Bifurcation properties of the two process model

Abstract Daan's two process model is known to be one of the most powerful models, covering various situations from free-running to sleep deprivation. In this study, bifurcation properties of the model dynamics as function of a gap, D , between the threshold processes are clarified using a circle map. As a function of D , we will show that the model has the different types of the mutual entrainment regions that are intervened by the tangent bifurcation. The variable behavior of human circadian rhythm is suggested to be systematically understood based on the bifurcation properties of the two process model.     

三次抛物线配合方法在碘缺乏病区居民患病率分析中的应用

<正>在碘缺乏病区,居民甲状腺肿患病率在年鹅分布上的特征,可用二次抛物线加以描述[l].根握资料类型的不同,可选择更为适合的三次抛物线来描述.根据现场调查资料,本文采用三次抛物线方法进行配合,并将配合结果与二     

大白鼠游泳输出功测定仪的研制和疲劳方程Y＝A＋B／T的建立

研制了可以直接连续测量大鼠游泳输出功率的仪器，建立了一个理想的动物模型，通过分析对功率曲线进行函数拟合，得出了代表疲劳发生、作功能力下降的双曲线方程，通过分析衰竭时间和功、功率等参数的关系提出了衰竭阈概念。     

Modification of DiFrancesco-Noble equations to simulate the effects of vagal stimulation onin vivo mammalian sinoatrial node electrical activity

We present a new mathematical model for vagal control of rabbit sinoatrial (SA) node electrical activity based on the DiFrancesco-Noble equations. The original equations were found to be unstable, resulting in progressive cycle by cycle depletion or accumulation of ions in intra- and extracellular compartments. This problem was overcome by modifying the maximum Na−K pump current and the time constant for uptake of intracellular calcium. We also included a formulation for the acetylcholine (ACh)-activated potassium current which was consistent with experimental data. This formulation was based on kinetics first proposed by Osterrieder and later modified by Yanagihara. The resulting model exhibits cycle-cycle ionic stability, and includes an ACh-activated potassium current which accurately reproduces experimentally observed effects of vagal stimulation on both the membrane potential and its timederivative. Simulations were performed for both brief-burst and prolonged vagal stimulation using simplified square wave profiles for the concentration of ACh in the synaptic cleft space. This protocol permits the isolation of cardiac period dynamics caused by changes in membrane potential and intra- and extracellular ionic concentrations from those caused by other mechanisms including the dynamics of ACh release, diffusion, hydrolysis and washout. Simulation results for the effects of brief-burst single cycle stimulation on the cardiac period agree closely with experimental data reported in the literature, accurately reproducing changes in membrane potential and the phasic dependency of the response to the position of vagal stimulus bursts within the cycle. Simulation of the effects of prolonged vagal stimulation accurately reproduced the steady-state characteristics of heart period response, but did not yield the complex multimodal dynamics of the recovery phase, or the pronounced post vagal tachycardia observed experimentally at the termination of the stimulus. Our results show that the major chronotropic effects of vagal stimulation on the SA cell membrane can be explained in terms of the ACh-activated potassium current. The effects of this membrane current however are generally fast acting and cannot contribute to any long lasting dynamics of the cardiac period response. The modified DiFrancesco-Noble model presented in this article provides a valuable theoretical tool for further analysis of the dynamics of vagal control of the cardiac pacemaker.     

Comparison of mathematically determined blood lactate and heart rate “threshold” points and relationship with performance

Summary The purpose of this study was to investigate the relationship between threshold points for heart rate ( ) and blood lactate (Th_1a) as determined by two objective mathematical models. The models used were the mono-segmental exponential (EXP) model of Hughson et al. and the log-log (LOG) model of Beaver et al. Inter-correlations of these threshold points and correlations with performance were also studied. Seventeen elite runners (mean, SD = 27.5, 6.5 years; 1.73, 0.05 m; 63.8, 7.3 kg; and maximum oxygen consumption of 67.8, 3.7 ml · kg^–1 · min^–1) performed two maximal multistage running field tests on a 183.9-m indoor track with inclined turns. The initial speed of 9 km · h^–1 (2.5 m · s^–1) was increased by 0.5 km · h^–1 (0.14 m · s^–1) every lap for thef _c test and by 1 km · h^–1 (0.28 m · s^–1) every 4 min for the la test. After fitting the la or thef _c data to the two mathematical models, the threshold speed was assessed in the LOG model from the intersection of the two linear segments (LOG-1a; LOG-f _c) and in the EXP model from a tangent point (TI-1a; TI-f _c). Th_1a and speeds computed with the two models were significantly different (P<0.001) and poorly correlated (LOG-1a vs LOG-f _c:r=0.36, TI-1a vs TI-f _c:r=0.13). In general, were less well correlated with performance than Th_1a. With two different objective mathematical models, this study has shown significant differences and poor correlations between Th_1a and . Thus thef _c inflection point with Conconi's protocol is a poor indicator of the la breakpoint with a conventional multistage protocol and a weaker indicator of running performance.     

