Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches

Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Prejaas Tewarie [verfasserIn] Bastian Prasse [verfasserIn] Jil M. Meier [verfasserIn] Fernando A.N. Santos [verfasserIn] Linda Douw [verfasserIn] Menno M. Schoonheim [verfasserIn] Cornelis J. Stam [verfasserIn] Piet Van Mieghem [verfasserIn] Arjan Hillebrand [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Structural network Structural connectome Functional network Functional MRI (fMRI) Diffusion tensor imaging (DTI) Neural mass

Übergeordnetes Werk:	In: NeuroImage - Elsevier, 2020, 216(2020), Seite 116805-
Übergeordnetes Werk:	volume:216 ; year:2020 ; pages:116805-

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1016/j.neuroimage.2020.116805

Katalog-ID:	DOAJ007998236

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spelling	10.1016/j.neuroimage.2020.116805 doi (DE-627)DOAJ007998236 (DE-599)DOAJ842f1afc221d4bb8ae4866cdfde13952 DE-627 ger DE-627 rakwb eng RC321-571 Prejaas Tewarie verfasserin aut Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks. Structural network Structural connectome Functional network Functional MRI (fMRI) Diffusion tensor imaging (DTI) Neural mass Neurosciences. Biological psychiatry. Neuropsychiatry Bastian Prasse verfasserin aut Jil M. Meier verfasserin aut Fernando A.N. Santos verfasserin aut Linda Douw verfasserin aut Menno M. Schoonheim verfasserin aut Cornelis J. Stam verfasserin aut Piet Van Mieghem verfasserin aut Arjan Hillebrand verfasserin aut In NeuroImage Elsevier, 2020 216(2020), Seite 116805- (DE-627)268125503 (DE-600)1471418-8 10959572 nnns volume:216 year:2020 pages:116805- https://doi.org/10.1016/j.neuroimage.2020.116805 kostenfrei https://doaj.org/article/842f1afc221d4bb8ae4866cdfde13952 kostenfrei http://www.sciencedirect.com/science/article/pii/S1053811920302925 kostenfrei https://doaj.org/toc/1095-9572 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 216 2020 116805-
allfields_unstemmed	10.1016/j.neuroimage.2020.116805 doi (DE-627)DOAJ007998236 (DE-599)DOAJ842f1afc221d4bb8ae4866cdfde13952 DE-627 ger DE-627 rakwb eng RC321-571 Prejaas Tewarie verfasserin aut Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks. Structural network Structural connectome Functional network Functional MRI (fMRI) Diffusion tensor imaging (DTI) Neural mass Neurosciences. Biological psychiatry. Neuropsychiatry Bastian Prasse verfasserin aut Jil M. Meier verfasserin aut Fernando A.N. Santos verfasserin aut Linda Douw verfasserin aut Menno M. Schoonheim verfasserin aut Cornelis J. Stam verfasserin aut Piet Van Mieghem verfasserin aut Arjan Hillebrand verfasserin aut In NeuroImage Elsevier, 2020 216(2020), Seite 116805- (DE-627)268125503 (DE-600)1471418-8 10959572 nnns volume:216 year:2020 pages:116805- https://doi.org/10.1016/j.neuroimage.2020.116805 kostenfrei https://doaj.org/article/842f1afc221d4bb8ae4866cdfde13952 kostenfrei http://www.sciencedirect.com/science/article/pii/S1053811920302925 kostenfrei https://doaj.org/toc/1095-9572 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 216 2020 116805-
allfieldsGer	10.1016/j.neuroimage.2020.116805 doi (DE-627)DOAJ007998236 (DE-599)DOAJ842f1afc221d4bb8ae4866cdfde13952 DE-627 ger DE-627 rakwb eng RC321-571 Prejaas Tewarie verfasserin aut Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks. Structural network Structural connectome Functional network Functional MRI (fMRI) Diffusion tensor imaging (DTI) Neural mass Neurosciences. Biological psychiatry. Neuropsychiatry Bastian Prasse verfasserin aut Jil M. Meier verfasserin aut Fernando A.N. Santos verfasserin aut Linda Douw verfasserin aut Menno M. Schoonheim verfasserin aut Cornelis J. Stam verfasserin aut Piet Van Mieghem verfasserin aut Arjan Hillebrand verfasserin aut In NeuroImage Elsevier, 2020 216(2020), Seite 116805- (DE-627)268125503 (DE-600)1471418-8 10959572 nnns volume:216 year:2020 pages:116805- https://doi.org/10.1016/j.neuroimage.2020.116805 kostenfrei https://doaj.org/article/842f1afc221d4bb8ae4866cdfde13952 kostenfrei http://www.sciencedirect.com/science/article/pii/S1053811920302925 kostenfrei https://doaj.org/toc/1095-9572 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 216 2020 116805-
