SEARCH · PubMed Health
Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Explore the source record for details and available documents.
A mathematical model was constructed to predict motor performance in rats for 8 weeks after spinal cord injury. The model is based on experimental data generated from an investigation of the static-load technique of inducing cord injury and was derived using multiple linear regression. The regression coefficients for weight of the injury-producing load were statistically significant (P less than 0.001), and it was found that the weight of the load contributes over 95% of the posttrauma motor deficit, whereas the time duration of the load resting on the cord contributes less than 5% to the deficit. Sex, pretrauma motor performance, and pretrauma body weight are insignificant covariates. The model may be used to establish expected motor deficits and to derive dose-response curves.
A simple mathematical model of photosynthetic carbon metabolism as driven by ATP and NADPH has been formulated to analyse photosynthetic oscillations. Two essential assumptions of this model are: (i) reduction of 3-phosphoglycerate to triosephosphate in the Clavin cycle is limited by ATP, not by NADPH, and (ii) photophosphorylation is affected by the availability of both ADP and NADP, while electron transport is limited by NADP only. The model produces oscillations of observed damping and period in ATP and NADP concentrations which are about 180 degrees out of phase, while three alternative proposals regarding coupling of electron transport and photophosphorylation do not produce oscillatory model solutions. The phases of ATP and NADPH are in reasonable agreement with the available experimental data. The model (which assumes that redox control of photophosphorylation is part of the oscillatory mechanism) is compared with an alternative proposal (that oscillations are due to interdependence of turnover of adenylates and Calvin cycle intermediates). From the similarity of the mathematical structures of both models it is inviting to speculate that both models are partial aspects of 'the oscillatory mechanism'.
A simple mathematic model describing the activation Na,K-ATPase system by univalent cations is proposed. The constants for the enzyme activation values by each of the ions in the presence of a fixed concentration of the other ion have been calculated. The substitution of these values into the common equation describing the behaviour of the whole system according to the given model gives the curve of Na,K-ATPase activity change in dependence of Na/K ration at the same total concentration 150 mM. The experimental points correspond to the curve.
In vitro and mathematical models of continuous arteriovenous hemofiltration (CAVH) have been developed. Human erythrocytes resuspended in normal saline containing 5% bovine albumin were used to perfuse the circuit from a gravity driven pressure source. Membrane hydraulic permeability was observed to decline from 31.2 x 10(-5) +/- 11.9 x 10(-5) cm/(min.mm Hg) before use to 12.3 x 10(-5) +/- 3.3 x 10(-5) (mean +/- SD) after use. This fall occurred during the first one to two hours whether perfused with blood or 5% albumin alone. Pressure-flow relationships of each circuit component, measured with 40% sucrose as a calibration medium, conformed to Poiseuille's equation. Use of high resistance blood access on the venous end of the circuit resulted in a low blood flow rate and high filtration fraction. The same access, when placed on the arterial end, produced both low blood flow rate and low filtration fraction. These results were a consequence of pressure distribution within the circuit as demonstrated by measurements of perfusion, prefilter, and postfilter pressures. The importance of negative pressure applied to the filter chamber in order to maintain favorable Starling forces, when the system was operated with a small bore arterial access, was demonstrated by similar methods. Enhancement of urea clearance by predilution was verified. Model simulations suggest that predilution will be of less benefit or even detrimental for other solutes which fail to distribute across the erythrocyte membrane. Comparison of results with predictions of a mathematical model demonstrated good agreement, but with some tendency to overestimate filtrate production. The latter was attributed to neglect of concentration polarization of plasma proteins in model development.
Explore the source record for details and available documents.
A mathematical model for describing the caloric response over time offers many important advantages over the commercially-available qualitatively-fitted curves that are now used by the clinician for evaluating caloric results. In this report advances in the development of a nonlinear least-squares mathematical model are discussed and the roles and derivations of fitting parameters and curve-derived indices are outlined. This model provides a rigorous and objective description of the caloric response in its entirety with four continuous parameters. These fitting parameters make it possible to 1) describe individual caloric responses precisely and uniquely, 2) compare pairs of individual caloric responses or groups of caloric responses statistically, 3) extract information not previously available, 4) quantify variability within the caloric response, and 5) model physical properties of the caloric stimulus and physiological variables affecting the caloric response. Results from this model are compared with the results from our earlier models and with traditional multiparameter caloric results.
A simple mathematical model describing the generation and propagation of epileptiform activity in a cerebral cortical network is presented. The model consists of a system of nonlinear delay differential equations. Physiological properties are taken into account as nonlinear transmission of signals at the synapse, temporal and spatial summation of incoming signals at the soma, active membrane characteristics, and dendritic and axonal propagation times. The influence of the connectivity and the temporal parameters on the oscillatory properties of the model is studied. The computer simulations are in agreement with experimental observations in cortical networks: whereas a weak excitatory or strong inhibitory synaptic connection strength produces a stationary status with short-lasting responses to external stimuli, increases in excitation or decreases in inhibition induce spontaneous and stimulus-evoked rhythmic discharges. Synaptic burst-like activity is observed only for an intermediate range of excitatory and inhibitory connection strengths and external inputs. The form and duration of the bursts can also be controlled by the temporal parameters. The results demonstrate that relatively simple mathematical equations are sufficient to model some of the network properties underlying the generation and propagation of epileptiform activity.
