Cerebral cortex: directed brain connection recognition widespread functional network abnormalities in Parkinson's disease

Parkinson's disease (PD) It is a neurodegenerative disease characterized by topological abnormalities of large-scale brain functional networks , It is usually analyzed by the undirected correlation of activation signals between brain regions . This method assumes that brain regions are activated at the same time , Although previous evidence suggests , Brain activation is accompanied by causality , Signals are usually generated in one area , Then spread to other areas . To address this limitation , We developed a new method to evaluate the whole brain directed functional connectivity of Parkinson's disease participants and healthy controls , Use antisymmetric delay correlation , Better capture this potential causal relationship . Our results show that , Whole brain directed connections calculated from functional magnetic resonance imaging data , Compared with undirected method , Identified PD Wide differences in functional networks between participants and controls . These differences are characterized by the improvement of overall efficiency 、 Clustering and transitivity are combined with lower modularity . Besides , Anterior cuneiform lobe 、 The directional connection pattern of thalamus and cerebellum is related to PD The patient's movement 、 Execution is related to memory deficits . All in all , These findings indicate that , Compared with the standard method , Directed brain connection pair PD Functional network differences that occur in are more sensitive , For brain connection analysis and development tracking PD New markers of progress offer new opportunities .

1. brief introduction

Parkinson's disease (PD) It is a complex neurodegenerative disease , Characterized by a variety of motor and non motor symptoms , Like memory 、 perform 、 Visual space or olfactory defect . The appearance of these different symptoms indicates ,PD The brain changes that occur in cannot be directly related to the dysfunction of a single brain region , It is related to extensive changes in functional connections between many regions or brain networks .

Functional connectivity can be measured by functional magnetic resonance imaging (MRI) To measure , This is a non-invasive technique for detecting signal dependent changes in blood oxygen levels , It is thought to reflect potential neuronal brain activity . In patients with Parkinson's disease , A number of studies have shown that , Due to the loss of integrity of these functional connections , Exercise and non exercise symptoms may occur . Especially, the abnormal functional connection of thalamic cortical network in basal ganglia is related to the motor symptoms of Parkinson's disease , The default mode 、 Pay attention to your back 、 Frontal parietal lobe 、 Saliency and associative visual networks have been shown to be associated with cognitive deficits in these participants .

In the past few years , Some studies use functionality MRI To evaluate the brain functional connectivity Group , This is a whole brain network that summarizes the complete pairwise functional connections in the brain . This network consists of a set of nodes ( Or brain regions ) form , Connected by edges , Represents the strength of functional connection . then , By calculating several global and local measurements , The connection network can be analyzed using graph theory , These measurements reflect whether brain regions are effectively connected through short network paths ( Global efficiency ), Or whether it is well integrated into its neighborhood ( clustering ) Or community ( modularization ). These analyses show that the whole brain or PD Overall efficiency within the participant's specific network 、 Significant changes in local efficiency and clustering coefficient . Changes in the node network topology of the prefrontal lobe and auxiliary motor areas, as well as the striatum and thalamus, have also been reported in Parkinson's disease , Sometimes it is related to clinical measurement .

Although these studies are important for evaluation PD Network changes in are very useful , But these studies are based on such assumptions : The activities of different brain regions occur at the same time , Therefore, it can be captured by the undirected correlation of the activation signals between them . therefore , They do not convey information about the direction of interaction between brain regions , This is important , Because more and more studies show ,PD Patients' directed brain activity patterns will change . Use a dynamic causal model , Structural equation modeling , Psychophysiological interaction , Or Granger causality method to evaluate these directed patterns . Due to the complexity and the long calculation time required by these methods , Their application is currently limited to evaluating brain connections between several regions or the analysis of functional MRI data obtained in a specific task , Brain regions that usually depend on a priori assumptions should be tested . Besides , Recently, several generalizations about directed whole brain connectivity assessment have been proposed . However , These methods are still limited by computational efficiency and identifiability . Besides , Their application in studying functional networks to evaluate functional changes in neurodegenerative diseases has not been systematically evaluated .

Here it is , We propose an intuitive and computationally simple method to evaluate resting state whole brain directed functional networks based on antisymmetric lag correlation . First , We calculate the lag correlation between all brain region pairs , Get the lag correlation adjacency matrix of each participant . then , The antisymmetric correlation is derived as the antisymmetric part of the lag correlation adjacency matrix . We prove , Compared with the functional network constructed by the standard undirected method , The topology of these functional networks is right PD Related pathological changes are more sensitive .

