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1.
Article in English | MEDLINE | ID: mdl-38713564

ABSTRACT

BACKGROUND: Posttraumatic stress disorder (PTSD) causes heightened fight-or-flight responses to traumatic memories (i.e., hyperarousal). Although hyperarousal is hypothesized to cause irregular breathing (i.e., respiratory variability), no quantitative markers of respiratory variability have been shown to correspond with PTSD symptoms in humans. OBJECTIVE: In this study, we define interpretable markers of respiration pattern variability (RPV) and investigate whether these markers respond during traumatic memories, correlate with PTSD symptoms, and differ in patients with PTSD. METHODS: We recruited 156 veterans from the Vietnam-Era Twin Registry to participate in a trauma recall protocol. From respiratory effort and electrocardiogram measurements, we extracted respiratory timings and rate using a robust quality assessment and fusion approach. We then quantified RPV using the interquartile range and compared RPV between baseline and trauma recall conditions, correlated PTSD symptoms to the difference between trauma recall and baseline RPV (i.e., ∆RPV), and compared ∆RPV between patients with PTSD and trauma-exposed controls. Leveraging a subset of 116 paired twins, we then uniquely controlled for factors shared by co-twins via within-pair analysis for further validation. RESULTS: We found RPV was increased during traumatic memories (p .001), ∆ RPV was positively correlated with PTSD symptoms (p .05), and patients with PTSD exhibited higher ∆ RPV than trauma-exposed controls (p .05). CONCLUSIONS: This paper is the first to elucidate RPV markers that respond during traumatic memories, especially in patients with PTSD, and correlate with PTSD symptoms. SIGNIFICANCE: These findings encourage future studies outside the clinic, where interpretable markers of respiratory variability are used to track hyperarousal.

2.
Psychophysiology ; 60(3): e14197, 2023 03.
Article in English | MEDLINE | ID: mdl-36285491

ABSTRACT

Post-traumatic stress disorder (PTSD) is an independent risk factor for incident heart failure, but the underlying cardiac mechanisms remained elusive. Impedance cardiography (ICG), especially when measured during stress, can help understand the underlying psychophysiological pathways linking PTSD with heart failure. We investigated the association between PTSD and ICG-based contractility metrics (pre-ejection period (PEP) and Heather index (HI)) using a controlled twin study design with a laboratory-based traumatic reminder stressor. PTSD status was assessed using structured clinical interviews. We acquired synchronized electrocardiograms and ICG data while playing personalized-trauma scripts. Using linear mixed-effects models, we examined twins as individuals and within PTSD-discordant pairs. We studied 137 male veterans (48 pairs, 41 unpaired singles) from Vietnam War Era with a mean (standard deviation) age of 68.5(2.5) years. HI during trauma stress was lower in the PTSD vs. non-PTSD individuals (7.2 vs. 9.3 [ohm/s2 ], p = .003). PEP reactivity (trauma minus neutral) was also more negative in PTSD vs. non-PTSD individuals (-7.4 vs. -2.0 [ms], p = .009). The HI and PEP associations with PTSD persisted for adjusted models during trauma and reactivity, respectively. For within-pair analysis of eight PTSD-discordant twin pairs (out of 48 pairs), PTSD was associated with lower HI in neutral, trauma, and reactivity, whereas no association was found between PTSD and PEP. PTSD was associated with reduced HI and PEP, especially with trauma recall stress. This combination of increased sympathetic activation and decreased cardiac contractility combined may be concerning for increased heart failure risk after recurrent trauma re-experiencing in PTSD.


Subject(s)
Heart Failure , Stress Disorders, Post-Traumatic , Veterans , Humans , Male , Aged , Stress Disorders, Post-Traumatic/complications , Electric Impedance , Twins , Heart Failure/complications
3.
Psychophysiology ; 60(2): e14167, 2023 02.
Article in English | MEDLINE | ID: mdl-35959570

