while ( ) *Y f i* is complex for other frequencies.

epoch and *b* is the forgetting factor (0<*b*<1).

similarly to the described for the MSC, 2ˆ ( ) *p*

with a given significance level :

spectra, as follows:

being

by:

The critical value can be alternatively calculated by the following analytical expression:

$$
\hat{\kappa}\_{\text{crit}}^2 = 1 - \alpha^{\frac{1}{M'-1}} \tag{17}
$$

#### **4.1.6 Component Synchrony Measure (CSM)**

The Component Synchrony Measure (CSM) or Phase Synchrony Measure (PSM) quantifies the degree of synchronism between frequencies of a signal, taking into account only the phase of its Fourier Transform (Simpson et al., 2000):

$$\hat{\rho}^2(f) = \left[\frac{1}{M} \sum\_{i=1}^M \cos \phi\_i(f)\right]^2 + \left[\frac{1}{M} \sum\_{i=1}^M \sin \phi\_i(f)\right]^2 \tag{18}$$

where *i*(*f*) is the phase of the Fourier Transform of the *i*th EEG epoch and *M* is the number of epochs used in the CSM estimation.

Assuming that the phase is uniformly distributed between 0 and 2 (absence of synchronism between stimulus and response), the probability density function is given by 1/2 and the functions cosi and seni present zero mean and variance ½ (Miranda de Sá and Felix, 2003), as follows:

$$\begin{aligned} \mu &= \int\_0^{2\pi} \cos\phi \frac{1}{2\pi} \, d\phi = \int\_0^{2\pi} \sec\phi \frac{1}{2\pi} \, d\phi = 0 \\\\ \sigma^2 &= \int\_0^{2\pi} \cos^2\phi \frac{1}{2\pi} \, d\phi = \int\_0^{2\pi} \sec^2\phi \frac{1}{2\pi} \, d\phi = \frac{1}{2\pi} \end{aligned}$$

According to the Central Limit Theorem, the summation of sins (and co-sins) in the expression 18 tends asymptotically to a normal distribution with zero-mean and variance M/2:

$$\sum\_{i=1}^{M} \cos \phi\_i \sim N\left(0, \frac{M}{2}\right) \qquad \text{and} \qquad \sum\_{i=1}^{M} \text{sen}\phi\_i \sim N\left(0, \frac{M}{2}\right).$$

Hence, it can be shown that:

$$\frac{\left(\sum\_{i=1}^{M} \cos \phi\_i\right)^2 + \left(\sum\_{i=1}^{M} \sin \phi\_i\right)^2}{M/2} \sim \chi\_2^2$$

where 2 2 is the chi-squared distribution with 2 degrees of freedom. From this expression, the CSM can be related to the 2 2 distribution by:

Frequency-Domain Objective Response

column element of ˆ ( ) *yy* **S** *f* is

of a set of signals that is caused by the stimulation.

2

( )

1 1 cos ( ) *N i ij j C f N*

and

*i*

for the MCSM can be expressed by (Felix et al., 2007):

**4.2.2 Multiple Component Synchrony Measure (MCSM)**

ˆ *crit*

*N*

for a significance level

where *Fcrit N M N*

( 2 2 ˆ ˆ ( ) *N Ncrit*

Felix, 2003):

being

mean phase angle, ( ) *i*

2004):

Detection Techniques Applied to Evoked Potentials: A Review 59

being ( ) *Y f ki* the Fourier Transform of the *i*th epoch of the *k*th EEG derivation; *H* and *T* superscripts mean, respectively, Hermitian and the matrix transpose; and the *p*th-row, *q*th-

The distribution of the MC estimates can related to the F-distribution and the critical value

*crit N M N*

*F MNN*

*f* ). As a multivariate extension of the MSC, MC quantifies the amount of power

,2 ,2( ) is the critical value of the F distribution with 2*N* and 2(*M*-*N*) degrees of

freedom. The detection is identified based on the rejection of the null hypothesis (H0) of response absence, which is achieved when the estimate values exceed the critical value

A multivariate extension of the CSM was proposed by Miranda de Sá and Felix (2003) as a way of measuring the synchronism of the ith epoch of the Fourier Transform of *N* EEG derivations (*y1*[*k*], *y2*[*k*],…, *yN*[*k*]) caused by a rhythmical stimulation only considering their

detecting the evoked response and can be mathematically defined by (Miranda de Sá and

1 1 1 1 ˆ ( ) cos ( ) sin ( ) *M M Ni i i i ff f M M*

tan 0

tan 0 *ii i*

*S C if C*

*i i i*

Assuming that the mean phase angle is uniformly distributed between 0 and 2, it can be showed, in a similar way to the performed to the CSM, that the asymptotical critical value

*S C if C f*

where the *M* is the number of EEG epochs and the mean phase angle can be calculated by:

1

1

, *M* epochs and *N* signals can be expressed as (Miranda de Sá et al.,

(24)

*f* . This technique, called Multiple CSM (MCSM), can be used for

2 2

(25)

1 1 sin ( ) *N i ij j S f N*

1 ˆ () () () *M yp yq pi qi i*

*f Y fY f* **S** .

2 ,2 ,2( ) ,2 ,2( )

*crit N M N F*

$$
\hat{\rho}^2(f) \sim \frac{1}{M^2} \frac{M}{2} \chi\_2^2 = \frac{\chi\_2^2}{2M} \tag{19}
$$

Thus, for the null hypothesis of absence of synchronism, the critical value for a given significance level α and *M* EEG epochs can be obtained by (Mardia, 1972):

$$
\rho\_{crit,a}^2 = \frac{\mathcal{X}\_{2\,crit,a}^2}{2M} \tag{20}
$$

where 2 2 , *crit* is the critical value of the chi-squared distribution for the significance level . It is worth noting that CSM expression corresponds to the square of the Phase Coherence (PC).

Alternatively, the critical value for CSM can be calculated based on the probability density function of the chi-squared distribution given as:

$$p\_{\chi^{\frac{z}{2}}\_2}(z) = \frac{1}{2}e^{-\frac{z}{2}}.$$

The analytical critical value of 2 2 for a given significance level is obtained from

$$\int\_0^{\frac{z}{2\alpha i}} \frac{1}{2} e^{-\frac{z}{2}} dz = 1 - a\_{\prime\prime}$$

which yields to:

$$\mathcal{X}\_{2\,crit,\alpha}^2 = 2\ln\left(\frac{1}{\alpha}\right). \tag{21}$$

Hence, substituting expression (21) in (20) leads to:

$$
\rho\_{crit, \alpha}^2 = \frac{\ln\left(1/\alpha\right)}{M} \tag{22}
$$

#### **4.2 Multivariate ORD (MORD) techniques**

#### **4.2.1 Multiple Coherence (MC)**

The Multiple Coherence (MC) - which is the multivariate version of MSC - between a periodic signal and a set of *N* random ones (yj[k], j = 1..*N*) is given by (Miranda de Sá et al., 2004):

$$
\hat{\kappa}\_N^2(f) = \mathbf{V}^H(f)\hat{\mathbf{S}}\_{yy}^{-1}(f)\mathbf{V}(f)\Big/\mathcal{M}\tag{23}
$$

where \*\* \* 1 2 11 1 () () () () *T MM M i i Ni ii i f Yf Yf Y f* **V**

being ( ) *Y f ki* the Fourier Transform of the *i*th epoch of the *k*th EEG derivation; *H* and *T* superscripts mean, respectively, Hermitian and the matrix transpose; and the *p*th-row, *q*th-

$$\text{column element of } \hat{\mathbf{S}}\_{yy}(f) \text{ is } \hat{\mathbf{S}}\_{ypyq}(f) = \sum\_{i=1}^{M} Y\_{pi}^{\*}(f) Y\_{qi}(f) \dots$$

The distribution of the MC estimates can related to the F-distribution and the critical value for a significance level , *M* epochs and *N* signals can be expressed as (Miranda de Sá et al., 2004):

$$
\hat{\kappa}\_{N\_{cit}}^2 = \frac{F\_{crit\,\alpha, 2N, 2(M-N)}}{F\_{crit\,\alpha, 2N, 2(M-N)} + [M-N] \stackrel{\text{(24)}}{\text{(25)}}} \tag{24}
$$

where *Fcrit N M N* ,2 ,2( ) is the critical value of the F distribution with 2*N* and 2(*M*-*N*) degrees of freedom. The detection is identified based on the rejection of the null hypothesis (H0) of response absence, which is achieved when the estimate values exceed the critical value ( 2 2 ˆ ˆ ( ) *N Ncrit f* ). As a multivariate extension of the MSC, MC quantifies the amount of power of a set of signals that is caused by the stimulation.

#### **4.2.2 Multiple Component Synchrony Measure (MCSM)**

A multivariate extension of the CSM was proposed by Miranda de Sá and Felix (2003) as a way of measuring the synchronism of the ith epoch of the Fourier Transform of *N* EEG derivations (*y1*[*k*], *y2*[*k*],…, *yN*[*k*]) caused by a rhythmical stimulation only considering their mean phase angle, ( ) *i f* . This technique, called Multiple CSM (MCSM), can be used for detecting the evoked response and can be mathematically defined by (Miranda de Sá and Felix, 2003):

$$\hat{\rho}\_N^2(f) = \left[\frac{1}{M} \sum\_{i=1}^M \cos\left(\overline{\theta}\_i(f)\right)\right]^2 + \left[\frac{1}{M} \sum\_{i=1}^M \sin\left(\overline{\theta}\_i(f)\right)\right]^2 \tag{25}$$

where the *M* is the number of EEG epochs and the mean phase angle can be calculated by:

$$
\overline{\partial}\_i(f) = \begin{cases}
\tan^{-1}\left(\overline{S}\_i / \overline{C}\_i\right) & \text{if} \quad \overline{C}\_i \ge 0 \\
\tan^{-1}\left(\overline{S}\_i / \overline{C}\_i\right) + \pi & \text{if} \quad \overline{C}\_i < 0
\end{cases}
$$

being

58 Applied Biological Engineering – Principles and Practice

2 2 2 2 2 1 ˆ ( )~ 2 2 *M f M M*

Thus, for the null hypothesis of absence of synchronism, the critical value for a given

*crit M*

It is worth noting that CSM expression corresponds to the square of the Phase Coherence

Alternatively, the critical value for CSM can be calculated based on the probability density

*p z e*

2

1 1 , 2

1 2ln .

2

The Multiple Coherence (MC) - which is the multivariate version of MSC - between a periodic signal and a set of *N* random ones (yj[k], j = 1..*N*) is given by (Miranda de Sá et al., 2004):

> 2 1 ˆ ˆ () () ()() *H N yy*

ln 1 *crit M*

,

*T MM M i i Ni*

11 1 () () () ()

*ii i f Yf Yf Y f*

2 1 () . 2

2 2

*crit z e dz*

2 2

0

2 2 ,

 *crit*

2 2 2 , , 2

*crit*

is the critical value of the chi-squared distribution for the significance level

*z*

2 for a given significance level is obtained from

function of the chi-squared distribution given as:

Hence, substituting expression (21) in (20) leads to:

**4.2 Multivariate ORD (MORD) techniques**

where \*\* \* 1 2

**V**

**4.2.1 Multiple Coherence (MC)**

The analytical critical value of 2

which yields to:

where 2 2 , *crit*

(PC).

significance level α and *M* EEG epochs can be obtained by (Mardia, 1972):

2

(19)

(21)

(22)

*f f f fM* **VS V** (23)

.

(20)

$$\overline{\mathbf{C}}\_i = \frac{1}{N} \sum\_{j=1}^{N} \cos \theta\_{ij}(f) \quad \text{and} \quad \overline{S}\_i = \frac{1}{N} \sum\_{j=1}^{N} \sin \theta\_{ij}(f).$$

Assuming that the mean phase angle is uniformly distributed between 0 and 2, it can be showed, in a similar way to the performed to the CSM, that the asymptotical critical value for the MCSM can be expressed by (Felix et al., 2007):

Frequency-Domain Objective Response

1985, Beagley *et al.*, 1979).

performance than any technique.

