Regional Analysis of Spontaneous MEG Rhythms in Patients

with Alzheimer’s Disease Using Spectral Entropies

JESUS POZA,1 ROBERTO HORNERO,1 JAVIER ESCUDERO,1 ALBERTO FERNANDEZ,2 and CLARA I. SANCHEZ1

1Biomedical Engineering Group, Department T.S.C.I.T., E.T.S. Ingenieros de Telecomunicacion, University of Valladolid,Camino del Cementerio s/n, 47011 Valladolid, Spain; and 2Centro de Magnetoencefalografıa Dr. Perez-Modrego, Complutense

University of Madrid, Madrid, Spain

(Received 3 July 2007; accepted 30 October 2007; published online 10 November 2007)

Abstract—Alzheimer’s disease (AD) is the most commonform of dementia. Ageing is the greatest known risk factorfor this disorder. Therefore, the prevalence of AD is expectedto increase in western countries due to the rise in lifeexpectancy. Nowadays, a low diagnosis accuracy is reached,but an early and accurate identification of AD should beattempted. In this sense, only a few studies have focused onthe magnetoencephalographic (MEG) AD patterns. Thiswork represents a new effort to explore the ability of threeentropies from information theory to discriminate betweenspontaneous MEG rhythms from 20 AD patients and 21controls. The Shannon (SSE), Tsallis (TSE), and Renyi(RSE) spectral entropies were calculated from the time-frequency distribution of the power spectral density (PSD).The entropies provided statistically significant lower valuesfor AD patients than for controls in all brain regions(p<0.0005). This fact suggests a significant loss of irregu-larity in AD patients’ MEG activity. Maximal accuracy of87.8% was achieved by both the TSE and RSE (90.0%,sensitivity; 85.7%, specificity). The statistically significantresults obtained by both the extensive (SSE and RSE) andnon-extensive (TSE) spectral entropies suggest that ADcould disturb long and short-range interactions causing anabnormal brain function.

Keywords—Magnetoencephalogram, Time-frequency distri-

bution, Shannon spectral entropy, Tsallis spectral entropy,

Renyi spectral entropy.

INTRODUCTION

Alzheimer’s disease (AD) is a progressive neurode-generative disorder of unknown etiology. It is theleading form of dementia representing about 50–60%of all cases.7 Several risk factors have been identified.7

However, the greatest known risk factor for AD isageing, which is especially important in western

countries where an increase in life expectancy isexpected.7 Early symptoms of AD include memory lossand concentration problems, while as the dementiaprogresses AD patients may suffer aphasia, apraxia,and agnosia, accompanied with general cognitivesymptoms such as confusion, personality and behaviorchanges, impaired judgment, and disorientation.6

Brain changes in AD are related to the appearanceof two characteristic lesions: senile or neuritic plaquesand neurofibrillary tangles. They both are formed byclusters of proteins accumulated in two specific brainregions: the hippocampus and the cerebral cortex.Whereas the small clumps of beta-amyloid may inducea degeneration of synapses, the neurofibrillary tanglesdestroy a vital cell transport system made of proteins.11

Several potential biomarkers for AD have beenproposed. Among them, the levels Ab1-42 and isoformsof tau protein in cerebrospinal fluid (CSF) have beenextensively reported in the literature.7 Many other fluidbiomarkers have been analyzed in both serum andCSF, including isoprostanes and glycation, inflamma-tion and oxidative stress markers.44 Various plasmamarkers are also being investigated, including amyloidpeptide proteins and similar molecules to those ana-lyzed in CSF.44 Structural neuroimaging studies offercomplementary advantages to the biological markers.Thus, positron emission tomography (PET) imaging ofglucose metabolism and magnetic resonance imaging(MRI) volumetry of medial temporal lobe have shownpromising results as diagnostic screening in clinicaltrials.26 Nevertheless, their routinely use is not rec-ommended in any consensus guidelines for diagnosis ofthe disease.7

Clinical diagnosis of AD is based on a completemedical history together with physical, psychiatric, andneurological examinations.25,34 Additionally, labora-tory studies, such as thyroid-function tests andassessment of vitamin B12 deficiency, are recom-mended to identify other forms of dementia and

Address correspondence to Jesus Poza, Biomedical Engineering

Group, Department T.S.C.I.T., E.T.S. Ingenieros de Telecom-

unicacion, University of Valladolid, Camino del Cementerio s/n,

47011 Valladolid, Spain. Electronic mail: jespoz@tel.uva.es

Annals of Biomedical Engineering, Vol. 36, No. 1, January 2008 (� 2007) pp. 141–152

DOI: 10.1007/s10439-007-9402-y

0090-6964/08/0100-0141/0 � 2007 Biomedical Engineering Society

141

coexisting disorders associated with ageing.25 Struc-tural neuroimaging techniques such as computertomography (CT) or MRI are also appropriate toexclude other causes of dementia.25 Nevertheless, thediagnosis accuracy is low, with sensitivity of around81% and specificity of 70%.25 Hence, a definite con-firmation of AD can be only made by post-mortemexamination of brain tissue.7,34

