alzheimer 's disease ( ad ) is a neurodegenerative disorder clinically characterized by progressive dementia and neuropsychiatric symptoms . a breakdown in connectivity , both in the functional and structural system domain ,
the human brain is organized as a complex network , allowing for segregation and integration of information processing . by modeling
the brain as a complex network , data from recent studies suggest that ad - associated brain network changes may be related to cognitive decline and neuropsychological impairment .
. demonstrated the topological alterations in ad patients using interregional correlation of cortical thickness as a metric of the structural basis underlying brain dynamics in structural networks .
reported diminished functional connectivity between the hippocampus and posterior cingulate cortex for functional networks that are prominently involved in the processes of episodic memory in patients at prodromal stages of ad .
two basic topological measurements of a complex network are clustering coefficient ( cc ) and characteristic path length ( cpl ) .
the cc quantifies the local efficiency of information transfer while cpl quantifies the global efficiency of parallel information transmission .
although previous studies have indicated that the cognitive deficits may be due to topological deteriorations of the brain network , a consensus regarding the nature of the alteration pattern has not been reached . a study by stam et al .
found that the network cc was unchanged in patients with ad although the average cpl was elongated .
contradictorily , supekar et al . indicated that ad patients had a lower cc , but no changes in cpl compared with healthy controls .
. demonstrated a higher cc and longer cpl in patients with ad . to account for these discrepancies ,
one suggestion is to compare structural and functional networks simultaneously in the same group of people .
, most studies just examined the large - scale brain network properties at a specific frequency band .
it is not clear whether the selection of a specific frequency band could impact the topological properties in patients with ad .
recent studies have reported the frequency specificity of functional connectivity in multiple functional networks derived from resting - state functional magnetic resonance imaging ( rs - fmri ) signals , as well as frequency - specific correlations between hemodynamic changes and electroencephalography oscillations in healthy people .
frequency - specific alterations of neuronal oscillations were revealed in patients suffering from schizophrenia using rs - fmri , and parkinson 's disease by simultaneous magnetoencephalography ( meg ) and local field potential recordings . in our study
, we expected to find frequency - specific changes in the topological properties of ad patients .
focusing on rs - fmri data only , large - scale topological properties of moderate ad patients and healthy controls were investigated at three distinct frequency bands ( 0.010.06 hz , 0.060.11 hz , and 0.110.25 hz ) .
the global efficiency , the cc , the cpl and the  small - world  property of the subjects were quantified to describe the alterations in each frequency band .
all participants were screened and enrolled according to the procedure used in former studies of the same group . finally , according to the nincds - adrda criteria for probable ad
the patients were all clinically categorized as those at moderate stages of ad according to the clinical dementia rating ( cdr ) scale of 2 .
ten right - handed healthy controls with no history of neurological disorder or head trauma and normal neurologic examination findings ( cdr = 0 ) were recruited from the local community .
global cognitive function of all subjects was evaluated using the mini - mental state examination .
subject characteristics ad : alzheimer s disease ; mmse : mini - mental state examination . a 3 t mr scanner ( signa hdxt , ge healthcare , usa ) with 8-channel head array coil was used in this study .
each subject was scanned in a supine , head - first position with symmetrically placed cushions on both sides of the head to ensure stability . during the rs - fmri scanning , the subjects were instructed to keep as still as possible , with eyes closed , and think of nothing in particular while maintaining wakefulness .
a gradient - echo planar sequence was performed for the acquisition of rs - fmri data , with the acquisition parameters as follows : repetition time ( tr)/echo time ( te ) 2000/30 ms , field of view ( fov ) 240 mm  240 mm , phase fov 1 , matrix 64  64 , slices 33 , slice thickness 4.0 mm , slice gap 0.5 mm , scan time 8 min .
a three - dimensional fast spoiled gradient recalled - echo sequence covering the whole brain was used for structural data acquisition with tr / te / inversion time 6.5/2.1/400 ms , fov 256 mm  256 mm , phase fov 1 , matrix 256  256 , slice thickness 1.0 mm , slice gap 0 mm , number of signal averages ( nsa ) 1 , flip angle 15 , scan time 4 min 8 s. spm8 ( http://www.fil.ion.ucl.ac.uk/spm/ ) was used for the preprocessing of fmri datasets . after the first 10 time points were discarded ,
the remaining images of all subjects were then normalized to montreal neurological institute 152 space .
