Consequences of the existence of a double afferent system (2).

<p>The correctness of the hypothesis that the pain threshold is higher when triggered by Aδ-fibers than when triggered by C-fibers has other implications. <b>- A</b> When one considers the temporal evolution of the temperature of the skin during the application of thermal stimuli of various intensities, one must take into account the two afferent systems. The relationship AT = f(t_R) comprises two components, namely AT_A = f(t_RA) and AT_C = f(t_RC), respectively. These are hyperbolic functions with t = Lψ_A and t = Lψ_C as vertical asymptotes and T = Tψ_A and T = Tψ_C as horizontal asymptotes, respectively. The respective domains of heating curves that provide responses elicited by Aδ- and C-fibers are shown as blue and red areas. The two components can be seen in terms of squared temperature variations (right graph). The relationship ΔAT² = f(t_R) are hyperbolic functions with t = Lψ_A and t = Lψ_C as vertical asymptotes and T = ΔTψ_A² and T = ΔTψ_C² as horizontal asymptotes respectively. In both graphs, the transition is determined by the borderline case (“_AC”) represented in purple, for which the reaction is triggered at the very same moment by C- and Aδ-fibers (t_RA = t_RC = t_RAC). <b>- A</b>’ One can predict the existence of two singular points of coincidence for the heating curves when these are settled on the reaction: the points of coordinates [−Lψ_A, Tψ_A] and [−Lψ_C, Tψ_C]. When the curves are linearized by expressing the results in terms of square of differences of temperature (right graph), these curves cross each other at two points of coordinates [−Lψ_A, ΔTψ_A²] and [−Lψ_C, ΔTψ_C²]. In both graphs, the transition is determined by the borderline case shown in purple. <b>- B</b> Corresponding ΔAT² = f(α) relationships. The intercepts and the slopes of these 2 linear functions represent ΔTψ_A², ΔTψ_C² and Lψ_A, Lψ_C, respectively. From ΔTψ_A² and ΔTψ_C², one can easily deduct the psychophysical thresholds Tψ_A = T₀+(ΔTψ_A²)^0,5 and Tψ_C = T₀+(ΔTψ_C²)^0,5. <b>- C</b> The corresponding t_R = f(1/α) relationships lead to the same values, the intercepts and the slopes of these 2 linear functions representing Lψ_A, Lψ_C and ΔTψ_A², ΔTψ_C², respectively.