Construction and Analysis of Weighted Brain Networks from SICE for the Study of Alzheimer's Disease

Jorge Munilla, Andrés Ortiz, Juan M. Górriz, Javier Ramírez, the Alzheimer's Disease Neuroimaging Initiative, Michael W. Weiner, Paul Aisen, Michael Weiner, Paul Aisen, Ronald Petersen, Clifford R. Jack, William Jagust, John Q. Trojanowki, Arthur W. Toga, Laurel Beckett, Robert C. Green, Andrew J. Saykin, John Morris, Leslie M. Shaw, Zaven Khachaturian, Greg Sorensen, Maria Carrillo, Lew Kuller, Marc Raichle, Steven Paul, Peter Davies, Howard Fillit, Franz Hefti, David Holtzman, M. Marcel Mesulam, William Potter, Peter Snyder, Adam Schwartz, Robert C. Green, Tom Montine, Ronald Petersen, Paul Aisen, Ronald G. Thomas, Michael Donohue, Sarah Walter, Devon Gessert, Tamie Sather, Gus Jiminez, Archana B. Balasubramanian, Jennifer Mason, Iris Sim, Laurel Beckett, Danielle Harvey, Michael Donohue, Clifford R. Jack, Matthew Bernstein, Nick Fox, Paul Thompson, Norbert Schuff, Charles DeCArli, Bret Borowski, Jeff Gunter, Matt Senjem, Prashanthi Vemuri, David Jones, Kejal Kantarci, Chad Ward, William Jagust, Robert A. Koeppe, Norm Foster, Eric M. Reiman, Kewei Chen, Chet Mathis, Susan Landau, John C. Morris, Nigel J. Cairns, Erin Franklin, Lisa Taylor-Reinwald, Leslie M. Shaw, John Q. Trojanowki, Virginia Lee, Magdalena Korecka, Michal Figurski, Arthur W. Toga, Karen Crawford, Scott Neu, Andrew J. Saykin, Tatiana M. Foroud, Steven Potkin, Li Shen, Kelley Faber, Sungeun Kim, Kwangsik Nho, Michael W. Weiner, Lean Thal, Zaven Khachaturian, Leon Thal, Neil Buckholtz, Michael W. Weiner, Peter J. Snyder, William Potter, Steven Paul, Marilyn Albert, Richard Frank, Zaven Khachaturian, John Hsiao, Jeffrey Kaye, Joseph Quinn, Lisa Silbert, Betty Lind, Raina Carter, Sara Dolen, Lon S. Schneider, Sonia Pawluczyk, Mauricio Becerra, Liberty Teodoro, Bryan M. Spann, James Brewer, Helen Vanderswag, Adam Fleisher, Judith L. Heidebrink, Joanne L. Lord, Ronald Petersen, Sara S. Mason, Colleen S. Albers, David Knopman, Kris Johnson, Rachelle S. Doody, Javier Villanueva-Meyer, Valory Pavlik, Victoria Shibley, Munir Chowdhury, Susan Rountree, Mimi Dang, Yaakov Stern, Lawrence S. Honig, Karen L. Bell, Beau Ances, John C. Morris, Maria Carroll, Mary L. Creech, Erin Franklin, Mark A. Mintun, Stacy Schneider, Angela Oliver, Daniel Marson, David Geldmacher, Marissa Natelson Love, Randall Griffith, David Clark, John Brockington, Erik Roberson, Hillel Grossman, Effie Mitsis, Raj C. Shah, Leyla deToledo-Morrell, Ranjan Duara, Maria T. Greig-Custo, Warren Barker, Marilyn Albert, Chiadi Onyike, Daniel D'Agostino, Stephanie Kielb, Martin Sadowski, Mohammed O. Sheikh, Ulysse Anaztasia, Gaikwad Mrunalini, P. Murali Doraiswamy, Jeffrey R. Petrella, Salvador Borges-Neto, Terence Z. Wong, Edward Coleman, Steven E. Arnold, Jason H. Karlawish, David A. Wolk, Christopher M. Clark, Charles D. Smith, Greg Jicha, Peter Hardy, Partha Sinha, Elizabeth Oates, Gary Conrad, Oscar L. Lopez, MaryAnn Oakley, Donna M. Simpson, Anton P. Porsteinsson, Bonnie S. Goldstein, Kim Martin, Kelly M. Makino, M. Saleem Ismail, Connie Brand, Steven G. Potkin, Adrian Preda, Dana Nguyen, Kyle Womack, Dana Mathews, Mary Quiceno, Allan I. Levey, James J. Lah, Janet S. Cellar, Jeffrey M. Burns, Russell H. Swerdlow, William M. Brooks, Liana Apostolova, Kathleen Tingus, Ellen Woo, Daniel H.S. Silverman, Po