Development of a time-dependent model of the human pupil with adaptive receptor weighting

近年来，关于人类瞳孔直径的研究项目越来越多，取得了很大的进展，特别是将瞳孔直径作为生物标志物在跨学科应用领域的应用。例如，可以通过人类瞳孔大小的时间变化来评估人类的认知表现或检测各种生理状态，如疲劳、觉醒或深度抑郁。在照明技术中，瞳孔直径被认为是一个相关的话题，特别是在眼科光学仪器和面向应用的室内照明的背景下。瞳孔直径的大小会改变视网膜的照度，从而间接影响人的亮度感知或视敏度。固有光敏性视网膜神经节细胞（ipRGCs）的发现引起了对瞳孔传入控制路径和瞳孔光响应的深入研究。从神经生理学基础研究结果可以推断，光适应性瞳孔光反应是由视网膜外部光感受器和iprgc共同控制的。不同类型的光感受器控制瞳孔光响应的比例不仅与时间有关，而且还取决于光的各种性质和实验条件，如呈现时间、光的光谱组成、强度和适应时间。尽管在瞳孔光反射的神经生理学研究领域取得了突出的研究成果，但仍然缺乏一个能够预测人类瞳孔绝对直径在不同光谱下的时间变化的数学模型。现有的瞳孔模型主要采用V(k)加权量作为独立参数，未考虑iprgc的影响，导致使用LED光谱对瞳孔直径的预测误差较大。该项目涉及开发一种预测光致瞳孔直径的新模型，该模型通过使用人工神经网络（深度学习）可能首次能够预测与时间和光谱相关的人类瞳孔直径。我们对测试数据集的初步建模尝试表明，采用所提出的方法，可以从光度量重建瞳孔直径，平均绝对误差（MAE）小于0.1 mm。在这一延续提案中，我们计划进一步发展基于深度学习的方法，并在其他方面，开辟了将光诱导瞳孔行为的神经生理机制的最新发现整合到数学模型中的可能性。

Research projects concerning the human pupil diameter have intensified in recent years, achieving considerable progress, especially in the application of the pupil diameter as a biomarker in interdisciplinary fields of application. For example, it is possible to assess the human cognitive performance or to detect various physiological states such as fatigue, arousal, or deep depression via the temporal variation of the human pupil size. In lighting technology, the pupil diameter is considered a relevant topic, especially in the context of the ophthalmic optical apparatus and application-oriented indoor lighting. The size of the pupil diameter varies the retinal illuminance, which can indirectly affect the humans' brightness perception or visual acuity. The discovery of intrinsically photosensitive retinal ganglion cells (ipRGCs) has led to more intense research in the field of the afferent pupillary control path and the pupillary light response. From the results of neurophysiological fundamental research, it can be deduced that the photopically adapted pupillary light response is controlled by a combination of outer retinal photoreceptors and the ipRGCs. The proportion of different photoreceptor classes in controlling the pupillary light response is not only time-dependent, but also depends on various properties of light and experimental conditions such as presentation time, spectral composition of the light, intensity, and adaptation time. Despite outstanding research successes in the field of neurophysiological research on the pupillary light reflex, there is still a lack of a mathematical model that can predict the temporal variation of the absolute human pupil diameter in response of different light spectra. Existing pupil models mainly apply a V(𝜆)-weighted quantity as an independent parameter and do not integrate the influence of the ipRGCs, which can lead to significant prediction errors of the pupil diameter when using LED spectra. This project is concerned with the development of a new model for predicting light-induced pupil diameter, which through the use of artificial neural networks (Deep Learning) might for the first time be able to predict the temporal and spectral-dependent human pupil diameter. Our preliminary modeling attempts on test data sets have clarified that with the proposed methodology, the temporal pupil diameter can be reconstructed from photometric quantities with a mean absolute error (MAE) of less than 0.1 mm. In this continuation proposal, we plan to develop the deep learning-based approach further and, among other things, open up the possibility to integrate the latest findings on the neurophysiological mechanism of light-induced pupil behavior into a mathematical model.