Kirschner, Panetta, 1998

Model Status

This model has been recoded using the nondimensionalized equations. This was suggested by the author to help with solving the problem, due to its very stiff nature. Some but not all output from the paper can be reproduced by this model. Values of s1 and s2 have been set to zero to represent a non-treatment situation. A value of 0.025 has been given to the variable c, which defines the antigenicity of the tumour, to represent the middle of the range given for this parameter. The model may be re-parameterised to give other relevant outputs, for example, if s1 is greater than 0 while s2 equals 0, the model can simulate adoptive cellular immunotherapy. This version is known to run in PCEnv and COR, and passes all unit checks (being non-dimensionalized).

Model Structure

Cancer is one of the leading causes of death in the world, yet little is understood about the mechanisms which underlie its establishment and destruction. While surgery and/or chemo- and radiotherapy are an important part of treating cancer, they do not represent an 100% effective cure, and often patients will experience a relapse. There is a great motivation to find preventative measures and more effective treatment strategies for cancer, and efforts are being channeled into immunotherapy. Immunotherapy refers to the use of cytokines in the treatment of cancer.

Cytokines are protein hormones that mediate both natural and specific immunity. They are mainly produced by activated T lymphocytes during cellular mediated immune responses. Interleukin-2 (IL-2) is the main cytokine responsible for lymphocyte activation, growth, and differnetiation. It is produced by CD4⁺ (or helper) T cells and to a lesser extent, by CD8⁺ (or cytotoxic) T cells. Because IL-2 acts on the same cells that produce it, it is referred to as an autocrine growth factor, although it can also act on nearby T cells, making it a paracrine growth factor. In clinical trials, IL-2 has been shown to enhance CD8⁺ T cell activity at different disease stages. Also, natural killer (NK) cell activity is restored and CD4⁺ and CD8⁺ T cell populations expand.

Adoptive cellular immunotherapy (ACI) refers to the injection of cultured immune cells that have anti-tumour activity into a patient with a tumour. Large amounts of IL-2 are also introduced in one of two ways:

1) LAK-(lymphocyte-activated killer cell) therapy - These cells are derived from in vitro culturing with high concentrations of IL-2 of peripheral blood leukocytes removed from patients with tumours. The LAKs are then injected back into the patient at the cancer site. These cells are mainly thaought to be NK cells.
2) TIL-(tumour infiltrating lymphocyte) therapy - These cells are derived from lymphocytes recovered from the patient's tumours. They are then incubated with high concentrations of IL-2 in vitro and are comprised of activated NK cells and CD8⁺ T cells. They are then injected back into the patient at the tumour site.

Kirschner and Panetta use ideas from pre-existing mathematical models of tumour-immune dymanics and combine them in the simple model shown in the figure below. They define three populations:

1) the activated immune system cells, which include CD8⁺ T cells, macrophages and NK cells, and are called effector cells;
2) the tumour cells; and
3) the concentration of IL-2.

The mathematical model describes the interactions between the effector cells, tumour cells and the cytokine IL-2.

The complete original paper reference is cited below:

Modeling immunotherapy of the tumor - immune interaction, Denise Kirschner and John Carl Panetta, 1998, Journal of Mathematical Biology , 37, 235-252. (A PDF version of the article is available to subscribers on the Journal of Mathematical Biology website.) PubMed ID: 9785481