Analysis of EEG tracings in frequency and time domain in hepatic encephalopathy

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 8 1 ( 2 0 0 6 ) 203–212

journal homepage: www.intl.elsevierhealth.com/journals/cmpb

Analysis of EEG tracings in frequency and time domain in hepatic encephalopathy D. Pascoli a,d , J.M. Gu´erit b , S. Montagnese c,d , M. de Tourtchaninoff b , T. Minelli a,d , A. Pellegrini c,d , F. Del Piccolo c,d , A. Gatta c,d , P. Amodio c,d,∗ a

Department of Physics University of Padova, Italy Unit´e pour la Recherche Neurophysiologique du Systeme Nerveux, Universit´e de Louvain Bruxelles, Belgium c Department of Clinical and Experimental Medicine, Via Giustiniani, 2, 33128 Padova, Italy d CIRMANMEC University of Padova, Italy b

a r t i c l e

i n f o

a b s t r a c t

Article history:

Spectral EEG analysis in hepatic encephalopathy (HE) is usually performed disregarding the

Received 28 November 2003

effect of epoch length, statistical errors and equipment noise. A study on these items was

Received in revised form 12 October

carried out. In addition, spectral analysis and a new analysis, performed in time domain,

2005

were compared in the assessment of HE.

Accepted 26 October 2005

The EEG tracings of 73 cirrhotic patients with HE were analyzed. Artifact-free periods of about 1 min were selected. Equipment noise was measured by short-circuiting all the elec-

Keywords:

trodes.

Digital EEG

The equipment noise was notable below 1.5 Hz; the best epoch length was 4 s and the sta-

Frequency-domain analysis

tistical errors were minimal for the band with the highest relative power. Nineteen per cent

Time-domain analysis

of the tracings were unstable. The spectral values were found to be related to liver function

Liver failure

and to the degree of HE, whereas the relationship with psychometric variables was poor. The

Encephalopathy

indexes computed by time-domain analysis were found to be better related to psychometric

Cognitive alterations

findings. We have provided information on the optimisation of spectral EEG analysis and presented a time-domain analysis giving results related to psychometric tests and liver function. © 2006 Elsevier Ireland Ltd. All rights reserved.

1.

Introduction

Psychometric and EEG assessment have long been considered to be fundamental tools for the diagnosis and the classification of hepatic encephalopathy (HE) both in its overt and its minimal or subclinical expression [1–8]. In more recent times, SPECT [9,10], PET [11,12] and NMR spectroscopy [13,14] have been used to study functional central nervous system (CNS) alterations in cirrhotic patients, but they mainly have a research value, since they are too costly to be used routinely. Moreover, information concerning their reliability, and their

∗

clinical-prognostic value in HE is still lacking. For these reasons, psychometric and neurophysiological assessment still remain the main tool for detecting and quantifying mild HE for clinical purposes [15,16]. EEG can be assessed by means of simple visual reading and by quantitative methods such as spectral analysis. The use of spectral analysis to assess overt HE was introduced by Van der Rijt et al. [17], who proved its relationship with mental impairment. Even minimal HE is detectable by EEG spectral analysis [2–5]. This technique provides more reliable and valid data than simple visual reading [3], is roughly related to psy-

Corresponding author at: Department of Clinical and Experimental Medicine, Via Giustiniani, 2, 33128 Padova, Italy. Tel.: +39 049 8218677. E-mail address: [email protected] (P. Amodio).

0169-2607/$ – see front matter © 2006 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.cmpb.2005.10.009

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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 8 1 ( 2 0 0 6 ) 203–212

chometric [2,18,19] and life-quality assessment [20], and has a good prognostic value on survival and occurrence of overt HE [21]. Van der Rijt et al. [17] assessed the severity of HE on the basis of the mean dominant frequency (MDF) of the EEG and power levels of spectral bands. However, the use of many parameters, each of them associated with an unknown confidence interval, may not be considered an optimal evaluation criterion. Moreover, spectral analysis may indeed be influenced by the procedure adopted; however, these features have not yet been clarified or discussed in detail. We therefore performed a study to assess the influence of noise, epoch length and stationarity of the EEG tracing on spectral analysis in a wide clinical spectrum of HE. Furthermore, we compared spectral analysis with a new quantification criterion based on a time-domain analysis and aimed at summarizing the EEG alterations of encephalopathy.