2. Method brief introduction

Activation signals are usually generated in an area of the brain , Then spread to other areas , This leads to the causality and hysteresis of the activation of various brain regions . This time lag also occurs , for example , Due to the spatial distribution of brain regions and the limited transmission speed between them . therefore , Capturing the information stored in this complex time lag framework is necessary to achieve a coherent representation of functional connectivity . In this work , We obtain additional information by using the lagged Pearson correlation to calculate the directed functional connections between brain regions . In this way , If the activation time series of one brain region is similar to the time shifted version of the activation pattern of the second brain region , It is believed that this brain region has direct interaction with other brain regions . Besides , Compared with indirectly connected brain regions , The delay of activation of brain regions that are more closely connected is much shorter . Based on the hypothesis that brain quasi synchronous activity mainly occurs between nodes connected by direct paths , We can interpret the different hysteresis of activation patterns between brain regions as an indicator of the topological connection distance between them . for example , The connection network with small time lag represents the brain region directly connected , A larger time lag indicates a network of brain regions connected by indirect connections of different lengths . therefore , In order to explore the brain function activation mode under different topological connection scales , We evaluated multiple time lag directed functional connections ( Method : Lag correlation ).

chart 1 It shows the different methods we use to calculate the functional connection network of a group of brain regions and its activation time series ( chart 1a). The connection matrix and corresponding network of these five brain regions calculated by the lag correlation adjacency method are shown in the figure 1b Shown : The lag correlation method evaluates the directed connection of two brain regions in two directions ; A pair of elements in the lagging adjacency matrix ( namely (i,j) and (j, i)) Provides brain regions i And brain regions j An estimate of the direct relationship between , vice versa . Because this is a measurement method based on Correlation , It does not attempt to evaluate the effective connection between two brain regions . contrary , We use it to quantify the directed functional connection between two regions , Direction depends on time priority ( namely , The early region is the source , The late region is the end of the connection ).

Like any other square , The delay dependent adjacency matrix can be uniquely expressed as the sum of symmetric and antisymmetric matrices . say concretely , Antisymmetric matrix captures the directionality of Functional Networks , Identify the relevant directed connections between pairs of brain regions ( chart 1c). We call this method antisymmetric Correlation ( Method : Antisymmetric correlation and symmetric correlation ).

To emphasize directed network detection PD Control the effectiveness of topology changes between participants , We compare our method with two undirected network methods . In the first way , The evaluation of functional connectivity is a symmetric matrix extracted from the lag correlation adjacency matrix ( chart 1d), The undirected connection between the two regions is the sum of the corresponding two directed connection weights ( Method : Antisymmetry and symmetry are related ). secondly , We also compare our method with the traditional method of quantifying functional connectivity , The traditional method calculates the zero lag between the activation time series Pearson s The correlation coefficient ( chart 1e) To estimate the strength of the connection between the two regions ( Method : Zero lag correlation ). Although lagging 0 These two methods are the same when calculating Symmetric Correlation , It shows a very high correlation with a small lag ( Supplementary drawing 1), However, the correlation between the two methods decreases with the increase of time lag . This shows that , Symmetric correlation captures different scales of undirected connections as a function of time lag , Thus, an appropriate framework is provided to compare the behavior of directed and undirected methods under different time lags . Because zero lag correlation cannot effectively capture these different connectivity scales , The consistency between the two methods decreases when the time lag is high .

We tested all four methods to detect 95 The ability of patients with Parkinson's disease to change topology , And with 15 Comparisons were made among control subjects , These controls used the function of Parkinson's progression marker project MRI data ( Method : participants ). The latest information about this study , Please visit www.ppmi-info.org. The nodes in the adjacency matrix correspond to from Craddock Obtained from the manual 200 Brain regions , And the edge is based on the above 4 There are ways to calculate , Generate for each participant 4 Different weighted adjacency matrices . For each adjacency matrix , We calculate a binary matrix , Where the correlation coefficient is higher than a certain threshold, it is considered 1 It is 0. Because there are many other threshold methods , At present, there is no consensus on which network density should be used , We are opposed to the network density of related networks (D) Full availability of (Dmin = 1% To Dmax = 50%, stay 1% In the process of ) Perform threshold segmentation , And compare the network topology within this range . Besides , We also compare our results with the results of another weighted analysis method , In this way , The network retains the weight of a single edge after binarization . The negative correlation coefficient and self connection are set to zero , Exclude from all analyses .

