Integrated brain and body mechanisms underlying acute stress and trauma-related vulnerability

Abstract

Dysregulated stress response has been linked to multiple health issues, yet the brain and body dynamics of acute stress remain poorly understood. Developing interpretable models is imperative in understanding this complex interplay. The present study sought to decode acute stress response by using a systematic data-driven and experimental approach to provide insights into its underlying mechanisms, with implications for accurate prediction, precision intervention, and trauma-related phenotyping. A total of 144 healthy adults (aged 18 – 44 years; 63 men) completed the Montreal Imaging Stress Task. Multimodal electrophysiological signals were recorded throughout the experiment. The interpretable predictive model achieved an excellent test accuracy of 85.37% and revealed several key stress-related features, such as shorter inspiration duration. Causal discovery analyses revealed stress-induced disruption of bottom-up inspiratory influences on frontal neural activity. Deep breathing interventions were found to increase inspiration duration and reduce perceived stress levels. The cluster analysis identified three phenotypes. The stress-vulnerable phenotype, in particular, was found to be more susceptible to stress and have greater exposure to lifetime trauma. These findings advance our understanding of the brain and body psychophysiology causal dynamics of acute stress, identify actionable targets for precision interventions, and reveal distinct phenotypes that may inform individualised stress profiles.

1. Introduction

In the dynamic world that we live in, we are constantly engulfed by an overwhelming array of challenges. The physiological, psychological, and behavioural reactivity to these challenges, known as the stress response, allows us to navigate and thrive in this complex environment (Roberts and Karatsoreos, 2021). Stress response is an essential adaptive response that helps mobilise energy in preparation for the body to respond to stressors while maintaining homeostasis (Russell and Lightman, 2019). This response is a complex psychophysiological phenomenon, involving multiple biological systems across the brain and body, manifesting as observable transient changes in neural activity, cardiovascular functioning, hormonal levels, respiratory patterns, and other bodily functions (Ulrich-Lai and Herman, 2009; Chu et al., 2024). Notably, a dysregulated stress response system is one of the most significant growing healthcare problems in our modern society, threatening both our physical and mental health (Turner et al., 2020; Lee et al., 2025). In particular, converging evidence indicates that early-life adversity and recent major life stressors are major factors implicated in enduring alterations in the stress regulatory system, thereby increasing vulnerability to psychopathology later in life (Lee et al., 2025; Jiang et al., 2025). This is consistent with the notion of allostatic load, in which significant life stressors may impose chronic overload on this system (McEwen, 1998, 2003, 2007; McEwen and Stellar, 1993). Hence, it is essential to adopt a holistic computational modelling approach that integrates a diverse range of physiological and neurophysiological measures to capture the complexity of the underlying biological processes, inform the design of precision interventions, and enable the identification of distinct stress-related phenotypes.

Stress response involves a complex cascade of physiological and psychological processes. In particular, the fast-reacting sympatho-adrenal medullary (SAM) axis is responsible for engaging our fight-or-flight response by releasing catecholamines (e.g., epinephrine and norepinephrine) from the adrenal medulla into the bloodstream to facilitate immediate energy mobilisation, resulting in the rapid increase of heart rate, respiration, and blood pressure (William and Lee Wong, 2014). By contrast, the comparatively slower reacting hypothalamic-pituitary-adrenal (HPA) axis is responsible for meeting longer sustained energy demands through the secretion of cortisol from the adrenal glands (Russell and Lightman, 2019). Furthermore, the amygdala, hippocampus, and prefrontal cortex are some of the key neural regions involved in the emotional evaluation and cognitive appraisal of a stressor, which have downstream regulatory effects on both the SAM and HPA axes (Ulrich-Lai and Herman, 2009). According to the allostasis framework, stress can be conceptualised as a brain-body state of predictive regulation, in which the central nervous system coordinates multiple physiological systems (e.g., cardiovascular, autonomic, respiratory) to meet anticipated energy demands, ensuring that the body is prepared to respond effectively to environmental challenges (McEwen, 1998, 2003, 2007; McEwen and Stellar, 1993; Theriault et al., 2025; Ganzel et al., 2010). Importantly, the chronic overloading of these stress regulatory systems, resulting from repeated, prolonged, or major stressors, can increase the risk of mental health issues (Lee et al., 2025; Jiang et al., 2025; Guidi et al., 2021). Overall, the complex interplay between the brain and body highlights the intricate neurobiological processes underlying stress response.

Consistent with this neurobiological framework of stress response, there is an accumulation of empirical evidence indicating that various electrophysiological biomarkers are sensitive to acute stress. For instance, various electroencephalography (EEG) metrics, such as delta, alpha, beta, and theta power, which index different neural activity, have been found to vary as a function of stress (Vanhollebeke et al., 2022). In addition, electrodermal activity (EDA) metrics, reflecting arousal levels, have also been found to be associated with stress (Man et al., 2023; Klimek et al., 2023). Furthermore, electrocardiography (ECG) metrics, particularly heart rate variability (HRV), which capture different autonomic nervous system processes, were also demonstrated to be stress-sensitive (Kim et al., 2018). Another downstream effect of acute stress includes changes in respiratory activity (Dampney, 2015). The release of catecholamines by the SAM axis also excites the respiratory neural network in the hindbrain (i.e., pons and medulla), resulting in more rapid, shallower breathing (Chu et al., 2024; Viemari, 2008; Tipton et al., 2017). As such, respiration rate and, more recently, respiration rate variability have been put forth as viable biomarkers of stress (Milagro et al., 2017; Kaplan et al., 2023). Taken together, these biomarkers allow us to track stress-related changes across neural, autonomic, cardiovascular, and respiratory systems. Monitoring them concurrently can potentially provide a multi-system perspective on the complex psychophysiological responses that occur during acute stress (Liang et al., 2026; Jin et al., 2025), consistent with the allostasis framework.