2.

Measuring and computational methods

2.1.

Patient sample groups

Two convenient groups of cirrhotic patients were included in the study: the first one (group A) was recruited in Padova (Italy) and comprised 64 patients (37 with grade 1 HE), the second one (group B) was recruited in Bruxelles (Belgium) and comprised nine patients with severe HE (grade 4). The diagnosis of liver cirrhosis was based on previous medical history, clinical examination, biochemical, endoscopic and ultrasound findings. When required, the diagnosis was confirmed by liverbiopsy (18 cases). No enrolled patient had: chronic obstructive lung disease or other lung diseases causing respiratory failure (PaO2 < 60 mm Hg and/or paCO2 < 50 mm Hg), renal failure (creatinine plasma level >200 ␮mol/L), coronary heart disease or heart failure of any origin (NYHA > 1), previous neurological focal episodes or other neurological or psychiatric illnesses, history of psychotropic drugs abuse or alcohol intake in the 6 months before the study. The main clinical and biochemical findings of the patients that were considered are those used to calculate the Child-Pugh score [22]. This is a composite scale based on albumin, prothrombin time, bilirubin and on the clinical appraisal of ascites and HE (Table 1). In addition, venous ammonia plasma level was taken into account, because ammonia has an important role in the pathophysiology of HE [23]. The main

Table 1 – The Child-Pugh classification of the severity of liver cirrhosis Score Bilirubin (␮mol/l) Albumin (g/l) Prothrombin time (%) Ascites Encephalopathy

1

2

<35 >34 >70 Absent Absent

35–51 28–34 40–70 Moderate Grade 1–2

Table 2 – Demographic, clinical, biochemical data of cirrhotic patients

Age (years) Males (%) Etiologyb (%) Child-Pugh class A (%) Child-Pugh class B (%) Child-Pugh class C (%) HE gradec (%) a

b c

54 ± 9 74 31/16/33/20 20 56 24 75/21/4/0/0

Group Aa

Group B

55 ± 9 75 42/16/23/19 20 56 24 71/23/4/0/0

54 ± 8 57 40/15/40/5 0 0 100 0/0/40/60/0

Of the original 64 patients that had been considered, 52 patients were included, as the EEG signal of the other patients did not satisfy analysis criteria. Alcohol/mixed/viral/other. HE was staged on the basis of the severity of mental alterations, according to Conn’s criteria [24]. Grade: 0/1/2/3/4.

clinical and biochemical data of the patients are reported in Table 2. The grade of HE was assessed by mental impairment quantified according to West Haven criteria [24]. In those patients that were suitable for a psychometric evaluation (because of a normal or near-normal vigilance and compliance) the existence of mild cognitive impairment was assessed by psychometric tests sensitive to the early stages of HE. The psychometric battery was composed by the Trialmaking test A (TMT-A) [25], the Symbol Digit test (SDT) [26], the Scan test [1], the Choice test [1] and the Posner test [18]. In the Posner test only reaction times in the neutral condition were considered, therefore the test has been used as a generic index of central nervous system activation. Psychometric test results were adjusted according to age and education level. Patients with two or more altered psychometric tests (≤2 standard deviations of the expected values) were considered to have mild cognitive impairment. The clinical and psychometric features of group A patients reflect fairly adequately those generally found in a nonselected population of hospitalized patients presenting with liver disease, mainly with decompensated cirrhosis, in whom mild cognitive impairment is detectable even in the absence of clear clinical evidence of HE [1,4,27]. The prevalence of such alterations was confirmed to be associated with the degree of liver failure. Group B patients comprised a highly selected population of cirrhotic patients with severe HE, who were hospitalized in an Intensive Care Unit. The study did not imply any clinical investigation in addition to those currently done in our patients for clinical reasons. The only additional element was the mathematical evaluation of digitalized EEG. The study was approved by the senior staff of the Departments involved.

