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PubMed1983

Analysis of epidemiological peculiarities of rubella based on a mathematical model (according to observations over 10 years in Moscow).

The main epidemiological values characterizing rubella in Moscow were calculated on the basis of a new mathematical model. Quantitative estimates of the intensity of infection in different age groups of the population were obtained. It has been established that the risk of infection in children is especially high in comparison with adult population. That is why 98% of the population aged 15 are immune. The probability of falling ill with rubella was determined for persons with different antibody levels. The cases of congenital rubella in Moscow are rare due to the low risk of infection in adults and to their immunity acquired in childhood. Consequently, there is no necessity for vaccination against rubella in Moscow at the present time, but it should be recommended to organize constant epidemiological surveillance of congenital rubella.

Adolescent↗
PubMed1980

A mathematical model of creatine metabolism in normal males--comparison between theory and experiment.

Based upon knowledge that the body creatine pool in normal males undergoes a constant fractional conversion rate to creatinine and that 24-hr urinary creatinine excretion is dependent upon creatine and protein intakes, we developed a mathematical model with feedback which describes the creatine pool size and, consequently, the 24-hr urinary creatinine excretion as a function of time after change in diet. Validity of the model was tested by comparing calculated with experimental changes in 24-hr urinary creatinine excretion rates of male volunteers who were participating in studies of effects of "high" and "low" protein diets on mineral requirements. The model was further verified by comparing published changes in creatinine excretion rates with changes predicted by the model. It is concluded that the effects of changes in creatine and protein intakes upon the body creatine pool size in healthy males can be described mathematically by a model with a feedback component. It is also cautioned that 24-hr urinary creatinine excretion may not be a good reference for quantifying other urinary substances under circumstances where the creatine or protein intakes are not constant.

Adult↗
PubMed1996

A mathematical model for fibro-proliferative wound healing disorders.

The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable. In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsen et al., J. theor. Biol. 177, 113-128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay. Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states-a central property of the model, which is evident from stability and bifurcation analyses. The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders.

Adult↗
PubMed1997

Generation of action potentials in a mathematical model of corticotrophs.

Corticotropin-releasing hormone (CRH) is an important regulator of adrenocorticotropin (ACTH) secretion from pituitary corticotroph cells. The intracellular signaling system that underlies this process involves modulation of voltage-sensitive Ca2+ channel activity, which leads to the generation of Ca2+ action potentials and influx of Ca2+. However, the mechanisms by which Ca2+ channel activity is modulated in corticotrophs are not currently known. We investigated this process in a Hodgkin-Huxley-type mathematical model of corticotroph plasma membrane electrical responses. We found that an increase in the L-type Ca2+ current was sufficient to generate action potentials from a previously resting state of the model. The increase in the L-type current could be elicited by either a shift in the voltage dependence of the current toward more negative potentials, or by an increase in the conductance of the current. Although either of these mechanisms is potentially responsible for the generation of action potentials, previous experimental evidence favors the former mechanism, with the magnitude of the shift required being consistent with the experimental findings. The model also shows that the T-type Ca2+ current plays a role in setting the excitability of the plasma membrane, but does not appear to contribute in a dynamic manner to action potential generation. Inhibition of a K+ conductance that is active at rest also affects the excitability of the plasma membrane.

Action Potentials↗
PubMed1992

Mathematical modeling of radionuclide dispersion in the Pripyat-Dnieper aquatic system after the Chernobyl accident.

The Chernobyl accident heavily contaminated the largest aquatic system in the Ukraine, requiring the development of a model-based decision support system in the field of aquatic radioecology. The main objectives of the system were to simulate and predict radionuclide dispersion in the Pripyat-Dnieper River-reservoir system, assess the effectiveness of special hydraulic countermeasures designed to decrease the rate of radionuclide dispersion in the water bodies, and support the Dnieper reservoirs' management operations. A hierarchy of mathematical models was developed. A two-dimensional (2-D) vertical-longitudinal model, a 2-D lateral-longitudinal model, a one-dimensional (1-D) channel model and a box-type model are briefly presented. These models describe the main features of radionuclide dispersion, including the processes governing radionuclide-sediment interactions. Examples of the models' applications are presented to show the peculiarities of radionuclide dispersion in this aquatic system.