In spite of the relatively low diagnosis accuracy, anearly and accurate identification of AD should beattempted. Current therapies are more effective if themedication is administered in the initial stages of thedisease.11 Additionally, an early diagnosis enables todevelop strategies for coping with the disease. Elec-troencephalographic (EEG) brain activity has beenextensively analyzed to obtain early markers of AD,while only a few studies have focused on the magne-toencephalographic (MEG) disease patterns.23,37 Al-though EEG and MEG recordings are generated bysynchronous oscillations of pyramidal neurons, theyreflect slightly different characteristics.20 The EEGmeasures the electric fields induced by all primarycurrents, whereas the MEG is sensitive only to currentflows oriented parallel to the scalp.20,21 Furthermore,the EEG is strongly influenced by a wide variety offactors such as head structures (e.g., skull and extra-cerebral tissues) or several technical and methodolog-ical issues (e.g., electrode placement, reference point oreven adhesive compound of the electrode to the skin).MEG recordings are less distorted than EEG signalson the scalp due to the insensitivity of magnetic fieldsto inhomogeneities in the head.21 In addition, MEGsignals are reference-free recordings and offer higherspatial resolution than conventional EEG.20

A few studies have found several abnormalities inspontaneous MEG recordings of AD patients whenthey were compared to those from healthy controls.MEG studies using relative power have shown in-creased slow rhythms and reduced fast activity inAD.4,14,28 This issue has been also observed by meansof spectral quantifiers such as mean frequency,13,31

individual alpha peak28,29,31 and transition fre-quency.31 Some authors have found a global decreasein irregularity31 and complexity19 in AD patients’MEG recordings at rest. However, the loss of com-plexity has been only described in the high frequencieswhen a detailed spectral analysis in several frequencybands was performed.8 From another point of view,other approaches have focused on analyzing functionalconnections rather than local abnormalities in AD.Their findings showed both a decrease of coherencevalues in the alpha band18 and a general decrease ofcoherence in all frequency bands.4 A reduced level ofsynchronization has also been reported in the upperalpha, beta, and gamma bands of AD patients in

comparison with controls suggesting a loss of func-tional connectivity.38 In a recent study analyzingMEG recordings at rest, it has been shown thatfunctional connectivity in AD is characterized byspecific changes of long and short distance interac-tions in several frequency bands.39 Decreased levels offunctional connectivity indicate that AD is related toan abnormal function of the large scale brain net-works. Nevertheless, further studies should confirmthis hypothesis.

We conclude that MEG signals stem from a com-plex system where both short and long-range (for in-terneural distances) phenomena are simultaneouslypresent. Information measures have recently demon-strated to be appropriate to characterize complexrecordings. Previous studies have successfully appliedseveral quantifiers based on extensive (e.g., Shannonand Renyi entropies) and non-extensive (e.g., Tsallisentropy) information measures to analyze EEG sig-nals.2,5,9,24,33,40,41 While extensive quantifiers, such asShannon and Renyi entropies, have proved successfulin describing systems with short-range interactions,non-extensive measures, such as Tsallis entropy, areable to describe a system where the effective interac-tions are of long-range.5,40 In addition, MEG record-ings, like EEG signals, are non-stationary and theircharacteristics may change over time. Non-stationaryanalysis techniques, such as time-frequency distribu-tions, are appropriate to accurately describe theirproperties. Previous efforts have exploited the analogybetween power spectral densities and probability den-sities to apply several entropic forms to time-frequencydistributions.2,3

The present study is a new approach to explore theability of several measures derived from informationtheory to characterize MEG rhythms in AD. Thiswork has been developed on the basis of the resultsobtained in a pilot study where we tested severalentropies using the averaged relative power over allsensors as a probability distribution.30 Our findingssuggested both a slowing of MEG rhythms and a lossof irregularity in AD. Further work should be devel-oped to obtain a temporal evolution of the quantifiers,to assess the influence of the entropic index and toperform a spatial analysis. The parameters used in thepresent study are extensive and non-extensive entropiesbased on the time-frequency distribution, which mea-sure the irregularity or disorder of MEG recordings.Initially, the Fourier transform (FT) was used tocompute the power spectral density (PSD) into non-overlapping temporal windows for each MEGrecording from AD patients and controls. Shannon(SSE), Tsallis (TSE), and Renyi (RSE) spectralentropies were then calculated to explore the irregu-larity of the MEG signals. Additionally, both the RSE

POZA et al.142

extensive and the TSE non-extensive entropies wereparameterized by the entropic index q, which wasmodified to emphasize particular characteristics of theassociated dynamics.

In ‘‘Experimental setup’’ section, the demographicand neuropsychological data of the study populationare presented, together with the characteristics of theMEG recordings. Section ‘‘Methods’’ briefly summa-rizes the definitions of Shannon, Tsallis, and Renyientropies and their application on time-frequencyplane. Results are presented in ‘‘Results’’ section,where the role of the parameter q is analyzed andregional entropy analyses are performed. In ‘‘Discus-sion’’ section the relevant results are discussed, while‘‘Conclusions’’ section summarizes the major contri-butions of the paper.

