Automatic quantification of the LV function and mass: a deep

learning approach for cardiovascular MRI

Ariel H. Curialea,∗, Flavio D. Colavecchiab,c, German Matoa,c

aCONICET - Departamento de Fısica Medica, Centro Atomico Bariloche, Avenida Bustillo 9500, 8400 S.C. de Bariloche, Rıo Negro, Argentina

bCONICET - Centro Integral de Medicina Nuclear y Radioterapia, Centro Atomico Bariloche, AvenidaBustillo 9500, 8400 S. C. de Bariloche, Rıo Negro, Argentina.

cComision Nacional de Energıa Atomica (CNEA).

Abstract

Cardiac function is of paramount importance for both prognosis and treatment of different

pathologies such as mitral regurgitation, ischemia, dyssynchrony and myocarditis. Cardiac

behavior is determined by structural and functional features. In both cases, the analysis

of medical imaging studies requires to detect and segment the myocardium. Nowadays,

magnetic resonance imaging (MRI) is one of the most relevant and accurate non-invasive

diagnostic tools for cardiac structure and function. In this work we use a deep learning

technique to assist the automatization of left ventricle function and mass quantification in

cardiac MRI. We study three new deep learning architectures specially designed for this task

where the generalized Jaccard distance is used as optimization objective function. Also, we

integrate the idea of sparsity and depthwise separable convolution into the U-net architec-

ture, as well as, a residual learning strategy level to level. Our results demonstrate a suitable

accuracy for myocardial segmentation (∼ 0.9 Dice’s coefficient), and a strong correlation with

the most relevant functional measures: 0.99 for end-diastolic and end-systolic volume, 0.97

for the left myocardial mass, 0.95 for the ejection fraction and 0.93 for the stroke volume

and cardiac output. It is important to note that the errors are comparable to the inter e

intra-operator ranges for manual contouring.

∗Address correspondence to: Ariel Hernan Curiale, Departamento de Fısica Medica, Centro AtomicoBariloche, Avenida Bustillo 9500, 8400 S. C. de Bariloche, Rıo Negro, Argentina.

Email address: ariel.curiale@cab.cnea.gov.ar (http://www.curiale.com.ar) (Ariel H. Curiale )

Preprint submitted to Computer Methods and Programs in Biomedicine December 17, 2018

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Keywords: Left Ventricle Quantification; Deep Learning; Myocardial Segmentation;

Convolutional Neural Network;

1. Introduction

Some of the most relevant global structural features for quantification of the cardiac

function are the left ventricular mass (LVM), the left ventricular volume (LVV) and the

ejection fraction (EF), which is directly derived from the left ventricle (LV) at end-diastole

(ED) and end-systole (ES). Left ventricle function and mass are of paramount importance

for both prognosis and treatment of different cardiac pathologies such as mitral regurgita-

tion, ischemia and myocarditis [8, 11, 18, 21, 31]. For instance, LVM is considered as an

independent predictor of cardiovascular events, while LVV is associated with adverse remod-

eling [1, 13, 32]. Cardiovascular magnetic resonance (CMR) is one of the most accurate

non-invasive diagnostic tools for imaging of cardiac structure and function [35]. Usually, it

is considered as the gold standard for LV mass and volume quantification [12]. In this way,

manual or semi-automatic delineation by experts is currently the standard clinical practice

for chamber segmentation from CMR images. This step is essential for quantification of

global features, such as the estimation of ventricular volume, ejection fraction and myocar-

dial mass. Despite the efforts of researchers and medical vendors, global quantification and

volumetric analysis still remain time consuming tasks which heavily rely on user interac-

tion. For example, a diastolic functional evaluation performed by using dedicated software

with manual segmentation of basal section commonly takes 25 minutes by an experienced

radiologist [14]. Thus, there is still a significant need for tools that allow automatic 3D quan-

tification. The main goal of this work is to provide an accuracy and suitable approach for

LV function and mass quantification for CMR based on deep convolutional neural networks.

Recently, convolutional neural networks (CNNs) [19] have been successfully used for

solving challenging tasks like classification, segmentation and object detection, achieving

state-of-the-art performance [20]. In fact, fully convolutional networks trained end-to-end

have been recently used for medical images, for example, for cell, prostate and myocardial

tissue segmentation [7, 24, 27]. These models, which serve as an inspiration for our work,

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employ different types of network architectures and were trained to generate a segmentation

mask that delineates the structures of interest in the image. Which in our case are the

myocardial tissue and blood pool for the LV.

Deep neural networks, such as CNN, are very useful tools for pattern recognition, how-

ever, one of the main disadvantages arises from the complexity of their training stage. For

instance, the distribution of each layer’s inputs changes along this process, as the parame-

ters of the previous layers change. This phenomenon is called internal covariate shift [29].