chart 1 Different methods of computing functional networks

3. result
3.1 The average group network shows different behaviors under different time delays

We use the average weighted 、 Participant specific adjacency matrix to calculate the group representative adjacency matrix under different time delays . chart 2 Shows lag ( chart 2a)、 antisymmetric ( chart 2b) And symmetry ( chart 2c) Histogram of relevant connection weights , They are functions of different time lags . chart 2 Show , Compared with the healthy control group ,PD The strength of the directed connection of participants has decreased on the whole . Besides , stay PD Among the participants , We observed that , The connectivity intensity distribution of all analyses narrows with the increase of time lag . This observation shows that , As the time delay increases , More nodes have similar functional connection strength . therefore , Large time lag is not suitable for analyzing topological differences between clusters , Because they cannot capture any changes in the directional flow in the network , Limit our analysis to a small time lag 1-7. Under different time delays , These results are further supported by the evaluation of the network diameter of the specific adjacency matrix of all participants ( Supplementary drawing 2).

chart 2 Connection strength distribution with different time delays

3.2 Differences between groups in the global network topology

To evaluate these methods detect PD The ability to change the global network between patients and controls , We calculated the global efficiency 、 Local efficiency 、 Clustering coefficient 、 Transitivity and modularity ( chart 3, From left to right ). Antisymmetric correlation shows PD There are wide and significant differences between participants and control group in network measurement ; This means that the difference is contained in the antisymmetric part of the lag correlation matrix . These differences include : Compared with the control group , At higher network density ,PD The clustering coefficient and transitivity of participants increase ( Clustering coefficient :16-50%; Transitivity :20-50%). Global and local efficiency also shows PD Differences between participants and controls , In most network densities PD The efficiency of participants has improved ( Global efficiency :2-50%; Local efficiency :6-50%). Last , We also found that , Compared with the control group ,PD The modularity of participants decreased significantly , Only in higher network density (21-50%). contrary , Undirected and lagged correlation methods are PD There were no significant differences in global network measurements between participants and the control group . chart 3 Summarize the time delay 1 Result ; lagging 2-7 The corresponding results are shown in the supplementary figure 3-8. The measurement diagram corresponding to the density function calculated by the antisymmetric correlation method under different time delays is shown in the supplementary figure 9 and 10 Shown . They were in the control group and PD Participants showed similar patterns , And it shows monotonic change in the range of density , It shows that the above differences reflect the changes of network topology , Instead of the potential mismatch in the number of antisymmetric connections in the two groups or the change in the overall functional connection strength .

chart 3 Control and PD Participants' differences in global network measurement .

3.3 Differences between packets in node network topology

Besides , Use the antisymmetric correlation method , We also found that compared with the control group ,PD The directed connections of several brain regions of the participants changed ( chart 4, See also supplementary figure 11-16 And supplementary tables 1). We found that PD Patient's precuneus 、 The overall efficiency of fusiform gyrus and parahippocampal gyrus was significantly improved ( Delay 7), The overall efficiency of lingual gyrus is significantly improved ( Delay 1). Besides , We found frontal orbital gyrus and cerebellum ( lagging 1) And frontal gyrus ( lagging 5) Out of - Increase in overall efficiency . Last , stay PD We also found thalamus ( lagging 4 and 5) Overall connectivity and precuneus ( lagging 3) The outflow connectivity of is reduced . The other three analysis methods cannot identify any significant nodal measurements of inter group differences , Even before multiple comparisons .

chart 4 Control group and PD The difference of participants in node network measurement

3.4 Correlation analysis between Parkinson's disease patients and clinical indicators

All global network measurements and all lagging UPDRS-III Sports scoring and execution scoring ( Letter - Digital sequencing test ) significant correlation . Besides , Clustering and transitivity are also related to lag 1 Execution score at (SDMT) relevant , And the overall efficiency and lag 5 The memory of time (Hopkins verbal learning test) relevant . Overall and local efficiency 、 Clustering and transitivity are related to visual space scores (Benton Line direction judgment test ) It's lagging behind 7 Time correlation . After adjusting the multiple comparisons between different densities and the control group (FDR, q = 0.05), The best result is 《 Supplementary materials 》( Supplementary drawing 17-21 And supplementary tables 2-18) To sum up .

