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At least 1,297 records · Page 72Linked to original sources
PubMed2000

A mathematical model of solute coupled water transport in toad intestine incorporating recirculation of the actively transported solute.

A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241-251), computations predict that 60-80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived.

Animals↗
PubMed2005

A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion.

In this paper we present a hybrid mathematical model of the invasion of healthy tissue by a solid tumour. In particular we consider early vascular growth, just after angiogenesis has occurred. We examine how the geometry of the growing tumour is affected by tumour cell heterogeneity caused by genetic mutations. As the tumour grows, mutations occur leading to a heterogeneous tumour cell population with some cells having a greater ability to migrate, proliferate or degrade the surrounding tissue. All of these cell properties are closely controlled by cell-cell and cell-matrix interactions and as such the physical geometry of the whole tumour will be dependent on these individual cell interactions. The hybrid model we develop focuses on four key variables implicated in the invasion process: tumour cells, host tissue (extracellular matrix), matrix-degradative enzymes and oxygen. The model is considered to be hybrid since the latter three variables are continuous (i.e. concentrations) and the tumour cells are discrete (i.e. individuals). With this hybrid model we examine how individual-based cell interactions (with one another and the matrix) can affect the tumour shape and discuss which of these interactions is perhaps most crucial in influencing the tumour's final structure.

Cell Adhesion↗
PubMed2005

A mathematical model of dynamic glioma-host interactions: receptor-mediated invasion and local proteolysis.

We present a mathematical model of glioma spread based on cellular movement by receptor-mediated haptotaxis, local proteolysis of healthy tissue components by glioma-derived proteinases, malignant proliferative enhancement and host up-regulation of specific key extracellular matrix (ECM) components in response to the invading glioma. We subsequently consider the nature of glioma-host interactions as predicted by our model in order to test the hypothesis given in (Knott et al. (1998) that production of adhesive ECM components by the brain in response to the invading glioma may have the counter-intuitive effect of enhancing glioma invasion by assisting haptotactic migration. We suggest that host production of certain adhesive ECM chemicals can have a profound effect on both glioma invasion speed and the character of the glioma-host interface. In particular, we conclude that up-regulation of host ECM production in the vicinity of the glioma may produce a less diffuse glioma, providing clearer demarcation between glioma and healthy tissue, and thus improving the possibility of surgical resection within reasonable bounds.

Animals↗
PubMed1992

Mathematical model of 137Cs migration in soil: analysis of observations following the Chernobyl accident.

The applicability of traditional mathematical models is studied on the basis of 3 y of observation of the vertical migration of 137Cs fallout after the Chernobyl accident. The most accurate description of the dependence of the radionuclide concentration on the depth of the soil layer is given by a lognormal distribution. The parameters of this distribution are determined and shown to be a solution to the Fokker-Planck equation, a special case of which is the diffusion-convection transport equation.

Accidents↗
PubMed1998

A mathematical model of the inner medullary collecting duct of the rat: pathways for Na and K transport.

A mathematical model of the inner medullary collecting duct (IMCD) of the rat has been developed representing Na+, K+, Cl-, HCO3-, CO2, H2CO3, phosphate, ammonia, and urea. Novel model features include: finite rates of hydration of CO2, a kinetic representation of the H-K-ATPase within the luminal cell membrane, cellular osmolytes that are regulated in defense of cell volume, and the repeated coalescing of IMCD tubule segments to yield the ducts of Bellini. Model transport is such that when entering Na+ is 4% of filtered Na+, approximately 75% of this load is reabsorbed. This requirement renders the area-specific transport rate for Na+ comparable to that for proximal tubule. With respect to the luminal membrane, there is experimental evidence for both NaCl cotransport and an Na+ channel in parallel. The experimental constraints that transepithelial potential difference is small and that the fractional apical resistance is greater than 85% mandate that more than 75% of luminal Na+ entry be electrically silent. When Na+ delivery is limited, an NaCl cotransporter can be effective at reducing luminal Na+ concentration to the observed low urinary values. Given the rate of transcellular Na+ reabsorption, there is necessarily a high rate of peritubular K+ recycling; also, given the lower bound on luminal membrane Cl- reabsorption, substantial peritubular Cl- flux must be present. Thus, if realistic limits on cell membrane electrical resistance are observed, then this model predicts a requirement for peritubular electroneutral KCl exit.