As the networks start to converge, a degradation problem occurs: with increasing network

depth, accuracy gets saturated. Unexpectedly, such degradation is not caused by overfitting,

and adding more layers to a suitably deep model leads to higher training error, as it was

reported by [15]. To overcome this problem the technique of batch normalization has been

proposed [17]. This procedure involves the evaluation of the statistical properties of the

neural activations that are present for a given batch of data in order to normalize the inputs

to any layer to obtain some desired objective (such as zero mean and unit variance). At the

same time, the architecture is modified in order to prevent loss of information that could

arise from the normalization. This technique allows to use much higher learning rates and

also acts as regularizer, in some cases eliminating the need for dropout [30].

Another recent performance improvement of deep neural networks has been achieved by

reformulating the layers as learning residual functions with reference to the layer inputs,

instead of learning unreferenced functions [16]. In other words, the parameters to be de-

termined at a given stage generate only the difference (or residual) between the objective

function to be learned and some fixed function such as the identity. It was empirically found

that this approach gives rise to networks that are easier to optimize, which can also gain

accuracy from considerably increased depth [16].

The most straightforward way of improving the accuracy of deep neural networks is by

increasing the number of levels (deep size) and units by level (width size). In this way,

it is possible to train higher quality models. However, bigger size implies an increase of

computational resources because a large number of parameters have to be trained which ends,

3

among other things, in overfitting. Both issues can be overcome by introducing the notion

of sparsity as it was proposed in the Inception network [33]. The fundamental hypothesis

behind Inception is that cross-channel correlations and spatial correlations are sufficiently

decoupled that it is preferable not to map them jointly as it was pointed out in the Xception

architecture [3]. Indeed, the Xception is based entirely on depthwise separable convolution

layers which allows to extremely reduce the network complexity regarding to the number of

trainable parameters, but maintaining or improving the generalization power.

In this work, we explore the idea of information sparsity described in the Inception,

and also, the notion of depthwise separable convolutions introduced by [3]. Both ideas

are introduced into a U-net architecture [27] for myocardial tissue classification and three

new deep learning networks are analyzed for this task. Then, the most accurate approach

for myocardial tissue classification is used for quantification of the LV function and mass.

Unlike previous works for myocardial tissue classification [7], we propose to use the gener-

alized Jaccard distance [6] as optimization objective to properly handle fuzzy sets. Results

demonstrate that the our approach outperforms previous methods based on the U-net ar-

chitecture [7] and provides a suitable automatic approach for myocardial segmentation and

cardiac function quantification.

The paper is structured as follows: in Section 2 the fully automatic approach based on

the U-net network is introduced. Additionally, the training strategy and the optimization

objective function is presented. In Section 3, the idea of information sparsity, depthwise

separable convolutions and residual learning level to level are evaluated for myocardial tissue

classification. Finally, we present the conclusions in Section 4.

2. Materials and methods

Materials

The proposed approach for automatic quantification of the LV function and mass was

trained and evaluated with 140 patients from two public CMR datasets: the Sunnybrook

Cardiac Dataset (SCD) [26] and the Cardiac Atlas Project (CAP) [9].

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The SCD dataset, also known as the 2009 Cardiac MR Left Ventricle Segmentation

Challenge data, consists of 45 cine-MRI images from a mix of patients and pathologies:

healthy, hypertrophy, heart failure with infarction and heart failure without infarction. A

subset of this dataset was first used in the automated myocardium segmentation challenge

from short-axis MRI, held by a MICCAI workshop in 2009. The whole complete dataset

is now available in the Cardiac Atlas Project dataset with public domain license1. The 45

cardiac cine-MR were acquired as cine steady state free precession (SSFP) MR short axis

(SAX) with 1.5T General Electric Signa MRI. All the images were obtained during 10-15

second breath-holds with a temporal resolution of 20 cardiac phases over the heart cycle, a

mean spatial resolution of 1.36 x 136 x 9.04 mm (255 x 255 x 11 pixels), and scanned from

the ED phase. In these SAX MR acquisitions, endocardial and epicardial contours were

drawn by an experienced cardiologist in all slices at ED, and only endocardial contours were

provided at ES. All the contours were confirmed by another cardiologist.

The Cardiac Atlas Project provides a set of CMR for 95 patients from a prospective,

multi-center, randomized clinical trials in patients with coronary artery diseases and mild-

to-moderate left ventricular dysfunction. All cines SSFP were acquired during a breath-hold

of 8-15 seconds duration with a typical thickness ≤ 10 mm, gap ≤ 2 mm, TR 30-50 ms, TE

1.6 ms, flip angle 60◦, FOV 360 mm, and mean spatial resolution of 1.48 x 1.48 x 9.3 mm

(245 x 257 x 12 pixels). Sufficient short-axis slices were acquired to cover the whole heart in

SAX. Also, in these acquisitions the myocardial manual segmentation were provided.