3 >51 <28 <40 Severe Grade 3–4

Child-Pugh class A: total score <7; Child-Pugh class B: total score 7–9; Child-Pugh class C: total score >9.

2.2.

Methods for neurophysiological assessment

2.2.1.

EEG recording

All patients underwent a digital EEG recording (equipment: Brainquick 3200, Micromed, Italy). A standard 21 differential channel cap was used and electrodes were placed according to the international “10–20” system [28]. The physical reference was Oz and the ground FpZ. Electrode impedance was kept

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below 5 k
. Each channel had its own analog-to-digital converter; signals were digitally filtered in the frequency range 0.3–120 Hz; sampling frequency was 256 Hz, and resolution 800 ␮V/12 bits (0.19 ␮V/bit). After an accurate visual analysis of the tracings, only artifact-free EEG recording periods were considered for the study. Analysis was performed on the derivations P3-Cz and P4-Cz, which were expected to be less influenced by muscle artifacts and eye blinks than peripheral and anterior derivations. To avoid the presence of artifacts, the length of the tracings analyzed in our study ranged from 48 s to 80 s, with the exception of one case that lasted 168 s. As the EEG signal is converted into digital numbers, from here onwards signal amplitude will be expressed in numerical units (counts), one count being equivalent to a 0.19 ␮V.

2.2.2.

Equipment noise

To evaluate a possible systematic error due to the equipment, equipment noise contribution to channel signals was measured for a time interval of 100 s. All cap channels were short-circuited by means of a conductive sheet and their electrode impedance was kept at 1 k
± 10%. In this condition, if electronic noise of the apparatus were negligible, the channel signals would be nil; therefore, any detectable signal would be a noise signal. Such a signal was characterised by its mean value, standard deviation, and total power.

2.2.3.

EEG stationarity

EEG tracing can be assessed if its structure is reasonably stable in time. In fact, if a computed property is time dependent, its value is function of the tracing length and does not provide meaningful information. The rather intuitive term “stability” corresponds to the mathematical notion of stationarity. A signal is referred to as being stationary when its properties computed over short time intervals do not vary significantly from one interval to the next. The non-stationarity we are dealing with in this paper is the one revealed by a time trend of the computed properties. To analyze tracings with a trend is meaningless; in fact if, for instance, the mean square value of signal amplitude is an increasing function of time, its mean value can be computed, but it is not reliable. Let Qi be the property value in the ith interval. The Qi set has no trend if its values distribute, on average, around a constant value (that does not depend on i) as the i value increases. In other words, if we plot the Qi values versus the interval number and fit them with a straight line, there is no trend if the fit line is parallel to i axis. To verify the stability of our EEGs, we divided the tracings in 2 s intervals, because such a short period is long enough to

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contain information that qualifies the tracing. The signal total power (evaluated in the time domain) and its mean square amplitude were computed for every interval. We chose to test the stability of the total power as it is related to the quantities we used to asses the tracings, while the mean square amplitude was only computed for comparison purposes. The “Reverse Arrangement Test” for stationarity [29] was applied to the computed quantities, fixing a significance level of 5%. In Fig. 1 the normalised power values versus tracing intervals are shown for a stable signal (left panel) and for an unstable one (right panel).

2.2.4.

Frequency-domain analysis

Power spectrum was calculated after having divided periods of the EEG tracing into N equal time intervals (epochs). Spectral power was computed for each epoch by means of the fast Fourier data transform obtaining a family of spectral powers Pi (fj ), where i varies from 1 to N and j from 0 to M, the M value depending on the epoch time length. For every frequency value fj there is, therefore, a set of N power values. Their mean value is the power spectrum (Ps):

Ps(fj ) =

N
Pi (fj )

N

i=0

(1)

and the statistical error is the related standard deviation. The parameters took into account to classify EEG alteration were the mean dominant frequency (MDF) and the relative power (Rp) of the delta, theta and alpha bands, defined as follows:

m2 MDF =

f Ps(fj ) j=m1 j

m2

j=m1

(2)

Ps(fj )

where fm1 and fm2 were 1.5 Hz and 40 Hz, respectively,

high Rp =

j=low

m2

j=m1

Ps(fj )

(3)

Ps(fj )

flow and fhigh were, in the three bands:

(4) As epoch time length is a crucial parameter in power computation, the values of the MDF and the power bands were

Fig. 1 – Normalised power vs. tracing interval number for a stable signal (left panel) and an unstable one (right panel). The unstable signal is characterized by a clear trend in time.

