Maja Cikes

Sergio Sanchez-Martinez

Brian Claggett

Nicolas Duchateau

Gemma Piella

Constantine Butakoff

Anne Catherine Pouleur

Dorit Knappe

Tor Biering-Sørensen

Valentina Kutyifa

Sergio Sánchez-Martinez

Arthur Moss

Kenneth Stein

MD Scott D Solomon
email: ssolomon@rics.bwh.harvard.edu

Bart Bijnens

Machine learning-based phenogrouping in heart failure to identify responders to cardiac resynchronization therapy

Keywords: Machine learning, Heart failure, Personalised medicine, Echocardiography, Cardiac resynchronisation therapy

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Introduction

The goal of personalized medicine is to optimize the tailoring of treatments to specific patients in order to maximise the treatment response, which, as a prerequisite, requires accurate patient phenogrouping. The syndrome of heart failure (HF) comprises particularly heterogeneous patient groups, burdened by limited success of some treatment options. Machine learning approaches have been applied in the diagnosis, classification, assessment of readmissions and medication adherence of HF patients [START_REF] Awan | Machine learning in heart failure: ready for prime time[END_REF] , as well as to identify distinct phenogroups in several disorders, including HF with preserved ejection fraction (HFpEF) [START_REF] Sanchez-Martinez | Characterization of myocardial motion patterns by unsupervised multiple kernel learning[END_REF][START_REF] Shah | Phenomapping for novel classification of heart failure with preserved ejection fraction[END_REF] , and to predict mortality in patients with suspected coronary artery disease [START_REF] Motwani | Machine learning for prediction of all-cause mortality in patients with suspected coronary artery disease: a 5-year multicentre prospective registry analysis[END_REF] . Supervised machine learning involves using iterative algorithms that "learn" from a large accurately labelled training dataset [START_REF] Gulshan | Development and Validation of a Deep Learning Algorithm for Detection of Diabetic Retinopathy in Retinal Fundus Photographs[END_REF] ; while often diagnostically "accurate", it is generally impossible to infer the "diagnostic reasoning" employed in these algorithms. Unsupervised approaches, however, do not attempt to identify a diagnostic or prognostic "truth" but instead group (or cluster) patients together based on multiple characteristics, which could be demographic, historical, or measured. By grouping similar patients together in multiple dimensions, it is then possible to analyse the characteristics of similarly grouped individuals and relate them to outcomes or therapeutic responses. We have previously shown that unsupervised multiple kernel learning (MKL) can be applied to find similarities among patients, based on a wide range of heterogeneous data, such as complex imaging-based descriptors of ventricular structure and function, in an "agnostic" manner [START_REF] Sanchez-Martinez | Characterization of myocardial motion patterns by unsupervised multiple kernel learning[END_REF] .

One such area where more accurate phenogrouping could improve selection of patients is cardiac resynchronization therapy (CRT) which, despite clear guidelines for which patients should be treated, a substantial proportion of patients do not respond to this therapy [START_REF] Abraham | Cardiac resynchronization in chronic heart failure[END_REF][START_REF] Young | Combined cardiac resynchronization and implantable cardioversion defibrillation in advanced chronic heart failure: The MIRACLE ICD trial[END_REF][START_REF] Saxon | Biventricular pacing in patients with congestive heart failure: two prospective randomized trials[END_REF][START_REF] Packer | Proposal for a new clinical end point to evaluate the efficacy of drugs and devices in the treatment of chronic heart failure[END_REF] We hypothesized that novel approaches based on machine learning (ML), integrating clinical parameters with complex echocardiographic data on myocardial deformation and LV volume changes measured over the entire cardiac cycle might be able to overcome some of the limitations of traditional approaches to patient selection for CRT, and provide an example of how machine learning can be utilized to better phenogroup patients with HF with respect to both outcomes and response to therapy. We therefore utilized data from Multicenter Automatic Defibrillator Implantation Trial with Cardiac 4 Resynchronization Therapy (MADIT-CRT), a large randomized clinical trial of 1820 patients with NYHA functional class ≤II symptoms, LVEF≤30% and QRS≥130 ms [START_REF] Moss | Cardiac-resynchronization therapy for the prevention of heart-failure events[END_REF] ,to determine whether unsupervised ML could aid in the identification of patients likely to respond to CRT.

Methods

Study population

The design and results of MADIT-CRT have been published previously [START_REF] Moss | Cardiac-resynchronization therapy for the prevention of heart-failure events[END_REF][START_REF] Moss | Multicenter Automatic Defibrillator Implantation Trial-Cardiac Resynchronization Therapy (MADIT-CRT): Design and clinical protocol[END_REF] . In brief, the MADIT-CRT trial enrolled 1820 patients from December 2004, through April 2008, at 110 centres in the United States, Canada, and Europe. These were mildly symptomatic patients with ischaemic heart disease (in New York Heart Association (NYHA) class I or II) or patients with nonischaemic heart disease (in NYHA class II) in sinus rhythm with an LVEF ≤30%, and a QRS duration ≥130 ms, who were randomly assigned in a 3:2 ratio to receive a CRT-D or an ICD alone. All recruited subjects met guideline indications for ICD therapy [START_REF] Epstein | ACC/AHA/HRS 2008 Guidelines of cardiac rhythm abnormalities. A report of the American College of Cardiology/American Heart Association task force on practice guidelines (writing committee to revise the ACC/AHA/NASPE 2002 Guideline update for implantation[END_REF] . The main objective was to determine whether CRT-D reduces the risk of death or HF events compared with ICD. The average follow-up period was 2.4 years. The protocol was approved by the institutional review board at each of the participating centres, and each subject gave written informed consent.

Echocardiography

Two-dimensional (2D) echocardiography was performed before device implantation (baseline) and at 1-year follow-up, following a study-specific protocol [START_REF] Solomon | Effect of cardiac resynchronization therapy on reverse remodeling and relation to outcome: Multicenter Automatic Defibrillator Implantation Trial: Cardiac Resynchronization Therapy[END_REF] . The echocardiographic core laboratory at Brigham and Women's Hospital performed the screening of the echocardiograms for quality, and the echocardiographic measurements relevant to the study. Left ventricular and atrial volumes were assessed by the biplane Simpson's method. LVEFs were calculated according to standard methods [START_REF] Solomon | Effect of cardiac resynchronization therapy on reverse remodeling and relation to outcome: Multicenter Automatic Defibrillator Implantation Trial: Cardiac Resynchronization Therapy[END_REF] .

Reproducibility of the primary volumetric measurements has been previously demonstrated [START_REF] Goldenberg | Predictors of response to cardiac resynchronization therapy in the Multicenter Automatic Defibrillator Implantation Trial with Cardiac Resynchronization Therapy (MADIT-CRT)[END_REF] .

The echocardiographic images of 1106 patients in this MADIT-CRT analysis (CRT-D, n=677; ICD-only, n=429) were analysed using the TomTec Arena software (v1.0, TomTec Imaging Systems, Unterschleissheim, Germany). Endocardial borders were traced in the end-systolic frame of the apical 4-and 2-chamber views, and automatically propagated over the course of 2 cardiac cycles. We stored 49 segmental LV longitudinal strain and 1 volume curves for a posteriori ML analysis. Previous studies report excellent reproducibility of the estimated LV myocardial deformation [START_REF] Knappe | Dyssynchrony, contractile function, and response to cardiac resynchronization therapy[END_REF] . The reasons to exclude patients from the analysis included: images in non-DICOM format, frame rate <30 Hz, missing of 4-or 2-chamber images, unacceptable 2D image quality, use of echocardiographic contrast agent, presence of endocardial dropout, or out-of-plane images.

Outcome measures

The primary endpoint of the trial was death from any cause or a non-fatal HF event, whichever came first [START_REF] Moss | Cardiac-resynchronization therapy for the prevention of heart-failure events[END_REF] . The adjudication of the endpoints was carried out by an independent endpoint committee, unaware of patient randomization status [START_REF] Moss | Cardiac-resynchronization therapy for the prevention of heart-failure events[END_REF] . In addition to determining the treatment effect on the primary outcome over an average follow-up of 2.3 years, we have also assessed the benefit on echocardiographic response at 1 year follow-up.

Baseline characteristics, data preprocessing and unsupervised machine learning

Seventy-seven baseline variables, consisting of clinical and echocardiographic parameters with <20 % missing data were identified. After filtering correlated variables using a cut-off Pearson's coefficient > 0.8, fifty variables including demographic and laboratory data, ECG and echocardiography measurements, data on medication use and recruitment centre were selected at baseline and were used as input for the ML algorithm (Table 1). These variables included both categorical and continuous data, with the continuous variables converted to ordinal by dividing their range into 10 uniform bins [START_REF] Dougherty | Supervised and unsupervised discretization of continuous features[END_REF] . Missing data for input variables ranged from 0% to 15.6% in the case of right ventricular fractional area change. They were imputed using the imputeFAMD function within 6 the missMDA package in R [START_REF] Josse | missMDA : A Package for Handling Missing Values in Multivariate Data Analysis[END_REF] , which allows imputing mixed datasets (with continuous and categorical variables) using a principal component method adapted for mixed data.

In addition to these common baseline characteristics, baseline LV strain and volume traces throughout the entire cardiac cycle as well as a temporal deformation vector (used to keep the relative changes in duration of the cardiac phases, relevant for improved HF characterization 2 ) were included in the further processing by the ML algorithm. In order to retain the wealth of data on LV geometry and deformation over a cardiac cycle contained in the traces, each one of them was defined and inputted to the algorithm as a set of data points (specifically, 102 variables per trace), instead of e.g. only a peak value (such as end-diastolic and end-systolic volume or peak systolic strain). Prior to analysis, these traces need to be referenced to a common temporal framework [START_REF] Duchateau | Quantification of local changes in myocardial motion by diffeomorphic registration via currents: Application to paced hypertrophic obstructive cardiomyopathy in 2D echocardiographic sequences[END_REF] (see online-only Data Supplement). The 49 segmental strain traces available from the 2ch and 4ch views were converted into 2 basal, 2 mid-LV and 2 apical segments, by isolating and averaging groups of 8 consecutive traces. The most apical trace was discarded.

