Systems and methods for modelling for 2d echocardiography-based prediction of right ventricular volume

Abstract

The disclosed subject matter provides systems and methods for calculating a right ventricular (RV) volume. An example system can include one or more processors configured to receive a testing image, tokenize a categorical input and a numerical input from the testing image, forward the categorical input and the numerical input to a cascaded transformer layer, transform the categorical input and the numerical input into an embedding, transform the embedding into a classification token, and provide a measurement of RV of the testing image based on the CLS token.

Description

[0001]Attorney Docket No. 070050.6849 SYSTEMS AND METHODS FOR MODELLING FOR 2D ECHOCARDIOGRAPHY-BASED PREDICTION OF RIGHT VENTRICULAR VOLUME CROSS-REFERENCE TO RELATED APPLICATION This application claims priority to the United States Provisional Application Serial Nos. 63 / 469,990, filed May 31, 2023, and 63 / 536,549 filed September 5, 2023, the contents of which are hereby incorporated by reference in its entirety. BACKGROUND Assessment of the right ventricular (RV) volume via non-invasive imaging can be the cornerstone of accurate RV size and function evaluation, and in turn the diagnosis and management of numerous cardiovascular diseases. While cardiac magnetic resonance imaging (CMR) can be considered the gold standard method for quantifying RV volumes, it is not widely available. For example, in the UK, there are only 6.1 magnetic resonance imaging scanners per million people, while at the same time, over 1 in 10 people are affected by heart and circulatory diseases alone. As a result, certain hospitals urgently need to deal with a huge backlog of scans for heart conditions, and the number of cardiac patients waiting for CMR imaging studies has been ballooning. Long wait times for imaging can lead to more deaths or other complications, and escalate the pressure on hospitals. In addition, it is costly to replace the aging CMR scanners. Accordingly, there is an unmet need for more accurate and cost-effective measurement of RV volumes. 1 Active 118327893.1 Attorney Docket No. 070050.6849 SUMMARY The disclosed subject matter provides techniques for calculating a right ventricular (RV) volume. An example system includes one or more processors configured to receive a testing image, tokenize a categorical input and a numerical input from the testing image, forward the categorical input and the numerical input to a cascaded transformer layer, transform the categorical input and the numerical input into an embedding, transform the embedding into a classification token and provide a measurement of RV of the testing image based on the classification token. In certain embodiments, the testing image can be an echocardiographic image. In non-limiting embodiments, the echocardiographic image can be a two-dimensional echocardiographic image. In certain embodiments, one or more processors can be configured to receive training data that can include end-diastolic and end-systolic RV volume values. In certain embodiments, the categorical input can include gender information, cardiac phase information, or a combination thereof. In non-limiting embodiments, the numerical input can include end-systole and end-diastole RV volumes in a predetermined view of a two-dimensional echocardiographic image. In non-limiting embodiments, the predetermined view can include a parasternal long axis view, a right ventricular flow view, a parasternal short axis view at a level of an aortic valve, a base view, a mid and apical left ventricular segment view, a four-chamber view, a subcostal view, or combinations thereof. In certain embodiments, the processor can be configured to provide an uncertainty score. In non-limiting embodiments, the uncertainty score is calculated using gradient- boosted regression trees (GBRTs) on two-dimensional echocardiographic image-derived tabular data. In non-limiting embodiments, the GBRTs can be configured to perform an instance-based uncertainty quantification. In non-limiting embodiments, the instance-based 2 Active 118327893.1 Attorney Docket No. 070050.6849 uncertainty quantification can utilize GBRTs to identify the nearest training data to a target instance and use a distribution type to provide the uncertainty score. In non-limiting embodiments, the distribution type can include a normal distribution, a parametric distribution, a non-parametric distribution, a skew-normal distribution, a lognormal distribution, a Laplace distribution, and a student t distribution. A logistic distribution, a Gumbel distribution, a Weibull distribution, a KDR distribution, or combinations thereof. The disclosed subject matter also provides methods for calculating a right ventricular (RV) volume. An example method can include receiving a testing image, tokenizing a categorical input and a numerical input from the testing image, forwarding the categorical input and the numerical input to a cascaded transformer layer, transforming the categorical input and the numerical input into an embedding, transforming the embedding into a classification token and providing a measurement of RV of the testing image based on the classification token. In certain embodiments, the testing image can be a two-dimensional echocardiographic image. In certain embodiments, the method can further include receiving training data that can include end-diastolic and end-systolic RV volume values. In certain embodiments, the categorical input can include gender information, cardiac phase information, or a combination thereof. In non-limiting embodiments, the numerical input can include end-systole and end-diastole RV volumes in a predetermined view of a two-dimensional echocardiographic image. In non-limiting embodiments, the predetermined view can include a parasternal long axis view, a right ventricular flow view, a parasternal short axis view at a level of an aortic valve, a base view, a mid and apical left ventricular segment view, a four-chamber view, a subcostal view, or combinations thereof. 3 Active 118327893.1 Attorney Docket No. 070050.6849 In certain embodiments, the method can include providing an uncertainty score calculated using gradient-boosted regression trees (GBRTs) on two-dimensional echocardiographic image-derived tabular data. In non-limiting embodiments, the GBRTs can be configured to perform an instance-based uncertainty quantification. The instance- based uncertainty quantification can utilize GBRTs to identify the nearest training data to a target instance and use a distribution type to provide the uncertainty score. The disclosed subject matter will be further described below, with reference to example embodiments shown in the drawings. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 provides images showing Instance-Based Uncertainty quantification for gradient-boosted regression trees (IBUG) flow chart in accordance with the disclosed subject matter. Figures 2A-2D provide graphs showing conditional output normal distributions predicted with high (2A and 2D) and low (2A and 2D) accuracy in accordance with the disclosed subject matter. Figures 3A-3D provide graphs showing conditional output logistic distributions predicted with high (3A and 3D) and low (3A and 3D) accuracy in accordance with the disclosed subject matter. Figure 4 provides a graph showing a feature plot for the IBUG model with CatBoost as the base learner in accordance with the disclosed subject matter. Figure 5 provides a diagram showing the disclosed deep learning (DL) model in accordance with the disclosed subject matter. 4 Active 118327893.1 Attorney Docket No. 070050.6849 Figures 6A-6B provide graphs showing (6A) ground truth vs predicted RV volumes and (6B) ground truth vs predicted RVEF values in accordance with the disclosed subject matter. Figure 7 provides a graph showing the feature importance of each 2DE RV view for prediction of RV volumes using machine learning explainability analysis in accordance with the disclosed subject matter. Figure 8 provides a graph showing the accuracy of DL models for prediction of RV volumes when tracings from different 2DE RV views are used as input. It is to be understood that both the foregoing general description and the following detailed description are exemplary and are intended to provide further explanation of the disclosed subject matter. DETAILED DESCRIPTION The disclosed subject matter provides systems and methods for calculating a right ventricular (RV) volume. The disclosed subject matter can provide RV volume measurements using two-dimensional echocardiography with improved accuracy. The disclosed technique also provides the measurements of RV with uncertainty scores that can enhance the clinician application of the disclosed subject matter. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. In case of conflict, the present document, including definitions, will control. Certain methods and materials are described below, although methods and materials similar or equivalent to those described herein can be used in the practice or testing of the presently disclosed subject matter. All publications, patent applications, patents, and other references mentioned herein 5 Active 118327893.1 Attorney Docket No. 070050.6849 are incorporated by reference in their entirety. The materials, methods, and examples disclosed herein are illustrative only and not intended to be limiting. As used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, a reference to “a compound” includes mixtures of compounds. The disclosed subject matter provides systems for calculating a right ventricular volume. An example system can include one or more processors configured to receive a testing image, tokenize a categorical input and a numerical input from the testing image, forward the categorical input and the numerical input to a cascaded transformer layer, transform the categorical input and the numerical input into an embedding, transform the embedding into a classification token and provide a measurement of RV of the testing image based on the classification token. In certain embodiments, the testing image can be an echocardiographic image. The echocardiographic image can be a two-dimensional echocardiographic image (2DE). For example, the right ventricular endocardial-myocardial interface can be imaged and traced in end-systole and end-diastole for the following 8 standardized echocardiographic views: parasternal long axis (PLAX), right ventricular inflow (RV Inflow), parasternal short axis at the level of the aortic valve (PSAX AV), basal (PSAX Base), mid (PSAX mid) and apical left ventricular segments (PSAX Distal), four chamber (Four C) and subcostal views (Sub C). In non-limiting embodiments, the 8 area measurements described above along with the patient age can be the numerical input variables of the disclosed subject matter, whereas the gender and cardiac phase information can serve as the categorical input variables. In non- limiting embodiments, the testing image can include less than 8 RV views, maintaining the accuracy of the RV volume measurement. For example, testing image can include less than 8, less than 7, less than 6, less than 5, or less than 4 RV views. In non-limiting embodiments, 6 Active 118327893.1 Attorney Docket No. 070050.6849 a maximum of three RV views (e.g., parasternal long axis, 4-chamber and parasternal short axis at the base) can be used for the disclosed RV volume measurement. In certain embodiments, the disclosed system can be configured to receive training data. The disclosed processor can be trained on a relatively small-scale dataset (e.g., 50 end-diastolic (ED) and 50 end-systolic (ES) RV volumes (100 in total)). For example, the training data can include planimetered right ventricular endocardial-myocardial echocardiographic areas with the 8 standardized echocardiographic views and the corresponding ED and ES RV volume measured and recorded by a cardiac magnetic resonance imaging system. In non-limiting embodiment, the mean squared error loss function can be used for training. In certain embodiments, the disclosed system can include the transformer architecture to 2DE tabular (both categorical and numerical) data. All categorical and numerical inputs can be tokenized and then forwarded to cascaded Transformer layers. The Feature-Tokenizer module transforms inputs to embeddings denoted by Token (T the input. Token (T) is the input embedding by the Feature Tokenizer. T0 is the output or classification [CLS] token. ^^^^is the ithTransformer layer. TL is the output product of the cascaded Transformers. The embedding for a feature xiis obtained by: where Biis the ithfeature bias, fi(num)is the element-wise multiplication of (numerical features) with vector Wi(num)∈ ℝw, whereas fi(cat)is a lookup table with Wi(cat)∈ ℝ^^ ^^× ^^for xi(cat) (categorical features). The whole process can be described by: 7 Active 118327893.1 Attorney Docket No. 070050.6849 Token( ^^) = stack[ where ^^^^^^is the one-hot vector for the corresponding categorical variable. The embeddings T are transformed into a classification token in Transformer layers. Then the [CLS] token or classification or output token can be appended to T and L Transformer layers F1, ..., FL giving: ^^0= stack The final representation of the [CLS] token (also used for prediction) can be: ^^ ^^ ^^ ^^ ^^ = Linear In certain embodiments, the disclosed system can include the transformer architecture to 2DE tabular (both categorical and numerical) data. All categorical and numerical inputs can be tokenized and then forwarded to cascaded Transformer layers. In certain embodiments, the processor is configured to provide an uncertainty score. In non-limiting embodiments, the uncertainty score can be calculated using gradient- boosted regression trees (GBRTs) on two-dimensional echocardiographic image-derivedtabular data. For example, for the disclosed GBRTs, the training set can be ^^ ∶= ^^ ^^ ∈ ^^ ⊂ ℝ. The disclosed gradient-boosting can be used for machine learning algorithm that constructs a model ^^ ∶ ^^ → ^^ by relying on stagewise additive modeling and minimizing the expected value of some empirical loss function ^^. The model can be obtained through the recursive relationship: ^^0(^^)= ^^, …, ^^^^(^^)= ^^^^−1(^^)+ ^^ ^^^^(^^). In this formulation, ^^0is the base learner, ^^ is an initial approximation, ^^^^is the model at iteration ^^, ^^^^represents the weak learner added during iteration ^^ to boost the model, and ^^ is the learning rate. 8 Active 118327893.1 Attorney Docket No. 070050.6849 In certain embodiments, ^^ can be the mean squared error (MSE), ^^ can be chosen as the average outcome of the training instances (1^^ ∑ ^^ ^^=1^^^^), and regression trees can represent the weak learners. The decision tree at iteration ^^ can be chosen to approximate the residual(or else the negative derivative of the loss function with respect to ŷ ^^ = ^^ ^^−1( ^^ ^^)), ^^ ^^ =2arg , where − ^^ ^^, ^^ = ^^ ^^( ^^ ^^+ŷ ^^)^^ŷ ^^ is the functional gradient of the^^-th training instance at iteration ^^. The decision tree at iteration ^^ recursively creates ^^^^disjoint regions { through partitioning the instance space. Each of these regions can be termed a leaf. The parameter value ^^^^^^for leaf ^^ at tree ^^ is determined (given a fixed structure) through a one-step Newton method: ^^ ^^ ^^= − where ^^^^^^= {(^^^^, ^^^^)| ^^^^∈ ^^^^^^}^^^^=1is the instance set of leaf ^^ for tree ^^, ℎ^^^^is the second derivative of the ^^-th training instance with respect to ŷ^^, and ⋋ acts as a regularization parameter. Hence, ^^^^can be denoted as: ^^^^( ^^) = 1 [ ^^ ∈ ^^^^^^] where 1 is the indicator function. To generate a prediction for a target sample ^^^^ ^^, the final GBRT model sums up the values of the leaves traversed by ^^^^ ^^over all ^^ iterations: ŷ^^ ^^=∑ ^^^^=1^^^^(^^^^ ^^). In certain embodiments, the GBRTs can be configured to perform an instance-based uncertainty quantification. The instance-based uncertainty quantification can utilize GBRTs to identify the nearest training data to a target instance and use a distribution type to provide the uncertainty score. For example, the disclosed subject matter can estimate the conditional probability distribution ^^(^^|^^)for some target variable ^^ given some input vector ^^. To allow probabilistic predictions for any GBRT point predictor, the disclosed system can use the instance-based learning and a supervised tree kernel, namely the Instance-Based Uncertainty quantification for GBRTs (IBUG) technique. In non-limiting 9 Active 118327893.1 Attorney Docket No. 070050.6849 embodiments, the IBUG technique can capitalize on the fact that GBRTs yield accurate point predictions and uses this scalar output to model the conditional mean in a probabilistic forecast. To further model the conditional output distribution, the disclosed IBUG can further use a supervised tree kernel to more effectively identify the ^^ training examples with the largest affinity to the target example. In particular, the affinity of the ^^-th training example to a target example ^^^^ ^^can be given by: where is the leaf (of the tree ^^) to which ^^^^is assigned. Such a metric uses the structure of the learned trees in the ensemble. The disclosed system can employ the set of those ^^ affinity scores, ^^( ^^), to produce a probabilistic prediction. In certain embodiments, the disclosed IBUG can provide numerous choices for modeling the conditional output distribution. For example, the distribution type can include a normal distribution, a parametric distribution, a non-parametric distribution, a skewnormal distribution, a lognormal distribution, a Laplace distribution, a student t distribution. a logistic distribution, a Gumbel distribution, a Weibull distribution, a KDR distribution, or combinations thereof. The disclosed subject matter also provides a method for calculating the RV volume using the disclosed operating system and processor. An example method can include receiving a testing image, tokenizing a categorical input and a numerical input from the testing image, forwarding the categorical input and the numerical input to a cascaded transformer layer, transforming the categorical input and the numerical input into an embedding, transforming the embedding into a classification token and providing a measurement of RV of the testing image based on the CLS token. In non-limiting 10 Active 118327893.1 Attorney Docket No. 070050.6849 embodiments, the testing image can be at least one