All content included on this site, such as text, graphics, logos, button icons, images, video/aud... more All content included on this site, such as text, graphics, logos, button icons, images, video/audio clips, downloads, data compilations and software, is the property of or is licensed to Frontiers Media SA ("Frontiers") or its licensees and/or subcontractors. The copyright in the text of individual articles is the property of their respective authors, subject to a license granted to Frontiers. The compilation of articles constituting this e-book, wherever published, as well as the compilation of all other content on this site, is the exclusive property of Frontiers. For the conditions for downloading and copying of e-books from Frontiers' website, please see the Terms for Website Use. If purchasing Frontiers e-books from other websites or sources, the conditions of the website concerned apply. Images and graphics not forming part of user-contributed materials may not be downloaded or copied without permission. Individual articles may be downloaded and reproduced in accordance with the principles of the CC-BY licence subject to any copyright or other notices. They may not be re-sold as an e-book. As author or other contributor you grant a CC-BY licence to others to reproduce your articles, including any graphics and third-party materials supplied by you, in accordance with the Conditions for Website Use and subject to any copyright notices which you include in connection with your articles and materials.
shot-FLASH" technique combines T1 contrast with short measurement time of approximately 1 second ... more shot-FLASH" technique combines T1 contrast with short measurement time of approximately 1 second per image on a conventional whole body system, if satisfactory spatial resolution (256 X 256 matrix size) is still required ( 1-6). After MR examination all patients underwent neurosurgery and all tumors were histopathologically confirmed, including a determination of the degree of vascularization . These histopathologic findings were compared with the results of the dynamic contrast-enhancement evaluation.
The intralaminar nuclei of the thalamus play a pivotal role in awareness, conscious experience, a... more The intralaminar nuclei of the thalamus play a pivotal role in awareness, conscious experience, arousal, sleep, vigilance, as well as in cognitive, sensory, and sexual processing. Nonetheless, in humans, little is known about the direct involvement of these nuclei in such multifaceted functions and their structural connections in the brain. Thus, examining the versatility of structural connectivity of the intralaminar nuclei with the rest of the brain seems reasonable. Herein, we attempt to show the direct structural connectivity of the intralaminar nuclei to diencephalic, mesencephalic, and cortical areas using probabilistic tracking of the diffusion data from the human connectome project. The intralaminar nuclei fiber distributions span a wide range of subcortical and cortical areas. Moreover, the central medial and parafascicular nucleus reveal similar connectivity to the temporal, visual, and frontal cortices with only slight variability. The central lateral nucleus displays a refined projection to the superior colliculus and fornix. The centromedian nucleus seems to be an essential component of the subcortical somatosensory system, as it mainly displays connectivity via the medial and superior cerebellar peduncle to the brainstem and the cerebellar lobules. The subparafascicular nucleus projects to the somatosensory processing areas. It is interesting to note that all intralaminar nuclei have connections to the brainstem. In brief, the structural connectivity of the intralaminar nuclei aligns with the structural core of various functional demands for arousal, emotion, cognition, sensory, vision, and motor processing. This study sheds light on our understanding of the structural connectivity of the intralaminar nuclei with cortical and subcortical structures, which is of great interest to a broader audience in clinical and neuroscience research.
Introduction: Spinal diffusion tensor imaging (DTI) is limited by severe motion artefacts and a l... more Introduction: Spinal diffusion tensor imaging (DTI) is limited by severe motion artefacts and a low signal-to-noise ratio (SNR). Current gradient coils, with low-eddycurrent designs, open the field for the usage of monopolar Stejskal-Tanner sequences [1]. With these schemes, smaller echo times and therefore a higher SNR can be achieved. Only a few studies of lumbar spinal DTI in humans already exist [2, 3], with a coarse and mainly sagittal acquisition. The aim of this preliminary study was to optimize the sequence parameter for high resolution axial spinal DTI of the lumbar spinal cord and to show relevant clinical implications.
Spondylotic stenosis of the spinal canal is a frequent phenomenon in elderly patients. Jeffreys (... more Spondylotic stenosis of the spinal canal is a frequent phenomenon in elderly patients. Jeffreys (1986) reports that 75% of people over 65 years old show a narrowing of the cervical spinal canal. But only a minority of patients suffer from cervical myelopathy due to cervical stenosis. The results of neurosurgical treatment are not uniform and depend on the operation technique.In general, however, surgery has disappointed with regard to an improvement of clinical symptoms.
The thalamus (Th) and basal ganglia (BG) are central subcortical connectivity hubs of the human b... more The thalamus (Th) and basal ganglia (BG) are central subcortical connectivity hubs of the human brain, whose functional anatomy is still under intense investigation. Nevertheless, both substructures contain a robust and reproducible functional anatomy. The quantitative susceptibility mapping (QSM) at ultra-high field may facilitate an improved characterization of the underlying functional anatomy in vivo. We acquired high-resolution QSM data at 9.4 Tesla in 21 subjects, and analyzed the thalamic and BG by using a prior defined functional parcellation. We found a more substantial contribution of paramagnetic susceptibility sources such as iron in the pallidum in contrast to the caudate, putamen, and Th in descending order. The diamagnetic susceptibility sources such as myelin and calcium revealed significant contributions in the Th parcels compared with the BG. This study presents a detailed nuclei-specific delineation of QSM-provided diamagnetic and paramagnetic susceptibility sources pronounced in the BG and the Th. We also found a reasonable interindividual variability as well as slight hemispheric differences. The results presented here contribute to the microstructural knowledge of the Th and the BG. In specific, the study illustrates QSM values (myelin, calcium, and iron) in functionally similar subregions of the Th and the BG.
Functional neuroimaging studies have lead to understanding the brain as a collection of spatially... more Functional neuroimaging studies have lead to understanding the brain as a collection of spatially segregated functional networks. It is thought that each of these networks is in turn composed of a set of distinct sub-regions that together support each network's function. Considering the subregions to be an essential part of the brain's functional architecture, several strategies have been put forward that aim at identifying the functional sub-units of the brain by means of functional parcellations. Current parcellation strategies typically employ a bottom-up strategy, creating a parcellation by clustering smaller units. We propose a novel top-down parcellation strategy, using time courses of instantaneous connectivity to subdivide an initial region of interest into sub-regions. We use split-half reproducibility to choose the optimal number of sub-regions. We apply our Instantaneous Connectivity Parcellation (ICP) strategy on high-quality resting-state FMRI data, and demonstrate the ability to generate parcellations for thalamus, entorhinal cortex, motor cortex, and subcortex including brainstem and striatum. We evaluate the subdivisions against available cytoarchitecture maps to show that the our parcellation strategy recovers biologically valid subdivisions that adhere to known cytoarchitectural features.