Detection Techniques Applied to Evoked Potentials: A Review 61

be statistically more powerful than the PC. However, Picton *et al.* (1987) have found small difference between the two methods when the auditory threshold was measured by means of the steady state AEP. Based on these results, the authors have reported that, for intensities near the threshold, most of the information about the signal is in the phase, since using the amplitude information (HT2) didn't result in an improvement in the response detection. Other studies also found that the phase is more important than magnitude (Greenblat *et al.*,

In 1989, Dobie and Wilson have proposed the use of the Magnitude-Squared Coherence (MSC), an ORD technique that uses magnitude and phase of the Fourier Transform of EEG epochs, for identifying the frequencies that significantly contribute to the auditory EP. In this work, the MSC was considered more sensible than the simple visual inspection of the replicated responses. In a later work, Dobie and Wilson (1990) have applied the coherence (MSC) to the AEP filtered with the "Optimum" Wiener Filtering and, compared to the nonfiltered version, it was verified that this procedure can be advantageous for signals with low signal-to-noise ratio, such as the obtained with stimulation near the auditory threshold.

Later, Victor and Mast (1991) have proposed a variant of HT2, named T2 circular (T2C). This method assumes that the real and imaginary parts of the Fourier Transform of the EEG epochs are independent and present equal variance. This assumption results in a simpler statistical approach, and the ellipse of confidence of HT2 becomes a circle of confidence in T2C. Moreover, in this study, a comparison between the performances of three ORD methods was performed: the HT2, the T2C and the Phase Rayleigh Criterion (PRC) – a technique that uses only the phase of the signal. The comparison was based on simulation and application to the steady state visual evoked potential. As a result, it was observed that, for low signal-to-noise (SNR) ratio values, HT2 and T2C have shown to be superior to the PRC. The authors consider that this result is due to the fact that the first two methods use information of amplitude, while the PRC discard it. Furthermore, it was verified that for low SNR, a high number of EEG epochs is needed in order to achieve statistical significance. On the other hand, for a low number of EEG segments, T2C and PRC presented advantage over HT2 and for intermediate SNR values T2C showed better

Dobie and Wilson (1993) also compared the performance of T2C, PC and MSC using simulated signals. Additionally, a variant version of the MSC, the MSC-WA (WA, of Weighted Averaging), which consists of the multiplication of each epoch by the inverse of its power, was investigated. This weighting assumes that epochs with high power are the ones that present lower SNR and, therefore, should have their weight reduced. This procedure can be particularly interesting in the cases of non-stationary noises, which can harm the performance of the MSC, leading it to have inferior results to the PC (Dobie and Wilson, 1993). According to these authors, the T2C is mathematically related to the MSC, and it is possible to obtain one estimator from the other, although the MSC is computationally simpler. The MSC (or T2C) weighted averaging was the technique that presented the best performance in the detection of response to the auditory stimulus. In a later study (Dobie and Wilson, 1994a), the MSC, the MSC-WA and the PC were applied to the steady state 40Hz AEP. The three techniques presented similar performance in the response detection, although a slightly advantage for the MSC-WA over the MSC and for

the MSC over the PC has been observed (Dobie and Wilson, 1994b).

$$
\rho\_{N\,crit,\alpha}^2 = \frac{\chi\_{2\,crit,\alpha}^2}{2M} = \frac{\ln\left(1/\alpha\right)}{M} \tag{26}
$$

where 2 2 , *crit* is the critical value of the chi-squared distribution with 2 degrees of freedom for the significance level *α* and *M* is the number of EEG epochs used in the estimation. Also for this technique, the detection is based on the null hypothesis (H0) rejection of synchronism absence, which is achieved when the estimate values exceed the corresponding critical value ( 2 2 ˆ*N N crit f* ).

## **5. A chronological review of ORD applied to the evoked potentials**

The waveform analysis of the evoked potential (EP) is based on the physician experience, ability and attention level, as well as in informal criteria (Dobie and Wilson, 1993). For the case of the somatosensory evoked potential used in surgical monitoring, for example, one considers a significant modification in its waveform, a reduction of 30% to 50% in the amplitude, an increase of 5% to 10% in the latency, or a combination of these criteria (Linden *et al.*, 1997). Such criteria, used as parameters of modification on the intra-operative strategy, are clearly subjective once they depend on the EEG recording quality, anesthesia regimen, and are hampered by the high variability inter-observer and inter-patient (Martin et al., 2002).

On the other hand, the techniques known as Objective Response Detection (ORD) have been suggested as a way to overcome this subjectivity and allow the stimuli-response detection with a maximum false positive rate *a priori* established. Dobie and Wilson (1993) numbered the advantages of the ORD application compared to the conventional analysis by visual inspection, such as avoiding the persistence of the trained observer and obtaining relevant information even for experienced observers in the judgment of questionable cases.

#### **5.1 Univariate ORD techniques**

In 1984, Galambos *et al.* (apud Stapells, 1987) introduced the ORD technique Phase Coherence (PC) in the analysis of the steady state auditory responses. This technique can be seen as a statistical measure of the phase variance and uses only the phase information of the Fourier Transform of the EEG epochs. Two years later, Stapells *et al.* (1987) have applied the PC for obtaining the auditory threshold of normal adults. This method showed to be accurate to establish the behavioral auditory threshold, being considered as fast as obtaining the brainstem responses by tones. Moreover, these authors pointed out that the PC showed better results for determining the optimal stimulation rate when compared to the amplitude inspection of the coherent average, since the latter presents higher variability than the PC.

Still in 1987, Picton *et al.* have applied the Hotelling T2 Test (HT2) and the PC to the steady state auditory evoked potential (AEP). The HT2 (Hotelling, 1931) takes into account both amplitude and phase of the Fourier Transformed EEG epochs and allows the calculation of a confidence ellipse for the response vectors (EP). In the case in which the ellipse do not encompass the origin (0,0), which corresponds to the absence response condition, its presence is assumed (Dobie and Wilson, 1993). Since the PC represents a kind of HT2 without considering the amplitude information (Picton *et al.*, 1987), theoretically, HT2 would 1985, Beagley *et al.*, 1979).

60 Applied Biological Engineering – Principles and Practice

2 2 , ,

**5. A chronological review of ORD applied to the evoked potentials**

hampered by the high variability inter-observer and inter-patient (Martin et al., 2002).

information even for experienced observers in the judgment of questionable cases.

where 2 2 , *crit*

critical value ( 2 2 ˆ*N N crit*

**5.1 Univariate ORD techniques**

 *f* ).

2 *crit N crit M M*

for the significance level *α* and *M* is the number of EEG epochs used in the estimation. Also for this technique, the detection is based on the null hypothesis (H0) rejection of synchronism absence, which is achieved when the estimate values exceed the corresponding

The waveform analysis of the evoked potential (EP) is based on the physician experience, ability and attention level, as well as in informal criteria (Dobie and Wilson, 1993). For the case of the somatosensory evoked potential used in surgical monitoring, for example, one considers a significant modification in its waveform, a reduction of 30% to 50% in the amplitude, an increase of 5% to 10% in the latency, or a combination of these criteria (Linden *et al.*, 1997). Such criteria, used as parameters of modification on the intra-operative strategy, are clearly subjective once they depend on the EEG recording quality, anesthesia regimen, and are

On the other hand, the techniques known as Objective Response Detection (ORD) have been suggested as a way to overcome this subjectivity and allow the stimuli-response detection with a maximum false positive rate *a priori* established. Dobie and Wilson (1993) numbered the advantages of the ORD application compared to the conventional analysis by visual inspection, such as avoiding the persistence of the trained observer and obtaining relevant

In 1984, Galambos *et al.* (apud Stapells, 1987) introduced the ORD technique Phase Coherence (PC) in the analysis of the steady state auditory responses. This technique can be seen as a statistical measure of the phase variance and uses only the phase information of the Fourier Transform of the EEG epochs. Two years later, Stapells *et al.* (1987) have applied the PC for obtaining the auditory threshold of normal adults. This method showed to be accurate to establish the behavioral auditory threshold, being considered as fast as obtaining the brainstem responses by tones. Moreover, these authors pointed out that the PC showed better results for determining the optimal stimulation rate when compared to the amplitude inspection of the coherent average, since the latter presents higher variability than the PC. Still in 1987, Picton *et al.* have applied the Hotelling T2 Test (HT2) and the PC to the steady state auditory evoked potential (AEP). The HT2 (Hotelling, 1931) takes into account both amplitude and phase of the Fourier Transformed EEG epochs and allows the calculation of a confidence ellipse for the response vectors (EP). In the case in which the ellipse do not encompass the origin (0,0), which corresponds to the absence response condition, its presence is assumed (Dobie and Wilson, 1993). Since the PC represents a kind of HT2 without considering the amplitude information (Picton *et al.*, 1987), theoretically, HT2 would

2

ln 1

is the critical value of the chi-squared distribution with 2 degrees of freedom

(26)

In 1989, Dobie and Wilson have proposed the use of the Magnitude-Squared Coherence (MSC), an ORD technique that uses magnitude and phase of the Fourier Transform of EEG epochs, for identifying the frequencies that significantly contribute to the auditory EP. In this work, the MSC was considered more sensible than the simple visual inspection of the replicated responses. In a later work, Dobie and Wilson (1990) have applied the coherence (MSC) to the AEP filtered with the "Optimum" Wiener Filtering and, compared to the nonfiltered version, it was verified that this procedure can be advantageous for signals with low signal-to-noise ratio, such as the obtained with stimulation near the auditory threshold.

Later, Victor and Mast (1991) have proposed a variant of HT2, named T2 circular (T2C). This method assumes that the real and imaginary parts of the Fourier Transform of the EEG epochs are independent and present equal variance. This assumption results in a simpler statistical approach, and the ellipse of confidence of HT2 becomes a circle of confidence in T2C. Moreover, in this study, a comparison between the performances of three ORD methods was performed: the HT2, the T2C and the Phase Rayleigh Criterion (PRC) – a technique that uses only the phase of the signal. The comparison was based on simulation and application to the steady state visual evoked potential. As a result, it was observed that, for low signal-to-noise (SNR) ratio values, HT2 and T2C have shown to be superior to the PRC. The authors consider that this result is due to the fact that the first two methods use information of amplitude, while the PRC discard it. Furthermore, it was verified that for low SNR, a high number of EEG epochs is needed in order to achieve statistical significance. On the other hand, for a low number of EEG segments, T2C and PRC presented advantage over HT2 and for intermediate SNR values T2C showed better performance than any technique.

Dobie and Wilson (1993) also compared the performance of T2C, PC and MSC using simulated signals. Additionally, a variant version of the MSC, the MSC-WA (WA, of Weighted Averaging), which consists of the multiplication of each epoch by the inverse of its power, was investigated. This weighting assumes that epochs with high power are the ones that present lower SNR and, therefore, should have their weight reduced. This procedure can be particularly interesting in the cases of non-stationary noises, which can harm the performance of the MSC, leading it to have inferior results to the PC (Dobie and Wilson, 1993). According to these authors, the T2C is mathematically related to the MSC, and it is possible to obtain one estimator from the other, although the MSC is computationally simpler. The MSC (or T2C) weighted averaging was the technique that presented the best performance in the detection of response to the auditory stimulus. In a later study (Dobie and Wilson, 1994a), the MSC, the MSC-WA and the PC were applied to the steady state 40Hz AEP. The three techniques presented similar performance in the response detection, although a slightly advantage for the MSC-WA over the MSC and for the MSC over the PC has been observed (Dobie and Wilson, 1994b).

Frequency-Domain Objective Response

normalizing transform in it.

the MLAEP's (L+15).

