Consequently, the development of PPG simulation models is of paramount importance for investigating the influence of different physiological factors on PPG signals. Among the available cardiovascular system models, the dual windkessel model Goldwyn and Watt (1967) proposed by Goldwyn and Watt stands out as one of the most frequently utilized frameworks. This model, along with its equivalent circuit representation, is depicted in Figure 2, providing a visual and theoretical foundation for understanding the complex dynamics of the cardiovascular system as they relate to PPG signal generation. This study constructed a simulation design for Simulink based on this model and obtained 7 variable parameters as shown in Table 1.

By systematically modulating the aforementioned variable parameters, significant alterations were observed in both the simulated PPG waveforms and their corresponding frequency spectra. As illustrated in Figure 3, the morphological state of the PPG waveforms exhibited visually discernible variations. Furthermore, distinct differences were identified in the spectral peaks of the frequency domain representation, demonstrating the sensitivity of these spectral components to parameter variations.

Our analysis reveals that the frequency-domain information of the photoplethysmography (PPG) signal is predominantly characterized by its fundamental frequency and two harmonic frequency bands. Consequently, we derived multiple power-related features and ratio-based features from these three frequency bands as shown in Figure 4. The specific features and their corresponding variations in response to parameter changes during the simulation are comprehensively presented in Table 2. The computation of these features was performed through the following procedure: First, the average heart rate (HR) was obtained through preliminary data processing. Subsequently, Fast Fourier Transform (FFT) analysis was applied to the data segment. The power spectral density within the frequency bands of ±0.2 Hz centered at the fundamental HR frequency was identified as the Basic Frequency component (BF). Similarly, the power within ±0.2 Hz bands centered at twice and three times the HR frequency were designated as the First Harmonic Frequency (FHF) and Second Harmonic Frequency (SHF) components, respectively. The computational methodology for these ratio-based features is further detailed in Table 2.

The analysis demonstrates distinct patterns in frequency features corresponding to variations in hemodynamic parameters: (1) Increased peripheral vascular resistance leads to attenuation of the fundamental frequency while enhancing harmonic frequencies. (2) Elevated vascular compliance results in amplification of the first harmonic frequency, accompanied by attenuation of both the fundamental frequency and the second harmonic frequency. (3) Augmented blood flow inertia induces enhancement of both the fundamental frequency and the first harmonic frequency, with the latter exhibiting more pronounced amplification, while simultaneously causing attenuation of the second harmonic frequency. Furthermore, other physiological parameters also exert significant influences on these features.

This dataset is anchored in Ekman and Friesen (1971) theory of discrete emotions, which posits that emotions are distinct, universally identified mental states. In alignment with this theoretical framework and to ensure the selection of authentic and impactful emotion-inducing materials, our research team referred to authoritative emotion databases. Notably, we took cues from the DECAF database (Abadi et al., 2015) in curating a selection of video materials designed to elicit a variety of emotional responses. Our team has conducted extensive prior research to thoroughly assess and validate the efficacy of these selected materials in inducing the intended emotions during emotion induction experiments (Wang et al., 2022). The specific materials chosen for this study are detailed in Table 3, where each entry corresponds to a particular emotional state aimed to be induced.

The experimental protocol for this dataset was granted approval by the Medical Ethics Committee of the Department of Psychology and Behavioral Sciences at Zhejiang University, as evidenced by the ethical review document (Zhejiang University Psychological Ethics Review [2022] No. 059). A total of 192 students from Zhejiang University were initially recruited to partake in the study. Eligibility criteria for participants included having normal vision, hearing, and perception abilities, as well as being free from any physical or psychological conditions that could potentially influence emotional responses. Throughout the experimental process, stringent quality control measures were implemented. Regrettably, the dataset was compromised due to several factors: (1) instrumental operational errors resulted in the unsuccessful acquisition of 12 cases; (2) 4 cases were excluded due to participants’ personal reasons; and (3) preliminary quality assessment led to the elimination of 19 cases owing to suboptimal physiological signal acquisition. This data attrition, while regrettable, was necessary to maintain the integrity and reliability of the study. Consequently, the dataset was refined to include data and relevant information from 157 participants who met the criteria, comprising 96 females and 61 males.

