Assessment of left ventricular twist by 3D ballistocardiography and seismocardiography compared with 2D STI echocardiography in a context of enhanced inotropism in healthy subjects

Ballistocardiography (BCG) and Seismocardiography (SCG) assess the vibrations produced by cardiac contraction and blood flow, respectively, by means of micro-accelerometers and micro-gyroscopes. From the BCG and SCG signals, maximal velocities (VMax), integral of kinetic energy (iK), and maximal power (PMax) can be computed as scalar parameters, both in linear and rotational dimensions. Standard echocardiography and 2-dimensional speckle tracking imaging echocardiography were performed on 34 healthy volunteers who were infused with increasing doses of dobutamine (5–10–20 μg/kg/min). Linear VMax of BCG predicts the rates of left ventricular (LV) twisting and untwisting (both p < 0.0001). The linear PMax of both SCG and BCG and the linear iK of BCG are the best predictors of the LV ejection fraction (LVEF) (p < 0.0001). This result is further confirmed by mathematical models combining the metrics from SCG and BCG signals with heart rate, in which both linear PMax and iK strongly correlate with LVEF (R = 0.7, p < 0.0001). In this setting of enhanced inotropism, the linear VMax of BCG, rather than the VMax of SCG, is the metric which best explains the LV twist mechanics, in particular the rates of twisting and untwisting. PMax and iK metrics are strongly associated with the LVEF and account for 50% of the variance of the LVEF.

Under the assumption that the cardiovascular system equates a Newtonian system, the propulsion of blood mass into the main vessels at each cardiac contraction makes the body's center of mass move rhythmically at each heartbeat, with a strength equal in magnitude but opposite in direction to the one of the ejected blood. Contraction of myocardial muscle, opening and closure of heart valves, blood flowing into cardiac chambers generate micro movements that are transmitted to the chest surface as low-frequency vibratory phenomena. Seismocardiography (SCG) and ballistocardiography (BCG) record the micro-vibrations generated rhythmically as a consequence of the movements of cardiac mass and blood in the major vessels, respectively, with microaccelerometers and gyroscopes placed on the body surface [1][2][3][4][5] . Modern BCG and SCG can measure linear and rotational velocities and accelerations of blood stream and cardiac mass using linear and rotational channels, respectively, and in three cardinal axes using three-axial sensors (x: latero-lateral axis; y: caudo-cranial axis; z: antero-posterior axis) 2,6 . In such a way, a multi-dimensional assessment of blood flow and cardiac function can be obtained with 12 degrees-of-freedom (DOF). Additionally, from the BCG and SCG waveforms, linear and rotational kinetic energy (K), its temporal integral (iK), maximal power (P Max ), displacements (D) and maximal velocities (V Max ) can be computed for each contractile cycle using specific algorithms based on Newtonian equation 2  www.nature.com/scientificreports/ A growing number of evidences provide the signals recorded with BCG and SCG as good indicators of myocardial function and dysfunction. Metrics of iK and P Max secured from BCG and SCG signals are well correlated to stroke volume (SV) and cardiac output (CO) 2 ; the peak of maximum energy well represents myocardial contractility expressed as dP/dt max in animal models 7 ; BCG and SCG signals provide information on myocardial dysfunction after an acute coronary syndrome 8,9 and can assess the clinical status of patients with heart failure 10 .
Left ventricular (LV) twist is the rotational movement of the LV along its longitudinal axis and results from the net difference between the torsional angles of the apical and basal rotations [11][12][13] . LV twist can robustly estimate myocardial function, expressed as LVEF [14][15][16] in some studies or dP/dt max in others [17][18][19][20] . LV untwisting rate provides the atrio-ventricular pressure gradients which assist cardiac chambers to fill during the early phase of relaxation 21,22 .
Recently, cardiac rotations have been evaluated using gyroscopes in animal models and results seem promising on the feasibility of measuring LV twist with this technique 23 .
Whether velocity and acceleration signals recorded with modern BCG and SCG can reliably estimate cardiac rotations in humans is not known.