Complement-derived polypeptide C3adesArg as a mediator of inflammation at the blood-brain barrier in a new experimental cat model

Summary The effect of the complement-derived polypeptide C3adesArg as a mediator of inflammation in the central nervous system was examined. Twenty-five anesthetized cats received 4 mg of this polypeptide by intraventricular injection, 20 cats who served as controls received saline. Cerebrospinal fluid (CSF) was sampled 3 h after intraventricular injection and the brains were removed. For assessment of the permeability of the blood-brain barrier the CSF penetration of four antibiotics, which were given intravenously, was measured. Five control animals were employed for each antibiotic (tobramycin, ampicillin, imipenem, fosfomycin), whereas six C3adesArg-treated animals were used for each antibiotic and seven for tobramycin. Besides CSF levels of glucose, the prostanoids 6-keto-prostaglandin F₁, thromboxane B₂ and prostaglandin E₂ were measured. The morphological examinations in the CSF sediments and histological brain sections in the C3adesArg-treated animals disclosed a distinct inflammation with leptomeningeal and perivascular infiltration of polymorphonuclear granulocytes compared to normal findings in the controls. The CSF/serum ratios of all of the antibiotics were markedly elevated compared to controls, indicating a blood-brain barrier disruption. The levels of all prostanoids were significantly higher in the treatment group than in the control group, whereas the glucose levels were lower. These findings are in accordance with a granulocytic meningitis as seen in some infections at the acute stage. It is concluded that C3adesArg acts as a mediator of inflammation in the central nervous system.     

The GABA hypothesis of kindling: Recent assay studies

The GABA (gamma-aminobutyric acid) hypothesis of kindling suggests that the permanent changes caused by the kindling procedure result from a loss of GABA-mediated inhibition. Pharmacological studies have generally supported this hypothesis: GABA-complex antagonists accelerate (or stimulate) kindling, whereas GABA-complex agonists retard (or reverse) it. Assay studies, however, have presented an inconsistent picture. Earlier studies found no GABAergic brain changes after kindling, whereas recent studies have reported postkindling changes in a number of GABA-related parameters. The crucial difference seems to be that earlier studies assayed GABA parameters in "whole tissue," whereas recent studies have concentrated on "synaptic" GABA. As indicated by recent studies, when the "metabolic pool" is excluded, kindled subjects show a variety of persistent abnormalities in the GABA system. These data are generally consistent with the GABA hypothesis of kindling.     

Short-term enzyme replacement in the murine model of Sanfilippo syndrome type B

The Sanfilippo syndrome type B (MPS III B) is an autosomal recessive disease caused by deficiency of alpha-N-acetylglucosaminidase (EC 3. 2.1.50), one of the lysosomal enzymes required for the degradation of heparan sulfate. The disease is characterized by profound neurodegeneration but relatively mild somatic manifestations, and is usually fatal in the second decade. A mouse model had been generated by disruption of the Naglu gene in order to facilitate the study of pathogenesis and the development of therapy for this currently untreatable disease. Recombinant human alpha-N-acetylglucosaminidase (rhNAGLU) was prepared from secretions of Lec1 mutant Chinese hamster ovary cells. The enzyme, which has only unphosphorylated high-mannose carbohydrate chains, was endocytosed by mouse peritoneal macrophages via mannose receptors, with half-maximal uptake at ca. 10(-7) M. When administered intravenously to 3 month-old mice, rhNAGLU was taken up avidly by liver and spleen but marginally if at all by thymus, lung, kidney, heart, and brain (in order of diminishing uptake). The half-life of the enzyme was 2.5 days in liver and spleen. Immunohistochemistry and electron microscopy showed that only macrophages were involved in enzyme uptake and correction in these two organs, yet the storage of glycosaminoglycan was reduced to almost normal levels. The results show that the macrophage-targeted rhNAGLU can substantially reduce the body burden of glycosaminoglycan storage in the mouse model of Sanfilippo syndrome III B.     