two-dimensional echocardiographic image. In certain embodiments, the method can further include receiving training data. For example, the training data can include planimetered right ventricular endocardial- myocardial echocardiographic areas with the 8 standardized echocardiographic views (e.g., parasternal long axis (PLAX), right ventricular inflow (RV Inflow), parasternal short axis at the level of the aortic valve (PSAX AV), basal (PSAX Base), mid (PSAX mid) and apical left ventricular segments (PSAX Distal), four chamber (Four C) and subcostal views (Sub C) and the corresponding ED and ES RV volume measured and recorded by a cardiac magnetic resonance imaging system. In non-limiting embodiment, the mean squared error loss function can be used for training. In certain embodiments, the categorical input can include gender information, cardiac phase information, or a combination thereof. In non-limiting embodiments, the numerical input can include end-systole and end-diastole RV areas in a predetermined view (e.g., 8 standardized echocardiographic views) of a two-dimensional echocardiographic image. In certain embodiments, the method can further include providing an uncertainty score calculated using gradient-boosted regression trees (GBRTs) on two-dimensional echocardiographic image-derived tabular data. In non-limiting embodiments, the GBRTs can be configured to perform an instance-based uncertainty quantification that can utilize GBRTs to identify the nearest training data to a target instance and use a distribution type to provide the uncertainty score. Example 1: Harnessing a Supervised Tree Kernel to Empower Ensemble Modelling for 2D Echocardiography-Based Prediction of Right Ventricular Volume 11 Active 118327893.1 Attorney Docket No. 070050.6849 The right ventricular (RV) function deterioration can predict clinical outcomes in numerous circumstances. The disclosed subject matter complements the volume predictions with uncertainty scores. The disclosed subject matter can employ an instance-based method which uses the learned tree structure to identify the nearest training samples to a target instance and then uses a number of distribution types to more flexibly model the output. The probabilistic and point-prediction performances of the proposed framework can be evaluated on a relatively small-scale dataset comprising 100 end-diastolic and end-systolic RV volumes. The reference values for point performance can be obtained from MRI. The results demonstrate that our flexible approach yields improved probabilistic and point performances over currently available techniques. The appropriateness of the proposed framework is showcased by providing exemplar cases. The estimated uncertainty embodies both aleatoric and epistemic types. This work can align with trustworthy artificial intelligence since it can be used to enhance the decision-making process and reduce risks. The feature importance scores of the disclosed framework can be exploited to reduce the number of required 2DE views, which could enhance the proposed pipeline’s clinical application. The disclosed subject matter can provide an uncertainty quantification framework when predicting RV volumes through the use of ensemble models, Gradient-Boosted Regression Trees (GBRTs), on 2DE-derived tabular data. GBRTs can be used for tabular data. To get an estimate of the prediction uncertainty, the disclosed subject matter uses a k- nearest neighbor that relies on a supervised tree kernel. Unlike other techniques (e.g., SOTA gradient-boosted algorithms) that provide probabilistic predictions, the disclosed subject matter can perform well on both probabilistic and point performances and can also use a number of distribution types to more flexibly model the output. 12 Active 118327893.1 Attorney Docket No. 070050.6849 The probabilistic and point-prediction performances of the disclosed framework were evaluated on a relatively small-scale dataset, comprising 100 end-diastolic (ED) and end-systolic (ES) RV volumes. The reference values for point performance were obtained from cardiovascular MRI (CMR). The disclosed subject matter was also compared to other SOTA techniques. Here, conditional output distributions and the respective confidence intervals for a couple of high and low accuracy (test set) predictions were also evaluated. Dataset: the test population was a retrospective cohort of 50 adult patients for which 2DE and CMR were acquired. For each patient the RV endocardial-myocardial interface was manually traced in end-systole and end-diastole (making a total of 100 data points) for the following eight standardized echocardiographic views: parasternal long axis (PLAX), right ventricular inflow (RV Inflow), parasternal short axis at the level of the aortic valve (PSAX AV), basal (PSAX Base), mid (PSAX mid) and apical left ventricular segments (PSAX Distal), four-chamber (Four C) and subcostal (Sub C) views. The eight area measurements along with the patient age were the numerical input variables of our model, whereas the gender and cardiac phase information were the categorical ones. The short-axis cine CMR-derived ED and ES RV volumes were recorded in a semi-automated way and served as the reference values. Gradient-Boosted Regression Trees: assume ^^ is the training set where ^^^^= ∈ ^^ ⊂ ℝ. Gradient-boosting can be a powerful machine learning algorithm that constructs a model ^^ ∶ ^^ → ^^ by relying on stage-wise additive modelling and minimizing the expected value of some empirical loss function ^^. The model is obtained through the recursive relationship: ^^0( ^^) = ^^, …, ^^^^( ^^) = ^^^^−1( ^^) + ^^ ^^^^( ^^). In this formulation, ^^0is the base learner, ^^ is an initial approximation, ^^^^is the model at iteration ^^, ^^^^represents the weak learner added during iteration ^^ to boost the model, and ^^ is the learning rate. 13 Active 118327893.1 Attorney Docket No. 070050.6849 In the case of GBRTs, the most frequently employed ^^ is the mean squared error (MSE), ^^ is chosen as the average outcome of the training instances (1^^ ∑ ^^ ^^=1^^^^), and regression trees represent the weak learners. The decision tree at iteration ^^ is chosen to approximate the residual (or else the negative derivative of the loss function with respect to the functional gradient of the ^^-th training instance at iteration ^^. The decision tree at iteration ^^ recursively creates ^^^^disjoint regions through partitioning the instance space. Each of these regions is termed a leaf. The parameter value ^^^^^^for leaf ^^ at tree ^^ is commonly determined (given a fixed structure) through a one-step Newton method: ^^^^^^= − is the instance set of leaf ^^ for tree ^^, ℎ^^^^is the second derivative of the ^^-th training instance with respect to ŷ^^, and ⋋ acts as aregularization parameter. Hence, ^^ can be deno ( ) ^^^^ ted as: ^^ ^^ ^^ 1 [ ^^ ∈ ^^ ^^ ] where1 is the indicator function. To generate a prediction for a target sample ^^ ^^ ^^, the final GBRTmodel sums up the values of the leaves traversed by ^^^^ ^^over all ^^ iterations: ŷ^^ ^^= Instance-based Uncertainty Quantification: instance-based uncertainty quantification was used to estimate the conditional probability distribution ^^(^^|^^)for some target variable ^^ given some input vector ^^. To allow probabilistic predictions for any GBRT point predictor, instance-based uncertainty quantification that adopts instance-based learning and a supervised tree kernel, namely the Instance-Based Uncertainty quantification for GBRTs (IBUG) was used. To start with, the method capitalizes on the fact that GBRTs yield accurate point predictions and uses this scalar 14 Active 118327893.1 Attorney Docket No. 070050.6849 output to model the conditional mean in a probabilistic forecast. Next, to further model the conditional output distribution, IBUG uses a supervised tree kernel to more effectively identify the ^^ training examples with the largest affinity to the target example. In particular, the affinity of the ^^-th training example ^^^^to a target example ^^^^ ^^is given by Equation (7), where ^^^^(^^^^)is the leaf (of the tree ^^) to which ^^^^is assigned. Such a metric uses the structure of the learned trees in the ensemble. The method employs the set of those ^^ affinity scores, ^^( ^^), to produce a probabilistic prediction. For a target instance, as shown in Figure 1, IBUG 100 collects the training instances 101 at each leaf 102 it traverses, keeps the ^^ most frequent samples 103, and then use those instances to model the output distribution 104. Unlike certain other SOTA methods, IBUG offers numerous choices for modeling the conditional output distribution; the simplest way is, of course, through normal distribution. In this case, the scalar output of the GBRT model is used to approximate the conditional mean and then the set is manipulated to compute the variance . To further improve or optimize the calculation of the prediction variance, the following calibration can be applied: where ^^ and ^^ are tuned on the validation set after the choice of ^^ has been made. The method acts as a wrapper around any GBRT model allowing one to try various GBRT point predictors and then select the model with the best performance. To provide more flexibly to model the output distribution using any