H. Lu, George Bartzokis, Neill R Graff-Radford, Francine Parfitt, Kim Poki-Walker, Martin R. Farlow, Ann Marie Hake, Brandy R. Matthews, Jared R. Brosch, Scott Herring, Christopher H. van Dyck, Richard E. Carson, Martha G. MacAvoy, Pradeep Varma, Howard Chertkow, Howard Bergman, Chris Hosein, Sandra Black, Bojana Stefanovic, Curtis Caldwell, Ging-Yuek Robin Hsiung, Benita Mudge, Vesna Sossi, Howard Feldman, Michele Assaly, Elizabeth Finger, Stephen Pasternack, Irina Rachisky, Dick Trost, Andrew Kertesz, Charles Bernick, Donna Munic, Marek-Marsel Mesulam, Emily Rogalski, Kristine Lipowski, Sandra Weintraub, Borna Bonakdarpour, Diana Kerwin, Chuang-Kuo Wu, Nancy Johnson, Carl Sadowsky, Teresa Villena, Raymond Scott Turner, Kathleen Johnson, Brigid Reynolds, Reisa A. Sperling, Keith A. Johnson, Gad Marshall, Jerome Yesavage, Joy L. Taylor, Barton Lane, Allyson Rosen, Jared Tinklenberg, Marwan N. Sabbagh, Christine M. Belden, Sandra A. Jacobson, Sherye A. Sirrel, Neil Kowall, Ronald Killiany, Andrew E. Budson, Alexander Norbash, Patricia Lynn Johnson, Thomas O. Obisesan, Saba Wolday, Joanne Allard, Alan Lerner, Paula Ogrocki, Curtis Tatsuoka, Parianne Fatica, Evan Fletcher, Pauline Maillard, John Olichney, Charles DeCarli, Owen Carmichael, Smita Kittur, Michael Borrie, T-Y Lee, Rob Bartha, Sterling Johnson, Sanjay Asthana, Cynthia M. Carlsson, Steven G. Potkin, Adrian Preda, Dana Nguyen, Pierre Tariot, Anna Burke, Ann Marie Milliken, Nadira Trncic, Adam Fleisher, Stephanie Reeder, Vernice Bates, Horacio Capote, Michelle Rainka, Douglas W. Scharre, Maria Kataki, Brendan Kelley, Earl A. Zimmerman, Dzintra Celmins, Alice D. Brown, Godfrey D. Pearlson, Karen Blank, Karen Anderson, Laura A. Flashman, Marc Seltzer, Mary L. Hynes, Robert B. Santulli, Kaycee M. Sink, Gordineer Leslie, Jeff D. Williamson, Pradeep Garg, Franklin Watkins, Brian R. Ott, Geoffrey Tremont, Lori A. Daiello, Stephen Salloway, Paul Malloy, Stephen Correia, Howard J. Rosen, Bruce L. Miller, David Perry, Jacobo Mintzer, Kenneth Spicer, David Bachman, Elizabeth Finger, Stephen Pasternak, Irina Rachinsky, John Rogers, Andrew Kertesz, Dick Drost, Nunzio Pomara, Raymundo Hernando, Antero Sarrael, Susan K. Schultz, Karen Ekstam Smith, Hristina Koleva, Ki Won Nam, Hyungsub Shim, Norman Relkin, Gloria Chiang, Michael Lin, Lisa Ravdin, Amanda Smith, Balebail Ashok Raj, Kristin Fargher, Michael W. Weiner, Paul Aisen, Michael Weiner, Paul Aisen, Ronald Petersen, Robert C. Green, Danielle Harvey, Clifford R. Jack, William Jagust, John C. Morris, Andrew J. Saykin, Leslie M. Shaw, Arthur W. Toga, John Q. Trojanowki, Thomas Neylan, Jordan Grafman, Robert C. Green, Tom Montine, Michael Weiner, Ronald Petersen, Paul Aisen, Ronald G. Thomas, Michael Donohue, Gessert Devon, Tamie Sather, Davis Melissa, Rosemary Morrison, Gus Jiminez, Thomas Neylan, Hayes Jacqueline, Finley Shannon, Danielle Harvey, Michael Donohue, Clifford R. Jack, Matthew Bernstein, Bret Borowski, Jeff Gunter, Matt Senjem, Kantarci Kejal, Ward Chad, William Jagust, Robert A. Koeppe, Norm Foster, Eric M. Reiman, Kewei Chen, Susan Landau, John C. Morris, Nigel J. Cairns, Erin Householder, Leslie M. Shaw, John Q. Trojanowki, Virginia Lee, Magdalena Korecka, Michal Figurski, Arthur W. Toga, Crawford Karen, Neu Scott, Andrew J. Saykin, Tatiana M. Foroud, Steven Potkin, Li Shen, Kelley Faber, Sungeun Kim, Kwangsik Nho, Michael