Detection Techniques Applied to Evoked Potentials: A Review 63

Miranda de Sá *et al.* (2001) proposed a coherence-based method to emphasize the stimulisynchronized responses and reduce the background EEG influence. Later (Miranda de Sá *et al.*, 2002), the confidence limits for the coherence estimates between one random and one periodic signal were calculated based on a monotonically increasing function of the estimates, which involves the non-central F-distribution. Miranda de Sá (2004) obtained the sampling distribution of this coherence estimate itself and found it to be non-central beta distributed. This allowed further investigations to be carried out (Miranda de Sá *et al.*, 2009) for assessing both bias and variance of the estimate as well as the performance of the

The MSC and the CSM were also applied for monitoring the anesthetic plan (Cagy *et al.*, 2000, Cagy, 2003). These studies showed that, during infusion of anesthetic, a reduction in values of both estimates is verified. Moreover, the results for MSC and CSM were quite similar, indicating the phase to be more important than the magnitude, as previously reported by Dobie and Wilson (1993). The MSC was also used to identify the maximum response band for the Brainstem Auditory Evoked Potential (BAEP) (Pacheco, 2003, Pacheco and Infantosi, 2005). Infantosi *et al.* (2004) applied the MSC to the Middle Latency Auditory Evoked Potential (MLAEP) of normal individuals for different sound pressure levels aiming at investigating the frequency bands that better characterize this evoked response for distinct stimulation intensities. They have found consistent response detection for frequencies within the gamma band (30-50 Hz). Furthermore, the application of the MSC to the AEP for determining the auditory threshold L, defined as the volunteer response to a click stimulation, resulted in the detection near the visual identification by a specialist of the BAEP waves (L and L+5) or of

Melges *et al.* (2005) employed the methodology suggested by Tierra-Criollo (2001), and used the temporal evolution of the MSC for a given frequency in order to evidence the transitions from tibial nerve somatosensory stimulation to resting condition, and conversely. The transition from a responsive to a no-responsive status is very important for surgical monitoring and this work have mimicked these statuses by presenting and omitting the stimulus. At the same year, Miranda de Sá *et al.* (2005) have investigated the coherence between two EEG derivations due to a visual rhythmic stimulation and the partial coherence (after removing the contribution of the stimulus) applied to the same signals. They concluded that these techniques present complementary role, since the coherence quantifies the degree of synchronism between the derivations, whereas the partial coherence informs about the relationship due to the non-phase locked activities, suggesting its use in

In 2006, Campos *et al.* (2006) applied the SFT to the EEG of epileptic patients during intermittent photic stimulation, and concluded that this technique should be employed as a complement to the traditional identification methods of photo-recruited responses, such as spectral analysis. By using EEG signals during the same type of stimulation, Miranda de Sá *et al.* (2006) studied the SFT applied to the signals of normal individuals. Moreover, they investigated the probability distribution of this test, as well as the confidence limits for its estimates, using simulated signals with different signal-to-noise ratio and *M*-values. Since the majority of the EP applications use periodic stimulation (intermittent photic stimulation, train of current pulses or clicks), Miranda de Sá (2006a) developed analytical expressions for calculating the trend, variance and probability density function for the coherence (MSC), in

ERD/ERS (event related desynchronization/synchronization) studies.

the particular case in which the input signal (stimulus) is periodic.

At the same year, Dobie and Wilson (1994b) have applied the MSC and the MSC-PW (PW, of Phase Weighting) to the steady state 40Hz AEP. In the MSC-PW, a weighting is applied and it is related to the phase error calculated as the difference between the phase of the averaged signal (coherent average) and an expected phase (or target-phase). The targetphase is calculated from the coherent average with a high M number of EEG epochs during stimulation with intensities higher than the commonly used for obtaining the AEP. As a result, it was verified that the phase weighting improved the performance of the MSC. At the same year, Miranda de Sá et al. (1994) investigated the theoretical confidence limits for the coherence estimate (MSC) comparing them to the limits obtained by simulation with random signals.

In 1995, Dobie and Wilson (1995) verified the superior performance for the MSC-WA, when compared to the human inspection. The MSC-WA allowed detecting the responses to auditory stimulation with a lower number of stimuli and with lower stimulation intensity. At the same year, Thakor *et al.* (1995) have proposed an adaptive algorithm for the coherence estimate, in order to detect changes in the somatosensory evoked response. This study showed that, during hypoxia in cats, the MSC presents a sharp decrease, confirming the applicability of the adaptive MSC for monitoring purposes.

In 1996, Dobie and Wilson (1996) compared the Spectral F Test (SFT) and the MSC in the detection of the steady state AEP and concluded that, as they presented the same performance, the choice for using one technique or other would be a convenience issue. Two years later, Liavas *et al.* (1998) used successfully an ORD technique based on the periodogram for detecting the steady state visual evoked potential, aiming at investigating neuropathies related to the visual system.

Applying a decreasing exponential weighting to the spectral estimates of the EEG epochs during somatosensory stimulation used for MSC calculation, Tierra-Criollo *et al.* (1998) showed that this technique leads to the detection of the evoked responses faster than its simple version. This weighting emphasizes the latest spectral estimates, making the MSC more representative of the current status of the patient. This technique was named MSC with exponential forgetting (MSC-EF). Due to its promising results, Tierra-Criollo (2001) suggested the application of both the MSC and MSC-EF to the posterior tibial nerve SEP as a method to be evaluated for real-time monitoring of surgical procedures.

In 2000, Ramos et al. compared the MSC and the CSM (Component Synchrony Measure), which corresponds to the square of the PC (Phase Coherence). They reported that there is no statistical difference in performance for response detection when applied to the EEG of children and newborns during click stimulation. However, the MSC showed higher specificity in the detection of auditory deficiency, which gives to this technique greater clinical interest. Moreover, this method presented higher potentiality for determining the auditory threshold in the studied age group (Ramos et al., 2000). Also in the detection of the somatosensory response, the MSC presented better performance when compared to the CSM and the SFT (Simpson *et al.*, 2000, Tierra-Criollo, 2001). The MSC was also applied to the EEG during intermittent photic stimulation in order to quantify the degree of cortical activation (Miranda de Sá, 2000) and in the identification of inter-hemisphere symmetry between homologues regions of the visual cortex at the stimulation frequency and its harmonics (Miranda de Sá and Infantosi, 2002).

At the same year, Dobie and Wilson (1994b) have applied the MSC and the MSC-PW (PW, of Phase Weighting) to the steady state 40Hz AEP. In the MSC-PW, a weighting is applied and it is related to the phase error calculated as the difference between the phase of the averaged signal (coherent average) and an expected phase (or target-phase). The targetphase is calculated from the coherent average with a high M number of EEG epochs during stimulation with intensities higher than the commonly used for obtaining the AEP. As a result, it was verified that the phase weighting improved the performance of the MSC. At the same year, Miranda de Sá et al. (1994) investigated the theoretical confidence limits for the coherence estimate (MSC) comparing them to the limits obtained by simulation with

In 1995, Dobie and Wilson (1995) verified the superior performance for the MSC-WA, when compared to the human inspection. The MSC-WA allowed detecting the responses to auditory stimulation with a lower number of stimuli and with lower stimulation intensity. At the same year, Thakor *et al.* (1995) have proposed an adaptive algorithm for the coherence estimate, in order to detect changes in the somatosensory evoked response. This study showed that, during hypoxia in cats, the MSC presents a sharp decrease, confirming

In 1996, Dobie and Wilson (1996) compared the Spectral F Test (SFT) and the MSC in the detection of the steady state AEP and concluded that, as they presented the same performance, the choice for using one technique or other would be a convenience issue. Two years later, Liavas *et al.* (1998) used successfully an ORD technique based on the periodogram for detecting the steady state visual evoked potential, aiming at investigating

Applying a decreasing exponential weighting to the spectral estimates of the EEG epochs during somatosensory stimulation used for MSC calculation, Tierra-Criollo *et al.* (1998) showed that this technique leads to the detection of the evoked responses faster than its simple version. This weighting emphasizes the latest spectral estimates, making the MSC more representative of the current status of the patient. This technique was named MSC with exponential forgetting (MSC-EF). Due to its promising results, Tierra-Criollo (2001) suggested the application of both the MSC and MSC-EF to the posterior tibial nerve SEP as a

In 2000, Ramos et al. compared the MSC and the CSM (Component Synchrony Measure), which corresponds to the square of the PC (Phase Coherence). They reported that there is no statistical difference in performance for response detection when applied to the EEG of children and newborns during click stimulation. However, the MSC showed higher specificity in the detection of auditory deficiency, which gives to this technique greater clinical interest. Moreover, this method presented higher potentiality for determining the auditory threshold in the studied age group (Ramos et al., 2000). Also in the detection of the somatosensory response, the MSC presented better performance when compared to the CSM and the SFT (Simpson *et al.*, 2000, Tierra-Criollo, 2001). The MSC was also applied to the EEG during intermittent photic stimulation in order to quantify the degree of cortical activation (Miranda de Sá, 2000) and in the identification of inter-hemisphere symmetry between homologues regions of the visual cortex at the stimulation frequency and its

the applicability of the adaptive MSC for monitoring purposes.

method to be evaluated for real-time monitoring of surgical procedures.

neuropathies related to the visual system.

harmonics (Miranda de Sá and Infantosi, 2002).

random signals.

Miranda de Sá *et al.* (2001) proposed a coherence-based method to emphasize the stimulisynchronized responses and reduce the background EEG influence. Later (Miranda de Sá *et al.*, 2002), the confidence limits for the coherence estimates between one random and one periodic signal were calculated based on a monotonically increasing function of the estimates, which involves the non-central F-distribution. Miranda de Sá (2004) obtained the sampling distribution of this coherence estimate itself and found it to be non-central beta distributed. This allowed further investigations to be carried out (Miranda de Sá *et al.*, 2009) for assessing both bias and variance of the estimate as well as the performance of the normalizing transform in it.

The MSC and the CSM were also applied for monitoring the anesthetic plan (Cagy *et al.*, 2000, Cagy, 2003). These studies showed that, during infusion of anesthetic, a reduction in values of both estimates is verified. Moreover, the results for MSC and CSM were quite similar, indicating the phase to be more important than the magnitude, as previously reported by Dobie and Wilson (1993). The MSC was also used to identify the maximum response band for the Brainstem Auditory Evoked Potential (BAEP) (Pacheco, 2003, Pacheco and Infantosi, 2005).

Infantosi *et al.* (2004) applied the MSC to the Middle Latency Auditory Evoked Potential (MLAEP) of normal individuals for different sound pressure levels aiming at investigating the frequency bands that better characterize this evoked response for distinct stimulation intensities. They have found consistent response detection for frequencies within the gamma band (30-50 Hz). Furthermore, the application of the MSC to the AEP for determining the auditory threshold L, defined as the volunteer response to a click stimulation, resulted in the detection near the visual identification by a specialist of the BAEP waves (L and L+5) or of the MLAEP's (L+15).

Melges *et al.* (2005) employed the methodology suggested by Tierra-Criollo (2001), and used the temporal evolution of the MSC for a given frequency in order to evidence the transitions from tibial nerve somatosensory stimulation to resting condition, and conversely. The transition from a responsive to a no-responsive status is very important for surgical monitoring and this work have mimicked these statuses by presenting and omitting the stimulus. At the same year, Miranda de Sá *et al.* (2005) have investigated the coherence between two EEG derivations due to a visual rhythmic stimulation and the partial coherence (after removing the contribution of the stimulus) applied to the same signals. They concluded that these techniques present complementary role, since the coherence quantifies the degree of synchronism between the derivations, whereas the partial coherence informs about the relationship due to the non-phase locked activities, suggesting its use in ERD/ERS (event related desynchronization/synchronization) studies.

In 2006, Campos *et al.* (2006) applied the SFT to the EEG of epileptic patients during intermittent photic stimulation, and concluded that this technique should be employed as a complement to the traditional identification methods of photo-recruited responses, such as spectral analysis. By using EEG signals during the same type of stimulation, Miranda de Sá *et al.* (2006) studied the SFT applied to the signals of normal individuals. Moreover, they investigated the probability distribution of this test, as well as the confidence limits for its estimates, using simulated signals with different signal-to-noise ratio and *M*-values. Since the majority of the EP applications use periodic stimulation (intermittent photic stimulation, train of current pulses or clicks), Miranda de Sá (2006a) developed analytical expressions for calculating the trend, variance and probability density function for the coherence (MSC), in the particular case in which the input signal (stimulus) is periodic.

Frequency-Domain Objective Response

allowing a faster detection of the elicited responses.

advantageous using only the 6th signal for estimating the MSC.

both simulated and real EEG signals.

2007).

