it has been shown that modifications of resting electroencephalographic ( eeg ) rhythms can be observed during pathological aging . when compared to healthy elderly ( nold )
subjects , alzheimer 's disease ( ad ) patients have been characterized by high power of  ( 04  hz ) and  ( 47  hz ) rhythms , and low power of posterior  ( 812  hz ) and/or  ( 1330  hz ) rhythms [ 17 ] .
these eeg abnormalities have been associated with altered regional cerebral blood flow / metabolism and with impaired global cognitive function , as evaluated by mini mental state examination ( mmse ; [ 5 , 811 ] .
furthermore , posterior  rhythms have shown a power decrement even in subjects with amnesic mild cognitive impairment ( mci ) , a clinical state between elderly normal cognition and dementia , which is characterized by the objective evidence of memory deficit either isolated or combined with other cognitive impairment [ 3 , 7 , 1215 ] .
more recently , the hypothesis that the amplitude of eeg rhythms , which are affected by ad processes , is relatively preserved in amnesic mci subjects in whom the cognitive decline is mainly explained by white - matter vascular load has been tested . despite the converging evidence of abnormal cortical eeg rhythms in mci and ad , eeg power alone
a reasonable hypothesis is that the amplitude of eeg rhythms per se does not capture one of the main features of ad , namely the impairment of functional neural connectivity . in this vein
, it has been reported that ad patients present an abnormal linear coupling of eeg rhythms between cortical regions , as revealed by spectral eeg coherence [ 1622 ] .
such a coherence denotes linear temporal synchronicity of coupled eeg rhythms , as a reflection of neural sources whose firing is oscillating with a nearly identical timing and phase .
it has been proposed that functional coupling of cortical rhythms is related to brain processes involving the coupled sources and is modulated by cholinergic systems ; ad is characterized by a disruption of basal forebrain cholinergic inputs to cortex and hippocampus .
this is why a decrease of cortical eeg coherence might be a sensible and reliable marker of ad .
both linear and nonlinear connectivity have an important limitation : they do not reflect the direction of the information flux within the functional coupling of brain rhythms at paired brain sites .
one can overcome this limitation by the computation of the directed transfer function ( dtf ; ) .
dtf has been proven to be reliable for the modeling of directional information flux within linear eeg functional coupling , as an intrinsic feature of cerebral functional connectivity [ 2628 ] . concerning the functional role of intrinsic directional connectivity in cognition ,
a dominant parietal - to - frontal directional flux within eeg coupling has been reported in healthy awake subjects during visuospatial information processing [ 15 , 29 ] .
across pathological aging , a reduction of parietal - to - frontal directional information flow within eeg functional coupling in both mci and mild ad subjects compared to nold subjects it has been shown , in line with the idea of a common pathophysiological background linking these conditions .   in the present study , we summarized the results of two previous studies [ 30 , 31 ] testing the hypothesis that directionality of frontoparietal functional coupling of eeg rhythms are affected by ad processes but relatively preserved in amnesic mci subjects in whom the cognitive decline is mainly explained by white - matter vascular load ( as revealed by mri ) .
resting eeg was recorded in nold , alzheimer , and amnesic mci subjects , while the directionality of frontoparietal functional coupling of eeg rhythms was estimated by dtf .
in the first multicentric eeg study , 73 ad patients , 69 amnesic mci patients , and 64 nold subjects were recruited . in the second study ,
furthermore , 40 cognitively normal elderly ( nold ) subjects were recruited to form control group .
all experiments were performed with the informed and overt consent of each participant or caregiver , in line with the code of ethics of the world medical association ( declaration of helsinki ) and the standards established by the author 's institutional review board .
patients were also rated with a number of standardized diagnostic and severity instruments that included the mini mental state examination ( mmse , ) , the clinical dementia rating scale ( cdr , ) , the 15-item version of the geriatric depression scale ( gds , ) , the hachinski ischemic scale ( his , ) , and the instrumental activities of daily living scale ( iadl , ) .
