Fractal geometry provides a method of analyzing natural and especially biological morphologies. To investigate the relationship between the complexity measure, which is indexed as fractal dimensionality (FD), and the traditional Euclidean metrics, such as the volume and thickness, of the brain in older age, we analyzed 483 MRI scans of 161 community-dwelling, nondemented individuals aged 70-90 years at the baseline and their 2-year and 6-year follow-ups. We quantified changes in neuroimaging metrics in cortical lobes and subcortical structures and investigated the effects of age, sex, hemisphere, and education on FD. We also analyzed the mediating effects of these metrics for further investigation. FD showed significant age-related decline in all structures, and its trajectory was best modeled quadratically in the bilateral frontal, parietal, and occipital lobes, as well as in the bilateral caudate, putamen, hippocampus, amygdala, and accumbens. FD showed specific mediating effects on aging and cognitive decline in some regions. Our findings suggest that FD is reliable yet shows a different pattern of decline compared with volumetric measures.

中文翻译：

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社区老年个体结构复杂性和体积测量的不同纵向变化

分形几何提供了一种分析自然形态，尤其是生物形态的方法。为了研究复杂性度量（索引为分形维数 (FD)）与传统欧几里德度量（例如老年大脑的体积和厚度）之间的关系，我们分析了 161 个社区住宅的 483 次 MRI 扫描， 70-90 岁的非痴呆个体在基线和 2 年和 6 年的随访中。我们量化了皮层叶和皮层下结构中神经影像指标的变化，并研究了年龄、性别、半球和教育对 FD 的影响。我们还分析了这些指标的中介效应以供进一步调查。FD 在所有结构中都显示出与年龄相关的显着下降，其轨迹最好在双侧额叶、顶叶、和枕叶，以及双侧尾状核、壳核、海马、杏仁核和伏隔核。FD 在某些地区对衰老和认知能力下降表现出特定的中介作用。我们的研究结果表明，与体积测量相比，FD 是可靠的，但显示出不同的下降模式。