The final input to the algorithm is shown in Figure 1 (left panel). For the 2ch and the 4ch views of every patient, a total of 8 echocardiographic descriptors (traces) were analysed per view (Figure 1, left panel): 1 volume trace, 6 strain traces, and 1 temporal deformation vector, which results from the temporal alignment step. Fifty clinical parameters inputted to the algorithm are listed in Table 1.

These echocardiographic descriptors (full traces) and baseline clinical parameters provided a total of 1682 input variables: each echocardiographic trace contains 102 data points, making a total of 1632 echocardiographic trace data points (8 traces x 2 views x 102 time instants) to which 50 clinical parameters were added. We then used unsupervised MKL (Figure 1, right panel), an ML algorithm already validated and extensively tested to combine cardiac motion data 2 , to convert the input dataset consisting of 1682 variables into a compact representation space where subjects are positioned according to their similarity, while blinded to the patient's outcome status with respect to both clinical events and volume response.

Once positioned in the compact representation space, subjects were clustered with the K-means algorithm (Figure 1, right panel) to identify phenotypically-distinct categories of CRT candidates. We ran the clustering algorithm with increasing number of predefined groups (from 3 to 8), however, the clinical interpretation of the clusters remained stable; ultimately, we chose the configuration that maximizes the statistical significance (minimizing P value for trend, adjusted for multiple testing) of the treatment effect on the primary outcome among clusters (henceforth referred as phenogroups).

Further details about our unsupervised ML method can be found in the online-only Data Supplement.

Comparison of Clinical and Echocardiographic Characteristics; Survival and Treatment effect on Primary Outcome and LV Reverse Remodelling

Categorical variables are expressed as counts and percentages, and differences among phenogroups were assessed using the chi-square test. Continuous variables are presented as mean  standard deviation, and inter-group differences were calculated using ANOVA. A p-value of less than 0.05 was considered statistically significant. The previous comparison was complemented with a physiologic interpretation of the found phenogroups in the form of a variability analysis of strain and volume patterns in the 2ch and 4ch views, using advanced regression techniques [START_REF] Duchateau | Adaptation of multiscale function extension to inexact matching . Application to the mapping of individuals to a learnt manifold[END_REF] . Kaplan-Meier estimates for HF or death in each phenogroup were determined and statistically compared with the log-rank test. Cox proportional hazards regression analyses were performed on each phenogroup to estimate the treatment effect on the primary endpoint. The treatment effect on volumetric response was expressed for every phenogroup as the difference between treated and untreated patients in LVEDVi percent change (from baseline to 1 year follow-up).

Stability and Internal Validation of the Unsupervised Machine Learning Model

We evaluated the generalizability of our dimensionality reduction solution assessing the correlation among low-dimensional space distributions obtained by analysing populations with an increasing number of subjects in common. We also checked the consistency among the K-means clustering configurations by computing the membership agreement when increasingly partitioning the space, from 3 to 8 clusters.

We assessed the stability of these results through internal validation, which involved running our ML algorithm in a randomly-selected portion of the database (75% = training set) to create clusters, finding the corresponding cluster for the remaining subjects (25% = validation set), and comparing both the training and the validation clustering solutions in terms of clinical characteristics and outcome. Further details on both the stability experiments and the internal validation can be found in the online-only Data Supplement.

The ML algorithm as well as the regression technique used to analyse the variability of echocardiographic patterns among phenogroups were implemented using MATLAB (R2016b, The MathWorks Inc., Natick, MA, 2016). Survival and treatment effect analyses were performed in Stata version 13 (StataCorp, College Station, TX, USA).

Results

Results of Machine Learning

The MKL algorithm reduced the dimensionality of the input data to equal the number of input subjects minus 1. However, only the first 2 dimensions of the output (low-dimensional) space were considered for clustering, as they encoded the most salient characteristics of these data 2 . Furthermore, they presented the highest standard deviations on the coordinates of subjects (with further dimensions showing a linear decay up to the 6 th dimension, from which the standard deviation is >98% smaller than the first dimension), and thus contributed to a higher extent to the cluster assignment computed by the K-means algorithm.

Baseline Characteristics of Patients by Phenogroups

Baseline characteristics of the patients included in this analysis were comparable to the remainder of the MADIT-CRT study, as reported previously [START_REF] Knappe | Dyssynchrony, contractile function, and response to cardiac resynchronization therapy[END_REF] . 9

The most statistically-significant clustering solution categorized the overall patient population into four clusters, i.e. phenogroups (Figure 1, right panel) with distinct clinical and echocardiographic characteristics (Table 1, Figure 2, Supplementary Figure S6). This solution was better at identifying CRT responders than those obtained by independently analysing clinical parameters or complex echocardiographic descriptors alone (see Supplemental Material). Phenogroups 1 and 3 were associated with the highest proportion of clinical characteristics known to be predictive of volumetric response to CRT [START_REF] Goldenberg | Predictors of response to cardiac resynchronization therapy in the Multicenter Automatic Defibrillator Implantation Trial with Cardiac Resynchronization Therapy (MADIT-CRT)[END_REF] : Phenogroups 1 and 3 comprised the highest proportion of patients with nonischaemic cardiomyopathy (54.8% and 57.4%, respectively) and LBBB (86.0% and 80.8%, respectively), the QRS duration was the longest in Phenogroup 1, which was also the Phenogroup with the lowest median age, while Phenogroup 3 consisted of the largest proportion of female patients. Conversely, Phenogroups 2 and 4 were associated with the highest proportion of male patients and ischaemic origin of HF, as well as the lowest proportion of patients with LBBB morphology on ECG.

The values of systolic blood pressure were the lowest and the heart rate was the highest in Phenogroup 1; this was also the phenogroup with the highest proportion of patients receiving diuretics and aldosterone antagonists. There was no significant difference in the proportion of patients receiving beta blockers or ACE inhibitors / angiotensin receptor blockers among the four phenogroups.

Furthermore, echocardiography measurements revealed that the patients in Phenogroup 1 had the most remodelled LVs at baseline (the largest LV end-diastolic and end-systolic volume index, LV mass index and LAVi) and the lowest LVEF and 12-segment global longitudinal strain (GLS), while the same was observed for the RV size and function in this phenogroup (largest RV diameter and lowest fractional area change (FAC)), with Phenogroup 4 having similarly remodelled RVs.

Conversely, these measurements of LA and LV structure demonstrated the lowest severity of remodelling in Phenogroup 2. RV size was the smallest and FAC and LVEF were the highest in Phenogroups 2 and 3 (group P values for all mentioned echo parameters <0.001). 10

In addition to the clinical and echocardiographic characteristics of the studied patients, the MKL algorithm also included data on LV volume traces and longitudinal strain traces. Representative "fingerprints" of such traces are shown for each phenogroup in Figure 3. In Phenogroup 1, the LV strain curves show late systolic stretch of the apical septal segment and a mirrored contraction of the apical lateral wall -a feature described as a part of the LBBB-related Septal Flash pattern. The volume trace shows a delayed peak, i.e. tardily achieved end-systolic volume. These patients had the largest end-diastolic LV volumes and the lowest LVEF values. The strain curves in Phenogroup 2 show nearly absent deformation only in the apical anterolateral region, with a normal shape of the strain trace and lower peak values in the septal and inferior regions. Along with Phenogroup 3, these were the least dilated ventricles with the highest LVEF values. In Phenogroup 3, there is early deformation of the apical septum while some early stretch is present in the lateral traces, mirroring an early deformation of the apical septum. Phenogroup 4 exhibits nearly absent deformation in the basal inferoseptum with very low deformation in all apical regions and somewhat preserved deformation in the basal anterolateral wall -this pattern is indicative of large apical infarcts extending to the inferoseptum. Although the volume curve in Phenogroup 4 peaks early, these patients also have markedly remodelled LVs.

Comparison of Survival among Phenogroups

The natural course of disease, as assessed in the ICD-only subgroup of patients, varied among the phenogroups (Figure 4 left panel, and Supplementary Figure S8): the Kaplan-Meier estimate of the probability of survival free of HF revealed a less severe disease course in Phenogroup 2 in which the primary event occurred in 15.4% of the patients in the ICD-only subgroup (2.1% of the patients died, 9.8% were hospitalized for HF and the remaining 3.5% had an out-of-hospital HF event). Conversely, the untreated patients in Phenogroup 1 had the highest incidence of the primary event, occurring in 38% of patients (1.4% had an all-cause death, 33.8% were hospitalized for HF and 2.8% had a HF event not requiring hospitalization). Overall, the primary outcome occurred in 220 patients from the current analysis, and differed significantly among phenogroups: it occurred most frequently in Phenogroups 1 and 4 (41 patients (26.1%) and 79 patients (27.4%), respectively) and was least 11 represented in Phenogroups 2 and 3 (55 patients (14.9%) and 45 patients (15.5%), respectively) (Figure 4 left panel). All-cause death did not differ significantly among the phenogroups; the difference in the primary endpoint was mainly driven by a significant difference in the occurrence of HF requiring hospitalization, occurring most often in Phenogroups 1 and 4 (21.0% and 20.5% of patients, respectively) and least frequently in Phenogroups 2 and 3 (10.3% and 11.3% of patients, respectively).