EXPERIMENTAL SETUP

Selection of Subjects

We analyzed MEG signals from 41 subjects re-corded in the ‘‘Centro de MagnetoencefalografıaDr. Perez-Modrego’’ of the Complutense Universityof Madrid (Spain). Twenty subjects (7 men and 13women, age = 73.05 ± 8.65 years, mean ± standarddeviation SD) were AD patients derived from the‘‘Asociacion de Familiares de Enfermos de Alzheimer’’(AFAL) and the Geriatric Unit of the ‘‘Hospital Clı-nico Universitario San Carlos’’ from Madrid. Theywere diagnosed on the basis of exhaustive medical,physical, neurological, psychiatric, and neuropsycho-logical examinations, which were complemented withbrain scans to exclude other causes of dementia. All ofthem fulfilled the criteria for probable AD according tothe clinical guidelines of the National Institute ofNeurological and Communicative Disorders andStroke and the AD and Related Disorders Association(NINCDS-ADRDA).27 Both the Mini-Mental StateExamination (MMSE)17 and the Functional Assess-ment Staging (FAST)32 were used to evaluate thecognitive function. AD patients obtained mean scoresof 17.85 ± 3.91 and 4.00 ± 0.32 on the MMSE andFAST, respectively. None of the AD patients sufferedfrom any other significant medical, neurological, andpsychiatric disorder. They were not taking any drugthat could affect the MEG recordings.

Twenty-one healthy subjects (9 men and 12 women,age = 70.29 ± 7.07 years, mean ± SD) were en-rolled in the study as control group. They were cog-nitively normal elderly controls with no history ofneurological or psychiatric disorders. The meanMMSE and FAST scores were 29.10 ± 1.00 and1.71 ± 0.46, respectively.

We did not obtain significant differences (p>0.05,Student’s t-test) when the mean age of AD patientsand controls was compared. In addition, all healthyvolunteers and patients’ caregivers accepted to partic-ipate in the study and gave written informed consent.The trial was approved by the study center’s ResearchEthics Committee.

MEG Recording

MEG signals were obtained using a 148-channelwhole-head magnetometer (MAGNES 2500 WH, 4DNeuroimaging), which was confined in a magneticallyshielded room. During the data acquisition, subjectswere asked to remain relaxed, awake and with eyesclosed in order to minimize the presence of artifacts inthe recordings. Additionally, MEG signals were con-tinuously monitored to prevent drowsiness. Five min-utes of spontaneous MEG activity were acquired witha sample frequency of 678.17 Hz. Initially, both a 0.1–200 Hz hardware band-pass filter and a 50 Hz notchfilter were applied. Then, each MEG recording wasdownsampled by a factor of four to reduce thedata length. Artifact-free epochs of length 10 s(26.43 ± 5.49 artifact-free epochs per channel andsubject, mean ± SD) were selected for further analy-sis. Prior to calculate spectral entropies, MEG signalswere processed using a 560th order finite impulse re-sponse (FIR) filter designed with a Hamming windowand cut-off frequencies at 0.5 and 70 Hz. The selectedfrequency range enables to keep the relevant spectralcontent and to minimize the presence of oculographicand myographic artifacts.

METHODS

Definition of Spectral Entropies

The FT is a well-known technique used to analyzethe spectral content of a signal. A common method toassess the distribution of the power as a function offrequency is the PSD. In the present work, the PSDwas calculated from the FT of the autocorrelationfunction.13,14,31 Then, the spectral content between 0.5and 70 Hz was selected and the PSD was normalizedto a scale from 0 to 1 leading to the normalized PSD(PSDn)

PSDn fð Þ ¼ PSD fð ÞP70Hz

f¼0:5Hz

PSD fð Þ: ð1Þ

After the normalization, it follows thatP70Hzf¼0:5Hz PSDn fð Þ ¼ 1: The PSDn can be considered

as a probability distribution with N points, whose

Entropy Analysis of MEG Rhythms in Alzheimer’s Disease 143

definition will be further extended to the time-fre-quency plane. This representation provides a suitabletool for analyzing and characterizing the power spec-trum, since it is possible to apply several entropiesbased on a probability density function. Thus, in thepresent work three entropies were calculated from thePSDn: the SSE, TSE, and RSE.

Shannon’s entropy is a disorder quantifier whoseoriginal meaning implies uncertainty of information interms of disorder, discrepancy and diversity.5 Thedefinition of Shannon’s entropy is based on a proba-bility distribution. Previous EEG and MEG studieshave used the PSDn to compute the SSE as a statisticaldescriptor of the signal’s irregularity in AD.1,31 Theirregularity is estimated in terms of the flatness of thePSDn.