ABSTRACT

Post-traumatic stress disorder (PTSD) has been associated with cardiovascular disease (CVD), but the mechanisms remain unclear. Autonomic dysfunction, associated with higher CVD risk, may be triggered by acute PTSD symptoms. We hypothesized that a laboratory-based trauma reminder challenge, which induces acute PTSD symptoms, provokes autonomic dysfunction in a cohort of veteran twins. We investigated PTSD-associated real-time physiologic changes with a simulation of traumatic experiences in which the twins listened to audio recordings of a one-minute neutral script followed by a one-minute trauma script. We examined two heart rate variability metrics: deceleration capacity (DC) and logarithmic low frequency (log-LF) power from beat-to-beat intervals extracted from ambulatory electrocardiograms. We assessed longitudinal PTSD status with a structured clinical interview and the severity with the PTSD Symptoms Scale. We used linear mixed-effects models to examine twin dyads and account for cardiovascular and behavioral risk factors. We examined 238 male Veteran twins (age 68 ± 3 years old, 4% black). PTSD status and acute PTSD symptom severity were not associated with DC or log-LF measured during the neutral session, but were significantly associated with lower DC and log-LF during the traumatic script listening session. Long-standing PTSD was associated with a 0.38 (95% confidence interval, -0.83,-0.08) and 0.79 (-1.30,-0.29) standardized unit lower DC and log-LF, respectively, compared to no history of PTSD. Traumatic reminders in patients with PTSD lead to real-time autonomic dysregulation and suggest a potential causal mechanism for increased CVD risk, based on the well-known relationships between autonomic dysfunction and CVD mortality.


Subject(s)
Cardiovascular Diseases , Cardiovascular System , Stress Disorders, Post-Traumatic , Veterans , Humans , Male , Aged , Stress Disorders, Post-Traumatic/complications , Autonomic Nervous System , Heart Rate/physiology
4.
PLoS One ; 17(11): e0278420, 2022.
Article in English | MEDLINE | ID: mdl-36449510

ABSTRACT

BACKGROUND: Obstructive sleep apnea (OSA) has been associated with incidence of cardiovascular disease and with nocturnal angina, but evidence of a link with coronary atherosclerosis and myocardial ischemia is limited and previous studies may have been affected by selection bias or unmeasured confounding factors. METHODS: We performed overnight polysomnography in 178 older male twins. The Apnea/Hypopnea Index (AHI) was calculated to assess OSA from the overnight sleep evaluation. AHI ≥15 was used as indicator of moderate/severe OSA. The following day, twins underwent myocardial perfusion imaging with [82Rb]-chloride positron emission tomography. Quantitative and semiquantitative measures of myocardial perfusion and absolute myocardial blood flow were obtained. RESULTS: The mean age was 68 years and 40% of the sample had an AHI≥15, which indicates moderate to severe OSA. Abnormal myocardial perfusion, both with stress and at rest, was more common in twins with elevated AHI. After adjusting for clinical, lifestyle and behavioral factors, and previous history of cardiovascular disease, twins with AHI ≥15 had 3.6 higher odds (95% CI, 1.5-8.9) of an abnormal total severity score, defined as a score ≥100, and for each 5-point increment in AHI, the odds of abnormality increased by 20% (95% CI, 7%-34%). Twin pairs where both twins had OSA exhibited the greatest risk. There were no differences in measures of ischemia and absolute myocardial blood flow and flow reserve by AHI status. CONCLUSIONS: OSA is associated with myocardial perfusion abnormalities that suggest prior subclinical myocardial scarring or infarction. Early environmental factors that affect both twins equally may play a role and should be further explored.


Subject(s)
Cardiovascular Diseases , Coronary Artery Disease , Sleep Apnea, Obstructive , Male , Humans , Aged , Tomography, X-Ray Computed , Sleep Apnea, Obstructive/diagnostic imaging , Polysomnography , Perfusion
5.
Psychophysiology ; 59(12): e14128, 2022 12.
Article in English | MEDLINE | ID: mdl-35717594

