  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.