The comprehensive experimental protocol for each participant was conducted in a dimly lit room, ensuring minimal interference from ambient light sources, with the exception of the computer display screen, as depicted in Figure 5. Prior to the commencement of the experiment, participants were provided with a comprehensive briefing on the experimental procedures and necessary precautions. They were required to sign an informed consent form, signifying their voluntary agreement to participate in the study. Subsequently, each participant was outfitted with a photoelectric sensor on their left index finger for the acquisition of PPG signals, as well as electrodes to capture additional physiological signals. The PPG signals were recorded using a physiological signal monitor (ePM-12M, Mindray, China), which operated at a sampling rate of 125 Hz. The video stimuli were presented on a computer screen positioned at a distance ranging from 0.5 to 1 m from the participant, allowing them to view the content from their most comfortable seated position. Throughout the experiment, each participant was exposed to a total of 8 distinct video materials designed to elicit various emotional responses. Upon completion of each video segment, participants were prompted to complete the Self-Assessment Manikin (SAM) Emotion Scale, followed by a brief respite. The sequence of video presentation and scale assessment was orchestrated by a specially designed experimental program, enabling participants to independently execute all steps of the experimental process until its conclusion.

PPG signals are among the most accessible physiological signals for collection; however, they are susceptible to various sources of noise and interference that can complicate the acquisition process. Despite the implementation of hardware-level denoising techniques, the integrity of PPG signals can still be compromised by factors such as respiration, bodily movement, and issues related to data transmission. To ensure the acquisition of high-fidelity PPG signals, it is imperative to employ additional processing measures. In the context of this study, all PPG recordings underwent a series of processing techniques aimed at enhancing signal quality.

Firstly, the 1–20 Hz bandpass filter was used to remove most of the noise and interference caused by breathing, body movements, and other factors, thereby focusing the signal on high-density information regions. Due to the presence of high-frequency disturbances, each PPG record y was smoothed by Formula 1 and the result was denoted as y ₁ , where x _i represented the sampling time of each point, i represented the sequence number of the data points, 3 ≤ i ≤ n -1, and n was the number of data points in the record. y 1 x 1 = y x 1 y 1 x 2 = y x 1 + y x 2 + y x 3 3 y 1 x i = y x i − 2 + y x i − 1 + y x i + y x i + 1 + y x i + 2 5 y 1 x n − 1 = y x n − 2 + y x n − 1 + y x n 3 y 1 x n = y x n (1)

Then, the method named “moving-pane” was used to identify fiducial points of each PPG record. This method created a pane with a specific width and moved it along the timeline of the PPG record. All maximum points in the pane and minimum points between every two maximum points were recorded during the movement and the maximum points that do not meet the following rules were excluded, as shown in Figure 6A: 1) The distance between this point P _i and P _i-1 less than 0.6s 2) The amplitude difference between this point p _i and T _i-1 less than 0.5 times the amplitude difference between P _i-1 and T _i-2 , or the amplitude difference between p _i and T _i-1 less than 0.5 times the amplitude difference between p _i+1 and T _i.

Following the application of the “moving-pane” method, a meticulous manual review was performed to identify and retain the extremum points within the PPG record, which correspond to the peaks and troughs that serve as the fiducial markers of the waveform. This process is crucial for the accurate characterization of the PPG signal’s morphology. Subsequently, to address the issue of baseline drift that can distort the PPG signal, the method illustrated in Figure 6B and encapsulated by Formula 2 was employed. This technique effectively removes the baseline wander, ensuring that the origin of all individual PPG waveforms is recalibrated to zero. This normalization is essential for the consistent analysis and comparison of PPG signals across different recordings. k = y x U − y x U ′ x U − x U ′ y ′ x i = y x i − k * x i − x U (2)

In the concluding phase of signal processing, the z-score normalization technique was applied to eliminate the variability in the scale of each PPG record. This standardization procedure ensures that all records are brought onto a common scale, facilitating a unified analysis. The aforementioned processing methodologies were executed using a combination of self-devised algorithms and the scipy package (Virtanen et al., 2020), which is a fundamental component of the Python ecosystem for scientific computing. Post-processing, each PPG record was meticulously segmented in accordance with the distinct emotional stimuli that served as the triggers. Specifically, the records were divided into segments every 20 s, with each segment annotated to reflect the predominant emotional state during that interval.