ABSTRACT

Pre-ejection period (PEP), an indicator of sympathetic nervous system activity, is useful in psychophysiology and cardiovascular studies. Accurate PEP measurement is challenging and relies on robust identification of the timing of aortic valve opening, marked as the B point on impedance cardiogram (ICG) signals. The ICG sensitivity to noise and its waveform's morphological variability makes automated B point detection difficult, requiring inefficient and cumbersome expert visual annotation. In this article, we propose a machine learning-based automated algorithm to detect the aortic valve opening for PEP measurement, which is robust against noise and ICG morphological variations. We analyzed over 60 hr of synchronized ECG and ICG records from 189 subjects. A total of 3657 averaged beats were formed using our recently developed ICG noise removal algorithm. Features such as the averaged ICG waveform, its first and second derivatives, as well as high-level morphological and critical hemodynamic parameters were extracted and fed into the regression algorithms to estimate the B point location. The morphological features were extracted from our proposed "variable" physiologically valid search-window related to diverse B point shapes. A subject-wise nested cross-validation procedure was performed for parameter tuning and model assessment. After examining multiple regression models, Adaboost was selected, which demonstrated superior performance and higher robustness to five state-of-the-art algorithms that were evaluated in terms of low mean absolute error of 3.5 ms, low median absolute error of 0.0 ms, high correlation with experts' estimates (Pearson coefficient = 0.9), and low standard deviation of errors of 9.2 ms. For reproducibility, an open-source toolbox is provided.


Subject(s)
Aortic Valve , Cardiography, Impedance , Humans , Cardiography, Impedance/methods , Aortic Valve/physiology , Electric Impedance , Reproducibility of Results , Algorithms
6.
Psychophysiology ; 59(7): e14013, 2022 07.
Article in English | MEDLINE | ID: mdl-35150459

ABSTRACT

Pre-ejection period (PEP) is an index of sympathetic nervous system activity that can be computed from electrocardiogram (ECG) and impedance cardiogram (ICG) signals, but sensitive to speech/motion artifact. We sought to validate an ICG noise removal method, three-stage ensemble-average algorithm (TEA), in data acquired from a clinical trial comparing active versus sham non-invasive vagal nerve stimulation (tcVNS) after standardized speech stress. We first compared TEA's performance versus the standard conventional ensemble-average algorithm (CEA) approach to classify noisy ICG segments. We then analyzed ECG and ICG data to measure PEP and compared group-level differences in stress states with each approach. We evaluated 45 individuals, of whom 23 had post-traumatic stress disorder (PTSD). We found that the TEA approach identified artifact-corrupted beats with intraclass correlation coefficient > 0.99 compared to expert adjudication. TEA also resulted in higher group-level differences in PEP between stress states than CEA. PEP values were lower in the speech stress (vs. baseline rest) group using both techniques, but the differences were greater using TEA (12.1 ms) than CEA (8.0 ms). PEP differences in groups divided by PTSD status and tcVNS (active vs. sham) were also greater when using the TEA versus CEA method, although the magnitude of the differences was lower. In conclusion, TEA helps to accurately identify noisy ICG beats during speaking stress, and this increased accuracy improves sensitivity to group-level differences in stress states compared to CEA, suggesting greater clinical utility.


Subject(s)
Carcinoembryonic Antigen , Cardiography, Impedance , Algorithms , Artifacts , Cardiography, Impedance/methods , Electrocardiography , Humans
7.
Biol Psychiatry ; 91(7): 615-625, 2022 04 01.
Article in English | MEDLINE | ID: mdl-34865854

ABSTRACT

BACKGROUND: The link between posttraumatic stress disorder (PTSD) and ischemic heart disease remains elusive owing to a shortage of longitudinal studies with a clinical diagnosis of PTSD and objective measures of cardiac compromise. METHODS: We performed positron emission tomography in 275 twins who participated in two examinations approximately 12 years apart. At both visits, we obtained a clinical diagnosis of PTSD, which was classified as long-standing (both visit 1 and visit 2), late onset (only visit 2), and no PTSD (no PTSD at both visits). With positron emission tomography, we assessed myocardial flow reserve (MFR), which, in absence of significant coronary stenoses, indexes coronary microvascular function. We compared positron emission tomography data at visit 2 across the three categories of longitudinally assessed PTSD and examined changes between the two visits. RESULTS: Overall, 80% of the twins had no or minimal obstructive coronary disease. Yet, MFR was depressed in twins with PTSD and was progressively lower across groups with no PTSD (2.13), late-onset PTSD (1.97), and long-standing PTSD (1.93) (p = .01). A low MFR (a ratio <2.0) was present in 40% of the twins without PTSD, in 56% of those with late-onset PTSD, and in 72% of those with long-standing PTSD (p < .001). Associations persisted in multivariable analysis, when examining changes in MFR between visit 1 and visit 2, and within twin pairs. Results were similar by zygosity. CONCLUSIONS: Longitudinally, PTSD is associated with reduced coronary microcirculatory function and greater deterioration over time. The association is especially noted among twins with chronic, long-standing PTSD and is not confounded by shared environmental or genetic factors.