36 A uniform PSDn with a broad spectral con-tent (e.g., a highly irregular signal like white noise)gives a high SSE value. On the contrary, a narrowPSDn with only a few spectral components (e.g., ahighly predictable signal like a sum of sinusoids) yieldsa low SSE value. In the present work, the definition ofthe SSE is based on Shannon’s entropy computed overthe PSDn from 0.5 to 70 Hz22 and it is written by

SSE ¼ �X70Hz

f¼0:5Hz

PSDn fð Þ � ln PSDn fð Þ½ �: ð2Þ

The second entropic form is the Tsallis entropy. It isa generalized information measure, which extends thenotion of Shannon’s entropy.42 The Tsallis entropy is anon-logarithmic entropy, which can be useful to ex-plore the properties of a probability distribution froma new mathematical framework in relation to Shan-non’s entropy.42,43 Previous EEG studies have suc-cessfully used the relative power distribution of waveletcoefficients to analyze different brain states in epi-lepsy.9,33 Given the fact that the Tsallis entropy is anon-extensive measure, it is able to characterize asystem where long-range interactions appear.5 Thedegree of non-extensivity is stated by the entropic in-dex q 2 <.12 The parameter q might be considered as azoom lens, which can be focused on long-range inter-actions (low q values) or on short abrupt changes (highq values).43 The Tsallis entropy recovers the definitionof the Boltzmann–Gibbs entropy in the limit q fi 1.42

The definition of the discrete version of the TSE isgiven by

TSE qð Þ ¼ 1

q� 1

X70Hz

f¼0:5Hz

PSDn fð Þ � PSDn fð Þ½ �qf g; q>0:

ð3Þ

Finally, the Renyi entropy is a generalized infor-mation measure, which also extends the definition ofShannon’s entropy.35 Similarly to Shannon’s entropy,

it is an additive entropy, which is based on a loga-rithmic transformation of a given probability distri-bution. The PSDn represents again the probabilitydensity function, analogously to previous EEG stud-ies.2,24 Hence, the Renyi entropy can be considered asan alternative way to estimate the irregularity of time-frequency distributions.3 This entropic form isparameterized by an entropic index q 2 <, in order thatthe Renyi entropy can be reduced to the Boltzmann–Gibbs entropy in the limit q fi 1.35 The definition ofthe RSE reads

RSE qð Þ ¼ 1

1� qln

X70Hz

f¼0:5Hz

PSDn fð Þ½ �q( )

; q>0: ð4Þ

The previous entropies (SSE, TSE, and RSE) werenormalized in order to take values in the 0–1 interval.Hence, the aforementioned entropic forms were dividedby their corresponding maximum possible values. Theywere ln(N) for both the SSE and the RSE and [1 - N (1-

q)] for the TSE, where N was the number of frequencybins and q represented the entropic index.5,33

Time Evolution of Spectral Entropies

The MEG recordings irregularity can be analyzedindirectly applying several entropy definitions to theirpower frequency distributions. In this way, entropyprovides a description of average uncertainty for agiven signal.41 However, MEGs are non-stationaryrecordings and their properties can be accurately de-scribed by using non-stationary signal analysis tech-niques, such as time-frequency distributions.2,3 In thepresent work, an alternative entropic form based onthe sliding temporal window technique was applied toobtain the entropy evolution.2,3 Each MEG epoch of10 s (M = 1696 samples) was divided into non-over-lapping temporal fragments of 0.5 s, whose length isdenoted as L (L = 84 samples) and each time intervalis identified by i (i = 1,..., NT, with NT = M/L). ThePSD is calculated for each temporal window and thePSDn is computed from the PSD

PSD ið Þn fð Þ ¼ PSD ið Þ fð Þ

P70Hz

f¼0:5Hz

PSD ið Þ fð Þ; i ¼ 1; . . . ;NT: ð5Þ

The evolution of the SSE, TSE, and RSE is com-puted from the PSD

ið Þn fð Þ and each value is assigned to

the central point of the corresponding interval

SSE ið Þ ¼�X70Hz

f¼0:5Hz

PSD ið Þn fð Þ � ln PSD ið Þ

n fð Þh i

; i¼ 1; . . . ;NT

ð6Þ

POZA et al.144

TSE ið Þ qð Þ ¼ 1

q� 1

X70Hz

f¼0:5Hz

PSD ið Þn fð Þ � PSD ið Þ

n fð Þh iqn o

;

i ¼ 1; . . . ;NT

ð7Þ

RSE ið Þ qð Þ ¼ 1

1� qln

X70Hz

f¼0:5Hz

PSD ið Þn fð Þ

h iq( )

;

i ¼ 1; . . . ;NT:

ð8Þ

Finally, the previous quantifiers are normalized bytheir maximum possible values, which were specified inthe previous section.

To characterize the entropy evolution by a singlevalue, the temporal average per parameter and subjectwas calculated for each quantifier

SSEh i ¼ 1

NT�XNT

i¼1SSE ið Þ ð9Þ

TSE qð Þh i ¼ 1

NT�XNT

i¼1TSE ið Þ qð Þ ð10Þ

RSE qð Þh i ¼ 1

NT�XNT

i¼1RSE ið Þ qð Þ: ð11Þ

All calculations were carried out with the softwarepackageMatlab (version 7.0;Mathworks,Natick,MA).

