The growth dynamics of tumor subject to both immune surveillance and external therapy intervention

• Published in: Chinese science bulletin 2007-06, Vol.52 (12), p.1635-1641
• Main Authors: Shao, YuanZhi, Zhong, WeiRong, Wang, FengHua, He, ZhenHui1, Xia, ZhongJun
• Format: Article
• Language: English
• Subjects: 免疫监视; 外部治疗; 生长动力学; 肿瘤学; 逻辑模型
• ISSN: 1001-6538; 1861-9541
• DOI: 10.1007/s11434-007-0234-9

Considering the growth of tumor cells modeled by an enzyme dynamic process under an immune surveillance, we studied in anti-tumor immunotherapy the single-variable growth dynamics of tumor cells subject to a multiplicative noise and an external therapy intervention simultaneously. The law of tumor growth of the above anti-tumor immunotherapy model was revealed through numerical simulations to the relevant stochastic dynamic differential equation. Two simulative parameters of therapy, i.e., therapy intensity and therapy duty-cycle, were introduced to characterize a treatment process similar to a tumor clinic therapy. There exists a critical therapy boundary which, in an exponent-decaying form, divides the parameter region of therapy into an invalid and a valid treatment zone, respectively. A greater critical therapy duty-cycle is necessary to achieve a valid treatment for a lower therapy intensity while the critical therapy intensity decreases accordingly with an enhancing immunity. A primary clinic observation of the patients with the typical non-hodgekin＇s lymphoma was carried out, and there appears a basic agreement between clinic observations and dynamic simulations.