Functional Disorganization of Small-World Brain Networks in Patients With Ischemic Leukoaraiosis

MMF-NNs: Multi-modal Multi-granularity Fusion Neural Networks for brain networks and its application to epilepsy identification

Structural and functional brain networks are generated from two scan sequences of magnetic resonance imaging data, which can provide different perspectives for describing pathological changes caused by brain diseases. Recent studies found that fusing these two types of brain networks improves performance in brain disease identification. However, traditional fusion models combine these brain networks at a single granularity, ignoring the natural multi-granularity structure of brain networks that can be divided into the edge, node, and graph levels. To this end, this paper proposes a Multi-modal Multi-granularity Fusion Neural Networks (MMF-NNs) framework for brain networks, which integrates the features of the multi-modal brain network from global (i.e., graph-level) and local (i.e., edge-level and node-level) granularities to take full advantage of the topological information. Specifically, we design an interactive feature learning module at the local granularity to learn feature maps of structural and functional brain networks at the edge-level and the node-level, respectively. In that way, these two types of brain networks are fused during the feature learning process. At the global granularity, a multi-modal decomposition bilinear pooling module is designed to learn the graph-level joint representation of these brain networks. Experiments on real epilepsy datasets demonstrate that MMF-NNs are superior to several state-of-the-art methods in epilepsy identification.

Long-range connections damage in white matter hyperintensities affects information processing speed

White matter hyperintensities, one of the major markers of cerebral small vessel disease, disrupt the integrity of neuronal networks and ultimately contribute to cognitive dysfunction. However, a deeper understanding of how white matter hyperintensities related to the connectivity patterns of brain hubs at the neural network level could provide valuable insights into the relationship between white matter hyperintensities and cognitive dysfunction. A total of 36 patients with moderate to severe white matter hyperintensities (Fazekas score ≥ 3) and 34 healthy controls underwent comprehensive neuropsychological assessments and resting-state functional MRI scans. The voxel-based graph-theory approach-functional connectivity strength was employed to systematically investigate the topological organization of the whole-brain networks. The white matter hyperintensities patients performed significantly worse than the healthy controls in episodic memory, executive function and information processing speed. Additionally, we found that white matter hyperintensities selectively affected highly connected hub regions, predominantly involving the medial and lateral prefrontal, precuneus, inferior parietal lobule, insula and thalamus. Intriguingly, this impairment was connectivity distance-dependent, with the most prominent disruptions observed in long-range connections (e.g. 100-150 mm). Finally, these disruptions of hub connectivity (e.g. the long-range functional connectivity strength in the left dorsolateral prefrontal cortex) positively correlated with the cognitive performance in white matter hyperintensities patients. Our findings emphasize that the disrupted hub connectivity patterns in white matter hyperintensities are dependent on connection distance, especially longer-distance connections, which in turn predispose white matter hyperintensities patients to worse cognitive function.

Decreased Local Specialization of Brain Structural Networks Associated with Cognitive Dysfuntion Revealed by Probabilistic Diffusion Tractography for Different Cerebral Small Vessel Disease Burdens

To reveal the network-level structural disruptions associated with cognitive dysfunctions in different cerebral small vessel disease (CSVD) burdens, we used probabilistic diffusion tractography and graph theory to investigate the brain network topology in 67 patients with a severe CSVD burden (CSVD-s), 133 patients with a mild CSVD burden (CSVD-m) and 89 healthy controls. We used one-way analysis of covariance to assess the altered topological measures between groups, and then evaluated their Pearson correlation with cognitive parameters. Both the CSVD and control groups showed efficient small-world organization in white matter (WM) networks. However, compared with CSVD-m patients and controls, CSVD-s patients exhibited significantly decreased local efficiency, with partially reorganized hub distributions. For regional topology, CSVD-s patients showed significantly decreased nodal efficiency in the bilateral anterior cingulate gyrus, caudate nucleus, right opercular inferior frontal gyrus (IFGoperc), supplementary motor area (SMA), insula and left orbital superior frontal gyrus and angular gyrus. Intriguingly, global/local efficiency and nodal efficiency of the bilateral caudate nucleus, right IFGoperc, SMA and left angular gyrus showed significant correlations with cognitive parameters in the CSVD-s group, while only the left pallidum showed significant correlations with cognitive metrics in the CSVD-m group. In conclusion, the decreased local specialization of brain structural networks in patients with different CSVD burdens provides novel insights into understanding the brain structural alterations in relation to CSVD severity. Cognitive correlations with brain structural network efficiency suggest their potential use as neuroimaging biomarkers to assess the severity of CSVD.