neuroimaging diagnostic procedures ( ct or mri ) and complete laboratory analyses were carried out to exclude other causes of progressive or reversible dementias , in order to have a homogeneous ad patient sample .
exclusion criteria included , in particular , evidence of ( i ) frontotemporal dementia , ( ii ) vascular dementia based on clinical and radiological grounds , ( iii ) extrapyramidal syndromes , ( iv ) reversible dementias , and ( v ) fluctuations in cognitive performance and visual hallucinations ( suggestive of a possible lewy body dementia ) . inclusion and exclusion criteria for amnesic mci diagnosis aimed at selecting elderly persons with objective cognitive deficits , especially in the memory domain , who did not meet the criteria for dementia or ad [ 37 , 38 ] .
inclusion criteria for amnesic mci subjects were ( i ) objective memory impairment on neuropsychological evaluation , as defined by performances 1.5 standard deviation below the mean value of age- and education - matched controls for a test battery including busckhe - fuld and memory rey tests , ( ii ) normal instrumental activities of daily living as documented by history and evidence of independent living as assessed by a formal questionnaire ( iadl , see above ) , and ( iii ) a clinical dementia rating score of 0.5 .
exclusion criteria for amnesic mci were ( i ) mci subjects without objective memory deficits , ( ii ) ad , as diagnosed by the procedures described above , ( iii ) evidence of concomitant dementia such as frontotemporal , vascular dementia , reversible dementias ( including dementia of depression ) , fluctuations in cognitive performance , and/or features of mixed dementias , ( iv ) evidence of concomitant extrapyramidal symptoms , ( v ) clinical and indirect evidence of depression as revealed by gds scores greater than 14 , ( vi ) other psychiatric diseases , epilepsy , drug addiction , alcohol dependence , and use of psychoactive drugs or drugs interfering with brain cognitive functions including acetylcholinesterase inhibitors , and ( vii ) current or previous uncontrolled systemic diseases or traumatic brain injuries .
subjects affected by chronic systemic illnesses , subjects receiving psychoactive drugs , and subjects with a history of present or previous neurological or psychiatric disease were excluded .
all nold subjects had a geriatric depression scale score lower than 14 ( no depression ) .
high - resolution sagittal t1-weighted volumetric magnetic resonance images ( mris ) were acquired in 80 mci subjects of the second study using a 1.0 t magnetom scanner ( siemens , erlangen , germany ) , with a gradient echo 3d technique : tr = 10  ms , te = 4  ms , ti = 300  ms , flip angle = 10 , field of view = 250  mm , acquisition matrix 160  256 , and a slice thickness of 1.3  mm .   in order to rate the subcortical vascular lesions ( svls ) , a single operator visually assessed digital mri images of mci subjects .
interrater reliability calculated with weighted k value was 0.67 , indicative of moderate agreement ( as indicated by the wahlund scale ) .
the svls were scored separately for the right and left hemispheres with the following scores : 0 ( no lesion ) , 1 ( focal lesions ) , 2 ( beginning confluence of lesions ) , or 3 ( diffuse involvement of the entire region ) . the mri data of an mci subject could not be used for technical problems .
another mci subject was not further considered due to an abnormal eeg spectrum . in total , 78 mci subjects were considered for the dtf analysis . based on the wahlund scale score , the mci subjects were subdivided in two subgroups : 36 with low degree of white - matter lesion ( mci v , score of wahlund scale <3 ) and 42 with higher degree of white - matter lesion ( mci v+ , score of wahlund scale 3 ) .
table 1 summarizes the relevant demographic and clinical data of mci , ad , and nold of the first study ( part a ) and the mci v , mci v+ , and nold of the second study ( part b ) . of note ,
age , education , gender , and iaf were used as covariates in all the statistical evaluations of the cortical sources of eeg rhythms to remove possible confounding effects .
eeg data were recorded in resting subjects ( eyes - closed ) by specialized clinical units .
