Photoplethysmographic Waveform Analysis for Autonomic Reactivity Assessment in Depression

<italic>Objective:</italic> In the present study, a photoplethysmographic (PPG) waveform analysis for assessing differences in autonomic reactivity to mental stress between patients with Major Depressive Disorder (MDD) and healthy control (HC) subjects is presented. <italic>Methods:</italic> PPG recordings of 40 MDD and 40 HC subjects were acquired at basal conditions, during the execution of cognitive tasks, and at the post-task relaxation period. PPG pulses are decomposed into three waves (a main wave and two reflected waves) using a pulse decomposition analysis. Pulse waveform characteristics such as the time delay between the position of the main wave and reflected waves, the percentage of amplitude loss in the reflected waves, and the heart rate (HR) are calculated among others. The intra-subject difference of a feature value between two conditions is used as an index of autonomic reactivity. <italic>Results:</italic> Statistically significant individual differences from stress to recovery were found for HR and the percentage of amplitude loss in the second reflected wave (<inline-formula><tex-math notation="LaTeX">$A_{13}$</tex-math></inline-formula>) in both HC and MDD group. However, autonomic reactivity indices related to <inline-formula><tex-math notation="LaTeX">$A_{13}$</tex-math></inline-formula> reached higher values in HC than in MDD subjects (Cohen's <inline-formula><tex-math notation="LaTeX">${d=\!-0.81},{\,\text {AUC}=0.74}$</tex-math></inline-formula>), implying that the stress response in depressed patients is reduced. A statistically significant (<inline-formula><tex-math notation="LaTeX">$p \,<\, 0.001$</tex-math></inline-formula>) negative correlation (<inline-formula><tex-math notation="LaTeX">$r=-0.5$</tex-math></inline-formula>) between depression severity scores and <inline-formula><tex-math notation="LaTeX">$A_{13}$</tex-math></inline-formula> was found. <italic>Conclusion:</italic> A decreased autonomic reactivity is associated with higher degree of depression. <italic>Significance:</italic> Stress response quantification by dynamic changes in PPG waveform morphology can be an aid for the diagnosis and monitoring of depression.

used as an index of autonomic reactivity. Results: Statistically significant individual differences from stress to recovery were found for HR and the percentage of amplitude loss in the second reflected wave (A 13 ) in both HC and MDD group. However, autonomic reactivity indices related to A 13 reached higher values in HC than in MDD subjects (Cohen's d = −0.81, AUC = 0.74), implying that the stress response in depressed patients is reduced. A statistically significant (p < 0.001) negative correlation (r = −0.5) between depression severity scores and A 13 was found. Conclusion: A decreased autonomic reactivity is associated with higher degree of depression. Significance: Stress response quantification by dynamic changes in PPG waveform morphology can be an aid for the diagnosis and monitoring of depression.

I. INTRODUCTION
D EPRESSION is a serious mental disorder causing the affected person to suffer from sadness, loss of interest, poor concentration, and feelings of tiredness [1]. Major depressive disorder (MDD) is a leading cause of disability worldwide, and it has an enormous socioeconomic impact both due to the direct costs of treatment and the productivity losses associated to it [2].
MDD is a major contributor to the overall global burden of disease in combination with cardiovascular diseases [2]. Several studies indicate that both diseases may share underlying pathophysiological disturbances such as systemic inflammation, endothelial dysfunction, hypothalamic-pituitary-adrenal axis hyperactivity, and autonomic imbalance [3]- [5].