Do cerebrovascular risk factors impact the clinical expression of idiopathic isolated adult-onset dystonia?

BACKGROUND

Although acquired dystonia may develop following ischaemic/haemorrhagic stroke, the relationship between cerebrovascular disease and idiopathic dystonia has been poorly investigated. This cross sectional study aimed at evaluating the impact of cerebrovascular risk factors on the clinical expression of idiopathic adult onset dystonia (IAOD), with reference to dystonia localization and dystonia-associated features.

METHODS

Data were obtained from the Italian Dystonia Registry. Patients with IAOD were stratified into two groups according to the presence of diabetes mellitus and/or arterial hypertension and/or dyslipidemia and/or heart disease. The two groups were compared for demographic features, dystonia phenotype, and dystonia-associated features (sensory trick, tremor, eye symptoms in blepharospasm, and neck pain in cervical dystonia).

RESULTS

A total of 1108 patients participated into the study. Patients who reported one cerebrovascular factor or more (n = 555) had higher age and longer disease duration than patients who did not. On multivariable logistic regression analysis, blepharospasm was the only localization, and sensory trick was the only dystonia-associated feature that was significantly associated with cerebrovascular risk factors. Linear regression analysis showed that the strength of the association between cerebrovascular factors and blepharospasm/sensory trick increased with increasing the number of cerebrovascular factors per patient.

CONCLUSIONS

Results of the present study showed that cerebrovascular risk factors may be associated with specific features of IAOD that is development of blepharospasm and sensory trick. Further studies are needed to better understand the meaning and the mechanisms underlying this association.

Disconnection of Network Hubs Underlying the Executive Function Deficit in Patients with Ischemic Leukoaraiosis

BACKGROUND

Cognitive impairment is the most common clinical manifestation of ischemic leukoaraiosis (ILA), but the underlying neurobiological pathways have not been well elucidated. Recently, it was thought that ILA is a "disconnection syndrome". Disorganized brain connectome were considered the key neuropathology underlying cognitive deficits in ILA patients.

OBJECTIVE

We aimed to detect the disruption of network hubs in ILA patients using a new analytical method called voxel-based eigenvector centrality (EC) mapping.

METHODS

Subjects with moderate to severe white matters hyperintensities (Fazekas score ≥3) and healthy controls (HCs) (Fazekas score = 0) were included in the study. The resting-state functional magnetic resonance imaging and the EC mapping approach were performed to explore the alteration of whole-brain network connectivity in ILA patients.

RESULTS

Relative to the HCs, the ILA patients exhibited poorer cognitive performance in episodic memory, information processing speed, and executive function (all ps < 0.0125). Additionally, compared with HCs, the ILA patients had lower functional connectivity (i.e., EC values) in the medial parts of default-mode network (i.e., bilateral posterior cingulate gyrus and ventral medial prefrontal cortex [vMPFC]). Intriguingly, the functional connectivity strength at the right vMPFC was positively correlated with executive function deficit in the ILA patients.

CONCLUSION

The findings suggested disorganization of the hierarchy of the default-mode regions within the whole-brain network in patients with ILA and advanced our understanding of the neurobiological mechanism underlying executive function deficit in ILA.

Parietal and occipital leukoaraiosis due to cerebral ischaemic lesions decrease the driving safety performance of healthy older adults

Leukoaraiosis, a common ischaemic lesion diagnosed using magnetic resonance imaging (MRI), can influence driving safety performance (DSP). Most older drivers with leukoaraiosis are unaware of their affliction. Japan is a super-aged country, where preventing accidents caused by older drivers is an urgent national issue. We investigated the subcortical and periventricular leukoaraiosis regions that were most involved in DSP decline. The driving skills of 101 drivers (49 men, 52 women; mean age, 77.88 ± 3.77 years) without dementia were assessed by official driving instructors, using actual vehicles on a closed-circuit course. Parietal and occipital (but not frontal or temporal) leukoaraiosis volumes were significantly correlated with decreased DSP scores regardless of age, especially when turning right at intersections, which needs more attention than turning left because left-side driving is legally enforced in Japan. Occipital leukoaraiosis was also involved via a decline in dynamic visual cognitive function. MRI-based assessment of leukoaraiosis volume and localisation may enable the identification of older drivers prone to DSP deterioration. Risk factors for leukoaraiosis include smoking and lifestyle-related diseases such as hypertension. Thus, brain healthcare in patients with MRI-diagnosed leukoaraiosis may be particularly useful for the risk management of traffic accidents caused by the elderly in Japan.