Methods

The method described in this section was intentionally designed to measure the LV func-

tion and mass by means of identifying the myocardial tissue an the blood pool for the LV

as it is shown in Fig. 1. To this end, a deep learning approach is introduced for detecting

a proper region of interest (ROI) around the LV, and also, for myocardial tissue and blood

pool classification. Then, the LV function and mass is derived as follows [10]:

1http://www.cardiacatlas.org/studies/sunnybrook-cardiac-data

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Deep Learning ROI detection

End-Diastole ROI End-Systole ROI

Deep Learning Myocardial Segmentation

LV Function and Mass Estimation

End-Diastole Seg. End-Systole Seg.End-SystoleEnd-Diastole

End-Diastole

Subsampling

Figure 1: Workflow of the proposed method.

• Left ventricle mass (LVM): is directly derived from the myocardial segmentation

by making two main assumptions: (a) the interventricular septum is assumed to be

part of the LV and (b) the myocardial volumen is equal to the total volume contained

within the epicardial borders of the ventricle, Vepi, minus the chamber volume, Vendo

at end-diastolic frame (tED):

LVM = ρ · (Vepi(tED)− Vendo(tED)) ,

where ρ = 1.05 g/cm3 corresponds to the myocardial tissue density. LVM is usu-

ally normalized to total body surface area or weight in order to facilitate interpatient

comparisons.

• Stroke volume (SV): is defined as the volume ejected between the end of diastole

and the end of systole:

SV = Vendo(tED)− Vendo(tES) ,

• Cardiac Output (CO): The blood flow which is delivered by the heart with oxy-

genated blood to the body is known as the cardiac output and is expressed in liters

per minute.

CO = SV · hr ,

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Figure 2: Network Architecture proposed for myocardial segmentation in cardiac MRI. The number of

channels/features is denoted on top of the box and the input layer dimension is provided at the lower left

edge of the box. The arrows denote the different operations according to the legend. Withe blocks correspond

to the differences with respect to previous approaches.

where hr is the heart rate. Since the magnitude of CO is proportional to body surface,

if an interpatient comparison is required, it should be adjusted by the body surface

area.

• Ejection Fraction (EF): is a global index which is generally considered as one of the

most meaningful measures of the LV pump function. It is defined as the ratio between

the SV and the end-diastolic volumen:

EF =SV

Vendo(tED)× 100% .

The LV-ROI detection and blood/myocardial tissue classification are performed by using

the same CNN approach based on the U-net . This CNN architecture is depicted in Fig. 2.

The LV-ROI detection is carried out by using low spatial resolution images at end-diastole,

while the blood pool and myocardial tissue classification is done by using the original infor-

mation in the previously detected ROI around the LV (128 x 128 pixels with 190 x 190 mm).

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In particular, the ROI size was defined to ensure that the whole myocardial tissue will be

covered.

In the proposed deep learning architecture, the network learns how to encode information

about features presented in the training set (left branch on Fig. 2). Then, in the decode

path the network learns about the image reconstruction process from the encoded features

learned.

The specific feature of the U-net architecture lies on the concatenation between the

output of the encode path, for each level, and the input of the decoding path (denoted

as big gray arrows on Fig. 2). These concatenations provide the ability to localize high

spatial resolution features to the fully convolutional network, thus, generating a more precise

output based on this information. As mentioned in [27] this strategy allows the seamless

segmentation of large images by an overlap-tile strategy.

The encoding path consists of two 3 x 3 convolution, each followed by a batch normal-

ization and a residual learning just before performing the 2 x 2 max pooling operation with

stride 2 as it was described in [7]. In fact, the batch normalization is performed right after

each convolution and before activation, following [17]. Also, non rectified linear unit (ReLU)

is applied right after the addition used for residual learning as it is depicted in Fig. 2. At

each downsampling step we double the number of feature channels, that is initially set to 64.

Every step in the decoding path can be seen as the mirrored step of the encode path,

i.e. each step in the decoding path consists of an upsampling of the feature map followed

by a 2 x 2 convolution (“up-convolution”) that halves the number of feature channels, a

concatenation with the corresponding feature map from the encoding path, and two 3 x 3

convolutions, each followed by a batch normalization and a residual learning. Finally, a

residual output learning is introduced from the upsampled previous level (left side Fig. 2).

At the final layer, a 1 x 1 convolution is carried out to map the 64 feature maps to the two

classes used for the myocardial segmentation (myocardium and endocardium). The output of

the last layer, after soft-max non-linear function, represents the likelihood of a pixel belongs

to the myocardium or endocardium of the left ventricle. Indeed, only those voxels with

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higher likelihood (> 0.5) are considered as part of the left ventricle tissue.

