Alexandre Fenneteau

Pascal Bourdon

David Helbert

Christine Fernandez-Maloigne

Christophe Habas

Rémy Guillevin

Investigating efficient CNN architecture for multiple sclerosis lesion segmentation

Keywords: MRI, CNN, segmentation, multiple sclerosis, architecture, efficient

Purpose: The automatic segmentation of multiple sclerosis lesions in magnetic resonance imaging has the potential to reduce radiologists' efforts on a daily time-consuming task and to bring more reproducibility. Almost all new segmentation techniques make use of convolutional neural networks, with their own different architecture. Architectural choices are rarely explained. We aimed at presenting the relevance of a U-net like architecture for our specific task and at building an efficient and simple model. Approach: An experimental study was performed by observing the impact of applying different mutations and deletions to a simple U-net like architecture. Results: The power of the U-net architecture is explained by the joint benefits of using an encoderdecoder architecture and by linking them with long skip connections. Augmenting the number of convolutional layers and decreasing the number of feature maps allowed us to build an exceptionally light and competitive architecture, the MPU-net, with only approximately 30,000 parameters.

Conclusion:

The empirical study of the U-net has led to a better understanding of its architecture. It has guided the building of the MPU-net, a model far less parameterized than others (at least by a factor of seven). This neural network achieves a human level segmentation of multiple sclerosis lesions on FLAIR images only. It shows that this segmentation task does not necessitate overly complicated models to be achieved. This gives the opportunity to build more explainable models which can help such methods to be adopted in a clinical environment.

Introduction

Multiple Sclerosis (MS) is an autoimmune and inflammatory disease affecting the central nervous system. It affects up to 0.2% of people depending on the geographical region. It was estimated to cause approximately [START_REF] Fenneteau | Learning a CNN on multiple sclerosis lesion segmentation with self-supervision[END_REF],000 deaths and the disability of more than 1,000,000 people worldwide in 2016 [START_REF] Pugliatti | The worldwide prevalence of multiple sclerosis[END_REF][START_REF] Wallin | Global, regional, and national burden of multiple sclerosis 1990-2016: a systematic analysis for the global burden of disease study 2016[END_REF]. The disease induces demyelination and inflammatory lesions. Magnetic Resonnance (MR) exams are commonly used for the diagnosis and the monitoring of the disease as they allow radiologists to localize and characterize lesions, by using the McDonald criteria [START_REF] Thompson | Diagnosis of multiple sclerosis: 2017 revisions of the mcdonald criteria[END_REF]. This screening is a repetitive, time-consuming, and prone to inter-observer variability [START_REF] García-Lorenzo | Review of automatic segmentation methods of multiple sclerosis white matter lesions on conventional magnetic resonance imaging[END_REF].

Consequently, its automation has been encouraged via few segmentation challenges [START_REF] Styner | 3d segmentation in the clinic: A grand challenge ii: Ms lesion segmentation[END_REF][START_REF] Commowick | Msseg challenge proceedings: Multiple sclerosis lesions segmentation challenge using a data management and processing infrastructure[END_REF][START_REF] Carass | Longitudinal multiple sclerosis lesion segmentation: resource and challenge[END_REF].

State of the art

In the last decade, several supervised and unsupervised attempts have been performed to automatically segment the MS lesions. The review of Danelakis et al. [START_REF] Danelakis | Survey of automated multiple sclerosis lesion segmentation techniques on magnetic resonance imaging[END_REF] shows that the recently published automatic lesion segmentation algorithms use clustering techniques, such as the Lesion Toolbox [START_REF] Schmidt | An automated tool for detection of flair-hyperintense white-matter lesions in multiple sclerosis[END_REF], classification techniques such as K-nearest neighbors [START_REF] Fartaria | Segmentation of cortical and subcortical multiple sclerosis lesions based on constrained partial volume modeling[END_REF] or Random Forests [START_REF] Vera-Olmos | Random forest for multiple sclerosis lesion segmentation[END_REF] and more recently artificial neural networks.

The use of neural networks is promising due to their potential to deliver better performances. To the best of our knowledge the first known attempt to use artificial neural networks in segmentation of MS lesions began in 1998 with the work of Goldberg et al. [START_REF] Goldberg-Zimring | Automated detection and characterization of multiple sclerosis lesions in brain mr images[END_REF]. They used such networks for segmentation artifact removal. Later, Kuwazuru et al. [START_REF] Jumpei Kuwazuru | Automated detection of multiple sclerosis candidate regions in mr images: false-positive removal with use of an ann-controlled level-set method[END_REF] used a fully connected network for false positive removal. More recently, Convolutional Neural Networks (CNNs) have been increasingly used with success by researchers.

