Lee Hong-Hsi, Novikov Dmitry S, Fieremans Els, Huang Susie Y
Radiology, Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, Massachusetts, USA.
Harvard Medical School, Boston, Massachusetts, USA.
Magn Reson Med. 2025 Mar;93(3):1329-1347. doi: 10.1002/mrm.30335. Epub 2024 Oct 29.
The nonmonotonic dependence of diffusion kurtosis on diffusion time has been observed in biological tissues, yet its relation to membrane integrity and cellular geometry remains to be clarified. Here we establish and explain the characteristic asymmetric shape of the kurtosis peak. We also derive the relation between the peak time , when kurtosis reaches its maximum, and tissue parameters.
The peak shape and its position qualitatively follow from the adiabatic extension of the Kärger model onto the case of intra-cellular diffusivity time-dependence. This intuition is corroborated by the effective medium theory-based calculation, as well as by Monte Carlo simulations of diffusion and exchange in randomly and densely packed spheres for various values of permeability, cell fractions and sizes, and intrinsic diffusivity.
We establish that is proportional to the geometric mean of two characteristic time scales: extra-cellular correlation time (determined by cell size) and intra-cellular residence time (determined by membrane permeability). When exchange is barrier-limited, the peak shape approaches a universal scaling form determined by the ratio .
Numerical simulations and theory provide an interpretation of a specific feature of kurtosis time-dependence, offering a potential biomarker for in vivo evaluation of pathology by disentangling the functional (permeability) and structural (cell size) integrity in tissues. This is relevant as the time-dependent diffusion cumulants are sensitive to pathological changes in membrane integrity and cellular structure in diseases, such as ischemic stroke, tumors, and Alzheimer's disease.
在生物组织中已观察到扩散峰度对扩散时间的非单调依赖性，但其与膜完整性和细胞几何形状的关系仍有待阐明。在此，我们建立并解释峰度峰值的特征不对称形状。我们还推导了峰度达到最大值时的峰值时间与组织参数之间的关系。
峰值形状及其位置定性地源于将卡尔格模型绝热扩展到细胞内扩散率随时间变化的情况。基于有效介质理论的计算以及对各种渗透率、细胞分数和大小以及固有扩散率值的随机密集堆积球体中的扩散和交换进行的蒙特卡罗模拟证实了这种直觉。
我们确定峰值时间与两个特征时间尺度的几何平均值成正比：细胞外相关时间（由细胞大小决定）和细胞内停留时间（由膜渗透率决定）。当交换受屏障限制时，峰值形状接近由该比率决定的通用标度形式。
数值模拟和理论为峰度时间依赖性的一个特定特征提供了解释，通过区分组织中的功能（渗透率）和结构（细胞大小）完整性，为体内病理学评估提供了一种潜在的生物标志物。这是相关的，因为随时间变化的扩散累积量对诸如缺血性中风、肿瘤和阿尔茨海默病等疾病中膜完整性和细胞结构的病理变化敏感。