Almost all functional processing in the cortex strongly depends on thalamic interactions. However... more Almost all functional processing in the cortex strongly depends on thalamic interactions. However, in terms of functional interactions with the cerebral cortex, the human thalamus nuclei still partly constitute a terra incognita. Hence, for a deeper understanding of thalamiccortical cooperation, it is essential to know how the different thalamic nuclei are associated with cortical networks. The present work examines network-specific connectivity and taskrelated topical mapping of cortical areas with the thalamus. The study finds that the relay and higher-order thalamic nuclei show an intertwined functional association with different cortical networks. In addition, the study indicates that relay-specific thalamic nuclei are not only involved with relay-specific behavior but also in higher-order functions. The study enriches our understanding of interactions between large-scale cortical networks and the thalamus, which may interest a broader audience in neuroscience and clinical research.
Introduction: Unarguably, the thalamus is a core structure of the human brain (Sherman, 2016), an... more Introduction: Unarguably, the thalamus is a core structure of the human brain (Sherman, 2016), and all individual thalamic nuclei are integral components of very different functional systems in the brain (Jones, 2007). However, only a few studies have addressed the structural and functional diversity of the thalamic substructures in detail. Using diffusion tensor (DTI) or resting state functional MRI (r-fMRI) most 1.5, 3, and 7 Tesla MRI studies were able to determine 7 to 31 thalamic parcels with different spatial resolution (Calamante et al., 2012; Johansen-Berg et al., 2005; Kim et al., 2013; Kumar et al., 2017). Although most nuclei like the pulvinar complex, the lateral geniculate nucleus (LGN), and others are composed of numerous subnuclei (Baldwin et al., 2011, Andrews et al., 1997), we thought to examine whether a higher imaging resolution could assess a more detailed functional diversity of thalamic substructures. We, therefore, decided to use 1 mm isotopic resting state MRI data acquired at 9.4 Tesla to assess a high dimensional parcellation of the human thalamus. Methods: r-fMRI Acquisition: The r-fMRI was acquired at 9.4 T Siemens (Erlangen, Germany) in six right-handed male volunteers. We used the psf method for the distortion correction. The FOV covered thalamus (s. Fig. 1a) consisted of 45 slices, TR of 2.5 sec., 1 mm isotropic resolution and 220 scans. The volunteers kept their eyes closed during the resting state scans. Besides, two structural scans, i.e., MP2RAGE (600 microns iso) and a 3D GRE (400 microns iso) were acquired. r-fMRI Analysis: The preprocessing was performed with a modified pipeline using SPM12. It included slice timing, motion correction, coregistration, normalization and smoothing (3x3x3mm kernel). ICA Analysis: The normalized subject data were temporally concatenated. We performed the probabilistic-ICA (Beckmann et al., 2005) on the left and right thalamus. The optimal number of component estimation was done using default melodic model order selection. In the last step, the z-stat of all components were used to compute the winner map for the right and left thalamus. Results: The ICA automatic model order selection detected 82 components within the right thalamus and 83 components within the left thalamus (s. Fig 1b). In comparison with the histological atlas of Morel (Morel et al., 1997), which is restricted to a set of 29 bilateral nuclei (s. Fig. 1c), we observed an of 2.8 fold increase of parcels. Furthermore, our parcels varied in size, location, and distribution between both hemispheres (Fig. 2). This variable distribution with different temporal pattern within the left and right thalamus probably reflects functional differences between both hemispheres. The composite analysis in respect to the histological atlas revealed a varying number of parcels for each Morel nucleus; for example, we observed 6-7 left and right sub-parcels within the layered lateral geniculate nuclei (Andrews et al., 1997). Conclusions: Our study revealed that the thalamus exhibits a high-dimensional functional segregation even at rest. The detected parcels differed in size, location, and lateralization. In comparison with the histological defined thalamic nuclei, we observed a variable parcel assignment to all major nuclei groups in both hemispheres. However, further work is required to establish a valid and high-dimensional functional atlas of the thalamus, which could enhance our understanding of the concerted thalamo-cortical interaction at rest and under task conditions
The presented study explores the capability of high resolution functional MRI (fMRI) at 9.4 Tesla... more The presented study explores the capability of high resolution functional MRI (fMRI) at 9.4 Tesla to study functional changes in the primary visual cortex and the human thalamus during rest and natural picture viewing. We found increased intrinsic thalamic connectivity during both eyes open (EO) and eyes closed (EC) condition in the viewing task compared to rest
Introduction: Statistical inference in fMRI data analysis remains a challenging problem. Current ... more Introduction: Statistical inference in fMRI data analysis remains a challenging problem. Current techniques were mostly developed for 3T data, but are often unsatisfactory in terms of spatial acuity and sensitivity when applied to ultrahigh field data (>=7T). Furthermore, a recent publication by Eklund et al. [1] has highlighted problems with inflated false positive rates which can be alleviated by using very stringent initial cluster-forming thresholds (p < 0.001), but possibly at the expense of inflated false negative rates. Here we propose a new method to address these problems. It is called "LISA" because it is inspired by hot spot analysis of geographical information systems where hot spots are identified using so-called Local Indicators of Spatial Association (LISA) [2]. With LISA, every voxel receives a hot spot score which serves as a new test statistic and may be seen as a compromise between cluster-level and voxel-level inference. Methods: If operated at the second (group) level, the algorithm LISA expects as input a set of contrast maps obtained from a first level GLM analysis. First a voxelwise t-test is applied yielding a map in which each voxel has a z-value uncorrected for multiple comparisons. We now apply a bilateral filter to this map which suppresses noise while preserving spatial acuity [3]. The parameters of this filter were determined using simulated data and were kept constant for all experiments reported below. The filtered map highlights hot spots of activation which LISA aims to detect. Statistical inference is performed by controlling the false discovery rate (FDR). Note that the classical FDR algorithm [4] assumes that all data points are independent and under the null hypothesis z-values follow a standard Gaussian distribution. Both assumptions may be violated here. Therefore, we use a different FDR procedure which is based on a two-component model [5] in which we estimate the null distribution using random permutations of the contrast maps. The LISA algorithm can also be used at the first level (single subject analysis) in which case it expects as input a preprocessed fMRI data set and the experimental design information. To ensure exchangeability, the null distribution is obtained using random permutations of labels [6,7]. Otherwise, the algorithm works as described above. Results: We subjected LISA to a battery of tests. Test 1: We analysed 127 data sets of