Following the preprocessing of PPG signals, the data were segmented according to different emotional stimuli protocols. The continuous recordings were subsequently divided into 20-s epochs, with each epoch being annotated with corresponding emotional labels. This segmentation procedure yielded a total of 2,474 epochs for low arousal states, 5,560 epochs for high arousal states, 3,229 epochs for low valence states, and 4,805 epochs for high valence states, thereby establishing a comprehensive dataset for emotional state classification.

For each 20-s epoch, nine frequency-domain features (as specified in Table 3) were extracted. To account for inter-individual variability and other potential confounding factors, feature normalization was performed using a z-score-like transformation according to Equation 3. This standardization procedure ensures comparability across different subjects while preserving the relative distribution characteristics of the extracted features. F r e m o v e = F e m o t i o n − F m e a n / F s t d (3)

Among them, for specific feature F and a certain subject S , F _mean and F _std were the average and standard deviation of feature F for all sections of subject S , F _emotion was the value of feature F before processing for a specific emotional section of subject S , and F _remove was the processed feature value.

The Mann Whitney U-test (Rosner and Grove, 1999), a non-parametric statistical method, serves as a robust tool for assessing significant differences between two independent datasets, especially when the data does not meet the assumptions of parametric tests. In this study, the U-test, facilitated by Python’s SciPy library (Virtanen et al., 2020), was employed to scrutinize the variability in the newly extracted PPG frequency-domain features across different emotional dimensions, specifically comparing the high and low arousal states, as well as the high and low valence states. The preliminary evaluation of the emotion-discriminative capability of the extracted PPG frequency-domain features was conducted through two complementary approaches: (1) statistical analysis using p-values derived from the two-tailed U-test, and (2) comparative examination of feature distribution patterns across different emotional states. This dual-method assessment framework provides robust evidence for evaluating the effectiveness of the proposed features in emotion differentiation.

Subsequently, based on the preliminary analysis, the identified emotion-discriminative features were utilized to construct a machine learning model for emotion recognition using Support Vector Machines (SVM). In this study, the SVM was implemented using the Scikit-learn algorithm package in Python (Fabian et al., 2011). To effectively partition the dataset, the train_test_split function from the Scikit-learn package was utilized, segregating the feature set into training and testing subsets with a ratio of 7:3. Given the modest size of the dataset, traditional cross-validation could potentially result in overfitting. Consequently, the study opted for a leave-one-point-out method for model training, a technique that iteratively excludes a single data point from the training process. This approach was iterated 100 times, ensuring a comprehensive assessment of the model’s performance (Ma et al., 2023). The Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC) curve was computed for each iteration. The median AUC value, derived from the 100 models, was adopted as the representative performance metric for the SVM model.

ROC curves (Rodellar-Biarge et al., 2015) were employed to evaluate and visualize the discriminatory power of the features in identifying distinct emotional states. The model’s predictive accuracy, the AUCs for the ROC curves, and the precision metric were computed to quantitatively assess the model’s efficacy in recognizing emotions.

To further validate the effectiveness of the extracted PPG frequency-domain features while maintaining the exclusive use of PPG as the sole physiological signal, we additionally extracted two well-established feature sets that have been extensively validated by numerous researchers for emotion recognition: pulse rate variability (PRV) features and PPG morphological features, as detailed in Table 4. Following the same analytical protocol applied to the frequency-domain features, these comparative features underwent preliminary screening before being utilized to construct SVM-based machine learning models, thereby obtaining their respective emotion recognition accuracy metrics for systematic comparison. Furthermore, to investigate the underlying relationships among different feature sets, we conducted correlation analysis between the PPG frequency-domain features and the two additional feature groups. This analysis facilitated the development of an integrated feature set through optimal feature fusion, potentially enhancing the overall emotion recognition performance.

To ascertain the efficacy and generalizability of the methodologies and features delineated in this research, an expanded dataset of PPG recordings was sourced from the DEAP database, which is publicly accessible. The DEAP dataset (Koelstra et al., 2012) serves as a multimodal repository for affective analysis, encompassing physiological signal recordings from 32 participants exposed to 40 distinct video stimuli. For the purpose of this analysis, PPG recordings were exclusively selected. Consistent with the methodology applied to the aforementioned dataset, participants were prompted to rate the arousal, valence, and additional pertinent attributes of each video stimulus. The models established in the preceding section were then applied to discern the emotional states associated with the DEAP dataset entries. Subsequently, the derived accuracy metrics were utilized to assess the models’ performance in emotion recognition and their adaptability across different datasets.