Mathematical Modelling and Optimisation of Pembrolizumab Therapy for MSI-H/dMMR Colorectal Cancer

Abstract

Colorectal cancer (CRC), with more than 1.85 million cases and 850,000 deaths annually, is the third most commonly diagnosed cancer and the second leading cause of cancer-related deaths. The microsatellite instability-high (MSI-H) and deficient mismatch repair (dMMR) phenotypes constitute 15% of all CRC and 4% of metastatic CRC, and, while less responsive to chemotherapy than microsatellite stable (MSS) CRC, they exhibit sensitivity to immunotherapy, especially programmed cell death protein 1 (PD-1) checkpoint inhibitors. In particular, immunotherapy often results in complete eradication in locally advanced MSI-H/dMMR CRC (laMCRC), yet only a partial immune response in metastatic MSI-H/dMMR CRC (mMCRC).

This motivates the use of mathematical models to capture the complex interplay of biological processes in MSI-H/dMMR CRC, and we employ a novel framework driven by delay integro-differential equations to mechanistically model laMCRC and de novo mMCRC (dnmMCRC). These models are used to mechanistically analyse factors influencing treatment success and perform treatment optimisation, focusing on pembrolizumab—a widely used PD-1 inhibitor—to balance efficacy, efficiency, and toxicity. In doing so, we demonstrate that a single medium-to-high dose of pembrolizumab may be sufficient for tumour eradication in laMCRC while being efficient, safe and practical. We also propose regimens that may improve upon FDA-approved therapies for dnmMCRC and compare immune dynamics with those in laMCRC.

Finally, we performed sensitivity analysis on the dnmMCRC model using global variance-based methods. We use this to guide model reduction and construct two simplified models of dnmMCRC: one that faithfully reproduces all of the original model’s trajectories, and a second, minimal model that accurately replicates the original dynamics while being highly extensible for future inclusion of additional components to explore various aspects of the anti-tumour immune response.