Table 18 displays some of the meta-analyses that use mathematics/statistics. For an early review see [Fox et al., 1998]. For a more recent overview see [Wager et al., 2007].
Meta-analysis of Talairach coordinates was pioneered by Peter T. Fox et al. under the name ``functional volumes modeling'' (FVM) [Fox et al., 1997b,Fox et al., 1999,Fox et al., 1997a]. These original studies used parametric Gaussian models. Non-parametric modeling of the distribution of brain foci was first described in two unpublished studies with Gaussian mixture modeling [Nielsen and Hansen, 1999] and adaptive Gaussian kernel density modeling [Nielsen and Hansen, 2000]. Later studies include adaptive Gaussian kernel density modeling for database outlier detection [Nielsen and Hansen, 2002c,Nielsen et al., 2001,Nielsen et al., 2000], Gaussian kernel density modeling in connection with single word processing [Turkeltaub et al., 2002,Turkeltaub et al., 2001], kernel density estimation in connection with Broca's area and verbal working memory [Chein et al., 2002,Chein et al., 2001], kernel density modeling with a spheric uniform kernel in emotion [Wager et al., 2003], and a model combining kerndel density modeling with a Gaussian mixture model [Neumann et al., 2008]. Another study is [Wager et al., 2004]. A large number of similar studies appears in a special issue of the Human Brain Mapping, volume 25, issue 1 [Fox et al., 2005b]. Functional volumes modeling is sometimes referred to as ``voxelization'' or ``activation likelihood estimation'' (ALE). Some form of meta-analysis with the use the BrainMapTM database has been briefly described [Mahurin et al., 1995].
Determining statistical thresholds in one set of voxelized Talairach coordinates is described in [Turkeltaub et al., 2002,Turkeltaub et al., 2001] and [Nielsen, 2005]. Statistical methods for determining whether two sets are different are described in [Christoff and Grabrieli, 2000,Duncan and Owen, 2000] and [Nielsen and Hansen, 2004a,Nielsen et al., 2004b,Nielsen et al., 2005,Nielsen et al., 2004a] and [Laird et al., 2005a]. The multidimensional Kolmogorov-Smirnov used in [Duncan and Owen, 2000] is originally from [Peacock, 1983] and is also described and implemented in [Press et al., 1992, section 14.7]. Hotelling's test was also used in [Berman et al., 1999, page 212] but not in connection with a meta-analysis. Statistical tests on warped coordinates are described in [Steel and Lawrie, 2004].
The Brede Toolbox automatically performs multivariate analyses such as singular value decomposition (principal component analyses), independent component analyses, non-negative matrix factorization and K-means on voxelized Talairach coordinates on the entire Brede Database [Nielsen, 2003,Nielsen et al., 2004c]. Another multivariate analysis method, ``replicator dynamics'', is suggested in [Neumann et al., 2005].
A number of meta-analytic studies have grown out of the BRAID database: [Herskovits et al., 1999,Megalooikonomou et al., 1999,Megalooikonomou et al., 2000,Megalooikonomou and Herskovits, 2001,Lazarevic et al., 2001,Herskovits et al., 2002].
Descriptive statistics of activation foci appears in [Markowitsch and Tulving, 1994], where the fraction of fundus activations over 30 PET studies is found.
Function/location meta-analysis without spatial information other than the text can also extract relevation associations. Name entities has been extracted from well over 100,000 PubMed abstracts with the use of Unified Medical Language System (UMLS) and manually developed rules for rule-based name entity extraction [Hsiao et al., 2007]. This system extracted phrases/terms for brain function and neuroanatomy and built an interactive visualization system to display the function-anatomy graph.
|Left inferior frontal cortex||Semantic and phonological processing||Tables, plots||Phonological processing dorsally while semantic ventrally||[Poldrack et al., 1999]|
|Anterior cingulate||Cognition, emotion||[Bush et al., 2000]|
|Many||Cognition||Tables, plots||[Cabeza and Nyberg, 2000]|
|Inferior frontal||Phonological processing||Plots||[Burton, 2001]|
|Prefrontal||Cognition, emotion||Plots, warp transformation, MANOVA, KDE||Resampling was used for significance test||[Steel and Lawrie, 2004]|
|Orbitofrontal||Plots||[Kringelbach and Rolls, 2004]|
|Medial frontal||Self/Other||Clustering(?)||[Seitz et al., 2005]|
|Posterior cingulate||As many as possible||Text clustering, Hotelling's test||Text mining on PubMed abstract for clustering articles. Thereafter determination of segregation between coordinates in clustered articles||[Nielsen et al., 2005]|
An early program for connectivity analysis is ``Connection'' [Nicolelis et al., 1990].
[Kaiser and Hilgetag, 2004] used data from CoCoMac together with spatial positions from Caret to get an approximation for the wiring length in cortex.
[Toro and Paus, 2006] described a co-activation analysis of functional activation recorded in the BrainMapTM database and constructed a program for interactive visualization of the 6-D probabilistic map. A smaller co-activation study analysing data from 126 papers focused on connections from the basal ganglia [Postuma and Dagher, 2006].
A database with volumes for anatomo-functional connectivity might become available [Poupon et al., 2006].
There is a number of studies using the connectivity of the small worm Caenorhabditis elegans (WormAtlas), e.g., for examining the small-world phenomenon [Watts and Strogatz, 1998], or explaining the neuronal placement [Chen et al., 2006,Ahn et al., 2006] and (Kaiser and Hilgetag, 2005, Society for Neuroscience).
Meta-analysis of ERP in schizophrenia [Bramon et al., 2001].
[Young and Scannell, 2000]
Finn Årup Nielsen 2010-04-23