Background: Mental and physical health are both important for overall health. Mental health includes emotional, psychological, and social well-being; however, it is often difficult to monitor remotely. The objective of this scoping review is to investigate studies that focus on mental health and stress detection and monitoring using PPG-based wearable sensors. Methods: A literature review for this scoping review was conducted using the PRISMA (Preferred Reporting Items for the Systematic Reviews and Meta-analyses) framework. A total of 290 studies were found in five medical databases (PubMed, Medline, Embase, CINAHL, and Web of Science). Studies were deemed eligible if non-invasive PPG-based wearables were worn on the wrist or ear to measure vital signs of the heart (heart rate, pulse transit time, pulse waves, blood pressure, and blood volume pressure) and analyzed the data qualitatively. Results: Twenty-three studies met the inclusion criteria, with four real-life studies, eighteen clinical studies, and one joint clinical and real-life study. Out of the twenty-three studies, seventeen were published as journal-based articles, and six were conference papers with full texts. Because most of the articles were concerned with physiological and psychological stress, we decided to only include those that focused on stress. In twelve of the twenty articles, a PPG-based sensor alone was used to monitor stress, while in the remaining eight papers, a PPG sensor was used in combination with other sensors. Conclusion: The growing demand for wearable devices for mental health monitoring is evident. However, there is still a significant amount of research required before wearable devices can be used easily and effectively for such monitoring. Although the results of this review indicate that mental health monitoring and stress detection using PPG is possible, there are still many limitations within the current literature, such as a lack of large and diverse studies and ground-truth methods, that need to be addressed before wearable devices can be globally useful to patients.

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<abstract><p>This paper proposes a new very simply explicitly invertible function to approximate the standard normal cumulative distribution function (CDF). The new function was fit to the standard normal CDF using both MATLAB's Global Optimization Toolbox and the BARON software package. The results of three separate fits are presented in this paper. Each fit was performed across the range $ 0 \leq z \leq 7 $ and achieved a maximum absolute error (MAE) superior to the best MAE reported for previously published very simply explicitly invertible approximations of the standard normal CDF. The best MAE reported from this study is 2.73e–05, which is nearly a factor of five better than the best MAE reported for other published very simply explicitly invertible approximations.</p></abstract>

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