The link between psychological stress and depression can be found in the diathesis-stress model [6]. As the predisposition to depression (diathesis) increases, which can be attributed to either biological or psychological factors, a patient becomes psychologically more vulnerable, and thus the level of stress needed to precipitate an episode of depression decreases [7], [8]. Prolonged stress is a crucial factor underlying MDD considering that more than 40% of all depressed patients suffer from cooccurring anxiety. Negative emotions, such as depressive mood, could have adverse effects on neurohormonal regulatory circuits in a similar way to prolonged stress [3]. Thus, the comorbidity of anxiety and depressive disorders has been associated with poorer trajectories of depressive symptoms [9]. These observations 0018-9294 © 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
highlight the need of assessing the individual variation in stress susceptibility, resilience, and reactivity [4]. In the short term, the physiological response to acute stress is associated with changes in the autonomic nervous system (ANS). The variation in ANS activity during stressful experiences, which is known as autonomic reactivity, is particularly important for adaptive stress responses, since it reflects the ability of an individual to cope with a challenging situation. Maladaptive responses may have a negative impact on cognitive, emotional, and behavioral processes, thereby leading to development of depression [10], [11]. Current research on stress response in MDD patients is focused on heart rate variability (HRV), which has been widely used for assessing ANS in a noninvasive way. Recent reviews have pointed out that individuals with greater levels of resting HRV have greater emotion regulation and executive functioning, while hypo-reactivity during stress, evidenced by blunted HRV reactivity, is related to depression [12], [13].
Although autonomic reactivity in MDD patients using HRV indices derived from the electrocardiogram (ECG) has been widely investigated, the use of photoplethysmography (PPG) in this application remains largely unexplored. In [14], MDD patients showed a reduced high frequency component of the pulse rate variability (PRV) compared to healthy control subjects during a stressful stimuli. Similar results were reported by [15], where HRV indices derived from a PPG signal were studied before, during, and after executing a mental task.
However, a PPG signal does not only contain information about heart rate (HR). Pulse pressure propagation in arteries causes alterations in blood volume and accordingly changes in the PPG pulse shape and temporal characteristics [16]. Thus, PPG can provide a great amount of information about the cardiovascular system including autonomic function and vascular characteristics. One of the very few studies involving MDD patients investigated the association between autonomic dysregulation and arterial stiffness measured by PPG waveform characteristics but only during resting conditions [17].
The novelty of the present study consists in the use of morphological PPG changes for assessing autonomic reactivity induced by cognitive tasks in MDD and healthy subjects. Pulse waveform characteristics are calculated based on a pulse decomposition analysis (PDA) that consists of modeling the PPG pulse as a main wave superposed with several reflected waves [18]. The main hypothesis tested in the present study is that the stress response quantified by dynamic changes in vascular characteristics is useful for the diagnosis and monitoring of depression.

A. Participants
A database of 40 MDD patients (white males and females) recruited from consultation as well as from the psychiatric inpatient ward was recorded at the Hospital Clínico Lozano Blesa (Zaragoza, Spain) and the Mental Health Unit of the Parc Sanitari Sant Joan de Deú (Barcelona, Spain). The MDD group consists of subjects with clinically significant depression. The selection was based on the diagnostic and statistical manual  [19]. Depression severity was assessed with the Hamilton depression rating scale (HDRS) [20] and the Beck's depression inventory-II (BDI) [21]. Recordings of 40 healthy control (HC) subjects matched by age, sex, race, and body mass index (BMI) were acquired. Only participants without other comorbidities such as cardiovascular, endocrinological or neurological disorders were selected. Table I shows the demographic data and medication of the subjects.

B. Experimental Protocol and Data Acquisition
The experimental protocol had a duration of about 2 hours (starting time between 09:00 a.m. and 11:00 a.m. to avoid circadian rhythm changes) and it consists of three stages. The first stage consists in a basal condition (B), where the subjects were filling psychometric tests including state-trait anxiety inventory test, scale of stress symptoms, perceived stress scale, and visual analogue stress scale [22].
Then, in the second stage, stress was induced to participants by applying two cognitive tasks widely-used in the neuropsychological field for assessing executive function: first the trail making test (S T ) followed by the stroop color task (S C ), consisting in a non-verbal and verbal stressor, respectively [23], [24]. The S T consists of two parts. In Part A, the subjects are required to connect, by drawing a line, consecutive numbers, while in Part B, they are required to connect numbers and letters in an alternating progressive sequence. In S C , subjects are required to read, as fast as possible in 45 secs, from three different lists, the names of: (a) color-words printed in black ink, (b) different color patches, (c) ink color of color-words printed in an inconsistent color ink (incongruent condition).
