### Signal processing

QRS complexes in the ECG were detected by using a methodology described in[16]. Instantaneous heart rate was derived by integral pulse frequency modulation (IPFM) model, which also accounts for the presence of ectopic beats[17], and then evenly resampled at 4 Hz, using spline interpolation. Instantaneous heart period was then obtained as the reciprocal of instantaneous heart rate. The heart period variability (HPV) signal, *x*_{H}(*t*), was obtained by high pass filtering the heart period signal with a cut-off frequency of 0.03 Hz. The systolic arterial pressure series was obtained by taking the maximum of the pressure signal within a short interval following a QRS detection. The time series were subsequently interpolated at the time of occurrence of the systolic peak by splines with a sampling frequency of 4 Hz, and the SAPV signal, *x*_{S}(*t*), was obtained by high-pass filtering with a cut-off frequency of 0.03 Hz. The signal from the thoracic belt was decimated to 4 Hz to get the respiratory signal, *x*_{R}(*t*), which gives a measure correlated with instantaneous lung volume.

### Cross time-frequency analysis

In the following, signals {*x*_{i}(*t*),*x*_{k}(*t*)} ∈ {*x*_{H}(*t*),*x*_{S}(*t*), − *x*_{R}(*t*)}, indicate the complex analytical signal representation of HPV, SAPV and inverse respiratory signal, respectively. Owing to the inversion of the respiratory signal, and under physiological conditions, all the members of the triplet {*x*_{H}(*t*),*x*_{S}(*t*),−*x*_{R}(*t*)} are expected to increase and decrease together.

The TF cross spectrum, *S*_{ik}(*t*,*f*), is estimated by using a TF distribution (TFD) belonging to the Cohen’s class[18]:

\begin{array}{ll}{S}_{\text{ik}}(t,f)& ={\iint}_{-\infty}^{\infty}{\varphi}_{\text{d-D}}(\tau ,\nu ){A}_{\text{ik}}(\tau ,\nu ){e}^{j2\Pi (\mathrm{t\nu}-\mathrm{f\tau})}\mathrm{d\nu d\tau}\phantom{\rule{2em}{0ex}}\end{array}

(1)

\begin{array}{ll}{A}_{\text{ik}}(\tau ,\nu )& ={\int}_{-\infty}^{-\infty}{x}_{\text{i}}\left(t+\frac{\tau}{2}\right){x}_{\text{k}}^{\ast}\left(t-\frac{\tau}{2}\right){e}^{-j2\mathit{\text{\Pi \nu t}}}\mathit{\text{dt}},\phantom{\rule{2em}{0ex}}\end{array}

(2)

where *A*_{ik}(*τ* *ν*) is the narrow-band symmetric ambiguity function[19] of signals *x*_{i}(*t*) and *x*_{k}(*t*), that in (1) is windowed by an elliptical exponential kernel, defined in the ambiguity function domain as[13]:

{\varphi}_{\text{d-D}}(\tau ,\nu )=\text{exp}\left\{-\Pi {\left[{\left(\frac{\nu}{{\nu}_{\text{0}}}\right)}^{\text{2}}+{\left(\frac{\tau}{{\tau}_{\text{0}}}\right)}^{\text{2}}\right]}^{\text{2}\lambda}\right\}

(3)

The kernel function *ϕ*_{d-D}(*τ*,*ν*) can be equivalently defined in the TF domain as:

{\varphi}_{\text{t-f}}(t,f)=\underset{-\infty}{\overset{+\infty}{\iint}}{\varphi}_{\text{d-D}}(\tau ,\nu ){e}^{j2\Pi (\mathrm{t\nu}-\mathrm{\tau f})}\mathit{\text{d\tau d\nu}}

(4)

The choice of the kernel function is discussed in Section ‘Time-frequency filtering’.