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Fig. 2 – Tracing description by power spectrum (on the left) and by scaling function (on the right). The dominant frequency is given by sf/m1, where sf is the sampling frequency. The di index is the amplitude difference of the first maximum and the first minimum, normalized to the first one. The time unit (count) is 4 ms.

calculated on 2 s and 4 s epochs. As these quantities are function of power spectrum, their statistical errors are correlated to power spectrum errors and were computed applying the classical method of error propagation [30].1

2.2.5.

The EEG analysis by scaling properties

The goal was to give a compact description of the EEG spectral structure using an approach in the time domain. An EEG signal, in spite of its oscillatory behaviour, is unpredictable. There is, in fact, no explicit mathematical law predicting its time evolution, starting from a given initial condition. Therefore, a digital EEG signal can be described like a time series of random values whose properties can be evaluated by statistical methods. We described the spectral structure of the data by means of the signal amplitude variation (incremental amplitude) as a function of the time span, applying an approach derived from the description of random walk [31]. Let S(ti) be the signal amplitude value at time ti; (ti + 1 − ti) is the sampling time interval, i ranges from 1 to N, where N(ti + 1 − ti) is the total signal time span. If, for every ti we compute the difference: sm (ti ) = S(ti+m ) − S(ti )

with i ranging from 1 to N − m,

(5)

we obtain a set of N − m values giving the incremental amplitude in time intervals tm . The set has, on average, a mean value close to 0, while its standard deviation  m is a measure of the incremental amplitude. As different tracings have different amplitude and, therefore, different incremental amplitude, it is necessary to provide a normalized standard deviation.

1 If quantity f is function of k quantities x1 , x2 , . . ., xk , and  i is the standard deviation of xi , the standard deviation of f,  f , is given by:

 f =

k  2
∂f i=1

∂xi

i2

+



 ∂ f   ∂ f  i

j=1

∂xi

where Vij is the xi covariance matrix.

∂xj

1/2 Vij

The function: SF(m) =

m 1

(6)

provides the parameters for tracing properties qualification; where  1 is the standard deviation of the set: s1 (ti ) = S(ti+1 ) − S(ti ) If the tracing power spectrum is a narrow band around a central frequency (Fig. 2, left panel), the related SF function is a sinusoidal-like function of decreasing amplitude (Fig. 2, right panel). By detecting the first maximum of SF function, its first minimum and the related m value (m1), we computed two quantities, the dominant frequency (df) and the dominant index (di), defined as follows: df =

sf m1

di =

SFmax − SFmin SFmax

where sf is the sampling frequency

(7)

(8)

df provides the frequency related to the maximum value of spectral power, while di measures the predominance of df on the other spectrum frequencies. The value di ranges from 0 to 1: 0 means no dominant frequency; 1 is an asymptotic value that represents the di value of a pure sinusoidal signal. The wider the power spectrum band, the lower the di values. For instance, the df and di computed for the tracing of Fig. 2 are 9.18 Hz and 0.61, respectively, whereas, for the tracing shown in Fig. 3 df and di values are 6.91 Hz and 0.27. SF oscillatory behaviour tends to disappear when signal power distribution flattens; this occurs in severe encephalopathy like the one described by Fig. 4. Fig. 5 shows 4-s of the same EEG traces of Figs. 2–4, respectively. SF computation was repeated 10 times for every tracing; at each time the starting point was moved forward by 256 time steps (1 s). In this way a set of 10 uncorrelated measurements was provided for every tracing and the mean df value (DF), the mean di value (DI) and their related statistical errors (about 1% for both) were computed.