the "Beijing" sample of [1], using the same experimental designs and preprocessing regimes as in [1] (6mm spatial smoothing). In each of the four designs (B1,B2,E1,E2) , we randomly drew 100 samples consisting of 40 data sets and obtained the following family-wise error rates: 3/100 (B1), 0/100 (B2), 0/100 (E1), 2/100 (E2). Test 2: Simulated data. Comparison with FSL-TFCE [9], see fig.1. Test 3: fMRI data of the "emotion task" of the Human Connectome Project (HCP) [8]. We randomly selected 10 sets of 20 data sets each and compared the LISA results with results obtained by FSL-TFCE [9], see fig.2 (top). Test 4: Single subject data acquired at a 9.4T human whole-body scanner (Siemens) using a custom-built 31-channel receive coil array. Gradient Echo EPI, 30 slices, Grappa 4, 6/8 partial fourier, PSF-based distortion correction, resolution 0.8mm isotropic, 30 slices, 405 volumes, TR/TE=1580/22ms, FOV 171mm, working memory task, 8+8 trials (2back/0back), fig.2 (bottom) Conclusions: Lisa corrects for FDR, but under the Eklund test it produced even more conservative results than expected if corrected for the familywise error. LISA appears to be less conservative than FSL-TFCE, and shows a high spatial precision and sensitivity when applied to data acquired at an ultra-high field scanner. Applying an edge-preserving filter at a late stage in the analysis chain rather than during preprocessing
In this study we use relaxometry and susceptibility mapping to obtain enhanced contrast in the mi... more In this study we use relaxometry and susceptibility mapping to obtain enhanced contrast in the midbrain, in particular in the superior colliculus (SC). High resolution GRE images were obtained in 11 subjects at 9.4T. We calculated CNR values for each contrast for three midbrain regions (superior colliculus,red nucleus and aqueductal gray). were were obtained across 11 subjects in individual and MNI space. These measurement were validated with ex-vivo measurements in the 9.4T, 14.1T and PLI imaging
We assessed how improved static magnetic field (B 0 ) homogeneity with a dynamic multicoil shimmi... more We assessed how improved static magnetic field (B 0 ) homogeneity with a dynamic multicoil shimming can influence the blood oxygen level dependent (BOLD) contrast to noise when echo planar imaging (EPI) sequence is used for a motor task functional MRI study. We showed that a multicoil shim setup can be a proper choice for dynamic shimming of 2 spatially distant areas with different inhomogeneity distributions. Methods: A 16-channel multicoil shim setup is used to provide improved B 0 homogeneity by dynamic slice-wise shimming. The performance of dynamic B 0 shimming was investigated in 2 distinct brain regions, the motor cortex and the cerebellum, in the same experiment during a finger-tapping task. Temporal SNR (tSNR), geometric distortion of the EPIs, and results of an analysis with a general linear model before and after shimming with the multicoil were compared. Results: Reduced B 0 deviation by 30% and 52% in the cerebellum and motor cortex, respectively, resulted in higher tSNR and a reduction of distortions in the EPI. Statistical analysis applied to the EPIs showed higher t values and increased number of voxels above significance threshold when shimming with the multicoil setup. Conclusions: Improved B 0 homogeneity leads to higher tSNR and enhances the detection of BOLD signal. B 0 inhomogeneity, BOLD signal, multicoil, shimming, temporal SNR, ultrahigh field In most applications, functional MRI (fMRI) is performed with gradient echo planar imaging (EPI), a fast T * 2 -weighted sequence which has a high sensitivity to blood oxygen level dependent (BOLD) signal changes. EPI possesses a long readout duration, which makes the images susceptible to geometric distortion 1 and signal loss because of B 0 inhomogeneity. These effects are even more pronounced at ultra-high fields (UHFs) given that the magnetic field variations induced from susceptibility differences linearly increase with the magnetic field strength.
Whole-brain voxel-based morphometry (VBM) studies revealed patterns of patchy atrophy within the ... more Whole-brain voxel-based morphometry (VBM) studies revealed patterns of patchy atrophy within the cerebellum of Friedreich's ataxia patients, missing clear clinico-anatomic correlations. Studies so far are lacking an appropriate registration to the infratentorial space. To circumvent these limitations, we applied a high-resolution atlas template of the human cerebellum and brainstem (SUIT template) to characterize regional cerebellar atrophy in Friedreich's ataxia (FRDA) on 3-T MRI data. We used a spatially unbiased voxel-based morphometry approach together with T2-based manual segmentation, T2 histogram analysis, and atlas generation of the dentate nuclei in a representative cohort of 18 FRDA patients and matched healthy controls. We demonstrate that the cerebellar volume in FRDA is generally not significantly different from healthy controls but mild lobular atrophy develops beyond normal aging. The medial parts of lobule VI, housing the somatotopic representation of tongue and lips, are the major site of this lobular atrophy, which possibly reflects speech impairment. Extended white matter affection correlates with disease severity across and beyond the cerebellar inflow and outflow tracts. The dentate nucleus, as a major site of cerebellar degeneration, shows a mean volume loss of about 30%. Remarkably, not the atrophy but the T2 signal decrease of the dentate nuclei highly correlates with disease duration and severity.
All content included on this site, such as text, graphics, logos, button icons, images, video/aud... more All content included on this site, such as text, graphics, logos, button icons, images, video/audio clips, downloads, data compilations and software, is the property of or is licensed to Frontiers Media SA ("Frontiers") or its licensees and/or subcontractors. The copyright in the text of individual articles is the property of their respective authors, subject to a license granted to Frontiers. The compilation of articles constituting this e-book, wherever published, as well as the compilation of all other content on this site, is the exclusive property of Frontiers. For the conditions for downloading and copying of e-books from Frontiers' website, please see the Terms for Website Use. If purchasing Frontiers e-books from other websites or sources, the conditions of the website concerned apply. Images and graphics not forming part of user-contributed materials may not be downloaded or copied without permission. Individual articles may be downloaded and reproduced in accordance with the principles of the CC-BY licence subject to any copyright or other notices. They may not be re-sold as an e-book. As author or other contributor you grant a CC-BY licence to others to reproduce your articles, including any graphics and third-party materials supplied by you, in accordance with the Conditions for Website Use and subject to any copyright notices which you include in connection with your articles and materials.
shot-FLASH" technique combines T1 contrast with short measurement time of approximately 1 second ... more shot-FLASH" technique combines T1 contrast with short measurement time of approximately 1 second per image on a conventional whole body system, if satisfactory spatial resolution (256 X 256 matrix size) is still required ( 1-6). After MR examination all patients underwent neurosurgery and all tumors were histopathologically confirmed, including a determination of the degree of vascularization . These histopathologic findings were compared with the results of the dynamic contrast-enhancement evaluation.