Effect of Treatment on Primary Outcome and LV Reverse Remodelling

The effect of CRT-D treatment, compared to ICD-only, on the primary outcome of death or HF event assessed among the four phenogroups by Cox proportional hazard analysis is depicted on Figure 4 (right panel): patients categorized to Phenogroups 1 and 3 exhibited an 64% and 65% reduction in the risk of HF or death, respectively (HR, 0.36; 95% CI, 0.19 to 0.68; P=0.001 and HR, 0.35; 95% CI, 0.19 to 0.64; P=0.0005, respectively), which was a substantially higher treatment benefit than observed in the other groups (interaction P=0.02). Phenogroups 2 and 4 benefited from CRT-D therapy to a lesser extent compared to the overall cohort; however, the nonresponse did not reach statistical significance.

A significant treatment effect on LV reverse remodelling, defined as LVEDVi percent change, was noted in all phenogroups (Figure 4, right panel). However, Phenogroup 3, characterized by a lower severity of ventricular remodelling at baseline, was identified to be associated with a substantially better volume response: in this phenogroup CRT-D treatment was associated with an average 18.8 % decrease in LVEDVi, when corrected for ICD-only treatment (95% CI, -21.2 to -16.4; P<0.0001). A marked volume response was also detected in Phenogroup 1 with an average 18.2% decrease in LVEDVi (95% CI, -21.9 to -14.6; P<0.0001), while patients in Phenogroups 2 (HR -13.6; 95% CI, -15.8 to -11.5; P<0.0001) and 4 (HR -14.2; 95% CI, -16.8 to -11.5; P<0.0001) showed the lowest amount of LVEDVi percent change within 12 months.

Stability and Internal Validation 12

The similarity among low-dimensional space distributions increased with the number of subjects in common at the input of the machine learning analysis, resulting in excellent correlation when the subjects in common were above 500 (Pearson correlation coefficient > 0.90). We also observed a high degree of consistency across clustering configurations from 3 to 8 clusters. Lastly, similar trends were observed in the clinical parameters and the treatment effect when comparing the training and validation clustering configurations, emphasizing the capacity of our model to predict outcomes for new, unseen data. All these results are detailed in the online-only Data Supplement.

Discussion

In this analysis we have shown that unsupervised ML allows for a novel integration of entire cycle-wide LV volume and deformation traces from echocardiography, rather than only single data points, which can be combined with extensive clinical and medication parameters to phenotype patients with complex diseases such as HF. We have also demonstrated the added value of combining both sets of descriptors to find subjects that are more likely to respond to CRT, compared to the results obtained by independently analysing clinical parameters or complex echocardiographic descriptors alone. Our results serve as a proof-of-concept that unsupervised machine-learning based approaches can be used to combine both standard clinical parameters and complex echocardiographic data to provide a clinically interpretable and meaningful classification of a phenotypically heterogeneous HF cohort and to identify patients most likely to respond to specific therapies.

Integrating echocardiographic tracings to address the heterogeneity of a heart failure population

HF is a multifaceted syndrome and response to therapies is based on multiple clinical and imaging parameters as well as biomarkers. Traditional methods to define phenotypes and predict outcomes within groups of individuals with HF rely on the elucidation of individual phenotypic subgroups that focus on isolated characteristics (i.e., aetiology of HF, QRS morphology, presence or absence of 13 specific comorbidities, cardiac structure and function, etc.). Furthermore, while assessment of cardiac structure and function using current echocardiographic analysis tools can identify subgroups of HF patients at higher risk for adverse outcomes [START_REF] Cikes | Beyond ejection fraction: An integrative approach for assessment of cardiac structure and function in heart failure[END_REF] , standard approaches ascribe risk to a limited amount of individual measurements in a unidimensional fashion. Namely, data on cardiac structure and function provided by echocardiography contain a plethora of information representing multiple time points in a cardiac cycle (the number of data points correspond to the frame rate of the acquired images), but are typically under-exploited in standard quantitative data analyses and replaced by single measurements, thus failing to summarize the complexity of events over the cardiac cycle. Unlike previous studies that aimed, but failed, at finding a single echocardiographic measure of dyssynchrony to improve patient selection for CRT beyond current guidelines [START_REF] Chung | Results of the predictors of response to CRT (PROSPECT) trial[END_REF] , we integrated echocardiographic imaging in a more comprehensive and novel manner by integrating entire LV volume and strain patterns throughout the cardiac cycle rather than utilizing single measures such as LV end-diastolic and systolic volume or global longitudinal strain. By integrating over 1600 data points per cardiac cycle, this method also is able to incorporate complex patterns of regional cardiac function that are impossible to describe parametrically. These algorithms thus combine a detailed analysis of cardiac dynamics over an entire cardiac cycle with an extensive set of clinical parameters.

It is often emphasized that the management of HF patients requires improved integration of clinical data with echocardiography-the most widely used and accessible diagnostic tool for a comprehensive assessment of cardiac structure and function. Indeed, ML allows for the integration of very large amounts of continuous and discrete variables pertinent to clinical characteristics, laboratory values, ECG parameters and commonly analysed echocardiographic variables, as has been applied in HF and other cardiovascular diseases. Unsupervised ML techniques, such as the MKL version that we have utilized in this study, offer the advantage of exploiting these full acquired datasets to compare similarities amongst patients without assumptions on which single measurements (data points) are most relevant for the studied patient population. In addition to tissue Doppler trace analysis in HFpEF patients [START_REF] Sanchez-Martinez | Machine Learning Analysis of Left Ventricular Function to Characterize Heart Failure With Preserved Ejection Fraction[END_REF] , the analysis of LV strain traces has previously been performed in a study of 60 patients with acute myocardial infarction by applying principal component analysis [START_REF] Tabassian | Machine learning of the spatio-temporal characteristics of echocardiographic deformation curves for infarct classification[END_REF] . Furthermore, the 14 prediction of CRT response was also attempted in a smaller cohort of 34 CRT candidates [START_REF] Peressutti | A framework for combining a motion atlas with non-motion information to learn clinically useful biomarkers: Application to cardiac resynchronisation therapy response prediction[END_REF] . The strengths of our analysis as compared to both of these studies is in the use of a non-linear (more adequate to process cardiac motion patterns, compared to principal component analysis 2 ) and unsupervised analysis technique (compared to supervised MKL [START_REF] Peressutti | A framework for combining a motion atlas with non-motion information to learn clinically useful biomarkers: Application to cardiac resynchronisation therapy response prediction[END_REF] ), thus better suited to agnostically partition a population into homogeneous groups. Importantly, the richness of the analysed data obtained by integrating entire volume/strain traces provides enough information to enable identification of phenogroups (which have been "agnostically" defined by the K-means algorithm) of patients with similar (but not identical) properties without prior assumptions on outcomes. The performed dimensionality reduction aids in extracting the relevant clinical characteristics of the phenogroups, providing (patho)physiologically relevant and interpretable results. Indeed, ML has previously been successfully employed in the diagnosis, classification and prognostication of HF cohorts [START_REF] Awan | Machine learning in heart failure: ready for prime time[END_REF][START_REF] Ahmad | Machine learning methods improve prognostication, identify clinically distinct phenotypes, and detect heterogeneity in response to therapy in a large cohort of heart failure patients[END_REF] . In addition to the achieved advancements and ongoing efforts in the field [START_REF] Shameer | Machine learning in cardiovascular medicine: are we there yet?[END_REF] , we believe that the approach proposed in this analysis contributes to this growing field by providing novelty and strengthening the integration of detailed imaging data with standardly utilised clinical variables in an ML analysis dedicated to providing clinically interpretable results. Namely, our analysis was superior at identifying CRT responders compared to independently analysing clinical parameters or complex echocardiographic descriptors alone, which did not provide phenogroups with statistically significant differences in the treatment effect (see Supplemental Material).

Positioning unsupervised learning in the spectrum of machine learning approaches and the utility of interpretability

The current data analysis trend is towards powerful approaches such as deep learning, which uses neural networks to solve complex pattern recognition problems [START_REF] Castelvecchi | Can we open the black box of AI?[END_REF] such as object [START_REF] Krizhevsky | ImageNet classification with deep convolutional neural networks[END_REF] and speech [START_REF] Hinton | Deep neural networks for acoustic modeling in speech recognition: the shared views of four research groups[END_REF] recognition, but requires immense collections of data (often lacking in clinical medicine) to make reliable predictions [START_REF] Castelvecchi | Can we open the black box of AI?[END_REF] . Furthermore, the "black-box" nature of this methodology often provides results difficult to interpret [START_REF] Castelvecchi | Can we open the black box of AI?[END_REF] . Human interpretability is increasingly recognized as a highly relevant feature of ML methodologies, crucial in efforts towards data-driven precision medicine, based on informed and auditable decisions. Thus, we opted for a "simpler" and less data-demanding analysis approach, for which we reinforce aspects of interpretability (Figure 5). This approach was specifically designed to combine heterogeneous data in an unsupervised way, which ultimately allows finding groups of patients with similar characteristics and therapy response. Our unsupervised analysis approach, rather than classifying based on a priori knowledge as done in a recent study targeting the same clinical problem [START_REF] Kalscheur | Machine Learning Algorithm Predicts Cardiac Resynchronization Therapy Outcomes[END_REF] , allows for natural clustering of patients, and results in the identification of patient subgroups with defined treatment effects. Unlike the work by Kalscheur et al. [START_REF] Kalscheur | Machine Learning Algorithm Predicts Cardiac Resynchronization Therapy Outcomes[END_REF] , where the authors used a Random Forest regression model to predict outcome, we emphasized the interpretability of our model, which allows exploring the computed data "universe", and highlights the data features that are relevant to the clinical hypothesis under study. This provides for a more meaningful description and distinction of specific patient groups within the cohort. Specifically, Phenogroups 1 and 3 showed marked response to CRT (both in primary outcome and volume response) and shared similar clinical attributes known to be predictive of (volume) response to CRT while the LV strain traces revealed an LBBB-related strain pattern. In contrast, Phenogroups 2 and 4 represented the non-responder groups, characterised by a low proportion of LBBB, high proportion of ischemic heart disease and LV strain patterns consistent with ischaemia/scar. Phenogroup 2 consisted of patients with the least severe course of disease -those with the lowest NYHA class, lowest diuretic use and the least remodelled LVs. We postulate that, in conjunction with a different HF substrate (predominantly ischaemic heart disease and other comorbidities) this lead to a lack of response to CRT. Conversely, those in Phenogroup 4 exhibited a larger amount of biventricular remodelling and extensive scarring on the LV strain traces with a high primary outcome rate in the ICD-only subgroup, possibly inferring a more advanced stage of ischaemic heart disease, too advanced to respond to CRT (Figure 2). In summary, a combination of beneficial clinical parameters and strain patterns (some known to be typically associated to LBBB and describing LV mechanics in CRT responders) appear to predict a beneficial treatment effect of CRT, superior to echocardiographic and clinical parameters alone.