all images were then smoothed with a 4 mm  4 mm  4 mm gaussian kernel .
datasets were then drifted and filtered in three distinct frequency bands : 0.010.06 hz , 0.060.11 hz , and 0.110.25 hz .
nuisance covariates of whole brain , white matter , and cerebrospinal fluid signals were removed using regression .
the registered fmri data were segmented into 90 regions using an automated anatomical labeling template .
the pearson correlation coefficients were calculated between any two functionally connected regions at three different frequency bands ( 0.010.06 hz , 0.060.11 hz and 0.110.25 hz ) .
each subject was assigned a 90  90 correlation matrix at different filter bands . in order to detect the topological differences of functional brain network between ad patients and healthy controls , a wide range of thresholds
specifically , if the pearson correlation coefficient was greater than the threshold , the correlation coefficient was set to 1 ; otherwise , it was set to 0 .
the selected threshold ranged from 0.35 to 0.60 and increased by 0.01 at each step . in this study ,
the global efficiency , the cc , the cpl , and  small - world  property were calculated in a wide range of thresholds and averaged within each group .
the definition of these parameters can be found in bullmore and sporns . to compare the degree distributions of functional brain network between ad patients and healthy controls ,
the node degree was then calculated in each node and averaged within each group to generate the degree distribution curve .
network is characterized as a network with a shorter cpl than a regular network ( high cc and long cpl ) and a greater cc than a random network ( low cc and short cpl ) .
to detect the differences of  small - world  properties between ad patients and healthy controls , the ratio of cc and cpl was quantified in each subject and averaged within each group .
the differences of topological parameters between patients and controls were compared by two - sample t - test using spss 17.0 ( ssps inc . , chicago , il , usa ) software .
all participants were screened and enrolled according to the procedure used in former studies of the same group . finally , according to the nincds - adrda criteria for probable ad
the patients were all clinically categorized as those at moderate stages of ad according to the clinical dementia rating ( cdr ) scale of 2 .
ten right - handed healthy controls with no history of neurological disorder or head trauma and normal neurologic examination findings ( cdr = 0 ) were recruited from the local community .
global cognitive function of all subjects was evaluated using the mini - mental state examination .
subject characteristics ad : alzheimer s disease ; mmse : mini - mental state examination .
a 3 t mr scanner ( signa hdxt , ge healthcare , usa ) with 8-channel head array coil was used in this study .
each subject was scanned in a supine , head - first position with symmetrically placed cushions on both sides of the head to ensure stability . during the rs - fmri scanning , the subjects were instructed to keep as still as possible , with eyes closed , and think of nothing in particular while maintaining wakefulness .
a gradient - echo planar sequence was performed for the acquisition of rs - fmri data , with the acquisition parameters as follows : repetition time ( tr)/echo time ( te ) 2000/30 ms , field of view ( fov ) 240 mm  240 mm , phase fov 1 , matrix 64  64 , slices 33 , slice thickness 4.0 mm , slice gap 0.5 mm , scan time 8 min . a three - dimensional fast spoiled gradient recalled - echo sequence covering the whole brain was used for structural data acquisition with tr / te / inversion time 6.5/2.1/400 ms , fov 256 mm  256 mm , phase fov 1 , matrix 256  256 , slice thickness 1.0 mm , slice gap 0 mm , number of signal averages ( nsa ) 1 , flip angle 15 , scan time 4 min 8 s.
after the first 10 time points were discarded , slice timing and head motion correction were performed .
the remaining images of all subjects were then normalized to montreal neurological institute 152 space .
all images were then smoothed with a 4 mm  4 mm  4 mm gaussian kernel .
datasets were then drifted and filtered in three distinct frequency bands : 0.010.06 hz , 0.060.11 hz , and 0.110.25 hz .
nuisance covariates of whole brain , white matter , and cerebrospinal fluid signals were removed using regression .
the registered fmri data were segmented into 90 regions using an automated anatomical labeling template .
the pearson correlation coefficients were calculated between any two functionally connected regions at three different frequency bands ( 0.010.06 hz , 0.060.11 hz and 0.110.25 hz ) .
