Mathematical Models at Multiple Scales for Perineural Invasion in HNSCC

Objectives: Perineural invasion (PNI) is the phenotype in which tumor cells surround and enter nerves. PNI is associated with recurrence and metastasis of head and neck squamous cell carcinoma (HNSCC). Recent studies have demonstrated a mechanism by which HNSCC can induce neurite outgrowth towards itself: when stimulated by the neuropeptide galanin (Gal), the tumor secretes Gal, which leads to neurite outgrowth towards the tumor. In order to gain an understanding of the distances, spatial arrangements, and temporal sequences of these events, we must understand the parameters that control these features. The goals of this study were to develop mathematical models to simulate the spatiotemporal and chemical interaction of neurites and tumors based on in vivo studies, and to develop simple models for the effects of PNI on patient survival. These models could clarify which parameters dictate the dynamics of PNI in vivo and with respect to survival.
Methods: We simulated the mechanism of PNI by developing a hybrid model, which models Gal dynamics with a reaction-diffusion equation and neurites with a biased-random walk. The biased random walk incorporates several biological features of neurite outgrowth. We developed a simple compartmental model of HNSCC patient survival based on nerve/tumor-associated variables.
Results: The mechanistic model captures qualitative features of PNI. We performed a sensitivity analysis to demonstrate that uncertainty in biological parameter values can have a significant impact on the mechanistic model outputs. Using the survival model, we predicted what additional clinical data would be needed to estimate the rates of disease progression with respect to neural involvement.
Conclusions: Our models capture features of PNI at the mechanistic and patient survival scales. Our sensitivity analyses identify biologically relevant parameters that need additional experimental study: our results indicate that further biological research is needed to refine our understanding of the mechanisms of PNI, especially to elucidate spatiotemporal dynamics.