Temporal crossover from classical to quantal behavior near dynamical critical points.
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Biomedical subjects
Publications and source records attributed to S Fishman.
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A computerized model used to simulate calcium metabolism in growing chicks combines growth equations with differential equations that account for the amount and action of various components of the plasma calcium regulating subsystems--intestine, kidney and bone. These in turn are modulated by the calcium-regulating hormones: parathyroid hormone and 1,25-dihydroxycholecalciferol. Simulation with this model indicated oscillations in the plasma calcium concentration in growing chicks under normal dietary conditions. The oscillations diminish in amplitude and finally disappear when dietary calcium concentrations are either reduced or elevated. These oscillations, triggered by the perturbation imposed by growth, are the result of the dual action of parathyroid hormone on bone on the one hand and on intestinal calcium absorption via the 1,25-dihydroxycholecalciferol synthesizing system on the other and the difference in the response time between the two subsystems. Simulation also predicts that at high or low intakes of calcium, the capacity of the control systems is exceeded and oscillation in plasma. calcium diminish and finally disappear. Bone calcium, simulated for different calcium concentrations, mimics documented experimental results.
The process of growth was included in a model for simulation of calcium homeostasis in the chick, using data of carcass composition and a model of growth and energy intake. Computer simulations, made for chickens between 0 and 10 wk of age, predicted oscillations in plasma calcium and its major regulatory systems. Analysis of the oscillations indicated a periodicity of approximately 55 h. The oscillations were proportionally dependent on the rate of growth, disappearing almost completely when growth rate was made equal to zero. Subject to the validity of the model, it is suggested that the oscillations in plasma calcium and some of the components of the regulatory systems are induced by a continuous perturbation (growth) resulting in a dual response to the main regulatory hormone, parathyroid hormone, one rapid with a response time of minutes (bone), and one delayed, with a response time of hours (calcium absorption via the metabolism of 1,25-dihydroxychole-calciferol). It is also suggested that some of the normal variance and some of the rhythmicity observed previously in various components of the calcium regulatory system may be the results of spontaneous oscillations.
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A mathematical analysis of the kinetics of the hormone-receptor interaction was applied to the 1,25-dihydroxycholecalciferol-intestinal receptor system. The exact analytical solution and the numerical integration of the kinetic equation were installed in a Statistical Analysis System (SAS) computer program to estimate the rate constants of the reaction. Estimates of the parameters obtained by these two methods are similar, demonstrating that the numerical integration can be combined with the nonlinear regression procedure for least-squares parameter fitting using a simple SAS program. This enables estimation of kinetics rate constants when the kinetic equation cannot be solved analytically. The ratio of the rate constants (ka/kd) found by the nonlinear procedure is close to the independently determined equilibrium (Scatchard) constant in the nonlinear analysis.
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Gait analysis, like all clinical assessments, is subject to measurement error. Specification of the extent of measurement error is imperative before drawing conclusions from any test. The purpose of this study was to determine the within-rater and between-rater reliability of observational gait analysis in a pediatric sample wearing knee-ankle-foot orthoses. Three expert observers, using a 3-point scale, rated videotaped gait kinematics of 15 children who had lower limb disability and who wore braces. The rating sessions were then repeated, with one month between sessions. Total agreement (identical ratings), both between-raters and within-raters, occurred in two-thirds of the observations, and an additional 29% of the observations differed by one point. Between-rater intraclass correlation coefficient type 2, 1 was .73; within-rater Pearson product-moment correlation averaged .60. Observational kinematic gait analysis appears to be a convenient, but only moderately reliable, technique.
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The characteristics and number of children with limb amputations in North America are not known. In an effort to secure information concerning the nature of the child amputee population (to 21 years of age) in the United States and Canada, a census of patients treated at member clinics of the Association of Children's Prosthetic-Orthotic Clinics (ACPOC) was conducted. It was designed to obtain a rational basis for children's prosthetic design, development, research, and educational activities. Of the 74 ACPOC prosthetic clinics to which the questionnaire was sent, 45 replies were analyzed, representing a total of 4,105 children under treatment at the reporting clinics during 1980, of which 679 cases (17%) were seen for the first time in that year. The results are consistent with prior unpublished censuses. Overall, congenital limb deficiencies outnumbered acquired losses by a ratio of 2:1, but among unilateral cases, more lower-limb amputations were acquired postpartum than congenitally. Eighty percent of all child amputees had had only one limb involved, and 54% of these unilateral cases were left amputees. Males outnumbered females 3:2, and over half of the children currently under treatment at the reporting clinics had been under 6 years of age at the time of first admission.
A simulation model of calcium metabolism in the chick has been used to evaluate the response of the systems that regulate plasma calcium to a continuous input of 1,25-dihydroxycholecalciferol [1,25(OH)2D3] from the intestine. The results of simulation showed that the concentration of the vitamin D metabolite in the intestine increased during the first 24 h and thereafter decreased slightly due to suppression of endogenous hormone production. Metabolite accumulation was accompanied by an increase in calcium absorption, with a lag period of about 4 h. Most of the increase in absorbed calcium was excreted in the urine, with a lesser change in net bone calcium uptake. Plasma calcium increased with time, in proportion to the intake of the exogenous hormone. The validity of the predicted steady-state plasma calcium levels, and bone and kidney calcium flows, is discussed. The results of the simulation demonstrate the importance of the vitamin D-intestinal axis in regulation of plasma calcium.
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The system that regulates plasma calcium in the bird has been formalized into a model based on a series of differential equations and solved by computer simulation. Bone, kidney, and intestine have been considered as the control subsystems, with parathyroid hormone and 1,25-dihydroxycholecalciferol as the regulating hormones. The parameters used in the simulation model have been computed either from published results or by specifically designed experiments described here. For the estimation of parameters, an iterative procedure has been developed that was designed to minimize the sum of square errors between observed and system-simulated values. Parameters of 1,25-dihydroxycholecalciferol metabolism were experimentally obtained from the kinetic behavior of the 3H-labeled hormone in rachitic birds after a single dose. Model parameters have been adjusted using the results of in vivo calcium loading and validated by an EDTA infusion experiment. The simulation model has been used to study the hierarchy of the activities of the three control subsystems and of the regulating hormones, at different calcium intakes. Positive or negative errors in plasma calcium resulted in an asymmetry in the activities of the controlling systems, bone and kidney, whereas the intestine is characterized by its relatively long response time.
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