标题： 通过兴奋性适应控制与生酮饮食相关的神经元种群的癫痫样动力学 显示英文标题

标题： Control of seizure-like dynamics in neuronal populations with excitability adaptation related to ketogenic diet

摘要： 我们考虑一个异质的、全局耦合的兴奋性二次积分-发放神经元种群，其兴奋性适应是由于与生酮饮食相关的代谢反馈，生酮饮食是癫痫的一种治疗方法。 在下一代神经质量模型框架下导出的三维平均场系统的分岔分析使我们能够解释这些情景，并提出控制策略，以实现神经生理学上期望的非同步状态与具有集体振荡的同步、癫痫样状态之间的转换。 我们揭示了同步开始的两种定性不同的情景。 对于较弱的耦合，从尖点点开始，在低活动性和高活动性非同步状态之间展开双稳态区域，集体振荡通过超临界霍普夫分岔出现。 对于较强的耦合，发现七个共维二阶分岔点，包括布格丹诺夫-泰肯斯点和广义霍普夫点的对，使得低活动性和高活动性非同步状态都经历到集体振荡的转变，在亚临界霍普夫分岔附近观察到滞后和跳跃行为。 我们展示了三种在非同步和同步状态之间切换的控制机制，涉及三磷酸腺苷（ATP）生成速率的参数扰动、外部刺激电流或脉冲式ATP冲击，并指出滞后情景的潜在治疗优势。 显示英文摘要

摘要： We consider a heterogeneous, globally coupled population of excitatory quadratic integrate-and-fire neurons with excitability adaptation due to a metabolic feedback associated with ketogenic diet, a form of therapy for epilepsy. Bifurcation analysis of a three-dimensional mean-field system derived in the framework of next-generation neural mass models allows us to explain the scenarios and suggest control strategies for the transitions between the neurophysiologically desired asynchronous states and the synchronous, seizure-like states featuring collective oscillations. We reveal two qualitatively different scenarios for the onset of synchrony. For weaker couplings, a bistability region between the lower- and the higher-activity asynchronous states unfolds from the cusp point, and the collective oscillations emerge via a supercritical Hopf bifurcation. For stronger couplings, one finds seven co-dimension two bifurcation points, including pairs of Bogdanov-Takens and generalized Hopf points, such that both lower- and higher-activity asynchronous states undergo transitions to collective oscillations, with hysteresis and jump-like behavior observed in vicinity of subcritical Hopf bifurcations. We demonstrate three control mechanisms for switching between asynchronous and synchronous states, involving parametric perturbation of the adenosine triphosphate (ATP) production rate, external stimulation currents, or pulse-like ATP shocks, and indicate a potential therapeutic advantage of hysteretic scenarios.