parametric or non-parametric distribution, IBUG can use the set ^^( ^^)to directly fit (using maximum likelihood estimation) any continuous distribution ^^, including those with high-order moments: 15 Active 118327893.1 Attorney Docket No. 070050.6849 Choosing an appropriate value for ^^ is critical for producing accurate probabilistic predictions. The tuning of ^^ was performed in a held-out validation dataset ^^^^ ^^ ^^⊂ ^^ using the negative log likelihood (NLL) probabilistic scoring metric. To accelerate the tuning process, through avoiding the repetition of the computationally expensive affinity calculations, the procedure, where parameter ^^ was used to model instances of abnormally low variance, was used. Implementation: assessments were conducted utilizing an Intel Core i9 CPU 10900K Comet Lake, 10 Cores, 20 Threads @ 5.3GHz system equipped with 128GB of DDR4 RAM operating @ 2.6GHz. IBUG was applied to XGBoost, LightGBM, and CatBoost. K was tuned using values: [3, 5, 7, 9, 11, 15, 31, 61, 91, 121, 151, 201, 301, 401, 501, 601, 701]. The parameters ^^ and ^^ were tuned using values ranging from 1 × 10−8to 1 × 103with additional multipliers [1.0, 2.5, 5.0]. The number of trees, ^^, was tuned using values [10, 25, 50, 100, 250, 500, 1000, 2000] (early stopping was used for NGBoost). The learning rate was tuned using values [0.01, 0.1]. The followings were optimized: maximum number of leaves ℎ using values [15, 31, 61, 91], the minimum number of leaves using values [1, 20], and the maximum depth ^^ using values [2, 3, 5, 7, −1] (indicating no limit). The ^^ parameter was adjusted based on the minimum variance obtained from the validation set predictions. 5-fold cross-validation was used to generate 5 different 80 / 20 train / test folds. For each fold, the 80% training set was randomly divided into a 60 / 20 train / validation set for hyperparameter tuning. Upon tuning the hyperparameters, the model was retrained using the complete 80% training set. To test IBUG’s flexibility in posterior modelling, each probabilistic prediction was modeled using the following distributions: normal, skew normal, lognormal, Laplace, student t, logistic, Gumbel, Weibull, and KDE. Evaluation Metrics: To evaluate probabilistic performance, the continuous ranking probability score (CRPS), NLL, check score, and interval score were used. For all metrics, 16 Active 118327893.1 Attorney Docket No. 070050.6849 the lower the better. To gauge point performance, the root mean squired error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE), the R2measure, and correlation were used. IBUG was compared to three recent gradient boosting algorithms that provide probabilistic predictions, namely NGBoost, PGBM, and CatBoost with uncertainty (CBU). Exemplars: To facilitate a comprehensive understanding of our results, conditional output distributions and the respective confidence intervals (CIs) for two high and two low accuracy (test set) predictions were provided. Explainability: A benefit of using GBRTs is that it is straight-forward to retrieve feature importance scores that indicate how valuable each attribute was in the construction of the model. Feature importance scores were calculated for all models using the ‘Gain’ metric which quantifies the relative contributions. The final set of hyperparameters for each method and the corresponding tuning and training times are listed in Table 1. Table 2 compares the probabilistic performance of the IBUG model against the three SOTA probabilistic prediction methods. IBUG model with CatBoost as the base learner provided the lowest average scores in all CRPS, NLL, Check Score and Interval Score indices. In Table 3, the point performance of all methods is provided. In overall, IBUG method with CatBoost base learner displayed the best performance once again. Table 4 shows the importance of variance calibration in the probabilistic performance of IBUG. Table 5 demonstrates that the logistic (parametric) distribution better fits the underlying data than assuming normality. Fig 2 and Fig 3 show the conditional output distributions for four representative test cases (two that were predicted with high accuracy and two that were predicted with low accuracy), when normal and logistic probabilistic density functions were used for modelling, respectively. Figure 2 shows the conditional output normal distributions for test instances that were predicted with high [(2a) and (2b)] and low [(2c) and (2d)] 17 Active 118327893.1 Attorney Docket No. 070050.6849 accuracy. Figure 3 shows the conditional output logistic distributions for test instances that were predicted with high [(3a) and (3b)] and low [(3c) and (3d)] accuracy (low and high absolute percent error, respectively). Table 6 lists the 95% and 99% confidence intervals for the above cases. These results showcase the appropriateness of the proposed framework for providing uncertainty scores for RV volume predictions. Figure 4 shows the “Gain” feature importance score for all eleven features in the best IBUG model. The parasternal long axis (PLAX), four chambers (Four C) and parasternal short axis at base level (PSAX Base) standard views were the top three contributors to the model predictions. Parameter CatBoost XGBoost LightGBM NGBoost PGBM CBU K 5 15 3 - - - δ 1 0.5 0.5 5 10 1 Operation add mult mult add add add min scale 6.164 13.826 2.055 - - - n estimators (trees) 100 25 25 244 250 250 maximum depth 5 2 -1 - - - learning rate 0.1 0.1 0.1 0.01 0.01 0.1 minimum data in_leafv 1 - - - 20 1 minimum child weight - 20 20 - - - number of leaves - - 15 - 15 15 max bin 255 255 255 255 255 255 tune+train time (s) 67.369 19.932 14.260 5.370 872.663 81.929 Table 1: The final set of hyperparameters used for each method. Also shown are the tuning and training times. IBUG was applied to CatBoost, XGBoost, and LightGBM. Method NLL CRPS Check Score Interval Score IBUG 4.747 15.398 7.775 73.380 NGBoost 7.571 22.174 11.177 141.618 PGBM 6.136 20.796 10.492 122.401 CBU 5.780 19.524 9.853 110.140 Table 2: Probabilistic performance comparison on the test set (five folds). IBUG results are for the case when CatBoost was the base learner. IBUG results have been averaged over all nine posterior output distributions. Method MAE RMSE MAPE R2Correlation IBUG 22.75 26.292 20.22 0.666 0.824 NGBoost 28.114 32.269 24.406 0.496 0.736 18 Active 118327893.1 Attorney Docket No. 070050.6849 PGBM 27.479 31.27 25.147 0.527 0.768 CBU 26.378 30.127 22.974 0.561 0.772 Table 3: Point performance comparison on the test set (five folds). IBUG results are for the case when CatBoost was the base learner. Operation NLL CRPS Check Score Interval Score With Calibration 4.747 15.398 7.775 73.38 Without Calibration 4.781 15.457 7.805 74.044 Table 4: Probabilistic performance comparison of IBUG method with and without variance calibration. IBUG results are for the case when CatBoost was the base learner. Distribution NLL Normal 5.10466 Logistic 5.00837 Table 5: Probabilistic performance comparison when assuming normal and logistic distributions for modelling the underlying data. Prediction APE (%) Point Normal Distribution Logistic Distribution Accuracy Prediction 95% CI 99% CI 95% CI 99% CI High 3.090 103.090 35.979 47.286 30.196 42.697 0.508 87.553 46.739 61.428 39.227 55.466 Low 10.169 163.492 91.932 120.825 77.157 109.099 10.119 61.119 83.650 109.939 70.206 99.270 Table 6: The 95% and 99% Confidence Intervals for both Normal and Logistic distributions for four representative test set cases, two that were predicted with high accuracy (low APE) and two that were predicted with low accuracy (high APE). Explainability: A benefit of using GBRTs is that it is straight-forward to retrieve feature importance scores that indicate how valuable each attribute was in the construction of the model. Feature importance scores were calculated for all models using the ‘Gain’ metric which quantifies the relative contributions. In this paper, the disclosed subject matter provides an uncertainty quantification framework when predicting RV volumes through the use of GBRTs on 2DE tabular data (such as area measurements, age, gender and cardiac phase information). To get an estimate 19 Active 118327893.1 Attorney Docket No. 070050.6849 of the prediction uncertainty, the IBUG, which uses the learned tree structure to identify the ^^ nearest training samples to a target instance, was used. The results on a small-scale dataset demonstrate that this simple wrapper yields improved probabilistic and point performances over other SOTA methods. The appropriateness of the proposed framework for providing uncertainty scores for RV volume predictions was showcased by providing conditional output distributions and confidence intervals for four exemplar cases. The estimated uncertainty embodies both aleatoric and epistemic types of uncertainty since IBUG is an instance-based approach and also predictions on the training set were used to tune ^^, ^^, and ^^. Overfitting was observed in IBUG’s point performance, which is a typical finding when the size of the dataset is small. This work aligns with trustworthy artificial intelligence since it can be used to enhance the decision-making process and reduce risks. It could help overcome mistrust which is a major barrier to the deployment of machine learning