Tumor-Immune Dosing Models

ISEF Category: Biomedical and Health Sciences

Subcategory: Pathophysiology  ·  Difficulty: Advanced  ·  Setup: University Lab  ·  Time: Full Year

The Hook

Cancer drugs do not act like a light switch. A checkpoint inhibitor can keep changing the system after the dose is gone because the immune response keeps moving. That makes schedule design a math problem, not just a drug problem. Your model can test whether smaller, spaced doses might hold control with less total drug.

What Is It?

Checkpoint inhibitors are cancer drugs that take the brakes off immune cells. In a healthy immune system, checkpoints help stop T cells from attacking the wrong target. In cancer, tumors can exploit those brakes. Your model treats the tumor and immune response like two linked tanks, where one side pushes growth and the other side pushes killing.

A coupled ODE system, or ordinary differential equation system, tracks how those amounts change over time. One equation can represent tumor growth, another can represent immune activation, and a third can represent drug exposure or checkpoint effect. By fitting the model to published trial response curves, you can test whether intermittent dosing, like dose breaks or lower frequency dosing, can keep the tumor in check while using less drug than continuous dosing.

Why This Is a Good Topic

This topic works well for science fair because you can test real schedules without a wet lab. The question connects to cancer therapy, drug cost, and side effects, but the work stays in a student-friendly modeling space. You can learn differential equations, curve fitting, and sensitivity analysis while comparing schedules with clear numbers.

Research Questions

• How does intermittent dosing change the time tumor burden stays below a target compared with continuous dosing?
• What is the effect of the drug-free interval length on peak immune activation and tumor rebound?
• Does a lower total cumulative dose keep the tumor below the same threshold when the response curve is held fixed?
• To what extent do parameter uncertainty bands change the ranking of dose schedules?
• Which schedule gives the best tradeoff between tumor suppression and total drug exposure?
• How does changing the immune killing rate within published ranges shift the best schedule?

Basic Materials

• Laptop or Chromebook with internet access.
• Spreadsheet software such as Google Sheets.
• Python installed through Anaconda or a school device.
• Notebook for assumptions, parameter sources, and model checks.
• Published trial plots or response tables from journal articles.

Advanced Materials

• University workstation or server for large parameter sweeps.
• MATLAB or Python with SciPy, NumPy, pandas, and Matplotlib.
• R or another statistics package for uncertainty analysis.
• Access to journal databases such as PubMed, PubMed Central, or institutional subscriptions.
• Shared clinical response datasets or digitized trial curves from published papers.

Software & Tools

• Python: Solves the ODE system, runs parameter sweeps, and plots schedule outcomes.
• Jupyter Notebook: Keeps code, notes, and figures in one place while you test model choices.
• R: Fits curves, compares schedules, and checks how sensitive your results are to parameter changes.
• Google Sheets: Organizes literature values and lets you do quick sanity checks before coding.

Experiment Steps

1. Define the state variables your model will track, such as tumor cells, active immune cells, and drug effect.
2. Choose one published response curve or digitized dataset to anchor the parameters you fit.
3. Build a baseline schedule first, then change only one dosing feature at a time.
4. Set the outcome metrics you will compare, such as time below target, cumulative dose, and rebound size.
5. Add sensitivity tests so you can see whether the schedule ranking survives reasonable parameter shifts.

Common Pitfalls

• Fitting the model to one curve and then treating the result as universal, which overstates what the data support.
• Mixing parameters from papers that define response points differently, which makes the system hard to compare.
• Optimizing only for tumor shrinkage, which can hide schedules that demand too much cumulative dose.
• Ignoring parameter uncertainty, which makes one schedule look more certain than the evidence allows.
• Starting each schedule from different tumor sizes or immune baselines, which turns a fair comparison into a biased one.

What Makes This Competitive

A strong version of this project does more than pick one best schedule. It checks whether that choice still wins when you change patient-like parameters, starting conditions, and response curves. You can also rank schedules with more than one metric, such as tumor suppression, rebound risk, and total drug exposure. That kind of careful comparison makes the project feel like real treatment design, not just a curve fit.

Project Variations

• Compare PD-1 and CTLA-4 style response curves to see whether the best schedule changes by drug class.
• Start with a continuous schedule, then switch to intermittent dosing after the model reaches a chosen immune activation level.
• Reframe the outcome as dose sparing and rank schedules by tumor control per unit cumulative drug exposure.

Learn More

• PubMed: Search review articles on checkpoint inhibitors, tumor-immune modeling, and dose scheduling.
• PubMed Central: Read free full-text papers on mathematical oncology and immune response models.
• NCBI Bookshelf: Find free textbook chapters on cancer biology, immunity, and ordinary differential equations.
• NCI Dictionary of Cancer Terms: Check plain-language definitions for checkpoint inhibitors and related cancer terms.
• MIT OpenCourseWare: Review differential equations and mathematical modeling basics before you build the system.