The intralaminar nuclei of the thalamus play a pivotal role in awareness, conscious experience, a... more The intralaminar nuclei of the thalamus play a pivotal role in awareness, conscious experience, arousal, sleep, vigilance, as well as in cognitive, sensory, and sexual processing. Nonetheless, in humans, little is known about the direct involvement of these nuclei in such multifaceted functions and their structural connections in the brain. Thus, examining the versatility of structural connectivity of the intralaminar nuclei with the rest of the brain seems reasonable. Herein, we attempt to show the direct structural connectivity of the intralaminar nuclei to diencephalic, mesencephalic, and cortical areas using probabilistic tracking of the diffusion data from the human connectome project. The intralaminar nuclei fiber distributions span a wide range of subcortical and cortical areas. Moreover, the central medial and parafascicular nucleus reveal similar connectivity to the temporal, visual, and frontal cortices with only slight variability. The central lateral nucleus displays a refined projection to the superior colliculus and fornix. The centromedian nucleus seems to be an essential component of the subcortical somatosensory system, as it mainly displays connectivity via the medial and superior cerebellar peduncle to the brainstem and the cerebellar lobules. The subparafascicular nucleus projects to the somatosensory processing areas. It is interesting to note that all intralaminar nuclei have connections to the brainstem. In brief, the structural connectivity of the intralaminar nuclei aligns with the structural core of various functional demands for arousal, emotion, cognition, sensory, vision, and motor processing. This study sheds light on our understanding of the structural connectivity of the intralaminar nuclei with cortical and subcortical structures, which is of great interest to a broader audience in clinical and neuroscience research.
Introduction: Spinal diffusion tensor imaging (DTI) is limited by severe motion artefacts and a l... more Introduction: Spinal diffusion tensor imaging (DTI) is limited by severe motion artefacts and a low signal-to-noise ratio (SNR). Current gradient coils, with low-eddycurrent designs, open the field for the usage of monopolar Stejskal-Tanner sequences [1]. With these schemes, smaller echo times and therefore a higher SNR can be achieved. Only a few studies of lumbar spinal DTI in humans already exist [2, 3], with a coarse and mainly sagittal acquisition. The aim of this preliminary study was to optimize the sequence parameter for high resolution axial spinal DTI of the lumbar spinal cord and to show relevant clinical implications.
Spondylotic stenosis of the spinal canal is a frequent phenomenon in elderly patients. Jeffreys (... more Spondylotic stenosis of the spinal canal is a frequent phenomenon in elderly patients. Jeffreys (1986) reports that 75% of people over 65 years old show a narrowing of the cervical spinal canal. But only a minority of patients suffer from cervical myelopathy due to cervical stenosis. The results of neurosurgical treatment are not uniform and depend on the operation technique.In general, however, surgery has disappointed with regard to an improvement of clinical symptoms.
The thalamus (Th) and basal ganglia (BG) are central subcortical connectivity hubs of the human b... more The thalamus (Th) and basal ganglia (BG) are central subcortical connectivity hubs of the human brain, whose functional anatomy is still under intense investigation. Nevertheless, both substructures contain a robust and reproducible functional anatomy. The quantitative susceptibility mapping (QSM) at ultra-high field may facilitate an improved characterization of the underlying functional anatomy in vivo. We acquired high-resolution QSM data at 9.4 Tesla in 21 subjects, and analyzed the thalamic and BG by using a prior defined functional parcellation. We found a more substantial contribution of paramagnetic susceptibility sources such as iron in the pallidum in contrast to the caudate, putamen, and Th in descending order. The diamagnetic susceptibility sources such as myelin and calcium revealed significant contributions in the Th parcels compared with the BG. This study presents a detailed nuclei-specific delineation of QSM-provided diamagnetic and paramagnetic susceptibility sources pronounced in the BG and the Th. We also found a reasonable interindividual variability as well as slight hemispheric differences. The results presented here contribute to the microstructural knowledge of the Th and the BG. In specific, the study illustrates QSM values (myelin, calcium, and iron) in functionally similar subregions of the Th and the BG.
Functional neuroimaging studies have lead to understanding the brain as a collection of spatially... more Functional neuroimaging studies have lead to understanding the brain as a collection of spatially segregated functional networks. It is thought that each of these networks is in turn composed of a set of distinct sub-regions that together support each network's function. Considering the subregions to be an essential part of the brain's functional architecture, several strategies have been put forward that aim at identifying the functional sub-units of the brain by means of functional parcellations. Current parcellation strategies typically employ a bottom-up strategy, creating a parcellation by clustering smaller units. We propose a novel top-down parcellation strategy, using time courses of instantaneous connectivity to subdivide an initial region of interest into sub-regions. We use split-half reproducibility to choose the optimal number of sub-regions. We apply our Instantaneous Connectivity Parcellation (ICP) strategy on high-quality resting-state FMRI data, and demonstrate the ability to generate parcellations for thalamus, entorhinal cortex, motor cortex, and subcortex including brainstem and striatum. We evaluate the subdivisions against available cytoarchitecture maps to show that the our parcellation strategy recovers biologically valid subdivisions that adhere to known cytoarchitectural features.
Almost all functional processing in the cortex strongly depends on thalamic interactions. However... more Almost all functional processing in the cortex strongly depends on thalamic interactions. However, in terms of functional interactions with the cerebral cortex, the human thalamus nuclei still partly constitute a terra incognita. Hence, for a deeper understanding of thalamiccortical cooperation, it is essential to know how the different thalamic nuclei are associated with cortical networks. The present work examines network-specific connectivity and taskrelated topical mapping of cortical areas with the thalamus. The study finds that the relay and higher-order thalamic nuclei show an intertwined functional association with different cortical networks. In addition, the study indicates that relay-specific thalamic nuclei are not only involved with relay-specific behavior but also in higher-order functions. The study enriches our understanding of interactions between large-scale cortical networks and the thalamus, which may interest a broader audience in neuroscience and clinical research.