Among the top three best proposals of the Medical Image Computing & Computer Assisted Intervention (MICCAI) 2016 MS challenge [START_REF] Commowick | Objective evaluation of multiple sclerosis lesion segmentation using a data management and processing infrastructure[END_REF], two were using CNNs: Valverde et al. [START_REF] Valverde | Multiple sclerosis lesion detection and segmentation using a convolutional neural network of 3d patches[END_REF] with only two convolutional layers followed by a dense one and McKinley et al. [START_REF] Mckinley | Nabla-net: A deep dag-like convolutional architecture for biomedical image segmentation[END_REF] with their encoder-decoder network, the Nabla net.

More recently, other approaches have been proposed using CNNs. Nair et al. [START_REF] Nair | Exploring uncertainty measures in deep networks for multiple sclerosis lesion detection and segmentation[END_REF] proposed a method for estimating prediction uncertainty. Brosch et al. [START_REF] Brosch | Deep 3d convolutional encoder networks with shortcuts for multiscale feature integration applied to multiple sclerosis lesion segmentation[END_REF] proposed to pretrain their CNN as convolutional restricted Boltzmann machines. Other work to pretrain neural networks has been conducted using self-supervision [START_REF] Fenneteau | Learning a CNN on multiple sclerosis lesion segmentation with self-supervision[END_REF].

Another proposition for improving lesion segmentation consists of multi-class tissue segmentation at the same time as lesion segmentation [START_REF] Mckinley | Simultaneous lesion and neuroanatomy segmentation in multiple sclerosis using deep neural networks[END_REF]. Hashemi et al. [START_REF] Hashemi | Asymmetric loss functions and deep densely-connected networks for highly-imbalanced medical image segmentation: Application to multiple sclerosis lesion detection[END_REF] proposed an encoder-decoder CNN and studied the influence of β parameter of the F β loss function. All these studies used very different CNNs for assessing their training methods and achieved state-of-the-art performances. However, we do not know the extent of the influence of architecture on predictions not why these authors made particular network design choices.

Proposal

Generally, the design part of the neural networks is not clearly stated in articles and it is difficult to evaluate how architectural choices are made. We present here our experimental approach for the design of a new neural network that has been created for being compact and competitive. This manuscript provides discoveries and explanations about architecture for segmenting MS lesions. As eXplainable Artificial Intelligence (XAI) techniques [START_REF] Adadi | Peeking inside the black-box: A survey on explainable artificial intelligence (xai)[END_REF] are gaining importance in the medical imaging area with some successful attempts [START_REF] Eitel | Uncovering convolutional neural network decisions for diagnosing multiple sclerosis on conventional mri using layer-wise relevance propagation[END_REF], and with the idea that a simpler model is easier to explain [START_REF] Samek | Toward interpretable machine learning: Transparent deep neural networks and beyond[END_REF], we performed this work with the idea of attempting to define an efficient CNN in terms of number of learnable parameters.

With the success of using adaptations of U-net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] in medical imaging in general such as in brain tumor segmentation [START_REF] Isensee | Brain tumor segmentation and radiomics survival prediction: Contribution to the brats 2017 challenge[END_REF], pancreas tissue segmentation [START_REF] Oktay | Attention u-net: Learning where to look for the pancreas[END_REF] but also in MS lesion segmentation [START_REF] Nair | Exploring uncertainty measures in deep networks for multiple sclerosis lesion detection and segmentation[END_REF][START_REF] Hashemi | Asymmetric loss functions and deep densely-connected networks for highly-imbalanced medical image segmentation: Application to multiple sclerosis lesion detection[END_REF][START_REF] Feng | A self-adaptive network for multiple sclerosis lesion segmentation from multi-contrast mri with various imaging protocols[END_REF], this study focuses on U-net architecture.

The influence of design choices was analyzed throughout different experiments on a simple U-net like architecture. The analysis focused on the following points:

• Feature map down-sampling and up-sampling;

• Use or not of skip-connections;

• Complexity.