Recent advancements in computational power have led to the success of integrating these multimodal electrophysiological measures to predict stress status through various data-driven approaches (Siam et al., 2023; Mohammadi et al., 2022; Pourmohammadi and Maleki, 2020; Castaldo et al., 2016; Can et al., 2019; Arsalan and Majid, 2021; Gjoreski et al., 2015; Delmastro et al., 2020). For instance, a recent study combining electromyography, respiration rate, ECG, and EDA achieved a cross-validated accuracy of 98.2% in predicting driver stress using a random forest classifier (Siam et al., 2023). By contrast, another study using k-Nearest Neighbours with body temperature, respiration, ECG, and EDA as input features achieved a test accuracy of 96.0% in classifying stress status (Mohammadi et al., 2022). However, these aforementioned “black box” approaches are often criticised for the lack of interpretability (Zhang et al., 2023; Rudin, 2019). The attempts at using post hoc techniques to make these models explainable have several inherent limitations, such as the misrepresentation or the lack of sufficient detail of the inner workings of the model (Rudin, 2019). Interpretability poses a big challenge in domains like healthcare, especially where deep learning models dominate in today's healthcare research landscape (Ennab and Mcheick, 2024). Building interpretable models is essential for revealing complex psychophysiological relationships and profiles, providing actionable insights, and enabling informed decision-making to achieve the desired healthcare outcomes. For instance, interpretable models are critical for precision intervention, allowing researchers and clinicians to tailor treatments to individual patients by understanding how specific features contribute to treatment responses and outcomes (Allen, 2024). Hence, rather than trying to use post hoc means to explain these “black boxes”, there has been a steady development of a distinct class of data-driven approaches that focus on building interpretable models from the ground up (Koza, 1994; Cranmer, 2023; Mei et al., 2023; Reiser, 2022; Gerhardus and Runge, 2020; Spirtes et al., 2001; Peters et al., 2017; Makke and Chawla, 2024). Symbolic regression is one such approach that aims to uncover generalisable mathematical representations that best fit a given set of observed data (Koza, 1994; Cranmer, 2023). This method is unique in its ability to search a wide range of potential mathematical solutions, representing non-linearities and interactions between different features, through optimisation algorithms, such as genetic programming (Makke and Chawla, 2024). Causal discovery is another approach that seeks to reveal causal relationships amongst a given set of features (Spirtes et al., 2001; Peters et al., 2017). The Latent Peter-Clark Momentary Conditional Independence (LPCMCI) algorithm, in particular, is a recently developed constraint-based causal discovery method that can take into account potential hidden confounders (Reiser, 2022; Gerhardus and Runge, 2020). In addition, unsupervised machine learning approaches, such as k-means clustering (Lloyd, 1982), provide a method for identifying distinct groups of individuals based on a given set of features. By restricting to stress-sensitive biomarkers measured at baseline, the resulting clusters can be conceptualised as distinct psychophysiological phenotypes, capturing groups of individuals with similar trait-like patterns of stress-related functioning. Previous studies have also used such data-driven approaches on various biomarkers to identify distinct groups of individuals with similar neural or physiological response profiles (Liu et al., 2021; Wormwood et al., 2019; Keogh et al., 2023). Hence, combining symbolic regression with LPCMCI and k-means clustering can reveal key stress-related features and their causal influences, provide actionable insights for precision interventions, and identify distinct phenotypes.

The overarching aim of this study was to decode acute stress response to provide insights into its underlying mechanisms, with implications for prediction, intervention, and trauma-related phenotyping. There were four clear objectives to the study. The first objective was to build an interpretable predictive mathematical model of acute stress using symbolic regression and evaluate it against a benchmark deep learning model. The second objective was to further investigate the directionality of the relationships amongst the psychophysiological features revealed by the symbolic regression using a causal discovery approach. Consequently, we hypothesised that modulating one of the revealed actionable targets would lead to a reduction in perceived stress levels. Thus, the third objective was to experimentally manipulate one of the revealed features and assess its impact during stress recovery. The final objective was to identify distinct psychophysiological phenotypes characterised by different patterns of stress-related neural and physiological features at baseline and examine their associated psychosocial differences.

2. Methods

2.1. Participants

Prior to the start of the study, ethics approval was obtained from the Human Research Ethics Committee at the University of Hong Kong. Recruitment involved advertising through email listings, departmental intranet, and posters placed around the campus. Inclusion criteria included 1) 18 to 50 years old, 2) normal or corrected hearing and vision, and 3) no history of neurological or psychological disorders. The final sample consisted of 144 adults, of whom 63 were male, with ages ranging from 18 to 44 (Mage = 24.28; SDage = 4.46). Informed consent was obtained from all participants.

2.2. Computerised task

An adapted version of the Montreal Imaging Stress Task (MIST) (Dedovic et al., 2005) was administered to induce an acute stress response. The task was presented via Inquisit Lab™ 6 (Millisecond Software, Inc., Seattle, Washington, USA). This task involved two experimental conditions, training and stress. On each trial, an arithmetic question was presented to the participants. Participants were required to use the left and right mouse buttons to navigate through a rotary dial to select an answer. The middle mouse button was used to submit the selected number. Visual feedback (i.e., “correct”, “incorrect”, or “timeout”) was presented for 500ms at the end of each trial. Additionally, errors were accompanied by a loud buzz, whereas correct responses were accompanied by a soft bell sound. The bank of arithmetic questions was grouped into five different levels with progressively greater difficulty. Level one involved solving the addition or subtraction of two numbers (ranging from 0 to 9), whereas level five involved the addition, subtraction, multiplication, or division of four numbers (ranging from 0 to 99). All arithmetic solutions were restricted to 0 to 9. Each experimental condition consisted of all five levels, with each level lasting 1 min.

During the training condition, no time limit was set for each trial. Each participant's average response time for each level was calculated during this condition. To increase task difficulty during the stress condition, an initial time limit was set at 90% of the participant's average reaction time for each level during training. In addition, three consecutive correct responses resulted in a 10% reduction in the time limit. By contrast, three consecutive errors resulted in a 10% increase. Prior to the start of each stress condition, participants were reminded by the experimenter of the importance of meeting the minimum performance requirement (i.e., 80% to 90% accuracy) for their data to be useful for the study. An indicator bar showing the current performance of the participant and an experimentally manipulated normative average performance of other participants (i.e., always higher than the participant's current performance) was displayed at the top of the screen during the stress condition. Participants first completed the training condition, followed by three repetitions of the stress condition. Immediately after the first and second stress conditions, the experimenter informed the participants that they did not meet the required performance. Furthermore, to maximise acute stress response, the experimenter sat right behind the participant throughout the MIST to increase evaluation apprehension.

