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

Abstract

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.

Computational modeling of locoregional recurrence with spatial structure identifies tissue-specific carcinogenic profiles

“…These findings are in agreement with bulk sequencing data that shows the accumulation of cancer-related mutations as we age ( 32 ). A 2-step tumor initiation model provides insights into the relationship between different tissue kinetic parameters and the incidence of recurrent cancers ( 33 ) by using public datasets from the cancer genome atlas (TCGA), a valuable resource for genomic and clinical data analysis ( 34 , 35 ) but fails to account the varying number of mutational hits required for carcinogenesis ( 36 – 38 ). The cancer genome atlas (TCGA) is a rich computational resource for the genomic and mutational data for different cancer types ( 34 , 35 ) and will be helpful in validating our understanding of field cancerization.…”

“…Particularly, we focused on the relationship between the tissue compositions at the time of surgery and the time until the emergence of recurrent tumors. This model builds upon our previous work ( 33 ) by expanding the number of mutation steps for carcinogenesis via adding cell types as well as incorporating the spatial structure setting. Moreover, based on the public clinical datasets for locoregional recurrence rates, we succeeded in identifying tissue-specific carcinogenic parameters for various cancer types.…”