# Elevated brain pulsations in depression: insights from a pooled ultrasound cohort study

Ugoline Couvreur, Quentin Gallet, Jacques-Yves Campion, Bruno Brizard, Jean-Pierre Réméniéras, Valérie Gissot, Wissam El-Hage, Vincent Camus, Bénédicte Gohier, Thomas Desmidt

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Ugoline Couvreur, Quentin Gallet, Jacques-Yves Campion, Bruno Brizard, Jean-Pierre Réméniéras, et al.. Elevated brain pulsations in depression: insights from a pooled ultrasound cohort study. Interface Focus, 2024, 14 (6), 10.1098/rsfs.2024.0028. hal-04912321

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Elevated Brain Pulsations in Depression: Insights from a Pooled Ultrasound Cohort Study

Ugoline Couvreur<fnref n="1" />,<fnref n="2" />, Quentin Gallet MD<fnref n="1" />,<fnref n="2" />,<fnref n="3" />, Jacques-Yves Campion MD<fnref n="4" />,<fnref n="7" />, Bruno Brizard M.Sc<fnref n="5" />, Jean-Pierre Réméniéras, PhD<fnref n="5" />, Valérie Gissot MD<fnref n="6" />, Wissam El-Hage MD, PhD<fnref n="5" />,<fnref n="6" />,<fnref n="7" />, Vincent Camus MD, PhD<fnref n="5" />,<fnref n="7" />, Bénédicte Gohier MD, PhD<fnref n="1" />,<fnref n="2" />,<fnref n="3" />, Thomas Desmidt MD, PhD<fnref n="5" />,<fnref n="7" />,*

<footnote n="1">¹ Department of Psychiatry, University Hospital, Angers, France.</footnote>

<footnote n="2">² Université d'Angers, Angers, France.</footnote>

<footnote n="3">³ Université d'Angers, Université de Nantes, LPPL, SFR Confluences, F-49000 Angers, France.</footnote>

<footnote n="4">⁴ Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, CERIMED, Marseille, France</footnote>

<footnote n="5">⁵ UMR 1253, iBraiN, Université de Tours, Inserm, Tours, France.</footnote>

<footnote n="6">⁶ CIC 1415, CHU de Tours, Inserm, Tours, France.</footnote>

<footnote n="7">⁷ CHU de Tours, Tours, France.</footnote>

<footnote>* Corresponding author:</footnote>

<footnote>Thomas Desmidt, Département de Psychiatrie de la Personne Agée, CHRU de Tours, France</footnote>

<footnote n="2">2 Boulevard Tonnellé, 37044 Tours Cedex 9, France</footnote>

<footnote>Phone: +33 2 34 37 89 52</footnote>

<footnote>email: t.desmidt@chu-tours.fr</footnote>

<footnote>Abstract word count: 198</footnote>

<footnote>Core text word count: 2644</footnote>

<footnote>Tables: 2</footnote>

<footnote>Figures: 1</footnote>

<footnote>**Keywords:** Tissue Pulsatility Imaging; Brain Tissue Pulsations; Depression; Blood Pressure</footnote>
ABSTRACT

Excessive Brain Tissue Pulsations (BTP), measured by ultrasound, have been associated with depression and are hypothesized to contribute to brain damage in this population at risk for cerebrovascular lesions. However, previous research has been limited by small sample sizes. To address this issue, our study pooled data from three separate investigations, resulting in the largest cohort of depressed participants with BTP measurements to date.

We analysed 123 participants (74 individuals with depression, 49 healthy controls) using ultrasound Tissue Pulsatility Imaging (TPI) to assess resting BTP.

Results showed that both MeanBTP and MaxBTP were significantly associated with depression, as determined by multiple linear regression models that included age, sex, and blood pressure as covariates. Additionally, we found that age, sex, and diastolic blood pressure were significant predictors of BTP. Specifically, BTP decreased with age, was higher in men, and was more strongly predicted by diastolic blood pressure than by systolic blood pressure.

In this large cohort, we replicated the association between depression and increased BTP, supporting the notion that elevated BTP may be a potential mechanism underlying brain damage over time. Our findings suggest that TPI could serve as a valuable surrogate marker for brain health in clinical practice.
# 1. INTRODUCTION

Recent advancements in ultrasound technology now allow for the precise measurement of brain pulsations. Indeed, the brain pulsates within the cranial cavity and moves by a few micrometres with a period of about one second, primarily influenced by heartbeats transmitted to the brain parenchyma through the arteries. Our team and others have employed ultrasound measurement of Brain Tissue Pulsations (BTP) to investigate factors associated with BTP amplitude variations. A wide range of physiological and pathophysiological conditions, including blood pressure [1], aging [2], brain volume [3,4], cerebrovascular lesions [5,6], visual and auditory stimulation [7,8], neural activity [2], orthostatic hypotension [1], hypocapnia [9], and psychiatric disorders like neuroticism and depression [10-12], have been linked to BTP. However, most previous studies had relatively small sample sizes, and the determinants of BTP amplitude remain incompletely characterized.