2.3. Electrophysiological and physiological data acquisition and preprocessing

Continuous ECG, EDA, and impedance pneumography (IP) were recorded using a CGX Aim Physiological Monitor System (Cognionics, Inc., San Diego, California, USA). In addition, EEG was recorded using a CGX CAMP Wireless EEG System. The ECG electrodes were positioned in the lead-II position with the ground electrode position on the lower right rib. Two additional ECG electrodes were positioned adjacent to the lead-II position for the IP dongle. The EDA electrodes were positioned on the middle phalanges of the index and middle fingers of the non-dominant hand. 19 EEG electrodes were positioned on the scalp in accordance with the 10/20 system (Fp1, Fp2, Fz, F4, F3, F8, F7, Cz, C4, C3, T4, T3, Pz, P4, P3, P8, P7, O2, O1). Two additional electrodes were placed on the left and right mastoids. The left mastoid was set as the online reference. Site AFz was used as the ground electrode. All modalities were amplified and converted from analogue to digital at 24-bit resolution and 500Hz sampling rate.

Post-processing was conducted on Python (Version: 3.10). A zero-phase Butterworth bandpass filter of 0.1 – 35Hz (order = 4) was applied to all signals. The signals were segmented into 5-min windows to maximise the range of extractable features, as some features, particularly non-linear metrics, require a larger window of data for accurate analysis (Gu et al., 2023; Shaffer and Ginsberg, 2017). It should be noted that 5-min segments were taken from the period of active arithmetic task engagement during the MIST to reflect the state of acute stress. A robust automatic method for artefact correction for ectopic ECG peaks was applied (Lipponen and Tarvainen, 2019). The various HRV, respiratory, and skin conductance metrics were extracted using the default Neurokit2 (Version: 0.2.10) algorithms (Makowski et al., 2021). The EEG signal was first segmented into equally spaced 1-min epochs. Neural oscillations were extracted using the default Discrete Prolate Spheroidal Sequences multitaper method (Slepian, 1978) in MNE (Version: 1.5.0) (Gramfort, 2013). The power spectrum density was summed across all frequency bins within their respective neural oscillation bands for each EEG site (Delta: 0.5 – 4Hz, Theta: 4 – 8Hz, Alpha: 8 – 12Hz, Beta: 12 – 30Hz). The neural oscillations were averaged across a 5-min window to match the other features temporally.

The filtered signals were also converted to spectrograms across all modalities. Each 5-min window was transformed into the time-frequency domain using the Short-Time Fourier Transform with a Hanning window of 5000 samples and a hop length of 1000 samples. The Fast Fourier Transform length was set equal to the window length. The spectrograms were logarithmically transformed from power to the decibel scale. EEG spectrograms from all sites were stacked to form a 19-channel input, with each channel representing an EEG site. The spectrograms of other modalities were used as single-channel inputs.

2.4. Salivary cortisol assay

Salivary samples were collected using the Salivette® Cortisol tubes (Sarstedt, Art. No. 51.1534.500). As reported by the manufacturer, the functional sensitivity of the assay was 0.28 ng/ml, and the interassay coefficient of variation was 3.44% (Dubberke et al.). Participants were instructed to avoid 1) caffeine intake on the day, 2) alcohol intake within 24 h, 3) any food or beverage intake within 1 h, and 4) toothbrushing, chewing gum, smoking, flossing, or any other mint flavoured products within 1 h of the experiment. At each time point, participants had to chew on a cotton swab gently for 90 s and, thereafter, allow the cotton swab to absorb their saliva under the tongue for 30 s. The collected samples were stored at a temperature of −80 °C at the end of the experiment. Thereafter, the samples were preliminarily processed at an on-site laboratory in batches. The salivary samples were extracted from the tube by centrifugation at 3000×g for 5 min. The extracted samples were sent to an institutional core laboratory for liquid chromatography-tandem mass spectrometry salivary cortisol analysis (Raff and Phillips, 2019).

2.5. Self-report questionnaires

The visual analogue scale (VAS) is a single-item self-report measure used to assess perceived stress at the moment in time. The item was rated from 0 to 100, where a higher score indicated greater levels of perceived stress. The Connor-Davidson Resilience Scale (CD-RISC) is a questionnaire assessing trait resilience (Connor and Davidson, 2003). The 10-item version was used. The items were rated on a 5-point Likert scale, where a higher summed score indicated greater levels of trait resilience. The World Health Organization Well-Being Index (WHO-5) is an assessment of general psychological well-being over the last two weeks (World Health Organization, 1998). The items were rated on a 6-point Likert scale, where a higher summed score indicated greater levels of well-being. The Life Events Checklist for the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (LEC-5) is used to assess the exposure to various types of traumatic events (Weathers et al., 2013). Four summed scores were calculated to reflect the four varying degrees of exposure (i.e., happened personally, witnessed it, learned about it, and part of the job). A higher score indicated greater lifetime exposure to different types of major life stressors.

2.6. Procedure

After signing up for the study, potential participants were required to complete an online screening survey. Individuals meeting the requirements of the study were invited on-site for the experiment. On arrival, participants were required to read the information sheet and sign a consent form. Thereafter, the electrophysiological recording devices were fitted on the participants. There were three major phases to the experiment. Participants were first instructed to sit on a sofa to measure their baseline physiology. During this period, participants were only allowed to read magazines that were provided by the researcher. Participants were reminded that they were not allowed to fall asleep during this period. Following a 20-min baseline period, participants were ushered to a workstation for the MIST. Participants then completed a 30-min recovery stage. Self-report VAS and salivary cortisol were collected at various time points throughout the experiment (see Fig. 1) as part of a manipulation check to ensure the success of the stress induction. CD-RISC, WHO-5, and LEC-5 were completed either the day before or immediately after the on-site experiment. Participants were debriefed regarding the nature of the study at the end of the experiment.

Fig. 1.

An overview of the entire experimental procedure. The experiment consisted of 3 phases – baseline, Montreal Imaging Stress Task (MIST), and recovery. All electrophysiological measures were continuously recorded throughout the 3 experiment phases. This includes electrocardiogram (ECG), electrodermal activity (EDA), impedance pneumogram (IP), and electroencephalogram (EEG). Salivary cortisol and visual analogue scale (VAS) of stress were sampled at fixed time points (i.e., after baseline, after MIST, after recovery, and 10 min after recovery). Three additional VAS were administered after the training, first stress, and second stress conditions of the MIST. During the baseline phase, participants were seated on a sofa. Participants were ushered to a workstation to complete the MIST and remained at the workstation for the recovery phase. An experimenter was seated right behind the participant throughout the MIST. Note that only a subset of participants (N = 34) completed the entire cortisol and VAS sampling for the stress manipulation check. The last two sampling time points were not collected for the remaining participants.

