Mathematical Model and Ratiocination of Optimal Molecular Pathways in Hepatocellular Carcinoma

肝癌的分子標靶治療：簡化的理想數學模式及其推論

黃武雄(Wu-Shiung Huang) ； 楊彰師(Chang-Hsu Yang) ； 陳耀森(Yaw-Sen Chen)

《南臺灣醫學雜誌》 5卷2期 (2009/12) Pp. 54-60

https://doi.org/10.6726/MJST.200912_5(2).0001

摘要

目的：分子標靶治療是目前針對末期癌症的最新治療方式。我們嘗試簡化以尋求理想的數學模式用以解釋複雜的致肝癌過程，並且希望能推論一些想法以增進肝癌治療的研究及了解。方法：假定肝癌是由n個分子標靶路徑所組成。每種路徑在肝癌形成過程均有相同且獨立的影響，並且個別路徑本身都能形成肝癌。因此，所有可能產生肝癌的情形將有（2n-1）種情況。另一個假設是：末期肝癌是種較複雜的情形，它必須由m種路徑所組成（m≤n-1）。因此，在此情況下若它必須含有某一特定路徑的情形則有Ym種情況。Ym=C^(n-1)m-1 + C^(n-1)m+ C^(n-1)m+1+ - - -。合理的治療反應率=Ym/(2n-1)。結果：當n=6，m=3，Y3=26時，最符合目前的臨床數據。另一個可能是n=8，m=4，Y4=99（但它不符合Sorafenib phase II的partial/minor response rate數據）。這結果告訴我們：末期肝癌至少必須包含三個以上的分子標靶路徑才得以形成。而且末期肝癌占所有肝癌的2/3 (67%)。藉此數學模式，當我們用N種精準的標靶藥物治療肝癌，可求得最大的治療效應約為[1- (1/2)^N] x 100%。當使用1、2或3種合併精準的標靶藥物治療，它的治療效率將分別是41-51%、59-76%及65-90%不等。結論：肝癌的形成機制可能是六個分子路徑的排列組合。合併兩種精準的標靶藥物治療將可得最佳的治療效果。倘若考慮藥物價格及副作用， 使用≥四種以上的合併藥物治療將無法增加效益。

關鍵字

致肝癌過程 ； 分子標靶治療 ； 肝細胞癌

並列摘要

Objective: Molecular targeted therapy is currently the new treatment modality for advanced cancer. We tried to calculate by an ideal simplified mathematical model to simplify the complex hepatocarcinogenesis and highlight its ratiocination to offer some ideas in hepatocellular carcinoma treatment.Methods: We assumed these pathways had equal, independent impacts on hepatocarcinogenesis, which was made of n molecular pathways and every pathway can result in hepatocellular carcinoma by itself. All the hepatocellular carcinoma would have 2n-1 conditions. If the carcinogenic processes of advanced hepatocellular carcinoma needed ≧ m pathways, and this one molecular targeted therapy could completely block this hepatocarcinogenesis, then all the conditions would be Ym=C^(n-1)m-1 + C^(n-1)m+ C^(n-1)m+1+ - - - (m≦n-1). The reasonable response rate was γm=Ym/2n-1.Results: When n=6, m=3, Y3=26 the calculated result was close to present clinical data. It indicated that the advanced hepatocellular carcinoma needed at least 3 molecular pathways. If we combined N key molecular targeted therapy, the maximal response rate would be ~ [1- (1/2)^N] x 100%. The response rates of 1, 2 or 3 combined key molecular targeted therapy would be 41-51%, 59-76% and 65-90% respectively.Conclusions: By this simplified calculation, hepatocellular carcinoma might be made from 6 theoretical molecular pathways. Two differently combined key molecular targeted therapy would have the best effect in hepatocellular carcinoma treatment, and ≥ 4 key molecular targeted therapy couldn't increase the more benefits if we consider drugs cost and side effects.

並列關鍵字

hepatocarcinogenesis ； molecular targeted therapy ； hepatocellular carcinoma