Subject(s)
Coronary Artery Disease , Myocardial Perfusion Imaging , Stress Disorders, Post-Traumatic , Humans , Microcirculation , Myocardial Perfusion Imaging/methods , Perfusion , Positron-Emission Tomography , Stress Disorders, Post-Traumatic/diagnostic imaging
8.
Annu Int Conf IEEE Eng Med Biol Soc ; 2021: 1444-1447, 2021 11.
Article in English | MEDLINE | ID: mdl-34891557

ABSTRACT

Research has shown that transcutaneous cervical vagus nerve stimulation (tcVNS) yields downstream changes in peripheral physiology in individuals afflicted with posttraumatic stress disorder (PTSD). While the cardiovascular effects of tcVNS have been studied broadly in prior work, the specific effects of tcVNS on the reciprocal of the pulse transit time (1/PTT) remain unknown. By quantifying detectable effects, tcVNS can be further evaluated as a counterbalance to sympathetic hyperactivity during distress - specifically, we hypothesized that tcVNS would inhibit 1/PTT responses to traumatic stress. To investigate this, the electrocardiogram (ECG), photoplethysmogram (PPG), and seismocardiogram (SCG), were simultaneously measured from 24 human subjects suffering from PTSD. Implementing state-of-the-art signal quality assessment algorithms, relative changes in the pulse arrival time (PAT) and the pre-ejection period (PEP) were estimated solely from signal segments of sufficient quality. Thereby computing relative changes in 1/PTT, we find that tcVNS results in reduced 1/PTT responses to traumatic stress and the first minute of stimulation, compared to a sham control (corrected p < 0.05). This suggests that tcVNS induces inhibitory effects on blood pressure (BP) and/or vasoconstriction, given the established relationship between 1/PTT and these parameters.Clinical Relevance- Relative changes in 1/PTT are induced by varying vasomotor tone and/or BP - it has therefore piqued considerable interest as a potential surrogate of continuous BP. Studying its responses to tcVNS thus furthers understanding of tcVNS-induced cardiovascular modulation. The positive effects detailed herein suggest a potential role for tcVNS in the long-term management of PTSD.


Subject(s)
Stress Disorders, Post-Traumatic , Vagus Nerve Stimulation , Humans , Pulse Wave Analysis , Stress Disorders, Post-Traumatic/therapy , Vagus Nerve
9.
Cureus ; 13(9): e17937, 2021 Sep.
Article in English | MEDLINE | ID: mdl-34660127

ABSTRACT

Introduction Erectile dysfunction (ED) is a prevalent medical condition that affects millions of men globally. A number of pharmacological and complementary options are used in the management of ED, including Coenzyme Q10 (CoQ10). Oxidative stress has been linked to the progression of ED, and Co Q10 protects against oxidative damages and improves erectile function as well as the activity of antioxidant enzymes. This study aimed to determine the efficacy of CoQ10 in the treatment of erectile dysfunction in hypertensive males. Method An open-labeled parallel arm interventional study was conducted in the cardiology unit of Hayatabad Medical Complex Hospital, Peshawar, Pakistan, from March 2020 to March 2021. Hypertensive male patients (n = 230) were randomly allocated to either receiving 200-gram CoQ10 daily along with their current antihypertensive therapy (n=104) or anti-hypertensive treatment only (n=105). The patient's erectile function was assessed at baseline and three months using the International Index of Erectile Function Test (IIEF-5) during the study period. Result Of the total 230, 209 (90.87%) patients were included in the final analysis. There were no significant differences in demographics, history of illness, co-morbid conditions, and current medication of both groups. After three months, 21 (20.1%) participants scored more than 17 in the IIEF-5 and no longer had ED. Overall, no significant difference was found in the mean IIEF-5 score between the study group and control group (14.41 ± 4.49 Vs. 15.61 ± 4.82; p=0.06). However, in subgroup analysis, significant improvement in the study group was seen in participants with mild ED (p=0.03). Conclusion With the demonstration of its efficacy in hypertensive patients with mild ED, co-enzyme Q10 supplementation can be proposed as a potential candidate in patients with long-term hypertension and can play a role in erectile dysfunction.

