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.
Highlights
The language of fractal geometry is concerned with representing the seemingly intractable aspects of form of biological objects and systems
A Mann-Whitney test indicated significant differences in Fractal Dimension (FD) between patients and controls in the left hippocampus (FD was lower in SCZ patients relative to healthy controls (HC), U = 56, p
Because our goal was to study FD outcome measures for all subcortical gray matter (GM) structures, we looked to see if there was a systematic relationship between the size of the structure and variability of FD output
Summary
The language of fractal geometry is concerned with representing the seemingly intractable aspects of form of biological objects and systems. We note that pure fractals such as the Sierpinski triangle in Fig 1 exhibit self-similarity, a scaling property that refers to invariance, or the conservation of certain statistical properties of the object’s form and structure, as the spatial scale increases (ad infinitum in the case of pure fractals). It means that when a portion of an object is magnified, the zoomed-in portion is perceived similar to the whole object (Fig 1A)
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