each subject was assigned a 90  90 correlation matrix at different filter bands . in order to detect the topological differences of functional brain network between ad patients and healthy controls , a wide range of thresholds
specifically , if the pearson correlation coefficient was greater than the threshold , the correlation coefficient was set to 1 ; otherwise , it was set to 0 .
the selected threshold ranged from 0.35 to 0.60 and increased by 0.01 at each step .
in this study , the global efficiency , the cc , the cpl , and  small - world  property were calculated in a wide range of thresholds and averaged within each group .
the definition of these parameters can be found in bullmore and sporns . to compare the degree distributions of functional brain network between ad patients and healthy controls ,
the node degree was then calculated in each node and averaged within each group to generate the degree distribution curve .
network is characterized as a network with a shorter cpl than a regular network ( high cc and long cpl ) and a greater cc than a random network ( low cc and short cpl ) . to detect the differences of  small - world  properties between ad patients and healthy controls , the ratio of cc and cpl
the differences of topological parameters between patients and controls were compared by two - sample t - test using spss 17.0 ( ssps inc . , chicago , il , usa ) software .
the global efficiencies of ad patients and healthy controls at three different frequency bands are shown in figure 1 .
the global efficiencies of ad patients were always lower than healthy controls at the frequency bands of 0.010.06 hz and 0.060.11 hz under all thresholds .
no significant difference of global efficiency between groups at the frequency band of 0.110.25 hz was found at smaller thresholds .
however , within a higher threshold ( more than 0.5 ) , the global efficiency was still lower in ad patients than in healthy controls .
the global efficiencies of the functional brain networks in alzheimer 's disease patients ( marked in black ) and in healthy controls ( marked in red ) at the three different frequency bands . 

figure 2 shows the cc of the functional brain network of ad patients and healthy controls at different frequency bands .
the results indicate that the cc was always lower in ad patients than in controls at lower frequency bands of 0.010.06 hz and 0.060.11 hz . for higher frequency band ( 0.110.25 hz ) , no significant difference was found between groups .
the clustering coefficients of the functional brain networks in alzheimer 's disease patients ( marked in black ) and in healthy controls ( marked in red ) at the three different frequency bands .
the average cpl of the healthy controls was much shorter at the frequency band of 0.110.25 hz if the threshold was greater than 0.5 .
there was no significant difference in the cpl at lower frequency bands ( 0.010.06 hz , 0.060.11 hz ) .
the average shortest path length of the functional brain networks in alzheimer 's disease patients ( marked in black ) and in healthy controls ( marked in red ) at the three different frequency bands .  small - world 
figure 4 shows the  small - world  property of the healthy controls was always higher than that of ad patients under all the thresholds at three distinct frequency bands .
 properties of the functional brain networks in alzheimer 's disease patients ( marked in black ) and in healthy controls ( marked in red ) at the three different frequency bands .
the degree of a node is the number of connections that link it to the rest of the network .
the degree of each node was calculated at the frequency band of 0.060.11 hz with a threshold value of 0.45 in each subject and then averaged within each group .
table 2 shows the average node degrees in patient group and control group . among all 90 nodes ,
the proportion of nodes with a node degree higher than 17 was just 5.56% in ad patient group while in healthy controls the proportion was as high as 28.89% .
the probability of node degree in ad patient group and healthy control group ad : alzheimer s disease .
previous studies have shown that the degree distribution of the functional brain network is described by a gauss function curve .
figure 5 represents the degree distribution curve of ad patients and controls fitted with a gaussian distribution .
the probability distribution of node degree in the healthy group was higher than in the ad group when the node degree was > 15 .
the degree distribution of alzheimer 's disease group ( black curve ) and control group ( red curve ) after gaussian function curve - fitting .
the differences of node degree between ad patients and healthy controls are further investigated [ figure 6 ] .
the results demonstrate that a reduction of node degree was distributed in the left postcentral gyrus ( pocg.l ) , the right hippocampus ( hip.r ) , the left middle temporal gyrus ( mtg.l ) , the right middle occipital gyrus ( mog.r ) , the right orbital part of middle frontal gyrus ( orbsupmed.r ) , the right amygdala ( amyg.r ) , the left lingual gyrus ( ling.l ) , the medial part of right superior frontal gyrus ( sfgmed.r ) , and the medial part of left superior frontal gyrus ( sfgmed.l ) .