systems in the clinical setting. The calculated feature importance scores can be used to reduce the number of required 2DE views, which in turn can enhance the proposed pipeline’s clinical application. Example 2: Right Ventricular Volume Prediction by Feature Tokenizer Transformer- based Regression of 2D Echocardiography Small-Scale Tabular Data The disclosed subject matter provides a deep learning (DL) pipeline for accurately predicting RV volumes by relying on conventional 2D morphological (area) measurements from eight standardized 2DE views and also on gender, cardiac phase, and age information. One of the main components of the disclosed pipeline is a tabular feature tokenizer Transformer. The disclosed pipeline is trained and tested on a relatively small-scale dataset, comprising 50 end-diastolic (ED) and 50 end-systolic (ES) RV volumes (100 in total). The RV volumes, predicted by the disclosed subject matter, were compared to reference values 20 Active 118327893.1 Attorney Docket No. 070050.6849 obtained from CMR. The disclosed subject matter was also compared to other techniques (e.g., SOTA) for tabular data-based regression. The testing population was a retrospective cohort of 50 adult patients for which 2DE and CMR were obtained within 30 days from each other as part of routine cardiac care. Patients with prior cardiac surgery of the right ventricle, tricuspid or pulmonic valve repair or replacement, cyanotic congenital heart disease, L-transposition of the great arteries, more than small pericardial effusion, cardiac tamponade, atrial fibrillation at the time of either assessment, severe RV dysfunction or inadequate imaging quality were excluded. 2D Ultrasound & CMR Acquisition: Echocardiographic images were obtained using 4 types of Philips Ultrasound systems, namely iE33 x-Matrix, Epic CVx, Epic 7C and Affiniti 70C. Images were obtained by experienced sonographers and according to the standard institutional scanning protocol of the Columbia University Irving Medical Center Adult Echocardiography Laboratory. CMR images were obtained by 1.5T or 3T GE HealthCare scanners, namely 3T-Signa Premier, 1.5T Discovery (750 W / 450 W) and 1.5T Twin HDxT. Standard cine images were obtained for the quantitative evaluation of the right ventricle. Data Annotation & Data set: The right ventricular endocardial-myocardial interface was manually traced in end-systole and end-diastole by a single cardiologist with expertise in cardiovascular ultrasound for the following 8 standardized echocardiographic views: parasternal long axis (PLAX), right ventricular inflow (RV Inflow), parasternal short axis at the level of the aortic valve (PSAX AV), basal (PSAX Base), mid (PSAX mid) and apical left ventricular segments (PSAX Distal), four chamber (Four C) and subcostal views (Sub C). The cardiologist was blinded to the CMR results. Short-axis stack cine CMR was used to calculate ED and ES volumes in a semi-automated way. This analysis was performed by experienced cardiac radiologists. Echocardiographic annotations were performed using the 21 Active 118327893.1 Attorney Docket No. 070050.6849 Siemens Syngo Workstation software, whereas CMR RV volumes were derived using the Circle Cardiovascular Imaging cvi42 software. The 8 area measurements described above along with the patient age were the numerical input variables of our model, whereas the gender and cardiac phase information served as the categorical input variables. For each patient, the CMR-derived ED and ES RV volumes were recorded, making a total of 100 data points. Neural Network Architecture: the disclosed subject matter includes the Transformer architecture to 2DE tabular (both categorical and numerical) data. Figure 5 portrays the inner workings of an example pipeline 500. In essence, all categorical and numerical inputs are tokenized and then forwarded to cascaded Transformer layers. Xfeature501 is the input. Token (T) 502 is the input embedding by the Feature Tokenizer 503. T0504 is the [CLS] appended embedded token, where [CLS] is a special symbol added in front of every input example. ^^^^505 is the ithTransformer layer. TL 506 is the output product of the cascaded Transformers. The Feature-Tokenizer module transforms inputs to embeddings denoted by Token (T ∈ The embedding for a feature xi is obtained by Equation (1), where Bi is the ithfeature bias, fi(num) is the element-wise multiplication of xi(num) (numerical features) with vector Wi(num) ∈ ℝw, whereas fi(cat) is a lookup table with Wi(cat) ∈ ℝ^^ ^^× ^^for xi(cat) (categorical features). The whole process is described by Equations (2), (3), and (4), where ^^^^^^is the one-hot vector for the corresponding categorical variable. The embeddings T are transformed into a classification token in Transformer layers. Then the [CLS] token is appended to T and L Transformer layers F1, ..., FL giving Equation (5). The PreNorm variant was used for easier optimization. In addition, the first normalization from the first Transformer was discarded to achieve a good performance. The 22 Active 118327893.1 Attorney Docket No. 070050.6849 final representation of the [CLS] token (also used for prediction) is described in Equation (6) Implementation and Training: The data set was randomly split into training (70 data points), validation (10 data points) and testing (20 data points) sets. Each of the above sets involved equal numbers of ED and ES volumes, corresponding to the same patients. The mean squared error loss function was used for training. 500 epochs were used to train with batch size=1. The final hyperparameters are mentioned in Table 7. The hyperparameters were chosen by using the random search method. Parameter The disclosed pipeline Recommended #Layers 3 6 Feature embedding size 16 512 Residual Dropout 0.3 0.2 Attention Dropout 0.3 0.5 FFN Dropout 0.3 0.5 FFN Factor 4 / 3 4 / 3 Learning Rate 0.01 LogUniform[3e-5,3e-4] Weight Decay 0 LogUniform[3e-6,3e-3] Optimizer Adamax AdamW Table 7. The final hyperparameter values used. Model Evaluation: The disclosed subject matter was compared to other SOTA methods for tabular data, both shallow tree-based ensemble models (such as XGBoost and CatBoost) and attention-based deep architectures (such as the Tab-Transformer). All SOTA techniques were implemented according to the recommended values. To evaluate the predicted ES and ED volumes predicted by each method relative to the reference (CMR), the R2coefficient and the absolute percentage error (APE) were employed. Apart from volume prediction, the four methods are also compared in terms of right ventricular ejection fraction (RVEF) values, which is a clinical metric used to describe the percentage of blood leaving the right ventricle each time it contracts. Finally, all predicted volumes and calculated EF values are plotted against the reference (CMR) values for all four methods. 23 Active 118327893.1 Attorney Docket No. 070050.6849 Table 8 details the R2and APE values for predicting RV ED and ES volumes. Also given are the p-values obtained from the Wilcoxon signed-rank test. The disclosed subject matter method achieved a higher R2 score and a lower APE when compared to the SOTA methods. All the p-values are less than 0.05. The cross-validation set performance is comparable to the test set performance. Table 9 lists the APE in RVEF, which was derived from the predicted volumes. The proposed method retains the best performance among all the methods. Figure 6 displays the predictions for RV volumes (a) and RVEF values (b) for the proposed and SOTA methods, versus the ground truth. According to those plots, our predictions are closer to the CMR reference values than the other SOTA methods. Method R2Score APE (%) p-value mean (±SD) Proposed 0.975 5.46 (±4.87) — TabTransformer 0.784 21.05 (±16.74) 2.1 ×10−5CatBoost 0.797 15.13 (±10.81) 6.3 ×10−6XGBoost 0.600 15.90 (±18.62) 7.3 ×10−6Table 8. Quantitative comparison of the predicted RV volumes between the proposed and SOTA methods. APE stands for absolute percentage error. SD is the standard deviation. The p-values were obtained from the Wilcoxon signed-rank test (α = 0.05). Method APE in EF (%) p-value mean (±SD) Proposed 5.80 (± 3.91) - TabTransformer 11.29 (± 6.11) 0.004 CatBoost 13.48 (± 5.31) 0.048 XGBoost 21.93 (± 20.63) 0.013 Table 9. Quantitative comparison of the RVEF between the proposed and SOTA methods. All abbreviations are the same as in Table 8. The disclosed subject matter can solve the problem of quantifying RV ED and ES volumes by using attention-based models on tabular 2DE data. Morphological measurements (areas) from 8 standardized 2DE views were used as input to the model along with age, cardiac phase, and gender information. The disclosed subject matter achieved 24 Active 118327893.1 Attorney Docket No. 070050.6849 improved performance (R2=0.975) on a relatively small-scale dataset, while it outperformed other SOTA techniques methods. This result questions the superiority of tree-based ensemble models over DL-based solutions for tabular data in the context of functional imaging of the heart. The disclosed architecture includes a feature tokenizer module to transform all features (both categorical and numerical) to embeddings, before applying a stack of Transformer layers. Transformers can be the key modules in most SOTA architectures for natural language processing and computer vision. However, their performance on tabular data-based evaluation of the cardiac function had not been explored. The disclosed subject matter can be also appealing as it can allow building multi-modal pipelines for cardiovascular imaging problems, where only one part of the data is tabular, and other parts include images and text data. The disclosed techniques can be combined with DL approaches for RV segmentation and ES / ED frame detection towards developing a fully- automated end-to-end pipeline for RVEF estimation. Example 3: Attention-based deep learning for right ventricular quantification using 2D echocardiographic areas Quantitative evaluation of right ventricular (RV) volumes is of paramount importance to accurately distinguish normal from abnormal RVs and also grade the degree of RV dilatation and dysfunction. Cardiovascular magnetic resonance imaging (CMR) can be considered as a gold standard for RV volume measurement. However, CMR is costly and not widely available across all clinical settings. On the other hand, two-dimensional transthoracic echocardiography (2DE) allows for widely available, lost cost and bedside evaluation of the RV, but cannot reliably quantify RV volumes due to the complex RV shape which cannot be accurately approached geometrically by 2DE projections. 