Time-frequency coherence is estimated as[13]:

{\gamma}_{\text{ik}}(t,f)=\frac{\left|{S}_{\text{ik}}(t,f)\right|}{\sqrt{{S}_{\text{ii}}(t,f){S}_{\text{kk}}(t,f)}};\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}{\gamma}_{\text{ik}}(t,f)\in [0,1]

(5)

Time-frequency coherence quantifies the strength of the local coupling between two non-stationary signals, being *γ*_{ik}(*t*,*f*) = 1 in the TF regions where the signals are perfectly coupled and *γ*_{ik}(*t*,*f*) = 0 in the regions where signals are uncorrelated. Note that in[13] it was shown that the local averaging performed in (1) can be used to estimate non-stationary spectra, whose 4 definition includes expectation over different realizations of a given process. This implies that (5) can be used to estimate coherence function from only one pair of signals. Partial coherence is used to assess the coupling of two signals *x*_{i}(*t*) and *x*_{k}(*t*), after having removed the influence of a third signal *x*_{z}(*t*)[20]. Time-frequency partial coherence can be defined as:

\phantom{\rule{-15.0pt}{0ex}}\begin{array}{c}\phantom{\rule{0.3em}{0ex}}{\gamma}_{\text{ik/z}}(t,f)\hfill \\ \phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}\frac{\left|{S}_{\text{ik/z}}(t,f)\right|}{\sqrt{{S}_{\text{ii/z}}(t,f){S}_{\text{kk/z}}(t,f)}}\hfill \\ \phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}\frac{\left|{S}_{\text{ki}}(t,f){S}_{\text{zz}}(t,f)\phantom{\rule{0.3em}{0ex}}-\phantom{\rule{0.3em}{0ex}}{S}_{\text{kz}}(t,f){S}_{\text{zi}}(t,f)\right|}{\sqrt{\phantom{\rule{0.3em}{0ex}}\left({S}_{\text{kk}}\right(t,f\left){S}_{\text{zz}}\right(t,f)\phantom{\rule{0.3em}{0ex}}-\phantom{\rule{0.3em}{0ex}}|{S}_{\text{kz}}(t,f){|}^{\text{2}}\left)\right({S}_{\text{ii}}(t,f){S}_{\text{zz}}(t,f)\phantom{\rule{0.3em}{0ex}}-\phantom{\rule{0.3em}{0ex}}\left|{S}_{\text{iz}}\right(t,f\left){|}^{\text{2}}\right)}}\hfill \end{array}

(6)

In the TF regions where *x*_{z}(*t*) is uncorrelated with *x*_{i}(*t*) and *x*_{k}(*t*), i.e., wherever *S*_{zi}(*t*,*f*) = 0 and *S*_{zk}(*t*,*f*) = 0, TF partial coherence is equal to TF coherence, *γ*_{ik/z}(*t*,*f*) = *γ*_{ik}(*t*,*f*). Furthermore, partial coherence vanished, *γ*_{ik/z}(*t*,*f*) = 0, wherever *x*_{i}(*t*) = *a* *x*_{z}(*t*) and *x*_{k}(*t*) = *b* *x*_{z}(*t*), with\left(\right)close="">\n \n {\n a\n ,\n b\n }\n \u2208\n R\n \n. For any triplet of signals, the interpretation of TF partial coherence is as follows: if around a TF point (*t*_{0},*f*_{0}) *γ*_{ik/z}(*t*,*f*) < < *γ*_{ik}(*t*,*f*), then it follows that the TF structure of signal *x*_{z}(*t*) matches with that of *x*_{i}(*t*) and *x*_{k}(*t*) around (*t*_{0},*f*_{0}). Moreover, if in a given TF region *γ*_{ik/z}(*t*,*f*) < *γ*_{iz/k}(*t*,*f*) < *γ*_{kz/i}(*t*,*f*), it follows that *x*_{z}(*t*) better represents the communality shared by the three signals[21].

Partial spectra in (6) can be obtained as:

\begin{array}{ll}{S}_{\text{ik/z}}(t,f)& ={S}_{\text{ik}}(t,f)-\frac{{S}_{\text{iz}}(t,f){S}_{\text{zk}}(t,f)}{{S}_{\text{zz}}(t,f)}\phantom{\rule{2em}{0ex}}\\ =\left(\left|{S}_{\text{ik}}(t,f)\right|-\frac{\left|{S}_{\text{iz}}(t,f)\right|\left|{S}_{\text{zk}}(t,f)\right|}{{S}_{\text{zz}}(t,f)}\right){e}^{j{\theta}_{\text{ik}}(t,f)}\phantom{\rule{2em}{0ex}}\end{array}

(7)

\begin{array}{ll}{S}_{\text{ii/z}}(t,f)& ={S}_{\text{ii}}(t,f)-\frac{{S}_{\text{iz}}(t,f){S}_{\text{zi}}(t,f)}{{S}_{\text{zz}}(t,f)}\phantom{\rule{2em}{0ex}}\\ =(1-{\gamma}_{\text{iz}}^{\text{2}}(t,f\left)\right){S}_{\text{ii}}(t,f)\phantom{\rule{2em}{0ex}}\end{array}

