2Pa5-10
Quantitative Uncertainty Assessment of Lumen
Detection in Intravascular Ultrasound Images Using
Deep Ensembles
Deep Ensembles を用いた血管内超音波画像の血管内腔検出における不確実性の定量評価
Naoya Kanno1‡, Takashi Orihara1, Hiroyuki Yagami2, Masanori Kawasaki3, Munenori
Okubo3, Takuro Ishii1,4, Hitoshi Matsuo3, and Yoshifumi Saijo1 (1Grad. School ofBiomed. Eng., Tohoku Univ.; 2Terumo Corporation; 3Gifu Heart Center; 4Frontier
Research Institute for Interdisciplinary Sciences, Tohoku Univ.)
菅野尚哉 1‡，折原隆志 1，矢上弘之 2，川崎雅規 3，大久保宗則 3，石井琢郎 1,4，松尾仁司 3，西條芳文 1（1 東北大院 医工, 2 テルモ株式会社，3 岐阜ハートセンター, 4 東北大 学際科学フロンテ
ィア研究所）

1. Introduction
Intravascular ultrasound (IVUS) and thefractional flow reserve (FFR) tests are necessary
examinations that assess detailed structures andhemodynamics of the pathological coronary arteryand provide useful information to determine thenecessity of the invasive percutaneous coronary
intervention (PCI) treatment1). Since the FFR test
requires inserting pressure sensors into the stenosed
artery and administrating drugs to induce cardiac
stress, alternative methods that can estimate FFR
index without those cumbersome techniques havebeen studied. One of which is using IVUS images toextract changes in diameter around the pathologicalartery and estimating the FFR index from thosegeometrical features2). The major problem of themethod is that physicians must manually trace thearterial wall from consequent images as it isdemanding and sometimes impossible procedure
because the boundary is often unclear or invisible in
IVUS images. As a solution, Deep Learning models
to automatically trace the vessel wall has beenreported. However, the Deep Learning techniques
have a problem called overconfidence, where theestimated probability in classification problems isbiased towards 0 and 13), and the estimatedprobability value does not represent its uncertainty.
Therefore, the reliability of each extracted boundary
has not been considered. This study aimed to develop
a machine-learning based method for both detecting
the lumen of the coronary artery and quantifying its
uncertainty using Deep Ensembles algorithm.
2. Materials and Methods
2.1 Uncertainty Estimation
In order to estimate the uncertainty of a trained
deep learning network, a method combining multiple
convolutional neural network (CNN) models with

Averaging
BoundaryPrediction
Input Image
MutualInformation
CNNs

Lumen
Probabilities

Uncertainty

Fig. 1 Schematic of boundary and uncertainty
estimation from a IVUS image using Deep
Ensembles algorithm.

the same structure, so-called Deep Ensembles, wasemployed. Fig. 1 shows the schematic of Deep
Ensembles. Essentially, each trained CNN model has
its unique prediction result depending on the initialvalues. If a feature in the test data set was not
sufficiently included in the training data set,
extracted boundaries around the feature frommultiple models trained with different initial values
would show high variability. Deep Ensembles
algorithm uses the variability of the predictedprobability as the uncertainty map of the extracted
boundaries.
In this paper, our model was a two-label
classification problem, identifying intra- and extralumen of the blood vessel to extract the boundary.
Since the predicted probability of the lumen is
distributed from 0 to 1, high uncertainty means thatthe probability is close to 0.5. To quantify thecharacteristics of the uncertainty, mutual information(MI)4) was used in this study and expressed as
𝑀𝐼 = [−𝑝̅ log 𝑝̅ − (1 − 𝑝̅ ) log(1 − 𝑝̅ )]𝐿

1− ∑[−𝑝𝑙 log 𝑝𝑙 − (1 − 𝑝𝑙 ) log(1 − 𝑝𝑙 )] , (1)𝐿
𝑙=1where 𝑝̅ was the average of the prediction
probabilities, 𝑝𝑙 was the 𝑙 -th lumen prediction

Fig. 2 An example of detecting the lumen and quantifying its uncertainty using Deep ensemble; (a) Trueboundary, (b) Predicted boundaries from ﬁve models trained independently, (c) Error between true and mean
predicted boundaries, and (d) Mutual Information as the uncertainty map.

probability, and 𝐿 was the number of CNN models
for Deep Ensembles.

angle to analyze the uncertainty for each angle.