In the third stage, subjects were requested to relax and to remain silent. During this recovery stage (R), of about 5 minutes, individuals were supposed to achieve a resting state.
The duration (mean±SD) of each protocol stage was 11.5 ± 5.0 min (B), 3.5 ± 1.4 min (S T ), 4.3 ± 1.2 min (S C ), 5.2 ± 0.5 min (R). During the whole experimental protocol, a non-dominant hand fingertip PPG signal was continuously recorded at a sampling frequency of 250 Hz for each participant using the Medicom system (ABP10 module of Medicom MTD, Ltd, Russia).
This study was carried out in accordance with the recommendations of "Comité Ético de Investigación Clínica de Aragón  3 (n) are marked in red, green, and purple, respectively; the up-slope is marked with solid line, while the horizontally flipped up-slope with dashed line.
(CEICA)" and the Ethical Committee of "Fundació Sant Joan de Déu" under clinical studies PI16-0156 and PIC-148-16, respectively, including written informed consent from all subjects in accordance with the Declaration of Helsinki.

A. Pulse Decomposition Analysis
Intervals of the PPG signal containing artifacts are suppressed using the energy-based approach proposed in [25]. Then, PPG pulse detection is carried out using a low-pass differentiator (transition band from 7.7 Hz to 8 Hz) and a time-varying threshold [26]. For the i:th pulse, the fiducial point n F (i) consists in the maximum up-slope point of the low-pass differentiator filtered signal.
A pulse decomposition analysis (PDA) technique based on [18] is applied for pulse waveform modeling. Prior to PDA, the raw PPG signal is subjected to low-pass filtering (forth order bidirectional IIR with cut-off frequency of 5 Hz) for attenuating high frequency noise, with x PPG (n) denoting the filtered signal. In this study, due to low-pass filter operations, a percentage relative to the maximum up-slope value of the first derivative of x PPG (n) (x PPG (n)) is used for defining the pulse basal point (n B (i)). The point n B (i) is searched in the interval Ω = [n U (i) − 0.3F s , n U (i)] around the maximum up-slope point of x PPG (n) (n U (i)): . The point n U (i) is defined as the absolute maximum of x PPG (n) in a symmetrical fixed window of 10 msec around the time instant associated with n F (i). Linear interpolation of x PPG (n B (i)) series is subtracted from x PPG (n), yieldingx PPG (n). Thus, each pulse x i (n) begins and ends with zero amplitude: The i:th pulse wave x i (n) is decomposed into J symmetrical waves x i,1 (n), . . . , x i,J (n), and a residual signal. The j:th inner wave x i,j (n) is obtained by concatenating the up-slope of the running residual signalx i,j (n) (x i,1 (n) = x i (n)) with itself horizontally flipped, assuming that the reflected waves arrive after half of the incident pulse is over: where n O j and n E j denote the up-slope onset and end ofx i,j (n), respectively; the dependence of i in the up-slope onset n O j and end n E j is omitted for simplicity. After the up-slope interval has been defined, the j:th inner wave x i,j (n) is subtracted from the running residualx i,j (n), i.e.,x i,j+1 (n) =x i,j (n) − x i,j (n), and the (j +1):th inner wave is computed recursively from x i,j+1 (n); J is set to 3. Fig. 1 illustrates an example of PDA for two different pulse waveform morphologies. The up-slope end n E j is the position of the first relative maximum ofx i,j (n) and the up-slope onset [18], e.g., for the main wave n O 1 = n B (see Fig. 1(a)). However, relative maxima with low amplitude (see Fig. 1(c)), can lead to erroneous definition of inner waves. Thus, in this work, an inner wave is considered to exist only if the absolute maximum value ofx i,j (n), i.e.,x i,j (n E j ), exceeds the fixed (for the i:th pulse) amplitude threshold A P = 0.05 · max n {x i (n)}.