only a few regions show increased node degree in ad patients : the left inferior temporal gyrus ( itg.l ) , the left orbital part of superior frontal gyrus ( orbsup.l ) , and the right mtg ( mtg.r ) . the structure - specific alterations of node degrees in ad patients .
the red dots indicate increased node degrees in the ad group compared with healthy controls ; the blue dots indicate reduced node degrees in the ad group .
ad : alzheimer 's disease ; amyg.r : right amygdala ; hip.r : right hippocampus ; itg.l : inferior temporal gyrus ; ling.l : left lingual gyrus ; mog.r : right middle occipital gyrus ; mtg.l : left middle temporal gyrus ; mtg.r : right middle temporal gyrus ; orbsupmed.r : right orbital part of middle frontal gyrus ; pocg.l : left postcentral gyrus ; sfgmed.l : medial part of left superior frontal gyrus ; sfgmed.r : medial part of right superior frontal gyrus .
the global efficiencies of ad patients and healthy controls at three different frequency bands are shown in figure 1 .
the global efficiencies of ad patients were always lower than healthy controls at the frequency bands of 0.010.06 hz and 0.060.11 hz under all thresholds .
no significant difference of global efficiency between groups at the frequency band of 0.110.25 hz was found at smaller thresholds .
however , within a higher threshold ( more than 0.5 ) , the global efficiency was still lower in ad patients than in healthy controls .
the global efficiencies of the functional brain networks in alzheimer 's disease patients ( marked in black ) and in healthy controls ( marked in red ) at the three different frequency bands . 

figure 2 shows the cc of the functional brain network of ad patients and healthy controls at different frequency bands .
the results indicate that the cc was always lower in ad patients than in controls at lower frequency bands of 0.010.06 hz and 0.060.11 hz . for higher frequency band ( 0.110.25 hz ) , no significant difference was found between groups .
the clustering coefficients of the functional brain networks in alzheimer 's disease patients ( marked in black ) and in healthy controls ( marked in red ) at the three different frequency bands .
the average cpl of the healthy controls was much shorter at the frequency band of 0.110.25 hz if the threshold was greater than 0.5 .
there was no significant difference in the cpl at lower frequency bands ( 0.010.06 hz , 0.060.11 hz ) .
the average shortest path length of the functional brain networks in alzheimer 's disease patients ( marked in black ) and in healthy controls ( marked in red ) at the three different frequency bands .  small - world 
figure 4 shows the  small - world  property of the healthy controls was always higher than that of ad patients under all the thresholds at three distinct frequency bands .
 properties of the functional brain networks in alzheimer 's disease patients ( marked in black ) and in healthy controls ( marked in red ) at the three different frequency bands .
the degree of a node is the number of connections that link it to the rest of the network .
the degree of each node was calculated at the frequency band of 0.060.11 hz with a threshold value of 0.45 in each subject and then averaged within each group .
table 2 shows the average node degrees in patient group and control group . among all 90 nodes ,
the proportion of nodes with a node degree higher than 17 was just 5.56% in ad patient group while in healthy controls the proportion was as high as 28.89% .
the probability of node degree in ad patient group and healthy control group ad : alzheimer s disease .
previous studies have shown that the degree distribution of the functional brain network is described by a gauss function curve .
figure 5 represents the degree distribution curve of ad patients and controls fitted with a gaussian distribution .
the probability distribution of node degree in the healthy group was higher than in the ad group when the node degree was > 15 .
the degree distribution of alzheimer 's disease group ( black curve ) and control group ( red curve ) after gaussian function curve - fitting .
the differences of node degree between ad patients and healthy controls are further investigated [ figure 6 ] .
the results demonstrate that a reduction of node degree was distributed in the left postcentral gyrus ( pocg.l ) , the right hippocampus ( hip.r ) , the left middle temporal gyrus ( mtg.l ) , the right middle occipital gyrus ( mog.r ) , the right orbital part of middle frontal gyrus ( orbsupmed.r ) , the right amygdala ( amyg.r ) , the left lingual gyrus ( ling.l ) , the medial part of right superior frontal gyrus ( sfgmed.r ) , and the medial part of left superior frontal gyrus ( sfgmed.l ) .
only a few regions show increased node degree in ad patients : the left inferior temporal gyrus ( itg.l ) , the left orbital part of superior frontal gyrus ( orbsup.l ) , and the right mtg ( mtg.r ) . the structure - specific alterations of node degrees in ad patients .