Contrasting clinical features and strain patterns revealing more non-deforming regions suggest less successful treatment by CRT.

In the current manuscript, we did not aim to set out a specific "model" or scoring system for the prediction of response to CRT, which we believe requires further tool development as well as external validation. Rather, we aimed to ascertain the potential of unsupervised learning approaches in novel phenogrouping of a HF cohort, extended by its application in the prediction of response to a specific therapy, and to demonstrate the benefit of integrating complex imaging data and clinical parameters to accomplish robust phenogrouping. We believe that the novelty predominantly lies in the described methodology, and perhaps less so in the features detected to be associated with CRT response: while this agnostic approach identified features that were previously shown to predict response to CRT [START_REF] Goldenberg | Predictors of response to cardiac resynchronization therapy in the Multicenter Automatic Defibrillator Implantation Trial with Cardiac Resynchronization Therapy (MADIT-CRT)[END_REF][START_REF] Chung | Results of the predictors of response to CRT (PROSPECT) trial[END_REF] , we were able to accomplish this in a multivariable manner using both clinical and imaging based data, rather than by comparison of unidimensional subgroups. Our study is timely, since our echo-based analyses could be relatively easily programmed into echocardiographic post-processing equipment that already does extract the kind of deformation descriptors that we have used.

Limitations

Several limitations of this study should be acknowledged. The results are confined to a selected population of patients with mild HF enrolled in a clinical trial with robust inclusion and exclusion criteria, which have thus determined the input data to the algorithm. A longer follow up time than the average of 2.3 years available in our cohort may have been beneficial. Furthermore, an inherent limitation of echocardiographic studies applies to our study as well: the quality of data relies on acquired images and their quality, which was however minimized by excluding echo studies with unacceptable 2D image quality. Although our analysis approach is unsupervised, some human intervention in the form of specification of the most meaningful clustering configuration was required.

We demonstrated the overall stability of our results with different database sizes and different sets of descriptors; however, as with all statistical modelling, the results are dependent on the input data, and careful interpretation is needed to guarantee the generalizability of the results. Due to the overlapping between phenogroups, our findings lose power in areas close to the frontier between clusters ("grey zone"). However, if more subjects and clinical descriptors were available, our implementation would allow a more detailed phenotyping, enabling a more patient-specific approach. In such scenario, for every new case the algorithm could suggest similar subjects from its records and provide statistics on the likeliness that a certain subject may develop a disease (diagnosis) or may evolve in a determined way with time or therapy (prognosis). Finally, while external validation would be optimal, a comparable dataset is difficult to obtain, particularly in view of the detailed baseline characteristics and outcomes of the cohort, as well as in respect to the completeness of the dataset. However, we have assessed the stability of our data through internal validation (online-only Data Supplement).

Conclusion

In conclusion, this analysis confirms the utility of unsupervised ML for a novel approach to the integration of complex echocardiographic data (data on LV volume and deformation throughout the cardiac cycle instead of single data points) with clinical parameters to phenotype patients with HF with reduced ejection fraction. Our results serve as a proof-of-concept that fully unsupervised ML approaches can provide an interpretable and clinically meaningful classification of a heterogeneous cohort of HF patients, creating a basis of a data-driven platform that might aid in identifying patient subgroups most likely to respond to specific therapies. The feasibility and novelty of the proposed model for patient phenogrouping in heart failure and its added value in clinical decision making should be evaluated in a prospective controlled trial. diagnosis and clinical decision making. Both approaches utilise similar "input" sources, and depending on clinical experience or ML approach chosen, can use more or less complex data. Also, outcome data for a specific patient are known only a posteriori in clinical practice, most ML approaches integrate these data a priori. The proposed phenotyping approach based on dimensionality reduction of complex patterns and unsupervised grouping is agnostic to outcomes, allowing for phenogroup interpretation based on the integration of outcomes data a posteriori (dashed line).

Figure legends:

Figure 1 .

 1 Figure 1. Overview of the proposed analysis. Input data consist of both complex descriptors from

Figure 2 .

 2 Figure 2. Typical clinical characteristics, features of LV deformation patterns and outcome rates of the four Phenogroups. The green circles represent the Phenogroups more likely to respond to CRT, as

Figure 3 .

 3 Figure 3. Volume and strain traces corresponding to the representative patient of each phenogroup,

Figure 4 .

 4 Figure 4. Kaplan-Meier estimates of the probability of survival free of heart failure according to

Figure 5 .

 5 Figure 5. The comparison of current clinical practice and machine learning (ML) in the approach to

Figure 3 Figure 4 left 4 Hazard

 344 Figure 3

Figure 4 right

 4 Figure 4 right Click here to access/download;Figure;Fig 4_right.pdf

Table 1 .

 1 Baseline Characteristics of the Studied Patients by Phenogroups.

		Overall	Phenogroup 1	Phenogroup 2	Phenogroup 3	Phenogroup 4	Group
		average	(N=157)	(N=370)	(N=291)	(N=288)	P value
	Age, years	64 ± 11	62 ± 11	64 ± 11	67 ± 11	63 ± 11	<0.001
	Female	274 (25%)	35 (22.3%)	30 (8.1%)	195 (67.0%)	14 (4.9%)	<0.001
	Race, white	1006 (91%)	151 (96%)	324 (88%)	274 (94%)	257 (89%)	0.002
	Ischaemic CMP	622 (56%)	71 (45.2%)	264 (71.4%)	124 (42.6%)	163 (56.6%)	<0.001
	NYHA class II	934 (84%)	141 (89.8%)	287 (77.6%)	261 (89.7%)	245 (85.1%)	<0.001
	Hypertension	687 (62%)	77 (49.0%)	254 (68.7%)	174 (59.8%)	182 (63.2%)	<0.001
	Diabetes	311 (28%)	36 (22.9%)	118 (31.9%)	62 (21.3%)	95 (33.0%)	0.002
	Smoking	134 (12%)	27 (17.2%)	44 (11.9%)	30 (10.3%)	33 (11.5%)	0.18
	Prior CABG	312 (28%)	39 (24.8%)	129 (34.9%)	53 (18.2%)	91 (31.6%)	<0.001
	Prior non-CABG
		314 (28%)	30 (19.1%)	146 (39.5%)	60 (20.6%)	78 (27.1%)	<0.001
	revascularization
	Prior MI	497 (45%)	52 (33.1%)	215 (58.1%)	101 (34.7%)	129 (44.8%)	<0.001
	Prior CVA	66 (6%)	9 (5.7%)	33 (8.9%)	9 (3.1%)	15 (5.2%)	0.016
	Prior HF
		409 (37%)	56 (35.7%)	108 (29.2%)	125 (43.0%)	120 (41.7%)	<0.001
	hospitalization
	Number of hospitalisations prior to enrolment				0.73
	None	590 (53%)	88 (56%)	195 (53%)	160 (55%)	147 (51%)
	One	374 (34%)	48 (31%)	130 (35%)	96 (33%)	100 (35%)
	Two	97 (9%)	18 (12%)	29 (8%)	24 (8%)	26 (9%)
	Three or more	45 (4%)	3 (2%)	16 (4%)	11 (4%)	15 (5%)
	Prior ventricular
		71 (6%)	17 (10.8%)	23 (6.2%)	14 (4.8%)	17 (5.9%)	0.09
	arrhythmias
	Prior atrial
		115 (10%)	15 (9.6%)	44 (11.9%)	19 (6.5%)	37 (12.9%)	0.06
	arrhythmias
	SBP, mmHg	123 ± 18	117 ± 16	125 ± 18	123 ± 18	123 ± 17	<0.001
	DBP, mmHg	72 ± 10	71 ± 11	73 ± 10	71 ± 10	72 ± 11	0.07
	Heart rate, bpm	63 ± 11	66 ± 11	62 ± 11	64 ± 11	64 ± 12	<0.001
	Height, cm	173 ± 9.6	171 ± 8	177 ± 7	163 ± 8	178 ± 7	<0.001
	BMI, kg/m 2	28.3 ± 5.0	27.4 ± 4.0	29.6 ± 4.7	25.5 ± 4.7	29.8 ± 5.0	<0.001

Preprint version accepted to appear in European Journal of Heart Failure. Final version of this paper available at https://onlinelibrary.wiley.com/doi/full/10.1002/ejhf.1333

Sources of funding

The work of S. Sanchez-Martinez was supported by a fellowship from "la Caixa" Banking Foundation. C. Butakoff was supported by a grant from the Fundació La Marató de TV3 (nº 20154031), Spain. N. Duchateau was supported by "Programme Avenir Lyon Saint-Etienne" (PALSE-IMPULSION-2016, Lyon, France). MADIT-CRT was sponsored by Boston-Scientific, while no additional funding was provided for this analysis. This study was also partially supported by the Spanish Ministry of Economy and Competitiveness (grant TIN2014-52923-R; Maria de Maeztu Units of Excellence Programme -MDM-2015-0502) and FEDER.