After experimenting, we took the observations on performances into account and designed our own U-net like architecture, the Minimally Parameterized U-net (MPU-net). It is designed with the constraint of having a very limited number of learnable parameters. We compared its performance to state-of-the-art methods by submitting the results to the Institute of Electrical and Electronics Engineers (IEEE) International Symposium on Biomedical Imaging (ISBI) 2015 MS segmentation [START_REF] Carass | Longitudinal multiple sclerosis lesion segmentation: resource and challenge[END_REF] online leader-board1 .

Most of the time, the relevance of CNN architectures for MS lesion segmentation is rarely explained, except by a final performance score. The aim of the study is to experimentally assess architectural choices in a U-net, in order to build an efficient architecture.

Materials and Methods

Data

The work has been performed using the ISBI 2015 MS segmentation challenge [START_REF] Carass | Longitudinal multiple sclerosis lesion segmentation: resource and challenge[END_REF] data set. It has been chosen since it is the newest publicly available data set containing a training and a testing set, which can be submitted and compared to other sets, by using its online leader-board. Only one data set was used among all publicly available MS segmentation data sets, thus avoiding working with images that were differently acquired and preprocessed.

The training set consists of 21 preprocessed MR exams from different time points of 5 patients with ground truth and the test set provides 61 MR exams from 14 patients without expert segmentations. Each consecutive time point is separated by almost a year. All exams are preprocessed and the segmentation of MS lesions was performed by two different experts.

The data sets provide T1, T2, T2-fluid-attenuated inversion recovery (FLAIR) and Proton Density (PD) images for each MR exam. In T1 images, MS lesions can be seen as hypo-intensities. In this set, T1 images are mainly used for anatomical purposes since no contrast enhancing agent is injected to patients. The T2 images are more valued and lesions appear as hyper-intensities. One problem with the T2 sequence is that some periventricular lesions can be difficult to detect. FLAIR images counter this effect by attenuating fluid signal in ventricles while keeping the advantages of the T2 sequence. This is the reason why, this sequence is preferred in practice. The PD images are sometimes used as an assistance, since in these images, lesions can be seen as hyper-intensities and can help to reveal subtentorial lesions. Among all available MR sequences, we chose to select only the FLAIR images. The main reason for that was that we wished to keep the training as simple as possible since our study required to train many different architectures and that adding input would augment the complexity of the task. According to the McDonald criteria [START_REF] Thompson | Diagnosis of multiple sclerosis: 2017 revisions of the mcdonald criteria[END_REF], the MS lesions can be seen in T2 images, and in practice, FLAIR images are more frequently used. Furthermore, according to Feng et al. [START_REF] Feng | A self-adaptive network for multiple sclerosis lesion segmentation from multi-contrast mri with various imaging protocols[END_REF], FLAIR imaging is the most effective. To the best of our knowledge, this sequence is used in every recent deep learning approach [START_REF] Brosch | Deep 3d convolutional encoder networks with shortcuts for multiscale feature integration applied to multiple sclerosis lesion segmentation[END_REF][START_REF] Valverde | One-shot domain adaptation in multiple sclerosis lesion segmentation using convolutional neural networks[END_REF][START_REF] Rosa | Shallow vs deep learning architectures for white matter lesion segmentation in the early stages of multiple sclerosis[END_REF].

All the images are provided in 181 × 217 × 181 voxels with voxel size of 1 × 1 × 1 mm 3 . These images were previously preprocessed for the challenge by Carass et

Additional preprocessing

Before using the images, few image preprocessing steps were performed in order to have compact images, with comparable and normalized intensities.

The images were all cropped in the same way to avoid unnecessary calculations. Then all images were histogram matched [START_REF] Nyúl | New variants of a method of mri scale standardization[END_REF] using Insight Toolkit (ITK) [START_REF] Mccormick | Itk: enabling reproducible research and open science[END_REF][START_REF] Yoo | Engineering and algorithm design for an image processing api: a technical report on itk-the insight toolkit[END_REF], with the image with the maximum dynamic range, in order to make intensities comparable while not reducing the dynamic range. The final step was to normalize each image. The intensity mean and standard deviation were calculated only for brain voxels in training images.

Normalization was performed by subtracting the mean and by dividing by the standard deviation. The background voxels were excluded from the calculation of statistics because they do not represent the data directly and would influence the normalization process.