This paper presents studies of the coordination of voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements. Coordination is modeled mathematically by defining an objective function, a measure of performance for any possible movement. The unique trajectory which yields the best performance is determined using dynamic optimization theory. In the work presented here, the objective function is the square of the magnitude of jerk (rate of change of acceleration) of the hand integrated over the entire movement. This is equivalent to assuming that a major goal of motor coordination is the production of the smoothest possible movement of the hand. Experimental observations of human subjects performing voluntary unconstrained movements in a horizontal plane are presented. They confirm the following predictions of the mathematical model: unconstrained point-to-point motions are approximately straight with bell-shaped tangential velocity profiles; curved motions (through an intermediate point or around an obstacle) have portions of low curvature joined by portions of high curvature; at points of high curvature, the tangential velocity is reduced; the durations of the low-curvature portions are approximately equal. The theoretical analysis is based solely on the kinematics of movement independent of the dynamics of the musculoskeletal system and is successful only when formulated in terms of the motion of the hand in extracorporal space. The implications with respect to movement organization are discussed.
A mathematical formula that allows for the computation of the true angle between the upper and lower canaliculi using dacryocystograms is described. It was used to determine the true canalicular angle in 33 patients. The mean calculated angle at the 1.0 mm distance was 57.2 degrees +/- 13.0 degrees, and at the 0.5 mm distance was 65.2 degrees +/- 16.2 degrees. The true calculated angle was highly correlated with the angle measured in the Waters view. There was no statistically significant correlation between the right and left sides in the same patient. There was no statistically significant difference between the canalicular angle in males and females, and there was no correlation between canalicular angle and patient's age. A clinical application of this model is discussed.
A mathematical description of autotolerance and autoimmunity based on the previous model of immune response for normal antigen stimulation is given. In particular, the clonal deletion theory and non-specific stimulation of T-helper cells are included. Thus, an idea about the origin of autoimmune disease and the qualitative description of its course is presented. Possible therapies, such as immunosuppression and extracorporeal removal of autoantibodies, are also discussed.
A mathematical description of cardiac anatomy is presented for use with finite element models of the electrical activation and mechanical function of the heart. The geometry of the heart is given in terms of prolate spheroidal coordinates defined at the nodes of a finite element mesh and interpolated within elements by a combination of linear Lagrange and cubic Hermite basis functions. Cardiac microstructure is assumed to have three axes of symmetry: one aligned with the muscle fiber orientation (the fiber axis); a second set orthogonal to the fiber direction and lying in the newly identified myocardial sheet plane (the sheet axis); and a third set orthogonal to the first two, in the sheet-normal direction. The geometry, fiber-axis direction, and sheet-axis direction of a dog heart are fitted with parameters defined at the nodes of the finite element mesh. The fiber and sheet orientation parameters are defined with respect to the ventricular geometry such that 1) they can be applied to any heart of known dimensions, and 2) they can be used for the same heart at various states of deformation, as is needed, for example, in continuum models of ventricular contraction.
Nitric oxide (NO) is a remarkable free radical gas whose presence in biological systems and whose astonishing breadth of physiological and pathophysiological activities have only recently been recognized. Mathematical models for NO biotransport, just beginning to emerge in the literature, are examined in this review. Some puzzling and paradoxical properties of NO may be understood by modeling proposed mechanisms with known parameters. For example, it is not obvious how NO can survive strong scavenging by hemoglobin and still be a potent vasodilator. Recent models do not completely explain how tissue NO can reach effective levels in the vascular wall, and they point toward mechanisms that need further investigation. Models help to make sense of extremely low partial pressures of NO exhaled from the lung and may provide diagnostic information. The role of NO as a gaseous neurotransmitter is also being understood through modeling. Studies on the effects of NO on O2 transport and metabolism, also reviewed, suggest that previous mathematical models of transport of O2 to tissue need to be revised, taking the biological activity of NO into account.
The study of mathematical models to describe bone mass behavior throughout life is a possibility for assessing the main factors of peak bone mass and bone loss. We developed a mathematical model to predict spinal bone mass behavior on a sample of 181 healthy Italian women whose lumbar bone mineral content was determined by Gd-153 dual photon absorptiometry. This model proved to be both efficient, showing the best fit (r = 0.7 on spinal bone mineral content) when compared to other previously suggested models, and also reliable as its fit remained the best when applied to a subsequent sample of 519 women whose lumbar spine was measured by dual X-ray photon absorptiometry. This model suggests that body height and body weight (but not age) are determinants of bone mass in premenopausal women. In postmenopausal women, an accelerated phase of bone loss starting at menopause is dependent on age and time since menopause, whereas body mass index acts as a protective factor. This model confirms the influence on spinal bone mass not only of age and time since menopause but also of body size parameters.