all eeg recordings were performed ( 0.370  hz bandpass ) from 19 electrodes positioned according to the international 1020 system ( i.e. , fp1 , fp2 , f7 , f3 , fz , f4 , f8 , t3 , c3 , cz , c4 , t4 , t5 , p3 , pz , p4 , t6 , o1 , o2 ) . to monitor eye movements ,
all data were digitized in continuous recording mode ( 5  min of eeg ; up to 256  hz sampling rate ) .
state of vigilance was controlled by visual inspection of eeg traces during recording session and subjects ' drowsiness was avoided by verbal warnings . at the time of eeg recording , no patient received medications that could influence eeg rhythms such as benzodiazepines . before computing the dtf , the eeg data were preliminarily normalized by subtracting the mean value and dividing by the variance , according to standardized rules by kaminski and blinowska . an important step of the dtf method was the computation of the so - called mvar model [ 2527 ] .
eeg data at 9 electrodes ( f3 , fz , f4 , c3 , cz , c4 , p3 , pz , p4 ) were simultaneously given as an input to the mvar model towards the computation of the directional information flux among all the pair combinations of these electrodes .
this model was used to estimate the  direction  of the information flow within the eeg rhythms between the frontal and parietal regions ( f3-p3 , fz - pz , f4-p4 ) . in nonmathematical terms , coefficients of the mvar model fitted to the data
can be interpreted as causal influence of signal recorded from electrode a on signal recorded from electrode b , or information flow between electrodes a and b. a direction of information flow from a to b is stated when that case is statistically more probable than a directionality from b to a. this mvar model has already been used successfully to estimate the  direction  of the corticocortical and corticomuscular information flow [ 4042 ] .
the mathematical core of the mvar algorithm used in this work is based on the arfit programs running on the platform matlab 6.5 .
the model order was 7 , as estimated by the akaike criterion suggested in previous dtf studies ; that order has been demonstrated to be valid for the evaluation of eeg rhythms at both low- and high - frequencies along wakefulness and sleep [ 2527 ] .
the goodness of fit was evaluated by visual inspection of the values of noise matrix v of the mvar model .  
the mvar model is defined as 
 ( 1)j=0pajxtj = et , 
							 where xt is the l - dimensional vector representing the l - channel signal at time t ; et is white noise ; aj is the ll matrix of the model coefficients , and p is the number of time points considered in the model . from the identified coefficients of the model aj
, spectral properties of the signals can be obtained by the following z - transformation of the above equation : 
 ( 2)x(z)=h(z)e(z ) , 
							 where h(z ) is a transfer function of the system  
 ( 3)h(z)=(j=0pajzj)1,z(j)=exp  ( 2ijfdt ) , 
							 where f is frequency and dt is the time step . since the transfer function h(f )
is not a symmetric matrix , the information transmission from the jth to the ith channel is different from that from the ith to the jth channel .
the dtf from the jth channel to the ith channel is defined as the square of the element of h(f ) divided by the squared sum of all elements of the relevant row , 
 ( 4)dtfij(f)=|hij|2m=1l|him(f)|2 . 
 
a substantial difference between dtf(f)ij and dtf(f)ji may suggest an asymmetric information flow from electrode i to electrode j. when dtf(f)ij is greater in magnitude than dtf(f)ji , the  direction  of the information flow is from electrode j to electrode i. on the other hand , the  direction  of the information flow is from electrode i to electrode j , when dtf(f)ji is greater in magnitude than dtf(f)ij . of note ,
the normalization of the dtf depends on the denominator of the previous formula .   to simplify the visualization and statistical analysis of the dtf results , the anterior - posterior directional flow of information of eeg functional coupling was indexed as  parietal - to - frontal  minus  frontal - to - parietal  dtf values , namely anterior - to - posterior dtfdiff values .
positive anterior - to - posterior dtfdiff values indicated a prevalence of parietal - to - frontal over frontal - to - parietal direction of the information flux .
the fact that the dtf analysis was done on the difference between the two reciprocal dtf directions should require a careful interpretation of the results .
