Peripheral and Central Determinants of a Nociceptive Reaction: An Approach to Psychophysics in the Rat

BACKGROUND: The quantitative end-point for many behavioral tests of nociception is the reaction time, i.e. the time lapse between the beginning of the application of a stimulus, e.g. heat, and the evoked response. Since it is technically impossible to heat the skin instantaneously by conventional means, the question of the significance of the reaction time to radiant heat remains open. We developed a theoretical framework, a related experimental paradigm and a model to analyze in psychophysical terms the "tail-flick" responses of rats to random variations of noxious radiant heat. METHODOLOGY/PRINCIPAL FINDINGS: A CO(2) laser was used to avoid the drawbacks associated with standard methods of thermal stimulation. Heating of the skin was recorded with an infrared camera and was stopped by the reaction of the animal. For the first time, we define and determine two key descriptors of the behavioral response, namely the behavioral threshold (Tbeta) and the behavioral latency (Lbeta). By employing more than one site of stimulation, the paradigm allows determination of the conduction velocity of the peripheral fibers that trigger the response (V) and an estimation of the latency (Ld) of the central decision-making process. Ld (approximately 130 ms) is unaffected by ambient or skin temperature changes that affect the behavioral threshold (approximately 42.2-44.9 degrees C in the 20-30 degrees C range), behavioral latency (<500 ms), and the conduction velocity of the peripheral fibers that trigger the response (approximately 0.35-0.76 m/s in the 20-30 degrees C range). We propose a simple model that is verified experimentally and that computes the variations in the so-called "tail-flick latency" (TFL) caused by changes in either the power of the radiant heat source, the initial temperature of the skin, or the site of stimulation along the tail. CONCLUSIONS/SIGNIFICANCE: This approach enables the behavioral determinations of latent psychophysical (Tbeta, Lbeta, Ld) and neurophysiological (V) variables that have been previously inaccessible with conventional methods. Such an approach satisfies the repeated requests for improving nociceptive tests and offers a potentially heuristic progress for studying nociceptive behavior on more firm physiological and psychophysical grounds. The validity of using a reaction time of a behavioral response to an increasing heat stimulus as a "pain index" is challenged. This is illustrated by the predicted temperature-dependent variations of the behavioral TFL elicited by spontaneous variations of the temperature of the tail for thermoregulation

Psychophysics of a nociceptive test in the mouse: Ambient temperature as a key factor for variation

Background: The mouse is increasingly used in biomedical research, notably in behavioral neurosciences for the development of tests or models of pain. Our goal was to provide the scientific community with an outstanding tool that allows the determination of psychophysical descriptors of a nociceptive reaction, which are inaccessible with conventional methods: namely the true threshold, true latency, conduction velocity of the peripheral fibers that trigger the response and latency of the central decision-making process. Methodology/Principal Findings: Basically, the procedures involved heating of the tail with a CO2 laser, recording of tail temperature with an infrared camera and stopping the heating when the animal reacted. The method is based mainly on the measurement of three observable variables, namely the initial temperature, the heating rate and the temperature reached at the actual moment of the reaction following random variations in noxious radiant heat. The initial temperature of the tail, which itself depends on the ambient temperature, very markedly influenced the behavioral threshold, the behavioral latency and the conduction velocity of the peripheral fibers but not the latency of the central decision-making. Conclusions/Significance: We have validated a psychophysical approach to nociceptive reactions for the mouse, which has already been described for rats and Humans. It enables the determination of four variables, which contribute to the overall latency of the response. The usefulness of such an approach was demonstrated by providing new fundamental findings regarding the influence of ambient temperature on nociceptive processes. We conclude by challenging the validity of using as "pain index" the reaction time of a behavioral response to an increasing heat stimulus and emphasize the need for a very careful control of the ambient temperature, as a prevailing environmental source of variation, during any behavioral testing of mice. © 2012 Pincedé et al

Thermoregulatory vasomotor tone of the rat tail and paws in thermoneutral conditions and its impact on a behavioral model of acute pain

laser-directed to the tail depends on these variations. Consequently, the fluctuations in tail and paw temperature thus represent a serious confound for thermal nociceptive tests, particularly when they are conducted at thermal neutrality

Modeling and simulation of the tail-flick “latency".