2.7. Data analysis plan

First, manipulation checks on MIST behavioural performance and salivary cortisol response were conducted using the MGCV: Mixed Generalized Additive Model Computation Vehicle with Automatic Smoothness Estimation package (Version: 1.9.1) in R (Wood, 2017). Generalised additive model (GAM) is a flexible framework for modelling linear and non-linear effects, accommodating both fixed and random factors (Hastie and Tibshirani, 1990), which makes it well-suited for examining non-linear temporal changes during the experiment, pre-post intervention effects, and group differences. Second, to build the predictive models of acute stress, the dataset was split subject-wise into training, validation, and hold-out test subsets, with approximately one-third of the subjects allocated to each. PySR (Version: 0.19.4) is an open-source Python package used to perform the symbolic regression analysis for building the interpretable model (Cranmer, 2023). TensorFlow (Version: 2.10.1) was used to implement the convolutional neural network model (Abadi et al., 2016). Third, causal discovery was conducted using the Python package Tigramite: Time Series Graph-based Measure of Information Transfer (Version: 5.2.7.0) to examine directional relationships amongst the features revealed by the symbolic regression (Gerhardus and Runge, 2020). Fourth, the effects of the interventions were examined using GAMs. Fifth, k-means cluster analysis was conducted via the Python package scikit-learn (Version: 1.5.2) to identify potential distinct baseline psychophysiological profiles (Pedregosa et al., 2011). Finally, the psychosocial differences between these profiles were also examined using GAMs.

Based on previously reported small-to-medium meta-analytic effect (Cohen's f ≈ 0.175) of breathing-based interventions on perceived stress (Fincham et al., 2023), our pre-post design with three groups, assuming a correlation of 0.5 amongst repeated measures, 80% power, and an alpha level of 0.05, required at least 84 participants. It should be noted that missing or invalid values, representing approximately 0.17% of the entire dataset, were time series in nature. Gaps within these time series were imputed using cubic spline interpolation (Nickerson et al., 2018), without extrapolation beyond observed data. One participant was omitted from subsequent analyses that require respiration data due to poor signal quality.

3. Results

3.1. MIST behavioural performance and salivary cortisol response

A parametric GAM revealed a significant effect of conditions on accuracy, F(3, 510.67) = 3404.96, p < .001 (see Supplementary Table 1 for descriptive statistics). As illustrated in Fig. 2a, the accuracy of the training condition was significantly higher than the accuracy across all stress conditions. Post hoc analysis (Hommel-corrected) showed that the accuracy of the training condition was significantly higher than the accuracy across all stress conditions (1st Stress Condition: p < .001; 2nd Stress Condition: p < .001; 3rd Stress Condition: p < .001). In addition, accuracy was also significantly lower on the first stress condition as compared to the second (p = .012) and third stress (p = .012) conditions. In the context of reaction time, another parametric GAM revealed a significant effect of conditions, F(3, 448.43) = 230.47, p < .001 (see Fig. 2b). Post hoc analysis (Hommel-corrected) revealed that reaction time during training was significantly longer than reaction time across all stress conditions (1st Stress Condition: p < .001; 2nd Stress Condition: p < .001; 3rd Stress Condition: p < .001; see Fig. 2b). In addition, reaction time during the third stress condition was significantly faster than the second stress condition (p = .002). The reaction time of both the second (p = .017) and third stress (p < .001) conditions was also significantly faster than the first stress condition. As expected, the pattern of behavioural performance across the MIST conditions indicated that the stress conditions were more challenging as compared to the training condition and remained so across the three stress conditions, indicating a successful experimental manipulation of behavioural performance.

Fig. 2.

Bar plots of the estimated marginal means of the behavioural performance, accuracy (a) and reaction time (b), of the MIST across the different conditions. Gaussian distribution with identity link function and inverse Gaussian distribution with inverse link function were used for the generalised additive models for accuracy and reaction time, respectively. Partial effect plots of time on cortisol concentration (c) and perceived stress (d) across the experiment. Gamma distribution with log link function and Gaussian distribution with identity link function were used for the generalised additive models for cortisol concentration and perceived stress, respectively. Random intercept of subject was included in all models. Only significant pairwise comparison with reference to the baseline is illustrated for cortisol concentration and perceived stress. Error bars and purple shaded areas represent ±1 standard error of the mean. ∗∗∗p < .001, ∗∗p <. 01, ∗p < .05 (Hommel-corrected). MIST = Montreal Stress Imaging Task. VAS = Visual Analogue Scale.

A nonlinear GAM revealed that time was a significant nonlinear predictor of cortisol concentration, F(2.82, 168.46) = 18.97, p < .001 (see Supplementary Tables 2 and 3 for descriptive and model statistics). As can be seen in Fig. 2c, cortisol concentration was lowest at baseline, peaked immediately after recovery, and returned to baseline 50 min after the recovery phase. Another nonlinear GAM revealed that time was also a significant nonlinear predictor of perceived stress, F(5.72, 269.13) = 131.31, p < .001, whereby perceived stress levels peaked immediately after participants completed the MIST and returned to baseline levels 10 min after the recovery phase (see Fig. 2d). Consistent with the delayed response of the HPA axis, cortisol concentration peaked approximately 30 min after peak perceived stress levels. Overall, the perceived stress levels and cortisol concentration patterns, along with behavioural performance, were indicative of a successful acute stress manipulation.