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Fig. 3 – Power spectrum and mean scaling function of a tracing with high power value in theta band. With respect to a normal tracing, the scaling function oscillation decreases.

The product DF × DI was also calculated to provide a synthetic information on the DF and its predominance.

2.3.

Statistics

Unless otherwise specified, results are expressed as mean ± standard deviation. When needed, standard deviation is expressed as a percentage of the mean value (S.D.%). The relationship between the neurophysiological variables and the indexes of liver function or the psychometric variables was carried out by the Spearman’s rank order correlation. Multivariate stepwise forward analysis was applied to assess which of the neurophysiological variables are the predictors of clinical and biochemical findings. The package “Statistica 6.0” (StatSoft, Inc., Tulsa, OK) was used for the statistical analysis.

2.4.

Software implementation

The equipment noise value and the EEG tracings features were calculated by especially developed functions in MATLAB lan-

guage, running under Window XP. MATLAB (The Mathworks, Inc., Natick, MA) was chosen as it integrates a computing language in an easy-to-use interactive environment for algorithm development, data visualization, data analysis.

3.

Results

3.1.

Quality of the EEG recording

The noise mean value (averaged on all the channels) of shortcircuited channels was 7 counts (±3%) and the S.D. mean value was 3.3 counts (±12%). The mean total power, computed by integrating spectral power from 0.3 Hz to 40 Hz, was 1.65 × 103 counts2 /Hz (±10%). The mean value is a constant offset due to a steady potential generated at the electrodes, therefore, in EEG analysis, it can be easily removed. This is not the case for signal fluctuation due to intrinsic noise of the amplifier chain, which increases as the electrode impedance value does. As the maximum S.D. value of EEG signals was about 100 counts, a noise of 3.3 counts implies a minimum

Fig. 4 – Power spectrum and scaling function of a tracing with high power value in the theta–delta band. The oscillation of the scaling function tends to disappear.

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Fig. 5 – The shape of EEG tracings related to Figs. 2–4, respectively.

statistical error of about 3%. Fortunately, such a poor accuracy was related to signal low frequency components. Noise power spectrum (Fig. 6) followed a law of type P(f) = f−˛ with ˛ > 0. Power was very high for low frequencies while it hit 0 for high frequencies. The noise power in the range 0.3–1.5 Hz was 80% of the total power and the S.D. mean value of signals, after a low pass filter set to 1.5 Hz, was 0.5 counts. Therefore, the lowest frequency was set to 1.5 Hz to remove any systematic error of the recording equipment. By means of the reverse arrangement test, 12 tracings were found to be unstable. Therefore, 52 tracings were included in this article.

3.2.

Frequency-domain analysis

The difference between the two hemispheres was actually negligible. Therefore we chose to consider only the right

derivation P4-Cz for practical reasons and in order to avoid excessive multiple comparisons.

3.2.1.

3.2.2.

Fig. 6 – Noise power spectrum of the apparatus showing a sharp increase at low frequencies.

Influence of epoch length

The MDF, the relative powers of frequency bands and their errors were found to be influenced by epoch length (Table 3). For both epoch lengths, errors were minimal for the band with the highest relative power. This was not surprising, because the highest power band qualifies the tracing and it is expected to be more stable. The error in the band of maximum relative power was lower or equal in 4 s epochs when compared to 2 s epochs in 29 tracings, the reverse was observed in 25 cases. Therefore, spectral analysis was performed on 4 s epochs, because they provided higher resolution and comparable statistical error, in spite of the lower number of epochs used in the computation.

