Poster H4 - Mathematical modeling to optimize response to combination radiotherapy and immunotherapy in a murine model of lung cancer

Friday, October 25, 2024

3:30 PM - 4:30 PM EST

Location: Exhibit Hall E, F & G

Presenting Author(s)

CD

Cade M. Dulaney

Summer Intern at the University of Texas' Oden Institute
Texas A&M University
Austin, Texas, United States

Co-Author(s)

BS

Bhanu Sharma (he/him/his)

Researcher
The University of Texas at Austin
Baytown, Texas, United States
SJ

Steve Jiang

Researcher
The University of Texas Southwestern Medical Center, United States
RT

Robert Timmerman

Researcher
The University of Texas Southwestern Medical Center, United States
MS

Michael Story

Researcher
The University of Texas Southwestern Medical Center, United States
DS

Debabrata Saha

Researcher
The University of Texas Southwestern Medical Center, United States
TA

Todd Aguilera

Researcher
The University of Texas Southwestern Medical Center, United States
DN

Dan Nguyen

Researcher
The University of Texas Southwestern Medical Center, United States
SR

Samiha Rouf

Researcher
The University of Texas Southwestern Medical Center, United States
EB

Emily Brooks

Researcher
The University of Texas Southwestern Medical Center, United States
CF

Cheryle Fisher

Researcher
The University of Texas Southwestern Medical Center, United States
JS

Jennifer Staples

Researcher
The University of Texas Southwestern Medical Center, United States

Primary Investigator(s)

Thomas Yankeelov, PhD

Professor
The University of Texas at Austin, United States

Last Author(s)

Ernesto A B F Lima, PhD (he/him/his)

Research Associate
The University of Texas at Austin, United States

Introduction: The challenge of determining the optimal dosing and scheduling of PULSAR (Personalized Ultrafractionated Stereotactic Adaptive Radiotherapy) combined with a single-agent immune checkpoint therapy is crucial for improving patient outcomes. Currently, there is a lack of mathematical models that utilize in vivo data to inform model parameters which is central to enhancing a model’s ability to accurately capture tumor growth and response to treatments. In this study, we aim to develop a mathematical model that accurately reproduces experimental data and provides interpretable insights into the coupling of PULSAR and immune checkpoint blockade. Using data from experiments with mice, we calibrate the models and optimize the treatment protocols, identifying the optimal combinations of radiotherapy and immunotherapy.

Materials and

Methods: The data consist of mice injected with Lewis Lung Carcinoma, divided into four treatment protocols over three rounds of studies: control (n = 8 or 9 per round), immunotherapy (n = 8 or 9), radiotherapy (n = 8 or 9), and radiotherapy combined with immunotherapy (n = 8 or 9). Tumor volumes were obtained by caliper measurements approximately every three days at four to nine time points.
Given the tumor volume data over time, our goal was to develop a model with minimal parameters that could accurately capture tumor behavior. Towards that end, we developed a system of three ordinary differential equations to describe the effects of radiotherapy, immunotherapy, and their combination on tumor volume. Tumor volume was assumed to increase exponentially, with decreases due to cell death from therapies and an additional term for combined therapy effects. The radiotherapy effect is highest immediately after each dose and then diminishes over time. A similar equation was developed to capture the effects of immunotherapy. Using a Bayesian framework, we calibrated our model through a staggered approach: first to control and immunotherapy data, followed by radiotherapy data, and finally the combination therapy. This allowed us to systematically isolate and capture the different therapeutic effects by quantifying them as probability distributions for each parameter. Once the complete model was calibrated, we developed an optimization framework treating radiotherapy and immunotherapy administration as continuous control variables. Our objective function minimized the final tumor volume and the total amount of administered therapies.

Results, Conclusions, and Discussions: Results
We calibrated parameters including tumor cell growth rate, death rates due to radiotherapy, immunotherapy, their combination, and the decay rates of both therapies. Immunotherapy alone had minimal effect and was excluded from further modeling. Radio- and combination therapy impacted tumor growth. Figure 1 shows model predictions against all 17 treatment scenarios. The model accurately predicted tumor responses except for the protocol requiring four doses of fifteen grays of radiation—the highest dose in all protocols. The predictions achieved a mean concordance correlation coefficient (CCC) and mean absolute percentage error (MAPE) of 0.81 ± 0.28 and 55.01 ± 58.90, respectively. Given the model’s accuracy, we used it to optimize treatment protocols to outperform experimental protocols. Table 2 presents final tumor volumes for each scenario predicted based on optimized and experimental protocols. The optimized protocol significantly reduced tumor volume (p = 0.004) in 8/17 scenarios. The mean difference was 241.41 ± 161.17 mm³ when the optimal protocol performed better, and 72.33 ± 27.99 mm³ when the experimental protocol performed better.
Conclusions
We developed a model capable of accurately predicting tumor behavior under radiotherapy combined with immunotherapy in a murine lung cancer model. Immunotherapy alone had modest efficacy, but combined with PULSAR, it reduced tumor burden. Using optimal control theory, we developed treatment protocols that outperformed current protocols in nearly 50% of scenarios.
Discussion
Optimal, individualized treatment protocols depend on a mathematical model accurately predicting tumor response to treatments. This study produced such a model, demonstrating its predictive capability across various protocols. The model allowed us to design protocols that matched or significantly (p = 0.004) reduced tumor volume compared to standard treatments. Limitations include the model’s inability to predict responses to high radiation doses and the assumption that therapies can be delivered continuously, which is clinically impractical. Ongoing work focuses on developing a framework and numerical methods to identify an optimal discrete dosing schedule.

Acknowledgements (Optional):