Detection Techniques Applied to Evoked Potentials: A Review 65

named MORD (Multivariate ORD), which use information of more than one EEG derivation. In this study, they introduced the Multiple Coherence (MC), a multivariate version of the MSC, and verified that the detection percentages can be improved by augmenting the number of EEG channels used. These authors also verified that, similar to the proved to the uni-variate version (MSC), the estimate of the MC, for a periodic and deterministic stimulation, is independent of the stimulation signal. Moreover, they showed, by means of simulation, that even the addition of a second EEG signal with lower signal to noise-ratio than the first could result in an increase in the probability detection. Since the MORD does not require increasing the number of epochs for obtaining higher detection rates, the MC has been suggested as a useful tool to be applied in the surgical monitoring,

In the following year, Miranda de Sá and Felix (2003) proposed a multivariate extension for the Component Synchrony Measure (CSM), the MCSM (Multiple CSM), for which it was verified that the detection rates for the intermittent photic stimulation responses increase by augmenting the number of signals used in its calculation. Such results were observed for

In 2004, Miranda de Sá *et al.* (2004) proposed a matrix-based algorithm for the calculation of the Multiple Coherence. The results obtained by simulation showed that for achieving a detection probability of 95%, for example, the signals added to the set of EEG channels used for the MC estimate can present SNR lower than the first one. This can be observed until the 6th signal, from which a signal with SNR higher than the first one should be employed in order to maintain the detection rate (95%). However, in this case it would be more

Later, Ferreira and Miranda de Sá (2005) compared the simple, multiple and partial coherences applied to the EEG during intermittent photic stimulation and consider these techniques promising in the analysis of the EEG during sensory stimulation. In the same year, Infantosi *et al.* (2005) verified, as theoretically predicted (Miranda de Sá and Felix, 2002, Miranda de Sá *et al.*, 2004), a better performance of the MC when compared to the MSC applied to the EEG during somatosensory stimulation of the tibial nerve. In this study, the MSC was applied to the bipolar derivations [Cz'-Fpz'] and [C3'-C4'] (where [Fpz'] is midway between [Fpz] and [Fz]; [Cz'], [C3'], and [C4'] are 2 cm posterior to [Cz], [C3] and [C4], respectively) - very often used for scalp SEP recording - and the MC was applied to both derivations. Using EEG signals from the same derivations during electric stimulation, Melges *et al.* (2006a) have found the MCSM to be useful for tibial nerve SEP detection. At the same year, Melges *et al.* (2006b) compared the performance of the MC and the MCSM, observing higher detection rates for the former. This result was observed for different values of *M* epochs (100, 200, 400, 800) used in the calculation of the estimates. A comparison between the two techniques applied to the EEG during intermittent photic stimulation (Felix *et al.*, 2007) has also resulted in higher detection percentages for the MC over the MCSM. By means of simulation, it was observed that the presence of noise correlated with the responses degrades the detection rates (Felix *et al.*,

In 2008, Miranda de Sá *et al.* (2008) derived the probability density function of the MC and a set of evoked responses embedded in additive noise for the zero-coherence case (null hypothesis of response absence). In this work, it was also demonstrated the influence of the

Tierra-Criollo (2001) and Infantosi *et al.* (2006), by applying the MSC to the responses evoked by electric stimulation, identified the low gamma band (30-60 Hz) as the one that better represents the short-latency components of the somatosensory evoked potential. Also in 2006, Klein *et al.* (2006) have introduced a variant of the MSC, the Wavelet Coherence (WC), which allowed obtaining the temporal information that is lost when frequencydomain techniques are used.

Infantosi and Miranda de Sá (2006) proposed a methodology based on the MSC in order to study EEG activities that are synchronized in time (time-locked) with the stimulation signal, but non-synchronized in phase (non phase-locked). Such technique was investigated using the visual evoked potential, elicited by intermittent photic stimulation. In another study, Miranda de Sá (2006b) developed an expression for the partial coherence between two signals, removing the contribution of the stimulation, and showing that this estimates is independent of the stimulus signal. In 2007, Miranda de Sá and Infantosi (2007) introduced a method based on the estimates of the MSC and the Partial Coherence in order to quantify the similarity between two EEG activities that are not synchronized in phase with the stimulation signal. At the same year, Cagy and Infantosi (2007) showed that the MSC is capable of indicating modification both in amplitude and latency of the MLAEP.

Later, Melges *et al.* (2008a) investigated the topographic distribution of the tibial nerve somatosensory evoked potential (SEP) using the MSC and verified that the best regions for SEP recording, in an ORD approach, includes the central and parietal leads at the midline and parasagittal line ipsilateral to the stimulated limb. Two years later, Farina *et al.* (2010) proposed a novel ORD technique based on the Rice distribution, obtaining the analytical critical values and using simulated signals to calculate the probability of detection for different values of signal-to-noise ratio.

More recently, Melges *et al.* (2011a) showed that, although the variation of the stimulation frequency to values higher than 5 Hz produces distortion in the tibial nerve SEP waveform, hampering the visual inspection, the detection rates obtained with the MSC (and CSM) are statistically equivalent for different stimulation frequencies. Hence, higher values can be used in order to fasten the detection. The maximum frequency, however, is limited to about 10 Hz, since higher values could lead to steady state tibial nerve SEP, instead of transient one.

## **5.2 Multivariate ORD (MORD) techniques**

The introduction of the ORD techniques represented an advance in the study of the evoked potentials, since these methods are based in statistical tests for inferring about the absence of stimulus-response (Dobie and Wilson, 1989). These techniques present the advantage (over traditional methods of identification of response), since they have a maximum false-positive rate (false alarm) a priori defined. However, for a fixed signal-to-noise ratio, it is only possible to improve the response detection rates, at the expense of increasing the recording length (number *M* of EEG epochs). This aspect may limit the application of ORD techniques, especially for surgical monitoring, case in which a fast detection of EP variations is needed, aiming at modifying the intra-operative strategy to avoid the occurrence of neurological damages.

In order to overcome this drawback and improve the detection rates, Miranda de Sá and Felix (2002) suggested the employment of multivariate extensions of the ORD techniques,

Tierra-Criollo (2001) and Infantosi *et al.* (2006), by applying the MSC to the responses evoked by electric stimulation, identified the low gamma band (30-60 Hz) as the one that better represents the short-latency components of the somatosensory evoked potential. Also in 2006, Klein *et al.* (2006) have introduced a variant of the MSC, the Wavelet Coherence (WC), which allowed obtaining the temporal information that is lost when frequency-

Infantosi and Miranda de Sá (2006) proposed a methodology based on the MSC in order to study EEG activities that are synchronized in time (time-locked) with the stimulation signal, but non-synchronized in phase (non phase-locked). Such technique was investigated using the visual evoked potential, elicited by intermittent photic stimulation. In another study, Miranda de Sá (2006b) developed an expression for the partial coherence between two signals, removing the contribution of the stimulation, and showing that this estimates is independent of the stimulus signal. In 2007, Miranda de Sá and Infantosi (2007) introduced a method based on the estimates of the MSC and the Partial Coherence in order to quantify the similarity between two EEG activities that are not synchronized in phase with the stimulation signal. At the same year, Cagy and Infantosi (2007) showed that the MSC is

Later, Melges *et al.* (2008a) investigated the topographic distribution of the tibial nerve somatosensory evoked potential (SEP) using the MSC and verified that the best regions for SEP recording, in an ORD approach, includes the central and parietal leads at the midline and parasagittal line ipsilateral to the stimulated limb. Two years later, Farina *et al.* (2010) proposed a novel ORD technique based on the Rice distribution, obtaining the analytical critical values and using simulated signals to calculate the probability of detection for

More recently, Melges *et al.* (2011a) showed that, although the variation of the stimulation frequency to values higher than 5 Hz produces distortion in the tibial nerve SEP waveform, hampering the visual inspection, the detection rates obtained with the MSC (and CSM) are statistically equivalent for different stimulation frequencies. Hence, higher values can be used in order to fasten the detection. The maximum frequency, however, is limited to about 10 Hz,

The introduction of the ORD techniques represented an advance in the study of the evoked potentials, since these methods are based in statistical tests for inferring about the absence of stimulus-response (Dobie and Wilson, 1989). These techniques present the advantage (over traditional methods of identification of response), since they have a maximum false-positive rate (false alarm) a priori defined. However, for a fixed signal-to-noise ratio, it is only possible to improve the response detection rates, at the expense of increasing the recording length (number *M* of EEG epochs). This aspect may limit the application of ORD techniques, especially for surgical monitoring, case in which a fast detection of EP variations is needed, aiming at modifying the intra-operative strategy to avoid the occurrence of neurological

In order to overcome this drawback and improve the detection rates, Miranda de Sá and Felix (2002) suggested the employment of multivariate extensions of the ORD techniques,

since higher values could lead to steady state tibial nerve SEP, instead of transient one.

capable of indicating modification both in amplitude and latency of the MLAEP.

domain techniques are used.

different values of signal-to-noise ratio.

**5.2 Multivariate ORD (MORD) techniques**

damages.

named MORD (Multivariate ORD), which use information of more than one EEG derivation. In this study, they introduced the Multiple Coherence (MC), a multivariate version of the MSC, and verified that the detection percentages can be improved by augmenting the number of EEG channels used. These authors also verified that, similar to the proved to the uni-variate version (MSC), the estimate of the MC, for a periodic and deterministic stimulation, is independent of the stimulation signal. Moreover, they showed, by means of simulation, that even the addition of a second EEG signal with lower signal to noise-ratio than the first could result in an increase in the probability detection. Since the MORD does not require increasing the number of epochs for obtaining higher detection rates, the MC has been suggested as a useful tool to be applied in the surgical monitoring, allowing a faster detection of the elicited responses.

In the following year, Miranda de Sá and Felix (2003) proposed a multivariate extension for the Component Synchrony Measure (CSM), the MCSM (Multiple CSM), for which it was verified that the detection rates for the intermittent photic stimulation responses increase by augmenting the number of signals used in its calculation. Such results were observed for both simulated and real EEG signals.

In 2004, Miranda de Sá *et al.* (2004) proposed a matrix-based algorithm for the calculation of the Multiple Coherence. The results obtained by simulation showed that for achieving a detection probability of 95%, for example, the signals added to the set of EEG channels used for the MC estimate can present SNR lower than the first one. This can be observed until the 6th signal, from which a signal with SNR higher than the first one should be employed in order to maintain the detection rate (95%). However, in this case it would be more advantageous using only the 6th signal for estimating the MSC.

Later, Ferreira and Miranda de Sá (2005) compared the simple, multiple and partial coherences applied to the EEG during intermittent photic stimulation and consider these techniques promising in the analysis of the EEG during sensory stimulation. In the same year, Infantosi *et al.* (2005) verified, as theoretically predicted (Miranda de Sá and Felix, 2002, Miranda de Sá *et al.*, 2004), a better performance of the MC when compared to the MSC applied to the EEG during somatosensory stimulation of the tibial nerve. In this study, the MSC was applied to the bipolar derivations [Cz'-Fpz'] and [C3'-C4'] (where [Fpz'] is midway between [Fpz] and [Fz]; [Cz'], [C3'], and [C4'] are 2 cm posterior to [Cz], [C3] and [C4], respectively) - very often used for scalp SEP recording - and the MC was applied to both derivations. Using EEG signals from the same derivations during electric stimulation, Melges *et al.* (2006a) have found the MCSM to be useful for tibial nerve SEP detection. At the same year, Melges *et al.* (2006b) compared the performance of the MC and the MCSM, observing higher detection rates for the former. This result was observed for different values of *M* epochs (100, 200, 400, 800) used in the calculation of the estimates. A comparison between the two techniques applied to the EEG during intermittent photic stimulation (Felix *et al.*, 2007) has also resulted in higher detection percentages for the MC over the MCSM. By means of simulation, it was observed that the presence of noise correlated with the responses degrades the detection rates (Felix *et al.*, 2007).

In 2008, Miranda de Sá *et al.* (2008) derived the probability density function of the MC and a set of evoked responses embedded in additive noise for the zero-coherence case (null hypothesis of response absence). In this work, it was also demonstrated the influence of the

Frequency-Domain Objective Response

**ORD and MORD application:** 2

respectively. The significance level

values exceeded the critical value.

