↗
PubMed2006

A mathematical model of plants as ecosystem engineers.

Understanding the structure and dynamics of plant communities in water-limited systems often calls for the identification of ecosystem engineers--key species that modify the landscape, redistribute resources and facilitate the growth of other species. Shrubs are excellent examples; they self-organize to form patterns of mesic patches which provide habitats for herbaceous species. In this paper we present a mathematical model for studying ecosystem engineering by woody plant species in drylands. The model captures various feedbacks between biomass and water including water uptake by plants' roots and increased water infiltration at vegetation patches. Both the uptake and the infiltration feedbacks act as mechanisms for vegetation pattern formation, but have opposite effects on the water resource; the former depletes the soil-water content under a vegetation patch, whereas the latter acts to increase it. Varying the relative strength of the two feedbacks we find a trade-off between the engineering capacity of a plant species and its resilience to disturbances. We further identify two basic soil-water distributions associated with engineering at the single patch level, hump-shaped and ring-shaped, and discuss the niches they form for herbaceous species. Finally, we study how pattern transitions at the landscape level feedback to the single patch level by affecting engineering strength.

Biomass↗
PubMed1997

A mathematical model of production, distribution, and metabolism of melatonin in mammalian systems.

Melatonin is a neuroendocrine hormone which is currently receiving considerable attention as a treatment for jet lag, a treatment for insomnia and, by some, a possible "magic bullet" for delaying the effects of aging and preventing cancer. Production of melatonin is focused primarily in the pineal gland with very wide daily shifts in production controlled by the day/night cycle. The potential for increased disease as a consequence of lower or higher than average production of this hormone has not been well studied, although potential environmental agents may modulate circulating levels (e.g., electric and magnetic fields). In this manuscript, a physiologically realistic mathematical model for the production, distribution, and metabolism of melatonin is developed as a precursor to a future study of the role of chemicals and environmental agents in altering this system. Values for key aspects of the system (e.g., diurnal rates of production of the hormone in the pineal gland) were obtained from the literature and the model was validated against data on circulating levels. The mathematical equations and model parameters are presented.

Animals↗
PubMed2004

A mathematical model for the transmission of Salmonella Typhimurium within a grower-finisher pig herd in Great Britain.

In a study of pigs slaughtered at British abattoirs, approximately 23% carried Salmonella in their cecal (large intestine) contents. The most frequent serotype was Salmonella Typhimurium (STM), which was the second most common cause of human salmonellosis in Great Britain. A pig industry-monitoring program was developed to reduce Salmonella infection on British farms. The control of STM infection on the farm requires an understanding of STM transmission dynamics within the herd, and a mathematical model has been developed for an infected grower-finisher farm. The model estimates the probability of a random pig being infected with STM. There are three broad categories of STM infection in pigs: pigs that are infected but unable to transmit the infection (latent); pigs that are infectious, i.e., able to transmit the infection (shedders); and pigs that have stopped shedding but harbor STM in their internal organs (carriers). The model estimates that 21.0% (5th and 95th percentiles, 0.05 to 77.5%) of slaughter-age pigs on an infected farm are likely to be shedding STM. Although this range is wide, it is biologically plausible. Sensitivity analysis of the total number of infected pigs revealed that the most significant input parameters are the probability of effective contact between a specific infectious and susceptible pig and the duration of shedding. The model predicted that 11.5% of pigs would be shedding STM at slaughter age. This value is close to the estimate obtained from a British abattoir survey that 11. 1% of pigs carried STM in their ceca, indicating that the model has reasonable validity.

Animals↗
PubMed1988

Formal comparison of the antihypertensive effects of torasemide and other diuretics by the Montevideo mathematical model.

A formal comparison is carried out of the antihypertensive effect of torasemide (1-isopropyl-3- ([4-(3-methylphenylamino)pyridine]-3-sulfonyl)urea) and various other diuretics used as monotherapy. The analyzed data are the results of various independent studies. The time (t) courses of the mean values of supine or sitting systolic (S) and diastolic (D) arterial blood pressure (P) during treatment are analyzed by fitting the "Montevideo mathematical model", described here, to the clinical (experimental) data. Clinically-important values of P and t evaluated from the fitted functions permit the formal comparisons. Decays in P were evaluated by the reductions in SP and DP occurred at 1.17 and 7.54 weeks of treatment, by the times at which the fitted functions showed diminutions of 10, 15 and 20 mmHg and of 10%, 15% and 20% with respect to pretreatment SP and DP mean values, and by the time at which DP attained a value of 90 mmHg. In studies in which the pretreatment mean value of DP ranged between 105.6 and 110.5 mmHg, standard-dose indapamide (2.5 to 5 mg/d), and low-dose torasemide (2.5 to 5 mg/d) elicited similar decays in SP and DP; the antihypertensive effects of etozoline (200 to 400 mg/d) and of hydrochlorothiazide (25 to 50 mg/d) were slower than those of torasemide and indapamide. Cyclothiazide (5 mg/d) and a coprescribed sodium-restricted diet reduced DP, from a pretreatment mean value of 114 mmHg, slower than torasemide and indapamide but quicker than etozoline and hydrochlorothiazide. Torasemide and indapamide should be consequently preferred for the chronic treatment of uncomplicated essential hypertension in terms of efficacy.(ABSTRACT TRUNCATED AT 250 WORDS)

Blood Pressure↗
PubMed1982

Mathematical model for the postnatal growth of the human lung.

