A mathematical model for drug administration by using the phagocytosis of red blood cells

 A mathematical model for the delivery of drug directly to the macrophages by using the phagocytosis of senescent red blood cells is proposed. The model is based on the following assumption: At time t=0 a preassigned red blood cell population n(0, a)=φ(a), a>0, loaded by the drug, is injected in the blood circulation. Among the cells of that population only those with an age a≧ā (ā=120 days) will be phagocytosed by macrophages. Of course, the lifetime of the drug must be higher than ā. Within the red blood cells it cannot be metabolized, neither can it diffuse through their membranes. The emphasis of the paper is on the mathematical properties and on the formulation of the control problem. Received 15 December 1994; received in revised form 20 July 1995     

Evaluation method for coalmining-based cities ecosystem based on attribute mathematical model with Huainan City as an example

Attributive recognition model of coalmining-based cities ecosystem classification is developed in terms of attributive mathematical theory. Based on the analysis of main causes of coalmining-based cities ecosystem, the city vitality, city structure strength, city resilience ability, service functions and health status are chosen as the criterion indicators of coalmining-based cities ecosystem classification; the attributive measurement functions are constructed to compute the attributive measurement of single indicator and multi-indicator; and the synthetic attributive measurement is calculated by the AHP; the health classification of cities ecosystem are recognized by the confidence criterion. An empirical analysis is made by the proposed model and method, the synthetic evaluation results are better than fuzzy comprehensive evaluation method which validates the proposed model feasible, effective and reliable in coalmining-based cities ecosystem classification. As attributive recognition theory can success fully resolve certain issues with a number of fuzzy attribution in comprehensive evaluation, its confidence criterion is established on the basis of the ordered evaluation sets, consequently it will make the evaluation results more reliable.     

基于层次分析法的旗舰物种遴选方法

旗舰物种是保护生物学中一个广泛应用的概念, 用于获得公众对保护行为的支持, 在生物多样性保护领域发挥着重要作用。但目前尚未见量化分析遴选和确定旗舰物种的公开报道, 致使学术界对旗舰物种的定义和使用相对主观, 缺乏科学依据。本文对旗舰物种的定义进行了梳理, 探讨了旗舰物种的内涵, 确定了旗舰物种的属性, 制定了遴选标准和量化遴选方法, 以便读者更好地理解和运用这一概念。目前旗舰物种的定义仍然局限在其社会学属性, 作者建议今后应加强其生物生态学属性。作者认为除了公众的关注度和认可度之外, 旗舰物种还应具备以下3个生态生物学和社会文化特征: (1)物种在当地的濒危程度及生存现状; (2)物种在当地生态系统中的重要性; (3)物种在当地民众中的影响力和认可度。基于此, 本文确定了表征旗舰物种社会文化属性和生态生物学属性的8个要素, 基于层次分析法提出了一种量化的旗舰物种遴选方法。该方法综合上述8个要素进行评判和计算分值, 以塔吉克斯坦境内分布的14种大型濒危哺乳动物的生态生物学属性和社会文化影响力为基础, 描述基于层次分析法遴选塔吉克斯坦哺乳类旗舰物种的方法和过程, 最终依据每个备选物种所得分值高低排序, 得到塔吉克斯坦旗舰物种的优先备选物种。本文首次提出了一种量化遴选旗舰物种的方法, 期望今后可基于该方法开发更加合理的旗舰物种遴选模型和算法。     

A balance control model of quiet upright stance based on an optimal control strategy

Models of balance control can aid in understanding the mechanisms by which humans maintain balance. A balance control model of quiet upright stance based on an optimal control strategy is presented here. In this model, the human body was represented by a simple single-segment inverted pendulum during upright stance, and the neural controller was assumed to be an optimal controller that generates ankle control torques according to a certain performance criterion. This performance criterion was defined by several physical quantities relevant to sway. In order to accurately simulate existing experimental data, an optimization procedure was used to specify the set of model parameters to minimize the scalar error between experimental and simulated sway measures. Thirty-two independent simulations were performed for both younger and older adults. The model's capabilities, in terms of reflecting sway behaviors and identifying aging effects, were then analyzed based on the simulation results. The model was able to accurately predict center-of-pressure-based sway measures, and identify potential changes in balance control mechanisms caused by aging. Correlations between sway measures and model parameters are also discussed.     

A perturbation method for the analysis of impulse propagation in a mathematical neuron model

A perturbation method is presented for the calculation of signal propagation velocities in a mathematical neuron model. Impulse frequencies and waveforms are also determined. The method uses a non-linear conduction model containing a small parameter, such that analytical solutions are possible, yet the inherently non-linear physiological phenomena involved, can be explained. A simple two-variable membrane equation is used, but the method is generally applicable to various more complete systems.     

基于归一化法的小麦干物质积累动态预测模型

为探讨基于归一化法的不同分蘖力小麦品种干物质积累动态预测模型和参数特征,实现不同小麦品种干物质积累的有效预测,以3个分蘖力不同的小麦品种(豫麦49-198、兰考矮早8和偃展4110)为材料,对3个密度(75、225和375万株/hm2)下的干物质积累动态进行了研究。结果表明,高成穗率小麦品种(豫麦49-198和偃展4110)的干物质重均以375万株/hm2密度最高,而分蘖力高成穗率低的小麦品种(兰考矮早8)以225万株/hm2最高。建立的基于相对干物质积累量和相对积温的干物质积累预测模型中最佳模型方程式为y=1.1435/(1+e0.2776-4.6558 x)1/0.1130,r=0.9927,可较好地对小麦干物质积累动态进行模拟。通过对小麦干物质积累模型的特征参数分析发现,干物质积累过程可划分为前、中和后期3个阶段,且干物质积累平均速率与最终干物质重呈极显著正相关,较高的干物质积累平均速率对小麦干物质重的稳定和提高都有十分重要的作用。     

A mathematical high bar–human body model for analysing and interpreting mechanical-energetic processes on the high bar

The aims of this study were:

1. To study the transfer of energy between the high bar and the gymnast.

2. To develop criteria from the utilisation of high bar elasticity and the utilisation of muscle capacity to assess the effectiveness of a movement solution.