Features of EEG spectra in cirrhotic patients

Many of the spectral variables were proved to be correlated with the biochemical and clinical indexes of liver failure, in agreement with the well-known relationship between liver dysfunction and HE (Table 4). The EEG tracings of the patients with grade 1 HE were slower than those of patients without clinical signs of encephalopathy (grade 0) (MDF = 7.9 ± 2.7 Hz versus 9.6 ± 1.4 Hz, p < 0.01), they had lower alpha relative power (29 ± 10 versus 47 ± 20, p = 0.02), and higher delta relative power (13 ± 7 versus 9 ± 6, p = 0.03). The patients with mild cognitive impairment had lower alpha relative power (27 ± 24 versus 42 ± 8, p < 0.01) and higher delta relative power (22 ± 23 versus 11 ± 8, p < 0.001). At any rate, the correlation between spectral analysis variables and the psychometric tests was poor (Table 5). In contrast, the EEG findings in group B

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Table 3 – Spectral variables and the related standard deviations (in %) in five patients Patient code

MDF

1

8.85 8.83

2

S.D. (%)

Alfa

S.D. (%)

Theta

S.D. (%)

Delta

S.D. (%)

0.94 1.1

35.34 29.52

9.88 12.82

55.18 62.11

6.83 6.8

1.97 1.56

14.38 14.83

9.89 9.77

2.17 2.22

47.88 46.12

8.31 7.83

17.21 17.99

12.3 11.75

14.3 16.02

13.63 13.88

3

6.92 6.88

1.4 1.18

8.83 6.95

9.06 9.25

74.39 78.69

2.69 1.98

12.12 10.61

12.51 10.73

4

8.76 8.72

0.87 1.21

42.03 29.92

7.83 12.15

47.14 60.04

7.2 6.9

3.99 3.73

11.78 14.9

5

9.57 9.48

2.22 2.28

55.48 46.28

9.33 12.4

26.03 34.76

20.93 17.57

6.53 6.46

16.69 27.24

For each patient the first row refers to 2 s epoch length, the second one to 4 s epoch length.

Table 4 – Matrix of correlations (Spearman’s rank order correlations R) of the variables obtained by spectral EEG analysis and time-domain analysis with the main clinical and biochemical indices of liver disease Neurophysiologic parameter

Child-Pugh score −0.36 −0.40** 0.22 0.34* −0.32* −0.29 −0.38*

MDF Alpha relative power Theta relative power Delta relative power DF DI DF × DI ∗ ∗∗

Prothrombin activity

*

Ammonia −0.34 −0.51** 0.40* 0.27 −0.36* −0.17 −0.32* *

0.28 0.29* −0.36* −0.13 0.25 0.18 0.31*

Bilirubin −0.23 −0.23 0.16 0.33* −0.16 −0.27 −0.31*

P < 0.05. P < 0.01.

comatose patients were fairly typical and characterized by severe MDF reduction (5.0 ± 1.4 Hz) with the spectral power almost completely displaced in the delta (relative power: 52 ± 22) and theta bands (relative power 33 ± 18).

3.3.

Time-domain analysis

Only the right hemisphere was consider for the sake of simplicity, as for the case of spectral analysis. The values obtained by time-domain analysis were found to be well related with those derived by spectral analysis, but not equivalent to them (Table 6), possibly because even if both techniques provide

information on the overall structure of the tracing, their approaches are deeply different. Most interestingly, correlations were found between the product DI × DF and indexes of liver function (Table 4). The EEG of the patients with grade 1 HE had a lower DI (0.26 ± 0.12 versus 0.44 ± 0.15 p < 0.01), but an equivalent DF (9.2 ± 2.7 vs 9.2 ± 1.0 Hz) when compared to grade 0 patients. The patients with mild cognitive impairment had both lower DI (0.31 ± 0.17 versus 0.46 ± 0.14, p < 0.01) and DI × DF (2.5 ± 1.5 versus 4.1 ± 1.3 Hz, p < 0.01) when compared to patients without any psychometric alteration. The relationship between the psychometric tests and the variables obtained by time-domain

Table 5 – Matrix of correlations (Spearman’s rank order correlations R) between the psychometric tests and the variables obtained by spectral and time-domain analysis SCAN test

CHOICE

Rt

TMT-A

Spectral analysis MDF Alpha relative power Theta relative power Delta relative power

−0.11 −0.20 0.10 0.16

−0.21 −0.17 0.21 −0.01

0.07 −0.25 0.09 0.16

−0.03 −0.11 0.01 0.22

Time-domain analysis DF DI DF × DI

−0.07 −0.27 −0.31#

−0.33# 0.05 −0.07

−0.09 −0.35# −0.28*

−0.08 −0.31# −0.38#

∗ ∗∗ #

P < 0.01. P < 0.001. P < 0.05.

