房室模型的建模与仿真

Linear compartmental model:
一切速率系数 Kij 及
K
（
0i
i,
j
1,2,,
n
j
;
i j ）都不依赖于任何
xi (i 1,2,,n)
Non – linear compartmental model:
至少有一个速率系数 Kij（i, j 1,2,, n j ; i j）依赖于 xi (i 1,2,, n)
房室模型的发展背景
Physiological models were build for analyzing absorption（吸收), distribution and elimination（排除）of ethyl ether (无水乙醚)
(Haggard, 1920).
Pharmocokenetic model
Basic principles were laid down by Teorell (1937).
Compartment (Sheppard, 1948)
f10
1
K2
1
f20 K3
2
2
K0
K2Байду номын сангаас
3
2
3
K0
3
Fig. 8.1 药物动力学房室模型
药物动力学系统的房室模型
The classical compartment models have been very useful for the determination of the time course of concentrations (浓度） if sufficient concentration measurements were available. Mathematical methods for solving ordinary differential equations (e.g. Laplace transforms) are used to obtain explicit equations which can be fitted to data or which are used to simulate kinetics. Methods have been provided to account for various clinical drug application routes .
本章内容
8.1 房室模型系统的基本概念 8.1.1 房室的定义 8.1.2 房室间物质转运的速率系数 8.1.3 房室系统的分类
8.2 房室模型的建模 8.2.1 房室模型的建模思路 8.2.2 房室模型的建模
8.3 房室模型的仿真 8.3.1 一房室模型 8.3.2 二房室模型 8.3.3 多房室模型
➢ 具有固定的容量, 在每一时刻在房室内部都含有均匀分布的单一物质； ➢ 各房室之间可以进行物质（能量）交换, ➢ 外环境可以和一个或多个房室进行物质（能量）交换; ➢ 系统中各物质的交换服从物质（能量）守恒定律： 即在任一时刻，系统中物质（能量）的改变等于输入总量和输出总量之差。
Compartmental model is a simplification of the real system.
环境向第i个房室的 输入速率 (M/T)
第i个房室转运至第j个
fi0
房室的速率系数 (1/T)
Kji
Xi(t), Vi
Xj(t) , Vj
Kij
K0j
第j个房室向环境的 排泄速率系数(1/T)
8.1.3 房室模型的分类
➢ Linear and Non-linear compartmental model
➢ Time-invariant and time-variant compartmental model
Time invariant compartmental model
一切速率系数 Kij（ i, j 1,2,, n j ; i j ）均与时间 t 无关，即不是时间的函数。
Time variant compartmental model
X1(t), V1
X2(t), V2
K12
can be obtained by output
K02 e.g. urine (尿)
The concentration in the twoocuotmpartments are different.
f10 — 根据不同的给药方案,具有不同的表达方式。
生物系统房室模型举例
8. 1 Basic Concepts of Compartmental Model
房室模型的基本概念
8.1.1 房室模型与房室的定义 Compartment model is a system of a finite number of macroscopic
subsystems, each subsystem is defined as a compartment.
➢ In pharmocokinetics —— 确定最佳的用药方案，预测药效。
e.g. 羧苄青霉素静脉输液
选用 two compartment model: Blood and Kidney
in f10
unknown K21
o – environment f10 – external input
同一系统可能有不同房室模型: 房室个数根据药物特性和所研究问题要求决定。
8.1.2 房室间物质转运的速率系数
设 n 个房室组成的系统,在 t 时刻第 i 个房室的物质为xi(t) ( i = 1, 2, ……,n)。
各个房室的物质转运速率为 kji, 表示为从第 i 个房室到第j个房室。
设环境为 0, 输入为 f i0
In metabolism (新陈代谢) system Glucose metabolism (糖尿病患者体内糖代谢动态规律）
Model with 2-13 compartments Non-linear model: Kij are functions of Xi ，i.e. Kij(x)； Time varying model: Kij are functions of time t, i.e. Kij(t) In blood dialysis —— artificial kidney