Accidents↗
PubMed2002

GATA-3 transcriptional imprinting in Th2 lymphocytes: a mathematical model.

Immunological memory involves the fast recall of cytokine expression by T helper (Th) lymphocytes. Two distinct profiles of cytokine expression, Th1 and Th2, can be induced by antigen and polarizing signals during activation of naive Th cells and can subsequently be reexpressed on stimulation by antigen alone. The transcription factor GATA-3 induces Th2 development. GATA-3 is activated by the Th2-polarizing stimulus, IL-4, and has recently been observed to autoactivate its transcription. Based on these experimental data, we developed a mathematical model of GATA-3 expression that assumes independent activation of GATA-3 transcription by IL-4 and by GATA-3. Cooperativity of GATA-3 transcriptional activation is shown to create a threshold for autoactivation, resulting in the coexistence of two distinct GATA-3 expression states: a state of basal expression and a state of high expression sustained by autoactivation. Suprathreshold IL-4 signals induce a transition from basal to high GATA-3 expression. Thus, GATA-3 autoactivation creates a bistable system that can memorize a transient inductive signal. The model further predicts conditions under which the state of high GATA-3 expression can be abolished, which may extinguish the Th2 cytokine memory.

Animals↗
PubMed1979

A two-dimensional transient mathematical model of human thermoregulation.

Current models of human thermoregulation are limited in that they fail to account for temperature distribution in any spatial direction other than radially outward from the body centerline. They are therefore incapable of accounting for nonuniform environmental conditions or nonuniform heat generation from muscles or organs within the body. However, for many situations, these nonuniform conditions are commonplace and lead to disparate skin temperatures and heat loss rates on different sides of the same body compartement. A new mathematical model of human thermoregulation that has been developed and is presented here has the capability of predicting transient temperature variations in two spatial dimensions, both radially and angularly, as measured from the body centerline. In so doing, the model accounts for nonuniform environments and internal heat generation rates. Typical results from the model are demonstrated, and comparisons with available experimental data are also presented.

Blood Circulation↗
PubMed1987

Evaluation of electrical conductivity-temperature curves using a mathematical model: temperature-dependent changes during thawing of frozen aqueous pharmaceuticals.

The information contained in the electrical conductivity curves of pharmaceuticals measured as a function of temperature can be represented by a small set of parameters. This is achieved by approximating the electrical conductivity curve as a number of consecutive steps, using a suitable empirical model. The three parameters describing each step are: transition temperature, slope factor and step height. The validity of the calculated transition temperatures was established by applying the model to electrical conductivity curves measured on aqueous solutions of KCl, NaCl and on a KCl-NaCl mixture. It appears that the transition temperatures calculated for these inorganic salts are in good agreement with the respective eutectic temperatures reported in the literature. Subsequently, the method was applied to the corticosteroids prednisolone sodium succinate and prednisolone disodium phosphate. The mathematical model yields a satisfactory fit for both experimental conductivity curves. The actual consequences of freeze-drying an aqueous solution of prednisolone sodium succinate below and above the respective transition temperatures calculated are discussed in relation to the experimental conductivity data.

Chemistry, Pharmaceutical↗
PubMedDate not supplied

[Qualitative analysis of a mathematical model of a open enzyme reaction].

A general case of the set of two differential equations, describing an open reaction v1 leads to S v reversible E P v2 leads to, has been considered. The requirements to the character of the functions v1([S]), v2([P]) and v([S], [P]) were formulated for the case of existence and absence of alternative steady states and sustained oscillations. The formulae were derived to determine the slope of the unstable portion of the quasi-steady state characteristic. The generalized model of Monod, Wyman and Changeux has been considered as an example of v([S], [P]). It has been shown that with monotonically decreasing v1 and monotonically increasing v2, the alternative steady states and oscillations are possible only in the presence of substrate inhibition or product activation. However, under the joint action of substrate inhibition and product activation, the system will exhibit bistability rather than an oscillatory behavior. In the case of an irreversible two-substrate reaction which can be described by a similar mathematical model, inhibition by the first and second substrate is equivalent to substrate inhibition and product activation.

