Thermal Load and Heat Transfer in Dental Titanium Implants: An Ex Vivo-Based Exact Analytical/Numerical Solution to the ‘Heat Equation’

Introduction: Heat is a kinetic process whereby energy flows from between two systems, hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating during bone-cutting and drilling for titanium (Ti) implant-site preparation and insertion, thereby preventing/minimizing early (as well as delayed) implant-related complications and failure. Objective: Given the low bone–thermal conductivity whereby heat generated by osteotomies is not effectively dissipated and tends to remain within the surrounding tissue (peri-implant), increasing the possibility of thermal-injury, this work attempts to obtain an exact analytical solution of the heat equation under exponential thermal-stress, modeling transient heat transfer and temperature changes in Ti implants (fixtures) upon hot-liquid oral intake. Materials and Methods: We, via an ex vivo-based model, investigated the impact of the (a) material, (b) location point along implant length, and (c) exposure time of the thermal load on localized temperature changes. Results: Despite its simplicity, the presented solution contains all the physics and reproduces the key features obtained in previous numerical analyses studies. To the best of our knowledge, this is the first introduction of the intrinsic time, a “proper” time that characterizes the geometry of the dental implant fixture, where we show, mathematically and graphically, how the interplay between “proper” time and exposure time influences temperature changes in Ti implants, under the suitable initial and boundary conditions. This fills the current gap in the literature by obtaining a simplified yet exact analytical solution, assuming an exponential thermal load model relevant to cold/hot beverage or food intake. Conclusions: This work aspires to accurately complement the overall clinical diagnostic and treatment plan for enhanced bone–implant interface, implant stability, and success rates, whether for immediate or delayed loading strategies.