A simplified mathematical model of cell metabolism describing ion pump, glycolysis and adenylate metabolism was developed and investigated in order to clarify the functional role of the adenylate metabolism system in human erythrocytes. The adenylate metabolism system was shown to be able to function as a specific regulatory system stabilizing intracellular ion concentration and, hence, erythrocyte volume under changes in the permeability of cell membrane. This stabilization is provided via an increase in adenylate pool in association with ATPases rate elevation. Proper regulation of adenylate pool size might be achieved even in the case when AMP synthesis rate remains constant and only AMP degradation rate varies. The best stabilization of intracellular ion concentration in the model is attained when the rate of AMP destruction is directly proportional to ATP concentration and is inversely proportional to AMP concentration. An optimal rate of adenylate metabolism in erythrocytes ranges from several tenths of a percent to several percent of the glycolytic flux. An increase in this rate results in deterioration of cell metabolism stability. Decrease in the rate of adenylate metabolism makes the functioning of this metabolic system inefficient, because the time necessary to achieve stabilization of intracellular ion concentration becomes comparable with erythrocyte life span.
A complete mathematical model of the periodic myoelectrical activity of a functional unit of the small intestine is presented. Based on real morphological and electrophysiological data, the model assumes that: the functional unit is an electromyogenic syncytium; the kinetics of L-type Ca2+, T-type Ca2+, Ca2+-activated K+, voltage dependent K+and Cl-channels determine the electrical activity of the functional unit; the enteric nervous system is satisfactorily represented by an efferent cholinergic neuron that provides an excitatory input to the functional unit through receptor-linked L-type Ca2+channels and by an afferent pathway composed of the primary and secondary sensory neurons; the dynamics of propagation of the wave of depolarization along the unmyelinated nerve axons satisfy the Hodgkin-Huxley model; the electrical activity of the neural soma reflects the interaction of N-type Ca2+channels, Ca2+-activated K+and voltage dependent Na+, K+and Cl-channels; the smooth muscle syncytium of the locus is a null-dimensional contractile system. With the proposed model the dynamics of active force generation are determined entirely by the concentration of cytosolic calcium. The model describes: the mechanical excitation of the free nerve endings of the mechanoreceptor of the receptive field of the pathway; the electrical processes of the propagation of excitation along the afferent and efferent neural circuits; the chemical mechanisms of nerve-pulse transmission at the synaptic zones; the slow wave and bursting type electrical activity; cytosolic calcium concentration; the dynamics of active force generation. Numerical simulations have shown that the model can display different electrical patterns and mechanical responses of the locus. The results show good qualitative and quantitative agreement with the results of experiments conducted on the small intestine.
An original mathematical model of the cardiovascular response to dynamic exercise is presented. It includes the pulsating heart, the pulmonary and systemic circulation, a separate description of the vascular bed in active tissues, the local metabolic vasodilation in these tissues and the mechanical effects of muscular contractions on venous return. Moreover, the model provides a description of the ventilatory response to exercise and various neural regulatory mechanisms working on cardiovascular parameters. These mechanisms embrace the so-called central command, the arterial baroreflex and the lung inflation reflex. All parameters in the model have been given in accordance with physiological data from the literature. In this work, the model has been used to simulate the steady-state value of the main cardiorespiratory quantities at different levels of aerobic exercise and the temporal pattern in the transient phase from rest to moderate exercise. Results suggest that, with suitable parameter values the model is able accurately to simulate the cardiorespiratory response in the overall range of aerobic exercise. This response is characterised by a moderate hypertension (10-30%) and by a conspicuous increase in systemic conductance (80-130%), heart rate (64-150%) and cardiac output (100-200%). The transient pattern exhibits three distinct phases (lasting approximately 5s, 15s and 2 min), that reflect the temporal heterogeneity of the mechanisms involved. The model may be useful to improve understanding of exercise physiology and as an educational tool to analyse the complexity of cardiovascular and respiratory regulation.
1. A mathematical model of diffusional Ca exchange in a continuously perfused heart has been formulated. Based on biochemical studies, sarcolemmal Ca binding on the extracellular surface of cardiomyocytes is taken into account. The changes in sarcolemmal Ca binding may affect the kinetics of Ca washout from the myocardium. The model is consistent with the real dynamics of 45Ca washout from rabbit heart septum reported by Philipson and Langer (F Mol Cell Cardiol 11, 857 (1979)). 2. The changes in the kinetics of Ca washout calculated according to the proposed model agree with the real changes in the kinetics of 45Ca washout from rabbit heart septum at two coronary flow rate values reported by Shine et al. (Am J Physiol 221, 1408 (1971)). 3. The calculated dynamics of the decrease in sarcolemmal Ca content is close to the real dynamics of the myocardial contractility decrease demonstrated by Philipson and Langer (1979). 4. The model offers an estimation of the contribution of different myocardial compartments to the kinetic components of Ca washout curves resolved by the method of Solomon (In: Mineral Metabolism 1A, p. 119, New York, Academic Press, (1960)). According to the results of the modeling, more than 80% of the fast exchanging pool 0 is composed of sarcolemmal Ca. 85 and 95% of the slowly exchanging pools 2 and 3 are composed of intracellular Ca; pool 1 is determined by both sarcolemmal and intracellular Ca.