癫痫是一种慢性神经系统疾病，主要特征是大脑神经元异常猝发性过度同步放电，其病理机制复杂且尚未完全理解。局灶性癫痫是癫痫的一种类型，起源于局部脑区的异常放电，由于其治疗的耐药性，往往最优的合理治疗思路是寻找到正确的致痫区（epileptogenic zone, EZ），而后进行有损切除。以往的研究聚焦于如何定位到正确的 EZ，并进行切除，而没有在得知正确的 EZ 后，探寻无损治理的思路方法。本文利用复杂网络理论探究了网络特性对于癫痫发作时传播和同步的影响，并用真实小鼠的脑连接图谱进行模拟验证，尝试提出了利用部分网络耦合强度的改变来抑制癫痫发作的新思路。

本文首先利用Epileptor模型构建慢变量耦合的动力学网络，其包含模拟SLE（seizure like event）致痫神经元和NS（normal state）正常神经元的两种节点。针对模拟的放电图，我们提出了全局癫痫发作指数，包括同步指数和能量指数，以评估系统的癫痫发作程度和强度。

然后，我们对三种人工复杂网络进行模拟：分别是随机网络、小世界网络和无标度网络，重点关注致痫节点数量、分布和网络耦合强度。我们观察了网络上异质节点分布的影响，以及在SLE神经元在集聚状态下不断增加耦合强度的结果。接着，我们分析了网络结构对于癫痫发作传播和同步的影响，探讨了致痫因素流动对癫痫发作的关键性作用。

最后，我们在真实的 Allen 小鼠网络上模拟讨论了非局部耦合出现的嵌合体状态（chimera）；随后我们验证了小鼠局灶性癫痫的真实发作传播的情况，在分析该脑图谱的网络拓扑结构后，提高部分网络耦合强度，模拟结果发现可以有效抑制全局的癫痫发作。

综上所述，本研究在癫痫动力学领域进行了网络分析与研究，分析并讨论了异质性网络中的传播与同步, 同时为理解癫痫发作机制和无损治疗提供了新的想法与见解。

本研究的创新性内容包括：1. 提出适用于全局评估癫痫发作的目标指数；2. 探究了网络结构与系统癫痫发作的关系；3. 利用Allen小鼠连接图谱验证了耦合强度无损控制癫痫的可能性。

Epilepsy is a chronic neurological disease, which is mainly characterized by abnormal bursts of excessive synchronous discharge of brain neurons. Its pathological mechanism is complex and not yet fully understood. Focal epilepsy is a type of epilepsy that originates from abnormal discharges in local brain areas. Due to its drug resistance, the best and most reasonable treatment idea is to find the correct epileptogenic zone (EZ). Then perform a destructive resection. Previous research focused on how to locate the correct EZ and perform resection, but did not explore ideas and methods for non-destructive treatment after knowing the correct EZ. This article uses complex network theory to explore the impact of network characteristics on the propagation and synchronization of epileptic seizures, and conducts simulation verification using the brain connection map of real mice. It attempts to propose a new idea of using changes in the coupling strength of some networks to suppress epileptic seizures.

This article first uses the Epileptor model to construct a slow variable coupling dynamic network, which contains two nodes that simulate SLE (seizure like event) epileptogenic neurons and NS (normal state) normal neurons. For the simulated discharge patterns, we propose a global seizure index, including synchronization index and energy index, to evaluate the degree and intensity of seizures in the system.
  
Next, we simulate three types of artificial complex networks: random networks, small-world networks, and scale-free networks, focusing on the number, distribution, and network coupling strength of epileptic nodes. We observe the impact of heterogeneous node distribution in the network and the results of continuously increasing coupling strength among clustered SLE neurons. Then, we analyze the influence of network structure on seizure propagation and synchronization, exploring the critical role of epileptogenic factor flow in seizure occurrences.
  
Finally, we simulate and discuss the emergence of chimera states due to non-local coupling in the real Allen mouse network. Subsequently, we validate the real propagation of focal epilepsy in mice. After analyzing the network topology of this brain atlas, we increase the coupling strength of specific network parts. Simulation results reveal that this can effectively suppress global seizures.
  
In summary, this study conducts network analysis and research in the field of epilepsy dynamics, analyzing and discussing the propagation and synchronization in heterogeneous networks. It also provides new ideas and insights for understanding seizure mechanisms and non-destructive treatments.
  
The innovative contributions of this study include: 1. Proposing target indices suitable for global seizure assessment; 2. Exploring the relationship between network structure and systemic seizures; 3. Verifying the possibility of non-destructive seizure control through coupling strength using the Allen mouse connectivity atlas.