Introduction: Unarguably, the thalamus is a core structure of the human brain (Sherman, 2016), an... more Introduction: Unarguably, the thalamus is a core structure of the human brain (Sherman, 2016), and all individual thalamic nuclei are integral components of very different functional systems in the brain (Jones, 2007). However, only a few studies have addressed the structural and functional diversity of the thalamic substructures in detail. Using diffusion tensor (DTI) or resting state functional MRI (r-fMRI) most 1.5, 3, and 7 Tesla MRI studies were able to determine 7 to 31 thalamic parcels with different spatial resolution (Calamante et al., 2012; Johansen-Berg et al., 2005; Kim et al., 2013; Kumar et al., 2017). Although most nuclei like the pulvinar complex, the lateral geniculate nucleus (LGN), and others are composed of numerous subnuclei (Baldwin et al., 2011, Andrews et al., 1997), we thought to examine whether a higher imaging resolution could assess a more detailed functional diversity of thalamic substructures. We, therefore, decided to use 1 mm isotopic resting state MRI data acquired at 9.4 Tesla to assess a high dimensional parcellation of the human thalamus. Methods: r-fMRI Acquisition: The r-fMRI was acquired at 9.4 T Siemens (Erlangen, Germany) in six right-handed male volunteers. We used the psf method for the distortion correction. The FOV covered thalamus (s. Fig. 1a) consisted of 45 slices, TR of 2.5 sec., 1 mm isotropic resolution and 220 scans. The volunteers kept their eyes closed during the resting state scans. Besides, two structural scans, i.e., MP2RAGE (600 microns iso) and a 3D GRE (400 microns iso) were acquired. r-fMRI Analysis: The preprocessing was performed with a modified pipeline using SPM12. It included slice timing, motion correction, coregistration, normalization and smoothing (3x3x3mm kernel). ICA Analysis: The normalized subject data were temporally concatenated. We performed the probabilistic-ICA (Beckmann et al., 2005) on the left and right thalamus. The optimal number of component estimation was done using default melodic model order selection. In the last step, the z-stat of all components were used to compute the winner map for the right and left thalamus. Results: The ICA automatic model order selection detected 82 components within the right thalamus and 83 components within the left thalamus (s. Fig 1b). In comparison with the histological atlas of Morel (Morel et al., 1997), which is restricted to a set of 29 bilateral nuclei (s. Fig. 1c), we observed an of 2.8 fold increase of parcels. Furthermore, our parcels varied in size, location, and distribution between both hemispheres (Fig. 2). This variable distribution with different temporal pattern within the left and right thalamus probably reflects functional differences between both hemispheres. The composite analysis in respect to the histological atlas revealed a varying number of parcels for each Morel nucleus; for example, we observed 6-7 left and right sub-parcels within the layered lateral geniculate nuclei (Andrews et al., 1997). Conclusions: Our study revealed that the thalamus exhibits a high-dimensional functional segregation even at rest. The detected parcels differed in size, location, and lateralization. In comparison with the histological defined thalamic nuclei, we observed a variable parcel assignment to all major nuclei groups in both hemispheres. However, further work is required to establish a valid and high-dimensional functional atlas of the thalamus, which could enhance our understanding of the concerted thalamo-cortical interaction at rest and under task conditions
The presented study explores the capability of high resolution functional MRI (fMRI) at 9.4 Tesla... more The presented study explores the capability of high resolution functional MRI (fMRI) at 9.4 Tesla to study functional changes in the primary visual cortex and the human thalamus during rest and natural picture viewing. We found increased intrinsic thalamic connectivity during both eyes open (EO) and eyes closed (EC) condition in the viewing task compared to rest
Introduction: Statistical inference in fMRI data analysis remains a challenging problem. Current ... more Introduction: Statistical inference in fMRI data analysis remains a challenging problem. Current techniques were mostly developed for 3T data, but are often unsatisfactory in terms of spatial acuity and sensitivity when applied to ultrahigh field data (>=7T). Furthermore, a recent publication by Eklund et al. [1] has highlighted problems with inflated false positive rates which can be alleviated by using very stringent initial cluster-forming thresholds (p < 0.001), but possibly at the expense of inflated false negative rates. Here we propose a new method to address these problems. It is called "LISA" because it is inspired by hot spot analysis of geographical information systems where hot spots are identified using so-called Local Indicators of Spatial Association (LISA) [2]. With LISA, every voxel receives a hot spot score which serves as a new test statistic and may be seen as a compromise between cluster-level and voxel-level inference. Methods: If operated at the second (group) level, the algorithm LISA expects as input a set of contrast maps obtained from a first level GLM analysis. First a voxelwise t-test is applied yielding a map in which each voxel has a z-value uncorrected for multiple comparisons. We now apply a bilateral filter to this map which suppresses noise while preserving spatial acuity [3]. The parameters of this filter were determined using simulated data and were kept constant for all experiments reported below. The filtered map highlights hot spots of activation which LISA aims to detect. Statistical inference is performed by controlling the false discovery rate (FDR). Note that the classical FDR algorithm [4] assumes that all data points are independent and under the null hypothesis z-values follow a standard Gaussian distribution. Both assumptions may be violated here. Therefore, we use a different FDR procedure which is based on a two-component model [5] in which we estimate the null distribution using random permutations of the contrast maps. The LISA algorithm can also be used at the first level (single subject analysis) in which case it expects as input a preprocessed fMRI data set and the experimental design information. To ensure exchangeability, the null distribution is obtained using random permutations of labels [6,7]. Otherwise, the algorithm works as described above. Results: We subjected LISA to a battery of tests. Test 1: We analysed 127 data sets of the "Beijing" sample of [1], using the same experimental designs and preprocessing regimes as in [1] (6mm spatial smoothing). In each of the four designs (B1,B2,E1,E2) , we randomly drew 100 samples consisting of 40 data sets and obtained the following family-wise error rates: 3/100 (B1), 0/100 (B2), 0/100 (E1), 2/100 (E2). Test 2: Simulated data. Comparison with FSL-TFCE [9], see fig.1. Test 3: fMRI data of the "emotion task" of the Human Connectome Project (HCP) [8]. We randomly selected 10 sets of 20 data sets each and compared the LISA results with results obtained by FSL-TFCE [9], see fig.2 (top). Test 4: Single subject data acquired at a 9.4T human whole-body scanner (Siemens) using a custom-built 31-channel receive coil array. Gradient Echo EPI, 30 slices, Grappa 4, 6/8 partial fourier, PSF-based distortion correction, resolution 0.8mm isotropic, 30 slices, 405 volumes, TR/TE=1580/22ms, FOV 171mm, working memory task, 8+8 trials (2back/0back), fig.2 (bottom) Conclusions: Lisa corrects for FDR, but under the Eklund test it produced even more conservative results than expected if corrected for the familywise error. LISA appears to be less conservative than FSL-TFCE, and shows a high spatial precision and sensitivity when applied to data acquired at an ultra-high field scanner. Applying an edge-preserving filter at a late stage in the analysis chain rather than during preprocessing
In this study we use relaxometry and susceptibility mapping to obtain enhanced contrast in the mi... more In this study we use relaxometry and susceptibility mapping to obtain enhanced contrast in the midbrain, in particular in the superior colliculus (SC). High resolution GRE images were obtained in 11 subjects at 9.4T. We calculated CNR values for each contrast for three midbrain regions (superior colliculus,red nucleus and aqueductal gray). were were obtained across 11 subjects in individual and MNI space. These measurement were validated with ex-vivo measurements in the 9.4T, 14.1T and PLI imaging
We assessed how improved static magnetic field (B 0 ) homogeneity with a dynamic multicoil shimmi... more We assessed how improved static magnetic field (B 0 ) homogeneity with a dynamic multicoil shimming can influence the blood oxygen level dependent (BOLD) contrast to noise when echo planar imaging (EPI) sequence is used for a motor task functional MRI study. We showed that a multicoil shim setup can be a proper choice for dynamic shimming of 2 spatially distant areas with different inhomogeneity distributions. Methods: A 16-channel multicoil shim setup is used to provide improved B 0 homogeneity by dynamic slice-wise shimming. The performance of dynamic B 0 shimming was investigated in 2 distinct brain regions, the motor cortex and the cerebellum, in the same experiment during a finger-tapping task. Temporal SNR (tSNR), geometric distortion of the EPIs, and results of an analysis with a general linear model before and after shimming with the multicoil were compared. Results: Reduced B 0 deviation by 30% and 52% in the cerebellum and motor cortex, respectively, resulted in higher tSNR and a reduction of distortions in the EPI. Statistical analysis applied to the EPIs showed higher t values and increased number of voxels above significance threshold when shimming with the multicoil setup. Conclusions: Improved B 0 homogeneity leads to higher tSNR and enhances the detection of BOLD signal. B 0 inhomogeneity, BOLD signal, multicoil, shimming, temporal SNR, ultrahigh field In most applications, functional MRI (fMRI) is performed with gradient echo planar imaging (EPI), a fast T * 2 -weighted sequence which has a high sensitivity to blood oxygen level dependent (BOLD) signal changes. EPI possesses a long readout duration, which makes the images susceptible to geometric distortion 1 and signal loss because of B 0 inhomogeneity. These effects are even more pronounced at ultra-high fields (UHFs) given that the magnetic field variations induced from susceptibility differences linearly increase with the magnetic field strength.