Training

The CNN used for detecting a ROI around the LV was trained with low spatial resolution

images and their corresponding manual segmentation (64 x 64 pixels) with a mean spatial

resolution of 5.76 x 5.76 mm. In contrast, the blood pool and myocardial tissue classification

was performed by training a CNN with cropped images in short-axis (128 x 128 pixels)

according to the previously LV-ROI detection with a mean spatial resolution of 1.44 x 1.44

mm. A 5 fold cross-validation strategy is used for training the CNN’s due to the reduced

number of patients. In this way, 5 sets of training/validation were used for each dataset. A

total of 4048 2D images were used for training (36 patients from SCD and 76 patients from

CAP) and 1003 2D images for testing (8 patients from SCD and 19 patients from CAP).

In both CNN’s the optimization was carried out by using the stochastic gradient descent

(Adaptive Moment Estimation) implementation of Keras [2] with a learning rate of 10−4.

Also, the generalized Jaccard distance [6] is used as the loss objective function to properly

handle fuzzy sets:

Jd(X, Y ) = 1−∑

i min(Xi,Yi)∑i max(Xi,Yi)

,

(1)

where X and Y are the myocardial segmentation prediction and the ground truth segmen-

tation, respectively.

Annotated medical information like myocardial classification is not easy to obtain due

to the fact that one or more experts are required to manually trace a reliable ground truth

of the myocardial classification. So, in this work it was necessary to augment the original

training dataset in order to increase the examples from 4048 to 20000 2D images. Also,

data augmentation is essential to teach the network the desired invariance and robustness

properties. Heterogeneity in the cardiac MRI dataset is needed to teach the network some

shift and rotation invariance, as well as robustness to deformations. With this intention, the

input of the network was randomly deformed by means of a spatial shift in a range of 10%

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(a) (b)

Figure 3: Examples of the data augmentation used for training the CNN for one of the five cross-validation

set for the ROI detection (a) and tissue classification (b).

of the image size, a rotation in a range of 10◦ in the short axis, a zoom in a range of 2x or by

using a gaussian deformation field (µ = 0 and σ ∈ [0.7, 1.2] randomly chosen) and B-spline

interpolation (Fig. 3).

3. Results

Three sets of experiments are conducted to evaluate the proposed methodology on both

datasets (Sunnybrooks and CAP). First, the our approach was evaluated to measure the

accuracy of the LV-ROI detection. Second, the accuracy on myocardial tissue classification

was study for different CNN’s. Finally, the third set of experiments were designed to measure

the accuracy of the proposed automatic approach for quantification of the LV function and

mass as it was described in Section 2.

In the experiments, the papillary muscles (PM) were excluded because only the Sunny-

brooks dataset contains this information. So, the proposed method will avoid to detect the

PM as part of the myocardial tissue. The mean squared error and the Dice’s coefficient

were used to measure the accuracy of the proposed CNN for an easy comparison with others

methods described in the bibliography.

ROI detection

The spatial difference and the mean squared error between the center of mass derived

from the manual, Cm, and predicted upsampling segmentation (LV + myocardial tissue) are

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Figure 4: ROI detection accuracy. (a) 2D spatial error for detecting the center of the left ventricle. (b)

Absolute error.

used to measure the CNN accuracy for detecting a ROI around the LV. Results show that

the proposed CNN approach reaches a proper accuracy for detecting a ROI around the LV

with a mean error and a spatial difference below 2 and 4 pixels respectively (Fig. 4b and

Fig. 4a). Also, a qualitative analysis shows that the proposed approach reaches a suitable

precision for this task. An example of the LV-ROI detection approach is depicted in Fig. 5.

Myocardial tissue clasification

The U-net proposed in [7] was evaluated with respect to two new architectures on both

datasets with a shrink factor of two (i.e. the original input size was reduced by a factor of

2). These new architectures were designed to introduce the main ideas behind Inception and

Xception into the U-net architecture.

The sparsity of the information can be covered by convolutions over larger patches as

it was pointed out in the Inception architecture. This idea is introduced into the U-net

architecture (uInception) as it is shown in Fig. 6, where the main differences with respected to

the proposed approach are depicted as white blocks. To increase the kernel size and maintain

the same network complexity it is necessary to perform a dimension reduction/expansion as

it was done in the Inception architecture. In particular, this step is performed by a 1 x 1

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Figure 5: Example of the region around the left ventricle detected by the proposed approach. The myocardial

tissue and blood pool classification is depicted in red as well as the center of the left ventricle in the original

image.

convolution (N/2 and N features) without activation (see box (a) in Fig. 6). It is important

to note that the size of some of the convolution layers changes according to the level. These

convolution layers are described in Fig. 6 as Z x 1 and 1 x Z where Z = [7, 6, 5] and [5, 6, 7]

for the encoding and decoding path, and Z = 4 for the level 5.

The other architecture studied combines the concepts of the depthwise separable con-

volution described in the Xception [3] and the sparsity idea of the Inception architecture.

