A hybrid reaction-diffusion and mechanical stimulus model for mandibular bone remodeling under chewing and vibratory loading

Abstract Bone remodeling in the mandible is governed by the interplay between local mechanical loads, cellular population dynamics, and overload-induced resorption. While mastication is the primary physiological driver of mandibular adaptation, low-magnitude vibration has emerged as a promising noninvasive adjunct to enhance peri-implant bone stability. However, the mechanistic interaction between vibration and chewing-induced stimuli remains insufficiently clarified.This study presents a hybrid mechanobiological model that integrates a reaction--diffusion formulation for osteoblast, osteoclast, and mediator fields with a density evolution law combining adaptive regulation and overload penalization. The framework incorporates accumulated stimulus dynamics, a threshold-regulated lazy zone, and frequency-dependent vibratory modulation of cellular activity. Numerical simulations were performed under controlled physiological and mechanical conditions using spatially resolved density fields and Gaussian-distributed masticatory stresses.The model reproduced the canonical biphasic response of bone adaptation, with an initial anabolic phase followed by stabilization governed by overload-driven resorption. Under chewing alone, density stabilized near 1.02--1.03g/cm3, depending on load magnitude. When vibration was superimposed, a strong frequency-dependent anabolic effect emerged: 40~Hz increased steady-state density by approximately 3.5%, whereas 120Hz produced gains near 10% (0.08--0.10g/cm3), consistent with 80--100HU changes measurable by CBCT. Spatially, mastication alone generated localized densification, while vibration broadened and homogenized the anabolic region, particularly at 120Hz. Cellular simulations revealed accelerated and synchronized reductions in osteoblast and osteoclast populations under vibration, indicating enhanced mechanotransductive efficiency rather than increased metabolic demand. The agreement between simulated density gains, spatial adaptation patterns, and experimental observations demonstrates that the proposed hybrid model captures key mechanobiological features of mandibular adaptation. The framework offers a rigorous and computationally efficient tool for predicting peri-implant bone remodeling under combined masticatory and vibratory stimuli, supporting the development of patient-specific vibration-based therapeutic strategies in oral and maxillofacial biomechanics.