W. Weiner, Friedl Karl, Lon S. Schneider, Sonia Pawluczyk, Becerra Mauricio, James Brewer, Helen Vanderswag, Yaakov Stern, Lawrence S. Honig, Karen L. Bell, Debra Fleischman, Konstantinos Arfanakis, Raj C. Shah, Ranjan Duara, Daniel Varon, Maria T Greig, P. Murali Doraiswamy, Jeffrey R. Petrella, Olga James, Anton P. Porsteinsson, Bonnie Goldstein, Kimberly S. Martin, Steven G. Potkin, Adrian Preda, Dana Nguyen, Jacobo Mintzer, Dino Massoglia, Olga Brawman-Mintzer, Carl Sadowsky, Walter Martinez, Teresa Villena, William Jagust, Susan Landau, Howard Rosen, David Perry, Raymond Scott Turner, Kelly Behan, Brigid Reynolds, Reisa A. Sperling, Keith A. Johnson, Gad Marshall, Marwan N. Sabbagh, Sandra A. Jacobson, Sherye A. Sirrel, Thomas O. Obisesan, Saba Wolday, Joanne Allard, Sterling C. Johnson, J. Jay Fruehling, Sandra Harding, Elaine R. Peskind, Eric C. Petrie, Gail Li, Jerome A. Yesavage, Joy L. Taylor, Ansgar J. Furst, Steven Chao, Norman Relkin, Gloria Chiang, Lisa Ravdin, Lisa Ravdin

Alzheimer's Disease (AD) is the most common neurodegenerative disease in elderly people, and current drugs, unfortunately, do not represent yet a cure but only slow down its progression. This is explained, at least in part, because the understanding of the neurodegenerative process is still incomplete, being sometimes mistaken, particularly at the first steps of the illness, with the natural aging process. A better identification of how the functional activity deteriorates is thus crucial to develop new and more effective treatments. Sparse inverse covariance estimates (SICE) have been recently employed for deriving functional connectivity patterns from Positron Emission Tomography (PET) of brains affected by Alzheimer's Disease. SICE, unlike the traditional covariance methods, allows to analyze the interdependencies between brain regions factoring out the influence of others. To analyze the effects of the illness, connectivity patterns of brains affected by AD are compared with those obtained for control groups. These comparisons are, however, carried out for binary (undirected and unweighted) adjacency matrices with the same number of arcs. Additionally, the effect of the number of subjects employed or the validity of the regularization parameter used to compute the SICE have been not hitherto analyzed. In this paper, we delve into the construction of connectivity patterns from PET using SICE. In particular, we describe the effect that the number of subjects employed has on the results and identify, based on the reconstruction error of linear regression systems, a range of valid values for the regularization parameter. The amount of arcs is also proved as a discriminant value, and we show that it is possible to pass from unweighted (binary) to weighted adjacency matrices, where the weight of a connection corresponding to the existence of a relationship between two brain areas can be correlated to the persistence of this relationship when computed for different values of the regularization parameter and sets of subjects. Finally, network measures are computed for the connectivity patterns confirming that SICE may be particularly apt for assessing the efficiency of drugs, since it produces reliable brain connectivity models with small sample sizes, and that connectivity patterns affected by AD seem much less segregated, reducing the small-worldness.