交联葡聚糖凝胶中反常扩散的Hausdorff分形导数扩散成像模型

Hausdorff Fractal Derivative Diffusion Imaging Model for Anomalous Diffusion in Sephadex Gel

本文通过考虑复杂介质的分形特征,并结合交联葡聚糖凝胶的磁共振信号,给出了基于Hausdorff分形导数的磁共振信号衰减模型.该模型包含三个参数,其中分形导数的阶数可以表征介质的分形特性,扩散系数可以表征介质的复杂程度.通过交联葡聚糖凝胶的磁共振实验验证了模型的有效性.结果表明,模型参数的大小与介质内部结构和外部结构有关.与传统的模型相比,基于分形导数的模型参数更符合介质的物理特性,可以准确地描述水分子在复杂介质中的反常扩散,并用于区分不同介质结构特征.

In this paper, the Hausdorff fractal derivative diffusion imaging model is established by considering the fractal characteristics of complex media and combining the magnetic resonance signals of Sephadex gel. The model contains three parameters, among which the fractal derivative orders can characterize the fractal properties of the media and the diffusion coefficient can characterize the complexity of the media. The effectiveness of the proposed model is validated by the magnetic resonance experiments on Sephadex gel. The results show that parameters of the model are related to the internal and external structure of the Sephadex gel. Compared with the traditional model, parameters in this Hausdorff fractal derivative model are more consistent with the physical properties of the media and can be used to distinguish the structural characteristics of different media. This model can also accurately describe the anomalous diffusion of water molecules in complex media.