the red dots indicate increased node degrees in the ad group compared with healthy controls ; the blue dots indicate reduced node degrees in the ad group .
ad : alzheimer 's disease ; amyg.r : right amygdala ; hip.r : right hippocampus ; itg.l : inferior temporal gyrus ; ling.l : left lingual gyrus ; mog.r : right middle occipital gyrus ; mtg.l : left middle temporal gyrus ; mtg.r : right middle temporal gyrus ; orbsupmed.r : right orbital part of middle frontal gyrus ; pocg.l : left postcentral gyrus ; sfgmed.l : medial part of left superior frontal gyrus ; sfgmed.r : medial part of right superior frontal gyrus .
the present study shows that the global efficiency , the cc , and the  small - world  properties in the ad patient group changes with different frequency bands , suggesting the existence of disrupted global and local functional organization associated with ad . specifically , at lower - frequency bands ( 0.010.06 hz , 0.060.11 hz ) , the global efficiency , the cc and the  small - world  properties of ad patients decreased compared with healthy controls while the cpl elongated within a wide range of thresholds .
however , at higher - frequency bands ( 0.110.25 hz ) , the global efficiency and the cc showed no significant differences compared with healthy controls , while the  small - world  properties were lower and the cpl were much longer in ad than in controls , particularly at a higher threshold .
comparisons of node degree indicate that the probability distribution of node degree in healthy groups was higher than in ad group if the node degree exceeded 15 . for structure - specific alterations ,
there was a significant reduction of node degree in brain regions of pocg.l , hip.r , mtg.l , mog.r , orbsupmed.r , amyg.r , ling.l , sfgmed.r , and sfgmed.l ; while in areas of itg.l , orbsup.l , and mtg.r , the node degree increased .
the results of this study demonstrate that the topological property of large - scale functional brain networks in ad patients is frequency dependent .
previous studies have suggested that the hemodynamic responses measured by rs - fmri reflect spontaneous neural activity which largely fluctuates at a lower - frequency band .
it has been demonstrated that spontaneous low - frequency fluctuations ( 0.010.1 hz ) are physiologically meaningful .
higher - frequency fluctuations are usually affected by respiratory signal frequency ( 0.10.5 hz ) and cardiovascular signal frequency ( 0.10.5 hz ) . in this study ,
the topological properties of ad patients and healthy controls exhibited different properties at different frequency bands .
one possibility is that topological properties are frequency - dependent , which contributed to the discrepancies observed in previous studies .
stam et al . demonstrated that within an extensively wide range of thresholds , ad patients exhibited a longer cpl than healthy controls but no significant changes in the cc were found .
however , supekar et al . showed a decline of cc in patients with ad .
meanwhile , in 2009 , using meg data , stam et al . demonstrated that ad patients had a lower cc and a longer cpl . in 2010 , using rs - fmri data , sanz - arigita et al . reported no significant changes in cc in ad but with a shorter cpl
the inconsistent results of these studies may be caused by the selection of different frequency bands .
our report agrees with reports from de haan et al . , which suggest that various frequency bands impact the topological properties of a functional brain network .
global efficiency is one of the most pertinent parameters for quantifying the parallel information propagation capability of a network . in this study ,
the global efficiency of ad patients was always lower than healthy controls at lower - frequency bands ( 0.010.06 hz , 0.060.11 hz ) [ figure 1 ] , data which agrees with zhao et al .
the decline of global efficiency in ad patients indicates that pathological changes in the brain have reduced connectivity strength and blocked information communication in remote functional regions .
a wealth of studies has demonstrated that the global efficiency of the brain network declines if the brain is pathologically impaired .
this may be one major factor contributing to the cognitive decline of patients with ad .
however , compared with healthy controls , there was no significant difference of the global efficiency at a higher frequency band ( 0.110.25 hz ) .
we suggest that higher - frequency fluctuations may result from coexisting noise during the acquisition of mri signals in both ad patients and healthy controls .
the cc of a network quantifies the number of local connections that exist as a proportion of the maximum number of possible connections .
our study demonstrates that at lower - frequency bands within a higher range of thresholds , the cc of ad patients is diminished compared with healthy controls , in line with previous studies .
this finding indicates a decline in coupling , robustness , as well as the local functional connectivity strength between nodes in patients with ad .