Furthermore, slope changes prior to the first relative maximum can lead to erroneous decomposition (see Fig. 1(e)). When x i (n) is decomposed to inner waves, the up-slope of the running residualx i,j (n) might not be a strictly increasing function in [n O j , n E j ], i.e., the first derivative ofx i,j (n) (x i,j (n)) is not always positive (see Fig. 1(i)) or has more than one inflection points (see Fig. 1(k)). This is either due to the presence of a relative maximum with amplitude lower than A P at the beginning of the up-slope interval (see Fig. 1(i)), or due to a slope change at the end of up-slope interval which, however, does not appear as a relative maximum inx i,j (n) (see Fig. 1(k)). Thus, n O j is redefined as the next sample after the last negative-amplitude sample ofx i,j (n), so thatx i,j (n) ≥ 0. Then, n E j is redefined as the position of the first relative minimum ofx i,j (n) for which x i,j (n E j ) > A P is fulfilled ensuring that the j:th inner wave can be defined. Fig. 2 illustrates a block diagram with the PDA steps.

B. Pulse Waveform Characteristics
Several morphological features associated with systolic arterial pressure and vascular compliance measures are extracted from each PDA based modeled PPG pulse. The amplitude A j (i) and the position T j (i) of an inner wave are defined as the amplitude and the position of the absolute maximum of x i,j (n), respectively. The width of x i,j (n), denoted by W j (i), is estimated by the full-width at half maximum.
The time delay between the position of the main wave and the first reflected wave T 12 = T 2 − T 1 as well as the percentage of amplitude loss in the first reflection A 12 = 100 · (A 1 − A 2 )/A 1 are calculated (the dependence of i is omitted for simplicity). Similarly, T 13 and A 13 are calculated for the second reflected wave. The position T 1 and the width W 1 of the main wave are also subjected to analysis. Finally, the instantaneous HR is calculated using the fiducial points n F (i). Fig. 3 shows an example of pulse waveform characteristics. The pulse-to-pulse interval for the pulses that were considered in PDA is given by T BB (i) = (n B (i + 1) − n B (i))/F s .
In this study, distorted pulses are discarded. They are considered as such when at least one of the following criteria are satisfied: (a) the pulse wave is decomposed to less than 3 waves, (b) the amplitude of the main wave is not the largest of the three waves, i.e., A 2 > A 1 or A 3 > A 1 , (c) the second wave is located at the end of the pulse interval, i.e., T 2 > 0.8T BB , or (d) the third wave occurs earlier than 0.35T BB , i.e., T 3 < 0.35T BB . For each feature, outlier rejection is complemented with a median absolute deviation (MAD)-based rule [27]; the threshold is defined as 5 times the running MAD of the previous 50 pulses.

C. Statistical Analysis
The median value of a pulse waveform characteristic is obtained for each subject and condition C, C ∈ {B, S T , S C , R}. In this study, only the first 5 minutes of B are taken into account since the time required for filling the psychometric tests can differ among subjects or groups.
Individual differences are assessed separately for HC and MDD group. A non-parametric Friedman test of differences among repeated measures is conducted for evaluating the individual differences across the stages of the experimental protocol. To identify which data come from a different distribution, a multi-comparison test (post hoc analysis) with Bonferroni correction is carried out using the paired t-test, and the Wilcoxon signed rank test when appropriate.
Differences in autonomic reactivity between MDD patients and HC subjects are assessed using the Cohen's d parameter and the area under the curve (AUC) of the receiver operating characteristic curve, which measure the size of an effect (depression) and the degree of separability between groups, respectively. The intra-subject difference of a feature F, F ∈ {HR, W 1 , T 1 , T 12 , T 13 , A 12 , A 13 }, between two conditions C 1 and C 2 , denoted as Δ(F) C 2 C 1 , is used as an index of autonomic reactivity. The reactivity indices are calculated by subtracting the value of the feature F in C 1 from C 2 . The changes from basal to stress, from stress to recovery or from basal to recovery stage are studied for assessing autonomic reactivity.