**6.2 The tibial nerve somatosensory evoked potential waveform**

even for an untrained observer at 40 ms and 50 ms.

frequencies 29.0 and 33.8 Hz (nominal values: 30 and 35 Hz).

evidences the importance of phase in the Objective Detection.

it can be visualized the similarity of values of 2

ˆ ( ) *f* , 2ˆ *crit* , 2 ˆ*N* ( ) *f* , 2ˆ *N crit* , 2

Infantosi *et al* (2006).

analysis.

Detection Techniques Applied to Evoked Potentials: A Review 67

epoch to ensure that the late components of the artifact are also attenuated. Noisy epochs were next discarded by a semi-automatic artifact rejection algorithm, which rejects epochs with more than 5% of continuous samples or more than 10% of samples exceeding ± 3 SD (where SD is the standard deviation of 20 s of noise-free background EEG selected as reference signal). Details about the windowing and artifact rejection can be found in

were calculated for the EEG signals using expressions (9),(11),(23),(24),(18),(20), (25), (26),

and is cited for each illustration that follows. The detection was achieved when the estimate

As mentioned in the Section 2, the waveform quality of SEP is very dependent on the number of stimulus presented. Figure 2 illustrates this characteristic of the analysis performed by visual inspection. For the coherent average obtained with *M*=50 epochs for derivation Cz of volunteer #35, the tibial nerve SEP waveform is very noisy and it is difficult to identify its characteristic waves. For *M*=200 epochs, the P37 (at 40 ms) and N45 (at 52 ms) are visible, respectively with amplitudes equal to -2.86 μV and 0.86 μV. However, it can be seen that, when a higher number of epochs (*M* = 500 epochs) is used, the waveform is smoother and the identification of the short-latency SEP components can be easily pointed

Even for the SEP obtained with high signal-to-noise ratio, the components P37 and N45 presents high amplitude and latency (time duration from the stimulus to a peak or valley occurrence) variability, as it can be observed in Figure 3, which presents the SEP for six individuals calculated by averaging 500 epochs. This variability, associated with low signalto-noise SEP recording obtained in hospital units, reinforces the subjectivity of such

The application of MSC to the EEG of volunteer #40 (stimulated at 6 mA) is illustrated in Figure 4. The horizontal black dashed line represents the detection threshold; when the corresponding MSC tracing surpasses its critical value, the detection is assumed for that (those) specific frequency (frequencies). As it can be observed, the MSC presents low values for derivation [C3] and higher values for [C4], that is, the higher response effects occur ipsilateral to the stimulated limb (the well known paradoxical lateralization (Cruse et al., 1982)). For derivation [C4], the detection is evident, predominantly at the frequencies from 30 to 65 Hz. On the other hand, for [C3], MSC exceeds the critical value only for the

Both the CSM and MSC of derivation [C4] of volunteer #38 are showed in Figure 5, in which

obtained from the MSC when the amplitude information is discarded, this similarity

ˆ [ 4] *C* and 2

ˆ [ 4] *C* . Since the CSM can be

**6.3 ORD techniques applied to the somatosensory evoked response detection**

ˆ ( ) *f* , 2 ˆ *crit* , 2

= 5% was generally adopted, but the *M*-value varied

ˆ*N* ( ) *f* , 2 ˆ*N crit*

number of EEG epochs (*M*) in both bias and variance of the MC estimates. At the same year, Melges *et al.* (2008b) compared the performance of MSC applied to the bipolar derivations [Cz-Fz] and [C3-C4] with the MC applied to the pairs of unipolar derivations [Cz][Fz] and [C3][C4]. The results showed that if two leads are available, it is better to use the MC of unipolar recordings than the MSC applied to the difference of the leads (bipolar derivation).

Since the use of unipolar derivations seemed to be more adequate, the performance for the MC and MCSM were compared, by applying both techniques to the pairs of unipolar derivations [Cz][Fz] and [C3][C4] (Melges *et al.*, 2010). The comparison was performed for *M*=100 and 800 epochs. The MC outperformed the MCSM, regardless the pair of derivations or the number of EEG epochs used for the estimates calculation.

More recently, Melges *et al.* (2011b) compared the MSC applied to the unipolar derivations [Cz], [Fz], [C3] and [C4] - usually employed in a bipolar SEP recording, as above mentioned - and the MC applied to the pairs [Cz][Fz] and [C3][C4]. The results evidenced the detection improvement by using synergically the information of two derivations, showing to be more advantageous using the MC than the MSC.

## **6. Examples and applications of ORD and MORD techniques**

This section presents examples of using ORD and MORD techniques to the EEG during somatosensory stimulation. Following, the experimental protocol of EEG acquisition, the pre-processing and processing steps, and some results are shown.

## **6.1 EEG acquisition, pre-processing and processing**

**EEG Acquisition:** EEG signals during somatosensory stimulation were collected from forty adult volunteers aging from 21 to 41 years old (mean ± standard deviation: 28.6 ± 4.6 years), without history of neurological pathology and with normal SEP. The signals were collected using the EEG BNT-36 (EMSA, Brazil, www.emsamed.com.br) according to the 10-20 International System and all leads referenced to the earlobe average. The volunteers were laid down in the supine position with eyes closed. The stimuli were applied by means of current pulses (200 µs width) to the right posterior tibial nerve using the Atlantis Four (EMSA, Brazil, www.emsamed.com.br). About 1000 to 1400 stimuli were applied at the motor threshold (the lowest intensity that produces toe oscillations) and at the rates of 1.99, 4.83, 6.68, 8.51 Hz (nominal values: 2, 5, 7, 9 Hz). The motor threshold was determined by an accelerometer tied in the toe that allowed the recording of the oscillations. The stimuli in the frequencies of 7 and 9 Hz were applied to 32 of the 40 volunteers. The ground electrode was attached to the poplitea fossa. Surface silver and gold electrodes were used, respectively, for recording and stimulation. An Institutional Review Board approved this research and all volunteers signed informed consent forms.

**Pre-processing:** The signals were band-filtered (0.5 – 100 Hz) and digitized (16-bits resolution) with BNT-36 at the sampling rate of 600 Hz. Then, the EEG was segmented into epochs of 501, 207, 149 and 117 ms, stimuli-synchronized, leading to spectral resolution of 2.0, 4.83, 6.71 and 8.55 Hz, respectively. In order to minimize the interference of the stimulus artifact in the ORD and MORD techniques we have set to zero the first 5 ms after each stimulus. Furthermore, the final 5 ms were zero padded to ensure window symmetry. A Tukey window with 7 ms rising (falling) time has been next applied to each

number of EEG epochs (*M*) in both bias and variance of the MC estimates. At the same year, Melges *et al.* (2008b) compared the performance of MSC applied to the bipolar derivations [Cz-Fz] and [C3-C4] with the MC applied to the pairs of unipolar derivations [Cz][Fz] and [C3][C4]. The results showed that if two leads are available, it is better to use the MC of unipolar recordings than the MSC applied to the difference of the leads (bipolar derivation). Since the use of unipolar derivations seemed to be more adequate, the performance for the MC and MCSM were compared, by applying both techniques to the pairs of unipolar derivations [Cz][Fz] and [C3][C4] (Melges *et al.*, 2010). The comparison was performed for *M*=100 and 800 epochs. The MC outperformed the MCSM, regardless the pair of derivations

More recently, Melges *et al.* (2011b) compared the MSC applied to the unipolar derivations [Cz], [Fz], [C3] and [C4] - usually employed in a bipolar SEP recording, as above mentioned - and the MC applied to the pairs [Cz][Fz] and [C3][C4]. The results evidenced the detection improvement by using synergically the information of two derivations, showing to be more

This section presents examples of using ORD and MORD techniques to the EEG during somatosensory stimulation. Following, the experimental protocol of EEG acquisition, the

**EEG Acquisition:** EEG signals during somatosensory stimulation were collected from forty adult volunteers aging from 21 to 41 years old (mean ± standard deviation: 28.6 ± 4.6 years), without history of neurological pathology and with normal SEP. The signals were collected using the EEG BNT-36 (EMSA, Brazil, www.emsamed.com.br) according to the 10-20 International System and all leads referenced to the earlobe average. The volunteers were laid down in the supine position with eyes closed. The stimuli were applied by means of current pulses (200 µs width) to the right posterior tibial nerve using the Atlantis Four (EMSA, Brazil, www.emsamed.com.br). About 1000 to 1400 stimuli were applied at the motor threshold (the lowest intensity that produces toe oscillations) and at the rates of 1.99, 4.83, 6.68, 8.51 Hz (nominal values: 2, 5, 7, 9 Hz). The motor threshold was determined by an accelerometer tied in the toe that allowed the recording of the oscillations. The stimuli in the frequencies of 7 and 9 Hz were applied to 32 of the 40 volunteers. The ground electrode was attached to the poplitea fossa. Surface silver and gold electrodes were used, respectively, for recording and stimulation. An Institutional Review Board approved this research and all

**Pre-processing:** The signals were band-filtered (0.5 – 100 Hz) and digitized (16-bits resolution) with BNT-36 at the sampling rate of 600 Hz. Then, the EEG was segmented into epochs of 501, 207, 149 and 117 ms, stimuli-synchronized, leading to spectral resolution of 2.0, 4.83, 6.71 and 8.55 Hz, respectively. In order to minimize the interference of the stimulus artifact in the ORD and MORD techniques we have set to zero the first 5 ms after each stimulus. Furthermore, the final 5 ms were zero padded to ensure window symmetry. A Tukey window with 7 ms rising (falling) time has been next applied to each

or the number of EEG epochs used for the estimates calculation.

**6. Examples and applications of ORD and MORD techniques**

pre-processing and processing steps, and some results are shown.

**6.1 EEG acquisition, pre-processing and processing**

advantageous using the MC than the MSC.

volunteers signed informed consent forms.

epoch to ensure that the late components of the artifact are also attenuated. Noisy epochs were next discarded by a semi-automatic artifact rejection algorithm, which rejects epochs with more than 5% of continuous samples or more than 10% of samples exceeding ± 3 SD (where SD is the standard deviation of 20 s of noise-free background EEG selected as reference signal). Details about the windowing and artifact rejection can be found in Infantosi *et al* (2006).

**ORD and MORD application:** 2 ˆ ( ) *f* , 2ˆ *crit* , 2 ˆ *N* ( ) *f* , 2ˆ *N crit* , 2 ˆ ( ) *f* , 2 ˆ *crit* , 2 ˆ*N* ( ) *f* , 2 ˆ *N crit* were calculated for the EEG signals using expressions (9),(11),(23),(24),(18),(20), (25), (26), respectively. The significance level = 5% was generally adopted, but the *M*-value varied and is cited for each illustration that follows. The detection was achieved when the estimate values exceeded the critical value.

## **6.2 The tibial nerve somatosensory evoked potential waveform**

As mentioned in the Section 2, the waveform quality of SEP is very dependent on the number of stimulus presented. Figure 2 illustrates this characteristic of the analysis performed by visual inspection. For the coherent average obtained with *M*=50 epochs for derivation Cz of volunteer #35, the tibial nerve SEP waveform is very noisy and it is difficult to identify its characteristic waves. For *M*=200 epochs, the P37 (at 40 ms) and N45 (at 52 ms) are visible, respectively with amplitudes equal to -2.86 μV and 0.86 μV. However, it can be seen that, when a higher number of epochs (*M* = 500 epochs) is used, the waveform is smoother and the identification of the short-latency SEP components can be easily pointed even for an untrained observer at 40 ms and 50 ms.

Even for the SEP obtained with high signal-to-noise ratio, the components P37 and N45 presents high amplitude and latency (time duration from the stimulus to a peak or valley occurrence) variability, as it can be observed in Figure 3, which presents the SEP for six individuals calculated by averaging 500 epochs. This variability, associated with low signalto-noise SEP recording obtained in hospital units, reinforces the subjectivity of such analysis.