SDT 0.04 0.24 −0.07 −0.27 0.05 0.49** 0.47**

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Table 6 – Matrix of correlations (Spearman’s rank order correlations R) of the variables obtained by spectral EEG analysis and time-domain analysis DF MDF MDF S.D.% Alpha relative power Alpha relative power S.D. (%) Theta relative power Theta relative power S.D. (%) Delta relative power Delta relative power S.D. (%) ∗ ∗∗ #

DF S.D. (%) **

0.92 −0.01 0.77 ** −0.57* −0.70** 0.68** −0.28# 0.30#

0.18 0.74** −0.26 0.19 −0.17 0.12 0.65 −0.11

DI

DI S.D. (%)

0.04 −0.86** 0.45 ** −0.32# 0.16 −0.07 −0.87** 0.36*

0.04 0.78** −0.37** 0.22 −0.23 0.12 0.76** −0.38*

DF × DI

DF × DI S.D. (%)

*

0.40 −0.77** 0.72** −0.53** −0.21 0.25 −0.87** 0.40*

0.19 0.82 0.33# 0.24 −0.23 0.18 0.76** −0.22

P < 0.01. P < 0.001. P < 0.05.

analysis was closer than that with variables obtained by spectral EEG analysis (Table 5). Multivariate analysis comparing the EEG indexes with biochemical and neuropsychological variables showed that while spectral indexes were related to biochemical findings, timedependent analysis was mainly related to cognitive variables (Table 7). In five of the patients with severe HE (group B) the DF (and, consequently, the DI) was not measurable.

4.

Discussion

Firstly, even in the best recording conditions, the equipment noise was significant at frequencies below 1.5 Hz; this precludes reliable analysis at these low frequencies. This noise was detectable even with an electrode impedance as low as 1 k
± 10% and such finding sheds doubts on the validity of

recordings performed with a less careful electrode placement. Therefore, more attention should be paid to electrode placement technique as to obtain comparable low impedance values, thereby providing EEG tracings suitable for quantitative analysis. Nevertheless, the steep decrease of equipment noise for frequencies higher than 1.5 Hz suggests good confidence levels for routine power analysis of HE which, especially in mild HE, concerns higher frequencies. Secondly, the finding that stationarity was dissatisfactory in 19% of the tracings justifies the search for its levels and the exclusion of dissatisfactory tracings in methodological studies, such as the present one. This finding confirms that spectral analysis should be repeated at least twice in clinical practice [3], as it is generally the case with evoked potential and other commonly used clinical variables, e.g., the measuring of blood pressure. Thirdly, the influence of epoch length on spectral EEG analysis was found to be significant, in at least some of the cases. In

Table 7 – Multivariate analysis comparing the predictive value of the indexes obtained by spectral and time-domain EEG analysis on biochemical and psychometric variables Predictors ChildPugh score