Correlation (Pearson) analyses are carried out for testing bivariate associations between the most significant autonomic reactivity indices and depression severity scores assessed either with HDRS or BDI scores. Differences in demographic data between groups are assessed with the t-test for independent samples, and the Mann-Whitney U non-parametric test when appropriate. The significance threshold in this study is set to p < 0.01.

IV. RESULTS
The percentage (mean±SD) of discarded pulses for each stage was 2.3% ± 4.8% (B), 4.4% ± 6.6% (S T ), 4.0% ± 6.7% (S C ), and 3.6% ± 5.7% (R) suggesting that few distorted pulses are present in the PPG recordings. The number of analyzed pulses (mean ± SD) was 370 ± 102 (B), 262 ± 137 (S T ), 317 ± 105 (S C ), and 369 ± 102 (R). As can be seen from the boxplots in Fig. 4, patients with depression show higher values of HR and vascular compliancerelated parameters A 12 and A 13 compared to healthy controls. In contrast to that, the healthy controls show higher values for the pulse transit time surrogates T 12 and T 13 and the temporal parameters related to the main wave, i.e, W 1 and T 1 .
Friedman tests indicated that there are statistically significant differences in HR and A 13 for both groups, while only the HC group showed significant differences in the rest of parameters across the different stages. The post hoc analysis revealed which stage in particular differs from each other. Table II illustrates the statistical significance of the multi-comparison paired tests. Results show that HC subjects exhibit statistical differences in all characteristics during the verbal stressor compared either to basal (B vs S C ) or to recovery stage (S C vs R). On the other hand, statistically significant (p < 0.001) individual differences were found in MDD patients mainly for HR and A 13 indices, which were associated with changes from stress to recovery, i.e., S T vs R and S C vs R. An example of average pulse waveforms for a HC and a MDD subject (matched by sex, age  and BMI) is shown in Fig. 5. For each stage, prior to averaging operation, the pulses are aligned to the position of the pulse start (basal point). This figure highlights the fact that across different stages within the same subject minimal changes of waveform characteristics, including HR, T 13 , and A 13 , are observed for the MDD compared to the HC subject.
Results of the differences in autonomic reactivity between MDD and HC subjects are summarized in Table III. Results show that the amplitude loss in the second A 13 reflection is associated with larger effect sizes compared to HR or other pulse waveform characteristics. A higher degree of separability between groups is observed when changes from either basal (B) or stressful stages (S T , S C ) to recovery phase (R) are considered,   Table IV indicate that there is a statistically significant negative correlation between depression severity scores and autonomic reactivity indices. Comparing the results between the most promising features, it can be seen that Δ(A 13 ) S C R is associated with higher (absolute) correlation values; r = −0.50 and r = −0.43 for HDRS and BDI scores, respectively. Note that depression severity scores are transformed using the squared root (log transformation is avoided due to zeros in HDRS) to increase the linear relationship with the autonomic reactivity indices. Fig. 6 shows the scatter plots of √ HDRS and Δ(A 13 ) pairs together with the line of best fit (least-squares minimization).

V. DISCUSSION
The present paper investigates the differences in autonomic reactivity to mental stress between MDD and healthy subjects by measuring changes in PPG morphology. The response to stress, induced by verbal and non-verbal cognitive tasks, is evaluated by means of PDA.
The intra-subject difference of PDA-derived features between two conditions, e.g., basal and stress, are considered as indices of autonomic reactivity. Results show that the stress response of MDD compared to HC subjects is different (Table III). Changes in PPG morphology quantified by Δ(A 13 ) show a higher degree of separability between groups, i.e., larger AUC values, compared to all the indices considered in the study. This implies that vascular characteristics could provide complementary information about autonomic function.
Elevated HR values and increased amplitude loss in wave reflections, e.g. A 13 , are observed during stress conditions ( Fig. 4(a)-(c)) and they are associated with higher levels of sympathetic activity. Acute mental stress may increase aortic stiffness [28]. An increased arterial stiffness implies that the stroke volume flows through the arterial system and peripheral tissues mainly during systole due to the reduced distensibility of the elastic arteries and the aorta [29]. This causes both a larger peak in systolic part and a larger decline during diastolic part. Thus, an increment of A 13 values during stressful tasks can be related to the inverse relationship between systolic (increased) and diastolic blood pressure (decreased).