Animals↗
PubMed2006

Mathematical models of proprioceptors. II. Structure and function of the Golgi tendon organ.

We developed a physiologically realistic mathematical model of the Golgi tendon organ (GTO) whose elements correspond to anatomical features of the biological receptor. The mechanical interactions of these elements enable it to capture all salient aspects of GTO afferent behavior reported in the literature. The model accurately describes the GTO's static and dynamic responses to activation of single motor units whose muscle fibers insert into the GTO, including the different static and dynamic sensitivities that exist for different types of muscle fibers (S, FR, and FF). Furthermore, it captures the phenomena of self- and cross-adaptation wherein the GTO dynamic response during motor unit activation is reduced by prior activation of the same or a different motor unit, respectively. The model demonstrates various degrees of nonlinear summation of GTO responses resulting from simultaneous activation of multiple motor units. Similarly to the biological GTO, the model suggests that the activation of every additional motor unit to already active motor units that influence the receptor will have a progressively weaker incremental effect on the GTO afferent activity. Finally, the proportional relationship between the cross-adaptation and summation recorded for various pairs of motor units was captured by the model, but only by incorporating a particular type of occlusion between multiple transduction regions that were previously suggested. This occlusion mechanism is consistent with the anatomy of the afferent innervation and its arrangement with respect to the collagen strands inserting into the GTO.

Afferent Pathways↗
PubMed1991

[Optimal pressure support ventilation as studied in a mathematical model].

To determine the optimal pressure support (PS) level in pressure support ventilations (PSV), we combined a mathematical model representing lung mechanics and alveolar gas exchange with a PS respirator model. As suggested by Fiastro et al. (1988), we defined the optimal PS level with regard to the work of breathing in such a way that the external inspiratory work of breathing equalled zero. We found that the optimal PS level determined as above resulted in the mean airway pressure calculated during an inspiratory phase being equal to zero (or a CPAP level). Thus we suggest that the optimal pressure support in terms of the work of breathing could be accomplished without a direct calculation of the work of breathing.

Airway Resistance↗
PubMed1980

[A mathematical model for the study of the kinetics of serum alkaline phosphatase inhibition by sodium diethyldithiocarbamate (NaDDTC)].

A mathematical model for the kinetic of the serum alkaline phosphatase inhibition by NaDDTC is described in this paper. The model is tested over an experimental data set consisting on measured % residual activity of enzyme in human serum, after inhibition. The Bessey method is used. The solution of the differential equations for the model is found to be the best fitting for the observed time-dependent phenomena. The rate constant, K, for the inhibition reaction is then computed.

Alkaline Phosphatase↗
PubMed1996

A simple mathematical model of intradialytic sodium kinetics: "in vivo" validation during hemodialysis with constant or variable sodium.

A simple mathematical model of the intradialytic relationship between natraemia and dialysate sodium concentration is presented. The model includes a bicompartmental description of sodium, urea and fluid kinetics and an algebraic characterization of diffusive/convective mass-transfer across the dialysis membrane. Its ability to provide realistic responses has been validated comparing model predictions by a priori parameter tuning against quantities measured during in vivo sessions with both constant and variable dialysate sodium concentration. A quantitative analysis of model predictions indicates that the mean deviation between data calculated by the model and those measured in vivo is 1.32 mEq/l for sodium and 0.76 mmol/l for urea, values which do not greatly exceed the measurement errors of current instruments. The model's predictive capacity thus proves reliable. The ability of the model to calculate the amount of sodium removed and the time course of intra-extracellular volumes during the dialysis session makes it possible to forecast the patient's clinical tolerance to a given sodium dialysate concentration.

