An Extensive-Form Game Paradigm for Visual Field Testing via Deep Reinforcement Learning

Glaucoma is the leading cause of irreversible but preventable blindness worldwide, and visual field testing is an important tool for its diagnosis and monitoring. Testing using standard visual field thresholding procedures is time-consuming, and prolonged test duration leads to patient fatigue and decreased test reliability. Different visual field testing algorithms have been developed to shorten testing time while maintaining accuracy. However, the performance of these algorithms depends heavily on prior knowledge and manually crafted rules that determine the intensity of each light stimulus as well as the termination criteria, which is suboptimal. We leverage deep reinforcement learning to find improved decision strategies for visual field testing. In our proposed algorithms, multiple intelligent agents are employed to interact with the patient in an extensive-form game fashion, with each agent controlling the test on one of the testing locations in the patient's visual field. Through training, each agent learns an optimized policy that determines the intensities of light stimuli and the termination criteria, which minimizes the error in sensitivity estimation and test duration at the same time. In simulation experiments, we compare the performance of our algorithms against baseline visual field testing algorithms and show that our algorithms achieve a better trade-off between estimation accuracy and test duration. By retaining testing accuracy with reduced test duration, our algorithms improve test reliability, clinic efficiency, and patient satisfaction, and translationally affect clinical outcomes.

I. Introduction

Eighty million people worldwide are estimated to have glaucoma, and more than 111 million people are expected to be affected by 2040 [1]. Visual field testing is a critical tool routinely used by ophthalmologists to determine the visual function of the eye to diagnose and monitor eye diseases such as glaucoma, and helpful for identifying defects with retinal and neuro-ophthalmic disorders, such as optic nerve head diseases, brain tumors, and other visual pathway disorders. Different eye diseases have characteristic patterns of visual field loss. For standard visual field testing, patients place their heads within a Ganzfield bowl that presents stimuli of varying contrasts at standardized locations throughout the bowl in different degrees of field of vision. Patients fix their gaze at the center of the dome so the peripheral and central visual field is tested. Patients respond, typically by pressing a button or handheld clicker, to indicate whether or not a stimulus is observed as testing progresses. In its first formal iteration, dynamic Goldmann perimetry, visual field testing was performed manually with hand-held stimuli of varying sizes. Since then, static automated algorithms have emerged and are predominantly used over manual methods due to their standardization, convenience, and reproducible results. The first iteration of this was developed almost 50 years ago and was referred to as standard automated perimetry (SAP), which resulted in testing times of approximately 15–20 minutes per eye, depending on the testing strategy and the degrees of visual field tested. Proprietary algorithms that have improved upon SAP, such as the Swedish Interactive Testing Algorithm (SITA), used in the commercial Humphrey Field Analyzer (HFA),¹

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reduce testing time while maintaining relative accuracy and are predominantly used today.