Poster No:
1619
Submission Type:
Abstract Submission
Authors:
Amy Romanello1, Stephan Krohn1, Nina von Schwanenflug1, Jerod Rasmussen2, Claudia Buss1, Sofie Valk3, Christopher Madan4, Carsten Finke1
Institutions:
1Charité - Universitätsmedizin Berlin, Berlin, Berlin, 2University of California, Irvine, CA, 3Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Saxony, 4University of Nottingham, Notthingham, Nottinghamshire
First Author:
Amy Romanello
Charité - Universitätsmedizin Berlin
Berlin, Berlin
Co-Author(s):
Stephan Krohn
Charité - Universitätsmedizin Berlin
Berlin, Berlin
Claudia Buss
Charité - Universitätsmedizin Berlin
Berlin, Berlin
Sofie Valk
Max Planck Institute for Human Cognitive and Brain Sciences
Leipzig, Saxony
Carsten Finke
Charité - Universitätsmedizin Berlin
Berlin, Berlin
Introduction:
The neonatal period constitutes a critical phase of human brain development. Recently, we have shown that this period is characterized by a rapid formation of brain shape beyond known changes in brain size (Krohn et al., 2023). Therein, brain shape was quantified as fractal dimensionality (FD) (Mandelbrot, 1967) – a geometrical measure of structural complexity that is estimated from the scaling properties of a 3D segmentation mask over different voxel sizes (Krohn et al., 2019). In a large dataset of structural neuroimaging data from human newborns (Edwards et al., 2022), we observed a highly consistent spatial pattern of age-FD associations: While the FD of cortical gray matter (GM) systematically increased with infant age, the FD of white matter (WM) consistently decreased with age. This GM-WM dichotomy was observed both cross-sectionally and longitudinally and replicated in an independent validation dataset. However, the reason for these tissue-specific effect directions remains unknown. Empirically, we observed a strong link between FD and the ratio of surface voxels to all voxels of a structure (SVR). Therefore, we here built upon the theoretical framework of fractal geometry and conducted a simulation study to help explain the tissue-specific empirical age effects.
Methods:
According to the common notion of Euclidean geometry, a plane is characterized by a dimension of 2, while a cube is attributed with a dimension of 3. However, Mandelbrot and others have shown that these whole-integer dimensions are only special cases of a more general framework (Cannon & Mandelbrot, 1984) and that many theoretical and real-world objects are characterized by a dimension 2≤D≤3 – a fractal dimension (from Latin: fractus, fragmented, irregular). Accordingly, we run a simulation that starts from a Euclidean plane (theoretical FD=2) and slowly 'grows' into a Euclidean cube (theoretical FD=3). To this end, we construct a binary matrix (100x100x100 voxels) of zeros into which we insert a plane of ones (100x100 voxels). We then index all voxels that are on the surface of the simulated object and randomly choose one surface voxel as the center of a 5x5x5 cube that we set to 1. We then repeat this process over many iterations, gradually filling the matrix with ones until we arrive at a volume of all ones (i.e., a cube). For each iteration, we compute the FD of the simulated object using the dilation algorithm of the calcFD toolbox (Madan & Kensinger, 2016) with default spatial scales (as in the empirical analyses). Furthermore, we compute the SVR as the sum of surface voxels over the sum of all voxels of the simulated object for every iteration.
Results:
We first confirm the theoretical extrema of FD: a plane embedded in an empty cube has an FD of exactly 2, while the filled cube has an FD of exactly 3. Over 100 runs of 30,000 iterations each, we find a highly consistent, inverse relationship between FD and SVR (r = -0.99, p = 0). As the plane becomes more cube-like, we observe a monotonically increasing trend in FD (τ=0.99, Z=5.50, p=2x10-8) and a monotonically decreasing trend in SVR (τ=-0.99, Z=-4.66, p=1.6x10-6). For both FD and SVR, these trends were better fit by logarithmic rather than linear functions (FD: AIC-log= -162127.4, AIC-lin= -72678.2; SVR: AIC-log= -167533.9, AIC-lin= -70346.1). Overall, these results confirm that bidirectional changes in FD over time are plausible and depend on the Euclidean dimensions by which an object's growth is bounded.
Conclusions:
These findings offer a principled explanation of tissue-specific age-FD effects in human brain development: cortical GM starts out as a more 'plane-like' structure and gradually develops into a more 'cube-like' structure, while the opposite is true for WM. Taken together, this suggests that our empirical FD-age effects are divergent because GM and WM have different trajectories of geometric development, respectively captured as increases and decreases in FD over time.
Lifespan Development:
Normal Brain Development: Fetus to Adolescence
Modeling and Analysis Methods:
Methods Development 2
Other Methods 1
Keywords:
Cortex
Development
Modeling
White Matter
Other - Simulation; Fractal dimensionality; Algorithm design
1|2Indicates the priority used for review
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Healthy subjects only or patients (note that patient studies may also involve healthy subjects):
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Was this research conducted in the United States?
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Were any human subjects research approved by the relevant Institutional Review Board or ethics panel?
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Other, Please specify
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Simulation study
Provide references using APA citation style.
Cannon, J.W. (1984). The Fractal Geometry of Nature. The American Mathematical Monthly, 91(9), 594.
Edwards, A.D. (2022). The Developing Human Connectome Project Neonatal Data Release. Frontiers in Neuroscience, 16, 886772.
Krohn, S. (2019). Evaluation of the 3D fractal dimension as a marker of structural brain complexity in multiple‐acquisition MRI. Human Brain Mapping, 40(11), 3299–3320.
Krohn, S. (2023). The formation of brain shape in human newborns [Preprint]. bioRxiv (neuroscience).
Madan, C.R. (2016). Cortical complexity as a measure of age-related brain atrophy. NeuroImage, 134, 617–629.
Mandelbrot, B. (1967). How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science, 156(3775), 636–638.
No