Adult↗
PubMed1997

Mathematical modelling of the contribution of mechanical inhomogeneity in the myocardium to contractile function.

Earlier we developed a mathematical model of the cardiac muscle that allowed for inactivation through the effects of cooperativity of contractile proteins. In the present work we used the model to analyze the mechanical function of an inhomogeneous myocardium. To simulate the latter we chose, as the simplest sytstem, a duplex in which muscles with different mechanical properties were connected in series and in parallel. Numerical experiments showed that the basic effect due to the inhomogeneity consists in the non-additivity of the mechanical characteristics of the muscle, e.g., of the relationship between end-systolic length and end-systolic force (Les - Pes). As a rule, non-additivity consists in a negative inotropic effect. The analysis showed that the cause of non-additivity is redistribution of loads between muscles (in a parallel duplex), redistribution of lengths (in a serial duplex), changes in the rate of contraction of each muscle compared to contraction that when working separately, shifts in time to Les. Also, the model predicts that additional inactivation of contractile proteins in a muscle within a duplex against isolation is the substantial mechanism of enhanced non-additivity. Among the factors of inhomogeneity studied the basic determinants are difference in amplitudes between isometric tensions developed by each muscle in isolation and the asynchronism in the development of these tensions.

Biomechanical Phenomena↗
PubMed1978

Compact anisotropic bone: elastic constants, in vitro aging effects and numerical results of a mathematical model.

This paper briefly examines the experimentally observed effects in, and symmetry arguments for, the constituents of bone which lead to a transversely isotropic configuration for the elastic behavior of bone. Based on this, a regime for computing the anisotropic elastic constants is considered in terms of ultrasonic transit time measurements. To extend the usefulness of ultrasonic techniques to an in vivo situation, a mathematical model for bone is developed in outline form and numerical results for the characteristic frequency equation discussed.

Aging↗
PubMed1986

[Mathematical model of brain edema and optimal control of intracranial pressure].

It is necessary to analyse various parameters responding to hypertonic solutions such as mannitol or glycerol, in order to achieve the best therapeutic results for patients having increased intracranial pressure (ICP). The responding model system for the ICP composing of multi-compartments of blood and brain tissue was mathematically introduced. By analysing the changes of the ICP under administration of glycerol using this system, the mathematical model for brain edema was developed. The cause of water transfer in this model system was indicated as the difference of the osmotic pressure and determined as ICP increasing factor, V. It was demonstrated that this theoretical model responded quite similarly to human ICP monitored by sumulating this system for clinical cases. The ICP controller was further developed. The automatic control of ICP was clinically achieved by using this controller. The minimal effective dose of glycerol can be automatically administered by presetting a desirable ICP for each patient.

Aged↗
PubMedDate not supplied

A dynamic mathematical model to clarify signaling circuitry underlying programmed cell death control in Arabidopsis disease resistance.

Plant cells undergo programmed cell death in response to invading pathogens. This cell death limits the spread of the infection and triggers whole plant antimicrobial and immune responses. The signaling network connecting molecular recognition of pathogens to these responses is a prime target for manipulation in genetic engineering strategies designed to improve crop plant disease resistance. Moreover, as alterations to metabolism can be misinterpreted as pathogen infection, successful plant metabolic engineering will ultimately depend on controlling these signaling pathways to avoid inadvertent activation of cell death. Programmed cell death resulting from infection of Arabidopsis thaliana with Pseudomonas syringae bacterial pathogens was chosen as a model system. Signaling circuitry hypotheses in this model system were tested by construction of a differential-equations-based mathematical model. Model-based simulations of time evolution of signaling components matched experimental measurements of programmed cell death and associated signaling components obtained in a companion study. Simulation of systems-level consequences of mutations used in laboratory studies led to two major improvements in understanding of signaling circuitry: (1) Simulations supported experimental evidence that a negative feedback loop in salicylic acid biosynthesis postulated by others does not exist. (2) Simulations showed that a second negative regulatory circuit for which there was strong experimental support did not affect one of two pathways leading to programmed cell death. Simulations also generated testable predictions to guide future experiments. Additional testable hypotheses were generated by results of individually varying each model parameter over 2 orders of magnitude that predicted biologically important changes to system dynamics. These predictions will be tested in future laboratory studies designed to further elucidate the signaling network control structure.