Comorbid depressive symptoms can aggravate the functional changes of the pain matrix in patients with chronic back pain: A resting-state fMRI study

Objective

The purposes of this study are to explore (1) whether comorbid depressive symptoms in patients with chronic back pain (CBP) affect the pain matrix. And (2) whether the interaction of depression and CBP exacerbates impaired brain function.

Methods

Thirty-two patients with CBP without comorbid depressive symptoms and thirty patients with CBP with comorbid depressive symptoms were recruited. All subjects underwent functional magnetic resonance imaging (fMRI) scans. The graph theory analysis, mediation analysis, and functional connectivity (FC) analysis were included in this study. All subjects received the detection of clinical depressive symptoms and pain-related manifestations.

Result

Compared with the CBP group, subjects in the CBP with comorbid depressive symptoms (CBP-D) group had significantly increased FC in the left medial prefrontal cortex and several parietal cortical regions. The results of the graph theory analyses showed that the area under the curve of small-world property (t = −2.175, p = 0.034), gamma (t = −2.332, p = 0.023), and local efficiency (t = −2.461, p = 0.017) in the CBP-D group were significantly lower. The nodal efficiency in the ventral posterior insula (VPI) (t = −3.581, p = 0.0007), and the network efficiency values (t = −2.758, p = 0.008) in the pain matrix were significantly lower in the CBP-D group. Both the topological properties and the FC values of these brain regions were significantly correlated with self-rating depression scale (SDS) scores (all FDR corrected) but not with pain intensity. Further mediation analyses demonstrated that pain intensity had a mediating effect on the relationship between SDS scores and Pain Disability Index scores. Likewise, the SDS scores mediated the relationship between pain intensity and PDI scores.

Conclusion

Our study found that comorbid depressive symptoms can aggravate the impairment of pain matrix function of CBP, but this impairment cannot directly lead to the increase of pain intensity, which may be because some brain regions of the pain matrix are the common neural basis of depression and CBP.

Topologic Efficiency Abnormalities of the Connectome in Asymptomatic Patients with Leukoaraiosis

Leukoaraiosis (LA) is commonly found in aging healthy people but its pathophysiological mechanism is not entirely known. Furthermore, there is still a lack of effective pathological biomarkers that can be used to identify the early stage of LA. Our aim was to investigate the white matter structural network in asymptomatic patients with the early stage of LA. Tractography data of 35 asymptomatic patients and 20 matched healthy controls (HCs) based on diffusion kurtosis imaging (DKI) were analysed by using graph theory approaches and tract-based spatial statistics (TBSS). Diffusion parameters measured within the ALAs and HCs were compared. Decreased clustering coefficient and local efficiency values of the overall topological white matter network were observed in the ALAs compared with those of the HCs. Participants in the asymptomatic group also had lower nodal efficiency in the left triangular part of the inferior frontal gyrus, left parahippocampal gyrus, right calcarine fissure and surrounding cortex, right temporal pole of the superior temporal gyrus and left middle temporal gyrus compared to the ALAs. Moreover, similar hub distributions were found within participants in the two groups. In this study, our data demonstrated a topologic efficiency abnormalities of the structural network in asymptomatic patients with leukoaraiosis. The structural connectome provides potential connectome-based measures that may be helpful for detecting leukoaraiosis before clinical symptoms evolve.

Network dynamics scale with levels of awareness

Small world topologies are thought to provide a valuable insight into human brain organisation and consciousness. However, functional magnetic resonance imaging studies in consciousness have not yielded consistent results. Given the importance of dynamics for both consciousness and cognition, here we investigate how the diversity of small world dynamics (quantified by sample entropy; dSW-E¹) scales with decreasing levels of awareness (i.e., sedation and disorders of consciousness). Paying particular attention to result reproducibility, we show that dSW-E is a consistent predictor of levels of awareness even when controlling for the underlying functional connectivity dynamics. We find that dSW-E of subcortical and cortical areas are predictive, with the former showing higher and more robust effect sizes across analyses. We find that the network dynamics of intermodular communication in the cerebellum also have unique predictive power for levels of awareness. Consequently, we propose that the dynamic reorganisation of the functional information architecture, in particular of the subcortex, is a characteristic that emerges with awareness and has explanatory power beyond that of the complexity of dynamic functional connectivity.