(8)

Expression (7) shows that *S*_{ik}(*t*,*f*) and *S*_{ik/z}(*t*,*f*) are complex functions characterized by same phase and different magnitude. Time-frequency phase difference (TFPD) spectrum is defined as:

\begin{array}{ccc}{\theta}_{\text{ik}}(t,f)\hfill & =\hfill & \text{arg}\left[{S}_{\text{ik}}(t,f)\right]\hfill \\ =\hfill & \text{arctan}\left[\frac{\mathfrak{I}\left[{S}_{\text{ik}}(t,f)\right]}{\mathfrak{R}\left[{S}_{\text{ik}}(t,f)\right]}\right];\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}{\theta}_{\text{ik}}(t,f)\in [-\Pi ,\Pi ]\hfill \end{array}

(9)

Within this framework, in a given TF region, a change in *x*_{i}(*t*) precedes (leads) a correlated change in *x*_{k}(*t*) wherever *θ*_{i k}(*t*,*f*) ∈[0,*Π*], while a change in *x*_{i}(*t*) lags behind a correlated change in *x*_{k}(*t*) wherever *θ*_{ik}(*t*,*f*) ∈[−*Π*,0].

Note that according to the open-loop assumption of cross spectral analysis, *θ*_{ik}(*t*,*f*) = −*θ*_{ki}(*t*,*f*). Moreover, phase spectra *θ*_{RS}(*t*,*f*), *θ*_{RH}(*t*,*f*) and *θ*_{SH}(*t*,*f*) are related by *θ*_{SH}(*t*,*f*) = *θ*_{RH}(*t*,*f*)−*θ*_{RS}(*t*,*f*). Finally, it is worth mentioning that, given two signals {*x*_{i}(*t*),*x*_{k}(*t*)}, if *x*_{z}(*t*) = −*x*_{k}(*t*) ⇒ *θ*_{iz}(*t*,*f*) = *θ*_{ik}(*t*,*f*) ± *Π*.

#### Time-frequency filtering

The kernel function determines the degree of TF filtering, and, consequently, the TF resolution of the spectra and the interference terms (ITs) reduction. In this study, time resolution is quantified by *Δ*_{t}, the full width at half maximum of *ϕ*_{t-f}(*t*,0), while frequency resolution is quantified by *Δ*_{f}, the full width at half maximum of *ϕ*_{t-f}(0,*f*). These quantities measure the degree of spreading of a line in the TF domain: *Δ*_{t} and *Δ*_{f} are equal to the full width at half maximum of the TFD of a Dirac impulse, evaluated along *t* for a given frequency, and of a sinusoid, evaluated along *f* for a given time instant, whose ideal TF representations would be straight lines[13]. The kernel function used in this study gives a TF resolution of {*Δ*_{t},*Δ*_{f}} = {10.9 s,0.039 Hz}.

The choice of the kernel is especially important in coherence analysis, because to obtain reliable coherence estimates, i.e., *γ*_{ik}(*t*,*f*) ∈[0,1], the filtering provided by the kernel should be able to completely remove the ITs that characterize the Wigner-Ville distribution[13, 22]. A necessary, but not sufficient, condition to obtain reliable coherence estimates is the positiveness of the auto-spectra[13]. This condition is not sufficient, since residual (oscillating) ITs present in positive TFDs may cause coherence estimates to be higher than 1. Reducing ITs and obtaining reliable coherence estimates are two aspects of the same problem. Thus, our strategy consists in finding a kernel function able to provide *γ*_{ik}(*t*,*f*) ∈[0,1], which in turn implies ITs canceling.

In this study, we used a kernel function (3) that is a particular case of the multiform, tiltable exponential kernel proposed in[23]. Among all the possibilities given by this kernel, we used a function whose isocontours are, in the ambiguity function domain, ellipses with major and minor axes along *τ* and *ν*[24]. The choice of an elliptical shape is motivated by its good concentration around the origin of the ambiguity function domain (where auto-terms are located). Parameters *ν*_{0} and *τ*_{0} are used to change the length of the ellipse axes aligned along *ν* (the degree of time filtering) and *τ* (the degree of frequency filtering), respectively. The parameter *λ* sets the roll-off of the filter as well as the size of the tails of the kernel. Several simulation studies demonstrated the effectiveness of this kernel in reducing ITs[13, 14, 25, 26]. In particular, in[13], it was shown that this kernel offers the possibility of obtaining TF coherence estimates bounded between 0 and 1, as well as spectra characterized by a better TF resolution than multitaper spectrogram and continuous wavelet transform. The simulation study carried out in Section ‘Simulation study’ confirms these previous results.