Apoptosis↗
PubMed1996

A mathematical model for collagen fibre formation during foetal and adult dermal wound healing.

Adult dermal wounds, in contrast to foetal wounds, heal with the formation of scar tissue. A crucial factor in determining the nature of the healed tissue is the ratio of collagen 1 to collagen 3, which regulates the diameter of collagen fibres. We develop a mathematical model which focuses on the stimulus for collagen synthesis due to the secretion of the different isoforms of the regulatory chemical transforming growth factor beta. Numerical simulations of the model lead to a value of this ratio consistent with that of healthy tissue for the foetus but corresponding to scarring in adult wound healing. We investigate the effect of topical application of TGF beta isoforms during healing and determine the key parameters which control the difference between adult and foetal repair.

Animals↗
PubMed1993

Propriomuscular coding of kinaesthetic sensation. Experimental approach and mathematical modelling.

The role of propriomuscular information in kinaesthetic sensation was studied. Experiments were carried out on human subjects in whom kinaesthetic illusions were induced by applying tendon vibration with a variable frequency. Six patterns of frequency modulation were used, four of which had an arbitrary form and the other two mimicked natural Ia discharges. The results show that the shape of the illusory movements recorded depended on the type of vibratory pattern used. A mathematical model for the propriomuscular information decoding process is proposed. It takes into account both the agonist and antagonist muscle spindle populations as sources of kinaesthetic information and is based on the assumption that position and velocity information are additively combined. The experimental data show a good fit with the theoretical data obtained by means of model simulation, thus validating our initial hypothesis. Various aspects of the experimental results and the hypotheses involved in the model are discussed.

Adult↗
PubMed1999

Mathematical model of oxygen transport in the cerebral cortex.

To estimate the magnitude of hyperemia necessary to support oxidative metabolism in the cerebral cortex during functional activation, a mathematical model of O2 transport from capillary to tissue was developed. Radial and axial gradients of O2 pressure in tissue surrounding a single capillary were calculated at normal and increased cerebral metabolic rates for O2. Cone-shaped tissue geometry and nonlinear oxyhemoglobin dissociation were assumed. Local O2 consumption was assumed to be supported with local tissue pO2 greater than 1 mmHg. The distribution of tissue pO2 was also calculated during moderate hypoxemia (paO2=42 mmHg), using experimental values of red blood cell velocity measured in individual capillaries of the rat cerebral cortex using intravital video-microscopy. The model predicted that moderate increases (</=50%) in cerebral O2 consumption were supported by proportional increases in capillary blood flow. Large increases in O2 consumption (50-110%) were supported by disproportional increases in flow. During moderate hypoxemia, average tissue pO2 decreased but oxygen utilization was sustained when capillary flow was increased to a level measured in experiments. The results suggest a proportional relationship between cerebrocortical blood flow and oxygen consumption in the normal physiological range of functional activation.

Animals↗
PubMed1995

Mathematical modeling of the loss of telomere sequences.

hortening of telomeres is one of the supposed mechanisms of cellular aging and death. An important question related to this so-called "end-replication" hypothesis is whether it can explain in quantitative detail the dynamic of cell sensescence in vitro and in vivo. A natural way to answer this question is to use mathematical modeling. In this paper, the models were successfully fitted to data on cultured fibroblasts from two different sources assuming that after reaching the Hayflick checkpoint on a single chromosome cells cease to proliferate. The main conclusion is that the end-replication hypothesis provides an explanation for the cell aging process which is quantitatively consistent with the data. As a secondary outcome, estimates were obtained of the rate of shortening of telomeres and several interesting mathematical results for branching processes with infinite type spaces arise.

Animals↗