Impaired functional network properties contribute to white matter hyperintensity related cognitive decline in patients with cerebral small vessel disease

Background

White matter hyperintensity (WMH) is one of the typical neuroimaging manifestations of cerebral small vessel disease (CSVD), and the WMH correlates closely to cognitive impairment (CI). CSVD patients with WMH own altered topological properties of brain functional network, which is a possible mechanism that leads to CI. This study aims to identify differences in the characteristics of some brain functional network among patients with different grades of WMH and estimates the correlations between these different brain functional network characteristics and cognitive assessment scores.

Methods

110 CSVD patients underwent 3.0 T Magnetic resonance imaging scans and neuropsychological cognitive assessments. WMH of each participant was graded on the basis of Fazekas grade scale and was divided into two groups: (A) WMH score of 1–2 points (n = 64), (B) WMH score of 3–6 points (n = 46). Topological indexes of brain functional network were analyzed using graph-theoretical method. T-test and Mann–Whitney U test was used to compare the differences in topological properties of brain functional network between groups. Partial correlation analysis was applied to explore the relationship between different topological properties of brain functional networks and overall cognitive function.

Results

Patients with high WMH scores exhibited decreased clustering coefficient values, global and local network efficiency along with increased shortest path length on whole brain level as well as decreased nodal efficiency in some brain regions on nodal level (p < 0.05). Nodal efficiency in the left lingual gyrus was significantly positively correlated with patients' total Montreal Cognitive Assessment (MoCA) scores (p < 0.05). No significant difference was found between two groups on the aspect of total MoCA and Mini-mental State Examination (MMSE) scores (p > 0.05).

Conclusion

Therefore, we come to conclusions that patients with high WMH scores showed less optimized small-world networks compared to patients with low WMH scores. Global and local network efficiency on the whole-brain level, as well as nodal efficiency in certain brain regions on the nodal level, can be viewed as markers to reflect the course of WMH.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12880-022-00769-7.

Disrupted topological organization of resting-state functional brain networks in cerebral small vessel disease

We aimed to investigate alterations in functional brain networks and assess the relationship between functional impairment and topological network changes in cerebral small vessel disease (CSVD) patients with and without cerebral microbleeds (CMBs). We constructed individual whole‐brain, region of interest (ROI) level functional connectivity (FC) networks for 24 CSVD patients with CMBs (CSVD‐c), 42 CSVD patients without CMBs (CSVD‐n), and 36 healthy controls (HCs). Then, we used graph theory analysis to investigate the global and nodal topological disruptions between groups and relate network topological alterations to clinical parameters. We found that both the CSVD and control groups showed efficient small‐world organization in FC networks. However, compared to CSVD‐n patients and controls, CSVD‐c patients exhibited a significantly decreased clustering coefficient, global efficiency, and local efficiency and an increased shortest path length, indicating a disrupted balance between local specialization and global integration in FC networks. Although both the CSVD and control groups showed highly similar hub distributions, the CSVD‐c group exhibited significantly altered nodal betweenness centrality (BC), mainly distributed in the default mode network (DMN), attention, and visual functional areas. There were almost no global or regional alterations between CSVD‐n patients and controls. Furthermore, the altered nodal BC of the right anterior/posterior cingulate gyrus and left cuneus were significantly correlated with cognitive parameters in CSVD patients. These results suggest that CSVD patients with and without CMBs had segregated disruptions in the topological organization of the intrinsic functional brain network. This study advances our current understanding of the pathophysiological mechanisms underlying CSVD.

Effects of Motor Imagery Tasks on Brain Functional Networks Based on EEG Mu/Beta Rhythm

Motor imagery (MI) refers to the mental rehearsal of movement in the absence of overt motor action, which can activate or inhibit cortical excitability. EEG mu/beta oscillations recorded over the human motor cortex have been shown to be consistently suppressed during both the imagination and performance of movements, although the specific effect on brain function remains to be confirmed. In this study, Granger causality (GC) was used to construct the brain functional network of subjects during motor imagery and resting state based on EEG in order to explore the effects of motor imagery on brain function. Parameters of the brain functional network were compared and analyzed, including degree, clustering coefficient, characteristic path length and global efficiency of EEG mu/beta rhythm in different states. The results showed that the clustering coefficient and efficiency of EEG mu/beta rhythm decreased significantly during motor imagery (p < 0.05), while degree distribution and characteristic path length increased significantly (p < 0.05), mainly concentrated in the frontal lobe and sensorimotor area. For the resting state after motor imagery, the changes of brain functional characteristics were roughly similar to those of the task state. Therefore, it is concluded that motor imagery plays an important role in activation of cortical excitability.