allfieldsSound	10.1016/j.neuroimage.2020.116805 doi (DE-627)DOAJ007998236 (DE-599)DOAJ842f1afc221d4bb8ae4866cdfde13952 DE-627 ger DE-627 rakwb eng RC321-571 Prejaas Tewarie verfasserin aut Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks. Structural network Structural connectome Functional network Functional MRI (fMRI) Diffusion tensor imaging (DTI) Neural mass Neurosciences. Biological psychiatry. Neuropsychiatry Bastian Prasse verfasserin aut Jil M. Meier verfasserin aut Fernando A.N. Santos verfasserin aut Linda Douw verfasserin aut Menno M. Schoonheim verfasserin aut Cornelis J. Stam verfasserin aut Piet Van Mieghem verfasserin aut Arjan Hillebrand verfasserin aut In NeuroImage Elsevier, 2020 216(2020), Seite 116805- (DE-627)268125503 (DE-600)1471418-8 10959572 nnns volume:216 year:2020 pages:116805- https://doi.org/10.1016/j.neuroimage.2020.116805 kostenfrei https://doaj.org/article/842f1afc221d4bb8ae4866cdfde13952 kostenfrei http://www.sciencedirect.com/science/article/pii/S1053811920302925 kostenfrei https://doaj.org/toc/1095-9572 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 216 2020 116805-
language	English
source	In NeuroImage 216(2020), Seite 116805- volume:216 year:2020 pages:116805-
sourceStr	In NeuroImage 216(2020), Seite 116805- volume:216 year:2020 pages:116805-
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Structural network Structural connectome Functional network Functional MRI (fMRI) Diffusion tensor imaging (DTI) Neural mass Neurosciences. Biological psychiatry. Neuropsychiatry
isfreeaccess_bool	true
container_title	NeuroImage
authorswithroles_txt_mv	Prejaas Tewarie @@aut@@ Bastian Prasse @@aut@@ Jil M. Meier @@aut@@ Fernando A.N. Santos @@aut@@ Linda Douw @@aut@@ Menno M. Schoonheim @@aut@@ Cornelis J. Stam @@aut@@ Piet Van Mieghem @@aut@@ Arjan Hillebrand @@aut@@
publishDateDaySort_date	2020-01-01T00:00:00Z
hierarchy_top_id	268125503
id	DOAJ007998236
language_de	englisch
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callnumber-first	R - Medicine
author	Prejaas Tewarie
spellingShingle	Prejaas Tewarie misc RC321-571 misc Structural network misc Structural connectome misc Functional network misc Functional MRI (fMRI) misc Diffusion tensor imaging (DTI) misc Neural mass misc Neurosciences. Biological psychiatry. Neuropsychiatry Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches
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topic_title	RC321-571 Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches Structural network Structural connectome Functional network Functional MRI (fMRI) Diffusion tensor imaging (DTI) Neural mass
topic	misc RC321-571 misc Structural network misc Structural connectome misc Functional network misc Functional MRI (fMRI) misc Diffusion tensor imaging (DTI) misc Neural mass misc Neurosciences. Biological psychiatry. Neuropsychiatry
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title	Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches
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title_full	Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches
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author_browse	Prejaas Tewarie Bastian Prasse Jil M. Meier Fernando A.N. Santos Linda Douw Menno M. Schoonheim Cornelis J. Stam Piet Van Mieghem Arjan Hillebrand
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title_sort	mapping functional brain networks from the structural connectome: relating the series expansion and eigenmode approaches
callnumber	RC321-571
title_auth	Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches
abstract	Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks.
abstractGer	Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks.
abstract_unstemmed	Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks.
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title_short	Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches
url	https://doi.org/10.1016/j.neuroimage.2020.116805 https://doaj.org/article/842f1afc221d4bb8ae4866cdfde13952 http://www.sciencedirect.com/science/article/pii/S1053811920302925 https://doaj.org/toc/1095-9572
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Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches

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