Conflict of interest

Drs. Solomon, and Moss have received research grants from Boston Scientific. Dr. Kutyifa has received research grant support and speaker honoraria from Zoll and Boston Scientific. Dr. Stein is employed by Boston Scientific. All other authors have reported that they have no relationships relevant to the contents of this paper to disclose.


Nicolas Duchateau
email: nicolas.duchateau@creatis.insa-lyon.fr

Filip Loncaric

Maja Cikes

Adelina Doltra

Marta Sitges

Bart Bijnens

Variability in the assessment of myocardial strain patterns: Implications for adequate interpretation

Keywords: Speckle-tracking, Myocardial strain, Spatiotemporal analysis, Reproducibility, Educational course

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Myocardial strain is a valuable indicator to better understand cardiac mechanics on a wide range of diseases, and obtain reference values for diagnosis and prognosis [START_REF] Amzulescu | Myocardial strain imaging: review of general principles, validation, and sources of discrepancies[END_REF]. However, its quantification from imaging data raises several concerns: validation of the software, standardization of the measurements, and interpretation of the results. Several efforts have been recently deployed to address the first two issues, in terms of definitions and computational aspects [START_REF] Papachristidis | Standardized delineation of endocardial boundaries in three-dimensional left ventricular echocardiograms[END_REF][START_REF] Voigt | Definitions for a common standard for 2D speckle tracking echocardiography: consensus document of the EACVI/ASE/Industry Task Force to standardize deformation imaging[END_REF], and performance assessment [START_REF] Alessandrini | Detailed evaluation of five 3D speckle tracking algorithms using synthetic echocardiographic recordings[END_REF]De Craene et al. 2013;[START_REF] D'hooge | EACVI/ASE/Industry Task Force to Standardize Deformation Imaging. Two-dimensional speckle tracking echocardiography: standardization efforts based on synthetic ultrasound data[END_REF].

Peak and timing values from global and regional strain have proven value over the ejection fraction [START_REF] Cikes | Beyond ejection fraction: an integrative approach for assessment of cardiac structure and function in heart failure[END_REF][START_REF] Smiseth | Myocardial strain imaging: how useful is it in clinical decision making?[END_REF], and have been the main focus of standardization and reproducibility studies [START_REF] Barbier | Reliability and feasibility of longitudinal AFI global and segmental strain compared with 2D left ventricular volumes and ejection fraction: intra-and inter-operator, test-retest, and inter-cycle reproducibility[END_REF][START_REF] Cheng | Reproducibility of speckle-tracking-based strain measures of left ventricular function in a community-based study[END_REF]Mirea et al. 2018a;[START_REF] Oxborough | Intraobserver reliability of two-dimensional ultrasound derived strain imaging in the assessment of the left ventricle, right ventricle, and left atrium of healthy human hearts[END_REF][START_REF] Shiino | Intervendor consistency and reproducibility of left ventricular 2D global and regional strain with two different high-end ultrasound systems[END_REF]. Nonetheless, a finer understanding of pattern changes with disease is highly recommended [START_REF] Bijnens | Velocity and deformation imaging for the assessment of myocardial dysfunction[END_REF][START_REF] Bijnens | Myocardial motion and deformation: What does it tell us and how does it relate to function?[END_REF][START_REF] Cikes | Beyond ejection fraction: an integrative approach for assessment of cardiac structure and function in heart failure[END_REF][START_REF] Fornwalt | It's time for a paradigm shift in the quantitative evaluation of left ventricular dyssynchrony[END_REF]. The spatial distribution of myocardial motion and deformation (regionally or even locally) and their temporal evolution along the cycle provide complementary information that is missed by peak measurements [START_REF] Cikes | The role of echocardiographic deformation imaging in hypertrophic myopathies[END_REF][START_REF] Duchateau | A spatiotemporal statistical atlas of motion for the quantification of abnormal myocardial tissue velocities[END_REF][START_REF] Duchateau | Myocardial motion and deformation patterns in an experimental swine model of acute LBBB/CRT and chronic infarct[END_REF][START_REF] Liu | Longitudinal strain bull's eye plot patterns in patients with cardiomyopathy and concentric left ventricular hypertrophy[END_REF][START_REF] Mcleod | Spatio-temporal tensor decomposition of a polyaffine motion model for a better analysis of pathological left ventricular dynamics[END_REF][START_REF] Parsai | Toward understanding response to cardiac resynchronization therapy: left ventricular dyssynchrony is only one of multiple mechanisms[END_REF][START_REF] Tabassian | Machine learning of the spatio-temporal characteristics of echocardiographic deformation curves for infarct classification[END_REF].

Besides, the selection of peaks on challenging traces may be confusing [START_REF] Anderson | Patient selection and echocardiographic assessment of dyssynchrony in cardiac resynchronization therapy[END_REF][START_REF] Duchateau | Myocardial motion and deformation patterns in an experimental swine model of acute LBBB/CRT and chronic infarct[END_REF].

However, data about the local variability in the spatiotemporal deformation patterns (namely, at each point of the myocardium and each temporal instant) are missing. One may wonder to which extent the etiologyspecific local strain abnormalities are preserved among operators, and what this could imply for disease interpretation.

In the context of a practical training course organized on a yearly basis, we set up a study to quantify the variability in a set of representative strain patterns measured by a large pool of operators with heterogeneous practice and profiles -clinicians and scientists. Our objectives were two-fold: (i) to report on the variability in spatiotemporal pattern observations and go beyond to the well-documented peak measurements -as explicitly required by the latest standardization initiatives (Mirea et al. 2018a) -and (ii) state on its implications for adequate disease understanding.

Materials and methods

Studied population

Preprint version accepted to appear in Ultrasound in Medicine and Biology. Final version of this paper available at https://www.umbjournal.org/ 4

The course took place in 2018, and provided cases collected by the organizers during the past five years and covering a broad range of pathologies. Six representative cases with known deformation patterns were selected for this study: (1) a healthy adult individual, (2) a patient with cardiac amyloidosis [START_REF] Cikes | The role of echocardiographic deformation imaging in hypertrophic myopathies[END_REF][START_REF] Liu | Longitudinal strain bull's eye plot patterns in patients with cardiomyopathy and concentric left ventricular hypertrophy[END_REF], (3a-3b) two athlete brothers with familial hypertrophic cardiomyopathy [START_REF] Cikes | The role of echocardiographic deformation imaging in hypertrophic myopathies[END_REF][START_REF] Liu | Longitudinal strain bull's eye plot patterns in patients with cardiomyopathy and concentric left ventricular hypertrophy[END_REF]), (4) a candidate for cardiac resynchronization therapy (CRT) with dilated cardiomyopathy and intraventricular dyssynchrony (Parsai et al. 2009), and (5) an athlete that died from sudden cardiac death. All echocardiographic examinations were performed in line with current international recommendations, and were recorded with a transthoracic probe (M4S or M5S, GE Healthcare, Milwaukee, WI, USA) using a commercially available system (Vivid 7 or 9, GE Healthcare, Milwaukee, WI, USA). The standard acquisition included both B-mode and tissue Doppler sequences, centered on the left ventricle, and Doppler flow analysis over the mitral and aortic valves. Additional sequences centered on the right ventricle were also acquired depending on the pathology. Machine settings (gain, time gain compensation, and compression) were adjusted for optimal visualization, including harmonic imaging. Frame rates of the analyzed sequences corresponded to standard acquisitions (Table 1).

The patients' and exam characteristics are summarized in Table 1. The analyzed cases were part of the clinical studies under investigation at the organizers' institutions, which complied with the Declaration of Helsinki and were accepted by the institutions' ethics committees, with written informed consent from all subjects.

Speckle-tracking analysis during the training course

Forty participants enrolled in the training course were distributed on 20 workstations equipped with a single commercial speckle-tracking tool (Echopac v.201, GE Healthcare, Milwaukee, WI, USA). Information on the participants' professional background and level of experience with speckle-tracking analysis was collected through a brief questionnaire at the beginning of the course. Results are summarized in Figure 1.

The participants were given training regarding the identification of mitral and aortic valve opening and closure on the Doppler sequences, manual delineation of the endocardial border on the B-mode sequence at endsystole, readjustments of delineations according to local wall thickness, and visual checking of the tracking quality -in particular at the apex and valve levels. After the initial training, the participants performed speckletracking analysis independently for each of the six cases. For consistency checking, the healthy case was analyzed both at the beginning and the end of the course. Myocardial segmentations and longitudinal strain patterns were obtained from 4-chamber views using speckle-tracking on the left ventricle (LV) or the right ventricle (RV), depending on the studied case. To assess the intra-observer variability, a single expert clinician repeated the measurements 10 times in a row for each of the clinical cases one month after the training course.

The cases were analyzed in random order to reduce bias in the analysis.

Statistical analysis of myocardial delineations and strain patterns

The output of speckle-tracking performed by the participants was exported through the "store full trace" option, which provides the position of all myocardial control points along the sequence, with spatial smoothing disabled in the software interface. The amount of exports saved during the course by participants is reported for each case in Table 2 andFigures 2, 3 and4, and in the Supplementary Material.

The myocardial delineations and the spatiotemporal longitudinal strain patterns were obtained from these exported data using standard computations, implemented in Matlab (v.R2016, MathWorks, Natick, MA, USA).