25 Active 118327893.1 Attorney Docket No. 070050.6849 The disclosed subject matter provides a non-geometric, attention-based deep learning (DL) method of RV volume quantification that can provide similar accuracy of CMR using areas derived from planimetry of 2DE views. 2DE images from 50 adult patients (age 47±18, 42% women) who had CMR performed within 1 month of 2DE for standard care were analyzed. Patients with prior cardiac surgery of the right ventricle, tricuspid or pulmonic valve repair or replacement, complex congenital heart disease, more than small pericardial effusion, cardiac tamponade, atrial fibrillation at the time of either study, severe RV dysfunction or inadequate imaging quality, were excluded. RV endocardial planimetry was performed in end-diastole (ED) and end-systole (ES) for 8 standardized views (parasternal long axis, inflow, parasternal short axis at the level of the aortic valve, base, mid and apical left ventricular segments, four chamber and subcostal) and areas were calculated. The DL model includes a feature tokenizer module and a stack of transformer layers with areas, age and gender as inputs and RV volume as output (ED or ES). The data set was randomly split into training, validation and testing subsets (35, 5 and 10 patients respectively). Mean RVEDV, RVESV and RV ejection fraction (EF) in the entire cohort were 163±70ml, 82±42ml and 51±8% respectively without differences among subsets. The disclosed system pipeline achieved improved prediction of RV volumes (R2=0.975, absolute percentage error [APE]=5.46±4.87%) and RVEF (APE=5.80± 3.91%). The method performed better for RVESV compared to RVEDV. Based on the explainability results (feature importance scores), further analysis using the feature tokenizer transformer on a smaller number of views and testing various combinations was conducted. For each 2DE view combination, the 100 volumes were shuffled and split into five non-overlapping sets of 20 volumes. Then, the disclosed model was trained using one of those five sets as the testing set, and the remaining four sets 26 Active 118327893.1 Attorney Docket No. 070050.6849 as the training set. This was repeated five times, using a different testing set every time. Table 10 shows the results on the testing set, averaged across the five folds. Table 10. Results of different combinations of views. The orange combination uses 3 views to predict RV volumes, i.e. Four chamber, Parasternal long axis and parasternal short axis at the base. Given the variability of RV shape in pathologic states, this combination can be used for clinical application as it can sustain its predictive accuracy in different RVs. Example 4: A novel deep learning method for assessment of right ventricular volume using three 2D- echocardiographic views Calculation of RV end-diastolic and end-systolic volumes (RVEDV and RVESV respectively) as well as ejection fraction (RVEF) using 2DE is challenging due to the complex RV shape and incomplete penetration of ultrasound beams. The disclosed subject matter provides systems and techniques for calculating RVEDV and RVESV with the reduce the number of required RV views to a maximum of 3 while maintaining improved accuracy in order to develop a new, clinically applicable method that can allow for 2DE quantification of the RV, similar to the Simpson’s rule for the left ventricle. Patient cohort and imaging analysis: a cohort of 50 adult patients who underwent 2DE and CMR within 30 days as part of routine cardiac care was utilized. In all cases, both 27 Active 118327893.1 Attorney Docket No. 070050.6849 CMR and 2DE were performed as part of an initial diagnostic evaluation. Patients with prior cardiac surgery of the RV, complex congenital heart disease, more than small pericardial effusion, atrial fibrillation at the time of either study, severe RV dysfunction or inadequate imaging quality were excluded. Imaging acquisition and preprocessing: 2DE was performed with a minimum of 22 anatomic views using commercially available equipment (Philips Epic 7C, CVx and i33 ultrasound systems). The RV endocardial-myocardial interface was traced in end-systole (ES) and end-diastole (ED) by a single cardiologist with expertise in echocardiography. This process of planimetry was performed for 8 standardized RV views using commercially available software (Syngo Dynamics, Siemens): parasternal long axis (PLAX), RV-Inflow, parasternal short axis at the level of the aortic valve (PSAX-AV), base (PSAX-base), mid (PSAX-mid) and apex of the left ventricle (PSAX-distal), standard four-chamber (Four-C) and subcostal four chamber (Sub-C). If the Four-C had poor image quality, a focused RV view was used. An area was automatically calculated for each ED and ES tracing by the software. Two additional sets of measurements were performed for a random subset of 10 patients to allow for intra- and interobserver variability assessment. CMR acquisition was obtained using commercially available equipment (Signa 1.5 Tesla MRI scanner, General Electric, Milwaukee, WI). Short-axis cine images were acquired using a steady-state free precession pulse sequence with the following typical parameters: TR 3.0 ms, TE 1.0 ms, flip angle of 60°, 16 views per segment, field of view 35 x 35 mm, acquisition matrix 256 x 256, slice thickness 8 mm with no gap, and receiver bandwidth 125 kHz. Analysis was performed using commercially available software (cvi42 v5.11, Circle Cardiovascular Imaging, Calgary) by cardiovascular radiologists that were blinded to the 2DE results. Cine loops were used to select images in ED and ES. Four chamber cine images were used as a reference to help define the atrioventricular valves and 28 Active 118327893.1 Attorney Docket No. 070050.6849 apical planes. Endocardial-myocardial segmentation was performed by manual tracing of each ED and ES short-axis view and used to calculate RVEDV, RVESV and RVEF. Gender specific CMR cutoffs was applied for RV dilatation and dysfunction. Variability of 2DE measurements: intraclass correlation coefficients (ICC) was used to evaluate the intra- and inter-observer reliability of 2DE tracings using a 2-way fixed and a 2-way random effects model respectively. An absolute agreement criterion was applied in both cases. ICC values of less than 0.5 indicated poor reliability, whereas values between 0.5-0.75, 0.75-0.9 and above 0.9 indicated moderate, good and excellent reliability, respectively. Machine learning model explainability analysis: the relative importance of each one of the eight 2DE RV views-features for the prediction of RV volumes was assessed using gain metric-powered explainability analysis. Gradient-Boosted Regression Trees (GBRTs) was first used as ensemble models to predict RV volumes from the areas of the 8 standardized RV views. Following that, the Instance-Based Uncertainty quantification method for GBRTs (IBUG) was used to calculate the relative feature importance (RFI) of each view-feature to the RV volume. DL algorithm implementation: the disclosed Feature-Tokenizer & Transformer (FTT) is a DL algorithm for tabular data where all categorical and numerical inputs (features) are tokenized and then forwarded to cascaded Transformer layers (Figure 5). Utilizing this DL architecture, ED and ES areas derived from RV planimetry along with patient age, gender and cardiac phase are used to predict the corresponding, CMR-derived, RVEDV or RVESV, and subsequently calculate RVEF. 5-fold cross-validation was used for training and evaluation of the FTT models. 