## **6.3 ORD techniques applied to the somatosensory evoked response detection**

The application of MSC to the EEG of volunteer #40 (stimulated at 6 mA) is illustrated in Figure 4. The horizontal black dashed line represents the detection threshold; when the corresponding MSC tracing surpasses its critical value, the detection is assumed for that (those) specific frequency (frequencies). As it can be observed, the MSC presents low values for derivation [C3] and higher values for [C4], that is, the higher response effects occur ipsilateral to the stimulated limb (the well known paradoxical lateralization (Cruse et al., 1982)). For derivation [C4], the detection is evident, predominantly at the frequencies from 30 to 65 Hz. On the other hand, for [C3], MSC exceeds the critical value only for the frequencies 29.0 and 33.8 Hz (nominal values: 30 and 35 Hz).

Both the CSM and MSC of derivation [C4] of volunteer #38 are showed in Figure 5, in which it can be visualized the similarity of values of 2 ˆ [ 4] *C* and 2 ˆ [ 4] *C* . Since the CSM can be obtained from the MSC when the amplitude information is discarded, this similarity evidences the importance of phase in the Objective Detection.

Frequency-Domain Objective Response

the stimulation frequency.

**0.00**

represent the critical value: 2ˆ 0.006

ˆ [ 3] *C* and 2

**0.02**

**0.04**

**0.06**

**MSC**

Fig. 4. 2

dimensionless.

**0.08**

**0.10**

**0.12**

positive alarm can be as lower as desired, setting up

**6.4 Topographic distribution of the evoked responses**

Detection Techniques Applied to Evoked Potentials: A Review 69

As it should be clear, establishing a statistical threshold for identifying the response detection reduces the subjectivity of the analysis. It is worth noting that the maximum false

The localization on the scalp of the response to a specific kind of stimulation is a critical issue for the detection performance, since it determines the best regions for the evoked potential recording. In Melges et al. (2008), we have described that the leads with best signal-to-noise ratio for electrical stimulation of the right posterior tibial nerve are [Pz], [P4], [Cz], [C4] that is, leads at the parietal and central regions midsagital and ipsilateral to the stimulated limb. The results were obtained with the MSC applied to the SEP using 5 Hz as frequency of stimulation (fstim). In fact, although the SEP is known to change its waveform characteristics with the stimulation frequency, the best detection percentages were obtained in the same leads for all investigated frequencies (2, 5, 7 and 9 Hz). Figure 6 shows the performance of the MSC for all the casuistry stimulated at the motor threshold and with fstim = 9 Hz. As it can be seen, the same leads [Pz], [P4], [Cz], [C4] present the best detection rates. The ordinate presents the percentage of volunteers for whom it was possible to detect the evoked response for each frequency from the 1st to 12nd harmonics of

**10 20 30 40 50 60 70 80 90 100**

ˆ [ 4] *C* of volunteer #40, stimulated at 6 mA and 5 Hz. Horizontal line

=0.05). Vertical axis (MSC) is

**Frequency (Hz)**

*crit* (*M* = 500 epochs and

for the corresponding value.

 crit [C3] [C4]

^

^ ^

Fig. 2. Coherent Average (M = 50, 200 and 500 epochs) of derivation [Cz] of volunteer #35, stimulated at 24 mA and 5 Hz.

Fig. 3. Coherent Average (M = 500 epochs) of derivation [Cz] of volunteers #12, #13, #14, #22, #24, #26, respectively stimulated at 10, 10.5, 18, 12.5, 16 and 15 mA (these currents correspond to the individual motor threshold) and 5 Hz.

 M=50 M=200 M=500

**10 20 30 40 50 60 70 80 90 100**

**10 20 30 40 50 60 70 80 90 100**

**Time (ms)**

Fig. 3. Coherent Average (M = 500 epochs) of derivation [Cz] of volunteers #12, #13, #14, #22, #24, #26, respectively stimulated at 10, 10.5, 18, 12.5, 16 and 15 mA (these currents

**Time (ms)**

Fig. 2. Coherent Average (M = 50, 200 and 500 epochs) of derivation [Cz] of volunteer #35,

 #12 #13 #14 #22 #24 #26

**-4**

stimulated at 24 mA and 5 Hz.

**-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8**

correspond to the individual motor threshold) and 5 Hz.

**SEP (**

**V)**

**-2**

**0**

**SEP (**

**V)**

**2**

**4**

As it should be clear, establishing a statistical threshold for identifying the response detection reduces the subjectivity of the analysis. It is worth noting that the maximum false positive alarm can be as lower as desired, setting up for the corresponding value.

#### **6.4 Topographic distribution of the evoked responses**

The localization on the scalp of the response to a specific kind of stimulation is a critical issue for the detection performance, since it determines the best regions for the evoked potential recording. In Melges et al. (2008), we have described that the leads with best signal-to-noise ratio for electrical stimulation of the right posterior tibial nerve are [Pz], [P4], [Cz], [C4] that is, leads at the parietal and central regions midsagital and ipsilateral to the stimulated limb. The results were obtained with the MSC applied to the SEP using 5 Hz as frequency of stimulation (fstim). In fact, although the SEP is known to change its waveform characteristics with the stimulation frequency, the best detection percentages were obtained in the same leads for all investigated frequencies (2, 5, 7 and 9 Hz). Figure 6 shows the performance of the MSC for all the casuistry stimulated at the motor threshold and with fstim = 9 Hz. As it can be seen, the same leads [Pz], [P4], [Cz], [C4] present the best detection rates. The ordinate presents the percentage of volunteers for whom it was possible to detect the evoked response for each frequency from the 1st to 12nd harmonics of the stimulation frequency.

Fig. 4. 2 ˆ [ 3] *C* and 2 ˆ [ 4] *C* of volunteer #40, stimulated at 6 mA and 5 Hz. Horizontal line represent the critical value: 2ˆ 0.006 *crit* (*M* = 500 epochs and =0.05). Vertical axis (MSC) is dimensionless.

Frequency-Domain Objective Response

Detection Techniques Applied to Evoked Potentials: A Review 71

(Melges *et al.*, 2011a). In this case, the use of the higher investigated frequency 9 Hz, represent a gain of 9:5 in the time of detection, if we consider the very often used stimulation frequency (5 Hz). Figure 7 presents the detection rates for derivation [Cz] and *M* = 200 epochs. In this figure it is possible to visualize the similarity in the profile of the detection percentage tracings, showed to be statistically equivalent for the maximum

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

**F8**

**T4**

**T6**

**Fp2**

**F4**

**C4**

**P4**

**O2**

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

After identifying the more responsive frequencies and have optimized the stimulation frequency aiming the fast detection, it is possible to choose one or some frequencies for monitoring its temporal evolution. In Figure 8A, a modulus of a Virtual Instrument

Fig. 6. Percentage of volunteers whose response to the stimulation could be detected using the MSC for multiples from 1 to 12 (9 to 100 Hz) of the stimulation frequency (9 Hz). Horizontal lines indicate 70, 80 and 90% of detection. For derivations Fp2 (31), F8 (31) and C4 (31), it was not possible to obtain 500 artifact-free epochs for the 32 volunteers, hence, the percentages were calculated with the number of volunteers

**Fz**

**Cz**

**Pz**

**Oz**

response frequency band, for both M = 100 and 500 epochs (Melges *et al.*, 2011a).

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

**Fp1**

**F3**

**C3**

**P3**

**O1**

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

in parenthesis.

**6.7 ORD temporal evolution**

**F7**

**T3**

**T5**

Fig. 5. 2 ˆ [ 4] *C* and 2 ˆ [ 4] *C* of volunteer #38, stimulated at 14 mA and 5 Hz. Horizontal lines represent the critical values: 2 ˆ 0.005 *crit* and 2ˆ 0.006 *crit* (*M* = 500 epochs and =0.05). Vertical axis (ORD) is dimensionless.

#### **6.5 Maximum response frequency band**

Apart from choosing suitable sites for EP recording, selecting the frequencies that are more responsive to a specific kind of stimulation is also important, since it leads to a more reliable objective neurophysiologic evaluation during surgical procedures.

From Figure 6, it is also possible to identify, in the derivations with best detection percentages, that the frequency range that includes from 2nd to the 6th harmonics of the stimulation frequency (9Hz) - frequencies from 18 to 54 Hz - is the more responsive. Hence, the presence of stimuli-response leads to positive detection in these frequencies, which were classified as the maximum response frequency band (Tierra-Criollo, 2001, Infantosi *et al.*, 2006); that is, frequencies within this range should be selected in order to augment the probability and rapidness of detection.

#### **6.6 Stimulation frequency**

The increase of the stimulation frequency is the simplest way of obtaining faster the response to a set of *M* stimuli, and enhances the time of detection. However, this frequency increase is known to cause changes in the SEP waveform (Chiappa, 1997, p. 307 and 323), whose characteristics are the basis for neurophysiologic monitoring. Fortunately, the detection rates obtained with an ORD approach is not statistically modified for different stimulation frequencies, as it was shown in a recent study of ours

**10 20 30 40 50 60 70 80 90 100**

ˆ [ 4] *C* of volunteer #38, stimulated at 14 mA and 5 Hz. Horizontal lines

*crit* (*M* = 500 epochs and

=0.05).

**Frequency (Hz)**

*crit* and 2ˆ 0.006

Apart from choosing suitable sites for EP recording, selecting the frequencies that are more responsive to a specific kind of stimulation is also important, since it leads to a more reliable

From Figure 6, it is also possible to identify, in the derivations with best detection percentages, that the frequency range that includes from 2nd to the 6th harmonics of the stimulation frequency (9Hz) - frequencies from 18 to 54 Hz - is the more responsive. Hence, the presence of stimuli-response leads to positive detection in these frequencies, which were classified as the maximum response frequency band (Tierra-Criollo, 2001, Infantosi *et al.*, 2006); that is, frequencies within this range should be selected in order to augment the

The increase of the stimulation frequency is the simplest way of obtaining faster the response to a set of *M* stimuli, and enhances the time of detection. However, this frequency increase is known to cause changes in the SEP waveform (Chiappa, 1997, p. 307 and 323), whose characteristics are the basis for neurophysiologic monitoring. Fortunately, the detection rates obtained with an ORD approach is not statistically modified for different stimulation frequencies, as it was shown in a recent study of ours

 2 crit 2 [C4] 2 crit [C4]

^

^ ^ ^

**0.00**

represent the critical values: 2 ˆ 0.005

**6.5 Maximum response frequency band**

probability and rapidness of detection.

**6.6 Stimulation frequency**

Vertical axis (ORD) is dimensionless.

objective neurophysiologic evaluation during surgical procedures.

ˆ [ 4] *C* and 2

**0.02**

**0.04**

**0.06**

**ORD**

Fig. 5. 2

**0.08**

**0.10**

**0.12**

**0.14**

(Melges *et al.*, 2011a). In this case, the use of the higher investigated frequency 9 Hz, represent a gain of 9:5 in the time of detection, if we consider the very often used stimulation frequency (5 Hz). Figure 7 presents the detection rates for derivation [Cz] and *M* = 200 epochs. In this figure it is possible to visualize the similarity in the profile of the detection percentage tracings, showed to be statistically equivalent for the maximum response frequency band, for both M = 100 and 500 epochs (Melges *et al.*, 2011a).

Fig. 6. Percentage of volunteers whose response to the stimulation could be detected using the MSC for multiples from 1 to 12 (9 to 100 Hz) of the stimulation frequency (9 Hz). Horizontal lines indicate 70, 80 and 90% of detection. For derivations Fp2 (31), F8 (31) and C4 (31), it was not possible to obtain 500 artifact-free epochs for the 32 volunteers, hence, the percentages were calculated with the number of volunteers in parenthesis.

1 2 3 4 5 6 7 8 9 101112

1 2 3 4 5 6 7 8 9 101112

1 2 3 4 5 6 7 8 9 101112

#### **6.7 ORD temporal evolution**

After identifying the more responsive frequencies and have optimized the stimulation frequency aiming the fast detection, it is possible to choose one or some frequencies for monitoring its temporal evolution. In Figure 8A, a modulus of a Virtual Instrument

Frequency-Domain Objective Response

operative application.

**A**

**B**

Fig. 8. 2

ˆ ( ) *f* of the frequency 36.8 Hz (

B) *M*=400 epochs ( 2ˆ 0.0075

Portuguese Regional Settings.