Theoretical particle deposition studies for children and youths in practical health physics or medical aerosol therapy require detailed information on alterations of anatomical as well as physiological parameters during postnatal growth. Based on the commonly used anatomical model A of Weibel, assuming regular dichotomy, for an adult human lung, a mathematical model was developed for the calculation of airway parameters, such as geometrical dimensions and number of airways as functions of age. Sometimes widely scattered experimental data obtained by different authors were fitted to analytical functions by a multiregressional procedure. Due to the lack of these data for most of the generations of the anatomical model, theoretical considerations had to be applied. For changes of respiration parameters with progressing age, e.g., tidal volume or respiratory frequency, also experimental data were used. The results of these calculations can then serve as a base for the determination of deposition probabilities in different regions of the human respiratory tract.

Adolescent↗
PubMed2003

Pathologic sampling of laparoscopically morcellated kidneys: a mathematical model.

BACKGROUND AND PURPOSE: Kidney morcellation permits tissue removal through a port site; however, standard methods of histopathologic examination of the numerous specimen fragments thus produced have not been established. We developed a model to guide pathologic evaluation of the morcellated kidney. MATERIALS AND METHODS: A mathematical model was created to determine the quantity of morcellated tissue needed to establish a diagnosis. Inputs into the equation included estimated lesion size, total specimen volume, and the desired certainty of identifying at least a portion of the lesion on pathologic analysis. Nomograms were calculated to illustrate the model and provide clinically relevant guidelines. RESULTS: The hypergeometric distribution was used to develop the formula: P = 1 - (1 - k/N)(n), where k/N represents the fraction of total specimen with tumor, n is the amount of specimen that must be sampled to yield a diagnosis, and P is the probability of encountering the tumor in the sampled tissue. The model provided nomograms that were feasible and would guide a practical approach to the pathologic analysis of laparoscopically morcellated specimens. CONCLUSIONS: The increasing application of laparoscopy to the removal of solid organs with suspected tumors has raised several important issues. Morcellation of these specimens precludes traditional pathologic examination and necessitates an alternative method of specimen sampling and diagnosis. We describe a novel, systematic model to assist in the histopathologic examination of morcellated specimens. Issues of pathologic staging remain unresolved, but this sampling system provides a nonarbitrary framework to help arrive at a histologic diagnosis.

Humans↗
PubMedDate not supplied

Bioassay designs for validating biologically based mathematical models of carcinogenesis for risk assessment.

Bioassays that include various types of discontinuous exposure to carcinogens are somewhat rare and are far from routine. However, discontinuous-dosing groups represent a valuable enhancement of the ordinary bioassay design. My hope is that efforts to include discontinuous-exposure groups in cancer-bioassays will become widespread, and that discontinuous-dosing designs will eventually be a matter of routine. To me, such designs represent an easy (although perhaps costly) way to increase the sophistication of the tumor incidence data for model fitting, and to provide valuable data for validating (or perhaps invalidating) postulated mathematical models of the cancer process. Certainly discontinuous-dosing data at least provide a valuable ancillary resource to be utilized along with data on postulated mechanisms in the effort to implement biologically based models of the cancer process for quantitative risk assessment. Such data might even be indispensible.

Animals↗
PubMed1989

Mathematical model of dependence of heart rate on tissue concentration of acetylcholine.

The change in sinus period elicited by vagal stimulation depends on the rate of acetylcholine (ACh) release from the nerve endings, the rate of ACh degradation in the nodal tissue, and the responsiveness of the sinus node to ACh. Vagal stimulation in anesthetized dogs prolonged sinus period. After cessation of vagal stimulation, the sinus period returned to the prestimulation period. We developed a mathematical model to analyze the dynamics of ACh degradation in the neuroeffector junction and the dependence of sinus period on the concentration of ACh. From the in vitro reaction kinetics of acetylcholinesterase, we derived an analytical expression for the rate of ACh degradation in the intact animal. Our model represents the electrical behavior of the sinus node by the electrical activity of one pacemaker cell with six membrane ionic currents. This model predicts the decline in sinus period of the intact anesthetized dog as acetylcholinesterase degrades ACh in the neuroeffector junction. The half-life of ACh after cessation of vagal stimulation was estimated to be 2.7 s. We conclude that following termination of vagal stimulation, the sinus node of the intact animal responds to ACh as if the sinus node were one oscillator.

Acetylcholine↗