凝血系统中蛋白C抑制模型的周期解

蛋白Ｃ的抑制作用对凝血系统是非常重要的．对其深入研究发现当正负反馈同时发生时系统存在极限环．本文对极限环的存在性给出了严格的数学证明．此即说明凝血系统中存在着生物节律,这在医学上有着深远的意义．     

A Mathematical Model of the Human Respiratory Control System

The respiratory system exhibits the properties of a control system of the regulator type. Equations describing this biological control system have been derived. Transient and steady-state solutions for various CO₂ and O₂ step input disturbances were obtained utilizing a digital computer and are compared with experimental results. The effectiveness of the respiratory system as a regulator is investigated. Further extensions of the model are suggested.     

A Mathematical Model of the Calvin Cycle: Analysis of the Steady State

A complete steady-state solution of a recently published mathematicalmodel of the Calvin photosynthesis cycle is obtained in termsof the rate constants of the cycle and certain conservationrules. By means of analytical and numerical tests, the steadystate is shown to be effectively stable over a wide range ofinitial conditions and parameter values. Other properties ofthe steady state, such as its variation with the rate of carbondioxide fixation, are also discussed. Mathematical model, Calvin cycle, photosynthesis, steady state, stability analysis     

A Mathematical Model of the Human Metabolic System and Metabolic Flexibility

In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the postprandial state and predominantly fats in the fasted state. Many of the pathways involved with human metabolism are controlled by insulin and insulin-resistant states such as obesity and type-2 diabetes are characterised by a loss or impairment of metabolic flexibility. In this paper we derive a system of 12 first-order coupled differential equations that describe the transport between and storage in different tissues of the human body. We find steady state solutions to these equations and use these results to nondimensionalise the model. We then solve the model numerically to simulate a healthy balanced meal and a high fat meal and we discuss and compare these results. Our numerical results show good agreement with experimental data where we have data available to us and the results show behaviour that agrees with intuition where we currently have no data with which to compare.     

A Simplified Mathematical Model and Simulations of the Hypophysis-Ovarian Endocrine Control System

The dynamic relationship between the follicle stimulating hormone of the hypophysis and the estrogenic hormone of the ovaries is investigated. A mather matical model for this system is proposed, which unlike previous models, includet the growing follicle as an explicit part of the model. The size of this estrogen-producing follicle is postulated as a determining factor in the periodicity of the system. Simulation of this simplified piece-wise linear model yields solutions which are persistent and periodic. In addition, the results are in good agreement with known physiological data. The results also suggest that the modeling approach is extremely useful in understanding the changes in the system's behavior caused by alterations in its parameters, whether produced by disease or therapeutic measures.     

凝血、纤溶和纤维化与慢性乙型肝炎病毒感染状态的关系

目的:探究凝血、纤溶和纤维化与慢性乙型肝炎病毒感染状态的关系。方法:选取我院收治的慢性乙型病毒肝炎患者120例,经检测后将患者分为免疫清除组40例、免疫耐受组40例、非活动性组40例和对照组40例,分别检测每组患者的凝血功能、纤溶和纤维化的水平以及统计与感染状态的相关程度。结果:与对照组相比,其余各组凝血功能降低(P0.05),纤溶和纤维化水平明显升高(P0.05);与非活动组和免疫耐受组相比,免疫清除组患者的各项指标变化明显(P0.05);非活动组与免疫耐受组相比各项指标大多无统计学差异(P0.05);经统计凝血、纤溶和纤维化与HBV具有相关性,凝血功能与HBV呈负相关,纤溶与HBV呈正相关,纤维化与HBV呈正相关。结论:患者慢性乙型肝炎病毒感染状态不同,其凝血、纤溶和纤维化水平含量有明显差异,可作为疾病发展的监测依据,临床上值得推广。     

A Mathematical Model of the Tuberculosis Epidemic

Acta Biotheoretica - Tuberculosis has continued to retain its title as “the captain among these men of death”. This is evident as it is the leading cause of death globally from a single...     

The Blood Platelet as a Model for Regulating Blood Coagulation on Cell Surfaces and Its Consequences

Platelets actively participate in regulating thrombin production following physical or chemical injury to blood vessels. Injury to blood vessels initiates activation of the large numbers of platelets that appear in the subendothelium where they become exposed to tissue factor and to molecules adhesive for platelets and normally found in the extracellular matrix. The complex of plasma factor VIIa with extravascular tissue factor both initiates and localizes thrombin production on platelets and on extravascular cells. Thrombin production at these sites in turn enhances platelet activation and the subsequent hemostatic plug formation to minimize bleeding. Thrombin production and platelet activation also initiate the process of wound healing requiring thrombin-dependent cell activation and platelet-dependent formation of new blood vessels (angiogenesis). Activated platelets release from their storage granules several proteins and other factors that regulate local thrombin formation and the responses of blood vessel cells to injury to assure hemostasis and effective wound healing. Failure to localize and adequately regulate thrombin production and/or platelet activation can have pathological consequences, including the development and propagation of atherosclerosis and enhancement of tumor development. The primary basis for the pathological consequences of the failure to adequately regulate thrombin production is that the multi-functional thrombin activates several types of cells to initiate their mitogenesis. Mitogenesis precedes many of the undesirable consequences of poorly regulated thrombin production and platelet activation. In addition, activated platelets release a variety of products which influence the functions of several cell types to the extent that inadequate regulation of platelet activation (by excessive thrombin production) could contribute to the pathogenesis of acute and chronic arterial thrombosis and to tumor development. Activated platelets participate in tumor development by releasing several factors that positively (and negatively) regulate blood vessel formation.     