2.2 Experimental Setup

3. Results and Discussion

Fifty-three cases of IVUS images consisting of
3,027 images taken in Gifu heart center were used totrain and test the deep ensembles model. IVUS
imaging was performed using a mechanical IVUS
system (VISICUBE for Ueda Japan Radio Corp.,
Japan) with 60MHz (AltaView) imaging catheters(Terumo Corp., Japan). As preprocessing, the IVUS
images were resized from 512×512 to 256×256
pixels and converted to 8-bit grayscale. The trueboundaries of the arterial wall in all the images weremanually drawn by a skilled technician and then thelabel images were generated as the inside and theoutside of the boundary are to be 1 and 0,respectively. The 53 sequences of IVUS images of
the coronary artery of each patient were divided into
40 cases (2,323 images) for the training and 13 cases(704 images) for the testing.
For the deep learning model, we used U-Net,
which is a CNN model for semantic segmentation5).
For Deep Ensembles, five U-Net models weretrained independently with a batch size of 16 and a
training epoch of 50. The predicted probability was
the average of the probabilities of the lumen to beoutput for each pixel from the models. The boundary
between the lumen and the wall was defined as theline where the predicted probability was 0.5.

The mean of the IoU achieved in 5 trainedmodels was 0.824 ± 0.152, indicating that all themodels were comparably trained well.
Fig. 2 (a) shows the input image and theboundary. The input IVUS image contained artifacts
derived from the guidewire due to multiple
reflections and shadows, and Fig. 2 (b) shows theboundaries that the models predicted. Theboundaries show the line where the probability
predicted by each model was 0.5 and varied in thearea where the artifacts occurred. Fig. 2 (c) shows theoutput boundary from the models and the error fromthe target boundary. The estimation error was larger
in the artifact part. Fig. 2 (d) shows the MI values at
each angle. The MI values were high in the areas
where artifacts occurred. This was because of thehigher mutual information in the areas where theoutput probability of each model varied. Thisobservation suggested that it would be possible toestimate the uncertainty of the model predictions bylooking at the variability of the model estimation
results using the mutual information values.

2.3 Evaluation Criteria
To verify the global accuracy of thepredictions, the Intersection over Union (IoU) that
evaluates the overlap between the target region andthe predicted region was used. In addition, to analyze
the local accuracy of the predictions, the difference
between the target and prediction boundary wascalculated for each angle in the polar coordinates.
The target and the prediction boundary between thelumen and the wall were transformed into the polar
coordinates, then the error was calculated for eachangle. Furthermore, the MI value was transformed
into the polar coordinates, and was summed for eachnaoya.kannno.s8@dc.tohoku.ac.jp

4. Conclusion
In this paper, we proposed a method toestimate the uncertainty of IVUS images using Deep
Ensembles. The differences in the prediction resultsfrom multiple neural network models suggested thatthe increased uncertainty due to artifacts can bevisualized.
References
1. N. H. J. Pijls et al.: Circ. 92 (1995) 3183.
2. F. Seike et al.: Circ. J. 82 (2018) 815.
3. C. Guo et al.: Proc. 34th Int. Conf. Mac. Learn.
PMLR 2017 70 (2017) 1321.
4. L. Smith and Y. Gal: 4th Conf. Uncertain. Artif.
Intell. 2018 UAI 2018 2 (2018) 560.
5. O. Ronneberger et al.: Med. Image Comput.
Comput. Assist. Interv. MICCAI 2015 9351
(2015) 234.