The aims of the present study were: (1) to examine the relationships between LV twist mechanics with displacements and velocities metrics computed from the BCG and SCG signals; (2) to estimate myocardial function expressed as LVEF through the metrics of iK and P Max obtained from the BCG and SCG signals.

Methods
Study protocol. The present study is based on a previous randomized, double-blind, placebo-control, cross-over study in 34 healthy volunteers aged between 18 and 50 years (code NCT03107352 on ClinicalTrials. gov). The protocol has been approved by the local Ethics Committee and subjects gave written informed consent before being enrolled. Each subject received increasing doses of dobutamine (5-10-20 µg/kg/min) or normal saline as placebo (5-10-20 µg/kg/min). Allocation to the group receiving dobutamine first (group 1) or placebo first (group 2) was randomly determined. For each session, echocardiographic study was performed before any drug infusion (referred to as baseline) and during infusion of 5-10-20 µg/kg/min of dobutamine and placebo. According to the aims previously listed, only the dobutamine arm was considered in the present study for analysis and interpretation of results. Because of obvious changes in cardiac echocardiography following dobutamine infusion, investigators were not blinded for data analysis. Details about the protocol can be found in our previous work 2 .
Each echocardiographic study was followed by a 90-s record of linear acceleration and angular velocity signals with BCG and SCG on the skin surface.
Echocardiographic study. Standard echocardiography was performed with the GE VIVID E95 by an expert cardiologist in non-invasive imaging. Two dimensional images of the LV were obtained from the apical 2-, 3-and 4-chamber views along the parasternal long-axis. LV volumes and LVEF were calculated by Simpson biplane methods. Stroke volume (SV), cardiac output (CO), left ventricle ejection fraction (LVEF), LV outflow tract velocity (LVOT V max ) and its temporal integral (LVOT VTI) were measured 24,25 .
For the 2D-STI speckle tracking study, parasternal basal and apical short axis views were obtained for the measurement of basal and apical rotations. The basal level was defined from the tip of mitral valve, while the apical level was defined as the level of LV cavity without papillary muscles 26 . Three consecutive beats were recorded in a cine-loop image and analyses were performed with a dedicated software (EchoPAC version 20.1, GE Healthcare). The LV endocardial border was manually traced at the basal and apical levels and the speckle tracking thickness of LV wall was automatically selected, as previously described 15 . The width of the selected region was accommodated to the LV wall as needed.
By convention, counterclockwise rotations are expressed with positive values and clockwise rotations with negative values, looking from the apex 13 .
LV twist is defined as the net difference of angular displacements between the basal and apical rotations along the LV longitudinal axis 13 .
For the analysis of apical and basal rotation/rotational rates, LV twist and LV twisting/untwisting rates, shortaxis views were considered. Data plots were then exported to Excel version 16 (Microsoft) and the peak of LV twist as well as angular rates were calculated.
The highest positive peak of the LV strain curve has been considered as the maximal angular displacement occurring during systole and is expressed in °. Rotational rates have been obtained as the temporal derivation of LV twist according to the following equation: where ω is the angular rate and θ the angular displacement.
Rates are expressed in °/s. The positive peak of the rate of LV twist is termed "LV twisting rate", the negative peak "LV untwisting rate". Figure 1 shows the parameters of LV twist mechanics synchronized with SCG and BCG signals according to the ECG. SCG and BCG signal acquisition. A wearable device with two modules, one for the BCG acquisition and one for the SCG acquisition, was used. Each module contains a microelectromechanical systems (MEMS) accelerometer and gyroscope sensor (LSM6DSL, STMICROELECTRONICS) and is attached to the body with ω = dθ dt SCG and BCG signaling processing. The BCG module was placed in the lumbar lordosis curve, between the second and the third lumbar vertebrae, close to the subject's center of mass. The SCG module was placed on the manubrium of the sternum below the clavicle where the great vessels emerge from the heart. A 90-s record was acquired after each echocardiographic study using a tablet remotely connected to the device via Bluetooth and data were sent to the main server for further processing. Data were subsequently exported and processed offline using a specific toolbox written in MATLAB (version 9.5, R2018b). Further details describing this methodology can be found in previous publications 2, 6,27,28 . Linear kinetic energy (K Lin ) and rotational kinetic energy (K Rot ) of BCG and SCG are shown on Fig. 1.
