本文主要探討二筆實際的資料，並運用基礎之四個空腔的PBTK 模型(Leung,
1992; Tomas et al 1996)描述化學物質在身體內的運行機制，接著應用貝氏架構與
MCMC 方法(Gelman 1996; Bois 1996)求出PBTK 模型的參數並同時求得外在的
曝露濃度，首先探討的化學物質為三氯乙烯(TCE; Trichloroethylene)，資料來自
Fisher et al. (1998)的文章，包含一群健康的自願實驗對象，實驗過程曝露在50ppm
與100ppm TCE 下四小時，詳細紀錄血液與尿液中化學物質的濃度，我們先利用
血液中的TCE 濃度推估當時的暴露濃度與PBTK 體內參數，接著再推廣探討只
利用單筆血液資料與多筆尿液資料的推估；第二筆討論的資料來自Wang et al
(1996)的文章，化學物質為苯乙烯(Styrene)，由資料中觀察得知，資料中的誤差
項同時包含量測誤差與過程誤差，我們將PBTK 模型先簡化成為單個空腔的模
型，並將化學物質濃度隨時間變化的常微分方程式(Ordinary differential
equation;ODE)轉化成隨機微分方程式(Stochastic differential equation; SDE)討論。

Physiologically based toxicokinetic (PBTK) modeling has been well established
to study the distributions of chemicals in target tissues. In addition, to address the
uncertainties in model parameters and inter-individual variability in PBTK models,
the hierarchical Bayesian statistical approach using Markov Chain Monte Carlo
(MCMC) simulations has been successfully applied for parameter estimation. Thus,
employing PBTK models would be a highly plausible way to estimate the constant
inhalation exposure concentration using hierarchical Bayesian approaches.
In this dissertation, we first discuss the estimations of parameters for PBTK model
and exterior exposure. By treating the exterior exposure as an unknown parameter of a
four-compartment PBTK model, we apply MCMC simulations to obtain the posterior
distributions of the exposure and other model parameters with prior information from
the literature. Next, considering stochastic variations to the toxicokinetic model, the
solution to the resultant stochastic differential equation (SDE), together with
measurement error, is transformed into a dynamic linear state-space model. The
proposed method is used in the analysis of the styrene data (Wang et al. in Occup
Environ Med 53:601–605, 1996) to backward estimate the exterior exposure.

第一章 前言
1.1 研究動機 1
1.2 本文架構 3
第二章 應用MCMC 方法估計PBTK 模型參數與外在暴露濃度:以三氯乙烯為例
2.1 統計模型的建立 4
2.1.1 四個空腔的PBTK 模型 4
2.1.2 HBF 與MCMC 方法 7
2.1.3 TCE 靜脈濃度資料來源 10
2.1.4 先驗分配與參數 11
2.2 量測血液濃度資料的MCMC 模擬結果 12
2.2.1 估計外在曝露濃度模擬結果 12
2.3 外在暴露濃度隨時間變化 16
2.3.1 模擬當外在暴露濃度隨時間變化時的估計結果 16
2.4 尿液樣本 V.S. 血液樣本 17
2.5 討論量測值只有單筆血液資料 18
2.6 單筆血液資料與多筆尿液資料 19
2.6.1 TCE 的代謝過程 19
2.6.2 TCOH 與TCOG 的代謝 20
2.6.3 尿液中TCOG 資料來源 22
2.6.4 模擬流程 22
2.6.5 應用累積TCOG 尿液濃度與單一血液量測 22
2.7 綜合討論 27
第三章 應用MCMC 與state space 方法估計PBTK 模型參數與外在暴露濃度:以Styrene 為例
3.1 簡化四個空腔的PBTK 模型為單個空腔的模型 29
3.2 state-space模型 31
3.3 應用state-space模型的MCMC 模擬結果 33
3.3.1 苯乙烯資料模擬結果 35
3.3.2 過程誤差與量測誤差的模擬討論 38
第四章 結論 43
附錄 SIR演算法 45
Metropolis-Hasting 演算法 46
吉柏司樣本法(Gibbs Sampler) 46
MCMC收斂檢驗 46
符號表 47
參考文獻 48

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