<p>t_R = (T_R – T₀)²/α+(D – D_c)/V_t+D_c/V_c+Lδ+Lμ. Taking into account the following relationships T_R = f(T₀), V_t = f(T₀), V_c = f(T_c) and the length D_c = 49 mm, one obtain: t_R = f(α, D, T_c, T₀) = (42,17 – 0.81_*T₀)²/α+(D – 49)/(0.04_*T₀ – 0.44)+49/(0.04_*T_c – 0.44)+Lδ+Lμ (see text). <b>Upper graphs (A, B)</b>: theoretical curves; the blue and red lines are computations for stimulation of two sites on the tail, proximal and distal, 50 and 150 mm from the dorsal root entry zone, respectively. <b>Lower graphs (A’, B’)</b>: corresponding experimental data obtained from eight mice. The numerical values of the parameters used in the equation are shown in the inserts. <b>A. Results of simulations of the variations in the reaction time (t_R or TFL) introduced by varying the power of a radiant heat source (α varying).</b> As expected from the form of the equation, the t_R = f(α) computation produced hyperbolas, with the horizontal asymptote representing L_R (left graph). The right graph shows the relation t_R = f(1/α), which transforms this curve into a linear relationship. The slope and the intercept with the ordinate of the straight line represent (T_R – T₀)² and L_R, respectively. These computations were made for four temperatures of the tail: 20, 25, 30 and 35°C, the last being achieved when the animal dissipates heat by vasodilatation of the tail for any reason. <b>B. Role of basal skin temperature (T₀ varying):</b> theoretical curves made for three α values: 0.5, 1 and 5. <b>A’. Role of heating power (α varying): experimental data</b> and corresponding regression lines obtained from 8 animals are presented for three ranges of skin temperatures T₀, namely 20 (violet), 25 (black) and 35°C (brown). The respective regression equations are shown as an insert. <b>B’. </b><b>Role of basal skin temperature (T₀ varying): experimental data</b> and corresponding regression lines from the same animals are presented for three ranges of heating rate expressed as α, namely 0.5 (violet), 1 (black) and 5 (brown). For an averaged distance D = 100 mm, the reaction time was computed as t_R = f(α, T₀) = 0.656/α_*T₀² – 34.2/α_*T₀+(1781+136.37α)/α+1275/(T₀ – 1.1). The parameters and coefficients of regression were then estimated by a nonlinear least squares fit to the data in the form t_R = a_*T₀² – b_*T₀+c+d/(T₀+e): t_R = 2.37_*T₀² – 209.64_*T₀+4943+208.7/(T₀ – 27.9); t_R = 0.037_*T₀² – 42.03_*T₀+1844 – 151.3/(T₀ – 22.5); t_R = – 0.223_*T₀² – 3.02_*T₀+613 – 35.7/(T₀ – 23.9); for α = 0.5, 1 and 5, respectively (r² = 0.878, 0.686 and 0.661 respectively; p<0.001 for all).</p

Individual example of the behavioral responses elicited by stimulation at three rostro-caudal levels on the tail, 25 mm apart.

<p>The mean temperature of the tail was 24.8 (24.6-25.0)°C. <b>A. Temporal evolution of the temperature of the skin during the application of various powers of stimulation</b> (70-320 mJ) with the time origin being adjusted to the actual moment of triggering of the reaction, T = f(t – t_R), recorded in the center of the heating spot applied on the proximal (a: 25 trials), medial (b: 31 trials) and distal (c: 28 trials) parts of the tail. Note the clear tendency of these curves to cross each other in a privileged zone (open circles) and the progressive shift of this zone backward in time when the stimulation site moved from proximal to distal parts of the tail (white dashed line). <b>B. Relationships between the apparent threshold AT and the slope α</b>, ΔAT² = f(α), calculated for the 3 sites of stimulation. The strong linear relationships provided accurate calculations of T_R and L_R for each level of stimulation (dotted lines: ±95% CI). <b>C. Relationship between the calculated behavioral threshold T_R and the distance D</b> that separated the site of stimulation on the tail from the entry zone in the cord, as obtained from data shown in B. <b>D. Relationship between the calculated behavioral latencies L_R and the distance D</b> that separated the site of stimulation on the tail from the entry zone in the cord, as obtained from data shown in B. L_R was directly proportional to D. The reciprocal of the slope represents the conduction velocity (0.59 m/s) of the fibers that triggered the reaction, in that part of their course which is within the tail.</p

Measurable and calculated variables.