**6.8 MORD techniques applied to SEP**

stimulated at MT and IT for A) *M*=50 epochs (Horizontal orange line: 2ˆ 0.0593

condition at: A) t=830, 2296, 3164, 4591, 5459, 6889, 7781 and 9204 elapsed epochs. B) t=480, 1946, 2814, 4241, 5109, 6539, 7431 and 8854 elapsed epochs. Horizontal scale in elapsed epochs. Vertical axis (ORD-MSC) is dimensionless. The decimal separator in the coordinates scale is "comma", since the virtual instrument was developed using Brazilian

The use of more than one derivation, as suggested by Miranda de Sá and Felix (2002), can improve the detection rates without the need of augmenting the exam duration (the number of EEG epochs used for ORD estimation). Figure 9 shows the MSC (*M* = 100 epochs) for [C3] and [C4], and the MC (*M* = 100 epochs) using both leads of volunteer #17. Since the somatosensory region on the contralateral hemisphere presents SEP with very low

=0.05) for derivation [Fpz'-Cz'] of volunteer

*crit* ). Transitions from/to stimulated to/from no-stimulated

*crit* );

i.e., the first line of it, by the new epoch and return to step 1.

Detection Techniques Applied to Evoked Potentials: A Review 73

expression 9; 3) When a new EEG epoch is acquired, substitute the older EEG epoch of AEEG,

From Figure 8A, one can note that even for a low *M*-value (*M*=50 epochs), the MSC was capable to follow the transition from rest to stimulated condition (Figure legend indicates the instant when the stimulus started and stopped), and conversely. Since the increase of *M* is known to improve the detection rate, the time evolution of MSC was also evaluated using *M*=400 epochs (Figure 8B). As it can be noted, the MSC estimate with *M*=50 epochs (MSCM50) presents higher variability than the obtained with *M*=400 epochs (MSCM400). On the other hand, MSC400 presents a higher inertia to change from one status to the other. Hence, the *M*-value should be parsimoniously chosen for the clinical or intra-

(software) for Evoked Potential Objective Detection developed in Melges (2005) is shown, containing the temporal evolution of the MSC for the frequency of 36.8 Hz (Horizontal line represents the detection threshold). This signal was collected from volunteer #6, using parameters very commonly applied during surgical procedures. That is, the EEG was collected from derivation [Fpz'-Cz'] and with stimulation frequency of 5 Hz. In order to evaluate the capability of the MSC to reflect the transition of a responsive status to a noresponsive one, these conditions were mimicked by periods with and without electrical stimulation, respectively. Moreover, four periods with stimulation (S) were alternated with no-stimulation (NS) periods (starting without stimulation). The first S-period corresponds to the stimulation with the motor threshold intensity level (MT). In the following three Speriods, an intermediary intensity (IT) level was used; this intensity value was obtained by the arithmetic mean between MT and the sensitivity threshold, which corresponds to the lowest current level that is felt by the individual.

Fig. 7. Percentage of volunteers for whom the stimulation response was detected using the MSC (*M* = 200 epochs) for the frequencies from 2 to 100 Hz at the derivation [Cz] for the stimulation frequencies 2, 5, 7, 9 Hz.

The MSC estimates can be dynamically estimate as follows: 1) Store *M* EEG epochs in a matrix (AEEG); 2) Calculate the MSC estimate using the *M* EEG epochs of AEEG and

(software) for Evoked Potential Objective Detection developed in Melges (2005) is shown, containing the temporal evolution of the MSC for the frequency of 36.8 Hz (Horizontal line represents the detection threshold). This signal was collected from volunteer #6, using parameters very commonly applied during surgical procedures. That is, the EEG was collected from derivation [Fpz'-Cz'] and with stimulation frequency of 5 Hz. In order to evaluate the capability of the MSC to reflect the transition of a responsive status to a noresponsive one, these conditions were mimicked by periods with and without electrical stimulation, respectively. Moreover, four periods with stimulation (S) were alternated with no-stimulation (NS) periods (starting without stimulation). The first S-period corresponds to the stimulation with the motor threshold intensity level (MT). In the following three Speriods, an intermediary intensity (IT) level was used; this intensity value was obtained by the arithmetic mean between MT and the sensitivity threshold, which corresponds to the

**0 10 20 30 40 50 60 70 80 90 100**

 7Hz 5Hz 2Hz

9Hz

**Frequency (Hz)**

Fig. 7. Percentage of volunteers for whom the stimulation response was detected using the MSC (*M* = 200 epochs) for the frequencies from 2 to 100 Hz at the derivation [Cz] for the

The MSC estimates can be dynamically estimate as follows: 1) Store *M* EEG epochs in a matrix (AEEG); 2) Calculate the MSC estimate using the *M* EEG epochs of AEEG and

lowest current level that is felt by the individual.

**0**

stimulation frequencies 2, 5, 7, 9 Hz.

**10**

**20**

**30**

**40**

**50**

**% detection**

**60**

**70**

**80**

**90**

**100**

expression 9; 3) When a new EEG epoch is acquired, substitute the older EEG epoch of AEEG, i.e., the first line of it, by the new epoch and return to step 1.

From Figure 8A, one can note that even for a low *M*-value (*M*=50 epochs), the MSC was capable to follow the transition from rest to stimulated condition (Figure legend indicates the instant when the stimulus started and stopped), and conversely. Since the increase of *M* is known to improve the detection rate, the time evolution of MSC was also evaluated using *M*=400 epochs (Figure 8B). As it can be noted, the MSC estimate with *M*=50 epochs (MSCM50) presents higher variability than the obtained with *M*=400 epochs (MSCM400). On the other hand, MSC400 presents a higher inertia to change from one status to the other. Hence, the *M*-value should be parsimoniously chosen for the clinical or intraoperative application.

Fig. 8. 2 ˆ ( ) *f* of the frequency 36.8 Hz (=0.05) for derivation [Fpz'-Cz'] of volunteer stimulated at MT and IT for A) *M*=50 epochs (Horizontal orange line: 2ˆ 0.0593 *crit* ); B) *M*=400 epochs ( 2ˆ 0.0075 *crit* ). Transitions from/to stimulated to/from no-stimulated condition at: A) t=830, 2296, 3164, 4591, 5459, 6889, 7781 and 9204 elapsed epochs. B) t=480, 1946, 2814, 4241, 5109, 6539, 7431 and 8854 elapsed epochs. Horizontal scale in elapsed epochs. Vertical axis (ORD-MSC) is dimensionless. The decimal separator in the coordinates scale is "comma", since the virtual instrument was developed using Brazilian Portuguese Regional Settings.

### **6.8 MORD techniques applied to SEP**

The use of more than one derivation, as suggested by Miranda de Sá and Felix (2002), can improve the detection rates without the need of augmenting the exam duration (the number of EEG epochs used for ORD estimation). Figure 9 shows the MSC (*M* = 100 epochs) for [C3] and [C4], and the MC (*M* = 100 epochs) using both leads of volunteer #17. Since the somatosensory region on the contralateral hemisphere presents SEP with very low

Frequency-Domain Objective Response

Fig. 10. Detection rates (*M* = 100 epochs) for A) 2

**% detection**

ˆ [ 4] *C* and 2

2

[Cz][C4] were calculated over 39.

**% detection**

Detection Techniques Applied to Evoked Potentials: A Review 75

**10 20 30 40 50 60 70 80 90 100**

**10 20 30 40 50 60 70 80 90 100**

ˆ [ ] *Cz* , 2

ˆ [ 3][ 4] *C C* . For derivation [Cz], it was only possible to obtain 100 artifact-free

ˆ [ 4] *C* and 2

2

ˆ [ ][ 4] *Cz C* ; B) 2

**Frequency (Hz)**

B

ˆ [ 3] *C* , 2

epochs for 39 from the 40 volunteers, hence, the percentages of detection for [Cz] and

 [Cz] [C4] [Cz][C4]

> [C3] [C4] [C3][C4]

**Frequency (Hz)**

A

amplitude, as expected, the MSC values are low and under the detection threshold. On the other hand, the lead ipsilateral to the stimulated limb, [C4], shows detection for the nominal frequencies 35, 40, 50-60 Hz. It is worth noting that the employment of the 2 2 ˆ [ 3][ 4] *C C* resulted in estimate values higher than 2 ˆ [ 3] *C* and 2 ˆ [ 4] *C* , and the MC tracing surpasses its corresponding critical value for 35-60 Hz.

Fig. 9. 2 ˆ [ 3] *C* , 2 ˆ [ 4] *C* and 2 2 ˆ [ 3][ 4] *C C* of volunteer #17, stimulated at 10 mA and 5 Hz. Horizontal lines represent the critical values: 2ˆ 0.0300 *crit* and 2 2ˆ 0.0470 *crit* for =0.05, *M* = 100 epochs and *N*=2. Vertical axis (MSC and MC) is dimensionless.

The detection rates for the MSC applied to [Cz] and [C4] and for MC applied to [Cz][C4] is showed in Figure 10A. It is easy to note that the percentages for 2 ˆ [ ] *Cz* are higher than the observed for 2 ˆ [ 4] *C* , and both are lower than 2 2 ˆ [ ][ 4] *Cz C* . Hence, "adding" the information from [Cz] to the [C4] resulted in an increase in the overall response detection performance.

In fact, even when a derivation with lower signal-to-noise ratio ([C3]) is added to the estimation of the Multiple Coherence, the detection rates can be improved (Figure 10B), as theoretically predicted by Miranda de Sá and Félix (2002).

amplitude, as expected, the MSC values are low and under the detection threshold. On the other hand, the lead ipsilateral to the stimulated limb, [C4], shows detection for the nominal

ˆ [ 3] *C* and 2

**10 20 30 40 50 60 70 80 90 100**

ˆ [ 3][ 4] *C C* of volunteer #17, stimulated at 10 mA and 5 Hz.

2

*crit* and 2

**Frequency (Hz)**

The detection rates for the MSC applied to [Cz] and [C4] and for MC applied to [Cz][C4]

information from [Cz] to the [C4] resulted in an increase in the overall response detection

In fact, even when a derivation with lower signal-to-noise ratio ([C3]) is added to the estimation of the Multiple Coherence, the detection rates can be improved (Figure 10B), as

2

ˆ [ 4] *C* , and the MC tracing surpasses

 2 crit 2 [C3]

 [C4] 2 2 crit

C3C4

2ˆ 0.0470

*crit* for

ˆ [ ][ 4] *Cz C* . Hence, "adding" the

=0.05,

ˆ [ ] *Cz* are higher than

ˆ [ 3][ 4] *C C*

frequencies 35, 40, 50-60 Hz. It is worth noting that the employment of the 2

resulted in estimate values higher than 2

**0.00**

ˆ [ 3] *C* , 2

the observed for 2

performance.

ˆ [ 4] *C* and 2

2

*M* = 100 epochs and *N*=2. Vertical axis (MSC and MC) is dimensionless.

is showed in Figure 10A. It is easy to note that the percentages for 2

ˆ [ 4] *C* , and both are lower than 2

Horizontal lines represent the critical values: 2ˆ 0.0300

theoretically predicted by Miranda de Sá and Félix (2002).

**0.02**

**0.04**

**0.06**

**0.08**

**MSC and MC**

Fig. 9. 2

**0.10**

**0.12**

**0.14**

**0.16**

**0.18**

its corresponding critical value for 35-60 Hz.

Fig. 10. Detection rates (*M* = 100 epochs) for A) 2 ˆ [ ] *Cz* , 2 ˆ [ 4] *C* and 2 2 ˆ [ ][ 4] *Cz C* ; B) 2 ˆ [ 3] *C* , 2 ˆ [ 4] *C* and 2 2 ˆ [ 3][ 4] *C C* . For derivation [Cz], it was only possible to obtain 100 artifact-free epochs for 39 from the 40 volunteers, hence, the percentages of detection for [Cz] and [Cz][C4] were calculated over 39.

Frequency-Domain Objective Response

**9. Abbreviations**

**11. References**

**10. Acknowledgements**

providing infrastructure support.

York, Wiley-Interscience.

Mar/Apr, pp. 202-207.

17, No.6, pp. 362-366.