Statistical Analysis

Both the Kolmogorov–Smirnov and the Shapiro–Wilk tests were used to evaluate the normal distribu-tion of each variable, while homoscedasticity wasassessed with Levene’s test. After the descriptiveanalysis, log-transformed variables met parametric testassumptions. Firstly, the mean entropy values aver-aged over all channels were analyzed using two-wayrepeated measures ANOVAs (with group as between-subject factor and parameter q as within-subject fac-tor) with age as a covariate. Secondly, optimal meanentropy values at five brain regions (anterior, central,left lateral, posterior, and right lateral) were comparedbetween AD patients and controls by means of two-way repeated measures ANOVAs (with group as be-tween-subject factor and brain region as within-subjectfactor) with age as a covariate. Finally, univariateANOVAs with contrasts and age as a covariate wereperformed when previous analyses showed significantinteractions. In order to correct possible violations ofthe sphericity assumption and to reduce type I errors,Greenhouse-Geisser epsilon was used in all repeated

measures analyses. Differences were considered statis-tically significant for p<0.05.

The classification performance of each parameterwas evaluated using a linear discriminant analysis(LDA) with a leave-one-out cross-validation proce-dure. Classification statistics were shown in terms ofsensitivity (percentage of AD patients with a correctdiagnosis), specificity (proportion of controls properlyrecognized) and accuracy (total fraction of AD pa-tients and healthy subjects well classified).

All statistical analyses were performed using SPSSsoftware (version 14.0; SPSS Inc, Chicago, Ill).

RESULTS

Optimization of the Entropic Index q

In a first stage, we analyzed the role of the entropicindex q in the parameterized entropies: TSE and RSE.The evolution of the TSE and RSE over each of the10 s MEG segments was computed taking non-over-lapping temporal windows of 0.5 s. Results wereaveraged for each channel and each subject to obtainan entropy evolution per channel and subject. Finally,temporal averages for the TSE and the RSE werecomputed to obtain a quantitative measure per subjectand q value. The dependence of the TSE and RSE onthe entropic index q was explored modifying its values(q = {0.25, 0.5,...,5}) according to previous EEGstudies.2,3,9,24,33

The TSE showed a significant main effect of group(F(1,38) = 27.909; p = 0.000005) and a significantgroup by q interaction (F(19,722) = 13.792;p = 0.000514). Figure 1 depicts the evolution of thep-values from the univariate ANOVAs with contrastsand age as a covariate in function of the entropic indexq, when the ÆTSEæ averaged over all channels is com-pared between AD patients and controls. As it can beseen, the TSE with both low and high q valuesachieved the greatest p-values. The most significant

FIGURE 1. Evolution of the statistical significance in func-tion of the entropic index q when the mean TSE over allchannels is compared between AD patients and controls.

Entropy Analysis of MEG Rhythms in Alzheimer’s Disease 145

differences (p = 0.000001) were obtained by theTSE(q = 2).

The RSE exhibited a significant main effect of group(F(1,38) = 34.189; p = 0.000001) and a significantgroup by q interaction (F(19,722) = 7.794;p = 0.006891). Figure 2 illustrates the evolution of thep-values from the univariate ANOVAs with contrastsand age as a covariate in function of the entropic indexq, when the ÆRSEæ averaged over all channels is com-pared between AD patients and controls. The statisti-cal significance achieved with the RSE augmented asq increased. It can be observed that this trend isstable around q = 3. The most significant result(p<0.000001) was obtained with RSE(q = 3.5).

Regional Entropy Analysis

In a second step, we explored the regional patternsof the SSE, as well as the previously optimizedTSE(q = 2) and RSE(q = 3.5). The evolution of theprevious quantifiers over each of the 10 s MEG seg-ments was computed taking non-overlapping temporalwindows of 0.5 s. According to Fig. 3, five brain areas(anterior, central, left lateral, posterior, and right lat-eral) were defined to obtain a regional entropy analy-sis. Results were averaged in each of the five brainregions, obtaining an entropy evolution per regionand subject. Additionally, temporal averages for theentropies were computed to obtain a quantitativemeasure per region and subject.

The SSE showed a significant main effect of group(F(1,38) = 25.986; p = 0.000010), whereas no signifi-cant group by region interaction was observed(p = 0.072579). Results of univariate ANOVAs withcontrasts and age as a covariate are shown in Table 1.Classification analyses using LDA with a leave-one-outcross-validation procedure are shown in Table 2. ADpatients obtained significantly lower SSE values thancontrols in all cerebral regions, which suggests anirregularity decrease in AD patients’ MEGs, in terms

of the spectrum flatness. It is illustrated in Fig. 4,where the mean SSE evolution over a 10 s period foreach brain region in both groups is shown. Althoughthe most significant results were obtained in the rightlateral region (p-value = 0.000004; 80.5%, accuracy;80.0%, sensitivity; 81.0%, specificity), it is noteworthythat the statistical analyses showed similar statisticaldifferences and classification parameters in the leftlateral (p-value = 0.000019; 80.5%, accuracy; 75.0%,sensitivity; 85.7%, specificity) and anterior areas (p-value = 0.000053; 82.9%, accuracy; 85.0%, sensitiv-ity; 81.0%, specificity). In addition, the SSE displayeda higher variability over the 10 s interval in ADpatients than in healthy subjects.