The choice of the parameters was made as follows: First, the desired TF resolution {*Δ*_{t},*Δ*_{f}}, corresponding to the minimum amount of TF filtering, is decided based on a-priori information about the signals and the experimental settings. The set of parameters {*τ*_{0}, *ν*_{0}, *λ*} that provides the desired TF resolution is used as starting point. If using this set of parameters *γ*_{ik}(*t*,*f*) ∉[0,1], the degree of time (or frequency) filtering is maintained constant, while the frequency (or time) filtering is increased until reaching meaningful estimates over the entire TF domain. If at the end of the process, the frequency (or time) resolution is not satisfactory, the time (or frequency) resolution is decreased, i.e., the corresponding *ν*_{0} (or *τ*_{0}) is increased, and the process iterates. This process allows to adjust the TF filtering to the specific needs of analysis. In this study, we used {*τ*_{0}, *ν*_{0}, *λ*} = {0.05,0.046,0.300}, with 2048 frequency points (corresponding to {*Δ*_{t},*Δ*_{f}} = {10.9s,0.039Hz}), because among all the explored combination of parameters which gave *γ*_{ik}(*t*,*f*) ∈[0,1], this was associated to the minimum degree of TF filtering. An example of this scheme was given in[14].

### Estimation of synchronization indices

The time course of coherence, partial coherence, and phase difference is extracted by averaging the corresponding TF representation in specific TF regions.

The region where *γ*_{ik}(*t*,*f*) is significant, i.e., that where the two signals are sharing approximately the same instantaneous frequencies, is defined as:

{\Omega}_{\text{ik}}\equiv \left\{(t,f)\in ({\mathbb{R}}^{\text{+}}\times {\mathbb{R}}^{\text{+}})\phantom{\rule{1em}{0ex}}\left|\phantom{\rule{1em}{0ex}}{\gamma}_{\text{ik}}(t,f)>{\gamma}_{\text{TH}}(t,f)\right.\right\};

(10)

where *γ*_{TH}(*t*,*f*) is a threshold function, estimated by using surrogate data[13], and which depends on the TF resolution of the spectra. Briefly, *γ*_{TH}(*t*,*f*) is obtained by estimating the TF coherence between several realizations of uncorrelated white Gaussian noises, and taking at each TF point the 95th percentile of TF coherence estimates[13].

Given that we are interested in assessing the influence of respiration on HPV and SAPV, the TF region where the time course of spectral coherence is estimated is centered around respiratory rate, *f*_{R}(*t*), and is defined as:

{\Omega}^{\left(\gamma \right)}\equiv \left\{(t,f)\in ({\mathbb{R}}^{\text{+}}\times {\mathbb{R}}^{\text{+}})\phantom{\rule{1em}{0ex}}\left|\phantom{\rule{1em}{0ex}}f={f}_{\text{R}}\left(t\right)\pm \frac{{\Delta}_{\text{f}}}{2}\right.\right\}

(11)

where *Δ*_{f} is a term related to the frequency resolution. Respiratory rate, *f*_{R}(*t*), is estimated from the TF spectrum of the respiratory signal, as the frequency corresponding to the maximum of the instantaneous spectral peak.

The TF region\left(\right)close="">\n \n \n \n \Omega \n \n \n ik\n \n \n (\n \theta \n )\n \n \n \n where the time course of phase difference index is estimated is composed of those part of *Ω*^{(γ)} in which coherence is statistically significant:

{\Omega}_{\text{ik}}^{\left(\theta \right)}\equiv \left\{{\Omega}^{\left(\gamma \right)}\cap {\Omega}_{\text{ik}}\right\}\circ R(t,f);

(12)

In this expression, *R*(*t*,*f*) is a rectangle of sides 2 s\times \frac{{\Delta}_{\text{f}}}{2} Hz and ∘ denotes the opening (processing technique which involves erosion and dilation). The opening excludes from\left\{{\Omega}_{\text{ik}}^{\left(\gamma \right)}\cap {\Omega}_{\text{ik}}\right\} the portions of TF domain that are smaller than *R*(*t*,*f*), thus adding robustness to the final estimates.

