广义线性乳突模型的通解及其指数估计

GENERAL SOLUTION OF GENERALIZED LINEAR MAMMILLARY MODELS AND THE RANGE OF THEIR EXPONENTIAL VALUES

多室模型药物的经时过程可以用指数多项式来表征。尽管猜想这些指数“似乎”都是非正实数,但对指数范围的实情并不明确。本文证明了所有指数都位于负半平面上,然后给出了一个具有虚指数的三室模型的例子,最后提出了一类对药物的体内动态具有更广泛代表性的广义n室线性乳突模型,药物可以按任何速度特征进入该模型中的任何隔室并可按一级消除。用拉普拉斯变换法求出了它的通解。并基于线性代数理论证明了这种模型中的所有指数均为非正实数。

In multicompartment models the time courses of drug can be discribed by exponential polynomials. But the range of exponential values is still not clear although it seems that all exponents are nonpositive real numbers. It was prov- ed that all exponential values are located in the negative semi-plane. An ex- ample of 3-compartment model with imaginary exponents in its polynomials was given. In order to represent drug behavior in body more generally,a generalized N-compartment linear mammillary models were suggested, In the models drug can enter any compartment by any rate charactistic and can be eliminated by first order rate. General equations for this models were derived by Iaplace transform and based on the theory of linear algebra. It was proved that all exponents of this models are nonpositive real numbers.