3.2. Acute stress prediction models

A genetic programming optimised symbolic regression model was conducted using 216 ECG, EDA, IP, and EEG features (see Supplementary Table 4 for a list of all features) to classify stress status. Binary operators were limited to addition, multiplication, subtraction, division, and exponentiation, while unary operators were limited to negation, squaring, cubing, exponentiation, logarithm, and square rooting, to provide sufficient flexibility to model potential nonlinear relationships. Each solution was constrained to a complexity of 50 (i.e., each operator and feature was assigned a complexity of 1) and a maximum depth of 5, balancing model expressiveness and simplicity to ensure the interpretability of the final solution. The algorithm ran for 10000 iterations with 64 populations and a population size of 1000 to allow sufficient exploration of the solution space while maintaining computational feasibility. L2 margin loss was used to minimise differences between predicted outputs and binary target labels (−1 and 1) in the classification task. Model selection was based on the highest-scoring model, with the score reflecting the trade-off between loss and complexity (Cranmer, 2023; Schmidt and Lipson, 2009). Only models with losses no greater than 1.5 times that of the model with the lowest loss were considered to ensure robust predictive performance and parsimony of the final solution. The validation set was used to monitor potential overfitting or underfitting. The symbolic regression revealed three stress-related components (i.e., cardiorespiratory, cardiac, and neural components) and associated seven features (test accuracy = 85.37%; test sensitivity = 90.43%; test specificity = 80.32% specificity). Using Youden's threshold (Youden, 1950) derived from the validation dataset did not improve test accuracy (85.11%), but the balance between test sensitivity (86.17%) and specificity (84.04%) improved. These results demonstrated that threshold adjustment could help optimise the trade-off between false negatives and false positives, enabling flexible application of the model depending on practical priorities. The optimised mathematical expression is reported as follows:

$$StressState=\frac{CorrelationDimension}{InspirationDuration}-\left(0.001\ast TINN\right)-\frac{F8Beta+T4Theta}{F7Theta+T3Beta}$$ (1)

where Correlation Dimension is a nonlinear metric measuring the complexity of HRV, Triangular Interpolation of the Normal-to-normal Interval Histogram (TINN) is a geometric parameter of HRV, Inspiration Duration is a measure of the mean inhalation time, and Beta and Theta refer to the neural oscillations within the range of 12 – 30Hz and 4 – 8Hz, respectively. F8, F7, T4, and T3 are located on the right frontal, left frontal, right temporal, and left temporal regions of the scalp, respectively. Subsequent Shapley value analysis on the test dataset revealed that the features contributing most to stress status predictions, in descending order, were inspiration duration (|M_shap| = 0.20), F8 Beta (|M_shap| = 0.19), T3 Beta (|M_shap| = 0.19), F7 Theta (|M_shap| = 0.15), TINN (|M_shap| = 0.15), Correlation Dimension (|M_shap| = 0.14), and T4 Theta (|M_shap| = 0.03).

A multimodal late fusion convolutional neural network achieved a higher test performance (test accuracy = 93.88%; test sensitivity = 95.74%; test specificity = 92.02%; see Supplementary Fig. 1 for architecture). Using Youden's threshold further increased the test performance (test accuracy = 94.41%; test sensitivity = 95.21%; test specificity = 93.62%; see Table 1 for other validation and test performance metrics).

Table 1.

The performance metrics of the symbolic regression and multimodal late fusion convolutional neural network on predicting stress status.

		Symbolic Regression
		Validation Dataset				Test Dataset
Threshold		Default		Youden's		Default		Youden's
Accuracy		85.33		86.41		85.37		85.11
Sensitivity		89.67		89.13		90.43		86.17
Specificity		80.98		83.70		80.32		84.04
F1 Score		85.94		86.77		86.08		85.26
Predicted		Actual
		Relax	Stress	Relax	Stress	Relax	Stress	Relax	Stress
	Relax	149	35	154	30	151	37	158	30
	Stress	19	165	20	164	18	170	26	162

		Multimodal Late Fusion Convolutional Neural Network
		Validation Dataset				Test Dataset
Threshold		Default		Youden's		Default		Youden's
Accuracy		96.74		97.28		93.88		94.41
Sensitivity		96.20		95.65		95.74		95.21
Specificity		97.28		98.91		92.02		93.62
F1 Score		96.72		97.24		93.99		94.46
Predicted		Actual
		Relax	Stress	Relax	Stress	Relax	Stress	Relax	Stress
	Relax	179	5	182	2	173	15	176	12
	Stress	7	177	8	176	8	180	9	179

Note that the symbolic regression Youden's threshold of 0.05 was derived from the validation dataset (default threshold is 0). The multimodal late fusion convolutional neural network Youden's threshold of 0.57 was derived from the validation dataset (default threshold is 0.50).

3.3. Causal discovery analysis

To further investigate the brain-body dynamics during acute stress response, we adopted a causal discovery framework (Runge et al., 2019) to uncover directional associations amongst the various features revealed in the symbolic regression. Given that the optimisation process of the symbolic regression model inherently selects only a restricted subset of features, we utilised the LPCMCI algorithm to uncover contemporaneous and time-lagged dependencies between features, while accounting for potential hidden latent confounders (Reiser, 2022; Gerhardus and Runge, 2020). In addition, since the symbolic regression model revealed only linear relationships, we adopted partial correlation as the test for conditional independence. As illustrated in the directed partial ancestral graphs (see Fig. 3a and b), the results revealed top-down influence from the right frontal region on the autonomic nervous system and bottom-up influence from the autonomic nervous system on the left frontal region during baseline. There were also bottom-up inspiration-related influences on the frontal neural regions. During acute stress, however, top-down regulation of the autonomic nervous system dominated. In addition, there was greater frontotemporal connectivity across beta and theta neural oscillations as compared to baseline. Furthermore, the bottom-up influence of inspiration activity on the frontal neural oscillations was absent during acute stress.

Fig. 3.

Directed partial ancestral graphs showing the contemporaneous and time-lagged directional influences between features during baseline (a) and acute stress (b). Note that the feature extraction time window was 1 min to maximise temporal resolution (τ_min = 0 and τ_max = 4). Correlation dimension is a nonlinear metric measuring the complexity of heart rate variability. Triangular interpolation of the normal-to-normal interval histogram (TINN) is a geometric parameter of heart rate variability. Inspiration duration is a measure of mean inhalation time. Beta and theta refer to the neural oscillations within the range of 12 – 30Hz and 4 – 8Hz, respectively. F8, F7, T4, and T3 are located on the right frontal, left frontal, right temporal, and left temporal regions of the scalp, respectively. The colour bar indicates the strength and polarity of intra-time series links (node colour) and inter-node links (arrow colour). Straight links represent contemporaneous relationships, whereas curved links represent time-lagged relationships.

