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

Andreas Wagner; Pirmin Schlicke; Marvin Fritz; Christina Kuttler; J. Tinsley Oden; Christian Schumann; Barbara Wohlmuth; Andreas Wagner; Pirmin Schlicke; Marvin Fritz; Christina Kuttler; J. Tinsley Oden; Christian Schumann; Barbara Wohlmuth

doi:10.3934/mbe.2023828

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 18670-18694. doi: 10.3934/mbe.2023828

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Research article

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

1.
School of Computation, Information and Technology, Technical University of Munich, Munich, Bavaria, Germany
2.
Computational Methods for PDEs, Johann Radon Institute for Computational and Applied Mathematics, Linz, Upper Austria, Austria
3.
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
4.
Clinic of Pneumology, Thoracic Oncology, Sleep and Respiratory Critical Care, Klinikverbund Allgäu, Kempten, Bavaria, Germany

Academic Editor: Russell Rockne

Received: 17 June 2023 Revised: 22 August 2023 Accepted: 23 August 2023 Published: 07 October 2023

Formulating mathematical models that estimate tumor 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. Our model covers the case in which the immunotherapy is successful and limits the tumor size, as well as the case 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 demonstrate the predictive benefits that a more detailed patient-specific simulation including spatial information as a possible generalization within our framework could yield in the future.
- 3D Tumor growth,
- NSCLC,
- immunotherapy,
- phase-field model,
- numerical simulation
Citation: Andreas Wagner, Pirmin Schlicke, Marvin Fritz, Christina Kuttler, J. Tinsley Oden, Christian Schumann, Barbara Wohlmuth. A phase-field model for non-small cell lung cancer under the effects of immunotherapy[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18670-18694. doi: 10.3934/mbe.2023828

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Abstract

Formulating mathematical models that estimate tumor 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. Our model covers the case in which the immunotherapy is successful and limits the tumor size, as well as the case 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 demonstrate the predictive benefits that a more detailed patient-specific simulation including spatial information as a possible generalization within our framework could yield in the future.

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