The new architecture, named uXception, is depicted in Fig. 7. In a similar way as it was

done for the uInception, the main differences with respected to the proposed approach are

depicted as white blocks. In this case, the first level is exactly the same as the uInception

and U-net with batch normalization (BN) and residual learning (RS). Then, each level of the

encode path introduce a residual input learning with a 1 x 1 convolution without activation.

Also, a mirrored residual learning is introduced into the decode path by means of an 1 x 1

up-convolution (see the red arrow after the ReLu activation for the decode path in Fig. 7).

Finally, the last level consists of four blocks of two 5 x 5 separable convolution, followed each

convolution with a batch normalization and summed up with a residual learning (Fig. 7 box

(b)). Furthermore, the size of some of the convolution layers changes according to the level

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N

ReLU

N

conv Zx1 + batch normalization + ReLu

copy / input / outputmax pool 2x2up-conv 2x2conv 1x1 sigmoid

conv 3x3 + batch normalizationconv 1x1 + batch normalization

conv 1xZ + batch normalization

conv 3x3 + batch normalization + ReLu

64 64

(a)

N

Input Image

Myocardial Segmentation

Figure 6: The proposed uInception architecture for myocardial segmentation in cardiac MRI which introduces

the idea of sparsity described in the Inception architecture. The number of channels/features is denoted on

top of the box and the input layer dimension is provided at the lower left edge of the box. The arrows denote

different operations according to the legend. Withe blocks correspond to the differences with respect to the

proposed approache. The Zx1 and 1xZ convolutions refer to convolutions with different sizes according to

the level, i.e. Z = [7, 6, 5] and [5, 6, 7] for the encoding and decoding path, and Z = 4 for the level 5.

in the same way as it was described in the uInception architecture.

Empirical results show that the uInception and uXception outperform the U-net accuracy

on the first 25 epochs, and they achieve similar performance after 200 epochs (Fig. 8 and

Table 1). We believe that this similar behavior is due to the reduced number of images used

for training. Indeed, if the size of the dataset increases, it is expected that the uInception

and uXception outperform the U-net with BN and RL because they present differences in

the network capacity. Also, it is important to note that the uXception approach reduces

the network complexity in about 25.5% with respect to the number of parameters to be

trained (Table 1 parameter count), and it keeps the same accuracy for myocardial tissue

classification. In the same way as the Xception improves the accuracy of the Inception

when the dataset size increase [3], we expect that the uXception outperforms the uInception

architecture too.

13

ReLUReLU

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ReLU

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(c)

ReLU

ReLU

ReLU

sep. conv 3x3 + batch normalization + ReLu (a), (b), (c)

copy / inputmax pool 2x2up-conv 2x2conv 1x1 sigmoid

conv 1x1 + batch normalization (a), (b), (c)

sep. conv Zx1 + batch normalization + ReLusep. conv 1xZ + batch normalization + ReLu

sep. conv 5x5 + batch normalizationsep. conv 5x5 + batch normalization + ReLuconv 3x3 + batch normalization

conv 1x1 stride=2 + batch normalization (encode)up-conv 1x1 + batch normalization (decode)

conv 1x1 + batch normalization

conv 3x3 + batch normalization + ReLu

Figure 7: The proposed uXception architecture for myocardial segmentation in cardiac MRI which introduces

the idea of depthwise separable convolution used in the Xception and the sparcity described in the Inception.

The number of channels/features is denoted on top of the box and the input layer dimension is provided at

the lower left edge of the box. The arrows denote different operations according to the legend. Withe blocks

correspond to the differences with respect to the proposed approache. The Zx1 and 1xZ convolutions refer

to convolutions of different sizes according to the level, i.e. Z = [9, 7, 5] and Z = [5, 7, 9] for the encoding

and decoding phases.

The residual learning from level to level used in the Xception architecture was introduced

into the uXception approach as the residual input and output learning (see Fig. 7 red arrows

in the encode and decode path). Both residual reinforcement, input and output (RO), were

evaluated first into the uXception architecture, and then into the U-net . Results show that

the residual input can be removed from the uXception approach without losing accuracy.

Instead, it was observed a small improvement on the myocardial tissue classification if it is

removed (Fig. 9a). Then, the effect of the residual output learning was analyzed for the U-net

architectures. The analysis of the residual input learning was omitted because it showed to

degrade the myocardial tissue classification for the uXception architecture. Figure 9b shows

14

0 25 50 75 100 125 150 175 200Number of epochs

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

Dice

's ac

cura

cy

Accuracy on Training performance

U-net + BN + RLuInceptionuXception

Figure 8: Mean accuracy over the 5 fold cross-validation for the architectures studied with an input shrink

factor of 2 (i.e. the original input size was reduced by a factor of 2).