3.4. Deep breathing interventions

To exemplify the notion that an interpretable model of acute stress can provide insight into potential targets for designing precision interventions for stress recovery, we conducted an intervention-based experiment with a subset of participants during their recovery phase. Given that the bottom-up influence of inspiration activity was disrupted during acute stress, we designed and randomly allocated two types of deep breathing interventions (i.e., individualised vs static) to participants to examine their effects during the recovery phase. Specifically, visual guidance for the static deep breathing group is constant at six bpm (10 s per breathing cycle) throughout the intervention. By contrast, the visual guidance for the individualised group starts at the breathing rate of each participant (measured before the start of the recovery phase) and gradually decreases to the target of six bpm by increasing 1 s per breathing cycle every minute. In both conditions, breathing was guided by animated circles expanding and contracting on the screen, with red indicating inhalation, blue indicating the hold phase, and green indicating exhalation.

A likelihood ratio test indicated a significant interaction effect, whereby the nonlinear GAM with time by intervention interaction provided a significantly better fit as compared to the model without the interaction term, F(7.14, 538.74) = 10.49, p < .001 (ΔAIC = −66.07). Post hoc analysis (Hommel-corrected) revealed that the inspiration duration of the control group was significantly shorter as compared to the deep breathing groups across the recovery phase (p < .001; see Fig. 4a), indicating that both deep breathing exercises increased the duration of inspiration.

Fig. 4.

The partial effect plots of the mean duration of inspiration across time for each intervention (i.e., individualised deep breathing intervention, static deep breathing intervention, and control group) during the recovery phase (a). Gamma distribution with inverse link function was used for the generalised additive model for inspiration duration. Bar plots of the estimated marginal means of perceived stress recovery across the different interventions (i.e., individualised deep breathing intervention, static deep breathing intervention, and control group) (b). Perceived stress recovery was calculated by taking the difference between perceived stress levels measured after the recovery phase and perceived stress levels measured after MIST. Gaussian distribution with identity link function was used for the generalised additive model for perceived stress recovery. Random intercept of subject was included in all models. Error bars and shaded areas represent ±1 standard error of the mean. ∗∗∗p < .001, ∗∗p <. 01, ∗p < .05 (Hommel-corrected). Note that N = 34 (Control), N = 38 (Individualised Deep Breathing), and N = 38 (Static Deep Breathing). However, one participant was removed from the control condition for the inspiration duration analysis due to having a poor respiration signal.

To examine the effects of the interventions on stress recovery, we conducted a parametric GAM with the differences between perceived stress measured after the recovery phase (i.e., immediately and after 10 min) and after MIST as the outcome variable. Time by intervention interaction term was included in the model. Baseline measures of perceived stress and cortisol, as well as age and gender, were included in the models as covariates. The results revealed a significant interaction effect of time by intervention on perceived stress recovery, F(2, 117.54) = 4.50, p = .013. As can be seen in Fig. 4b, there was a significant decrease in perceived stress 10 min after the recovery phase across all conditions. However, the magnitude of change for the control group is relatively smaller (p = .010, Cohen's d = −0.63) as compared to the static (p < .001, Cohen's d = −1.59) and individualised (p < .001, Cohen's d = −1.39) interventions, indicating that both deep breathing interventions resulted in greater stress recovery. Baseline cortisol (β = −0.95, SE = 2.78, p = .732), age (β = 0.15, SE = 0.53, p = .782), and gender (β = 2.02, SE = 4.82, p = .676), were not significant predictors of stress recovery. By contrast, baseline perceived stress was a significant predictor (β = 0.34, SE = 0.14, p = .014), suggesting that those with higher perceived stress levels at baseline had worse stress recovery outcomes.

3.5. Psychophysiological phenotypes and associated psychosocial differences

To further interpret the three symbolic components derived from the mathematical model, we conducted a k-means cluster analysis to explore potential distinct baseline physiological profiles. Analyses were restricted to baseline physiology to capture individual differences independent of the experimental manipulation, enabling the investigation of trait-like psychophysiological profiles and their associations with other psychosocial factors. The symbolic components were averaged across all baseline windows and standardised (z-score) prior to conducting the analysis. The number of clusters was determined using the elbow method based on the within-cluster sum of squares, systematically evaluating solutions ranging from two to ten clusters. The analysis revealed that a three-cluster solution was the most parsimonious. These clusters reflected distinct psychophysiological phenotypes, grouping individuals who exhibited similar patterns across the three symbolic components. In addition, we assessed cluster stability using 100 repeated runs with different random initialisations. The average Adjusted Rand Index across runs was 0.91, indicating highly stable cluster assignments. As illustrated in Fig. 5a, the three clusters were characterised by distinct profiles across the cardiorespiratory, cardiac, and neural components. The green and red clusters were characterised by a relatively lower ratio on the neural component as compared to the blue cluster (aka right hemisphere dominance phenotype). By contrast, the blue and green clusters were characterised by relatively lower levels of TINN as compared to the red cluster (aka high HRV phenotype). Lastly, the blue and red clusters were characterised by a relatively lower ratio of the correlation dimension of HRV to the mean duration of inspiration as compared to the green cluster. Notably, some individuals in the green cluster (aka stress-vulnerable phenotype) exceeded the symbolic regression threshold for acute stress during baseline, indicating a heightened predisposition to stress even at rest.

Fig. 5.

3D scatterplot illustrating the three k-means derived clusters (a). Each datapoint is colour-coded in red, green, and blue by cluster membership, and the overlaid plane represents the classification boundary of the symbolic regression stress prediction model. Bar plots of the estimated marginal means of the psychosocial factors across the three k-means clusters (b). Gaussian distribution with identity link function was used for all the generalised additive models, except for LEC-5, which used Poisson distribution with log link function to account for count data. Error bars represent ±1 standard error of the mean. ∗∗∗p < .001, ∗∗p <. 01, ∗p < .05 (Hommel-corrected). Red (N = 37), green (N = 63), and blue (N = 43) clusters. CD-RISC = Connor-Davidson Resilience Scale, WHO-5 = World Health Organization Five Well-Being Index, and LEC-5 = Life Events Checklist for DSM-5.