there was no significant difference in cpl between ad and controls , demonstrating that short - range connections are maintained in ad patients .
short paths promote effective interactions between neuronal elements within and across cortical regions , and are essential for functional integration . in 1998 ,
watts and strogatz first explored the characteristic of a  small - world  network .
it has been suggested that hierarchical organizations of ad and controls differ with each other , resulting in a significant decline in cc among ad patients .
it not only facilitates both modularized and distributed information processing but also maximizes the efficiency of information transfer at a relatively low wiring cost . in a  small - world 
network , there are many clusters ( small groups of nodes connected to each other ) or node clusters of which the number of connections is less than the number of clusters .
in addition , any two nodes are usually connected by at least one short path .
numerous studies have demonstrated that the  small - world  properties of ad patients suffer significantly deterioration .
properties indicates that the efficiency of information transfer within different brain regions has also declined , a factor which may play a major role in the cognitive decline observed in ad patients . at a threshold of 0.45 ,
the structure - specific alterations of node degree in ad patients were further investigated at the frequency band of 0.060.11 hz . the results indicate that areas with node degree reduction are located mostly in the temporal lobe and frontal lobe .
previous studies have demonstrated that a deposition in ad occurs preferentially in locations of cortical hubs ( nodes ) , accounting for the observed activity - dependent mechanism associated with connectional hubs .
the cortical components of the medial temporal lobe and the frontoparietal lobe of these hubs are especially vulnerable to ad .
furthermore , three regions show an increased node degree in ad patients ( itg.l , orbsup.l and mtg.r ) , indicating a coexisting functional compensation in the temporal lobe and frontal lobe . in conclusion , based on data analysis of resting - state functional networks ,
large - scale functional brain networks of ad patients and healthy controls were constructed and compared for a wide range of thresholds at different frequency bands . compared with healthy controls ,
the patients with ad exhibited lower global efficiency , lower cc , and also lower  small - world 
furthermore , a decline in the node degree was observed in the large majority of pathologically attacked regions , with other areas increasing as functional compensations .
our study accurately depicts the frequency - specific topological alterations in ad - related large - scale functional brain networks , providing fundamental support for optimal frequency selection in future related research .
previous studies have suggested that the hemodynamic responses measured by rs - fmri reflect spontaneous neural activity which largely fluctuates at a lower - frequency band .
it has been demonstrated that spontaneous low - frequency fluctuations ( 0.010.1 hz ) are physiologically meaningful .
higher - frequency fluctuations are usually affected by respiratory signal frequency ( 0.10.5 hz ) and cardiovascular signal frequency ( 0.10.5 hz ) . in this study ,
the topological properties of ad patients and healthy controls exhibited different properties at different frequency bands .
one possibility is that topological properties are frequency - dependent , which contributed to the discrepancies observed in previous studies .
stam et al . demonstrated that within an extensively wide range of thresholds , ad patients exhibited a longer cpl than healthy controls but no significant changes in the cc were found .
however , supekar et al . showed a decline of cc in patients with ad .
meanwhile , in 2009 , using meg data , stam et al . demonstrated that ad patients had a lower cc and a longer cpl . in 2010 , using rs - fmri data , sanz - arigita et al . reported no significant changes in cc in ad but with a shorter cpl
the inconsistent results of these studies may be caused by the selection of different frequency bands .
our report agrees with reports from de haan et al . , which suggest that various frequency bands impact the topological properties of a functional brain network .
global efficiency is one of the most pertinent parameters for quantifying the parallel information propagation capability of a network . in this study ,
the global efficiency of ad patients was always lower than healthy controls at lower - frequency bands ( 0.010.06 hz , 0.060.11 hz ) [ figure 1 ] , data which agrees with zhao et al .
the decline of global efficiency in ad patients indicates that pathological changes in the brain have reduced connectivity strength and blocked information communication in remote functional regions .
a wealth of studies has demonstrated that the global efficiency of the brain network declines if the brain is pathologically impaired .
this may be one major factor contributing to the cognitive decline of patients with ad .
however , compared with healthy controls , there was no significant difference of the global efficiency at a higher frequency band ( 0.110.25 hz ) .
we suggest that higher - frequency fluctuations may result from coexisting noise during the acquisition of mri signals in both ad patients and healthy controls .