Depression is a severe mental disorder not only because of its dramatically high prevalence worldwide [13] but also because it exposes to pathophysiological complications such as cerebrovascular lesions and stroke [14-16]. The mechanisms underlying the depression-cerebrovascular lesion link are not fully understood, but we have proposed that elevated BTP amplitudes may contribute to brain tissue damage over time. Indeed, our previous research observed larger BTP amplitudes in depressed participants compared to healthy controls and those with past but not current depression [17]. In addition, we observed that BTP amplitudes decreased after 2 months of a successful antidepressant therapy [18]. Moreover, changes in BTP can be used as maker for treatment response in depressed participants expose to one hour of nitrous oxide, a gas with rapid antidepressant properties [19]. Yet, these studies were limited by small sample sizes and require replication in larger cohorts. Larger studies would also allow for investigation of potential confounding factors using more robust statistical models.

This study aims to pool data from three studies conducted at the same location, all of which utilized identical BTP measurement procedures and included participants with depression. Our objectives were threefold: 1) to replicate the finding of increased BTP amplitude in depression with greater statistical power than previous studies, 2) to investigate potential confounding factors that might influence the association between depression and BTP, and 3) to confirm the previously observed relationships between BTP, age, sex, and blood pressure.
## 2. METHODS

### 2.1 Participants and study design

Data were pooled from 3 studies (the EMPHILINE study [17], the M-PULSE study [8] and the BIORESA study [18] - respectively, NCT02026622, NCT03867422 and NCT03118193 on clinicaltrials.gov) performed in the same location of the Clinical Investigation Centre of the university hospital of Tours, France. All these 3 studies included the same US procedure to measure BTP amplitude (notably the same US device and the same operators) at rest and had the same inclusion criteria for depressed participants and healthy controls.

A total of 123 participants were included in the analyses among which 74 were considered depressed and 49 healthy controls. All depressed patients had to meet the DSM-IV criteria for a major depressive disorder as assessed by a trained psychiatrist with a severity score > 20 on the Montgomery-Åsberg Depression Rating Scale (MADRS). All control subjects were recruited from the local community and from the records of the Clinical Investigation Centre of the Hospital of Tours, France. Non-inclusion criteria for the three trials included any history of psychiatric or neurological disorders, pregnancy, and legal guardianship. In the first two trials, individuals with a history of severe cardiovascular disease or currently taking beta-blockers or psychotropic medications were also excluded. Informed consent was obtained from all participants in each of these trials, and the local human ethics committee approved the research protocols.

### 2.2 Ultrasound Protocol

The US protocol was extensively described elsewhere [19]. It was carried out on an Antares medical scanner (Siemens Healthcare, Germany) by a biophysics technician trained for Tissue Pulsatility Imaging (TPI). Transcranial acquisitions were conducted using a PX4-1 phased-array transducer (Siemens Healthcare; 1.82 MHz emission frequency, 70° field of view, 112 x 3 elements (1.5D)). Measurements were taken through the right temporal bone window, with the probe placed perpendicular to the skull and stabilized by a mechanical holder to minimize artifacts from both operator and subject movements. Subjects were instructed to maintain a seated position. They were asked to stay still and breathe normally. The US scanner was first set to Doppler mode for transcranial doppler acquisition. Colour doppler was utilized to align the US beam with the right middle cerebral artery (MCA). The pulsatility index (PI—ratio of the difference between maximal and minimal velocities over mean velocity) and the maximum and mean velocities of the MCA were obtained and automatically calculated by the scanner from a 10-second Doppler sequence. Subsequently, the US scanner was switched to Echo-B mode for TPI measurements centred on the MCA. To reduce US attenuation, the acquisition depth was adjusted between 3 and 9 cm. This configuration enabled the
exploration of the circle of Willis and a transversal slice of the temporal hemispheres. For each participant, the protocol included four 10-second acquisitions that were repeated with an acquisition fame rate of 30/images/s (total of 297 frames). The US scanner provided direct access to beam-formed radiofrequency (RF) lines, which were utilized to estimate BTP. The data were then transferred for offline analysis using MATLAB software (MathWorks, USA).

