基于耗散结构的肿瘤转移机制的定量研究

目的：肿瘤转移是指恶性肿瘤细胞从原发部位侵入淋巴管、血管或体腔,迁移到其他部位继续生长,形成同样类型的肿瘤的过程。它是制约临床治疗效果的一种恶性生物学行为,也是导致患者死亡的主要原因。因此,诠释肿瘤转移的机制对于治疗肿瘤,提高患者的生存率至关重要。本文从耗散结构角度出发,对肿瘤转移机制给出Schlogl模型分析法,定量解释肿瘤的转移机制。方法：在分析人体肿瘤转移过程中耗散结构特征的基础上,构建了肿瘤转移的Schlogl模型,并对其进行稳定性和非稳定性分析,得出了肿瘤转移过程中的演化规律,从而为肿瘤的治疗提供依据。结果：肿瘤转移的两个阶段：从原发灶肿瘤细胞到极少数肿瘤细胞,及从极少数肿瘤细胞到继发瘤的过程符合Schlogl模型。并且当驱动压力和血液黏度固定时,各组分的沉积的变化方程也符合Schlogl模型给定的位函数方程。当肿瘤转移系统处于稳定时,即作用于肿瘤细胞的压力的合力必须与它上面的粘性合力相平衡,可以找到原发灶肿瘤细胞与继发瘤对应的位函数的解的形式。当肿瘤细胞发生变形,这时肿瘤转移的系统处于非稳定时,这时位函数的解符合尖点突变模型。求位函数的一次导数和二次导数联立并消去x,得到△。如果△〉0则v（x）只有一个极小值,而如果△〈0,则v（x）可以有两个极小值,对应三种状态。说明体系从一个稳定态突变到两个稳定的状态,而且可以找到这时方程对应的三个解。结论：对于稳定性分析,只要找到合适的细胞沉着率,就可以判断肿瘤是原位癌,否则为继发癌。对于非稳定性分析,只要我们找到合适的血液压力梯度和黏度,符合尖点突变模型。当△〉0,是一般正常状态下的转移。△〈0,阴影部分出现两个分支,对应三种状态：肿瘤持续增殖的状态,休眠状态,凋亡状态。

The Quantitative Interpretation of the Tumor Mechanism Based on Dissipative Structure Characters

Objective: Tumor metastasis process is referred to the intrusion of the malignant cells from the primary site into lymphatic,the blood vessels or a body cavity.These malignant cells will migrate to the other areas of the body,continue to grow and form the same type of cancer.A malignant biological behaviour is not only restricted by the clinical effects,but also the main cause of death for patients.Therefore,the interpretation of the tumor metastasis mechanism is very crucial for the treatment of cancer and improvement of survival rate.The dissipative structure has been analyzed and the quantitative interpretation of the tumor mechanism has been obtained in this paper.Methods: On the basis of analyzing the dissipative structure characters of the tumor metastasis,the Schlgl model of tumor metastasis is constructed,and the analysis of the stability and instability for Schlgl model has been carried on.Finally,the evolution of tumor metastasis is obtained,which is useful for the treatment of cancer.Results: Two phases of tumor metastasis,the change of a few tumor cell tumor from the original tumor cells,and the change of the secondary tumor from the tumor cells,are in accordance with the Schlgl model.When the driver pressure and blood viscosity are fixed,it is found that the changes of the components for the sedimentary are in accordance with the function equation given by Schlgl model.When the tumor metastasis system is stable,i.e.,the role of the pressure and viscous force for the tumor cells of are equal,the solution of the corresponding function of original tumor cells and secondary tumor cell,which is used to de scri-be the effect of v(x) has been received.When the tumor cells distorts,which means that the tumor metastasis system is unstable,the solution of the function conforms to being a type of the point mutations.By seeking the derivative and second derivative of the function,the variable x will be canceled from the function,and the variable △ will be obtained.If △>0,the function v(x) has only one minimum,while for △<0,two minimum will be occurred in the function v(x),which is corresponding to three states for the system.The system will change its state from a monostable state to bistable state,and three corresponding solutions will be obtained for the function.Conclusions: For the stability analysis of the model,as long as the right cellular calm rate is found,it can be determined that the tumor is carcinoma in situ,or subsequent carcinoma.For the unstability analysis of the model,when the right blood pressure gradient and viscosity are known,it conforms to the point mutations model.When △>0,it is a normal shift.However,the shaded part appears two branches for △<0,which are corresponding to three states: tumor proliferation of the continuous state,dormancy state,and the apoptosis state.