Mathematical modelling of the growth processes in the developing chick wing bud

This paper illustrates how a simple geometric model resembling the shape of the chick wing bud at an early growth stage can be mathematically expanded to simulate subsequent growth characteristics of the developing bud. The model was tested against several sets of experimental data and gave an acceptable representation of growth over the range considered. Representing growth patterns in this form enables the determination of differential growth characteristics in different parts of the bud and provides boundary constraints which will play an important part in the eventual evaluation of internal growth mechanisms.     

Dendritic spines in the visual cortex of the mouse: Introduction to a mathematical model

Summary The spines of apical dendrites of the layer V pyramidal cells of the area striata in the mouse represent a sequence of post-synaptic structures receiving a variety of contacts from terminal fibers derived fundamentally from short axon cells and superficial pyramidal cells. The study of Golgi preparations of mice 180 days old shows the existence of the most complicated terminal structures over portions of apical dendrites at the levels of layers III and IV. Observations on young mice reveals the terminations of the specific afferent fibers on the dendrites of short axon cells. A mathematical model which defines the distribution of spines along the apical dendrites is introduced. The principal equation of the model has been adjusted from the data processing of microscope countings through a series of programs written for an IBM 7070. The equation defines satisfactorily the different distributions of dendritic spines in mice 10–180 days old raised in normal conditions and in complete darkness. The equation defines also the distribution of dendritic spines in the visual cortex of mice enucleated at birth on one side, and the distribution along the apical dendrites of various cortical areas of the hamster, cat and man. The number of dendritic spines increases with the age of the subject and their distribution varies significantly according to the values of the parameters of the model.     

Determination of total body water by multifrequency bio-electric impedance: development of several models

Multifrequency bio-electronic impedance analysis (MF BIA) measurements are taken from a heterogeneous group of patients, varying in size between obese and slim. The measuring system uses four electrodes: two current and two potential electrodes. Three new models are developed to calculate total body water (TBW) from the BIA data, and the resulting TBW values are compared with TBW determined by D₂O dilution. The results demonstrate that the most simple model provides the best TBW values. For individual patients, TBW can be determined by means of bioimpedance measurement with an accuracy of 3 litres. In the most simple model (model 1), the body is electrically represented by a cylinder, and corrections are made for the amount of fat. This is an extension of the model used by Xitron. In the more advanced models (2 and 3), the body is represented by a cylinder for the trunk, and truncated cones represent the arms and legs. In model 2, ΔTBW amounts to 3 litres. It is shown that the resistance of the trunk is proportional to the square root of the length. In model 3, it is assumed that subcutaneous fat is a poor conductor if electric current. An equation is developed that describes the partition of subcutaneous fat, and the fat layer is then removed from the cones representing arms and legs and from the cylinder that models the trunk.     

A tidal ventilation model for oxygenation in respiratory failure

We develop tidal-ventilation pulmonary gas-exchange equations that allow pulmonary shunt to have different values during expiration and inspiration, in accordance with lung collapse and recruitment during lung dysfunction (Am. J. Respir. Crit. Care Med. 158 (1998) 1636). Their solutions are tested against published animal data from intravascular oxygen tension and saturation sensors. These equations provide one explanation for (i) observed physiological phenomena, such as within-breath fluctuations in arterial oxygen saturation and blood-gas tension; and (ii) conventional (time averaged) blood-gas sample oxygen tensions. We suggest that tidal-ventilation models are needed to describe within-breath fluctuations in arterial oxygen saturation and blood-gas tension in acute respiratory distress syndrome (ARDS) subjects. Both the amplitude of these oxygen saturation and tension fluctuations, and the mean oxygen blood-gas values, are affected by physiological variables such as inspired oxygen concentration, lung volume, and the inspiratory:expiratory (I:E) ratio, as well as by changes in pulmonary shunt during the respiratory cycle.     

Haemodynamic model of a unilateral iliac stenosis with an aortoiliac bypass

A hydrodynamic model for the part of the human arterial network below the renal arteries has been constructed using specially fabricated distensible tubes and a pulsatile pump to simulate an aortoiliac bypass. The experiments and the computer model indicated that no ‘steal’ occurred due to the insertion of the bypass graft. Also, the results showed that the length of the stenosis had a non-systematic apparent effect on the physiological significance of the obstruction and that the kinetic power represented only a small percentage of the total power. The total power efficiency of the bypass graft was unaffected by its elastic properties. The experimental investigation also indicated that the pressure drop across the stenosis was considerably larger than the drop calculated using the Poiseuille flow relationship when the stenosis was severe. Therefore, a critical arterial stenosis value cannot be defined as an obstruction of a constant percentage reduction of luminal area. It varies directly with the effective cross-sectional area and inversely with the flow rate. The value of angiography in assessing the functional significance of any arterial stenosis is there-fore limited. A better method for evaluation requires quantitative measurements of local blood pressure and blood flow, not only at rest, but also under conditions creating augmented flows due to exercise.     