The processed signals were used to compute the integral of kinetic energy (iK) and the maximal power (P Max ) for both linear and rotational channels ( iK MaxBCG ). Computation of these scalar parameters has been described previously 2 and are explained hereafter.
Knowing the acceleration of an object with a given mass m, the vector force ( − → F ), the kinetic energy (K) and the power (P) can be calculated according to Eqs. (1) to (3) for the linear components and Eqs. (4) to (6) for the rotational components.
(1) � F(t) = m� a(t) www.nature.com/scientificreports/ where m is the mass of the object, a human being in the case of the BCG and SCG application, K Lin is the linear kinetic energy, v x , v y , v z are components of the measured velocity vector − → v , − → F is the force vector and P Lin is the linear power.
For the rotational components, the scalar metrics are calculated according to Eqs. (4) to (6).
where − → τ is the torque of force, I is the momentum of inertia of the object and − → α is the angular acceleration, K Rot is the rotational kinetic energy, I xx , I yy , I zz are the orthogonal components of the momentum of inertia I of the object, ω x ,ω y , and ω z are components of the measured angular velocity − → ω , P Rot is the rotational power. The time integral of K Lin and K Rot over the cardiac cycle (CC) was computed for both SCG and BCG as in Eqs. (7) and (8).
Regarding the power metric, the maximal absolute value is taken to generate P Max for both SCG and BCG according to Eqs. (9) and (10).
The metrics of interest described so far are computed using a specific toolbox written in MATLAB (version 9.5 R2018b, MATHWORKS).
From the BCG and SCG accelerations signals, linear and angular velocities, as well as linear and angular displacements were computed by integration and twofold integration, respectively. Velocities and displacements signals were therefore obtained for each degree of freedom in the orthogonal axis (x, y, z). From these, the maximum of velocity (V Max ) and the maximum of displacement (D Max ) were computed (Eqs. 11 and 12 respectively): where v x , v y , v z , are components of the velocity vector − → v ; x, y, z are the components of the position vector − → OP . This was done for both linear and angular channels. D Max , V Max, iK, and P Max were normalized for the body surface area (BSA) of the subject. Normality of data distribution was assessed using the Kolmogorov-Smirnov test. One-way parametric or non-parametric ANOVA were applied according to data distribution. The Spearman's rank correlation was used to assess association between variables. Correlation coefficients range from − 1 to + 1 where 0 indicates no monotonic association and a value of 1 a perfect monotonically decreasing (− 1) or increasing (+ 1) relationship.
Generalized linear model was used to predict LV twisting and untwisting rates from velocity metrics and to predict the LVEF from metrics of P Max and iK.
P-values < 0.05 were considered statistically significant. Intra-observer variability was examined in 35 randomly selected echocardiographic images and expressed as the intraclass correlation coefficient (ICC) between the measurements of the two readings as well as their mean (± SD) difference.

Results
Baseline characteristics, echocardiographic parameters and SCG/BCG parameters of the entire study population are presented in Table 1. The linear accelerations and angular velocities of both chest and lower-back sensors were computed to get the metrics D Max , V Max , iK and P Max . 47.1% of the participants were men, the mean age was 25 years (± 1.72), the mean BMI was 22.48 kg/m 2 (± 2.07), while the mean SV, CO, and LVEF at baseline were respectively 62.78 ml (± 13.79), 4.32 l/min (± 0.1) and 63.3% (± 4.5).
Maximum of linear displacements and angular displacements computed with SCG and BCG have been associated with the LV twist. Results are shown in Table 2.
LV twist poorly correlated with displacements obtained from SCG and BCG signals. Specifically, it correlates with D Max from BCG signal both in the linear and in the rotational dimension (R = 0.18, p = 0.04; R = 0.30, p = 0.001, respectively) and with D Max from the SCG signal in the rotational dimension only (R = 0.17, p = 0.05), but the strength of association is very week.
Maximum of velocities computed with SCG and BCG have been associated with rates of LV twisting and untwisting. Results are shown in Table 3.
