## 3 Results and Discussion
### System Identification
#### 3.1.3 Modelling of Localized Intermittent Cooling Effect  
During the localised intermittent cooling (Exp.2, Phase II), none of the test subjects that showed the hunting reaction (CIVC/CIVD cycles) during the continuous cooling (Phase I) showed any episodes of CIVD. On the other hand, intermittent cooling induced an episode of CIVC, causing the finger's temperature to drop to the same level reached during continuous cooling (on average, \(16.2\pm 0.7\)\({}^{\circ}\)C) and continued until the end of the experiment. Figure 9 shows an example of the finger's temperature response to intermittent cooling. Additionally, a second-order (with number of poles \(n=2\) and zeros \(m=2\)) discrete-time TF described the dynamic responses of finger skin temperature (CIVC) to a series of cooling pulses (intermittent cooling) in the input (Peltier element's temperature) most accurately (i.e., \(R_{2}^{T}=0.92\pm 0.02\) and \(YIC=-11.67\pm 3.55\)) with same structure as the TF represented by (3). Table 5 shows the resulting average parameter estimates and delays from the identified DTF model describing the CIVC reaction to intermittent cooling.  
Figure 9: The dynamic response (upper graph) of the finger’s temperature (CIVC) to a series of pulses in Peltier’s element temperature (middle graph). Showing the measured and simulated finger’s temperature (upper graph) using a second-order DTF and the model residuals (lower graph).  
Although the finger skin temperature, under intermittent cooling, reached the same level (on average, 16.2 \(\pm\) 0.7 \({}^{\circ}\)C) as that under continuous cooling, the intermittent cooling did not induce reheating of the fingers (i.e., CIVD). This indicates that the temperature to which the skin was cooled is not the only triggering factor for the CIVD. Additionally, it was clear that the vasodilation here (CIVD) is typically transient, which may interrupt the original vasoconstriction. The current work suggests that the rate at which the skin was cooled (rate of dissipated heat from the skin) is one of the main triggering factors, aside from the skin temperature and the duration of cooling [7; 15; 19; 38]. The results showed that all test subjects exhibited the hunting reaction (i.e., episodes of CIVD occurred) during continuous cooling (Exp.2, phase I), when the rate of change in the dissipated heat from skin (\(\frac{dQ_{dis}}{dt}\)) was quasi zero (an example from one test subject is shown in Figure 10). On the other hand, for the same test subjects, under intermittent cooling (Exp.2, Phase II) the rate of change (\(\frac{dQ_{dis}}{dt}\)) oscillated around zero (\(\pm\)0.0016), and no evidence of vasodilation was noticed (an example from one test subject is shown in Figure 11).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{\(A(\mathbf{z}^{-1})\)} & \multicolumn{3}{c}{\(B(\mathbf{z}^{-1})\)} & \multicolumn{3}{c}{\(\mathbf{\delta}\) **(min)**} & \multicolumn{1}{c}{\(\mathbf{R}_{T}^{2}\)} & \multicolumn{1}{c}{\(\mathbf{YIC}\)} \\ \hline \(\mathbf{a}_{1}\) & \(\mathbf{a}_{2}\) & \(\mathbf{b}_{0}\) & \(\mathbf{b}_{1}\) & \(\mathbf{b}_{2}\) & & & \\ \hline \(-\)1.987 & 0.987 & 0.0 & \(-\)0.0016 & 0.0018 & 2.34 & 0.92 & \(-\)11.67 \\ \(\pm\)0.006 & \(\pm\)0.001 & \(\pm\)0.0010 & \(\pm\)0.0010 & \(\pm\)1.21 & \(\pm\)0.02 & \(\pm\)3.55 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average and standard deviation of parameter estimates, \(R_{2}^{T}\) and \(YIC\) of the identified second-order DTF model describing the CIVC reaction to the localised intermittent cooling experiment (Exp.2, Phase II).  
Figure 10: Dynamic response of finger skin temperature (upper graph), dissipated heat rate (\(\dot{Q}_{dis}\), middle graph), and first derivative of the dissipated heat rate (\(\frac{dQ_{dis}}{dt}\), lower graph) to localised continuous cooling obtained from test subject (s5) during the experiment (Exp.2, Phase I).  
The following section of this paper explores the different theories and mechanisms explaining the thermoregulatory CIVC/CIVD reactions.