The time course of the band coherence, as well as the time course of partial coherence, is then obtained by averaging *γ*_{ik}(*t*,*f*) and *γ*_{ik/z}(*t*,*f*) in *Ω*^{(γ)}:

\phantom{\rule{-14.0pt}{0ex}}{\gamma}_{\text{ik}}\left(t\right)=\frac{1}{{\Delta}_{\text{f}}}{\int}_{{\Omega}^{\left(\gamma \right)}}{\gamma}_{\text{ik}}(t,f)\mathrm{df};\phantom{\rule{1em}{0ex}}{\gamma}_{\text{ik/z}}\left(t\right)=\frac{1}{{\Delta}_{\text{f}}}{\int}_{{\Omega}^{\left(\gamma \right)}}{\gamma}_{\text{ik/z}}(t,f)\mathrm{df}

(13)

Index *θ*_{ik}(*t*) is estimated (in radians) by averaging the TFPD spectrum in\left(\right)close="">\n \n \n \n \Omega \n \n \n ik\n \n \n (\n \theta \n )\n \n \n \n:

{\theta}_{\text{ik}}\left(t\right)=\left[{\int}_{{\Omega}_{\text{ik}}^{\left(\theta \right)}}{\theta}_{\text{ik}}(t,f)\mathit{\text{df}}\right]\phantom{\rule{.5em}{0ex}}/\phantom{\rule{.5em}{0ex}}\left[{\int}_{{\Omega}_{\text{ik}}^{\left(\theta \right)}}\mathit{\text{df}}\right]\phantom{\rule{.5em}{0ex}}

(14)

The time delay associated to *θ*_{ik}(*t*) is estimated (in seconds) by index\left(\right)close="">\n \n \n \n D\n \n \n ik\n \n \n (\n t\n )\n \n, defined as:

{\mathcal{D}}_{\text{ik}}\left(t\right)=\frac{{\theta}_{\text{ik}}\left(t\right)}{2\Pi {f}_{\text{R}}\left(t\right)}

(15)

### A method to reduce the uncertainty of phase difference in non-stationary signals

The cross spectra *S*_{ik}(*t*,*f*) are complex functions, and as such, their phase is *θ*_{ik}(*t*,*f*) = arg[*S*_{ik}(*t*,*f*)exp(*j* 2*nΠ*)], with\left(\right)close="">\n \n n\n \u2208\n Z\n \n. The periodicity of 2*Π* introduces an uncertainty over the actual value of *θ*_{ik}(*t*,*f*), which may prevent one from drawing conclusions about the temporal sequence of events described by *x*_{i}(*t*) and *x*_{k}(*t*). For instance, it is not possible to determine whether *x*_{i}(*t*) precedes or lags behind *x*_{k}(*t*), since values for *θ*_{ik}(*t*) + *n* 2*Π* and\left(\right)close="">\n \n \n \n D\n \n \n ik\n \n \n (\n t\n )\n +\n n\n \n \n \n T\n \n \n R\n \n \n (\n t\n )\n \n, where *T*_{R}(*t*) = 1/*f*_{R}(*t*), are positive for *n* > 1 and negative for *n* < 1. Although in cardiovascular applications the range of values for *n* is usually reduced to *n* = {−1,0,1} by considering physiological information[10], the uncertainty still remains. In the contest of non-stationary signals, we propose to use TF coherence estimates as control parameters to reduce this uncertainty. The idea is that, the lowest the time delay between non-stationary spectral components, the highest the TF coherence. This is due to the fact that TF coherence is a measure of local correlation. Thus, to determine the actual time delay among\left(\right)close="">\n \n {\n \n \n D\n \n \n ik\n \n \n (\n t\n )\n \u2212\n \n \n T\n \n \n R\n \n \n (\n t\n )\n ,\n \n \n D\n \n \n ik\n \n \n (\n t\n )\n ,\n \n \n D\n \n \n ik\n \n \n (\n t\n )\n +\n \n \n T\n \n \n R\n \n \n (\n t\n )\n }\n \n, that is associated to phase difference *θ*_{ik}(*t*), one can use the following procedure: (i) Generate a set of pairs of delayed signals {*x*_{i}(*t*),*x*_{k}(*t* + *r* *t*_{0})}, with\left(\right)close="">\n \n r\n \u2208\n Z\n \n and being *t*_{0} a small time delay. (ii) Estimate *γ*_{ik}(*t*;*r*), *θ*_{ik}(*t*;*r*) and\left(\right)close="">\n \n \n \n D\n \n \n ik\n \n \n (\n t\n ;\n r\n )\n \n between each pair of signals for each *r*, as well as their temporal median\left(\right)close="">\n \n \n \n \gamma \n \n \n ik\n \n \n (m)\n \n \n \n (\n r\n )\n \n \n,\left(\right)close="">\n \n \n \n \theta \n \n \n ik\n \n \n (m)\n \n \n \n (\n r\n )\n \n \n and\left(\right)close="">\n \n \n \n D\n \n \n ik\n \n \n (m)\n \n \n \n (\n r\n )\n \n \n. (iii) Find *r*_{m}, as the sample for which\left(\right)close="">\n \n \n \n \gamma \n \n \n ik\n \n \n (m)\n \n \n \n (\n r\n )\n \n \n is maximal. (iv) Among the possible time delays\left(\right)close="">\n \n {\n \n \n D\n \n \n ik\n \n \n (\n t\n )\n \u2212\n \n \n T\n \n \n R\n \n \n (\n t\n )\n ,\n \n \n D\n \n \n ik\n \n \n (\n t\n )\n ,\n \n \n D\n \n \n ik\n \n \n (\n t\n )\n +\n \n \n T\n \n \n R\n \n \n (\n t\n )\n }\n \n, the closest to *r*_{m}*t*_{0} is the actual one.