The TSE(q = 2) exhibited a significant main effectof group (F(1,38) = 35.269; p = 0.000001) and asignificant group by region interaction (F(4,152) =4.372; p = 0.013079). Table 1 shows that AD patientsobtained a significantly lower TSE(q = 2) than con-trols in all brain regions. This result can be seen inFig. 5, which depicts the mean TSE(q = 2) evolutionover a 10 s period for each brain region in both groups,suggesting again a decrease in the irregularity of ADpatients’ MEGs. The inspection of Tables 1 and 2 re-veals that the most significant differences (p-value =0.000001) were achieved in the right lateral area, withan accuracy of 78.0% (75.0%, sensitivity; 81.0%,specificity). Similar statistical results were obtained inthe left lateral (p-value = 0.000003) and anterior re-gions (p-value = 0.000003). Nevertheless, in the leftlateral and anterior areas the accuracy reached 80.5%(75.0%, sensitivity; 85.7%, specificity) and 87.8%(90.0%, sensitivity; 85.7%, specificity), respectively.

FIGURE 2. Evolution of the statistical significance in func-tion of the entropic index q when the mean RSE over allchannels is compared between AD patients and controls.

FIGURE 3. Illustration of sensor grouping into the five brainregions considered for topographic analyses: anterior, cen-tral, left lateral, posterior and right lateral.

POZA et al.146

Analogously to the SSE, the TSE showed a highervariability over the 10 s interval in AD patients than inhealthy subjects.

Finally, the RSE(q = 3.5) exhibited a significantmain effect of group (F(1,38) = 35.440; p = 0.000001)and a significant group by region interaction(F(4,152) = 4.771; p = 0.006325). Table 1 indicatesthat AD patients obtained significantly lowerRSE(q = 3.5) values than controls in all brain regions.The statistically significant decrease in the irregularityof AD patients’ MEG recordings is shown in Fig. 6.The most significant differences (p-value<0.000001)

were obtained in the right lateral region with anaccuracy of 78.0% (75.0%, sensitivity; 81.0%, speci-ficity). Similar statistical results and higher classifica-tion parameters were found in the anterior (p-value = 0.000003; 87.8%, accuracy; 90.0%, sensitiv-ity; 85.7%, specificity), left lateral (p-value =0.000003; 82.9% accuracy; 80.0%, sensitivity; 85.7%,specificity) and central areas (p-value = 0.000008;82.9%, accuracy; 75.0%, sensitivity; 90.5%, specificity)than in the right lateral region.

DISCUSSION

We explored the ability of several measures derivedfrom information theory to discriminate betweenspontaneous MEG rhythms of 20 AD patients and 21control subjects. We calculated extensive (Shannonand Renyi) and non-extensive (Tsallis) entropies basedon the time-frequency plane2,3 to measure the irregu-larity of MEGs in AD. Initially, we analyzed thedependence of both the TSE and RSE on the entropicindex q for discriminating between AD patients andcontrols. We found q = 2 and q = 3.5 as optimalentropic indexes for the TSE and RSE, respectively.Detailed regional analyses were then performed usingthe SSE, TSE(q = 2) and RSE(q = 3.5) in order toexplore their spatial and temporal patterns in AD.MEGs from AD patients had significantly lower en-tropy values than those from controls in all brainregions, which suggests that AD is accompanied by anoverall irregularity decrease.

The dependence analysis of the entropies on theparameter q revealed that the TSE and RSE exhibited

TABLE 1. Mean SSE, TSE(q = 2) and RSE(q = 3.5) values averaged in each brain region for each group and the correspondingp-values from ANOVA with contrasts and age as a covariate.

Region Parameter

Controls AD patients

p-valueMean ± SD Mean ± SD

Anterior SSEh i 0.833 ± 0.003 0.720 ± 0.005 0.000053

TSEðq ¼ 2Þh i 0.969 ± 0.001 0.916 ± 0.003 0.000003

RSEðq ¼ 3:5Þh i 0.714 ± 0.006 0.524 ± 0.007 0.000003

Left lateral SSEh i 0.818 ± 0.003 0.723 ± 0.004 0.000019

TSEðq ¼ 2Þh i 0.969 ± 0.001 0.928 ± 0.002 0.000003

RSEðq ¼ 3:5Þh i 0.698 ± 0.006 0.556 ± 0.005 0.000003

Central SSEh i 0.859 ± 0.001 0.786 ± 0.004 0.000172

TSEðq ¼ 2Þh i 0.979 ± 0.000 0.951 ± 0.002 0.000022

RSEðq ¼ 3:5Þh i 0.760 ± 0.003 0.629 ± 0.006 0.000008

Right lateral SSEh i 0.823 ± 0.003 0.722 ± 0.005 0.000004

TSEðq ¼ 2Þh i 0.969 ± 0.001 0.928 ± 0.003 0.000001

RSEðq ¼ 3:5Þh i 0.702 ± 0.005 0.556 ± 0.007 0.000000

Posterior SSEh i 0.815 ± 0.002 0.735 ± 0.006 0.000137

TSEðq ¼ 2Þh i 0.968 ± 0.001 0.937 ± 0.004 0.000102

RSEðq ¼ 3:5Þh i 0.692 ± 0.005 0.577 ± 0.007 0.000023

SD: Standard deviation; p-value: Statistical significance.