LV twisting rate is related to V Max of the SCG (R = 0.41, p < 0.0001; R = 0.37, p < 0.0001 for the linear and rotational dimensions, respectively) and to V Max of the BCG (R = 0.50, p < 0.0001; R = 0.45, p < 0.0001 for the linear and rotational channels, respectively). LV untwisting rate correlates as well with V Max of the SCG (R = − 0.35, p < 0.0001; R = − 0.36, p < 0.0001, for the linear and rotational dimensions respectively) and with V Max of the BCG (R = − 0.45, p < 0.0001; R = − 0.47, p < 0.0001, for the linear and the rotational dimensions respectively).    www.nature.com/scientificreports/ The generalized linear model, where linear and rotational velocities of both SCG and BCG were taken into the model to predict the LV twisting and untwisting rates, shows that the linear V Max of the BCG is the best predictor of the LV twisting and untwisting rates, rather than the V Max of the SCG (Table 4).
For one unit increase of V Max of the BCG, the rate of LV twisting hastens of 78.5 units and the rate of LV untwisting accelerates of − 72.2 units. Linear V Max of SCG and rotational V Max of BCG and SCG do not estimate rates of LV twisting and untwisting.
Correlations of parameters of cardiac contractile function with iK and P Max derived from SCG and BCG waveforms have been calculated and are summarized in Table 5.
LVEF is associated with all the parameters derived from the BCG and SCG. The strongest association is observed with the metrics derived from the SCG, specifically iK Rot (R = 0.51), P Rot max (R = 0.52) and P Lin max (R = 0.51). When the linear channel for iK is considered as the comparative factor, the strength of association is lost to some extent, both for the SCG and the BCG (R = 0.36, p < 0.0001; R = 0.36, p < 0.0001, respectively).
The association is slightly weaker when the same metrics are computed from the rotational channel of the BCG (R = 0.45 for iK Rot ; R = 0.46 for P Rot Max ). Variables computed from the BCG and the SCG signals that best predict the LVEF are shown in Table 6.
The linear P Max of both BCG and SCG as well as the linear iK of the BCG are the variables that best estimate the LVEF. In particular, the LVEF increases by 0.12% for one unit increase of the linear P Max of the BCG (J/s/    By empirically combining the metrics computed from the BCG and SCG signals with the HR, two mathematical models have been built, in which P Max and iK are the metric which strongest correlates with LVEF (both R = 0.7, p < 0.0001), in line with the results from the generalized linear model (Fig. 2). In particular, the first model (panel A) combined the HR with P BCG Lin and P SCG Lin . The second model (panel B) combined the HR with 4 iK BCG Lin and 3 iK SCG Rot .

Discussion
The twisting motion of the heart makes the blood mass flow from the cardiac chambers to the main extracardiac vessels. This phenomenon can be measured with 2D STI echocardiography and rates of LV twisting and untwisting can be derived 13,[29][30][31] . From this study, we have observed that, in a context of incremental rise of myocardial inotropism in healthy subjects: 1. LV twisting and untwisting rates are well associated with the velocity signals measured with the BCG and SCG; velocity signals of BCG are best indicators of the twisting motion of the LV than those of the SCG. Indeed, among the velocity variables obtained from the BCG and SCG signals, the velocity vector of the BCG in the linear dimension, rather than the one of the SCG, is the one which best estimates the modifications of LV twisting and untwisting rates; 2. Signals of kinetic energy and power computed from the BCG and the SCG signals provide information on the contractility status of the heart and significantly predict changes in LVEF. In particular, the linear iK of the BCG is the metric that best predicts the changes of LVEF. When metrics of P Max and iK are combined with the HR, they are both related to the LVEF with a strength of 0.70.
Previously to our observations, Marcelli et al. proposed gyroscopic sensors as a feasible and reliable method to assess cardiac rotations in animal models 23 . In the present investigation, we confirm as well that 3-axis microaccelerometers and gyroscopes provide valuable information on the twisting motion of the heart, specifically on rates of twisting and untwisting. Indeed, associations have been found between velocity vectors of BCG and SCG and rates of twisting and untwisting. www.nature.com/scientificreports/ In particular, changes of LV twisting and untwisting rates are significantly predicted by the linear velocity of the BCG, rather than by the same metrics of the SCG.
