山东大学：《药物动力学》课程教学资源（PPT课件）第十二章 统计矩原理在药物动力学中的应用（主讲：张娜）

(一)零阶矩 时间零时到t时的药时曲线下面积可由梯形汯计算,则 +○ AuC= Ca 124 AC=yC1+C、)+一n2 12-5

时间零时到t*时的药时曲线下面积可由梯形法计算，则 (一) 零阶矩 12-4  + = 0 AUC Cdt  + = 0 AUC Cdt + C k C* k  + = 0 AUC Cdt C k C* k n i i n i i i C S AUC −t + + = = − =  (t ) 2 C C 1 0 -1 0  + = 0 AUC Cdt  + = 0 AUC Cdt + C k C* k  + = 0 AUC Cdt C k C* k n i i n i i i C S AUC −t + + = = − =  (t ) 2 C C 1 0 -1 0  n i i n i i i C S AUC −t + + = = − =  (t ) 2 C C 1 0 -1 0 12-5  n i i n i i i C S AUC −t + + = = − =  (t ) 2 C C 1 0 -1 0 1  n i i n i i i C S AUC −t + + = = − =  (t ) 2 C C 1 0 -1 0

(二)一阶矩 设在时间t,血药浓度 为C,则血药浓度-时 AUC= Cdt 间曲线下的总面积为 AUC 0-0o o 既然AUC为某种概率 C f(1)= 统计曲线,则其概率 AUc 密度函数为 (0≤t≤+∞)

• 设在时间t，血药浓度 为C，则血药浓度－时 间曲线下的总面积为 AUC 0→∞ 。 • 既然AUC为某种概率 统计曲线，则其概率 密度函数为  + = 0 AUC Cdt AUC C f (t) = (二) 一阶矩 (0  t  +)

(二)一阶矩 阶原点矩为: (数学期望值) L=otf(t)dt + dt AUC

一阶原点矩为： （数学期望值）  + =  0 dt AUC C  t (二) 一阶矩  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k   ( ) + − = x f x dx k k ( ) dt  + − = x f x dx k k ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( ) 0  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( ) 1  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k   ( ) + − = x f x dx k k ( ) dt  + − = x f x dx k k ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k   ( ) + − = x f x dx k k ( ) dt  + − = x f x dx k k ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k   ( ) + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k   ( ) + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k   ( ) + − = x f x dx k k ( ) dt  + − = x f x dx k k ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( ) 0  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( ) 1  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k   ( ) + − = x f x dx k k ( ) dt  + − = x f x dx k k ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k   ( ) + − = x f x dx k k ( ) dt  + − = x f x dx k k ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k   ( ) + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k   ( ) + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t k  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) t  + − = x f x dx k k  ( )  + − = x f x dx k k  ( ) dt  + − = x f x dx k k  ( )

(二)一阶矩 阶原点矩为: dt (数学期望值) 0 AUC l表示药物在体内的平均滞留时间 ( mean residence time,简写为MRT)

一阶原点矩为： （数学期望值） μ表示药物在体内的平均滞留时间 （mean residence time，简写为MRT）  + =  0 dt AUC C  t (二) 一阶矩

(二)一阶矩 因为随机变量药物在体 内的平均滞留时间的概 f()= 率密度函数为 AUC + o tC MRT=U= t cat Jo AUC JO AUC AUC 所以,貸的一阶矩MRT为药物在机体内的 平均滞留时间

（二）一阶矩 • 因为随机变量药物在体 内的平均滞留时间的概 率密度函数为： AUC C f (t) = • 所以，f(t)的一阶矩 MRT为药物在机体内的 平均滞留时间。    +   = =  = = 0 0 0 . . 1 t Cdt AUC dt AUC t C dt AUC C MRT  t