Catalysis↗
PubMed1998

Mathematical model for liquid-gas equilibrium in acetic acid fermentations

An experimental study was conducted to propose an adequate mathematical model for liquid-gas equilibrium in acetic acid fermentations. Three operation scales (laboratory, pilot plant, and industrial plant) were employed to obtain the sets of experimental data. The proposed model, based in the UNIFAC method for the estimation of activity coefficients of a solution consisting of several components, takes into account the effect of temperature. However, in the set of equations, it has been necessary to put in the degree of equilibrium (epsilon). This coefficient adequately reflects the physical conditions of fermentation equipment. The experimental and numerical results help to define the fundamental mechanisms for liquid-gas equilibrium in these systems and demonstrate the model validity in the three tested scales. It was also found that in an industrial setting, closed systems are those with lowest evaporation losses. Copyright 1998 John Wiley & Sons, Inc.

Journal Article↗
PubMed1996

Mathematical modeling of relations between the kinetics of free intracellular calcium and mechanical function of myocardium.

The paper describes a mathematical model of cardiac muscle contraction based on the assumption of two types of co-operativity which control the formation of calcium-troponin complexes and on a simplified scheme of free intracellular calcium kinetics. Calcium transients are shown to be different in isotonic and isometric conditions, being dependent on initial muscle length as well. Numerical experiments and analysis of the model suggest that calcium uptake by the sarcoplasmic reticulum slows down with an increase in the intracellular concentration of free calcium. This suggestion enables the model to explain the disappearance of load-dependent relaxation observed experimentally at cardiac hypertrophy.

Calcium↗
PubMed2006

Mathematical modeling as accounting: predicting the fate of serum proteins and therapeutic monoclonal antibodies.

This article reviews current efforts to mathematically model the half lives of serum proteins, especially antibodies. While it is recognized that the neonatal Fc receptor, FcRn, is necessary for longer serum persistence of certain proteins, particularly the high abundance IgGs and albumin, it is not clear that it is sufficient to completely determine the half lives of these proteins. More specifically, it is unclear why the high avidity (bivalent), high affinity FcRn-IgG interaction, with half saturation in the 10 to 100 nM range (at endosomal pH according to the currently proposed mechanism), would result in a salvage mechanism that saturates at serum concentrations in the 10 to 100 mg/ml range--a discrepancy of 4 to 5 orders of magnitude. Alternative explanations include the proposal that the very low affinity binding between FcRn and IgG at blood pH is also relevant to the salvage mechanism, and that factors in addition to FcRn binding modulate the maintenance and clearance of IgG from serum.

Animals↗
PubMed2002

Mathematical modelling of schistosomiasis japonica: comparison of control strategies in the People's Republic of China.

We present the first mathematical model on the transmission dynamics of Schistosoma japonicum. The work extends Barbour's classic model of schistosome transmission. It allows for the mammalian host heterogeneity characteristic of the S. japonicum life cycle, and solves the problem of under-specification of Barbour's model by the use of Chinese data we are collecting on human-bovine transmission in the Poyang Lake area of Jiangxi Province in China. The model predicts that in the lake/marshland areas of the Yangtze River basin: (1) once-yearly mass chemotherapy of humans is little better than twice-yearly mass chemotherapy in reducing human prevalence. Depending on the heterogeneity of prevalence within the population, targeted treatment of high prevalence groups, with lower overall coverage, can be more effective than mass treatment with higher overall coverage. Treatment confers a short term benefit only, with prevalence rising to endemic levels once chemotherapy programs are stopped; (2) depending on the relative contributions of bovines and humans, bovine treatment can benefit humans almost as much as human treatment. Like human treatment, bovine treatment confers a short-term benefit. A combination of human and bovine treatment will dramatically reduce human prevalence and maintains the reduction for a longer period of time than treatment of a single host, although human prevalence rises once treatment ceases; (3) assuming 75% coverage of bovines, a bovine vaccine which acts on worm fecundity must have about 75% efficacy to reduce the reproduction rate below one and ensure mid-term reduction and long-term elimination of the parasite. Such a vaccination program should be accompanied by an initial period of human treatment to instigate a short-term reduction in prevalence, following which the reduction is enhanced by vaccine effects; (4) if the bovine vaccine is only 45% efficacious (the level of current prototype vaccines) it will lower the endemic prevalence, but will not result in elimination. If it is accompanied by an initial period of human treatment and by a 45% improvement in human sanitation or a 30% reduction in contaminated water contact by humans, elimination is then possible.

