SIAM News Blog

New Form of Immunotherapy May Improve Outcomes of Melanoma Treatment

By Lina Sorg

Melanoma is a complex, aggressive form of skin cancer that originates in the melanocytes, the body’s melanin-producing cells that give skin its color. In its later stages, the tumor is typically resistant to standard treatments—such as surgical excision, radiology, and chemotherapy—and is therefore particularly challenging to manage. It also has a high level of immunogenicity, meaning that the body responds quickly to therapeutic antigens and produces anti-drug antibodies that inactivate treatments and favor tumor growth. Although immunotherapy has proven fairly successful in the treatment of advanced melanoma by helping the immune system recognize and eliminate cancel cells, the associated cost is often prohibitively high. 

During the 10th International Congress on Industrial and Applied Mathematics, which is currently taking place in Tokyo, Japan, Paulo Mancera of São Paulo State University in Brazil generated a mathematical model to explore the effectiveness of an immunotherapeutic treatment called chimeric antigen receptor (CAR) T-cell therapy in combatting advanced melanoma. During CAR T-cell therapy, scientists collect a blood sample to obtain a patient’s T-cells, genetically alter the T-cells in a lab, enable them with CARs, and reintroduce the new CAR T-cells to the bloodstream to more efficiently find and destroy cancer cells

Figure 1. Explanation of chimeric antigen receptor (CAR) T-cell therapy in the treatment of melanoma and other cancers. Figure courtesy of the Cleveland Clinic.
At the request of immunologists, Mancera and his colleagues created a simple model that accounts for CAR T-cell populations in addition to as the effect of tumor-associated macrophages (TAMs): antigen-presenting cells that contribute to the formation of the tumor microenvironment and can promote tumor growth, invasion, metastasis, drug resistance, and immunotherapy failure. Between four and seven percent of all melanoma cells are macrophages.

Despite its simplicity, Mancera’s model includes the following parameters: the natural rate of proliferation of tumor cells; the rate of macrophage proliferation promoted by the tumor; the proliferation rate of CAR T-cells due to contact with the tumor antigen; the tumor proliferation rate due to the pro-tumor action of TAMs; the tumor cell carrying capacity; the TAM carrying capacity; the saturation of CAR T-cell expansion; the tumor cell death rate due to the cytotoxic action of CAR T-cells; the TAM apoptosis (programmed cell death) rate; the rate of apoptosis and immunosuppression of CAR T-cells; and the initial condition of the tumor cells, TAMs, and CAR T-cells. All but three of these parameters come from the literature.

Mancera’s model yielded three equilibrium points. To guarantee the existence of these points, he imposed conditions of existence and observations—as well as linear stability conditions—and evaluated them numerically. He also identified regions wherein equilibrium \(E^*\) exists as either a stable spiral or a stable sink. Mancera then investigated the impact of parameter \(\beta_1\) (the tumor proliferation rate due to the pro-tumor action of TAMs) on the system’s behavior. An increase in this parameter—i.e., an increase in TAMs’ contribution to tumor growth—induces a limit cycle in which solutions oscillate around \(E^*\). In short, changing the parameters alters the system’s overall behavior.

After conducting global sensitivity analysis via Python’s SALib package to determine parameter sensitivity, Mancera introduced the kinetic phases of CAR T-cells:

  • Population decline occurs at the onset of the distribution phase because the cells begin to distribute themselves throughout the tissues.
  • The population expands during the expansion phase after it encounters the tumor antigen.
  • During the contraction and persistence phases, the population declines due to exhaustion and natural cell death.

Mancera then presented several scenarios that evaluate the way in which immunosuppressive effects influence CAR T-cell immunotherapy. When \(\kappa_3\) (the rate of apoptosis and immunosuppression of CAR T-cells) is low, the initial dose of immunotherapy can control the melanoma tumor for a certain amount of time. But when this rate increases, the tumor cell population is no longer reduced to undetectable levels. The same is true for other settings — the tumor cells eventually grow to carrying capacity. Given this result, Mancera considered an ongoing clinical trial as an alternative scenario, delivered the initial application, and simulated applications after seven and 14 days of different immunotherapy doses. He found that this form of cycle immunotherapy extends the capability of tumor control; after 14 days, this clinical trial scenario controlled the number of cancer cells for a longer time than the first two settings. “What you can see in this very simple numerical simulation is that this might be a new way to do CAR T-cell immunotherapy, even though the cost is very high,” he said.

Mancera concluded by affirming the value of CAR T-cell therapy in melanoma cancer cell treatment regimens when combined with other methods, such as radiotherapy. “In our point of view, CAR T-cells must be considered with other kinds of treatment,” he said. “Immunologists should try radiotherapy and then CAR T-cell therapy.”

Lina Sorg is the managing editor of SIAM News.
blog comments powered by Disqus