Our method, as described below, evaluates the z-axis component of brain displacements. The z-axis is perpendicular to the US probe surface while the x-axis extends along the surface of the probe. The US firing sequence consists of a series of M broad-view focused pulsing events transmitted sequentially. Between each firing, the transmission (TX) steering angle θ (i.e., the angle of propagation relative to the normal surface of the transducer) is incrementally adjusted to cover a range of M angles throughout the entire series of pulsing events. For each focused transmission TX at a specific θ angle, beamformed IQ data lines are generated from echoes captured by the transducers. At each time point t, we independently estimate brain tissue motion at all pixel positions. For a particular pixel of interest located on a US line identified by the transmit angle θ, we utilized the temporal lag-one autocorrelation algorithm [20] to determine the phase shift Δφ between successive complex IQ data. We employed the modified version [21] of the Doppler equation used for vector flow estimation, where $\vec{V}$ is the Doppler tissue velocity, λ the US wavelength, T the IQ temporal discretization interval, $\vec{n}_{TX}$ the direction of the US propagation in transmit mode TX, and $\vec{n}_{RX}$ the direction of the US RX beamforming.

1.

$$ \Delta\Phi = \frac{2\pi T}{\lambda} (\vec{V} \cdot \vec{n}_{TX} + \vec{V} \cdot \vec{n}_{RX}) $$

In our application, these two vectors' directions are identical and $\vec{n}_{TX} = \vec{n}_{RX} = \vec{n}$ with $\vec{n} = (\sin\theta, \cos\theta)$. Thus, the phase shift Δφ estimated by our algorithm expressed:

2.

$$ \Delta\Phi = \frac{4\pi T}{\lambda} \vec{V} \cdot \vec{n} = \frac{4\pi T}{\lambda} (V_x \sin\theta + V_z \cos\theta) $$

This Doppler phase shift Δφ is angle θ dependent and is also influenced by the lateral tissue velocity $V_x$. Within our applied setting, the circulation of blood causes the brain to swell, primarily resulting in a radial displacement. Given that the US probe is positioned perpendicular to the skull, and thus nearly perpendicular to the outer surface of the brain, the $V_x$ tissue velocity component aligned with x-axis in equation (2) is minimal, and therefore, it was disregarded. Consequently, the
expression or Doppler phase shift can be simplified to $\Delta\Phi = \frac{4\pi T}{\lambda}V_z\cos\theta$, enabling us to calculate the component $V_z$ of the brain tissue velocity along the depth axis from z-axis displacement. $u_z$ is obtained from the cumulative summation of $V_z$ in the temporal domain.

3.

$$V_z = \frac{\lambda}{4\pi T \cos\theta} \Delta\Phi$$

We acquired a 3D matrix of BTP, consisting of axial displacements $u_z$ (x, z, t) along the z-axis, x-axis and time t. Subsequently, we examined the temporal evolution of BTP at each position within the 2D plane.

Two criteria were employed to eliminate artifacts and emphasize physiological signals, which are presumed to be stable in terms of periodicity and amplitude. The first criterion investigated the periodicity of brain pulsations and involved the ratio of the second maximum peak to the central peak (SMP/CP) of the temporal autocorrelation function of each kernel. Records were validated if the SMP/CP ratio exceeded 0.6 and then subjected to the second criterion. The second criterion assessed the difference in amplitudes between pulsations in each curve. The cumulated standard deviation (CSTD) of the pulsations was calculated to assess data dispersion and normalized to the peak-to-peak amplitude (Umean) of the mean temporal curve. Records were validated if the CSTD/Umean ratio was less than 0.25; otherwise, they were rejected. The thresholds for the two criteria were based on previous studies [5;17].

From this final matrix, two curves, MaxBTP and MeanBTP, were extracted, corresponding to the curve with the maximum mean peak-to-peak amplitude (averaged between cycles) and the average of all curves in the matrix, respectively. MaxBTP and MeanBTP represent the pulsatility of the largest artery (i.e., MCA) and the mean pulsatility across the entire acquisition region, respectively.

## 2.3 Statistical Analyses

Clinical variables were described and compared according to the presence or absence of a depressive state. Quantitative variables were described using means and standard derivations and compared using a Student's t-test. Qualitative variables were described by numbers and percentages and compared using a chi-square test.