Animals↗
PubMed1998

Mathematical model of the lower extremity joint reaction forces using Kane's method of dynamics.

This report describes a new mathematical model for defining the joint reaction forces of the lower extremity using Kane's method of dynamics. Our model utilized average lower extremity joint motion and force/plate data from one healthy female patient during gait. From a cadaver specimen, the anatomical mass centers of the pelvis, femur, tibia, and foot were determined. Joint angular motion during the normal gait cycle was computed using Cardan angles for each distal segment relative to the proximal segment. Fluoroscopy of four normal knees determined average femorotibial and patellofemoral contact positions throughout flexion. A three-dimensional model of the lower extremity was defined in weight-bearing motion by 30 differential equations. During normal walking, the joint reaction forces for the subject tested ranged from 1.9 to 2.6 times body weight at the hip joint and 1.7-2.3 times body weight at the knee joint, depending primarily on gait speed. The method correlates well with known in vivo telemetrically measured forces at the hip joint.

Arthrography↗
PubMed2000

A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy.

A mathematical model is developed that describes the reduction in volume of a vascular tumor in response to specific chemotherapeutic administration strategies. The model consists of a system of partial differential equations governing intratumoral drug concentration and cancer cell density. In the model the tumor is treated as a continuum of two types of cells which differ in their proliferation rates and their responses to the chemotherapeutic agent. The balance between cell proliferation and death within the tumor generates a velocity field which drives expansion or regression of the spheroid. Insight into the tumor's response to therapy is gained by applying a combination of analytical and numerical techniques to the model equations.

Animals↗
PubMed1998

A mathematical model of the cerebellar-olivary system I: self-regulating equilibrium of climbing fiber activity.

We use a mathematical model to investigate how climbing fiber-dependent plasticity at granule cell to Purkinje cell (gr-->Pkj) synapses in the cerebellar cortex is influenced by the synaptic organization of the cerebellar-olivary system. Based on empirical studies, gr-->Pkj synapses are assumed to decrease in strength when active during a climbing fiber input (LTD) and increase in strength when active without a climbing fiber input (LTP). Results suggest that the inhibition of climbing fibers by cerebellar output combines with LTD/P to self-regulate spontaneous climbing fiber activity to an equilibrium level at which LTP and LTD balance and the expected net change in gr-->Pkj synaptic weights is zero. The synaptic weight vector is asymptotically confined to an equilibrium hyperplane defining the set of all possible combinations of synaptic weights consistent with climbing fiber equilibrium. Results also suggest restrictions on LTP/D at gr-->Pkj synapses required to produce synaptic weights that do not drift spontaneously.

Homeostasis↗
PubMed2004

Mathematical modeling for prediction of endo-xylanase activity and arabinoxylans concentration during mashing of barley malts for brewing.

A mathematical model describing the degradation of arabinoxylans by endo-xylanase during mashing process was developed. Endo-xylanase activities and arabinoxylans concentrations in laboratory scale mashing process at different temperature profiles were measured and then used for identifying the model parameters for Harrington barley malt. The modeling errors range for the final concentration of arabinoxylans in wort was -4% to +11.9%. The model developed was also used for predicting the other three different malts mashing processes in laboratory scale, and the prediction errors ranged from -9.5% to +13.6%. The model prediction accuracy for industrial scale mashing process was lower than that in laboratory scale. The simulation results showed that, a lower concentration of arabinoxylans could be achieved when maintaining the mashing-in at 45 degrees C and prolonging the mashing-in time.

Computer Simulation↗