### Statistical analysis

Statistical analysis of each data set is performed as follows. The time course of each general index from one subject *s* is denoted as\left(\right)close="">\n \n I\n (\n t\n ,\n s\n )\n \n, with\left(\right)close="">\n \n I\n (\n t\n ,\n s\n )\n \u2208\n {\n \n \n \gamma \n \n \n ik\n \n \n (\n t\n ,\n s\n )\n \n,\left(\right)close="">\n \n \n \n \gamma \n \n \n ik/z\n \n \n (\n t\n ,\n s\n )\n ,\n \n \n \theta \n \n \n ik\n \n \n (\n t\n ,\n s\n )\n ,\n \n \n D\n \n \n ik\n \n \n (\n t\n ,\n s\n )\n }\n \n, with {*x*_{i}(*t*),*x*_{k}(*t*)} ∈ {*x*_{H}(*t*),*x*_{S}(*t*),−*x*_{R}(*t*)}, and *s* ∈ {1,…,*N*}, being *N* the number of subjects.

The median time course of\left(\right)close="">\n \n I\n (\n t\n ,\n s\n )\n \n,\left(\right)close="">\n \n \n \n I\n \n \n (m)\n \n \n (\n t\n )\n \n, estimated across subjects, as well as the interquartile range, is used to describe the pattern of response of the population during a given condition.

The temporal median values of indices\left(\right)close="">\n \n I\n (\n t\n ,\n s\n )\n \n, denoted as\left(\right)close="">\n \n \n \n I\n \n \n (m)\n \n \n (\n s\n )\n \n, are estimated during epochs where stationarity is assumed, and are used to: (i) Assess inter-conditions differences, i.e., whether\left(\right)close="">\n \n \n \n I\n \n \n (m)\n \n \n (\n s\n )\n \n estimated during a given condition are statistically different from\left(\right)close="">\n \n \n \n I\n \n \n (m)\n \n \n (\n s\n )\n \n estimated during another condition. (ii) Assess the inter-indices differences, i.e., whether\left(\right)close="">\n \n \n \n I\n \n \n ik\n \n \n (m)\n \n \n (\n s\n )\n \n estimated during a given condition are statistically different from\left(\right)close="">\n \n \n \n I\n \n \n pq\n \n \n (m)\n \n \n (\n s\n )\n \n estimated during the same condition, with (*i*,*k*) ≠ (*p*,*q*).

Pairwise comparisons between the same indices evaluated in different epochs are performed by using the Wilcoxon signed rank test, while comparisons between different indices or between the same indices but in different data sets are performed by using the Wilcoxon ranksum test. Statistical significance is assumed for *P* < 0.05.