Dynamic response of cancer under the influence of immunological activity and therapy.
The dynamical basis of tumoral growth has been controversial. Many models have been proposed to explain cancer development. The descriptions employ exponential, potential, logistic or Gompertzian growth laws. Some of these models are concerned with the interaction between cancer and the immunological system. Among other properties, these models are concerned with the microscopic behavior of tumors and the emergence of cancer. We propose a modification of a previous model by Stepanova, which describes the specific immunological response against cancer. The modification consists of the substitution of a Gompertian law for the exponential rate used for tumoral growth. This modification is motivated by the numerous works confirming that Gompertz's equation correctly describes solid tumor growth. The modified model predicts that near zero, tumors always tend to grow. Immunological contraposition never suffices to induce a complete regression of the tumor. Instead, a stable microscopic equilibrium between cancer and immunological activity can be attained. In other words, our model predicts that the theory of immune surveillance is plausible. A macroscopic equilibrium in which the system develops cancer is also possible. In this case, immunological activity is depleted. This is consistent with the phenomena of cancer tolerance. Both equilibrium points can coexist or can exist without the other. In all cases the fixed point at zero tumor size is unstable. Since immunity cannot induce a complete tumor regression, a therapy is required. We include constant-dose therapies and show that they are insufficient. Final levels of immunocompetent cells and tumoral cells are finite, thus post-treatment regrowth of the tumor is certain. We also evaluate late-intensification therapies which are successful. They induce an asymptotic regression to zero tumor size. Immune response is also suppressed by the therapy, and thus plays a negligible role in the remission. We conclude that treatment evaluation should be successful without taking into account immunological effects.