These computations included spatial resampling using cubic splines to compare the data at similar locations along the myocardium. As all participants processed the same sequence for each subject, no additional spatiotemporal alignment [START_REF] Duchateau | A spatiotemporal statistical atlas of motion for the quantification of abnormal myocardial tissue velocities[END_REF] of the data was required. No additional smoothing was added to the data. Drift compensation (forcing the values at the end of the cycle to match the ones at the onset of the cycle, option provided in the commercial speckle-tracking tool) was included in the results display.

Strain patterns were displayed using color-coded maps inspired from anatomical M-mode, where time (the cardiac cycle) is used as horizontal axis, and the spatial position along the myocardium is used as vertical axis. The color scale was centered on 0%, which corresponds to a lack of deformation, and red/blue colors stand for negative/positive strain corresponding to myocardial shortening/stretching. Variability in the myocardial delineations was quantified at each point of the myocardial shape, by computing the covariance matrix of its 2D coordinates, and extracting the maximal variation as the square root of the first eigenvalue of this 2x2 matrix. This information was reported as the mean and maximum of these values over the whole myocardium, in millimeters.

Variability in the strain patterns was quantified through the standard deviation of strain values at each point of the myocardium and each instant of the cardiac cycle (bottom part of Figures 2 and3). Strain variability is therefore expressed in absolute strain values (not relative) -a variability of 5% for -20% strain means that strain values roughly lie within the [-25% / -15%] interval. The median and inter-quartile range of strain patterns were also examined (central part of Figures 2 and3). Intra-class correlation was not computed due to the varying Preprint version accepted to appear in Ultrasound in Medicine and Biology. Final version of this paper available at https://www.umbjournal.org/ 6 pool of raters who correctly exported the data for each studied case, and the small number of cases. Bland-Altman plots were not calculated for similar reasons, in addition to the high-dimensionality of the spatiotemporal strain patterns.

Differences in the strain patterns were further examined in two ways. First, abnormalities in the measurements were assessed at each point of the myocardium and each instant of the cardiac cycle, by computing the Mahalanobis distance between the strain pattern obtained by each operator and the strain patterns obtained by the rest of operators. This measure corresponds to the distance to the average pattern normalized by the pattern variability among operators. To better analyze the results, we computed the p-value associated to this distance, under the assumption that the distribution of strain values (at each point of myocardium and each instant of the cardiac cycle, among the pool of operators) is Gaussian, as done in our anterior works [START_REF] Duchateau | A spatiotemporal statistical atlas of motion for the quantification of abnormal myocardial tissue velocities[END_REF][START_REF] Duchateau | Atlas-based quantification of myocardial motion abnormalities: added-value for understanding the effect of cardiac resynchronization therapy[END_REF]. Additionally, we estimated the maximum of the 2D normalized crosscorrelation between the strain pattern obtained by each operator and the average strain pattern from the rest of operators, values of 0 and 1 meaning no correlation and perfect correlation, respectively.

The potential relation between the variability of the myocardial delineations and of the spatiotemporal strain patterns was assessed at each point of the myocardium by the Pearson correlation coefficient and its associated p-value, after averaging the inter-and intra-operator strain variability over time.

Finally, inter-and intra-operator variability in global and regional peak strain were quantified through the mean and standard deviation of peak strain values, expressed in percentages, after averaging the strain patterns over the whole myocardium or each segment and extracting the peak value of the averaged curve.

Results

To better understand the discussion around each processed case, snapshots of the speckle-tracking output and animated views of the tracked myocardium are provided as Supplementary Material (Figures S1 to S5). They are complemented by strain patterns from tissue Doppler acquisitions (Figures S3a andS3b) or motion assessment in anatomical M-mode (Figure S4), when relevant.

Variability in myocardial delineations

Figures 2 and 3 first illustrate the inter-and intra-operator variability in the myocardial delineations from the different participants and by an experienced clinician repeating the measurements. Delineations were made of 67±8 points along the myocardium. They were rather consistent between participants, with a mean inter-operator variability of 2.7 to 5.3 mm (maximal variability: 3.3 to 6.2mm). Main differences were observed along the lateral wall and at the valve level (for both LV and RV), and at the septal bulge level for the athlete case. For comparison, mean and maximal intra-operator variability was 1.3 to 2.9 mm and 1.9 to 5.4 mm, respectively. Delineations for the normal case were consistent between the beginning and the end of the course, with less outliers at the apex at the end of the course, but still substantial inter-operator variability over the lateral wall (mean inter-operator variability of 3.5 mm [before] against 3.8 mm [after], and 1.6 mm for the intra-operator measurements).

Observed strain patterns

Strain patterns are displayed in Figures 2 and3. The black arrows and the overlaid numbers point out the main characteristics of the strain patterns, summarized as follows:

-Healthy adult (Figure S1 and subplots in Figures 2 and3): Segmental strain curves reach a uniform peak value in the same timing. Shortening during systole and lengthening during early relaxation and atrial contraction are homogeneous over the myocardium. Some post-systolic thickening is present in the basal septum, while the signal quality is lower at the most basal part of the lateral wall close to the mitral ring resulting in an abnormal trace at this location.

-Amyloidosis (Figure S2 and subplots in Figures 2 and3): A clear bilateral basal-apical gradient in strain values is present with near normal values in the apex and severely reduced basal strain [START_REF] Cikes | The role of echocardiographic deformation imaging in hypertrophic myopathies[END_REF][START_REF] Liu | Longitudinal strain bull's eye plot patterns in patients with cardiomyopathy and concentric left ventricular hypertrophy[END_REF]). This represents the typical "Japanese flag" appearance of the apical sparing.

-Athlete with hypertrophic cardiomyopathy and his brother (Figures S3a andS3b, and subplots in Figures 2 and3): The LV looks enlarged and hypertrophic (see also Table 1), global strain is normal and most segments show normal deformation, but in both cases there is a region within the mid septum where deformation is much lower compared to both the direct proximal and distal regions [START_REF] Cikes | The role of echocardiographic deformation imaging in hypertrophic myopathies[END_REF][START_REF] Liu | Longitudinal strain bull's eye plot patterns in patients with cardiomyopathy and concentric left ventricular hypertrophy[END_REF]. This is confirmed by the strain pattern from tissue Doppler.

-CRT candidate with left bundle branch block (Figure S4 and subplots in Figures 2 and3): The ventricle is dilated and the strain pattern is consistent with a dilated cardiomyopathy in the presence of a left bundle branch block, with characteristic spatial and temporal abnormalities. At the onset of the QRS complex, the septum quickly shortens while the lateral wall is being stretched. By the end of the QRS complex (while activation is still taking place) the lateral wall starts shortening, which results in a decreased speed of deformation of the septum, and the lateral segments continue to shorten after aortic valve closure. This Preprint version accepted to appear in Ultrasound in Medicine and Biology. Final version of this paper available at https://www.umbjournal.org/ 8 pattern has been described as a "septal flash" and is also recognizable on the anatomical M-mode image, with the fast inward-outward motion of the septum within the QRS complex, reduced systolic excursion during the rest of ejection and the presence of post-systolic shortening [START_REF] Parsai | Toward understanding response to cardiac resynchronization therapy: left ventricular dyssynchrony is only one of multiple mechanisms[END_REF]. A complementary view on this pattern is given in Figure S8, with myocardial velocities in the radial direction using a display similar to Figures 2 and3.

-Athlete that experienced sudden cardiac death (Figure S5 and subplots in Figures 2 and3): This case shows an overall appearance of an athlete's heart with bi-ventricular dilatation and hypertrophy (see also Table 1) and enlarged atria. When assessing RV deformation, a difference in basal and apical strain can be expected, but here a clear and unexpected decrease/absence of systolic shortening in the basal segment of the RV lateral wall can be observed. The present study is after a period of detraining where this abnormally low basal strain did not recover as compared to the assessment during training. The patient was recommended to decrease the intensity of sports, but died suddenly during running.

Variability in strain patterns

The bottom rows of Figures 2 and 3 illustrate the inter-and intra-operator variability of strain patterns, meaning the strain values at each point of the myocardium and each instant of the cycle. The maximal values for the interoperator variability (maximal value observed in each strain variability map) ranged from 6.3 to 11.5%, mainly observed at the apex and the basal septal and lateral walls near the valve. The maximal values for the intraoperator variability ranged from 4.3 to 10.2%, also at these locations. Similarly to the myocardial delineations, the spatiotemporal strain patterns for the normal case were consistent between the beginning and the end of the course, with lower inter-operator strain variability at the apex at the end of the course, but still substantial interoperator strain variability at the mitral valve level on both walls (maximal inter-operator variability of 8.9%

[before] against 11.5% [after], against 6.0% for the intra-operator measurements). Low to moderate correlations were observed between the variability of the myocardial delineations and of the spatiotemporal strain patterns, as summarized in Figure 4.

The previously described pathology-specific strain abnormalities were visible in each of the six cases, consistently among participants regardless of the described inter-operator variability in myocardial delineations or strain patterns. Figure 5 confirms this by examining abnormalities and correlations in the measurements of the operators, and displaying the few strain patterns identified as outliers, which still allow identifying the main characteristics of each case.

Preprint version accepted to appear in Ultrasound in Medicine and Biology. Final version of this paper available at https://www.umbjournal.org/ Figures 2 and 3 but for the course organized on the previous year (2017), which served as a feasibility study on four cases (normal, first brother athlete, septal flash, and athlete with sudden death) and led to similar observations.

Variability in global and regional peak strain measurements

To complement the analysis with more conventional measurements, the variability in global and regional peak longitudinal strain is summarized in Table 2. Both inter-and intra-operator peak strain variability (global: 0.7 to 1.5% [inter-operator] and 0.4 to 1.1% [intra-operator]; regional: 0.5 to 4.1% [inter-operator] and 0.2 to 4.0%

[intra-operator]) were lower than the inter-and intra-operator variability in the strain patterns reported in the previous subsection.