During a contractile cycle, blood flows inside and outside cardiac chambers, forming vortexes, which relocates blood mass across the LV according to the cycle phase [32][33][34] . Myocardial wall mechanics may be involved in the dynamic relocation of blood flow across cardiac chambers 35 . Indeed, during early diastole, blood fills cardiac chambers creating vortex rings directed from the LV base to the apical regions 33,35,36 , while during systole, blood flow is relocated towards the LVOT and the flow-vector is thus directed from the LV apex to the outflow tract 32,33 . In the normal heart and great vessels, in the absence of a stenotic narrowing, the blood stream is laminar, meaning that the direction and velocity of blood flow in adjacent sections are similar and uniform. This laminar flow profile is termed "plug flow" 37 . As such, blood flow velocity in the LVOT is laminar, in the absence of aortic stenosis 37 . Early during filling, diastolic vortex rings transport blood mass across cardiac chambers, contributing to about 15% of the filling volume in normal hearts 38 . The LV untwisting rate plays a pivotal role in the generation of these diastolic vortex rings 33,39,40 .
On the basis of these consolidated knowledges, authors speculate that the better estimation of rates of LV twisting and untwisting by the BCG linear velocity probably reflects the laminar profile of the blood stream in the LVOT and the vortex formation during early filling, respectively 35,38 . This latter finding is of main importance since the untwisting rate is a crucial phenomenon assisting and driving the diastolic filling and contributes to the cardiac torsional reserve 41 , which can decline in failing hearts 42 .
According to what is stated in the current literature, that is, the SCG records the vibratory phenomena produced by myocardial contraction and then transmitted to the local chest surface 43,44 , we would have expected the SCG velocities vectors to better correlate with the torsional motion of the LV. This is not exactly what we observed, since velocity vectors of SCG do not explain the behavior of LV twist mechanic in this very context of enhanced inotropism, while the linear velocity obtained from the BCG signal provide more information on the global LV twist mechanic. One possible explanation is that, since the resultant SCG signal is generated by several physiological phenomena including not only cardiac contraction, but also heart valves closure and opening, blood turbulence, momentum changes 45 , the sum of these phenomena other than cardiac contraction only may be responsible for the weaker correlation with the LV torsion observed.
In our previous work, we introduced iK and P Max as reliable indexes of the contractile status of the heart, they can follow changes in cardiac contractility over a wide range of inotropic states and the linear iK of the BCG is the metric which best correlates with the SV 2 . In the current study, we provide the new evidence that the same metric is a good index also of the LVEF. In particular, we found that the linear iK of the BCG explains the largest changes of the LVEF in this very context of incremental rise of cardiac inotropism. The mathematical models obtained by combining metrics of P Max and iK confirm that these metrics are strongly associated with the LVEF (both R = 0.70), thus accounting for 49% of the variance of the LVEF. While this model is of interest, it was empirically constructed and its main contribution is not to be used as it is but rather to highlight that more www.nature.com/scientificreports/ advanced statistical techniques, such as machine learning algorithms, could allow to build a function explaining LVEF changes on the basis of BCG and SCG linear and rotational channels. LVOT V max is the maximal velocity of blood flow across the left ventricle outflow tract, and the temporal integral of LVOT V is the integrated velocity throughout a cardiac cycle (LVOT VTI) 37 ; both are important echocardiographic parameters of cardiac systolic function and cardiac output 46 . We found that all the metrics computed from the SCG and the BCG are correlated with LVOT V max and LVOT VTI, but metrics of the BCG are better associated than the same metrics of the SCG. This difference between metrics of SCG and metrics of BCG can be explained through the different genesis of the signals. As explained above, while the SCG signal is the resultant of several combined cardiac phenomena, BCG signals are generated mainly by blood acceleration and deceleration into the aorta and its main branches 47 .