Architecture Parameter count Dice’s (std) MSE (std) MAE (std)

U-net - BN - RL 32,455,682 0.870 (0.0053) 0.0135 (0.0006) 0.0137 (0.0006)

uInception 35,858,242 0.869 (0.0051) 0.0136 (0.0008) 0.0138 (0.0008)

uXception 24,181,570 0.868 (0.0047) 0.0138 (0.0007) 0.0140 (0.0007)

Table 1: Network complexity and myocardial segmentation accuracy over the 5-fold cross-validation (mean

and std) for the architectures studied with an input shrink factor of 2 (i.e. the original input size was reduced

by a factor of 2). MSE: mean squared error. MAE: mean absolute error. BN: Batch normalization. RL:

Residual learning revisar....

that the use of RO improves the tissue classification in an early stage of training for the U-net

architecture. Due to the reduced number of patient used in this study, both architectures get

similar accuracy after 200 epochs. But, we believe that U-net with RO will outperform the

U-net architecture when the dataset size increases because the network capacity increases

when the RO is introduced, in a similar way as what happened in [3] with the Xception and

Inception architectures.

Last, the proposed U-net architecture with RO and the uXception were evaluated on

both dataset without using a shrinking factor. Figure 10 shows that the U-net with RO

architecture is slightly more accurate than uXception for the datasets used. And, the U-net

15

0 25 50 75 100 125 150 175 200Number of epochs

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900Di

ce's

accu

racy

Accuracy on Training performance

uXceptionuXception RO

(a)

0 25 50 75 100 125 150 175 200Number of epochs

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

Dice

's ac

cura

cy

Accuracy on Training performance

U-net + BN + RLU-net + BN + RL + RO

(b)

Figure 9: Mean accuracy over the 5 fold cross-validation for the uXception and U-net architectures with an

input shrink factor of 2 (i.e. the original input size was reduced by a factor of 2). RO: residual output.

0 20 40 60 80 100Number of epochs

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

Dice

's ac

cura

cy

Accuracy on Training performance

uXception ROU-net + BN + RL + RO

Figure 10: Accuracy on training performance over the 5 fold cross-validation for the proposed U-net and

uXception architecture with residual output for myocardial segmentation in cardiac MRI.

with RO approach reaches a suitable accuracy in few training iterations. i.e. in 100 epochs.

In this case, the proposed CCN reaches a Dice’s median value of ∼ 0.9 for both dataset

(Fig. 11). However, it can be seen that the precision tends to be degraded at end-systole

(Fig. 11 right plot). This degradation happens, among other things, because the myocardial

tissue at end-diastole is generally more compact, and also, there is more end-diastole images

than end-systole. In fact, the Sunnybrooks dataset provides the myocardial contours in all

16

CA SB0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00Di

ce's

accu

racy

CA ED CA ES SB ED SB ES0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

Dice

's ac

cura

cy

Figure 11: Accuracy of the proposed architecture for myocardial segmentation in cardiac MRI for each

dataset (left), and also for end-diastole and end-systole (right). Only the endocardial contours were used

for the SB database at end-systole. CA: Cardiac Atlas dataset; SB: Sunnybrooks dataset; ED: end-diastole;

ES: end-systole.

slices at ED, and only the endocardial contours at ED.

A 3D examples of the proposed fully automatic myocardial tissue segmentation on the

CA dataset can be seen in Fig. 12. Figure 12a shows the myocardial segmentation in three

orthogonal views and Fig. 12b shows the segmentation in two 3D views. Qualitative details

of the proposed approach for myocardial segmentation for a patient on the Sunnybrooks

dataset can be seen in several slices in Fig. 13. They show that the proposed myocardial

segmentation provides a suitable approach for myocardial segmentation in cardiac MRI. In

brown it depicts those voxels where the manual myocardial segmentation and the proposed

automatic segmentation overlaps, in dark yellow and cian are depicted those pixels corre-

sponding to the GT and the automated segmentation without overlapping respectively. As it

can be seen only a reduced number of voxels correspond to a non-overlapping classification,

especially for the LV ventricle.

Physiological validation

Six physiological measures have been derived from the myocardial tissue classification:

end-diastolic volume (EDV), end-systolic volume (ESV), SV, LVM at ED, CO and EF. As

it was described in the introduction, these measures are one of the most relevant global

17

(a) (b)

Figure 12: Examples of the proposed method for myocardial tissue and endocardial (blood pool) classification

on a patient of the CA dataset for end-diastole (up-row) and end-systole (low-row). (a) The proposed

myocardial segmentation is presented in three orthogonal views. (b) 3D view of the proposed myocardial

segmentation.

structural features. In particular, the ESV measures for three patients were identified as

outliers and they will be discussed separately in the next section.

Table 2 summarizes the errors and the Pearson’s correlation coefficient of the six phys-

iological measures derived from the proposed method with respect to those derived from

the experts. Whereas in Table 3 a bibliographical comparison is performed. In general, our

measures are comparable to those reported by other authors.