After applying Hommel correction across all GAM models, there were no significant group differences in trait resilience, F(2, 140) = 1.26, p = .287, or psychological well-being, F(2, 140) = 1.31, p = .287. In terms of lifetime traumatic events, participants in the green cluster reported personally experiencing a greater number of traumatic event types compared with those in the red (p = .006) cluster, χ²(2, 140) = 10.10, p = .032 (see Fig. 5b). In addition, those in the green (p = .004) and red (p = .037) clusters also reported experiencing a greater number of traumatic event types as part of their job as compared to those in the blue cluster, χ²(2, 140) = 11.50, p = .019. There were no significant group differences in witnessing traumatic events, χ²(2, 140) = 4.84, p = .287, and learning about traumatic events, χ²(2, 140) = 3.29, p = .287. Overall, individuals in the green cluster were exposed to more types of major life stressors, followed by those in red, and then those in the blue cluster.

4. Discussion

The present study sought to decode acute stress response to provide insights into its underlying mechanisms, with implications for prediction, intervention, and phenotyping. Our interpretable model not only achieved high predictive performance but also revealed three stress-related symbolic components and associated features. Causal discovery modelling further revealed differences in the directional influences amongst these features. Notably, the bottom-up influence of inspiration on the frontal neural activity was found to be disrupted during acute stress. Subsequent experimental results demonstrated that deep breathing exercises resulted in increased inspiration duration as well as greater improvements in self-reported stress levels. Importantly, this improvement only emerged 10 min after the interventions, suggesting that the effects of deep breathing exercises may not be immediately observable, a factor future researchers should take into consideration. Arguably, the greater improvement in stress recovery may be due to controlled deep breathing accelerating the reestablishment of the bottom-up influence of inspiration on frontal neural activity, a hypothesis that future studies could investigate by directly examining frontal neural dynamics before and after deep breathing exercise as compared to control. Our cluster analysis also revealed three distinct baseline psychophysiological phenotypes, with the stress-vulnerable phenotype reporting a greater number of traumatic experiences. By integrating data-driven and experimental approaches, our holistic methodological framework provides a comprehensive means to elucidate the neurobiological basis of acute stress, guide precision-targeted interventions, and identify distinct psychophysiological phenotypes.

The cardiorespiratory component, revealed by our interpretable model, suggests that inspiration dynamics modulate the influence of HRV complexity on stress. In addition, our causal models also suggest that the bottom-up influences of inspiration activity on frontal neural regions appear to be disrupted during acute stress. In the context of our biological system, greater complexity in HRV could be seen as the manifestation of the ongoing interplay amongst the various stress-related biological mechanisms, such as the sympathetic and parasympathetic nervous systems (Calderón-Juárez et al., 2023; Porges, 2007). Arguably, a more complex autonomic nervous system might reflect the dynamic regulatory processes associated with adaptive functioning during acute stress response, striving to maintain homeostasis while mobilising sufficient energy to meet the demands of current challenges (Porges, 2007). By contrast, shorter inspiration duration likely reflects stress-related sympathetic activation (Viemari, 2008; Tipton et al., 2017). This is consistent with the downstream effects of the SAM axis during an acute stress response, which releases catecholamines and, consequently, increases respiratory activity and irregularities in respiratory patterns (Chu et al., 2024; Viemari, 2008; Tipton et al., 2017). On the flip side, taking longer breaths may promote parasympathetic dominance, mediated through respiratory sinus arrhythmia (Shaffer and Ginsberg, 2017; Shaffer et al., 2014), thereby attenuating the effects of stress. Indeed, our experimental findings corroborate this notion by demonstrating that taking slower breaths through guided deep breathing exercises aided stress recovery. All things considered, it appears that this cardiorespiratory component reflects a novel stress metric beyond what previous research has revealed by combining both HRV complexity and respiratory activity.

The cardiac component, which is the second component revealed, suggests that lower HRV varies as a function of acute stress. This finding is consistent with the general notion that lower HRV represents greater sympathetic dominance during acute stress response (William and Lee Wong, 2014; Kim et al., 2018). It should be noted that HRV, as well as associated complexity, have been demonstrated to decrease as a function of acute stress in past research (Castaldo et al., 2015). However, our causal models indicate more complex, dynamic, and time-dependent cardiorespiratory interactions during acute stress. Specifically, our findings suggest that faster inspiration contemporaneously increases HRV complexity, which in turn attenuates HRV. In addition, faster inspiration also leads to a delayed decrease in HRV complexity, which in turn causes a subsequent reduction in HRV. Furthermore, our findings also indicate greater top-down regulation of HRV complexity from frontotemporal neural regions during acute stress. Interestingly, recent research also reported an increase in HRV complexity as a function of cognitive load during a driving simulation task, which the researchers attributed to the adaptive functioning necessary for meeting task demands (Arutyunova et al., 2024). Consistent with our results, they also found a decrease in HRV as a function of cognitive load. Hence, our findings not only support the notion that HRV complexity reflects adaptive functioning during acute stress but also extend previous work by revealing the dynamic, time-dependent interplay between the brain and autonomic nervous system underlying this adaptive functioning through a computational approach.