An increased vagal tone following the stress induction may enhance differences in ANS regulation between MDD and HC subjects taking into consideration that Δ(A 13 ) indices (Table III) yielded to large effect sizes, i.e., |d| > 0.8. On the contrary, changes in autonomic reactivity from basal to stress show lower AUC and effect sizes compared to changes from stress to recovery. These results are suggestive of a higher sympathetic tone in B compared to R stage. Filling psychometric tests, during B stage, does not imply a cognitive stressor, but it may require the attention and effort of the subject, which could affect the ANS state. Indeed, statistically significant (Table II) lower values of HR and A 13 are observed for HC subjects in R compared to B (Fig. 4(a) and 4(c)).
Furthermore, a higher degree of depression is associated with a decreased autonomic reactivity. The autonomic reactivity indices and depression severity scores are negatively correlated (Table IV). Taking into account that the range of depression severity scores (Fig. 6) covers all types of depressive symptoms (mild, moderate, severe, and very severe), stress response quantified by dynamic changes in vascular characteristics might be useful for depression monitoring. Blunted autonomic reactivity to stress might reflect suboptimal functioning of the cortical and limbic brain regions that are involved in motivation and cognitive ability [30]. Thus, deviations from an optimal response, in the face of challenge, may indicate that MDD patients are less capable than healthy subjects, to adjust their mental state to abrupt behavioral changes.
These results are in agreement with previous studies which showed that patients with depression are associated with blunted cardiovascular reactivity to psychological stressors. Reduced HR and systolic blood pressure reactivity during a speech task and less HR recovery in depressed patients compared to healthy control subjects was reported in [31]. Other studies pointed out that high scores of depression or anxiety symptomatology are associated with blunted blood pressure and HR reactivity to psychological stressors [32], [33].
Decreased autonomic reactivity in depression has been documented in a growing number of studies using HRV indices [34], [35]. Moreover, joint analyses of respiration and HRV showed less stressor-induced suppression of cardiac parasympathetic activity in MDD patients compared to healthy subjects [36].
In [37], entropy measures of cardiorespiratory coupling showed an increasing trend with depression severity.
Although PPG signal has been widely used for quantifying mental stress [38]- [40], few studies have explored the ability of PPG-derived indices to assess autonomic reactivity in MDD patients. It should be noted that short-term variability is often overestimated by PRV and, in addition, it has been reported that some mental stressors reduce the accuracy of PRV as a surrogate of HRV [41]- [43]. The PRV is affected by measurement errors related to lower accuracy of fiducial point detection, and physiological factors such as respiration [42]. Changes in respiratory patterns imposed by the exposure to stressful stimuli may mask the vagal withdrawal [44], [45].
One of the very few studies which analyzed morphological PPG features in MDD patients showed that entropy indices of systolic and diastolic amplitude of pulse waveform were positively correlated with suicidal score [17]. Higher entropy values imply a more uniform distribution of PPG amplitudes in depressed patients with suicidal ideation, fact that could be related to minimal changes in ANS state. Seldenrijk et al. [46] showed that the early wave reflection in depressive or anxiety disorders was associated with higher arterial stiffness, which agrees with the findings of the present study. Altered vasomotor tone in MDD patients, owing to the autonomic imbalance (increased sympathetic activity), has been related to changes in endothelial function, which is considered a gauge of vascular health [47]. Systematic reviews have shown that depressive symptoms are associated with subclinical atherosclerosis [48], [49]. Arterial stiffness may increase the risk for structural abnormalities in the mood regulatory centers of the brain due to small vessel lesions, contributing to the development of late-life depression (vascular depression hypothesis) [50]- [52]. Irrespective of whether depression is a cause or effect of arterial stiffness, impaired arterial compliance might constitute a biomarker of mental health and might contribute to the increased frequency of cardiovascular diseases observed in MDD patients [53], [54].