Aging Brains Degrade Driving Safety Performances of the Healthy Elderly

The relationship between aging brains and driving safety performances (DSPs) of elderly drivers was studied. A total of 90 dementia-free participants (63 men and 27 women, mean age 75.31 ± 4.795 years) were recruited and their DSPs were analyzed on actual vehicles running through a closed-circuit course. DSPs were comprehensively evaluated on the basis of driving instructors' scores (DIS). Signaling and visual research behaviors, part of DSPs, were measured to supplement the DIS evaluation by driving recorders (DR) and wearable wireless sensors (WS), respectively. Aging brains were evaluated via magnetic resonance imaging (MRI) findings and experimentally assigned to two grades (high vs. low) of brain atrophy (BA) and leukoaraiosis (LA). Regression analyses on DIS and DR data, and logistic analysis on WS scores showed significant correlations of aging brains with degradation of DSPs. The participant group with more advanced BAs and LAs showed lower DIS, DR data, and WS scores representing degraded DSP regardless of age. These results suggest that MRI examinations from both volumetric and pathological perspectives of brains have the potential to help identify elderly drivers with dangerous driving behaviors. Brain healthcare, lifestyle improvements and medical treatments to suppress BA and LA, may contribute to preventing DSP degradation of elderly drivers with aging brains.

Identification of the Neural Circuit Underlying Episodic Memory Deficit in Amnestic Mild Cognitive Impairment via Machine Learning on Gray Matter Volume

Based on whole-brain gray matter volume (GMV), we used relevance vector regression to predict the Rey's Auditory Verbal Learning Test Delayed Recall (AVLT-DR) scores of individual amnestic mild cognitive impairment (aMCI) patient. The whole-brain GMV pattern could significantly predict the AVLT-DR scores (r = 0.54, p < 0.001). The most important GMV features mainly involved default-mode (e.g., posterior cingulate gyrus, angular gyrus, and middle temporal gyrus) and limbic systems (e.g., hippocampus and parahippocampal gyrus). Therefore, our results provide evidence supporting the idea that the episodic memory deficit in aMCI patients is associated with disruption of the default-mode and limbic systems.

Neuroimaging Anomalies in Community-Dwelling Asymptomatic Adults With Very Early-Stage White Matter Hyperintensity

White matter hyperintensity (WMH) is common in healthy adults in their 60s and can be seen as early as in their 30s and 40s. Alterations in the brain structural and functional profiles in adults with WMH have been repeatedly studied but with a focus on late-stage WMH. To date, structural and functional MRI profiles during the very early stage of WMH remain largely unexplored. To address this, we investigated multimodal MRI (structural, diffusion, and resting-state functional MRI) profiles of community-dwelling asymptomatic adults with very early-stage WMH relative to age-, sex-, and education-matched non-WMH controls. The comparative results showed significant age-related and age-independent changes in structural MRI-based morphometric measures and resting-state fMRI-based measures in a set of specific gray matter (GM) regions but no global white matter changes. The observed structural and functional anomalies in specific GM regions in community-dwelling asymptomatic adults with very early-stage WMH provide novel data regarding very early-stage WMH and enhance understanding of the pathogenesis of WMH.

Multivariate Machine Learning Analyses in Identification of Major Depressive Disorder Using Resting-State Functional Connectivity: A Multicentral Study

Diagnosis of major depressive disorder (MDD) using resting-state functional connectivity (rs-FC) data faces many challenges, such as the high dimensionality, small samples, and individual difference. To assess the clinical value of rs-FC in MDD and identify the potential rs-FC machine learning (ML) model for the individualized diagnosis of MDD, based on the rs-FC data, a progressive three-step ML analysis was performed, including six different ML algorithms and two dimension reduction methods, to investigate the classification performance of ML model in a multicentral, large sample dataset [1021 MDD patients and 1100 normal controls (NCs)]. Furthermore, the linear least-squares fitted regression model was used to assess the relationships between rs-FC features and the severity of clinical symptoms in MDD patients. Among used ML methods, the rs-FC model constructed by the eXtreme Gradient Boosting (XGBoost) method showed the optimal classification performance for distinguishing MDD patients from NCs at the individual level (accuracy = 0.728, sensitivity = 0.720, specificity = 0.739, area under the curve = 0.831). Meanwhile, identified rs-FCs by the XGBoost model were primarily distributed within and between the default mode network, limbic network, and visual network. More importantly, the 17 item individual Hamilton Depression Scale scores of MDD patients can be accurately predicted using rs-FC features identified by the XGBoost model (adjusted R² = 0.180, root mean squared error = 0.946). The XGBoost model using rs-FCs showed the optimal classification performance between MDD patients and HCs, with the good generalization and neuroscientifical interpretability.