40 and 10 randomly selected patents comprised the training and testing subcohorts in each fold. For each fold, 8 patients of the training subset (20%) were randomly selected to tune the DL hyperparameters. Once the 29 Active 118327893.1 Attorney Docket No. 070050.6849 hyperparameters were optimized, the model was retrained using the entire training set. The testing performance of the DL pipeline averaged over the 5 folds. Python was the programming language used for the implementation of the DL algorithm. DL evaluation and sensitivity analysis: for evaluation of each DL model, predicted RV volumes and RVEF against CMR-derived volumes and RVEF were compared by using the R2coefficient and the absolute percentage error (APE). The process of training and evaluation was performed for different combinations of the available 8 RV views according to the results of the machine learning model explainability analysis. A combination with a maximum of 3 RV views that maintains a high diagnostic accuracy was identified. The limit of 3 RV views was chosen in order to allow for clinical applicability of the method. Sensitivity analysis was performed for combinations using 2-4 views. Statistical analysis: continuous variables are presented as mean ± standard deviation or median with interquartile range, whereas categorical variables as absolute count and frequency. DL models with different numbers of RV views were compared in regard to RV volumes using the Wilcoxon signed-rank test. All tests were two-sided and p<0.05 was considered as statistically significant. STATA 17.0 BE (StataCorp LLC, Texas USA) was used for statistical analyses. Baseline characteristics: clinical and baseline imaging characteristics of the cohort are summarized in Table 11. Median age was 51 (interquartile range 32-62) and 42% were women. Nineteen patients (40%) had symptoms of heart failure. In terms of underlying cardiac disease, 11 patients (22%) had coronary artery disease, 7 (14%) hypertrophic cardiomyopathy and 6 (12%) simple congenital defects. Ten (20%) and 8 (16%) of patients were diagnosed with RV dilatation and dysfunction according to echocardiographic assessment by experienced cardiologists based on 2D assessment and quantitative indices. Five patients (10%) had moderate or more tricuspid regurgitation. Tricuspid annular 30 Active 118327893.1 Attorney Docket No. 070050.6849 systolic excursion (TAPSE), maximum tissue Doppler velocity in systole (RVS’) and fractional area change (FAC) were 18.8±5.6mm, 11.8±2.7 cm / s and 46±10% respectively. By CMR, RVEDV, RVESV and RVEF) were 163±70ml, 82±42ml and 51±8%. Six (12%) patients were diagnosed with RV dilatation and 9 (18%) with RV dysfunction when using published CMR criteria (12). All Clinical Data (n=50) Clinical Female gender 21 (42) Age 47±18 Coronary artery disease 11 (22) Diabetes 7 (14) Paroxysmal atrial fibrillation 6 (12) Hypertrophic cardiomyopathy 7 (14) Simple congenital heart disease (ASD,VSD, Bicuspid / unicuspid AV, ACA) 6 (12) Heart failure 19 (40) Prior cardiac surgery 6 (12) Echocardiography LV systolic dysfunction 14 (28) Mild 3 (6) Moderate 8 (16) Severe 3 (6) RV basal diameter [cm] (4-chamber)3.8±0.8RV dilatation 10 (20) Mild 6 (12) Moderate 4 (8) RV dysfunction 8 (16) Mild 7 (14) Moderate 1 (2) TAPSE [mm] 18.8±5.6 RVS’ [cm / s] 11.8±2.7 FAC [%] 46±10 TR moderate or more 5 (10) CMR Time between TTE & CMR [days] 9.9±5.6 RVEDV [ml] 163±70 RVESV [ml] 86±45 31 Active 118327893.1 Attorney Docket No. 070050.6849 RVEF [%] 50±8 RV dilatation # 6 (12) RV dysfunction # 9 (18) Table 11. Baseline clinical and imaging characteristics (presented as mean±SD or frequency (%)). Variability analysis of 2DE RV planimetry: measurements of areas from tracings of all available RV views were assessed for variability in both ED and ES. Results are shown in Tables 12 and 13. Poor reliability of the planimetered areas for the Sub-C view and poor to moderate reliability for the PSAX-mid and PSAX-distal views were identified. However, tracings from all other views showed good (ICC 0.75-0.90) to excellent (ICC>0.90) intra- and interobserver variability. 32 Active 118327893.1 Attorney Docket No. 070050.6849 Table 12. Intraclass correlation coefficients for intraobserver reliability of measured RV tracings. Based on 2-way fixed effects model and absolute agreement. 33 Active 118327893.1 Attorney Docket No. 070050.6849 Table 13. Intraclass correlation coefficients for interobserver reliability of measured RV tracings. Based on 2-way random effects model and absolute agreement Importance of RV views for RV volume prediction: the results of the machine learning model explainability analysis are shown in Figure 7. The 3 most important views according to their corresponding RFI were the following orthogonal views: PLAX (RFI = 0.215), Four-C (RFI=0.132) and PSAX-base (RFI=0.127). The fourth most important view was RV-inflow (RFI = 0.105). Of note, age and gender showed the least importance (RFI = 0.042 and 0.030 respectively) for the prediction of RV volumes. DL model performance for different view combinations: the performance of the DL model that used all eight 2DE RV views were evaluated, as well as the performance of DL models that used combinations of the most important 2 - 4 RV views as their input. Despite their low importance score, age and gender were entered into the models in order to increase accuracy, since they represent data that is typically collected for each 2DE. The performance of each DL model is shown in Figure 8 (top R2, bottom absolute percentage error (APE)). Compared to CMR, FTT demonstrated great accuracy for RV volume prediction (R2=0.985 and APE=3.81±8.43%) when using all 8 views. Overall, R2 34 Active 118327893.1 Attorney Docket No. 070050.6849 fell and APE increased when less RV views were used. However, accuracy did not significantly change when using the 4 most predictive RV views, i.e. PLAX, Four-C, PSAX- base and RV-inflow (R2=0.973 and APE=4.91±11.33%, p=0.48). The model maintained good accuracy when using the 3 most predictive RV views, i.e. PLAX, Four-C and PSAX- base (R2=0.964, APE=8.09±12.07%), however the change in accuracy was significant when compared to the 8-view model (p<0.001). For the same 3-view DL model, APE for RVEF was 9.86±10.68%. When using only the 2 most predictive RV views, i.e. PLAX and Four- C, RV volumes were predicted with R2=0.946 and APE=10.29±16.07%, which represented a borderline non-significant difference compared to the 3-view combination (p=0.06). For the 3-view model, the DL algorithm performed considerably less well when other combinations were used. For example, the 3-view combination of PLAX, Four-C and RV- inflow achieved R2=0.836 and APE=25.67±40.09 for RV volume prediction (p<0.001 when compared to the PLAX, Four-C and PSAX-base combination). Hyperparameters: the final hyperparameters for the 3-view DL model (PLAX, Four- C and PSAX-base) are show in Table 7. Based on the results of a machine learning explainability analysis, the disclosed subject matter suggests that planimetry of three 2DE RV views, i.e. PLAX, Four-C and PSAX-base, can predict RV volumes and therefore RVEF with accuracy close to that of CMR (Graphical Abstract). The input portion of this framework resembles the well-known Simpson’s rule for left ventricular ejection fraction. However, prediction is based on a DL algorithm without geometric assumptions. Optimal prediction would require the use of 4 RV views, but the 3-view combination still achieves good accuracy and is more clinically applicable. The disclosed subject matter can use 8 different RV views that can be used to numerically approximate RV volumes using the FTT algorithm. The disclosed subject 35 Active 118327893.1 Attorney Docket No. 070050.6849 matter can further reduce the number of RV views a maximum of 3 views) for accurate RV volume quantification. Using a machine learning explainability analysis without geometric assumptions, improved accuracy can be indeed achieved with 3 RV views. Cardiologists are widely familiar with 2DE planimetry of 2 and 3 views of the left ventricle in order to calculate ejection fraction (Simpson’s rule) and global longitudinal strain, respectively. The disclosed subject matter applies the same planimetry concept for quantifying the RV. Additionally, planimetry of these 3 views showed good to excellent intra- and interobserver variability according to our preliminary results, which further suggests clinical applicability. One of the important points regarding the selection of these RV views by machine learning explainability analysis is that they are orthogonal. This most likely maximizes the volumetric information captured by each one and at the same time minimizes the redundant information in order to numerically calculate RV volumes. * * * All patents, patent applications, publications, product descriptions, and protocols cited in this specification are hereby incorporated by reference in their entirety. In case of a conflict in terminology, the present disclosure controls. While it will become apparent that the subject matter herein described is well calculated to achieve the benefits and advantages set forth above, the presently disclosed subject matter is not to be limited in scope by the specific embodiments described herein. It will be appreciated that the disclosed subject matter is susceptible to modification, variation, and change without departing from the spirit thereof. Those skilled in the art will recognize or be able to ascertain, using no more than routine experimentation, many equivalents to the specific embodiments described herein. Such equivalents are intended to be encompassed by the following claims. 36 Active 118327893.1

