血液中酒精浓度的数学模型

把人体对酒精的吸收、排放简化为一般的房室模型,提出了吸收因子、消除因子的概念.针对短时间饮酒、长时间饮酒以及间断饮酒等情况,分别建立了关于人体体液中酒精浓度的微分方程模型,并且给出了显式解.对于特殊的周期性间断饮酒的模型,给出了更便于计算的叠加公式,并通过分析酒精浓度函数的极限过程,证明了其有界性.对短时间饮酒和长时间饮酒的情况分别计算了酒精浓度的最大值、取得最大值的时间和禁止驾车的时间范围,而且进行了比较,所得结论与实际吻合.

Mathematical Models of Alcohol Consistency in Blood

In this article,the courses of absorption and excretion of alcohol through bodies is simplified to general house models,and the conceptions of absorption factor and excretion factor are defined.For short-time drinking,long-time drinking and disconnected-time drinking,the corresponding differential equations models are designed,for which the apparent solutions are given,respectively.For special disconnected-time drinking model,An overlay formula more easy to calculate is offered,and the corresponding function of alcohol consistency is proved to be bounded by analyzing its limit process.For short-time drinking and long-time drinking models,the maximum values of alcohol consistency,the times that the maximum values of alcohol consistency reach and the time ranges in which driving are prohibited are computed respectively and are compared each other,the results from which are identical with realities.