CNNs training

Following the work on patch size by Snehashis et al. [START_REF] Roy | Multiple sclerosis lesion segmentation from brain mri via fully convolutional neural networks[END_REF], we decided to train our neural network with multiple small patches of size 32 × 32 × 32 voxels/mm 3 . For any lesion size, a patch can capture the lesion, or a great part of it, and the surrounding brain texture (see Fig. 1). This makes it possible to segment very locally while occupying little memory space. This multiple small patch approach has also the benefit of augmenting the number of training examples. This is the only type of data augmentation that we have performed. During testing, for each model, the prediction masks are the mean of patch predictions extracted in sliding window manner with strides 8 × 8 × 8. These stride values were set empirically to have a sufficient overlapping prediction consensus with a reasonable number of individual patch predictions.

As stated in 2.1, there are two manual segmentation maps: one for each radiologist involved in annotation.

The CNNs were trained with both maps at the same time, so as to evaluate their capacity to mimic each radiologist differently.

On designing reference

Guided by the success of the U-net architecture, we decided to take a very simple adaptation of this architecture as reference (see Fig. 2). We did not add any architecture regularizers, such as batch normalization [START_REF] Ioffe | Batch normalization: Accelerating deep network training by reducing internal covariate shift[END_REF] or dropout [START_REF] Srivastava | Dropout: a simple way to prevent neural networks from overfitting[END_REF] even if they may have improved performances. For the same reason, architecture testing began with only one convolution at each level of the neural network. Transposed convolutions were replaced by upsamplings for simplifying and avoiding checkerboard artifacts [START_REF] Isensee | Brain tumor segmentation and radiomics survival prediction: Contribution to the brats 2017 challenge[END_REF]. All convolutions were followed by a Leaky ReLU function [START_REF] Maas | Rectifier nonlinearities improve neural network acoustic models[END_REF] as non-linear activation with alpha=0.3 and convolutional filters were initialized with the Glorot uniform technique [START_REF] Glorot | Understanding the difficulty of training deep feedforward neural networks[END_REF].

For designing architectures, some arbitrary rules were followed to limit the complexity of architectures:

• The number of output feature maps of convolution has to be the same in the encoder and decoder at the same level, except for the output;

• The number of output feature maps of convolution has to be crescent with level depth;

• The number of feature maps rapidly augments for the first levels up to 80 and then slowly augments. The 4 and 5 leveled versions are not illustrated for clarity purposes but continue as in Fig. 2. The numbers of the different feature maps corresponding to each level can be found in Table 1. The deep learning part is developed with Keras [START_REF] Chollet | Keras[END_REF] and Tensorflow [START_REF] Abadi | TensorFlow: Large-scale machine learning on heterogeneous systems[END_REF] backend; the models are all trained with the Dice score loss and the Adam optimizer [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF]; the learning rate is set to 0.001 and the learning is stopped after 20 epochs without improvements over the test set.

3 Consequences of architectural changes

Training and testing subsets

The original testing set does not include the ground truth as its performances can only be assessed through submission, as described previously in 2.1. However, we needed to evaluate a lot of experiments for assessing architectural choices and did not want to flood the ISBI online leader-board. So, the original training set was split into a sub-training set of 17 exams from 4 different patients and a sub-test set of 4 exams from the remaining patient. All the models of the current section were trained and evaluated on these subsets.

Experiment setup

The experiments were performed to assess the influence of:

• Feature map size change throughout the U-net

• Skip connections

• Augmenting architectures in terms of:

-Depth

-Number of feature maps

To do so, the reference architecture in Fig. 2 and Fig. 3 was mutated. Again for greater clarity, the figures present only the architecture versions with two levels.

Metrics

The task of segmenting MS lesion voxels is a challenging task since only few voxels have to be detected in a large volume. To address this problem this study uses two interesting simple measures:

• Sensitivity = T P P , where TP and P denote true positives and ground truth positives, also known as the recall or True Positive Rate (TPR). Here, this metric measures the aptitude to detect a maximum number of voxel lesions.

• P recision = T P T P +F P , where FP denotes false positives, also known as the Positive Predictive Value (PPV). This metric is used to assess the capacity to detect correct voxels.