Parameters Mean error Std error Mean abs error Max. abs error ρ

EDV [cm3] 0.14 9.51 7.31 26.55 0.99

ESV [cm3] 1.37 9.15 7.12 25.42 0.99

SV [cm3] -1.23 8.38 6.82 21.54 0.93

EF [%] -0.71 4.76 3.73 15.84 0.95

LVM [g] -3.68 13.66 10.67 64.05 0.97

CO [L/min] -0.03 0.47 0.32 1.29 0.93

Table 2: Errors of the physiological measures studied for the proposed approach.

The BlandAltman plots (Fig. 14) shows a minimal bias of 0.14 ± 0.51 ml for EDV, a

small bias of 1.37± 9.15 ml for ESV, and −0.71± 4.76 % for EF (95% limits of agreement:

18

Figure 13: Qualitative results for a patient in the SB dataset. Three different short axis slices are plotted

from apex (upper) to base (down) of the left ventricle for the myocardial tissue and the endocardium (blood

pool) at end-diastole and only the endocardium at end-systole. In brown it depicts those voxels where the

manual and the proposed automatic classification overlaps, in dark yellow and cian are depicted those pixels

corresponding to the manual and automated classification without overlapping respectively.

19

Mean ± std. errors

Reference EDV [cm3] ESV [cm3] EF [%] LVM [g] Methodology Comments

[5] 1.0± 5.0 −3.0± 7.0 2.0± 5.5 — active contours Nine patients

[25] −1.8± 11.7 −10.8± 8.2 7.6± 5.6 — Fuzzy objects, Hough

Transform and mini-

mum cost

Six patients and eight

healthy subjects

[34] −8.1± 11.5 −5.9± 6.3 1.6± 3.5 7.2± 15.0 Fuzzy objects, smooth

convex hull and radial

minimum cost

Seven patients and

three healthy sub-

jects

[23] −6.1± 7.2 −3.0± 5.2 0.6± 4.3 6.2± 12.2 Bayesian flooding and

weighted least-squares

18 patients; semiau-

tomatic corrections

[4] −3.6± 8.2 −3.3± 7.2 1.5± 3.3 8.2± 11.6 MRF based deformable

model

43 patients affected

by an AMI

[22] 1.0± 22 9± 23 7± 11 — Maximum likelihood

based on active con-

tours

35 patients and 15

healthy subjects

ours 0.14± 9.5 1.4± 9.1 −0.7± 4.8 −3.7± 13.7 Deep learning 137 patients

Table 3: Errors (mean ± std.) in the measurement of the physiological parameters studied. Comparison

with other approaches.

-18.43 to 18.71 ml for EDV, -16.49 to 19.23 ml for ESV, and -10.02 to 8.59% for EF). Plots

of the linear regression of the measured parameters and those derived from the experts

(Fig. 15) show a high correlation between the manual and automatic measures, specially for

the EDV and ESV. As it was described in the previous section, myocardial tissue and blood

classification seems to be slightly more precise for end-diastole than for end-systole (see the

standard deviation and the mean absolute erro in Table 2). Nevertheless, the overall effect

of ESV inaccuracies in the EF calculation is negligible, and the proposed method is one of

the most accuracy for measuring the EF. Also, it is important to note that the EF and MM

errors are comparable to the inter e intra-operator ranges for manual contouring reported

in [28]. The presence of outliers in the measures is mainly due to the segmentation of most

basal and apical slices. The most basal slices are difficult to segment due to the myocardial

20

50 100 150 200 250 300 350Manual EDV [cm3]

30

20

10

0

10

20

30Er

ror E

DV [c

m3 ]

0.14

+ 1.9618.71

1.96-18.43

End-diastolic Volume (EDV) [cm3]

50 100 150 200 250 300Manual ESV [cm3]

30

20

10

0

10

20

30

Erro

r ESV

[cm

3 ]

1.37

+ 1.9619.23

1.96-16.49

End-systolic Volume (ESV) [cm3]

20 40 60 80 100 120Manual SV [cm3]

30

20

10

0

10

20

30

Erro

r SV

[cm

3 ]

-1.23

+ 1.9615.13

1.96-17.60

Stroke Volume (SV) [cm3]

10 20 30 40 50 60 70 80Manual EF [%]

20

15

10

5

0

5

10

15

20

Erro

r EF

[%]

-0.71

+ 1.968.59

1.96-10.02

Ejection Fraction (EF) [%]

50 100 150 200 250 300Manual MM [g]

80

60

40

20

0

20

40

Erro

r MM

[g]

-3.68

+ 1.9623.00

1.96-30.35

Myocardial Mass (MM) [g]

1 2 3 4 5 6 7 8 9Manual CO [L/min]

1.5

1.0

0.5

0.0

0.5

1.0

1.5

Erro

r CO

[L/m

in]

-0.05

+ 1.961.05

1.96-1.15

Cardiac Output (CO) [L/min]

Figure 14: Bland-Altman plots of the physiological measures studied.

tissue is not always complete in the slice and it changes the topology of the cavity. In the

same way, the most apical slices are also difficult to segment because the blood pool is not

always present in those slices which it changes the topology too.