Detection Techniques Applied to Evoked Potentials: A Review 77

derivations to be employed for both MC and MCSM estimation for each kind of stimulation, since the presence of a massive number of leads is undesirable for clinical and surgical monitoring purposes. Moreover, the exponential forgetting, suggested by Tierra-Criollo *et al.* (1998), should be applied for multivariate ORD in order to increase the rapidness of response detection. Finally, both ORD and MORD techniques should be incorporated in the EP analysis software to have their efficacy evaluated for diagnosis and neuro-monitoring.

EEG – Electroencephalogram; EP – Evoked Potential; AEP – auditory EP; SEP – somatosensory EP; VEP – Visual EP; ORD – Objective Response Detection; MORD – Multivariate ORD.

To the Brazilian research and education agencies, the Rio de Janeiro State Research Council (FAPERJ), the National Council for Scientific and Technological Development (CNPq - Ministry of Science and Technology) and CAPES (Ministry of Education) for the financial support. We also acknowledge the Military Police Central Hospital of Rio de Janeiro for

Angel, A, Linkens, DA, Ting, CH. 1999. Estimation of latency changes and relative

Beagley, HA, Sayers, BMcA, Ross, AJ. 1979. Fully objective ERA by phase spectral analysis,

Bendat, JS, Piersol, AG. 2000. *Random Data Analysis and Measurement Procedures* (3 ed), New

Bose, B, Sestokas, AK, Schwartz, DM. 2004. Neuropsychological monitoring of spinal cord

Cagy, M, Infantosi, AFC, Gemal, AE. 2000. Monitoring depth of anaesthesia by frequencydomain statistical techniques, *Braz J Biomed Eng*, Vol. 16, No. 2, pp. 95-107. Cagy, M, Infantosi, AFC. 2002. Unconsciousness indication using time-domain parameters

Cagy, M., 2003, Monitorização do plano anestésico usando o potencial evocado auditivo de

Cagy, M, Infantosi, AFC. 2007. Objective response detection technique in frequency-domain for reflecting changes in MLAEP, Medl Eng Phy, Vol 29, No 8, Oct, pp. 910-917. Campos, DV, Infantosi, AFC, Lazarev, VV. 2006. Aplicação do Teste F spectral na detecção

*Comput Biomed Res*, Vol. 32, No. 3, Jun, pp. 209-251.

COPPE/UFRJ, Rio de Janeiro, Rio de Janeiro, Brazil.

(CDROM), pp. 318-321, São Pedro, São Paulo, Brazil, Oct 2006.

*Acta otolaryngol*, Vol. 87, No. 3, Jan, pp. 270-278.

amplitudes in somatosensory evoked potentials using wavelets and regression,

function during instrumented anterior cervical fusion, *Spine J*, Vol. 4, No. 2,

extracted from mid-latency auditory evoked potentials, *J Clin Monit Comput*, Vol.

média latência: técnicas no domínio do tempo e coerência espectral. D.Sc. Thesis.,

de respostas fotorecrutantes no eletroencefalograma multicanal de pacientes epilépticos, *Anais do XX Congresso Brasileiro de Engenharia Biomédica - CBEB2006*

## **7. Conclusion**

The ORD approach allows the detection of sensory response with a maximum false-positive rate () that can be defined as strict as desired. This leads to techniques that can be employed for a variety of occasions ranging from children auditory screening to the fast intra-operative monitoring in order to avoid early or late neurological sequels, including the ones arising from surgical manipulation. The wide applicability of the ORD comes from its computational simplicity, being usually based on the calculation of parameters derived from the Fourier Transform of EEG epochs.

When a very low signal-to-noise ratio is observed, which is the circumstance expected in hospital units due to the presence of electrical/electro-mechanic devices that generate electrical/electromagnetic interference, the use of more than one derivation, in a multivariate ORD approach, may improve the probability of detection without increasing in the exam duration. For this purpose, both scalp regions and frequencies more responsive should be employed in the objective detection. Moreover, in order to obtain faster response detection, the most higher stimulation frequency that does not result in decrease in the detection rates should be used.

For the right posterior tibial nerve SEP, presented as an illustration in this review, the maximum response frequency range is within the high beta and low gamma band (20- 60 Hz); the best regions for SEP recording includes the central and parietal leads at the midline and parasagital line ipsilateral to the stimulated limb ([Cz], [C4] [Pz] and [P4]). The stimulation frequency of 9 Hz, instead of the often employed 5 Hz, can be used without diminishes the probability of detection. Hence, once the application of MORD produces an increase in the detection percentages compared to the MSC for the same *M*-value, it can, on the other hand, be employed to reduce the exam duration (*M*), whereas the detection probability is maintained.

Analogue results are expected for SEP obtained for the left tibial nerve and even for upper limbs, since the anatomical pathways follow similar routes, including decussation and somatotopic mapping. However, it should be effectively measured.

This review presented the theoretical background of ORD and MORD techniques applied to the Evoked Potential field. The historical aspects together with the included examples may be useful to many researches, since they encompass applications ranging from elementary goals up to the state of art in biosignal detection.

## **8. Future directions**

Based on the prominent results found by using multivariate objective response detection techniques, it would be useful to investigate it for a number of derivations higher than *N* = 2. The MCSM critical value does not vary with *N*, as stated on expression (26) (Felix and Miranda de Sá, 2003). Thus, augmenting the number of derivations would imply increasing the detection rate. However, it did not occur in practical applications (Melges, 2009, Felix *et al.*, 2007). This could be explained by the fact that the background activities are correlated and hence there would be no improvement by continuously adding new derivations. However, this hypothesis of correlated activities should be verified for different kinds of evoked potentials. Additionally, it would be worth to identify the optimal number of derivations to be employed for both MC and MCSM estimation for each kind of stimulation, since the presence of a massive number of leads is undesirable for clinical and surgical monitoring purposes. Moreover, the exponential forgetting, suggested by Tierra-Criollo *et al.* (1998), should be applied for multivariate ORD in order to increase the rapidness of response detection. Finally, both ORD and MORD techniques should be incorporated in the EP analysis software to have their efficacy evaluated for diagnosis and neuro-monitoring.

## **9. Abbreviations**

76 Applied Biological Engineering – Principles and Practice

The ORD approach allows the detection of sensory response with a maximum false-positive

When a very low signal-to-noise ratio is observed, which is the circumstance expected in hospital units due to the presence of electrical/electro-mechanic devices that generate electrical/electromagnetic interference, the use of more than one derivation, in a multivariate ORD approach, may improve the probability of detection without increasing in the exam duration. For this purpose, both scalp regions and frequencies more responsive should be employed in the objective detection. Moreover, in order to obtain faster response detection, the most higher stimulation frequency that does not result in decrease in the

For the right posterior tibial nerve SEP, presented as an illustration in this review, the maximum response frequency range is within the high beta and low gamma band (20- 60 Hz); the best regions for SEP recording includes the central and parietal leads at the midline and parasagital line ipsilateral to the stimulated limb ([Cz], [C4] [Pz] and [P4]). The stimulation frequency of 9 Hz, instead of the often employed 5 Hz, can be used without diminishes the probability of detection. Hence, once the application of MORD produces an increase in the detection percentages compared to the MSC for the same *M*-value, it can, on the other hand, be employed to reduce the exam duration (*M*), whereas the detection

Analogue results are expected for SEP obtained for the left tibial nerve and even for upper limbs, since the anatomical pathways follow similar routes, including decussation and

This review presented the theoretical background of ORD and MORD techniques applied to the Evoked Potential field. The historical aspects together with the included examples may be useful to many researches, since they encompass applications ranging from elementary

Based on the prominent results found by using multivariate objective response detection techniques, it would be useful to investigate it for a number of derivations higher than *N* = 2. The MCSM critical value does not vary with *N*, as stated on expression (26) (Felix and Miranda de Sá, 2003). Thus, augmenting the number of derivations would imply increasing the detection rate. However, it did not occur in practical applications (Melges, 2009, Felix *et al.*, 2007). This could be explained by the fact that the background activities are correlated and hence there would be no improvement by continuously adding new derivations. However, this hypothesis of correlated activities should be verified for different kinds of evoked potentials. Additionally, it would be worth to identify the optimal number of

somatotopic mapping. However, it should be effectively measured.

goals up to the state of art in biosignal detection.

) that can be defined as strict as desired. This leads to techniques that can be employed for a variety of occasions ranging from children auditory screening to the fast intra-operative monitoring in order to avoid early or late neurological sequels, including the ones arising from surgical manipulation. The wide applicability of the ORD comes from its computational simplicity, being usually based on the calculation of parameters derived from

**7. Conclusion**

the Fourier Transform of EEG epochs.

detection rates should be used.

probability is maintained.

**8. Future directions**

rate (

> EEG – Electroencephalogram; EP – Evoked Potential; AEP – auditory EP; SEP – somatosensory EP; VEP – Visual EP; ORD – Objective Response Detection; MORD – Multivariate ORD.

## **10. Acknowledgements**

To the Brazilian research and education agencies, the Rio de Janeiro State Research Council (FAPERJ), the National Council for Scientific and Technological Development (CNPq - Ministry of Science and Technology) and CAPES (Ministry of Education) for the financial support. We also acknowledge the Military Police Central Hospital of Rio de Janeiro for providing infrastructure support.

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evoked potential spinal cord monitoring reduces neurologic deficits after scoliosis

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**4**

*Poland*

**Extraction of 3D Geometrical**

Michal Rychlik and Witold Stankiewicz

*Poznan University of Technology Division of Machine Design Methods*

**Features of Biological Objects with**

**3D PCA Analysis and Applications of Results**

The Computer Aided Design (CAD) systems are very well known by designers in their every day practice and numerical analysis. Computer models of real objects with advanced numerical tools, significantly improves the quality and reduce time of design process. In addition to the three-dimensional modeling systems, there are many other tools and techniques (such as reverse engineering, rapid prototyping), which will further enhance the

Many of those engineering technologies, especially CAD/CAM techniques, have an application not only in mechanical design. These tools also can be used in different disciplines, like biomechanics, bioengineering, biometrics, etc. This interdisciplinary area of knowledge takes advantage of Reverse Engineering, three-dimensional modeling and simulation, FEM1 analysis and is equipped with Rapid Prototyping and CNC machines. The acquisition and processing of three-dimensional models with complicated shapes becomes the important issue in applications mentioned above. The 3D virtual models have numerous applications, simply such as visualization, but also more advanced like medical diagnostics (virtual endoscopes), pre-surgical planning (simulations of surgical operations), FEM and CFD2 analysis, CNC machining, Rapid Prototyping, preparation and fabrication of implants, etc. Several engineering technologies and tools can be used for advanced analysis of biological objects.

The first step in computer analysis of biological/medical objects is to obtain the correct and high accurate 3D model. This 3D modeling generally is made by reconstruction procedure. 3D reconstruction can be done by usage of medical imagining systems (such as CT, NMR) or 3D scanning systems. Reconstruction of 3D model based on DICOM3 images must be supported by image processing (segmentation of the region of interest) to extract 3D shape of the object. Dependent on the area of interest the bones, blood vessels or other soft tissues

**1. Introduction**

capabilities of engineers.

can be searched.

1FEM – finite element method 2CFD – computational fluid dynamics

3DICOM – Digital Imaging in Communications in Medicine

## **Extraction of 3D Geometrical Features of Biological Objects with 3D PCA Analysis and Applications of Results**

Michal Rychlik and Witold Stankiewicz *Poznan University of Technology Division of Machine Design Methods Poland*

## **1. Introduction**

84 Applied Biological Engineering – Principles and Practice

Victor, JD, Mast, J. 1991. A new statistic for steady-state evoked potentials, Electroencephalogr Clin Neurophysiol, Vol. 78, No. 5, May, pp. 378-388. Xu, S, Meyer, D, Yoser, S, Mathews, D, Elfervig, JL. 2001.Pattern visual evoked potential in

Zaeyen, EJB. 2005. Aplicação da Coerência ao eletroencefalograma para investigar

http://www.dominiopublico.gov.br/)

the diagnosis of functional visual loss, *Ophthalmology*, Vol. 108, No. 1, Jan, pp. 76-80.

características do Potencial Evocado Auditivo de Média Latência. M.Sc. Dissertation, COPPE/UFRJ, Rio de Janeiro, Rio de Janeiro, Brazil. (Available at: