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

【摘要】 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 simula- tions 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 expo- nent-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.更多还原

【Abstract】 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 simula- tions 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 expo- nent-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.更多还原