<p>The measurable variables are indicated with a yellow background and variables to be determined are indicated with a blue background. Abbreviations are available in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036699#pone-0036699-t001" target="_blank">Table 1</a>. <b>A. When the skin is exposed to a constant source of radiant heat, the temperature T increases with the square root of time</b> from the initial temperature T₀ according to the law of physics T = T₀+a_*T^0.5 (upper graph) or, expressed in terms of squared temperature variations, ΔT² = [T – T₀)]² = α_*t (lower graph). When a behavioral reaction R occurs, the reaction time t_R is the sum of the time L_p it takes to warm up the skin up to the behavioral threshold T_R (i.e. the true nociceptive temperature threshold) plus the time L_R it takes for the reaction to occur once this threshold has been reached. The first period L_p belongs to the physical and biophysical domains, including heating (Lφ) and transduction (Lτ) processes. During the second period L_R, the temperature of the skin continues to increase up to the apparent temperature threshold AT reached at the time of the reaction. This second period is the latency of the reaction L_R that includes Lπ (the transit time for the spikes to reach the CNS), Lδ (the “decision" time required by the CNS for interpreting and processing this information for an order to be sent to the motor system) and Lμ (the time required for a motor response to be triggered). Overall, four variables are potentially accessible to experimental measurement: T₀, AT, t_R and α (yellow background). The heating process can be described by three key moments: the beginning of stimulation, t = t₀ and T = T₀; the moment of the triggering of the reaction defined by ΔT_R² = (T_R – T₀)² = α_*(t_R – L_R) [<b>equation 1</b>]; the moment of the reaction defined by ΔAT² = (AT – T₀)² = α_*t_R [<b>equation 2</b>]. <b>B. The linear relationship ΔAT² = ΔT_R²+L_R*α [equation 3]</b> is obtained by substituting α_*t_R of equation 2 into equation 1 and is used for extraction of the two variables to be determined (blue background): the intercept and the slope of this linear function represent ΔT_R² and L_R, respectively (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036699#pone-0036699-g004" target="_blank">Fig. 4B</a>). <b>C. </b><b>Theoretical relationship between the distance D, separating the site of stimulation on the tail from the dorsal root entry zone, and the latency of the behavioral reaction L_R</b>. The available experimental data from the tail at T₀ are shown as a blue line (left graph). The reciprocal of the slope of this line corresponds to the conduction velocity V_t of the fibers that triggered the reaction. However, the conduction velocity of these fibers increases when the coccygeal nerves travel through the core of the animal, which is set at T_c by thermoregulatory processes. This second component of the peripheral process is shown in red (right graph). The latency of these two components is Lπ = Lπ_t+Lπ_c = D_t/V_t+D_c/V_c. The intercept y_c = y_t+D_c*(1/V_t – 1/V_c) of the red straight line with the ordinate represents the part of L_R that does not deal with the peripheral processes, i.e. Lδ+Lμ.</p

Spontaneous variations of the temperature of the tail.

<p><b>A. Individual example</b> of the concomitant recordings at 1 Hz of the ambient temperature T_a and 6 points spread out along the rostro-caudal extent of the tail (T₁-T₆, shown on the drawing on the right). Note the spontaneous fluctuations of the temperature (maximum 8°C) of the proximal two-third of the tail. <b>B. Relationship between the ambient temperature T_a and the temperature of the tail at point T₃.</b> Overall effects obtained in 15 mice placed in various ambient temperatures in the 20-32°C range. The blue points were obtained from sequences during which the ambient temperature decreased and included active thermoregulation processes (see an example in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036699#pone-0036699-g009" target="_blank">Figure 9</a>).</p

Overall influence of the levels of stimulation on behavioral thresholds and latencies.

<p>Observations were made on 6 mice with 3 stimulation sites. The mean basal temperature of the skin T₀ was 25.6 (25.0-26.1)°C. <b>A. Relationships between the calculated behavioral threshold T_R and the distance D</b> that separated the site of stimulation on the tail from the entry zone to the cord. On average, the behavioral threshold T_R was 46.7 (45.9-47.5)°C with a non-significant tendency to decrease from the proximal to the distal parts of the tail. <b>B. Corresponding relationships between the calculated behavioral latencies L_R and the distance D</b> that separated the site of stimulation on the tail from the entry zone in the cord (individual and overall regression lines are shown as fine and large lines, respectively). Overall, there was a very significant linear relationship between D and L_R (L_R = 51.2+1.69_*D; F_1-16 = 117.6; p<0.001; dotted lines: ±95% CI). The inverse of the slope of these relationships allowed the calculation of the conduction velocities of the fibers that triggered the reaction: 0.62 (0.47-0,78) m/s.</p

Effects of the ambient temperature on the behavioral responses.

<p>Ambient temperatures were ∼20°C (blue), ∼25°C (green), ∼35°C (red). <b>A. An individual example</b> from a mouse tested three days apart. The L_R = f(D) plots shown in (a) reveal a decrease of the slope when the temperature increased, witness of the increased conduction velocity, itself shown in (b) by the V_t = f(T₀) plot. The effects of the ambient temperature on the behavioral threshold are shown in (c) in terms of T_R = f(T₀) plot. <b>B. Corresponding overall effects</b> from 8 mice. (a) Bundle of overall L_R = f(D) straight lines obtained with various basal temperatures T₀. Note that these lines tend to cross each other in a privileged zone (white open circle) corresponding to the tail-trunk interface where the temperature of the nerves increases from T₀ to the core temperature T_c. The highest density of intersections was located at coordinates D_c = 49 mm and t_Rc = 128 ms. (b) V_t = f(T₀) plot. A highly significant linear relationship was seen: V_t = 0.04_*T₀ – 0.44 (F_19,1 = 59.5; p<0.01; dotted lines: ±95% CI). A mean Q₁₀ = 2.1 (1.9-2.4) between 20 and 30°C was calculated. (c) T_R = f(T₀) plots. A significant linear relationship was seen: T_R = 42.2+0.19_*T₀ (F_19,1 = 9.7; p<0.01; dotted lines: ±95% CI). This indicates that overall the threshold T_R increased as the temperature of the skin increased.</p