Investigation of Pulp Pressure Dynamics by Modeling the Topical Application of 50% Lidocaine HCl in the Human Premolar
LaViolette, Aaron K.; Furness, Samuel P.; Rodriguez, Alexander; Alamgir, Ashab S.
The purpose of this research is to perform a time study on local anesthetics in dental surgery to provide insight on the inner workings pulp pressure dynamics. The dynamics of the pulp pressure when the dentin surface is exposed to atmospheric conditions are currently not understood. Verifying the ability of a high drug concentration to overpower the tooth’s pressure gradient will provide evidence of a unique phenomenon in which diffusion overcomes fluid flow and uncover the physics of drug transport in the tooth. Quantifying this physics is the goal of this paper. The time for a tooth to lose and regain sensitivity was measured with finite element modeling in COMSOL Multiphysics ® version 5.3. This model was built based on a clinical study which shows that the high concentration of lidocaine used (50% w/v or 500 mg/mL) was strong enough to overcome the natural pressure gradient from the pulp to the outside air. The clinical study reported that patients lost tooth sensitivity between 20 and 30 minutes and regained tooth sensitivity between 50 and 60 minutes. Within the tooth, there are three distinct layers: enamel, dentin, and pulp. Inside of the pulp, there are blood vessels which cause degradation of the lidocaine and nerve endings which lose sensation upon binding to lidocaine. In the clinical study, a 3 mm diameter hole was drilled 3 mm deep through the enamel exposing the dentin layer (modeled at the center to retain axisymmetric geometry). The model used the mass transport and Darcy’s Law equations to model the physical situation. Drug application was modeled with 10 minutes of drug exposure in the hole followed by hydrated gauze. Pressure was modeled with an exponential pressure decay with varying time constants. The time constant was optimized to find which physical pressure situation produced results closest to the results of the clinical study. This was accomplished using an objective function which assigned penalties to each time constant based on whether the tooth was numb and sensitive at the appropriate times found during the clinical study. This gave a value for a time constant. Sensitivity analysis was run on parameters approximated from the literature. After sensitivity analysis, sensitive parameters were varied and new optimizations were run to produce a range of values for the time constant. This report found that tooth pulp pressure can be modeled with first order decay upon dentin exposure to atmospheric conditions. The decay was found to be governed by a time constant of 7 minutes and 5 seconds. After sensitivity analysis and variation of sensitive parameters, the time constant was found to fall in a range of 5 minutes and 15 seconds to 9 minutes and 25 seconds. The pressure dynamics were found to be particularly sensitive to hydraulic conductivity of pulpal fluid in dentin, and diffusivity of lidocaine in dentin. This paper offers a glimpse into the poorly understood pressure dynamics in a tooth during dental surgery. It is reported that bulk fluid movement from pressure in human dentin produces solvent drag or the effect of slowing inward diffusive flux of exogenous solutes. The quantitative description of these pressure effects is important for future medical applications and understanding this evolutionary phenomenon. Future research directions include first finding exactly accurate parameters by experimentation to fine tune the model. Also, using a 3D geometry with different drilled hole placements could produce a more accurate description of the process.
Lidocaine, Tooth Pulp Pressure, Dentin, Oral Surgery, Dentistry