In [18], the PDA-based inner waves of a PPG pulse were modeled as Gaussian waves using a Trust-Region algorithm for the fitting procedure, while, in this work, waveform characteristics are derived from the inner waves without the use of fitting. Similar results (not shown) are obtained for both approaches, thereby suggesting a faster feature extraction, which seems appealing for a future integration of PDA into wearable devices. A low sampling frequency might be also required for implementation in wearables, however, it may produce a jitter in fiducial point estimation [55]. To reduce the effect of jitter, an algorithm of interpolation (up-sampling) is commonly used for refining the fiducial point [56]. Based on additional analyses (not shown), where the PPG signal x PPG (n) was up-sampled from F s = 250 Hz to 1000 and 2000 Hz, the effect of F s on morphological indices was minimal leading to changes in the order of 1% for AUC values. Although up-sampling is crucial in PRV analyses, since the effect of jitter can alter spectral indices considerably [57], PPG signals recorded at low sampling frequency, e.g., F s = 250 Hz, may suffice for deriving morphological indices. Note also that if after up-sampling the same tendency for the raw values across conditions is observed, the study of individual differences through autonomic reactivity indices can be affected at even less extent. Further studies can be done by fusing information from different waveform characteristics to further improve the assessment of autonomic reactivity.
The main difference of the present technique with respect to other PDA techniques in the literature is that both main and reflected waves are assumed to be symmetrical and they are extracted one-by-one, instead of obtaining a modeled PPG by fitting several waves at once [58], [59]. This facilitates the interpretation of model parameters based on the pulse wave propagation physiology. Moreover, this decomposition is based on the hypothesis that half of the incidence pulse does not overlap with the reflected one, and same with the following pulses. However, in cases where fast propagation occurs, there might be overlapping between waves, but it should be minimum since it is an overlap of the maximum incident pulse with the lower tails of the reflected one. This point deserves a simulation study for evaluating hemodynamic responses to controlled fluxes, which, however, is out of the scope of this study.
A limitation of the present study is that the performance of PDA was studied mainly on a fingertip PPG signal. PPG signals recorded at different places on the body (wrist, forehead, ear) exhibit quite different morphologies from that of the fingers. Therefore, the current methodology can not be generalized automatically to all PPG signals. However, the database did not include PPG recordings at a second location on the body. Further studies, where PPG signals acquired from various sites of the body are available, should be conducted for evaluating the effect of the recording site on the PDA performance.
Another limitation is that most of MDD patients were in antidepressant treatment. Results of a recent cross-sectional study have shown that there is no association between arterial stiffness and longitudinal exposure to antidepressants [60]. In [61], [62], it was found that depressed patients who responded to antidepressant treatment presented sustained improvement in vascular function. Moreover, in a large cohort study, Dregan et al. [63] showed that the association of depression with arterial stiffness in midlife was mediated via both metabolic syndrome and inflammatory processes rather than antidepressant medication. The hypothesized bidirectional relationship between depression and arterial stiffness can be also mediated by the lack of physical activity and poor diet, rather than the use of antidepressants [64], [65]. However, the reduced number of MDD patients without medication (3 out of 40, see Table I) do not allow the impact of drug treatment on pulse waveform characteristics to be assessed. Furthermore, there are also differences in medication (types, doses, and duration), due to the severity of the depressive symptoms, which further complicate such an analysis.

VI. CONCLUSION
In this study, the autonomic reactivity to stressful stimuli in patients with depression and healthy subjects is assessed by quantifying dynamic changes in PPG morphology using a pulse decomposition analysis. Results show that the stress response of MDD compared to healthy subjects is different and a decreased autonomic reactivity is associated with higher degree of depression. Vascular characteristics such as the percentage of amplitude loss in wave reflections have a potential to become digital biomarkers for the diagnosis and monitoring of depression.

ACKNOWLEDGMENT
The computation was performed by the ICTS "NANBIOSIS", more specifically by the High Performance Computing Unit of the CIBER in Bioengineering, Biomaterials & Nanomedicine (CIBER-BBN) at the University of Zaragoza.