Claims

Attorney Docket No. 070050.6849 WHAT IS CLAIMED IS:

1. A system for calculating a right ventricular (RV) volume comprising: one or more processors configured to receive a testing image; tokenize a categorical input and a numerical input from the testing image; forward the categorical input and the numerical input to a cascaded transformer layer; transform the categorical input and the numerical input into an embedding; transform the embedding into a classification token; and provide a measurement of RV of the testing image based on the classification token.

2. The system of claim 1, wherein the testing image is an echocardiographic image.

3. The system of claim 2, wherein the echocardiographic image is a two-dimensional echocardiographic image.

4. The system of claim 1, wherein the one or more processors are configured to receive training data, wherein the training data comprises end-diastolic and end-systolic RV volume values.

5. The system of claim 1, wherein the categorical input comprises gender information, cardiac phase information, or a combination thereof.

6. The system of claim 1, wherein the numerical input comprises end-systole and end- diastole RV volumes in a predetermined view of a two-dimensional echocardiographic image.

7. The system of claim 6, wherein the predetermined view comprises a parasternal long axis view, a right ventricular flow view, a parasternal short axis view at a level of an 37 Active 118327893.1Attorney Docket No. 070050.6849 aortic valve, a base view, a mid and apical left ventricular segment view, a four- chamber view, a subcostal view, or combinations thereof.

8. The system of claim 1, wherein the processor is configured to provide an uncertainty score.

9. The system of claim 8, wherein the uncertainty score is calculated using gradient- boosted regression trees (GBRTs) on two-dimensional echocardiographic image- derived tabular data.

10. The system of claim 9, wherein the GBRTs are configured to perform an instance- based uncertainty quantification.

11. The system of claim 10, wherein the instance-based uncertainty quantification utilizes GBRTs to identify a nearest training data to a target instance and use a distribution type to provide the uncertainty score.

12. The system of claim 11, wherein the distribution type comprises a normal distribution, a parametric distribution, a non-parametric distribution, a skewnormal distribution, a lognormal distribution, a Laplace distribution, a student t distribution. a logistic distribution, a Gumbel distribution, a Weibull distribution, a KDR distribution, or combinations thereof.

13. A method for calculating a right ventricular (RV) volume by an operating system of a computing device comprising: receiving a testing image; tokenizing a categorical input and a numerical input from the testing image; forwarding the categorical input and the numerical input to a cascaded transformer layer; transforming the categorical input and the numerical input into an embedding; transforming the embedding into a classification token; and 38 Active 118327893.1Attorney Docket No. 070050.6849 providing a measurement of RV of the testing image based on the classification token.

14. The method of claim 13, wherein the testing image is a two-dimensional echocardiographic image.

15. The method of claim 13, further comprising receiving training data, wherein the training data comprises end-diastolic and end-systolic RV volume values.

16. The method of claim 13, wherein the categorical input comprises gender information, cardiac phase information, or a combination thereof.

17. The method of claim 13, wherein the numerical input comprises end-systole and end-diastole RV volumes in a predetermined view of a two-dimensional echocardiographic image.

18. The method of claim 13, wherein the predetermined view comprises a parasternal long axis view, a right ventricular flow view, a parasternal short axis view at a level of an aortic valve, a base view, a mid and apical left ventricular segment view, a four-chamber view, a subcostal view, or combinations thereof.

19. The method of claim 13, further comprising providing an uncertainty score calculated using gradient-boosted regression trees (GBRTs) on two-dimensional echocardiographic image-derived tabular data.

20. The method of claim 19, wherein the GBRTs are configured to perform an instance- based uncertainty quantification, wherein the instance-based uncertainty quantification utilizes GBRTs to identify a nearest training data to a target instance and use a distribution type to provide the uncertainty score. 39 Active 118327893.1

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