论文标题
癫痫发作的癫痫发作:神经系统中的扩散与稳定性
Fighting seizures with seizures: diffusion and stability in neural systems
论文作者
论文摘要
癫痫活性是一种普遍存在且有害的病理生理学,原则上应屈服于(神经元)整体动力学的数学处理,因此对随机混乱进行了干预。癫痫发作可以被描述为神经活动与稳定动力学状态的偏差,即信号仅在有限范围内波动的偏离。在对神经活动的计算机治疗中,是了解大脑如何达到稳定性的重要工具,以及病理学如何导致癫痫发作和潜在的减轻不稳定性的策略,例如通过外部刺激。在这里,我们证明,当考虑到沿结构连接的神经元活性传播时,动态因果建模中使用的(神经元)方程将成为福克 - 普朗克形式主义。使用此广义状态方程的雅各布式,我们表明最初不稳定的系统可以通过降低扩散率(即分散神经元波动的连接性)来稳定。我们表明,对于容易发癫痫发作的神经系统,可以通过外部刺激实现这种减少。具体而言,我们表明应以这种刺激的方式应用这种刺激,以临时反映与受影响的大脑区域相邻的区域中的癫痫活性,从而“与癫痫发作作斗争”。我们使用基于从特发性全身性癫痫患者收集的功能性神经影像数据的模拟提供原理证明,其中我们成功地抑制了独特的子网络中的病理活性。我们的希望是,这项技术可以构成能够以非侵入性抑制甚至防止癫痫发作的实时监控和干预设备的基础。
Seizure activity is a ubiquitous and pernicious pathophysiology that, in principle, should yield to mathematical treatments of (neuronal) ensemble dynamics - and therefore interventions on stochastic chaos. A seizure can be characterised as a deviation of neural activity from a stable dynamical regime, i.e. one in which signals fluctuate only within a limited range. In silico treatments of neural activity are an important tool for understanding how the brain can achieve stability, as well as how pathology can lead to seizures and potential strategies for mitigating instabilities, e.g. via external stimulation. Here, we demonstrate that the (neuronal) state equation used in Dynamic Causal Modelling generalises to a Fokker-Planck formalism when propagation of neuronal activity along structural connections is considered. Using the Jacobian of this generalised state equation, we show that an initially unstable system can be rendered stable via a reduction in diffusivity (i.e., connectivity that disperses neuronal fluctuations). We show, for neural systems prone to epileptic seizures, that such a reduction can be achieved via external stimulation. Specifically, we show that this stimulation should be applied in such a way as to temporarily mirror epileptic activity in the areas adjoining an affected brain region - thus 'fighting seizures with seizures'. We offer proof of principle using simulations based on functional neuroimaging data collected from patients with idiopathic generalised epilepsy, in which we successfully suppress pathological activity in a distinct sub-network. Our hope is that this technique can form the basis for real-time monitoring and intervention devices that are capable of suppressing or even preventing seizures in a non-invasive manner.