Mathematical Modeling of Locoregional Recurrence Caused by Premalignant Lesions Formed Before Initial Treatment

Locoregional recurrence after surgery is a major unresolved issue in cancer treatment. Premalignant lesions are considered a cause of cancer recurrence. A study showed that premalignant lesions surrounding the primary tumor drove a high local cancer recurrence rate after surgery in head and neck cancer. Based on the multistage theory of carcinogenesis, cells harboring an intermediate number of mutations are not cancer cells yet but have a higher risk of becoming cancer than normal cells. This study constructed a mathematical model for cancer initiation and recurrence by combining the Moran and branching processes in which cells require two specific mutations to become malignant. There are three populations in this model: (i) normal cells with no mutation, (ii) premalignant cells with one mutation, and (iii) cancer cells with two mutations. The total number of healthy tissue is kept constant to represent homeostasis, and there is a rare chance of mutation every time a cell divides. If a cancer cell with two mutations arises, the cancer population proliferates, violating the homeostatic balance of the tissue. Once the number of cancer cells reaches a certain size, we conduct computational resection and remove the cancer cell population, keeping the ratio of normal and premalignant cells in the tissue unchanged. After surgery, we considered tissue dynamics and eventually observed the second appearance of cancer cells as recurrence. Consequently, we computationally revealed the conditions where the time to recurrence became short by parameter sensitivity analysis. Particularly, when the premalignant cells' fitness is higher than normal cells, the proportion of premalignant cells becomes large after the surgical resection. Moreover, the mathematical model was fitted to clinical data on disease-free survival of 1,087 patients in 23 cancer types from the TCGA database. Finally, parameter values of tissue dynamics are estimated for each cancer type, where the likelihood of recurrence can be elucidated. Thus, our approach provides insights into the concept to identify the patients likely to experience recurrence as early as possible.