Suckling John, Wink Alle Meije, Bernard Frederic A, Barnes Anna, Bullmore Edward
Brain Mapping Unit, University of Cambridge, Department of Psychiatry, Addenbrooke's Hospital, Cambridge CB2 0QQ, UK.
J Neurosci Methods. 2008 Sep 30;174(2):292-300. doi: 10.1016/j.jneumeth.2008.06.037. Epub 2008 Jul 23.
The intuitive notion that a healthy organism is characterised by regular, homeostatic function has been challenged by observations that a loss of complexity is, in fact, indicative of ill-health. Monofractals succinctly describe complex processes and are controlled by a single time-invariant scaling exponent, H, simply related to the fractal dimension. Previous analyses of resting fMRI time-series demonstrated that ageing and scopolamine administration were both associated with increases in H and that faster response in a prior encoding task was also associated with increased H. We revisit this experiment with a novel, multifractal approach in which fractal dynamics are assumed to be non-stationary and defined by a spectrum of local singularity exponents. Parameterisation of this spectrum was capable of refracting the effects of age, scopolamine and task performance as well as a refining a description of the associated signal changes. Using the same imaging data, we also explored turbulence as a possible mechanism underlying multifractal dynamics. Evidence is provided that Carstaing's model of turbulent information flow from high to low scales has only limited validity, and that scale invariance of energy dissipation is better explained by critical-phase phenomena, supporting the proposition that the brain maintains a state of self-organised criticality.
健康机体以规律、稳态功能为特征这一直观概念受到了挑战，因为观察结果表明，复杂性的丧失实际上预示着健康不佳。单分形简洁地描述了复杂过程，并由单个与时间无关的标度指数H控制，H与分形维数简单相关。先前对静息态功能磁共振成像时间序列的分析表明，衰老和给予东莨菪碱均与H增加有关，并且在先前编码任务中更快的反应也与H增加有关。我们用一种新颖的多重分形方法重新审视了这个实验，在这种方法中，分形动力学被假定为非平稳的，并由一系列局部奇异性指数定义。该谱的参数化能够反映年龄、东莨菪碱和任务表现的影响，以及完善对相关信号变化的描述。使用相同的成像数据，我们还探讨了湍流作为多重分形动力学潜在机制的可能性。有证据表明，卡斯廷从高尺度到低尺度的湍流信息流模型仅具有有限的有效性，能量耗散的尺度不变性更好地由临界相现象解释，这支持了大脑维持自组织临界状态的观点。