3. To study the influence of varying segment movement upon release parameters.

For these purposes a model of the human body attached to the high bar (high bar–human body model) was developed. The human body was modelled using a 15-segment body system. The joint-beam element method (superelement) was employed for modelling the high bar. A superelement consists of four rigid segments connected by joints (two Cardan joints and one rotational–translational joint) and springs (seven rotation springs and one tension–compression spring). The high bar was modelled using three superelements. The input data required for the high bar–human body model were collected with video-kinematographic (50 Hz) and dynamometric (500 Hz) techniques. Masses and moments of inertia of the 15 segments were calculated using the data from the Zatsiorsky et al. (1984) model. There are two major phases characteristic of the giant swing prior to dismounts from the high bar. In the first phase the gymnast attempts to supply energy to the high bar–human body system through muscle activity and to store this energy in the high bar. The difference between the energy transferred to the high bar and the reduction in the total energy of the body could be adopted as a criterion for the utilisation of high bar elasticity. The energy previously transferred into the high bar is returned to the body during the second phase. An advantageous increase in total body energy at the end of the exercise could only be obtained through muscle energy supply. An index characterising the utilisation of muscle capacity was developed out of the difference between the increase in total body energy and the energy returned from the high bar. A delayed and initially slow but even reduction of hip and shoulder angles provided more advantageous release conditions. The total body energy could be improved by up to 15%, the vertical CM release velocity by up to 10% and the angular momentum by up to 35%.     

A mathematical analysis of a model for tumour angiogenesis

In order to accomplish the transition from avascular to vascular growth, solid tumours secrete a diffusible substance known as tumour angiogenesis factor (TAF) into the surrounding tissue. Neighbouring endothelial cells respond to this chemotactic stimulus in a well-ordered sequence of events comprising, at minimum, of a degradation of their basement membrane, migration and proliferation. A mathematical model is presented which takes into account two of the most important events associated with the endothelial cells as they form capillary sprouts and make their way towards the tumour i.e. cell migration and proliferation. The numerical simulations of the model compare very well with the actual experimental observations. We subsequently investigate the model analytically by making some relevant biological simplifications. The mathematical analysis helps to clarify the particular contributions to the model of the two independent processes of endothelial cell migration and proliferation.     

A mathematical model for selective differentiation of neural progenitor cells on micropatterned polymer substrates

The biological hypothesis that the astrocyte-secreted cytokine, interleukin-6 (IL6), stimulates differentiation of adult rat hippocampal progenitor cells (AHPCs) is considered from a mathematical perspective. The proposed mathematical model includes two different mechanisms for stimulation and is based on mass-action kinetics. Both biological mechanisms involve sequential binding, with one pathway solely utilizing surface receptors while the other pathway also involves soluble receptors. Choosing biologically-reasonable values for parameters, simulations of the mathematical model show good agreement with experimental results. A global sensitivity analysis is also conducted to determine both the most influential and non-influential parameters on cellular differentiation, providing additional insights into the biological mechanisms.     

A novel dual staining method for identification of apoptotic cells reveals a modest apoptotic response in infarcted mouse myocardium

Confocal scanning laser microscopy was used to investigate the myocardium of control C57BL/6 and plasminogen activator inhibitor 1 knockout (PAI-1KO) mice 3 days following persistent ligation of the left descending coronary artery. Paraffin sections taken from infarcted areas of the left ventricle were stained with antibodies recognizing cardiomyocytes, neutrophils, macrophages and apoptotic cells. In both animal groups, a strong neutrophil response was noted in the infarcted myocardium, with a large proportion of these cells also displaying staining for anti-α-sarcomeric actin in the PAI-1KO animals. Abundant macrophages were also identified in the infarcted regions of both animal groups, forming demonstrable streams at the border region in the C57BL/6 control animals. Surprisingly, only sparse cells from both animal groups were labeled with the apoptotic markers anti-cleaved caspase 3 antibody and anti-single stranded DNA antibody (following formamide treatment). A dual immunostaining protocol was developed to localize both of these apoptotic markers in the same cell. Again, only scattered cells were found displaying both markers in the zones of infarction, suggesting that 3 days of persistent ischemia results in a robust necrotic response, but only a very minor apoptotic response in this mouse model.     

A note on the use of a stochastic mammillary compartmental model as an environmental safety model

Environmental safety testing typically requires procedures for extrapolating from the relatively high experimental to the very low use doses of potentially harmful substances. In the present paper, a stochastic mammillary compartmental model for environmental safety testing is proposed and extrapolation procedures based on its dose-response relationship are developed. The proposed model is a direct generalization of one of the basic safety models, the one-hit model, in that a harmful reaction is assumed to occur if at any time any of the peripheral compartments attains a specified threshold of particles. Consideration of a closed model yields an upper bound on the probability of attaining a certain threshold level, thus providing a conservative procedure for extrapolating to a low dose, while a lower bound obtained from a related open model provides a useful monitoring device as to the sharpness of the upper, bound. The extrapolation procedure is illustrated with simulated data and approximations for initial values are developed.