Fluid mechanics in dentinal microtubules provides mechanistic insights into the difference between hot and cold dental pain

Abstract

Dental thermal pain is a significant health problem in daily life and dentistry. There is a long-standing question regarding the phenomenon that cold stimulation evokes sharper and more shooting pain sensations than hot stimulation. This phenomenon, however, outlives the well-known hydrodynamic theory used to explain dental thermal pain mechanism. Here, we present a mathematical model based on the hypothesis that hot or cold stimulation-induced different directions of dentinal fluid flow and the corresponding odontoblast movements in dentinal microtubules contribute to different dental pain responses. We coupled a computational fluid dynamics model, describing the fluid mechanics in dentinal microtubules, with a modified Hodgkin-Huxley model, describing the discharge behavior of intradental neuron. The simulated results agreed well with existing experimental measurements. We thence demonstrated theoretically that intradental mechano-sensitive nociceptors are not "equally sensitive" to inward (into the pulp) and outward (away from the pulp) fluid flows, providing mechanistic insights into the difference between hot and cold dental pain. The model developed here could enable better diagnosis in endodontics which requires an understanding of pulpal histology, neurology and physiology, as well as their dynamic response to the thermal stimulation used in dental practices.

Figure 1. Physiological relevant structures.

(A) Cut-away image of human tooth; (B) SEM image of dentine showing solid dentine material and dentinal microtubules (DMTs) running perpendicularly from pulpal wall toward dentine-enamel junction . (C) Schematic of DMT innervation system and nerve firing (NF) in response to outward dentinal fluid flow (DFF). Terminal fibril (TF) situated in tubule between odontoblast process and tubule wall . Slightly outward displacement of odontoblastic process (OP) and its cell body (CB) in response to outward flow. The dash line indicates the original position of the odontoblast. The outward movement of the OP reduces the dimension of the channel available for the DFF, resulting in increased shear stress on the terminal bead (TB) although the volume flow is low . (D) Slightly inward displacement of OP in response to inward flow. This movement tends to produce a smaller shear stress on the TB than that at its original position (dash line). (E) Physically realistic model for fluid dynamics simulation (inward flow). d _t, d _p and d _f are diameters of DMT, OP and TF, respectively; R _b is radius of TB; L is computational length. One side of OP surface is in contact with tubular surface , hence no dentinal fluid is allowed to pass through at this side. The TF and OP are modeled as rigid structures that do not deform due to DFF. We assumed that there is no synaptic structure between OP and TF , though different finding has been reported . TB containing varying amounts of receptor organelles is assumed as the sensory zone at the end of TF. The volume of TF is smaller as compared with odontoblast , and hence the movements of TF as caused by DFF is neglectable.

Figure 2. Variation of TB MSS (simulated) and neural discharge rate (measured[4]) as a function of fluid velocity (negative for inward flow; positive for outward flow).

Velocity thresholds: V _c1 = 460.4 µm/s, V _c2 = −849.9 µm/s .

Figure 3. Response of nociceptor membrane potential in cat tooth to flow velocity of ∼611.6 µm/s.

(A) Action potential simulated with the modified H-H model. (B and C) Experimental measurements by Vongsavan & Matthews and Andrew & Matthews , respectively. N is the number of neural impulses in 5 s.

Figure 4. Comparison of frequency response between experimental measurements and model predictions.

Note that cold stimulation (0∼5°C) is reported to cause outward flow velocities range between 531.2∼849.9 µm/s , , whilst hot stimulation (∼55°C) causes inward flow velocities range between 354.1∼779.1 µm/s .