The results of this investigation are of main importance since they shed further light on the physiological genesis of the SCG and BCG signals, enriching the current knowledges on the SCG and BCG. Indeed, we demonstrated that the twisting motion of the heart play a fundamental role in the genesis of the BCG signal but no in the one of the SCG. The BCG signal, specifically the linear velocity, can estimate rates of LV twisting and untwisting, thus providing significant information on the twisting motion of the heart. Since the LV twist is impaired early in a variety of cardiomyopathies 48,49 , scalar parameters secured from BCG signals may prove useful in the detection of LV dysfunction in patients with cardiac diseases. Scalar metrics secured from SCG and BCG signals can also estimate the LVEF. This information complements the current knowledge on the SCG and BCG, by adding that metrics of iK can estimate not only the CO and SV 2 , thus providing information on the hemodynamic aspect of cardiovascular system, but can estimate as well the LVEF, thus providing information on the contractility status of the heart.
Acknowledged that metrics of kinetic energy and velocities secured by the SCG and BCG signals seem promising in the monitoring of hemodynamic profile and cardiac contractility in healthy subjects, this technique may be extended to patients suffering from cardiovascular diseases, with the promise to remotely monitor their cardiovascular conditions. Thanks to the easy-to-use properties of the device, cardiac patients might be empowered to follow their own medical conditions in a near future. Additionally, to our knowledge, markers of myocardial contractility are not provided by the smartwatches currently in use and this device may complement the existing ones by adding the cardiac iK as a new parameter for myocardial contractility.
Limitations. Several possible limitations need consideration. Firstly, this is a retrospective data analysis based on a previous randomized double-blind investigation (code NCT03107352 on ClinicalTrials.gov), enrolling exclusively healthy subjects with a small final sample size (N = 34) 2 . Additionally, results should not be applied to cardiovascular patients. In this previous study, the sample size was calculated and accounted for 32 included subjects. The sample size was estimated by assuming that cardiac contractility measured by the SCG/BCG device would increase by over 10% for the smallest dose of dobutamine, similar to its effect on SV 50 . Power analysis demonstrated that to achieve 80% power at α = 0.05, at least 32 subjects were needed. Therefore, 36 subjects were recruited to account for possible dropouts and/or technical failures. For the final analysis, 34 participants completed all the echocardiographic, ECG, and SCG/BCG acquisitions (there were 2 dropouts) 2 .
Parameters from standard and 2D STI echocardiography were measured by only one operator for logistical reasons, thus precluding the calculation of interobserver variability. To test intra-observer variability, intraclass correlation coefficient (ICC) was calculated in 35 random 2D STI echocardiographs using a two-way mixed model. The ICC was 0.94 (IC95% 0.88; 0.97) for the LV twist, 0.90 (IC95% 0.80; 0.95) for the LV twisting rate and 0.92 (IC95% 0.92 0.85; 0.96) for the LV untwisting rate. Means (± SEM) of the difference between the measurements of first and the second readings were: 0.02° ± 0.61° for the LV twist (p = 0.97); 1.44 ± 6.51°/s for the LV twisting rate (p = 0.83); 6.88 ± 7.32°/s for the LV untwisting rate (p = 0.35).
Statements about the physiological relationship between the velocity parameters of SCG and BCG and LV twisting/untwisting rates are speculative and have been postulated on the basis of the current knowledge of blood fluid dynamics. Thus, our results do not enable us to confirm such a hypothesis, which remain conjectural. Indeed, a quantification of blood flow by mean of particle image velocimetry is needed to confirm this hypothesis and may be the object of further researches.
Despite what was highlighted up to this point, authors believe that these limitations do not preclude our conclusions.
We conclude the follow: (1) in a context of pharmacologically induced incremental rise of myocardial inotropism in healthy subjects, rates of LV twisting and untwisting play a central role in the physiological genesis of the BCG signal but not of the SCG signal; (2) the linear velocity of BCG, rather than the one of the SCG, predicts the behavior of LV twisting and untwisting rates and this estimation of LV twist mechanic by the BCG signals may reflect indirectly the blood stream and relocation within cardiac chambers driven by LV twist mechanic according to the phase of a contractile cycle; (3) metrics of P Max and iK secured from the SCG and BCG waveforms provide reliable information on the contractile status of the heart and account for 49% of the variance of the LVEF.

Data availability
Data are available from the authors upon reasonable request. www.nature.com/scientificreports/