a zero value of such a difference meant equivalence of the two opposite dtf directions within the period of eeg data acquisition ; namely , that the dtf directions were equally strong or equally weak or both equal to zero in the eeg period taken into account .
it should be emphasized that this equivalence is true for the whole eeg period , but not necessarily for subperiods . at this preliminary stage of the study , we preferred to evaluate the dtf values for the entire eeg period , since the dtf values for shorter periods are supposedly less reliable from the statistical point of view [ 6 , 43 ] .
the mauchley test evaluated the sphericity assumption and correction of the degrees of freedom was carried out using the greenhouse - geisser procedure .
subjects ' age , gender education , and iaf were used as covariates in the statistical design .
statistical analysis of the anterior - to - posterior dtfdiff values (  direction  of the information flow between frontal and parietal regions ) was performed using a three - way anova including the factors group ( ad , amnesic mci , and nold ; independent variable ) , band (  ,  , 1 , 2 , 1 , 2 ,  ) , and electrode pair ( f3-p3 , fz - pz , and f4-p4 ) for the first study , and group ( mci v , mci v+ , and nold ; independent variable ) , band (  ,  , 1 , 2 , 1 , 2 ,  ) , and electrode pair ( f3-p3 , fz - pz , and f4-p4 ) for the second study .
the working hypothesis was a statistical effect indicating a progressive reduction of anterior - to - posterior dtfdiff values across nold , mci v , and mci v+ subjects .
the nold subjects showed wide positive anterior - posterior dtfdiff values ( parietal - to - frontal dtf values prevailing over frontal - to - parietal values ) , which were maximum in magnitude at 1 for all electrode pairs of interest ( f3-p3 , fz - pz , f4-p4 ) .
compared to nold subjects , ad patients were characterized by a decrease of these dtfdiff values .
mci subjects presented a dtf trend similar to that of the ad , except for 1 , 2 , and 1 in which they showed intermediate values of anterior - to - posterior dtfdiff values , when compared to those of nold and ad .
in contrast to the anterior - to - posterior , inter - hemispheric dtfdiff values had similar magnitude values in the three groups , for all electrode pairs of interest ( f3-f4 , c3-c4 , p3-p4 ) .
statistical anova of the anterior - to - posterior dtfdiff values showed a two - way anova interaction ( f(12,1218 ) = 3.49 ; p < .00001 ) between the factors group ( ad , amnesic mci , nold ) and band (  ,  , 1 , 2 , 1 , 2 ,  ) .
duncan post hoc testing showed that the anterior - posterior dtfdiff values matched the patterns nold > mci > ad ( 1 : p < .05 to p < .000001 ) , nold > ad (  : p < .01 ; 1 : p < .000005 ; 2 : p < .000005 ; 2 : p < .05 ) , and nold > mci (  : p < .01 ; 1 : p <
the upper part of figure 1 shows the mean anterior - to - posterior dtfdiff values computed in the nold , amnesic mci , and ad subjects , for all frequency bands of interest (  ,  , 1 , 2 , 1 , 2 ,  ) , obtained by averaging the anterior - to - posterior dtfdiff values of the three electrode pairs ( f3-p3 , fz - pz , f4-p4 ) .
statistical anova of the inter - hemispheric dtfdiff values showed no statistically significant effect including the factor group ( ad , amnesic mci , nold ) .
the bottom part of figure 1 reports the mean inter - hemispheric dtfdiff values computed in the nold , amnesic mci , and ad subjects at all frequency bands of interest (  ,  , 1 , 2 , 1 , 2 ,  ) , obtained by averaging the inter - hemispheric dtfdiff values of the three electrode pairs ( f3-f4 , c3-c4 , p3-p4 ) .  
compared to nold subjects , mci v patients were characterized by a decrease of these dtfdiff values .
mci v+ subjects showed intermediate values of anterior - to - posterior dtfdiff values , when compared to those of nold and mci v. statistical anova of the anterior - to - posterior dtfdiff values showed a two - way anova interaction ( f(12,690 ) = 3.65 ; p < .000001 ) between the factors group ( mci v , mci v+ , nold ) and band (  ,  , 1 , 2 , 1 , 2 ,  ) .