We conducted two multiple linear regression analyses to examine the association between depression (independent variable) and MeanBTP (dependent variable in the first regression model) and MaxBTP (dependent variable in the second regression model). To control for potential
confounding factors, we included age, sex, systolic blood pressure, and diastolic blood pressure as covariates in both models. We evaluated these two models in the entire sample and in separate analyses for depressed and healthy control subgroups. The symbols $\beta$ and $t$, as presented in Table 2, denote the estimated coefficients of the regression models.

Finally, we tested associations in the depressed sub-group between MeanBTP and MaxBTP with depression severity (the MADRS) and duration of the episode, using Pearson's correlation. We also compared MeanBTP and MaxBTP between antidepressant users and non-users in the depressed sub-group using a Student's t-test. Statistical analysis was performed using JASP statistical software, version 0.18.1.
### 3. RESULTS

Demographic and clinical characteristics are shown in Table 1. There was no significant difference between the depressed and control groups regarding age, sex, systolic and diastolic blood pressure. Univariate comparison found that MeanBTP was significantly greater in the depressed group, whereas there was no significant difference in MaxBTP (Figure 1).

Results of the multiple linear regressions are shown in Table 2. In the whole sample, MeanBTP (F=3.187, p=0.010) was positively associated with depression (t=2.685, p=0.008) and sex (male) (t=2.697, p=0.008), whereas MaxBTP (F=7.489, p<0.001) was positively associated with depression (t=2.220, p=0.028) and sex (male) (t=2.602, p=0.010) and negatively associated with age ($\beta$ =-0.266, p=0.003) and diastolic blood pressure ($\beta$ =-0.370, p=0.008). In the depressed sub-sample, the only significant association was between MaxBTP and age ($\beta$=-0.288, p=0.018), although there were statistical trends for a negative association between MaxBTP and diastolic blood pressure ($\beta$=-0.331, p=0.082) and for a positive association between MaxBTP and sex (male) (t=1.693, p=0.095). In the healthy controls sub-group, MeanBTP was positively associated with sex (male), whereas MaxBTP was negatively associated with age ($\beta$=-0.272, p=0.049) and diastolic blood pressure ($\beta$=-0.432, p=0.048). There was also a statistical trend for a positive association between MaxBTP and sex (male) (t=1.851, p=0.071).

In the depressed sub-sample, we found no association between MeanBTP or MaxBTP and MADRS (respectively, r=0.014, p=0.909 and r=0.055, p=0.642) or duration of the episode (respectively, r=-0.185, p=0.114 and r=0.032, p=0.784). There was also no significant difference in either MeanBTP or MaxBTP between antidepressant users versus non-users (respectively, 11.0 (4.3) vs 11.6 (4.3), t=0.437, p=0.663 and 70.4 (26.8) vs 83.0 (25.5), t=1.495, p=0.139).
4. DISCUSSION

In this pooled ultrasound data study, we successfully replicated the finding of increased brain
pulsations in depression within a large cohort. Consistent with previous research, univariate analyses
showed that MeanBTP was significantly higher in depressed participants compared to healthy
controls, while MaxBTP did not show a significant association. However, in multivariate analyses,
which accounted for age, sex, and blood pressure, MaxBTP became significantly associated with
depression. Additionally, the association between depression and MeanBTP was further strengthened
when these covariates were included in the multivariate models.

Our results demonstrate a significant association between depression and brain pulsations, which is not solely attributable to age, sex, or blood pressure, known factors influencing BTP [1;2;22]. Our results also suggest that the relationship between brain pulsations and depression is confounded by age, sex, or blood pressure, in the way that these variables amplify the association between BTP and depression, potentially due to strong reciprocal correlations.

We replicated the previously reported effect of aging on decreased brain pulsation amplitudes [2]. Notably, we observed a stronger association with MaxBTP compared to MeanBTP, across both the entire sample and the two subgroups. Previous research has indicated that aging primarily impacts larger brain pulsations (MaxBTP) rather than average pulsations (MeanBTP), suggesting a greater influence on large arteries or brain parenchyma structure. However, it is essential to note that our study population primarily consisted of young adults, limiting our ability to assess the full impact of aging in older individuals.

The influence of sex on brain pulsations remains relatively understudied. Our findings indicate
a strong association between male sex and increased brain pulsation amplitudes in both the total
sample and the control subgroup. While there was a statistical trend towards a similar association in
the depressed subgroup for MaxBTP, it did not reach statistical significance. Given the higher risk of
brain damage, such as stroke, in men compared to women during mid-life [23], our results suggest
that larger brain pulsations in males may contribute to this increased risk.