10.
Ann Med Surg (Lond) ; 69: 102828, 2021 Sep.
Article in English | MEDLINE | ID: mdl-34512966

ABSTRACT

Coronavirus Disease 19 (COVID-19) has led to a global pandemic and has been the center of attention across the entire medical community. This novel virus was initially thought to affect primarily the respiratory system, but now it is evident that it has a multitude of effects on the human body. Our point of interest is to establish the effect of COVID-19 infection on the conducting system of the heart. We present a case series of four patients who developed complete heart block (CHB) shortly after being infected with COVID-19 without any previous known risk factors of complete heart block. There have only been a few previous case reports on the occurrence of CHB in COVID-19 patients highlighting the importance and the need of our case series to the literature of cardiovascular outcomes in COVID-19 patients. Our case series highlight that COVID-19 can indeed affect the conduction system of the heart and cause CHB in patients who then recovered spontaneously further elucidating the transient nature of cardiovascular effects caused by the novel virus.

11.
Brain Behav Immun ; 90: 294-302, 2020 11.
Article in English | MEDLINE | ID: mdl-32916271

ABSTRACT

Stress may contribute to progression of coronary heart disease (CHD) through inflammation, especially among women. Thus, we sought to examine whether increased inflammatory response to stress among patients with CHD is associated with a greater risk of cardiovascular events and whether this risk is higher in women. We examined inflammatory biomarkers known to increase with mental stress (speech task), including interleukin-6 (IL-6), monocyte chemoattractant protein-1 (MCP-1), and matrix metallopeptidase-9 (MMP-9) among 562 patients with stable CHD. Inflammatory response, the difference between post-stress and resting values, was examined as a predictor of major adverse cardiovascular events (MACE) using subdistribution hazards models for competing risks adjusting for demographics, cardiovascular risk factors, and medications. MACE was defined as a composite endpoint of cardiovascular death, myocardial infarction, unstable angina with revascularization, and heart failure. All biomarkers were standardized. The mean age was 63 years (range 34-79) and 24% were women. During a median follow-up of 3 years, 71 patients experienced MACE. Overall, there was no significant association between inflammatory response to stress and risk of MACE, but there were sex-based interactions for IL-6 (p = 0.001) and MCP-1 (p = 0.01). The risk of MACE increased 56% (HR: 1.56; 95% CI: 1.21, 2.01; p = 0.001) and 30% (HR: 1.30; 95% 1.09, 1.55; p = 0.004) for each standard deviation increase in IL-6 and MCP-1 response to mental stress for women, respectively, while there was no association among men. Increased inflammation in response to stress is associated with future adverse cardiovascular outcomes among women with CHD.


Subject(s)
Cardiovascular System , Coronary Artery Disease , Heart Failure , Myocardial Infarction , Adult , Aged , Female , Humans , Male , Middle Aged , Risk Factors , Sex Characteristics
12.
Sleep ; 43(8)2020 08 12.
Article in English | MEDLINE | ID: mdl-32006429

ABSTRACT

STUDY OBJECTIVES: The usage of wrist-worn wearables to detect sleep-wake states remains a formidable challenge, particularly among individuals with disordered sleep. We developed a novel and unbiased data-driven method for the detection of sleep-wake and compared its performance with the well-established Oakley algorithm (OA) relative to polysomnography (PSG) in elderly men with disordered sleep. METHODS: Overnight in-lab PSG from 102 participants was compared with accelerometry and photoplethysmography simultaneously collected with a wearable device (Empatica E4). A binary segmentation algorithm was used to detect change points in these signals. A model that estimates sleep or wake states given the changes in these signals was established (change point decoder, CPD). The CPD's performance was compared with the performance of the OA in relation to PSG. RESULTS: On the testing set, OA provided sleep accuracy of 0.85, wake accuracy of 0.54, AUC of 0.67, and Kappa of 0.39. Comparable values for CPD were 0.70, 0.74, 0.78, and 0.40. The CPD method had sleep onset latency error of -22.9 min, sleep efficiency error of 2.09%, and underestimated the number of sleep-wake transitions with an error of 64.4. The OA method's performance was 28.6 min, -0.03%, and -17.2, respectively. CONCLUSIONS: The CPD aggregates information from both cardiac and motion signals for state determination as well as the cross-dimensional influences from these domains. Therefore, CPD classification achieved balanced performance and higher AUC, despite underestimating sleep-wake transitions. The CPD could be used as an alternate framework to investigate sleep-wake dynamics within the conventional time frame of 30-s epochs.