Delta relative power ˇ = 0.32 ± 0.16, p < 0.049

Bilirubin

Delta relative power ˇ = 0.35 ± 0.14, p < 0.017

Prothrombin activity

Theta relative power ˇ = −0.71 ± 0.28, p < 0.015

Ammonia

Alpha relative power ˇ = −0.41 ± 0.16, p < 0.015

Scan test

–

Choice test

DF ˇ = −0.65 ± 0.20, p < 0.003

RT

DF ˇ = 0.32 ± 0.15, p < 0.04

TMT-A

SDT

DI ˇ = 0.58 ± 0.24, p < 0.019

–

–

DF × DI ˇ = −0.41 ± 0.16, p < 0.015

Delta relative power ˇ = −1.00 ± 0.38, p < 0.02

Alpha relative power ˇ = 1.00 ± 0.41, p < 0.02

DI9 ˇ = 2.44 ± 0.58, p < 0.001

Delta relative power ˇ = 1.13 ± 0.31, p < 0.001

MDF ˇ = 0.84 ± 0.25, p < 0.002

computer methods and programs in biomedicine

neurophysiological studies, epoch length varies from 1 s to 10 s [17,31–33], but rarely do the authors justify their choice; even when a justification is given, it is founded on generic a priori need of epoch stability, without any experimental verification. Epoch length has to ensure both a frequency resolution high enough to provide a good accuracy for spectrum values and a total number of epochs high enough to provide statistically significant information. Long epochs provide higher frequency resolution and, therefore, higher accuracy in power computation than short epochs. On the other hand, short epochs give larger number of samples and, consequently, a lower statistical error of computed quantities than long epochs. In tracings of about 1 min duration, as those that we analysed, epochs shorter than 2 s or longer than 4 s do not meet the requirements of sufficient resolution and sufficient low statistical error, respectively. The comparison of 2 s and 4 s epochs showed that they have fairly comparable statistical errors; therefore, the 4 s epoch might be preferable because of its higher frequency resolution when compared to 2 s epoch. For these reasons the values of spectral EEG analysis that we used in this study were those provided by analyzing 4 s epochs. The variables obtained by spectral analysis were confirmed to be related with the indexes of liver function [21,34] and highlighted the outstanding differences between patients with severe HE and those with low grade HE [17]. However, in the cirrhotic patients without any clinical sign of encephalopathy we confirmed that there was only a weak relationship between psychometric findings and the variables obtained by spectral EEG analysis [3,4,18,19]. Several, mutually non-exclusive hypotheses can be put forward to explain this finding: (i) EEG and cognitive alterations could reflect different features of encephalopathy [4], (ii) cognitive alterations have a multifactorial origin so they could depend on both the degree of intoxication due to liver failure and compensatory elements due to pre-morbid brain conditions [35], (iii) the variables provided by spectral analysis are insufficient to completely quantify all the information provided by the EEG, (iv) the EEG itself is not sensitive enough to study neurological dysfunction in mild HE. Noteworthy, the time-domain analysis suggests that the information provided by the EEG was not completely covered by spectral analysis. The variables obtained by frequency analysis were related to those obtained by time domain since they measure similar features of the EEG tracing. However, the incomplete correlation across the variables emphasizes that the information was not entirely redundant. In fact, the reduction of the DI in the patients with psychometric alterations without a clear reduction of the DF confirms that the first consequence of HE on EEG is not a mere slowing down of the main frequency, but the appearance of other rhythms that overlap the basic activity. Such a phenomenon is in keeping with the qualitative description of the appearance of random theta waves by Parsons-Smith et al. [8]. It appeared to be more readily expressed by the DI or by the product of the DF × DI (which provides information both on EEG slowing down and on the loss of a dominant frequency). Interestingly, multivariate analysis showed that some EEG features that was preferentially reflected by time-domain analysis reflected cognitive dysfunction better than spectral analysis which, in turn, provided indexes more related to liver dysfunction. If confirmed

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by further studies, this finding might disclose a better understanding of EEG dynamics in hepatic encephalopathy. Finally, the finding that in five comatose patients there was no computable DF may suggest progressive loss of order in the electrical activity of such patients.

5.

Conclusions and future plans

We reported the influence of noise, epoch length, and stationarity of the EEG tracing on spectral analysis in a wide clinical spectrum of hepatic encephalopathy. The comparison of spectral analysis with a new quantification criterion based on a time-domain analysis aimed at summarizing the EEG alterations of HE highlighted that such a technique provides data which were better correlated with psychometric alterations in low grade HE, but cannot be applied to cases of high grade HE. This last finding may reveal a peculiar severe disruption of the regulatory mechanisms of electrogenesis in severe coma. Further research is now planned to verify if the indexes obtained by the proposed time-dependent EEG analysis change in parallel with clinical and psychometric findings during follow-up and if they have prognostic value on patients survival and risk to develop severe HE. If the technique will produce data that are useful for clinical applications, a friendly usable software will be prepared to be tested in various clinical settings by independent observers.

references

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