A nonlinear model of the arterial vessels within a limb segment

The relationship between the arterial blood pressure and the volume of the arteries within a segment of an extremity is nonlinear. The present paper shows how the flow and volume pulsations of the arteries within a limb segment can be simulated taking this property into account. An electrical model was constructed comprising one resistor and two voltage dependent ‘capacitors’, the latter corresponding to the pressure dependent elasticity, or compliance, of the arteries. Adequate simulations were obtained over a wide pressure range, which is impossible with linear models. The nonlinear, i.e. pressure dependent, relationship between the volume and pressure of arteries, observed under static conditions, must also be taken into consideration when studying pulsatile events with models whether mathematical or physical.     

基于 Shapiro 模型推理算法的智能知识获取在中医知识库中的实现

本文应用现代计算机技术,将Shapiro模型推理算法运用于中医知识库中,使该知识库系统具有智能知识获取的能力.     

Model identification and estimation of organ-function parameters using radioactive tracers and the impulse-response function

Examination of the input-output events in functioning organs by the use of the impulse-response function (IRF) for a radioactive tracer is gaining more and more ground in nuclear medicine. This study summarizes the development of deconvolution analysis, laying special stress on the model-free approach. System linearity and time invariance are discussed, and means of eliminating noise in IRFs originating from the input and organ-time-activity curves are outlined. Typical IRFs are illustrated by flow diagrams, time-domain curves, and their representation by Laplace transforms. The cases of nondiffusible and diffusible tracers as well as parenchymally extracted and transported substances are discussed. Methods for the derivation of models and for the calculation of physiologically important parameters from theIRFs are suggested.At present, a guest scientist at the Institute for Medicine, Nuclear Research Center Jülich, Jülich, Federal Republic of Germany     

A pharmacokinetic approach to the establishment of biopharmaceutic characteristics of different acetylsalicylic acid formulations in man

Eleven acetylsalicylic acid (ASA) formulations were administered to 26 healthy volunteers in a cross-over design. The properties of the preparations differed from conventional, effervescent, buffered to buccal. The objectives of this study were:

• 1 Consideration of the general aspects of a biopharmaceutical study: which parameter for which biopharmaceutic characteristic?
• 2 Measurement of the kinetic parameters of ASA: first-pass effect, mean residence time, mean appearance time, total body clearance, apparent volume of distribution, half-lives, etc.
• 3 Comparison of the formulations.

Most of the formulations yield mean residence times for ASA of 0.3–1.0h, which do not differ significantly (p > 0.05). For most of the products the first-pass effect is about 40 per cent; the average values of the apparent volume of distribution and whole body clearance, corrected for the first-pass effect, are about 201 and 650 ml min^?1, respectively. Peak levels are reached slowly for the buccal formulations, and rapidly for the buffered products. It is difficult, especially for ASA, to characterize the gastro-intestinal absorption with pharmacokinetic model parameters, because the first-pass effect is large and often elimination of ASA is faster than absorption. The model-independent approach has the special advantages of calculating reliable pharmacokinetic parameters, and creating theoretical possibilities to characterize the absorption patterns of the different formulations in a quantitative way. No significant differences in the values of the parameters are found between most of the formulations. The ASA first-pass effect is reasonably constant and buccal application has no advantage. Enteric coating of the outer layer of ASA formulations causes inconsistent absorption and may be categorized under ‘artificial mistakes’.     

病例组合指数的内涵及应用探讨

国内普遍认为病例组合指数(CMI)属于医疗服务能力维度,体现收治疾病的疑难复杂程度和医疗服务的整体技术难度。通过结构方程模型分析发现,CMI与时间消耗指数、费用消耗指数等服务效率维度指标联系更紧密,与DRG组数、入组病例数及总权重等服务能力维度指标联系相对较弱,故应归属医疗服务效率维度。CMI的直接应用主要是对平均住院费用的预测控制及对科室绩效的评价;CMI的间接应用主要是对管理指标的调整/校正。医院管理者应准确把握CMI内涵,恰当应用CMI对不同层级及不同类别住院费用进行预测、评价与控制,并对其他管理指标进行调整后再评价。