Subject(s)
Actigraphy , Sleep Wake Disorders , Aged , Algorithms , Humans , Male , Polysomnography , Sleep
13.
Compr Psychoneuroendocrinol ; 4: 100012, 2020 Nov.
Article in English | MEDLINE | ID: mdl-35755625

ABSTRACT

Pituitary adenylate cyclase-activating peptide (PACAP) is a neuropeptide that plays a key role in the neurobiology of the stress response, and prior studies suggest that its function is dysregulated in post-traumatic stress disorder (PTSD). Transcutaneous cervical vagus nerve stimulation (tcVNS) acts through PACAP and other neurobiological systems to modulate stress responses and/or symptoms of PTSD. In this pilot study, we examined the effects of tcVNS on PACAP in a three day chronic stress laboratory paradigm involving serial traumatic and mental stress exposures in healthy individuals with a history of exposure to psychological trauma (n â€‹= â€‹18) and patients with PTSD (n â€‹= â€‹12). Methods: A total of 30 subjects with a history of exposure to psychological trauma experience were recruited (12 with PTSD diagnosis) for a three-day randomized double-blinded study of tcVNS or sham stimulation. Subjects underwent a protocol that included both personalized trauma recall and non-personalized mental stressors (public speaking, mental arithmetic) paired to tcVNS or sham stimulation over three days. Blood was collected at baseline and multiple time points after exposure to stressors. Linear mixed-effects models were used to assess changes in PACAP over time (in response to stressors) and its relation to active tcVNS or sham stimulation. Results: PACAP blood levels increased over the course of three days for both active tcVNS and sham groups. This increase was statistically-significant in the sham group at the end of the second (Cohen's drm â€‹= â€‹0.35, p â€‹= â€‹0.04), and third days (drm â€‹= â€‹0.41, p â€‹= â€‹0.04), but not in the active tcVNS group (drm â€‹= â€‹0.21, drm â€‹= â€‹0.18, and p â€‹> â€‹0.20). Conclusion: These pilot findings suggest tcVNS may attenuate this neurobiological stress-response. Larger studies are needed to investigate gender and interaction effects.

14.
Psychosom Med ; 82(3): 272-280, 2020 04.
Article in English | MEDLINE | ID: mdl-31842060

ABSTRACT

OBJECTIVE: This study aimed to investigate the relationship between waist circumference as a measure of abdominal obesity and brain responses to stress among patients with coronary artery disease (CAD). METHODS: Patients with CAD (N = 151) underwent acute mental stress tasks in conjunction with high-resolution positron emission tomography and radiolabeled water imaging of the brain. Brain responses to mental stress were correlated with waist circumference. RESULTS: Waist circumference was positively correlated with increased activation in the right and left frontal lobes (ß values ranging from 2.81 to 3.75 in the paracentral, medial, and superior gyri), left temporal lobe, left hippocampal, left amygdala, left uncus, and left anterior and posterior cingulate gyri (ß values ranging from 2.93 to 3.55). Waist circumference was also negatively associated with the left and right parietal lobes, right superior temporal gyrus, and right insula and precuneus (ß values ranging from 2.82 to 5.20). CONCLUSION: Increased brain activation in the brain regions involved in the stress response and autonomic regulation of the cardiovascular system during psychological stress may underlie stress-induced overeating and abdominal obesity in patients with CAD.


Subject(s)
Brain/physiopathology , Coronary Artery Disease/physiopathology , Obesity, Abdominal/physiopathology , Stress, Psychological/physiopathology , Adult , Aged , Aged, 80 and over , Brain/diagnostic imaging , Female , Frontal Lobe/diagnostic imaging , Frontal Lobe/physiopathology , Gyrus Cinguli/diagnostic imaging , Gyrus Cinguli/physiopathology , Hippocampus/diagnostic imaging , Hippocampus/physiopathology , Humans , Magnetic Resonance Imaging , Male , Middle Aged , Obesity, Abdominal/complications , Parietal Lobe/diagnostic imaging , Parietal Lobe/physiopathology , Positron-Emission Tomography , Stress, Psychological/complications , Waist Circumference
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