Intrathoracic pressure fluctuations move blood during CPR: Comparison of hemodynamic data with predictions from a mathematical model

Whether blood flow during cardiopulmonary resuscitation (CPR) results from intrathoracic pressure fluctuations or direct cardiac compression remains controversial. We developed a mathematical model that predicts that blood flow due to intrathoracic pressure fluctuations should be insensitive to compression rate over a wide range but dependent on the applied force and compression duration. If direct compression of the heart plays a major role, however, the model predicts that flow should be dependent on compression rate and force, but above a threshold, insensitive to compression duration. These differences in hemodynamics produced by changes in rate and duration form a basis for determining whether blood flow during CPR results from intrathoracic pressure fluctuations or from direct cardiac compression. The model was validated for direct cardiac compression by studying the hemodynamics of cyclic cardiac deformation following thoracotomy in four anesthetized, 21–32-kg dogs. As predicted by the model, there was no change in myocardial or cerebral perfusion pressures when the duration of compression was increased from 15% to 45% of the cycle at a constant rate of 60/min. There was, however, a significant increase in perfusion pressures when rate was increased from 60 to 150/min at a constant duration of 45%. The model was validated for intrathoracic pressure changes by studying the hemodynamics produced by a thoracic vest (vest CPR) in eight dogs. The vest contained a bladder that was inflated and deflated. Vest CPR changed intrathoracic pressure without direct cardiac compression, since sternal displacement was <0.8 cm. As predicted by the model and opposite to direct cardiac compression, there was no change in perfusion pressures when the rate was increased from 60 to 150/min at a constant duration of 45% of the cycle. Manual CPR was then studied in eight dogs. There was no surgical manipulation of the chest. Myocardial and cerebral blood flows were determined with radioactive microspheres and behaved as predicted from the model of intrathoracic pressure, not direct cardiac compression. At nearly constant peak sternal force (378–426 N), flow was significantly increased when the duration of compression was increased from short (13%–19% of the cycle) to long (40%–47%), at a rate of 60/min. Flow was unchanged, however, for an increase in rate from 60 to 150/min at constant compression duration. In addition, myocardial and cerebral flow correlated with their respective perfusion pressures. Thus vital organ perfusion pressures and flow for manual external chest compression are dependent on the duration of compression, but not on rates of compression of 60 and 150/min. These data are of course similar to those produced by vest CPR, where intrathoracic pressure is manipulated without sternal displacement, and to those predicted for movement of blood by intrathoracic pressure changes. These data are, however, opposite to those produced by cardiac deformation and to those predicted for movement blood by direct cardiac compression. We conclude that intrathoracic pressure fluctuations generate blood flow during manual CPR.     

The Validity of the Neale and Kendler Model-Fitting Approach in Examining the Etiology of Comorbidity

Given that knowledge regarding the etiology of comorbidity between disorders can have a significant impact on research regarding the classification, treatment, and etiology of the disorders, the ability to reject incorrect hypotheses regarding the causes of comorbidity is very important. A simulation study was conducted to assess the validity of the Neale and Kendler (1995) model-fitting approach in examining the etiology of comorbidity between two disorders. First, data were simulated under the assumptions of the 13 alternative comorbidity models described by Neale and Kendler. Second, model-fitting analyses testing the comorbidity models were conducted on the simulated datasets. Thirteen sets of data with varying model parameters were simulated to test Neale and Kendler's assertion that their model-fitting approach is appropriate across a range of potential prevalences and degrees of familiality. The validity of the model-fitting approach in examining unselected twin data and a combination of selected family data and unselected family data was explored. The model-fitting approach successfully discriminated several classes of comorbidity models, although discrimination between models within classes of related models was less accurate. Results suggest that the model-fitting approach can be a useful tool in examining the etiology of the comorbidity between disorders if the caveats of the present study's results are considered carefully. As predicted by Neale and Kendler, variations in the disorder prevalences and familial correlations did not affect the validity of their model-fitting approach, but affected the power to discriminate the correct model. As suggested by Neale and Kendler, the model-fitting approach can be applied to both unselected and selected data and to both twin and family data.