Discussion

In this study, we compared the local deformation patterns quantified by a large pool of in-training operators with heterogeneous profiles and experience, and reported on the variability of the observations at each point of the myocardium and each instant of the cycle. Strain patterns were consistent among operators despite high interoperator variability at specific locations (apex and near the valve on both walls). In particular, the etiologyspecific local strain abnormalities were visible in all patterns and did not hamper disease interpretations.

In the last years, there have been several initiatives to better assess the variability and reproducibility of strain measurements. Clinical, industrial and academic instances put a lot of efforts to discuss and better harmonize segmentation and tracking techniques [START_REF] Amzulescu | Myocardial strain imaging: review of general principles, validation, and sources of discrepancies[END_REF][START_REF] Papachristidis | Standardized delineation of endocardial boundaries in three-dimensional left ventricular echocardiograms[END_REF][START_REF] Voigt | Definitions for a common standard for 2D speckle tracking echocardiography: consensus document of the EACVI/ASE/Industry Task Force to standardize deformation imaging[END_REF]. State-of-the-art algorithms were evaluated on synthetic echocardiographic images for which ground-truth myocardial delineation and deformation are known [START_REF] Alessandrini | Detailed evaluation of five 3D speckle tracking algorithms using synthetic echocardiographic recordings[END_REF]De Craene et al. 2013;[START_REF] D'hooge | EACVI/ASE/Industry Task Force to Standardize Deformation Imaging. Two-dimensional speckle tracking echocardiography: standardization efforts based on synthetic ultrasound data[END_REF]. Carefully designed studies also assessed specific aspects of reproducibility when measuring peak global and regional strain from commercial software [START_REF] Barbier | Reliability and feasibility of longitudinal AFI global and segmental strain compared with 2D left ventricular volumes and ejection fraction: intra-and inter-operator, test-retest, and inter-cycle reproducibility[END_REF][START_REF] Cheng | Reproducibility of speckle-tracking-based strain measures of left ventricular function in a community-based study[END_REF]Mirea et al. 2018a;[START_REF] Oxborough | Intraobserver reliability of two-dimensional ultrasound derived strain imaging in the assessment of the left ventricle, right ventricle, and left atrium of healthy human hearts[END_REF][START_REF] Shiino | Intervendor consistency and reproducibility of left ventricular 2D global and regional strain with two different high-end ultrasound systems[END_REF]. In an educational perspective, the influence of the training level of the operators was also examined [START_REF] Chan | Left ventricular global strain analysis by two-dimensional speckletracking echocardiography: the learning curve[END_REF][START_REF] Negishi | Effect of experience and training on the concordance and precision of strain measurements[END_REF]Yamada et al. 2014). In our study, the questionnaire about the participants' background and experience with speckle-tracking was anonymous, which precluded from investigating the quality of each operator's measurements against his/her experience.

Preprint version accepted to appear in Ultrasound in Medicine and Biology. Final version of this paper available at https://www.umbjournal.org/ 10 In our study, the inter-and intra-operator variability in global and regional peak strain was rather low compared to the inter-and intra-operator variability in the strain patterns observable at specific locations. This is expected: peak measurements represent a single value along the cycle, not necessarily at the instant of highest variability, and encode strain values averaged over a region or the whole myocardium, which reduces differences between operators. While peak strain (either global or regional) is a practical measurement to situate a subject within a population or quantify its evolution, it disregards temporal dynamics more subtle to assess (e.g. the septal flash pattern from the CRT case presented here).

Several sources of variability (Mirea et al. 2018b) (number of control points, location of the control points, global and local thickness adjustments, etc.) were integrated into our evaluation, as participants had freedom to process the retained sequences. Acquisitions came from similar devices and were processed with the same tool, which limits differences in the measurements (Mirea et al. 2018a;[START_REF] Shiino | Intervendor consistency and reproducibility of left ventricular 2D global and regional strain with two different high-end ultrasound systems[END_REF]). The analysis was done in 4-chamber views, which have lower regional peak strain variability compared to other views [START_REF] Barbier | Reliability and feasibility of longitudinal AFI global and segmental strain compared with 2D left ventricular volumes and ejection fraction: intra-and inter-operator, test-retest, and inter-cycle reproducibility[END_REF]. Nonetheless, the purpose of this paper is not to make a sensitivity analysis of the measurements against each of possible source of variability but to reflect operators' practice. In this sense, our pool of in-training operators was interesting due to their heterogeneous background, knowing that some of them can be more aware of the algorithmic techniques behind tracking, and others of the physiological traits of each case. Variability may therefore differ from the ranges obtained for expert operators with similar background, as in previous reproducibility studies [START_REF] Barbier | Reliability and feasibility of longitudinal AFI global and segmental strain compared with 2D left ventricular volumes and ejection fraction: intra-and inter-operator, test-retest, and inter-cycle reproducibility[END_REF][START_REF] Cheng | Reproducibility of speckle-tracking-based strain measures of left ventricular function in a community-based study[END_REF]. Nonetheless, we did not specifically investigate the correspondence between the inter-operator variability in the measurements and the professional background of the participants. The statistical significance of differences between the inter-and intra-operator variability in strain patterns was tested using the Levene's test and the Brown-Forsythe test at each point of the myocardium and at each temporal instant. Although some statistically significant differences were locally observed for some cases, the outcome of this test was difficult to interpret and arguable given the limited sample size, which is why this experiment was not reported in the manuscript.

Carefully examining the spatiotemporal strain patterns in light of their variability is explicitly recommended by the recent reproducibility assessment initiatives (Mirea et al. 2018a), but has not been addressed yet. Here, we examined this for the educational purposes of a training course and to open the discussion on how this could be approached in clinical practice. With this analysis, we do not aim at standardizing the operators' measurements. Instead, we help them develop a critical view on the output of the analysis. Nonetheless, key issues should be taught to limit uncertainties on the interpretation: minimum

Limitations

This study was led within the guidance of a training course. This work is therefore different from a population study and has educational objectives. Although participants were free to perform the analysis in an independent way, the results were consistent between the beginning and the end of the course as exemplified on the normal case, even if no guarantee exists on their persistency afterwards. Within the context of the training course, we only included a limited set of cases in a 4-chamber view for illustration purposes. These cases had representative strain patterns that allowed examining the zones where variability between operators could be critical for interpretation. Similar observations were made for the other cases processed along the course, which covered ischemia, heart failure with preserved ejection fraction, and valve diseases, among others. Nonetheless, they had less representative strain patterns and the participants were therefore not asked to export their measurements for such cases. The selected data already depict a variety of common local shape and deformation abnormalities, including in regions subject to high inter-and intra-operator variability in the myocardial delineations and strain patterns (base and apex). Analyzing cases associated to different stages of a given disease was not performed.

Image quality may actually influence the accuracy of the results (Mirea et al. 2018b), but meets high standards in other reproducibility studies [START_REF] Chan | Left ventricular global strain analysis by two-dimensional speckletracking echocardiography: the learning curve[END_REF]Mirea et al. 2018a). Similarly, our study consisted of cases from the clinical routine of experienced echocardiographers, and had good image quality to pursue the course primary objectives.

Conclusion

Our study quantified the variability in spatiotemporal strain patterns on a substantial pool of in-training operators, which was not addressed before despite the value of the spatial and temporal strain abnormalities for disease understanding. We demonstrated that consistent pattern assessment is possible despite heterogeneous levels of experience with speckle-tracking. In light of minimum knowledge on the processing techniques involved and the pathophysiology of the studied cases, we actively recommend careful interpretation of abnormal deformation patterns in addition to systematic quantification of peak deformation values.

Figure legends

  Preprint version accepted to appear in Ultrasound in Medicine and Biology. Final version of this paper available at https://www.umbjournal.org/ knowledge on the processing techniques involved (what smoothing and drift compensation represent, what to expect from tracking in lower visible regions, what different number of control points or wider regions of interest may imply, does the tracking actually stick to the image, etc.), and careful understanding of the pathophysiology of the studied cases.

Figure 1 :

 1 Figure 1: Summary of the answers to the participants' survey, regarding their background and levels of experience in the analysis of cardiac images and their use of Echopac and speckle-tracking.

Figure 2 :

 2 Figure 2: Inter-operator variability in myocardial delineations (top) and strain patterns (central part: median and first/third quartile strain patterns, bottom row: variability in strain patterns). (1) homogeneous pattern; (2) "Japanese flag": preserved deformation only around the apex; (3) localized non-deforming region surrounded by more normal deformation; (4) intra-ventricular dyssynchrony with marked "septal flash"; (5) severely reduced RV basal lateral wall deformation. CRT: cardiac resynchronization therapy. Vertical dashed lines stand for the following events: Q1/Q2: onset of QRS; AVO/AVC/MVO/MVC: aortic/mitral valve opening/closure.

Figure 3 :

 3 Figure 3: Intra-operator variability in myocardial delineations and strain patterns. Display similar to Figure 2.

Figure 4 :

 4 Figure 4: Variability of the myocardial delineations against the variability of the strain patterns (at each point of the myocardium, after averaging the variability in strain patterns over time; similar trends observed when taking its maximal value over time). The Pearson correlation coefficient and its associated p-value are indicated in each subplot.

Figure 5 :

 5 Figure 5: Consistency in the measurements among the operators. Top row: abnormality in the strain pattern obtained by each operator compared to the strain patterns obtained by the rest of operators (p-value associated to the Mahalanobis distance, averaged over the whole spatiotemporal pattern, and displayed in a logarithmic scale).Central row: maximal value of the 2D normalized cross-correlation between the strain pattern obtained by each operator and the average strain pattern from the rest of operators. Bottom part: strain patterns identified as outliers, to compare with the median and first/third quartile strain patterns from Figure2. The p-value and correlation obtained are summarized in the top right corner of each pattern.