Whole-brain voxel-based morphometry (VBM) studies revealed patterns of patchy atrophy within the ... more Whole-brain voxel-based morphometry (VBM) studies revealed patterns of patchy atrophy within the cerebellum of Friedreich's ataxia patients, missing clear clinico-anatomic correlations. Studies so far are lacking an appropriate registration to the infratentorial space. To circumvent these limitations, we applied a high-resolution atlas template of the human cerebellum and brainstem (SUIT template) to characterize regional cerebellar atrophy in Friedreich's ataxia (FRDA) on 3-T MRI data. We used a spatially unbiased voxel-based morphometry approach together with T2-based manual segmentation, T2 histogram analysis, and atlas generation of the dentate nuclei in a representative cohort of 18 FRDA patients and matched healthy controls. We demonstrate that the cerebellar volume in FRDA is generally not significantly different from healthy controls but mild lobular atrophy develops beyond normal aging. The medial parts of lobule VI, housing the somatotopic representation of tongue and lips, are the major site of this lobular atrophy, which possibly reflects speech impairment. Extended white matter affection correlates with disease severity across and beyond the cerebellar inflow and outflow tracts. The dentate nucleus, as a major site of cerebellar degeneration, shows a mean volume loss of about 30%. Remarkably, not the atrophy but the T2 signal decrease of the dentate nuclei highly correlates with disease duration and severity.
How the brain enables humans to reach an outstanding level of performance typical of expertise is... more How the brain enables humans to reach an outstanding level of performance typical of expertise is of great interest to cognitive neuroscience, as demonstrated by the number and diversity of the articles in this Research Topic (RT). The RT presents a collection of 23 articles written by 80 authors on traditional expertise topics such as sport, board games, and music, but also on the expertise aspects of everyday skills, such as language and the perception of faces and objects. Just as the topics in the RT are diverse, so are the neuroimaging techniques employed and the article formats. Here we will briefly summarize the articles published in the RT. Board Games
The traditional expertise domain of board games has been covered in the RT by two articles, both employing the expertise approach of pitting experts against novices (Bilalić et al., 2010, 2012, 2014) but employing differing neuroimaging techniques. Bartlett et al. (2013) employed fMRI to demonstrate that chess experts engage the fronto-parietal network when they try to find a logical pattern in a “constellation” of randomly placed chess pieces. Jung et al. (2013) found structural differences as well as differences in brain networks between Baduk (Korean name for the board game Go) experts and novices, which point out the importance of visuospatial processing in problem solving and decision making of board-game experts. Sport
Wright et al. (2013) extended the research on anticipation of action in sport by showing that the neural basis for deception involves, besides the well-known action observation network, the structures responsible for social cognition and affection. Turella et al. (2013) review other recent studies on the anticipation of action in sport and connect them with the mirror neurons in animal research. The review by Chang (2014) deals with motor domains such as sports and music and the structural and functional changes associated with expertise. Debarnot et al. (2014) go a step further in their review and contrast the neural changes during skill acquisition with those in mental training techniques such motor imagery and mediation. Music
Music has been one of the most often investigated domains in expertise because its complexity and richness enable researchers to tackle diverse topics. The variety of themes in the domain of music is also evident in this RT. Tervaniemi et al. (2014), for example, pitted expert musicians against novices in a novel paradigm to investigate memory and attentional processes with EEG. On the other hand, Bergman Nutley et al. (2014) used the music domain to investigate longitudinal effects on cognitive processes such as working memory, speed of processing, and reasoning, while Fauvel et al. (2013) apply the promising findings of transfer and neural plasticity associated with musical practice to cognitive aging in their review. Language
Unlike the previous articles, which deal with specialized expertise domains, a number of contributions highlight the fact that even the everyday skills we often take for granted represent impressive feats of human expertise. One group of articles deals with language, which is one such everyday skill. Reichle and Reingold (2013) review the electrophysiological evidence of the link between eye movements and the mind during reading. The learning of a second language based on its similarity to one's native language was investigated by Grimaldi et al. (2014), while Dietrich et al. (2013) demonstrated the neural changes associated with the process of learning to comprehend speech that was several times faster than normal speech. Finally, Lotze et al. (2014) demonstrate by means of resting-state fMRI that people who write highly creatively have increased functional connectivity between the task-related brain regions in the right hemisphere but reduced interhemispheric connectivity. Perception
Similarly, a couple of articles deal with perception of own-race and other-race faces (Wiese, 2013) as well as with perception of familiar faces and objects and the functional connectivity within the medial temporal lobe (McLelland et al., 2014). The role of the fusiform face area (FFA) in expertise has been a bone of contention between Harel et al. (2013, 2014), on the one hand, and Wong and Wong (2014), on the other. Theoretical and Simulation Work
Finally, a number of articles provide either new theoretical ideas or revisions of already established theories. Campitelli and Speelman (2013) highlight the advantages of using the expertise paradigm in investigating memory, while Brogliato et al. (2014) expand the Sparse Distributed Memory (SDM) model to incorporate the effects of practice on memory retrieval. Guida et al. (2013) extend their two-stage framework of skill acquisition (Guida et al., 2012) by arguing for the functional cerebral reorganization (FCR) as being the neural signature of expertise. The way one structures training studies is considered by Coffey and Herholz (2013), who suggest a new approach for characterizing and deconstructing the task requirements in training studies. Finally, Harré (2013) demonstrates the parallels between two seemingly unrelated fields, perceptual expertise and social cognition. Conclusion
It is clear that we cannot do justice to all submissions in this brief editorial. We hope, however, that our brief summary demonstrates the diversity in topics and methods employed in research on human expertise and also, indirectly, the growing interest in the field of expertise. It should become evident that research on expertise is not only relevant for understanding exceptional human performance but also for understanding how mind and brain work more generally. We are grateful to all authors for their contribution and hope that the RT, with its broad and deep coverage, will provide a useful reference for the reader interested in expertise and, particularly, current approaches to its neural implementation. Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Despite the importance of mathematics in our educational systems, little is known about how abstr... more Despite the importance of mathematics in our educational systems, little is known about how abstract mathematical thinking emerges. Most research on mathematical cognition has been dedicated to understanding its more simple forms such as seriation and counting. Although these forms constitute the foundational plinth upon which all other maths skills develop, the gap between basic skills and the processing of complex mathematical concepts is poorly understood. What has come to be sufficiently well understood, however, is how numeracy is acquired. The 90s marked a change in our approach to human cognition in general and to mathematical cognition in particular. Neuroimaging technologies have enabled localization of neural activity, revealing that mathematical cognition, like other forms of cognition and skills, depends upon a network of activation. The key finding from neuroimaging and single cell recording is that numerical information is held in the intraparietal sulcus. Now that the core of mathematical cognition has been identified it is time to understand how basic skills are used to support the acquisition and use of abstract mathematical concepts. Chassy and Grodd (2012) opened the door for abstract mathematical cognition by examining for the first time the neural correlates of negative numbers, an abstract mathematical concept that emerges early on in mathematical curricula. The present issue reports crucial advances in our understanding of the neural underpinnings of abstract mathematical cognition.
