Köpf M, Corinth C, Haferkamp O, Nonnenmacher T F
Department of Pathology, University of Ulm, Germany.
Biophys J. 1996 Jun;70(6):2950-8. doi: 10.1016/S0006-3495(96)79865-X.
This article deals with the characterization of biological tissues and their pathological alterations. For this purpose, diffusion is measured by NMR in the fringe field of a large superconductor with a field gradient of 50 T/m, which is rather homogenous and stable. It is due to the unprecedented properties of the gradient that we are able not only to determine the usual diffusion coefficient, but also to observe the pronounced Non-Debye feature of the relaxation function due to cellular structure. The dynamics of the probability density follow a stretched exponential or Kohlrausch-Williams-Watts function. In the long time limit the Fourier transform of the probability density follows a long-tail Lévy function, whose asymptotic is related to the fractal dimension of the underlying cellular structure. Some of the properties of Lévy walk statistics are discussed and its potential importance in understanding certain biophysical phenomena like diffusion processes in biological tissues are pointed out. We present and discuss for the first time NMR data giving evidence for Lévy processes that capture the essential features of the observed power law (scaling) dynamics of water diffusion in fresh tissue specimens: carcinomas, fibrous mastopathies, adipose and liver tissues.
本文论述生物组织的特征及其病理改变。为此，利用核磁共振在一个场梯度为50 T/m的大型超导体边缘场中测量扩散，该边缘场相当均匀且稳定。由于该梯度具有前所未有的特性，我们不仅能够确定通常的扩散系数，还能观察到由于细胞结构导致的弛豫函数明显的非德拜特征。概率密度的动力学遵循拉伸指数或科尔劳施 - 威廉姆斯 - 瓦特函数。在长时间极限下，概率密度的傅里叶变换遵循长尾列维函数，其渐近线与底层细胞结构的分形维数相关。讨论了列维行走统计的一些性质，并指出其在理解某些生物物理现象（如生物组织中的扩散过程）方面的潜在重要性。我们首次展示并讨论了核磁共振数据，这些数据为列维过程提供了证据，该过程捕捉了新鲜组织标本（癌组织、纤维性乳腺病、脂肪组织和肝脏组织）中观察到的水扩散幂律（标度）动力学的基本特征。