duncan post hoc testing showed that the anterior - posterior dtfdiff values matched the patterns nold > mci v+ > mci v (  : p < .019 to p < .000002 ; 1 : p < .0016 to p < .000001 ; 2 : p < .0015 to p < .000001 ; 1 : p
< .015 to p < .000002 ) . 
 figure 2 shows the mean anterior - to - posterior dtfdiff values computed in the nold , mci v+ , and mci v subjects , for all frequency bands of interest (  ,  , 1 , 2 , 1 , 2 ,  ) , obtained by averaging the anterior - to - posterior dtfdiff values of the three electrode pairs ( f3-p3 , fz - pz , f4-p4 ) .
it has been shown previously that frontal - to - parietal direction of information flux within eeg functional coupling is an intrinsic feature of cerebral connectivity [ 6 , 15 , 29 , 43 , 44 ] . in the first study , we tested whether that direction of information flux is abnormal in pathological aging conditions such as amnesic mci and ad , in line with the hypothesis that amnesic mci is a preclinical stage of ad at the group level .
results showed that parietal - to - frontal direction of the information flux within eeg functional coupling was stronger in nold than in amnesic mci and/or ad subjects , principally at  and  rhythms .
in contrast , the directional flow within inter - hemispheric eeg functional coupling did not discriminate among the three groups .
these results suggest that directional information flux within eeg frontal - to - parietal coupling is quite sensitive to the preclinical stage of the ad at the group level . in the second study , we tested the hypothesis that dominant parietal - to - frontal eeg coupling , which is affected by ad processes as revealed in the first study , is relatively preserved in amnesic mci subjects in whom the cognitive decline is mainly explained by white - matter vascular load . as main results , the dominant parietal - to - frontal eeg coupling at  ,  , and  rhythms was maximum in nold , intermediate in mci v+ , and low in mci v subjects .
these results are in line with the additive model of cognitive impairment , postulating that the cognitive impairment arises as the sum of neurodegenerative and cerebrovascular lesions .
eeg might be especially sensitive to aging neurodegenerative processes and would be relatively spared in elderly subjects in whom the cognitive impairment is mainly explained by cerebrovascular lesions .
the results of the present studies motivate future investigations aimed at evaluating the functional coupling of frontal and parietal sources of eeg activity as revealed by high - resolution techniques including linear or nonlinear inverse estimation and realistic modeling of the head as a volume conductor [ 5 , 45 ] .
 is directionality of electroencephalographic ( eeg ) synchronization abnormal in amnesic mild cognitive impairment ( mci ) and alzheimer 's disease ( ad ) ? and , do cerebrovascular and ad lesions represent additive factors in the development of mci as a putative preclinical stage of ad ? here we reported two studies that tested these hypotheses . 
 eeg data were recorded in normal elderly ( nold ) , amnesic mci , and mild ad subjects at rest condition ( closed eyes ) . 
 direction of information flow within eeg electrode pairs was performed by directed transfer function ( dtf ) at  ( 24  hz ) ,  ( 48  hz ) , 1 ( 810  hz ) , 2 ( 1012  hz ) , 1 ( 1320  hz ) , 2 ( 2030  hz ) , and  ( 3040  hz ) . 
 parieto - to - frontal direction was stronger in nold than in mci and/or ad subjects for  and  rhythms . 
 in contrast , the directional flow within interhemispheric eeg functional coupling did not discriminate among the groups . 
 more interestingly , this coupling was higher at  , 1 , 2 , and 1 in mci with higher than in mci with lower vascular load . 
 these results suggest that directionality of parieto - to - frontal eeg synchronization is abnormal not only in ad but also in amnesic mci , supporting the additive model according to which mci state would result from the combination of cerebrovascular and neurodegenerative lesions . 
1. Introduction
2. Methods
3. Results
4. Discussion