For a general introduction to the topic the reader is referred to the article signed by Moeller et al. The article offers an excellent overview of the networks that are involved to some degree in processing quantities, the very basis of mathematical cognition. The authors' conclusion strengthens the view that a frontal parietal network constitutes the essence of our abilities in mathematics. The fronto-parietal network has been highlighted by a number of studies and is thought to underpin the learning of mathematical concepts. By increasing the complexity of the concepts stored in our memory, we improve the quality of our understanding of the physical world in the first stages of mathematical cognition. Abstract concepts are then able to emerge from concrete, physical quantities.
On the path of mathematical development, the first step toward an abstract representation of concepts is the shift from concrete, object-based cognition to the use of symbols. The symbols, though arbitrary, represent concrete quantities that help children quantify and thus understand the world around them. Roesch and Moeller support this view by suggesting that an internal representation of fingers contributes to the actual ability to represent quantities. In a similar vein, a cross cultural study authored by Bender and Beller compares the Western counting system to a Polynesian language of the Tonga island, offering a unique view of how concrete counting of different objects leads to an abstract representation of numbers; thus demonstrating that the roots of abstract mathematical cognition emerge from basic, sensory abilities (a long standing view that finds a new echo here). By highlighting the concrete roots of mathematical cognition, the authors of these studies open the debate on the inheritance of mathematical skill by pointing toward very concrete sensory performance.
The symbols in a later stage of mathematical development are used to represent concepts of an abstract nature. That is, once the notion of natural number is acquired, the next step toward expertise is to formalize operations as abstract entities. For example, the operation 5 + 4 = 9 is concrete and can be taught by using objects. Dowker demonstrates that pupils tend to use the same problem-solving strategies to solve problems in subtraction and addition problems. Since the properties of the two operations differ the application of the same strategy leads the pupil to commit errors. Pupils have to learn a new set of properties to be able to solve subtraction. Similarly, Huber et al. argue that mental representations of fractions do not differ from natural numbers; what do differ are the strategies used to encode information. Dowker's and Hubet et al.'s views are in line with the study of Mihulowicz et al. who, by comparing left and right lesioned patients, showed that arithmetic operations are underpinned by different networks. The view of some educators, that subtraction and addition are mirror operations, is mistaken. It is interesting to note that teaching might be adapted so that different approaches could be used to teach different operations. The studies highlight the fact that learning arithmetic includes knowledge that is not purely numerical. This is our first hint indicating that educational strategies might have a huge influence on the ability of students to learn abstract concepts. The next stage in mathematical learning is the step consisting in moving from concrete (arithmetic) to abstract (algebraic) relationships. A study by Susac et al. looked at this move and showed that it requires about 4 years of training to master this new step toward abstract thinking in mathematics. It is crucial to note that these 4 years are in addition to the many years required for correctly mastering the basics. Mathematical learning is a long road. It calls for pedagogical approaches that are specific to each level.
Two main variables might modulate the acquisition of mathematical expertise: Educational system and inherited factors. The idea that teaching practices impact heavily on the ability of students to develop their skills in abstract mathematical cognition is demonstrated by Prado et al. The authors ran a cross cultural study comparing Chinese and American students on problem-size effects, and show that educational practices, which differ in the 2 countries, impact on the wiring of the network in charge of symbolic arithmetic. In line with this result, McLean and Rusconi attempt to bridge the gap between the findings of academic science and the practical problems faced by teaching institutions when dealing with students with mathematical difficulties. After revealing the cognitive factors underpinning the acquisition of mathematical knowledge, McLean and Rusconi discuss the types of interventions that may help students with mathematical difficulties. With respect to inherited factors, Zhang et al. have shown that gifted adolescents display a highly integrated fronto-parietal network, hence displaying a more efficient link between the representation of numbers in the parietal cortex and working memory in the prefrontal cortex.
The many findings of the articles in this special topic call for further research to see how specific neural networks serve various abstract mathematical concepts.
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Papers by Wolfgang Grodd
Board Games
The traditional expertise domain of board games has been covered in the RT by two articles, both employing the expertise approach of pitting experts against novices (Bilalić et al., 2010, 2012, 2014) but employing differing neuroimaging techniques. Bartlett et al. (2013) employed fMRI to demonstrate that chess experts engage the fronto-parietal network when they try to find a logical pattern in a “constellation” of randomly placed chess pieces. Jung et al. (2013) found structural differences as well as differences in brain networks between Baduk (Korean name for the board game Go) experts and novices, which point out the importance of visuospatial processing in problem solving and decision making of board-game experts.
Sport
Wright et al. (2013) extended the research on anticipation of action in sport by showing that the neural basis for deception involves, besides the well-known action observation network, the structures responsible for social cognition and affection. Turella et al. (2013) review other recent studies on the anticipation of action in sport and connect them with the mirror neurons in animal research. The review by Chang (2014) deals with motor domains such as sports and music and the structural and functional changes associated with expertise. Debarnot et al. (2014) go a step further in their review and contrast the neural changes during skill acquisition with those in mental training techniques such motor imagery and mediation.