Interestingly, MaxBTP was also associated with blood pressure, with diastolic blood pressure being a stronger predictor than systolic blood pressure. Previous findings demonstrated a strong negative correlation between BTP and diastolic blood pressure, particularly evident during orthostatic challenges where BTP consistently decreased with rising diastolic blood pressure while systolic blood pressure remained relatively stable [18;22]. These observations align with the previously described influence of pulse pressure on BTP. As diastolic blood pressure increases and systolic blood pressure remains constant, pulse pressure diminishes, consequently reducing brain pulsations. Conversely, a decrease in diastolic blood pressure can lead to increased pulse pressure and larger brain pulsations.
This mechanism likely explains the negative association between diastolic blood pressure and MaxBTP.

We found no association between BTP and depression severity (as assessed by the MADRS), episode duration, or antidepressant use. This could be attributed to insufficient statistical power or the absence of a dose-response relationship between BTP and depression severity. Our findings suggest that all patients with depression, regardless of symptom severity, may be at risk for brain damage. This implies a need for equal attention to both severe and mild depression in terms of potential brain health implications.

Limitations of this study include its cross-sectional design, which precludes us from causal inference. However, our previous longitudinal research observed a decrease in brain pulsations following clinical improvement in depression after a two-month follow-up. Conversely, brain pulsations remained elevated in patients with persistent depression, suggesting that elevated brain pulsations may serve as a state marker for depression. Additionally, the study's limitations include the inability to account for potential confounding factors such as brain volume, which has been linked to both depression and brain pulsations, due to the absence of MRI data in a significant portion of the participants.
5. CONCLUSION

In conclusion, our findings support the potential of ultrasound-based BTP measurement using TPI as a valuable marker of brain health, particularly in individuals at risk for brain damage, such as those with depression, who are susceptible to stroke, white matter lesions, or brain atrophy. Furthermore, TPI shows promise as a bedside tool for assessing brain health in at-risk populations, including patients with neuropsychiatric disorders, complementing traditional methods like blood pressure monitoring and more costly, less accessible neuroimaging techniques such as MRI. The non-invasive, low-cost, and easily implementable nature of TPI makes it an attractive option for routine brain health monitoring, enabling the early identification of individuals with excessive BTP. This could allow for timely interventions aimed at reducing BTP, potentially mitigating the detrimental effects of excessive brain pulsatility on brain tissue. However, longitudinal studies in the general population and among patients with various brain-related conditions are necessary to further substantiate these findings.
## ACKNOWLEDGEMENTS

The EMPHILINE study received grant from the French National Research Agency (Agence Nationale de la Recherche: ANR-2011- Brain tissue pulsatility in midlife depression T Desmidt et al EMCO-005-‘Emphiline project’) and the Planiol Foundation for brain study (Fondation Planiol pour le Cerveau), Varennes, France.

The Biomarkers of Antidepressant Resistance – BIORESA – study was funded by the Region Centre-Val de Loire, France. The study funder had no role to play in the study design, data collection, data analysis, data interpretation, or writing of the report.

## CONFLICT OF INTEREST

TD holds shares in Synaptys Neuroscience and has received personal fees from Janssen, Lundbeck, Otsuka, and Eisai. WEH reports personal fees from Air Liquide, Boehringer Ingelheim, Eisai, Janssen, Lundbeck, Novartis, Otsuka, UCB and Chugai. VC reports personal fees from Janssen and Bristol Myers Squibb. All other authors declare no competing interests.
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<table><caption>**Table 1.** Comparisons of the clinical and ultrasound characteristics between depressed and healthy control groups. Values are expressed as mean (standard deviation) or n (%). Comparisons were performed with t-tests (quantitative data) and chi-squared tests (qualitative data).</caption><thead><tr><th></th><th>Depressed<br>(n=74)</th><th>Controls<br>(n=49)</th><th>p value</th></tr></thead><tbody><tr><td>Age (years)</td><td>33.5 (13.3)</td><td>33.3 (11.7)</td><td>0.955</td></tr><tr><td>Sex (female)</td><td>61 (82.4%)</td><td>40 (81.6%)</td><td>0.910</td></tr><tr><td>SBP (mmHg)</td><td>122.0 (14.2)</td><td>124.1 (16.1)</td><td>0.460</td></tr><tr><td>DBP (mmHg)</td><td>75.5 (11.5)</td><td>73.3 (10.3)</td><td>0.291</td></tr><tr><td>MADRS score</td><td>30.5 (4.9)</td><td>-</td><td>-</td></tr><tr><td>Duration of MDE (weeks)</td><td>26.0 (33.0)</td><td>-</td><td>-</td></tr><tr><td>Antidepressant use</td><td>11 (14%)</td><td>-</td><td>-</td></tr><tr><td>MeanBTP (μm)</td><td>11.5 (4.3)</td><td>9.4 (5.2)</td><td>0.014</td></tr><tr><td>MaxBTP (μm)</td><td>81.1 (25.9)</td><td>73.8 (27.4)</td><td>0.142</td></tr></tbody></table>

