Deriving Explainable Metrics of Left Ventricular Flow by Reduced-Order Modeling and Classification

Background Extracting explainable flow metrics is a bottleneck to the clinical translation of advanced cardiac flow imaging modalities. We hypothesized that reduced-order models (ROMs) of intraventricular flow are a suitable strategy for deriving simple and interpretable clinical metrics suitable for further assessments. Combined with machine learning (ML) flow-based ROMs could provide new insight to help diagnose and risk-stratify patients. Methods We analyzed 2D color-Doppler echocardiograms of 81 non-ischemic dilated cardiomyopathy (DCM) patients, 51 hypertrophic cardiomyopathy (HCM) patients, and 77 normal volunteers (Control). We applied proper orthogonal decomposition (POD) to build patient-specific and cohort-specific ROMs of LV flow. Each ROM aggregates a low number of components representing a spatially dependent velocity map modulated along the cardiac cycle by a time-dependent coefficient. We tested three classifiers using deliberately simple ML analyses of these ROMs with varying supervision levels. In supervised models, hyperparameter gridsearch was used to derive the ROMs that maximize classification power. The classifiers were blinded to LV chamber geometry and function. We ran vector flow mapping on the color-Doppler sequences to help visualize flow patterns and interpret the ML results. Results POD-based ROMs stably represented each cohort through 10-fold cross-validation. The principal POD mode captured >80% of the flow kinetic energy (KE) in all cohorts and represented the LV filling/emptying jets. Mode 2 represented the diastolic vortex and its KE contribution ranged from <1% (HCM) to 13% (DCM). Semi-unsupervised classification using patient-specific ROMs revealed that the KE ratio of these two principal modes, the vortex-to-jet (V2J) energy ratio, is a simple, interpretable metric that discriminates DCM, HCM, and Control patients. Receiver operating characteristic curves using V2J as classifier had areas under the curve of 0.81, 0.91, and 0.95 for distinguishing HCM vs. Control, DCM vs. Control, and DCM vs. HCM, respectively. Conclusions Modal decomposition of cardiac flow can be used to create ROMs of normal and pathological flow patterns, uncovering simple interpretable flow metrics with power to discriminate disease states, and particularly suitable for further processing using ML. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This study was supported by National Institutes of Health grants R01HL158667 and R01HL160024, and Medtronic. MGB and CN were partially supported by the National Science Foundation via grants NSF-GRFP 201241243 and NSF DGE-2140004. Support from the Comunidad de Madrid Synergy grant: Y2018/BIO-4858 PREFI-CM, the Spanish Research Agency and the European Regional Development Fund grant PID2019-107279RB-I00, and the PACER-1 & BBECHO studies PI21/00274 and ICI20/00011 from Instituto Carlos III de Salud, in Spain, are also acknowledged. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: The Institutional Ethics Committee at Hospital Gregorio Maranon (Madrid, Spain) approved the study, and all participants provided written informed consent. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced in the present study are available upon reasonable request to the authors