TABLE 2. Diagnostic test results derived from lineardiscriminant analysis with a leave-one-out cross-validationprocedure for the mean SSE, TSE(q = 2) and RSE(q = 3.5)

averaged in each brain region.

Region Parameter

Sensitivity

(%)

Specificity

(%)

Accuracy

(%)

Anterior SSEh i 85.0 81.0 82.9

TSEðq ¼ 2Þh i 90.0 85.7 87.8

RSEðq ¼ 3:5Þh i 90.0 85.7 87.8

Left lateral SSEh i 75.0 85.7 80.5

TSEðq ¼ 2Þh i 75.0 85.7 80.5

RSEðq ¼ 3:5Þh i 80.0 85.7 82.9

Central SSEh i 70.0 76.2 73.2

TSEðq ¼ 2Þh i 65.0 85.7 75.6

RSEðq ¼ 3:5Þh i 75.0 90.5 82.9

Right lateral SSEh i 80.0 81.0 80.5

TSEðq ¼ 2Þh i 75.0 81.0 78.0

RSEðq ¼ 3:5Þh i 75.0 81.0 78.0

Posterior SSEh i 65.0 81.0 73.2

TSEðq ¼ 2Þh i 70.0 76.2 73.2

RSEðq ¼ 3:5Þh i 75.0 85.7 80.5

Entropy Analysis of MEG Rhythms in Alzheimer’s Disease 147

different behaviors. Similarly, previous EEG studieshave observed that quantifiers based on Renyientropy are less sensitive to variations of the parameterq (q>1) due to its logarithmic form,33,41 whereasmeasures based on the Tsallis statistic showed a strongdependence on the entropic index.41 This result canalso be observed in the present work. Entropic indexesgreater than 1 produced changes in the significancelevel more important with the TSE than with the RSE.Figures 1 and 2 show that the ability of the TSE toaccurately detect AD is maximal using values of q closeto 2, while the statistical differences between groupsare gradually reduced as q either decreases or increaseswith respect to the previous q value. Regarding to theRSE, the statistical differences between AD patientsand controls gradually increased as q augmented.Nevertheless, entropic indexes higher than 3.5 did notoffer significant improvement to distinguish betweengroups. The ability of q to enhance the accuracy toidentify particular brain states has been previouslydiscussed. EEG studies detecting epileptic seizures andcharacterizing brain function by means of Tsallis andRenyi entropies have reported a decrease in the‘‘background EEG-detection-power’’ as the parameterq (q>1) increased.5,9,41 We have observed that theability to discriminate between AD patients and con-trols did not improve when the entropic index was

gradually increased. However, our results indicate thatthis trend appears with q values greater than 2 or 3.5by the TSE and RSE, respectively. Differences may bedue to the fact that we computed both the Tsallis andRenyi entropies from a time-frequency distribution,whereas the aforementioned works used an alternativetime-dependent entropy definition based on the slidingtemporal window technique.10

Regional analyses of the entropy patterns showedsignificant (p<0.0005) lower SSE, TSE(q = 2) andRSE(q = 3.5) values in AD patients’ MEGs than incontrols for all cerebral regions. The SSE decrease inAD suggests that the disease is accompanied by a lossof frequency components, which implies a decrease ofirregularity with respect to the flatness of the powerspectrum. The TSE(q = 2) and RSE(q = 3.5) evolu-tions reveal again that the disorder was reduced in ADpatients compared to controls, supporting the loss ofirregularity in AD. Previous MEG studies have alsoreported an overall decrease in both irregularity31 andcomplexity19 in AD using the SSE and the Lempel–Zivcomplexity, respectively. On the contrary, van Cap-pellen van Walsum et al.8 only described a complexityloss in the high frequencies when a detailed spectralanalysis in several frequency bands was performedusing the neural complexity. An advantage of themethods used in this work, compared to the previous

FIGURE 4. Grand-average of the SSE evolution over a 10 s period for AD and control groups in each brain region: anterior (A),central (C), left lateral (L), posterior (P), and right lateral (R).