3.5 The influence of dopaminergic drugs on the topology of Functional Networks

To evaluate the effect of levodopa equivalent dose on functional network organization , We compared the networks of participants who received medication with those who did not receive medication ( The details of the two subgroups are shown in the supplementary table 19). We did not find any differences in the global network topology between these groups . About the topology of nodes , It's lagging behind 1 when , The overall external efficiency of the precuneus and superior occipital gyrus of the participants taking the drug was significantly improved , It's lagging behind 2 and 3 The overall internal efficiency and degree of thalamus are significantly improved ( chart 5). It is worth noting that , These results do not overlap with the results of the main analysis .

chart 5 Taking drugs and not taking drugs PD Patients' differences in node network measurement .

3.6 The influence of mild cognitive impairment on functional network topology

Because previous evidence shows ,PD-MCI Participants showed more extensive network changes than subjects with normal cognition , We performed an additional analysis to compare the two groups ( Supplementary table of participant characteristics of two subgroups 20 Shown ). Only one significant difference was found in the cerebellum , Compared with participants with normal cognition , The cerebellum of patients with mild cognitive impairment is lagging 3 It decreases significantly .

3.7 Alternative threshold methods reveal similar inter group differences in global and nodal network measurements

We also evaluated the use of another threshold method in PD Whether similar results can be obtained in the comparison between group A and control group . In this method , We will assign each participant to the network within the density range 1-50% To binarize , And keep the weight of each edge . About global network topology , Weighted analysis confirms our previous results , Find out PD Global and local efficiency of participants in different density ranges and different time delays 、 Clustering and transitivity increased significantly ( Supplementary drawing 22 and 23). About node measurement , We found that , All regions consistent with our previous analysis showed similar significant increases or decreases under the same time delay . However , After multiple comparison control , Only a part is still significant (FDR, q = 0.05), As shown in the supplementary figure 24 -29 Shown . The other three analysis methods did not find significant differences between the groups .

3.8 Alternative methods of directed functional connection are not shown PD Differences between participants and controls

We also used Granger causality method to calculate the whole brain directed functional network , Group differences in global and regional topologies were assessed . Granger causality is another way , It is used to estimate the causal relationship between brain regions and low directed information in the network , Based on time lag . These analyses did not show significant differences between groups in the overall measurements of different model parameters ( Supplementary drawing 30 and 31). Again , At any density , No significant node differences were found between groups .

4. Discuss

In this study , We propose a new method to analyze directed functional connections using time-lapse information stored between activation of brain regions . As far as we know , At present, there is no method to evaluate the directed functional connection of the whole brain , And study the corresponding topology changes under multiple time delays . Our counter claim related methods are developed to address this gap , It shows that the whole brain directed connection can be characterized by detecting a wide range of functional changes PD The patient's connector , These changes cannot be recognized by the traditional zero marking method or the alternative method of directed connection . Besides , We found that , The change determined by antisymmetric correlation method is still significant under different threshold methods , And with PD Participants' movement 、 Execution is related to memory deficits , This shows that they have clinical significance . All in all , Our results show that , The directional flow of brain activation signals contains exclusive information that cannot be captured by other methods , It's possible to be PD New signs of functional network changes .

Functional connectivity describes the statistical dependence of activation patterns between brain regions , It is closely related to behavior and cognitive function . This statistical correlation can be quantified using metrics from graph theory , Graph theory generally believes that , If the Pearson correlation between the activation signals of the two regions is strong , Then the two areas are connected . However , The limitation of this method is , It can only capture linear between brain regions 、 At the same time 、 Directionless dependencies . There is evidence that , Brain activity is organized in multiple temporal functional patterns . therefore , The relationship between brain regions is not always linear , There is often a delay between their activation signals , This leads to a directed activation mode , Some of these areas are activation sources , Other areas are activation destinations . This lagging organization is highly repeatable , It can change in some diseases , Like autism 、 epilepsy 、 Schizophrenia or narcolepsy . therefore , Capturing the information stored in these time delays or lags is crucial to obtain more accurate brain functional connection characteristics . Although the dynamics of these hysteresis modes have been examined using ultrafast MRI , But from the perspective of functionality MRI The lag structure of the functional connection obtained in the scan is mainly evaluated by interpolating the single time lag of the maximum correlation in the whole scanning process . Contrary to this method , Our antisymmetric correlation method evaluates multiple time delayed whole brain functional connections . This can provide new insights into the communication pathways between different brain regions , And allows the evaluation of paths from different time lags , These pathways can change in the presence of neurodegenerative lesions .

reference ：Directed Brain Connectivity Identifies Widespread Functional Network Abnormalities in Parkinson’s Disease