the cc of a network quantifies the number of local connections that exist as a proportion of the maximum number of possible connections .
our study demonstrates that at lower - frequency bands within a higher range of thresholds , the cc of ad patients is diminished compared with healthy controls , in line with previous studies .
this finding indicates a decline in coupling , robustness , as well as the local functional connectivity strength between nodes in patients with ad .
there was no significant difference in cpl between ad and controls , demonstrating that short - range connections are maintained in ad patients .
short paths promote effective interactions between neuronal elements within and across cortical regions , and are essential for functional integration . in 1998 ,
watts and strogatz first explored the characteristic of a  small - world  network .
it has been suggested that hierarchical organizations of ad and controls differ with each other , resulting in a significant decline in cc among ad patients .
it not only facilitates both modularized and distributed information processing but also maximizes the efficiency of information transfer at a relatively low wiring cost . in a  small - world 
network , there are many clusters ( small groups of nodes connected to each other ) or node clusters of which the number of connections is less than the number of clusters .
in addition , any two nodes are usually connected by at least one short path .
numerous studies have demonstrated that the  small - world  properties of ad patients suffer significantly deterioration .
properties indicates that the efficiency of information transfer within different brain regions has also declined , a factor which may play a major role in the cognitive decline observed in ad patients .
at a threshold of 0.45 , the structure - specific alterations of node degree in ad patients were further investigated at the frequency band of 0.060.11 hz . the results indicate that areas with node degree reduction are located mostly in the temporal lobe and frontal lobe .
previous studies have demonstrated that a deposition in ad occurs preferentially in locations of cortical hubs ( nodes ) , accounting for the observed activity - dependent mechanism associated with connectional hubs .
the cortical components of the medial temporal lobe and the frontoparietal lobe of these hubs are especially vulnerable to ad .
furthermore , three regions show an increased node degree in ad patients ( itg.l , orbsup.l and mtg.r ) , indicating a coexisting functional compensation in the temporal lobe and frontal lobe . in conclusion , based on data analysis of resting - state functional networks ,
large - scale functional brain networks of ad patients and healthy controls were constructed and compared for a wide range of thresholds at different frequency bands . compared with healthy controls ,
the patients with ad exhibited lower global efficiency , lower cc , and also lower  small - world 
furthermore , a decline in the node degree was observed in the large majority of pathologically attacked regions , with other areas increasing as functional compensations .
our study accurately depicts the frequency - specific topological alterations in ad - related large - scale functional brain networks , providing fundamental support for optimal frequency selection in future related research .
 background : previous studies have indicated that the cognitive deficits in patients with alzheimer 's disease ( ad ) may be due to topological deteriorations of the brain network . however , whether the selection of a specific frequency band could impact the topological properties is still not clear . 
 our hypothesis is that the topological properties of ad patients are also frequency-specific.methods:resting state functional magnetic resonance imaging data from 10 right - handed moderate ad patients ( mean age : 64.3 years ; mean mini mental state examination [ mmse ] : 18.0 ) and 10 age and gender - matched healthy controls ( mean age : 63.6 years ; mean mmse : 28.2 ) were enrolled in this study . the global efficiency , the clustering coefficient ( cc ) , the characteristic path length ( cpl ) , and  small - world  
 property were calculated in a wide range of thresholds and averaged within each group , at three different frequency bands ( 0.010.06 hz , 0.060.11 hz , and 0.110.25 hz).results : at lower - frequency bands ( 0.010.06 hz , 0.060.11 hz ) , the global efficiency , the cc and the  small - world  properties of ad patients decreased compared to controls . while at higher - frequency bands ( 0.110.25 hz ) , the cpl was much longer , and the  small - world  
 property was disrupted in ad , particularly at a higher threshold . 
 the topological properties changed with different frequency bands , suggesting the existence of disrupted global and local functional organization associated with ad.conclusions:this study demonstrates that the topological alterations of large - scale functional brain networks in ad patients are frequency dependent , thus providing fundamental support for optimal frequency selection in future related research . 
I
M
Subjects
Magnetic resonance imaging examination
Data preprocessing
Construction of brain functional network
Topological properties of the functional brain network
Statistics
R
Topological parameter comparisons at different frequency bands
Changes of the node degree
D
Different topological properties at different frequency bands
Topological organizations of large-scale functional brain network
Regional alterations of node degree