Understanding the connection between different stimuli and the brain response represents a complex research area. However, the use of mathematical models for this purpose is relatively unexplored. The present study investigates the effects of three different auditory stimuli on cerebral biopotentials by means of mathematical functions. The effects of acoustic stimuli (S1, S2, and S3) on cerebral activity were evaluated by electroencephalographic (EEG) recording on 21 subjects for 20 minutes of stimulation, with a 5-minute period of silence before and after stimulation. For the construction of the mathematical models used for the study of the EEG rhythms, we used the Box-Jenkins methodology. Characteristic mathematical models were obtained for the main frequency bands and were expressed by 2 constant functions, 8 first-degree functions, a second-degree function, a fourth-degree function, 6 recursive functions, and 4 periodic functions. The values obtained for the variance estimator are low, demonstrating that the obtained models are correct. The resulting mathematical models allow us to objectively compare the EEG response to the three stimuli, both between the stimuli itself and between each stimulus and the period before stimulation.

中文翻译：

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特定听觉刺激下大脑活动的数学建模

了解不同刺激与大脑反应之间的联系是一个复杂的研究领域。然而，为此目的使用数学模型的情况相对较少。本研究通过数学函数研究了三种不同的听觉刺激对大脑生物电势的影响。声刺激（S1、S2 和 S3）对大脑活动的影响通过脑电图 (EEG) 记录对 21 名受试者进行 20 分钟的刺激进行评估，刺激前后有 5 分钟的沉默期。为了构建用于研究 EEG 节律的数学模型，我们使用了 Box-Jenkins 方法。获得了主要频段的特征数学模型，并用2个常数函数、8个一阶函数、一个二阶函数、一个四阶函数、6 个递归函数和 4 个周期函数。方差估计器获得的值很低，表明获得的模型是正确的。由此产生的数学模型使我们能够客观地比较 EEG 对三种刺激的反应，包括刺激本身之间以及每个刺激之间和刺激前的时期。