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efforts, is to take into account both temporal andspatial characteristics of the MEG signals. This is dueto the fact that the quantifiers were applied to the time-frequency plane. We have detected not only lowerentropy values, but also a more irregular entropyevolution in AD patients than in controls. Addition-ally, the decreasing entropy values should be inter-preted from a spectral point of view. We have observedthat AD implies a loss of spectral components, whichcan be associated with a reduction of informationcontent.3 Some authors claimed that the change ininformation entropy within the EEG may reflect a realvariation in cortical functional organization.24 Giventhe fact that entropy is usually identified with anindicator of the system’s disorder, it has beenhypothesized that a reduction in entropy may implyan information processing decrease at the cerebralcortex.24

Further inspection of the regional entropy analysesshows that both the TSE(q = 2) and RSE(q = 3.5)achieved higher significant levels (p<0.0001) than theSSE (p<0.0005) in all brain regions. Moreover, thegeneralized entropies reached greater classificationaccuracies (between 73% and 87.8%) than the SSE(between 73.2% and 82.9%). A similar result wasobtained in a previous study (p = 0.00023; 82.93%accuracy), where the SSE (among other spectral

measures) was used to characterize the PSD of MEGsin AD.31 However, it is noteworthy that the classifi-cation analyses were performed using a LDA without aleave-one-out cross-validation procedure. As it waspreviously mentioned, the TSE and RSE have beenused in the past to characterize long and short-rangeinteractions in complex systems, respectively.5,40 Ourfindings indicate that both entropic formalisms showedstatistically significant results. Therefore, we canhypothesize that the brain magnetic activity in ADmay be generated by a system where abnormal longand short-range interactions appear simultaneously.This issue has been previously suggested by Stamet al.,39 who found that the functional connectivity ofspontaneous MEG activity in AD was characterized byspecific changes of both long and short distanceinteractions in several frequency bands.

The most significant differences in the entropymeasures were found in the lateral and anterior regions.However, similar p-values were also obtained in bothcentral and posterior regions. Berendse et al.4 analyzedthe absolute power of spontaneous MEG recordings ofAD patients and controls. They reported significantchanges in the power patterns over the whole head,which can be summarized as a significant increase of thelow frequency power over the frontal and central areasand a significant decrease of the high frequency power

FIGURE 5. Grand-average of the TSE(q = 2) evolution over a 10 s period for AD and control groups in each brain region: anterior(A), central (C), left lateral (L), posterior (P), and right lateral (R).

Entropy Analysis of MEG Rhythms in Alzheimer’s Disease 149

over the occipital and temporal regions.4 MEG sourceanalyses have also found differences over the differentbrain regions in AD. Fernandez et al.15,16 described anincreased dipole density at the delta and theta bandsover the parietal and temporal cortices in AD. On theother hand, Osipova et al. observed that AD patientsshowed an increased activation of higher theta bandsources in the right temporal region,29 together with aparieto-occipital deficit.28

Finally, some limitations of the study should bementioned. It might be possible that the irregularitydecrease in AD could be drug-related. However, noneof the patients were receiving any medication whichcould affect spontaneous MEG activity. On the otherhand, the irregularity patterns in other neurodegener-ative diseases, which have shown alterations in thespectrum similar to those observed in AD, should beexplored. Further investigation should be attempted toextend the analyses in mild cognitive impairment,vascular dementia, Lewy body dementia, majordepression, dementia associated with Parkinson’s dis-ease, Pick’s disease, Huntington’s chorea and pro-gressive supranuclear palsy.

Other limitation of the work is related to the smallsample size. Considerations about type I (probabilityof a false positive) and type II (probability of a false

negative) errors should be made. The reduced numberof subjects enrolled in the study implies an increase ofbeta (probability of making a type II error) and adecrease of the power of the test (i.e., 1 - beta).Therefore, it should be appropriate to increase thenumber of subjects to both minimize type II errors andaugment the statistical power.

CONCLUSIONS

This study was performed as a new approach toanalyze the ability of information theory methods tocharacterize spontaneous MEG activity from AD pa-tients and controls. Only a few MEG studies haveexplored the irregularity and complexity patterns inAD.8,19,31 The parameters presented in this papercombine three entropies from information theory withtime-frequency signal processing tools. Our findingssupport the notion that AD involves an overall loss ofirregularity in the electromagnetic brain activity. Inaddition, the statistically significant results obtained byboth the extensive (SSE and RSE) and non-extensive(TSE) spectral entropies suggest that AD could disturblong and short-range interactions leading to anabnormal brain function.

FIGURE 6. Grand-average of the RSE(q = 3.5) evolution over a 10 s period for AD and control groups in each brain region:anterior (A), central (C), left lateral (L), posterior (P), and right lateral (R).

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Future efforts will be addressed to explore othermeasures from information theory to characterizeMEG rhythms in AD. Additionally, further workshould be attempted to increase the sample size and toextend the results to other dementias.

In summary, our findings suggest that the extensive(SSE and RSE) and non-extensive (TSE) spectralentropies may lead to a better understanding of theunderlying brain dynamics in AD. Furthermore, thesenew approaches extend the concept of irregularity andcan provide useful descriptors of the spontaneousMEG rhythms in AD.

ACKNOWLEDGMENTS

This work has been partially supported by the grantproject VA108A06 from ‘‘Consejerıa de Educacion deCastilla y Leon’’ and by the ‘‘Ministerio de Educaciony Ciencia’’ and FEDER grant MTM2005-08519-C02-01. The authors would like to thank the ‘‘Asociacionde Enfermos de Alzheimer’’ (AFAL) for supplying thepatients who have participated in this study.

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