利用細胞帕茲模型，我們建立了一個關於細胞分化與癌症發展模型。我們假設了細胞分化狀態與其分裂速度、以及細胞間的交互作用有關。利用這樣的模型，我們不只可以模擬胚胎發育過程，還能模擬癌化過程的病理切片下所觀察到的腫瘤結構。在電腦的模擬過程中，我們使用蒙地卡羅原則，利用二維格點分析，使質點可以在所有格點上面做隨機運動。此外，空的格點可以根據其鄰近的質點改變其狀態，用來模擬細胞分裂，並且所有的非零質點狀態皆有機會恢復為空的格點，用來模擬細胞死亡。根據模擬結果，我們發現當腫瘤細胞之間的作用力小於一個臨界點，會造成細胞的大量增生。另外，當細胞之間的作用力增加，會在腫瘤細胞的增生過程中，形成明顯的團狀結構；而當此作用力減小，腫瘤的生長則會形成比較類似擴散狀態的表現。而這些生長表現與腫瘤的預後相關，並可作為臨床病理切片的印證。 By utilizing the generalized cellular Potts model (CPO), we propose a model for both cell differentiation and carcinogenesis. Employing different cell-cell interaction energies, this model can describe different stages of cell differentiations. Cell aggregation and organogenesis during the processes of embryogenesis are simulated in the model by Monte Carlo method. The motions of different types of cells (q states) represent as random walkers on a two-dimensional square lattice. Besides, a vacant site can change its state according to its neighboring cells in order to mimic cell proliferations. And all the cells can have chances to become vacant to mimic cell death. This model can also describe the process of carcinogenesis and other tumorigenesis including both benign and malignant tumors. Our results suggest that there exists critical interaction strength and below which the number of the tumor cells will increase rapidly. Various pattern formations are also observed with different particle interactions, which can be associated to clinical findings. These cells may either aggregate into a cluster or appear more diffusively. These growth patterns relate to tumor prognosis and may provide some hints for further pharmacology design for anti-neoplasm agents.