Focal Subcortical White Matter Lesions Disrupt Resting State Cortical Interhemispheric Functional Connectivity in Mice

The corpus callosum is the largest white matter tract and critical for interhemispheric connectivity. Unfortunately, neurocognitive deficits after experimental white matter lesions are subtle and variable, limiting their translational utility. We examined resting state functional connectivity (RSFC) as a surrogate after a focal lesion in the lateral corpus callosum induced by stereotaxic injection of L-NIO in mice. RSFC was performed via optical intrinsic signal imaging through intact skull before and on days 1 and 14 after injection, using interhemispheric homotopic and seed-based temporal correlation maps. We measured the lesion volumes at 1 month in the same cohort. L-NIO induced focal lesions in the corpus callosum. Interhemispheric homotopic connectivity decreased by up to 50% 24 h after L-NIO, partially sparing the visual cortex. All seeds showed loss of connectivity to the contralateral hemisphere. Moreover, ipsilesional motor and visual cortices lost connectivity within the same hemisphere. Sham-operated mice did not show any lesion or connectivity changes. RSFC imaging reliably detects acute disruption of long interhemispheric and intrahemispheric connectivity after a corpus callosum lesion in mice. This noninvasive method can be a functional surrogate to complement neurocognitive testing in both therapeutic and recovery studies after white matter injury.

Functional connectivity changes in cerebral small vessel disease - a systematic review of the resting-state MRI literature

BACKGROUND

Cerebral small vessel disease (CSVD) is a common neurological disease present in the ageing population that is associated with an increased risk of dementia and stroke. Damage to white matter tracts compromises the substrate for interneuronal connectivity. Analysing resting-state functional magnetic resonance imaging (fMRI) can reveal dysfunctional patterns of brain connectivity and contribute to explaining the pathophysiology of clinical phenotypes in CSVD.

MATERIALS AND METHODS

This systematic review provides an overview of methods and results of recent resting-state functional MRI studies in patients with CSVD. Following the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) protocol, a systematic search of the literature was performed.

RESULTS

Of 493 studies that were screened, 44 reports were identified that investigated resting-state fMRI connectivity in the context of cerebral small vessel disease. The risk of bias and heterogeneity of results were moderate to high. Patterns associated with CSVD included disturbed connectivity within and between intrinsic brain networks, in particular the default mode, dorsal attention, frontoparietal control, and salience networks; decoupling of neuronal activity along an anterior-posterior axis; and increases in functional connectivity in the early stage of the disease.

CONCLUSION

The recent literature provides further evidence for a functional disconnection model of cognitive impairment in CSVD. We suggest that the salience network might play a hitherto underappreciated role in this model. Low quality of evidence and the lack of preregistered multi-centre studies remain challenges to be overcome in the future.

The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations

One of the biggest challenges in characterizing 2-D image topographies is finding a low-dimensional parameter set that can succinctly describe, not so much image patterns themselves, but the nature of these patterns. The 2-D cluster variation method (CVM), introduced by Kikuchi in 1951, can characterize very local image pattern distributions using configuration variables, identifying nearest-neighbor, next-nearest-neighbor, and triplet configurations. Using the 2-D CVM, we can characterize 2-D topographies using just two parameters; the activation enthalpy (ε0) and the interaction enthalpy (ε1). Two different initial topographies (“scale-free-like” and “extreme rich club-like”) were each computationally brought to a CVM free energy minimum, for the case where the activation enthalpy was zero and different values were used for the interaction enthalpy. The results are: (1) the computational configuration variable results differ significantly from the analytically-predicted values well before ε1 approaches the known divergence as ε1→0.881, (2) the range of potentially useful parameter values, favoring clustering of like-with-like units, is limited to the region where ε0<3 and ε1<0.25, and (3) the topographies in the systems that are brought to a free energy minimum show interesting visual features, such as extended “spider legs” connecting previously unconnected “islands,” and as well as evolution of “peninsulas” in what were previously solid masses.