The neural component of the symbolic regression indicates marked frontotemporal hemispheric asymmetry in beta and theta oscillations, suggesting a general trend of left-hemisphere dominance during acute stress. Notably, beta and theta oscillations between frontal and temporal regions are flipped across hemispheres, reflecting a nuanced interplay of bilateral neural processes. Our findings are consistent with previous research that has found that beta and theta oscillations in the frontal and temporal regions are sensitive to stress (Heinbockel et al., 2021; Ehrhardt et al., 2022; Hafeez et al., 2018; Aspiotis et al., 2022). Furthermore, a recent study found a similar but more rudimentary negative correlation between stress and the frontal theta/beta ratio (Yi Wen and Mohd Aris, 2020). It should be noted that our findings are inconsistent with a prior meta-analysis highlighting alpha oscillation as the only robust neural correlate of stress (Vanhollebeke et al., 2022). However, the studies included in the meta-analysis predominantly focused on individual frequency bands in isolation or, at most, considered simple combinations of two metrics (e.g., asymmetry, ratio), limiting their ability to capture the complexity of stress-related neural dynamics. In contrast, symbolic regression allows for greater flexibility in integrating different oscillatory activity across frequency bands and sites. By leveraging this approach, our findings reveal a more complex pattern of stress-related neural activity beyond what previous research has shown. Furthermore, our causal models suggest greater interhemispheric and interlobe connectivity during acute stress as well as a shift toward top-down regulation, with frontotemporal neural regions exerting dominant control over the autonomic nervous system. Consistent with our findings, recent functional magnetic resonance imaging research also demonstrated greater network integration, particularly in the frontotemporal neural regions, during acute stress (Wang et al., 2022). Previous research has also found that left frontal hemisphere lateralisation is implicated in cognitive reappraisal during stress and emotional regulation (Yang et al., 2021; Papousek et al., 2017). Moreover, the left hemisphere has also been found to be involved in the downregulation of the HPA axis through interhemispheric inhibition of the right hemisphere during stress and emotional regulation (Sullivan, 2004; Berretz et al., 2022). Indeed, the frontotemporal regions have been known to be involved in stress-related cognitive and emotional processing, which have downstream regulatory effects on both the SAM and HPA axes (Ulrich-Lai and Herman, 2009). Our findings build on previous research by revealing more intricate stress-related bilateral neural processes and associated top-down influence on the autonomic nervous system. Given that the MIST was used as part of the experimental manipulation, it should be noted that the increase in connectivity may also partly reflect increased cognitive load. Notably, previous neuroimaging research has demonstrated that increasing cognitive load was associated with strengthened connectivity between the frontoparietal network and the default mode network (Zuo et al., 2018). In addition, a lower frontal theta/beta ratio has also been linked to increased cognitive load (Laufer et al., 2022). Theta activity, in particular, has been thought to be involved in various cognitive-affective processes, such as multimodal sensorimotor integration, attention, episodic memory, cognitive control, and emotional regulation (Karakaş, 2020; Li et al., 2025). By contrast, beta activity has been associated with higher-order cognitive functions, such as planning, top-down control, working memory, and the maintenance of cognitive states (Spitzer and Haegens, 2017). Hence, it is not surprising that these neurocognitive functions are engaged under both cognitive load and stress. However, given the increase in top-down influence of frontotemporal neural activity on the autonomic nervous system during acute stress, it appears that increased cognitive load alone is unlikely to fully account for this pattern of activity. Instead, the shift towards greater top-down influence more likely reflects stress-related cortical modulation of the autonomic nervous system. In any case, future research should seek to disentangle these effects by independently manipulating cognitive demands and psychosocial stress.

Our data-driven findings also revealed three baseline psychophysiological phenotypes with distinctive psychosocial profiles. Amongst the three phenotypes, the stress-vulnerable phenotype appears to exhibit a heightened stress predisposition at baseline. This phenotype is characterised by greater left-hemisphere dominance and lower HRV relative to the other two phenotypes. Furthermore, our findings indicate that individuals with this phenotype are likely to have been exposed to a greater number of major life stressors. This is consistent with the notion that major life stressors increase allostatic load (Lee et al., 2025), which is the chronic overloading of the stress-regulatory systems (McEwen and Stellar, 1993). However, the differences in physiology did not manifest in self-reported trait resilience or psychological well-being. This discrepancy may allude to a potential dissociation between physiological vulnerability and subjective self-appraisal. Alternatively, it could also be argued that self-report inventories may lack the sensitivity to detect subtle inter-phenotypic differences in healthy individuals. Future research should adopt a longitudinal design to track the trajectories of these phenotypes over time, investigating whether the physiological vulnerability observed translates into increased susceptibility to psychopathology in the future. In any case, our findings build on previous research by revealing distinct physiological phenotypes associated with trauma, characterised by altered autonomic regulation and hemispheric asymmetry.

Arguably, the complex pattern, while potentially discoverable through traditional models such as generalised linear models, is unlikely to occur as the symbolic components involve complex arithmetic combinations, which highlights the strength of our computational approach. As expected, the symbolic regression model demonstrated slightly lower predictive performance as compared to the deep learning model. Indeed, deep learning excels at capturing complex nonlinear relationships between features and outcomes, which often leads to higher accuracy in classification at the expense of interpretability. In addition, the symbolic regression approach requires greater levels of abstraction and feature engineering, which involves transforming raw data into higher-level representations. This lossy process involves aggregation, dimension reduction, and discretisation, leading to the loss of critical information and, consequently, lower model accuracy. In healthcare research, interpretability may take precedence over absolute accuracy, as it facilitates insight into the psychophysiological correlates and causal pathways of acute stress. Indeed, consistent with the allostasis framework (McEwen, 1998, 2003, 2007; McEwen and Stellar, 1993; Theriault et al., 2025; Ganzel et al., 2010), our findings not only revealed several stress-related brain and body processes, spanning neural, cardiac, and respiratory systems, but also demonstrated the shift from bottom-up to top-down influence during acute stress, illustrating how the brain coordinates and regulates the body to meet the demands of the environment. In addition, our findings have several important clinical implications. First, our predictive models can be used to monitor stress levels in clinical settings, such as psychiatric and trauma care. Second, the interpretable nature of our approach offers multiple potential actionable targets for precision interventions to aid in stress recovery, as exemplified by our experimental findings. Third, our phenotyping approach can assist clinicians in detecting at-risk individuals with latent vulnerability to stress due to prior traumatic experiences, which may lead to stress-related complications if left unchecked. Taken together, our approach furthered the understanding of psychological stress to better help assess, manage, intervene, and potentially prevent stress-related negative health outcomes.

CRediT authorship contribution statement

Kar Fye Alvin Lee: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing. Li Liang: Data curation, Investigation, Methodology, Project administration, Writing – review & editing. Theparambil A. Suhail: Investigation, Software, Writing – review & editing. Tatia M.C. Lee: Conceptualization, Funding acquisition, Methodology, Supervision, Writing – review & editing.

Funding

This research was supported by the University of Hong Kong May Endowed Professorship in Neuropsychology and the Guangdong-Hong Kong Joint Laboratory for Psychiatric Disorders [2023B1212120004].

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Handling Editor: Dr. Rongjun Yu

Abbreviations

CD-RISC

Connor-Davidson Resilience Scale

EDA

Electrodermal activity

ECG

Electrocardiography

EEG

Electroencephalography

HRV

Heart rate variability

HPA

Hypothalamic-pituitary-adrenal

IP

Impedance pneumography

LPCMCI

Latent Peter-Clark Momentary Conditional Independence

LEC-5

Life Events Checklist for the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition

MIST

Montreal Imaging Stress Task

SAM

Sympatho-adrenal medullary

WHO-5

World Health Organisation Well-Being Index

Appendix A. Supplementary data

The following is the Supplementary data to this article:

Data availability

Data will be made available on request.