Music
Music has been one of the most often investigated domains in expertise because its complexity and richness enable researchers to tackle diverse topics. The variety of themes in the domain of music is also evident in this RT. Tervaniemi et al. (2014), for example, pitted expert musicians against novices in a novel paradigm to investigate memory and attentional processes with EEG. On the other hand, Bergman Nutley et al. (2014) used the music domain to investigate longitudinal effects on cognitive processes such as working memory, speed of processing, and reasoning, while Fauvel et al. (2013) apply the promising findings of transfer and neural plasticity associated with musical practice to cognitive aging in their review.
Language
Unlike the previous articles, which deal with specialized expertise domains, a number of contributions highlight the fact that even the everyday skills we often take for granted represent impressive feats of human expertise. One group of articles deals with language, which is one such everyday skill. Reichle and Reingold (2013) review the electrophysiological evidence of the link between eye movements and the mind during reading. The learning of a second language based on its similarity to one's native language was investigated by Grimaldi et al. (2014), while Dietrich et al. (2013) demonstrated the neural changes associated with the process of learning to comprehend speech that was several times faster than normal speech. Finally, Lotze et al. (2014) demonstrate by means of resting-state fMRI that people who write highly creatively have increased functional connectivity between the task-related brain regions in the right hemisphere but reduced interhemispheric connectivity.
Perception
Similarly, a couple of articles deal with perception of own-race and other-race faces (Wiese, 2013) as well as with perception of familiar faces and objects and the functional connectivity within the medial temporal lobe (McLelland et al., 2014). The role of the fusiform face area (FFA) in expertise has been a bone of contention between Harel et al. (2013, 2014), on the one hand, and Wong and Wong (2014), on the other.
Theoretical and Simulation Work
Finally, a number of articles provide either new theoretical ideas or revisions of already established theories. Campitelli and Speelman (2013) highlight the advantages of using the expertise paradigm in investigating memory, while Brogliato et al. (2014) expand the Sparse Distributed Memory (SDM) model to incorporate the effects of practice on memory retrieval. Guida et al. (2013) extend their two-stage framework of skill acquisition (Guida et al., 2012) by arguing for the functional cerebral reorganization (FCR) as being the neural signature of expertise. The way one structures training studies is considered by Coffey and Herholz (2013), who suggest a new approach for characterizing and deconstructing the task requirements in training studies. Finally, Harré (2013) demonstrates the parallels between two seemingly unrelated fields, perceptual expertise and social cognition.
Conclusion
It is clear that we cannot do justice to all submissions in this brief editorial. We hope, however, that our brief summary demonstrates the diversity in topics and methods employed in research on human expertise and also, indirectly, the growing interest in the field of expertise. It should become evident that research on expertise is not only relevant for understanding exceptional human performance but also for understanding how mind and brain work more generally. We are grateful to all authors for their contribution and hope that the RT, with its broad and deep coverage, will provide a useful reference for the reader interested in expertise and, particularly, current approaches to its neural implementation.
Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
For a general introduction to the topic the reader is referred to the article signed by Moeller et al. The article offers an excellent overview of the networks that are involved to some degree in processing quantities, the very basis of mathematical cognition. The authors' conclusion strengthens the view that a frontal parietal network constitutes the essence of our abilities in mathematics. The fronto-parietal network has been highlighted by a number of studies and is thought to underpin the learning of mathematical concepts. By increasing the complexity of the concepts stored in our memory, we improve the quality of our understanding of the physical world in the first stages of mathematical cognition. Abstract concepts are then able to emerge from concrete, physical quantities.
On the path of mathematical development, the first step toward an abstract representation of concepts is the shift from concrete, object-based cognition to the use of symbols. The symbols, though arbitrary, represent concrete quantities that help children quantify and thus understand the world around them. Roesch and Moeller support this view by suggesting that an internal representation of fingers contributes to the actual ability to represent quantities. In a similar vein, a cross cultural study authored by Bender and Beller compares the Western counting system to a Polynesian language of the Tonga island, offering a unique view of how concrete counting of different objects leads to an abstract representation of numbers; thus demonstrating that the roots of abstract mathematical cognition emerge from basic, sensory abilities (a long standing view that finds a new echo here). By highlighting the concrete roots of mathematical cognition, the authors of these studies open the debate on the inheritance of mathematical skill by pointing toward very concrete sensory performance.
The symbols in a later stage of mathematical development are used to represent concepts of an abstract nature. That is, once the notion of natural number is acquired, the next step toward expertise is to formalize operations as abstract entities. For example, the operation 5 + 4 = 9 is concrete and can be taught by using objects. Dowker demonstrates that pupils tend to use the same problem-solving strategies to solve problems in subtraction and addition problems. Since the properties of the two operations differ the application of the same strategy leads the pupil to commit errors. Pupils have to learn a new set of properties to be able to solve subtraction. Similarly, Huber et al. argue that mental representations of fractions do not differ from natural numbers; what do differ are the strategies used to encode information. Dowker's and Hubet et al.'s views are in line with the study of Mihulowicz et al. who, by comparing left and right lesioned patients, showed that arithmetic operations are underpinned by different networks. The view of some educators, that subtraction and addition are mirror operations, is mistaken. It is interesting to note that teaching might be adapted so that different approaches could be used to teach different operations. The studies highlight the fact that learning arithmetic includes knowledge that is not purely numerical. This is our first hint indicating that educational strategies might have a huge influence on the ability of students to learn abstract concepts. The next stage in mathematical learning is the step consisting in moving from concrete (arithmetic) to abstract (algebraic) relationships. A study by Susac et al. looked at this move and showed that it requires about 4 years of training to master this new step toward abstract thinking in mathematics. It is crucial to note that these 4 years are in addition to the many years required for correctly mastering the basics. Mathematical learning is a long road. It calls for pedagogical approaches that are specific to each level.
Two main variables might modulate the acquisition of mathematical expertise: Educational system and inherited factors. The idea that teaching practices impact heavily on the ability of students to develop their skills in abstract mathematical cognition is demonstrated by Prado et al. The authors ran a cross cultural study comparing Chinese and American students on problem-size effects, and show that educational practices, which differ in the 2 countries, impact on the wiring of the network in charge of symbolic arithmetic. In line with this result, McLean and Rusconi attempt to bridge the gap between the findings of academic science and the practical problems faced by teaching institutions when dealing with students with mathematical difficulties. After revealing the cognitive factors underpinning the acquisition of mathematical knowledge, McLean and Rusconi discuss the types of interventions that may help students with mathematical difficulties. With respect to inherited factors, Zhang et al. have shown that gifted adolescents display a highly integrated fronto-parietal network, hence displaying a more efficient link between the representation of numbers in the parietal cortex and working memory in the prefrontal cortex.
The many findings of the articles in this special topic call for further research to see how specific neural networks serve various abstract mathematical concepts.