Fractal Dimension Analysis of Subcortical Gray Matter Structures in Schizophrenia

Abstract

A failure of adaptive inference—misinterpreting available sensory information for appropriate perception and action—is at the heart of clinical manifestations of schizophrenia, implicating key subcortical structures in the brain including the hippocampus. We used high-resolution, three-dimensional (3D) fractal geometry analysis to study subtle and potentially biologically relevant structural alterations (in the geometry of protrusions, gyri and indentations, sulci) in subcortical gray matter (GM) in patients with schizophrenia relative to healthy individuals. In particular, we focus on utilizing Fractal Dimension (FD), a compact shape descriptor that can be computed using inputs with irregular (i.e., not necessarily smooth) surfaces in order to quantify complexity (of geometrical properties and configurations of structures across spatial scales) of subcortical GM in this disorder. Probabilistic (entropy-based) information FD was computed based on the box-counting approach for each of the seven subcortical structures, bilaterally, as well as the brainstem from high-resolution magnetic resonance (MR) images in chronic patients with schizophrenia (n = 19) and age-matched healthy controls (n = 19) (age ranges: patients, 22.7–54.3 and healthy controls, 24.9–51.6 years old). We found a significant reduction of FD in the left hippocampus (median: 2.1460, range: 2.07–2.18 vs. median: 2.1730, range: 2.15–2.23, p<0.001; Cohen’s effect size, U3 = 0.8158 (95% Confidence Intervals, CIs: 0.6316, 1.0)), the right hippocampus (median: 2.1430, range: 2.05–2.19 vs. median: 2.1760, range: 2.12–2.21, p = 0.004; U3 = 0.8421 (CIs: 0.5263, 1)), as well as left thalamus (median: 2.4230, range: 2.40–2.44, p = 0.005; U3 = 0.7895 (CIs: 0.5789, 0.9473)) in schizophrenia patients, relative to healthy individuals. Our findings provide in-vivo quantitative evidence for reduced surface complexity of hippocampus, with reduced FD indicating a less complex, less regular GM surface detected in schizophrenia.

Age-related differences in the structural complexity of subcortical and ventricular structures

“…Using these approaches, fractal dimensionality has been related to inter-individual differences in measures of fluid intelligence (Mustafa et al, 2012; Sandu et al, 2014), IQ (Im et al, 2006), and performance on the cognitive subscale of the Alzheimer’s Disease Assessment Scale (King et al, 2010). Fractal dimensionality has also been shown to differ between healthy adults and a number of patient populations, particularly in Alzheimer’s disease (King et al, 2009, 2010; Thompson et al, 1998) and schizophrenia (Ha et al, 2005; Narr et al, 2004; Nenadic et al, 2014; Sandu et al, 2008; Yotter et al, 2011; Zhao et al, 2016). Thus, while we have demonstrated the benefits of using fractal dimensionality to index age-related differences in subcortical structure, as well as cortical structure (Madan & Kensinger, 2016), the variability of this morphological measure also is related to inter-individual differences in cognitive measures and may hold promise as a biomarker for some neurological disorders.…”

“…A number of studies have demonstrated that the shape of subcortical structures can differ between patients and healthy controls. For instance, autism has been associated with differences in the shape of the amygdala (Chung et al, 2008), Alzheimer’s disease has been related to differences in several structures, particularly the hippocampus, amygdala, and lateral ventricles (Tang et al, 2014), and schizophrenic patients have shown differences in hippocampal and thalamus shape (Zhao et al, 2016; also see Smith et al, 2011, and Qiu et al, 2009). Though these studies provide evidence that shape characteristics can be a relevant measure for subcortical structures, it is possible that these systematic differences only occur in the presence of neurological or psychiatric disorders.…”

Cortical surface architecture endophenotype and correlates of clinical diagnosis of autism spectrum disorder

“…When examining cortical structure, surface‐based cortical matrices, such as cortical thickness (CT), fractal dimension (FD; a marker of cortical complexity), and sulcal depth (SD), are of particular interest. Unlike the conventional approach to examining regional gray matter volume, these surface‐based cortical measures focus on cortical folding . As they reflect different aspects of cortical architecture and stem from different genetic and cellular mechanisms in the brain, they have the potential to provide a more complete picture of the pathophysiology involved in the cortical architecture of ASD than gray matter volume.…”

“…Unlike the conventional approach to examining regional gray matter volume, these surface-based cortical measures focus on cortical folding. [7][8][9][10] As they reflect different aspects of cortical architecture and stem from different genetic and cellular mechanisms in the brain, 11,12 they have the potential to provide a more complete picture of the pathophysiology involved in the cortical architecture of ASD than gray matter volume.…”

Cortical surface architecture endophenotype and correlates of clinical diagnosis of autism spectrum disorder

“…Unlike the conventional approach to examine regional gray matter volume, these surface-based cortical measures focus on cortical folding. [7][8][9][10] Since they reflect different aspects of cortical architecture and stem from different genetic and cellular mechanisms in the brain, 11,12 they have the potential to provide a more complete picture of the pathophysiology involved in the cortical architecture of ASD than gray matter volume.…”