A phase-field model for non-small cell lung cancer under the effects of immunotherapy

Abstract

Formulating tumor models that predict growth under therapy is vital for improving patient-specific treatment plans. In this context, we present our recent work on simulating non-small-scale cell lung cancer (NSCLC) in a simple, deterministic setting for two different patients receiving an immunotherapeutic treatment. At its core, our model consists of a Cahn-Hilliard-based phase-field model describing the evolution of proliferative and necrotic tumor cells. These are coupled to a simplified nutrient model that drives the growth of the proliferative cells and their decay into necrotic cells. The applied immunotherapy decreases the proliferative cell concentration. Here, we model the immunotherapeutic agent concentration in the entire lung over time by an ordinary differential equation (ODE). Finally, reaction terms provide a coupling between all these equations. By assuming spherical, symmetric tumor growth and constant nutrient inflow, we simplify this full 3D cancer simulation model to a reduced 1D model. We can then resort to patient data gathered from computed tomography (CT) scans over several years to calibrate our model. For the reduced 1D model, we show that our model can qualitatively describe observations during immunotherapy by fitting our model parameters to existing patient data. Our model covers cases in which the immunotherapy is successful and limits the tumor size, as well as cases predicting a sudden relapse, leading to exponential tumor growth. Finally, we move from the reduced model back to the full 3D cancer simulation in the lung tissue. Thereby, we show the predictive benefits a more detailed patient-specific simulation including spatial information could yield in the future. Author summaryLung cancer is one of the deadliest diseases, with low long-term survival rates. Its treatment is still very heuristic since patients respond to the same treatment plans differs significantly. Therefore, patient-specific models for predicting tumor growth and the treatment response are necessary for clinicians to make informed decisions about the patients therapy and avoid a trial and error based approach. We made a first small step in that direction by introducing a model for simulating cancer growth and its treatment inside a 3D lung geometry. In this model, we represented tumor cells by a volume fraction field that varies over space and time. We described their evolution by a system of partial differential equations, which include patient- and treatment-specific parameters capturing the different responses of patients to the therapies. Our simulation results were compared to clinical data and showed that we can quantitatively describe the tumors behavior with a suitable parameter set. This enabled us to change therapies in simulation runs and analyze how these changes could have impacted the patients health.