  Figure 1

  Figure 5

  Figure S1

Table 1 : Patient and exam characteristics

 1

				Athlete	Athlete		Sudden
		Normal	Amyloid			CRT
				Brother #1	Brother #2		death
	General
	Frame rate (frames per second)	55	54	67	39	64	40
	Age (y)	31	53	21	19	46	47
	Sex	male	male	male	male	male	male
	LV measurements
	Basal septal thickness (cm)	0.8	1.6	1.6	1.4	1.0	1.2
	Posterior wall thickness (cm)	1.0	2.3	1.1	1.0	1.0	1.2
	LV end-diastolic diameter (cm)	4.1	4.1	4.6	4.6	6.7	5.2
	LV end-systolic diameter (cm)	3.3	3.0	2.6	3.2	6.3	4.5
	LVED volume (ml)	98	88	101	85	178	149
	LVES volume (ml)	40	30	34	30	131	65
	LVEF (%)	60	66	66	65	26	56
	E (m/s)	71	70	56	88	54	71
	A (m/s)	66	33	24	58	67	51
	E/A	1.09	2.12	2.36	1.52	0.82	1.39
	Septal e' (m/s)	10	4	12	12	5	-
	Septal a' (m/s)	10	5	7	7	8	-
	Lateral e' (m/s)	-	7	17	18	6	17
	Lateral a' (m/s)	-	11	7	6	4	6
	E/e'	7.1	11.7	3.9	5.9	9	4.2
	LV: left ventricle; ED: end-diastolic; ES: end-systolic; EF: ejection fraction; CRT: cardiac resynchronization
	therapy.

  Preprint version accepted to appear in Ultrasound in Medicine and Biology. Final version of this paper available at https://www.umbjournal.org/ 26

			Normal before	Normal after	Amyloid		Athlete brother #1	Athlete brother #2			CRT			Sudden death
	Inter-operator	strain variability (%)	(N=16) R=0.73 p=7.5e-11		(N=15) R=0.56 p=1.8e-6	(N=15) R=-0.36 p=0.005			(N=20) R=0.27 p=0.035			(N=16) R=0.38 p=0.003			(N=13) R=0.13 p=0.283			(N=16) R=0.41 p=7.3e-4
			Inter-operator
			shape variability (mm)
			Normal before		Amyloid		Athlete brother #1	Athlete brother #2			CRT			Sudden death
	Intra-operator	strain variability (%)	(N=10) R=0.74 p=2.8e-11			(N=10) R=0.29 p=0.024			(N=10) R=0.62 p=1.7e-7			(N=10) R=0.08 p=0.528			(N=10) R=0.16 p=0.188			(N=10) R=0.21 p=0.089
			2 Intra-operator 4	6	0	2	4	6	0	2	4	6	0	2	4	6	0	2	4	6	0	2	4	6
			shape variability (mm)

dimensional speckle-tracking and doppler tissue imaging between expert and novice readers during quantitative dobutamine stress echocardiography. J Am SocEchocardiogr. 2014;27:880-7.

(inward/outward motion of the septum during the isovolumic contraction), compared to the normal case (synchronous contraction/relaxation pattern between the septal and lateral walls). Again, variability exists between operators but still allows relevant assessment of the pattern abnormalities.

Acknowledgements

Funding: This work was partially supported by the Spanish Ministry of Economy and Competitiveness [grant TIN2014-52923-R; Maria de Maeztu Units of Excellence Programme -MDM-2015-0502] and FEDER, and the European Union H2020 programme [PIC H2020-MSCA-ITN-2017-764738].

Disclosures: In the recent years, MS received speaker fees from GE Healthcare, Toshiba, Medtronic, and Abbott; BB and MC received speaker fees from GE Healthcare. However, these did not influence the strain course related to this study, which was independently organized and not sponsored.

Preprint version accepted to appear in Ultrasound in Medicine and Biology. Final version of this paper available at https://www.umbjournal.org/

Video S4: idiopathic patient with dilated cardiomyopathy and intra-ventricular dyssynchrony (presence of a "septal flash" including apical rocking).

Video S5: athlete with local right ventricular deformation abnormalities who died suddenly.

Supplementary figures

Figure S1: normal control. Longitudinal strain from speckle-tracking. Longitudinal strain from speckle-tracking.


M Burger

P J Skrodzki

L Finney

J Hermann

J Nees

I Jovanovic

Optical Detection of Deuterium in Heavy Water: Towards Remote Detection of Tritium

Keywords:

Tritium detection poses a challenge because of the weak beta particle emission and absence of ionizing radiation. We demonstrate the isotopic analysis of deuterated water via laser-induced breakdown spectroscopy as a modality for measuring tritium.

Introduction

Performing standoff detection of radionuclides is relevant in fields such as nuclear security and radiological safety [1]. Standoff delivery of a laser interrogation source is commonplace, and bright laser-induced plasmas are sources of abundant characteristic optical signal, making the laser-induced breakdown techniques well-suited for detection of various radionuclides, including tritium (T). Here we investigate such an approach based on the optical emission spectroscopy of laser-induced plasma [2], with an emphasis on detection of radioisotopes of interest in mixtures containing multiple isotopes of the same element. One of the challenges in employing LIBS to identify isotopic species is the degree of separation between closely spaced (∼pm) spectral lines. Prior related efforts include the quantitative detection of deuterium (D) and hydrogen (H) retained in various fusion reactor components [3]. Due to the high cost and difficulty of obtaining T, we use D as a proxy. H and D are readily observable using optical emission spectroscopy at significant D concentrations under appropriate conditions. However, to detect lower D concentrations using this method, it is necessary to reduce the intense continuum emission and excessive Stark broadening, as well as enhance the characteristic line emission signal. Under reduced ambient pressure, species segregation in the plasma has also been shown to play a significant role, as the lighter species expand faster into surrounding gas.

The aim of this work is to investigate the effects of species segregation in laser-produced D-H plasma on the ability to resolve D α and H α isotope features and accurately reconstruct their relative concentrations.

Experiment, results and discussion

The experiments (Fig. 1(a)) were performed with a compact, double pulse (DP) Nd:YAG laser, producing ∼10-ns, up to 140-mJ pulses at the wavelength of 1064 nm and 10-Hz repetition rate. The single pulse (SP) ablation experiments used 75-mJ pulses, whereas DP experiments used 55 mJ and 75 mJ for the first and second pulse, respectively. Interpulse (IP) delay in the DP configuration was varied between short (50 ns) and long (1000 ns). The samples were prepared by mixing 40% deuterated water (D 2 O) with deionized water. The frozen mixture was mounted on a Peltier cooler. The plasma emission was collected with an f /2 collimator, coupled into an optical fiber bundle and transferred to a Czerny-Turner spectrometer with a 0.55-m focal length and a resolving power greater than 10 4 . The ICCD gate width was set to 1 µs. Spectroscopic data acquisition was performed in air by averaging over 200 ablation events. Plasma imaging (1:1) was performed by integrating over 30 ablation events using a 50-mm diameter, 75-mm focal length achromatic lens and an ICCD detector operating with a gate width of 3 ns. Figure 1(b) shows the SP experimental and computed profiles of superimposed D α and H α lines from the onset of spectral splitting (8 µs) to the final stage of the Balmer beta lifetime (11 µs). The electron density and excitation temperature trends were deduced from the simulated profiles, including contributions of plasma core and peripheral region (Fig. 1(c)).

Figure 2(a) compares the short and long IP delays for the DP scheme. The arrival of the second laser pulse in the short IP case causes elongation of the plume along the laser axis, whereas the second pulse in the long IP case causes a short-lived feature at the front edge of the plume, while having a negligible effect on the plume shape at later times. The negligible change of the plume shape seen in the long IP case indicates better laser-plasma coupling and a reduced rate of secondary ablation. Figure 2(b) shows one of the possible figures of merit (FOM) for distinguishing D from H. We note the relatively constant trend for all ablation schemes, signifying the absence of notable segregation effects. Finally, we observe (Fig. 2(c)) the greatest distinction between D α and H α lines for long IP delay at earlier time steps. As a consequence, the agreement between experimental data and simulation implies that the isotopic fraction remains unchanged during the Balmer beta spectral line lifetime. We find that species segregation for laser-produced plasma formed in air does not significantly impact the ability to distinguish D α and H α Balmer lines for both the SP and DP laser ablation schemes. Significant reduction of broadening was observed in comparison to the SP configuration by employing the second, reheating pulse in a collinear geometry while using a lower-energy initial pulse. Thus, DP-LIBS offers a promising pathway towards remote detection of hazardous low-Z radionuclides (such as tritium) in air.

Fig. 1 .

 1 Fig. 1. (a) Setup for DP LIBS on a frozen D 2 O-H 2 O mixture. The magnified section depicts the two-zone model [4]; (b) Measured and computed profiles of Balmer alpha spectral line at various delays after the laser pulse; Temporal evolution of (c) electron density and (d) excitation temperature of the plasma core and periphery.

Fig. 2 .

 2 Fig. 2. (a) Plasma emission comparing SP and DP ablation with short (50-ns) and long (1000-ns) IP delays (yellow frame); Figures of merit for distinguishing D from H based upon the: (b) relative intensities, (c) line widths of the D α line (w D ) and the H α line (w H ) and their isotopic separation d. The dashed line indicates the intensity ratio expected for the isotopic ratio of the sample.

  Funding & Acknowledgements: National Science Foundation Graduate Research Fellowships Program (DGE 1256260); Department of Energy National Nuclear Security Administration, Consortium for Verification Technology (DE-NA0002534) and Nuclear Science and Security Consortium (DE-NA0003180 and DE-NA0000979).