Theoretical Study of Retinoblastioma in the Hereditary and Non-hereditary Processes including the Cancer Growth

by Hiroshi Toki, Yoshiharu Yonekura, Yuichi Tsunoyama, and Masako Bando

Knudson’s two-hit hypothesis distinguished hereditary from sporadic cancers, but real-world incidence
often deviates from its predictions. Our 2P2H (two-period, two-hit) model refines this by incorporating
period-specific mutation rates, particularly after the proliferative phase of retinal cells. We propose that
mutation processes differ fundamentally between proliferative and post-developmental stages. Using
differential equations, we model the temporal evolution of mutation accumulation and cancer onset, while
also accounting for diagnostic time lag—a factor absent in Knudson’s theory. The 2P2H model
accurately reproduces observed incidence curves, resolving prior inconsistencies. We believe it provides
a more precise, biologically grounded framework for understanding cancer initiation.

The 2P2H Model.