SBP: Systolic Blood Pressure; DBP: Diastolic Blood Pressure; MDE: Major Depressive Episode; MADRS: Montgomery Asberg Depression Rating Scale; BTP: Brain Tissue Pulsations.
<table><caption>**Table 2.** Results of the multiple linear regression analyses that were conducted to examine the associations between MeanBTP or MaxBTP (dependent variables) and depression (in the whole sample only), age, sex, systolic blood pressure, and diastolic blood pressure (independent variables) across the whole sample and within depressed and control subgroups.</caption><thead><tr><th rowspan="2"></th><th colspan="2">Whole sample (n=123)</th><th colspan="2">Depressed sub-sample (n=74)</th><th colspan="2">Controls sub-sample (n=49)</th></tr><tr><th>MeanBTP</th><th>MaxBTP</th><th>MeanBTP</th><th>MaxBTP</th><th>MeanBTP</th><th>MaxBTP</th></tr></thead><tbody><tr><td>Depression</td><td>t=2.685, <b>p=0.008</b></td><td>t=2.220, <b>p=0.028</b></td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Age</td><td>β=0.117, p=0.907</td><td>β=-0.266, <b>p=0.003</b></td><td>β=0.037, p=0.777</td><td>β=-0.288, <b>p=0.018</b></td><td>β=-0.007, p=0.958</td><td>β=-0.272, <b>p=0.049</b></td></tr><tr><td>Sex (male)</td><td>t=2.697, <b>p=0.008</b></td><td>t=2.602, <b>p=0.010</b></td><td>t=1.474, p=0.145</td><td>t=1.693, p=0.095</td><td>t=2.108, <b>p=0.041</b></td><td>t=1.851, p=0.071</td></tr><tr><td>SBP</td><td>β=0.085, p=0.563</td><td>β=0.177, p=0.194</td><td>β=-0.187, p=0.342</td><td>β=0.182, p=0.309</td><td>β=0.310, p=0.210</td><td>β=0.174, p=0.459</td></tr><tr><td>DBP</td><td>β=-0.116, p=0.431</td><td>β=-0.370, <b>p=0.008</b></td><td>β=0.048, p=0.818</td><td>β=-0.331, p=0.082</td><td>β=-0.213, p=0.343</td><td>β=-0.432, <b>p=0.048</b></td></tr></tbody></table>

SBP: Systolic Blood Pressure; DBP: Diastolic Blood Pressure; MDE: Major Depressive Episode; MADRS: Montgomery Asberg Depression Rating Scale; BTP: Brain Tissue Pulsations

<figure><img src="image_2.png" /><figcaption>**Figure 1** – Scatter plots and boxplots of MeanBTP (left) and MaxBTP (right) in the depressed (green) versus healthy control (HC – orange) groups.</figcaption></figure>
Supplementary Material 1: equations of the linear regression models, figures of the Q-Q plots, residuals versus dependent, and calculations for the sample size estimation

Linear regression equation for MeanBTP:

$$MeanBTP = 3.027 + 2.685 (Depression) + 0.117 (Age) + 2.697 (Sex) + 0.085 (SBP) - 0.116 (DBP)$$

<figure><img src="image_3.png" /></figure>

Linear regression equation for MaxBTP:

$$MaxBTP = 6.512 + 2.220 (Depression) - 0.266 (Age) + 2.602 (Sex) + 0.177 (SBP) - 0.370 (DBP)$$

<figure><img src="image_4.png" /></figure>
Calculation of the sample size for future studies based on our findings:

To find a difference between groups with 80% statistical power, assuming a mean difference in MeanBTP of 2.2 (11.5 – 9.3) and a standard deviation of 4.3, we would need approximately 60 subjects in each group.

To find a difference between groups with 80% statistical power, assuming a mean difference in MaxBTP of 7.2 (81.1 – 73.9) and a standard deviation of 25.9, we would need approximately 204 subjects in each group.