21

100 200 300Manual EDV [cm3]

50

100

150

200

250

300

350Au

tom

at. E

DV [c

m3 ]

End-diastolic Volume (EDV) [cm3]

= 0.99

100 200 300Manual ESV [cm3]

50

100

150

200

250

300

Auto

mat

. ESV

[cm

3 ]

End-systolic Volume (ESV) [cm3]

= 0.99

20 40 60 80 100 120Manual SV [cm3]

0

20

40

60

80

100

120

Auto

mat

. SV

[cm

3 ]

Stroke Volume (SV) [cm3]

= 0.93

20 40 60 80Manual EF [%]

0

10

20

30

40

50

60

70

80

Auto

mat

. EF

[%]

Ejection Fraction (EF) [%]

= 0.95

50 100 150 200 250 300Manual MM [g]

50

100

150

200

250

300

Auto

mat

. MM

[g]

Myocardial Mass (MM) [g]

= 0.97

2 4 6 8Manual CO [L/min]

0

2

4

6

8

Auto

mat

. CO

[L/m

in]

Cardiac Output (CO) [L/min]

= 0.93

Figure 15: Regression plots and the Pearson coefficient of the physiological measures studied.

Discussion

The ESV measures for three patients were identified as outliers with error values grater

than 30 cm3. These errors were found extremely higher with respect to others patients.

So, they were excluded from the previous analysis and they are discussed in what follows.

An analysis on these patients reveals that the proposed approach for myocardial tissue

classification fails (Fig. 16). However, is important to note that in one of these three patient,

the method only fails in a basal slice as it can be seen in Figure 16 middle row. The effect

22

Figure 16: Patients excluded from the physiological analysis. The automatic and manual segmentation

is presented by patient (rows) in three orthogonal views (columns) at end-diastole (first row) and end-

systole (middle and bottom rows). The blood pool is depicted in blue and green for manual and automated

segmentation respectively. Also, the myocardial tissue is depicted in brown and yellow for manual and

automated segmentation. The manual myocardial contour is only depicted when it is available (i.e. at

end-diastole).

of this misclassification introduce an error of 49 and 46 cm3 for EDV and ESV respectively.

On the other hand, the proposed approach fails in different slices for the other two

patients as it is depicted in Figure 16 first and bottom row. The misclassification of the

patient presented in the firs row results in a high error, but it is produced only at end-

systole (30.5 cm3). In this case, the patient presents a severe dilated cardiomyopathy which

made the proposed approach for tissue classification fails. Similarly, the patient depicted in

the bottom row in Figure 16 presents an hypertrophic cardiomyopathy. This hypertrophic

myocardial tissue made the proposed approach reaches an error of 45.2 cm3. Nevertheless,

we believe that the proposed approach will be able to overcome these misclassifications just

by increasing the size of the dataset.

23

4. Conclusions

In this paper, we have proposed an automatic LV function and mass quantification ap-

proach by using deep learning networks. Unlike previous approaches, our method makes use

of the Generalized Jaccard distance as objective loss function and residual learning strate-

gies level to level to provide a suitable approach for myocardial segmentation and cardiac

functional quantification. Quantitative and qualitative results show that the proposed ap-

proach presents a high potential for being used to estimate different structural and functional

features for both prognosis and treatment of different pathologies. Thanks to data augmen-

tation with free form deformations, it only need very few annotated images (280 cardiac

MRI) and has a very reasonable training time of only 9 hours on a NVidia Tesla C2070 (6

GB) for reaching a suitable accuracy of ∼ 0.9 Dice’s coefficient for both public datasets.

Also, it is important to note that the methods achieves a strong correlation with the most

relevant functional measures (0.99 for EDV and ESV, 0.97 for myocardial mass, 0.95 for EF

and 0.93 for SV and CO). And the error are comparable to the inter e intra-operator ranges

for manual contouring. Additionally, this work leads to extensions for automatic detection

and tracking of the right and left ventricle. Myocardial motion is useful in the evaluation of

regional cardiac functions such as the strain and strain rate.

Acknowledgments

This work was partially supported by Consejo Nacional de Investigaciones Cientıficas y

Tecnicas (CONICET) and by grants M028-2016 SECTyP, Universidad Nacional de Cuyo,

Argentina; and PICTO 2016-0023, Agencia Nacional de Promocion Cientıfica y Tecnologica,

and Universidad Nacional de Cuyo, Argentina. German Mato acknowledges CONICET for

the grant PIP 112 201301 00256.

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