Disposition of Mulberry Pollen in the Human Respiratory System: A Mathematical Model

Inhaled particle deposition sites must be identified to effectively treat human airway diseases. We have determined distribution patterns of a selected aeroallergen, mulberry pollen, among human extrathoracic (ET: i.e., oronasopharyngeal) regions and the lung. A predictive model validated by inhalation exposure data from human subjects was utilized. Deposition locations were primarily functions of (1) mulberry particle parameters (geometric size, 11–18 μm; shape, spherical; and density, 1.14 g cm^?3), and (2) mode of breathing. In the general population, two styles of inhalation are prevalent, normal augmentors (NAs) and mouth breathers (MBs). Their clinical definitions are based on intra-ET airflow divisions. For a NA-mode breathing sedentary (minute ventilation = V_E = 10 L min^?1) adult, 93% of inhaled mulberry pollen was removed by the ET compartment and 7% collected within the lung. For a MB, the respective deposition efficiencies were 75% and 25%. To apply the model, we used a daily springtime mulberry pollen concentration of 1748 grains m^?3 and an exposure time of 0.5 hour to calculate actual doses for the respiratory system. Under the stipulated conditions, a MB would inhale 524 pollen grains per day and 131 would be deposited in the lung; the value is 37 grains for a NA. Preliminary epidemiological results suggest 15% of the study population are MBs in whom such pollen deposits are likely contributors to airway disease.     

A Computational Model of the Circulating Renin-Angiotensin System and Blood Pressure Regulation

The renin-angiotensin system (RAS) is critical in sodium and blood pressure (BP) regulation, and in cardiovascular-renal (CVR) diseases and therapeutics. As a contribution to SAPHIR project, we present a realistic computer model of renin production and circulating RAS, integrated into Guyton’s circulatory model (GCM). Juxtaglomerular apparatus, JGA, and Plasma modules were implemented in C ++/M2SL (Multi-formalism Multi-resolution Simulation Library) for fusion with GCM. Matlab^© optimization toolboxes were used for parameter identification. In JGA, renin production and granular cells recruitment (GCR) are controlled by perfusion pressure (PP), macula densa (MD), angiotensin II (Ang II), and renal sympathetic activity (RSNA). In Plasma, renin and ACE (angiotensin-converting enzyme) activities are integrated to yield Ang I and II. Model vs. data deviation is given as normalized root mean squared error (nRMSE; n points). Identification: JGA and Plasma parameters were identified against selected experimental data. After fusion with GCM: (1) GCR parameters were identified against Laragh’s PRA-natriuresis nomogram; (2) Renin production parameters were identified against two sets of data ([renin] transients vs. ACE or renin inhibition). Finally, GCR parameters were re-identified vs. Laragh’s nomogram (nRMSE 8%, n = 9). Validation: (1) model BP, PRA and [Ang II] are within reported ranges, and respond physiologically to sodium intake; (2) short-term Ang II infusion induces reported rise in BP and PRA. The modeled circulating RAS, in interaction with an integrated CVR, exhibits a realistic response to BP control maneuvers. This construction will allow for modelling hypertensive and CVR patients, including salt-sensitivity, polymorphisms, and pharmacotherapeutics.     

入口流动条件下血管壁运动的数学模型

根据血管入口流动条件,从血液流动、血管壁运动、血液－血管壁耦合运动３个方面出发,推导出血管生运动的教学模型．通过理论分析与实例计算,进一步明确了模型的物理意义．     

A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

A Mathematical Model of the Pancreatic Ductal Epithelium

A mathematical model of the HCO⁻ ₃-secreting pancreatic ductal epithelium was developed using network thermodynamics. With a minimal set of assumptions, the model accurately reproduced the experimentally measured membrane potentials, voltage divider ratio, transepithelial resistance and short-circuit current of nonstimulated ducts that were microperfused and bathed with a CO₂/HCO⁻ ₃-free, HEPES-buffered solution, and also the intracellular pH of duct cells bathed in a CO₂/HCO⁻ ₃-buffered solution. The model also accurately simulated: (i) the effect of step changes in basolateral K⁺ concentration, and the effect of K⁺ channel blockers on basolateral membrane potential; (ii) the intracellular acidification caused by a Na⁺-free extracellular solution and the effect of amiloride on this acidification; and (iii) the intracellular alkalinization caused by a Cl⁻-free extracellular solution and the effect of DIDS on this alkalinization. In addition, the model predicted that the luminal Cl⁻ conductance plays a key role in controlling both the HCO⁻ ₃ secretory rate and intracellular pH during HCO⁻ ₃ secretion. We believe that the model will be helpful in the analysis of experimental data and improve our understanding of HCO⁻ ₃-transporting mechanisms in pancreatic duct cells. Received: 18 October 1995/Revised: 5 July 1996