The evaluation of MS lesion segmentation is commonly computed by using the Dice score [START_REF] Brosch | Deep 3d convolutional encoder networks with shortcuts for multiscale feature integration applied to multiple sclerosis lesion segmentation[END_REF][START_REF] Mckinley | Simultaneous lesion and neuroanatomy segmentation in multiple sclerosis using deep neural networks[END_REF][START_REF] Feng | A self-adaptive network for multiple sclerosis lesion segmentation from multi-contrast mri with various imaging protocols[END_REF][START_REF] Valverde | One-shot domain adaptation in multiple sclerosis lesion segmentation using convolutional neural networks[END_REF]. This measure can be written as the harmonic mean of precision and sensitivity Equation 1. So, here the Dice score, measures equally the capacity of our predictors to detect a maximum number of voxel lesions and a maximum of correct ones.

Dicescore = 2T P 2T P + F P + F N Dicescore = 2 • P recision • Sensitivity P recision + Sensitivity (1)
As Dice score measure is relevant for assessing segmentation quality, all architectures use it as loss function.

Experiments

Each version of each type of architecture has been trained 5 different times. The plots show the mean performances of these trainings with the 99% confidence interval, which was computed using Bootstrap Methods [START_REF] Efron | Bootstrap methods: another look at the jackknife[END_REF].

The confidence interval is used here to represent the dispersion of performance for one specific version. It helps to evaluate the robustness and stability of the technique. For each different architecture, the segmentation maps are compared with those of the reference architecture (in Fig. 3).

Change of feature map size

Due to our interest in size reduction/increase in the U-net, we performed three experiments:

• Size reduction of feature maps with max-pooling in the encoder path and size increase with simple up-sampling (our reference): Fig. 3.

• Size reduction of feature maps with 3 × 3 × 3 convolution with stride of 2 in the encoder path and size increase with corresponding transposed convolution: Fig. 4.

• No feature map size change: Fig. 5 In the Fig. 6, the couple max-pooling / up-sampling seems to have the best performances for each ar- However it seems to bring more stability for these versions.

As the max-pooling / up-sampling version surpassed others in terms of Dice score and is slightly simpler than the strided convolution alternative for size reduction, we kept it as a reference for the following experiments.

As depicted here, size reduction is one clue indicating why U-net architectures perform well. One other main feature of U-net is skip-connections. In U-net, skip-connections are made between convolution of the same level in the encoder and decoder. In order to demonstrate the utility of skip-connections, two additional experiments were performed:

Skip-connections

• Without skip-connections: Fig. 7.

• Without skip-connections and size reduction (plain architecture): Fig. 8 Without skip connections, the quality of segmentation seems to collapse with depth in Fig. 9. Surprisingly, plain architectures (without skip connections and any change of feature map size), do not collapse with depth and performances are only slightly below the reference. Furthermore, compared to architecture without size change performances (Fig. 6), plain architecture performs better without skip-connections.

The previously analyzed architecture choices concerned structure, and the reference structure seemed the best. The following section focuses on the complexity of models.

On augmenting architecture

Architectures are augmented by adding more convolutional layers and by adding more feature maps.

More convolutional layers

As in the U-net, an architecture with two convolutional layers by level (Fig. 10) is tested in this experiment. In Fig. 11, doubling the number of convolutional layers gives acceptable results for the first two points but induces a large decrease of performance for the last two points in addition to having a very large dispersion on the last point. This dispersion reveals that this architecture version failed for some trainings. This indicates that it is not stable and not very reproducible.

However, interestingly, in Fig. 12, with a smaller number of parameters, the two convolution by level architecture surpasses the reference, but with more parameters, the performances collapse.

More feature maps

The original U-net uses a larger amount of feature maps than here, ans consequently to ensure that our choice was acceptable, we performed additional experiments in order to see the influence of augmenting this number. Obviously, adding more feature maps increases the number of learnable parameters without changing the depth. Two different numbers of feature maps are evaluated, as detailed in Table 2:

• Beginning with 9 feature maps: Fig. 14 Figure 15: The effect of augmenting the number of feature maps with confidence interval. Slightly augmenting the number of feature maps improves segmentation mostly for smaller models, and generally improves stability. However, augmenting this number excessively may cause a loss of performance.

In Fig. 15, adding more feature maps, and so increasing the number of parameters, helps the CNN to perform a better segmentation for the shallower versions. In addition to that, it also seems to limit the dispersion of results, so it seems to help to obtain more robust learning models.

Interestingly, the version beginning with 6 feature maps seems to be better than the version beginning with 9 feature maps, which has more learnable parameters. The number of parameters has to be sufficient, but this number should not be too high in order to deliver the best performances.

We firstly thought that beginning with only 3 feature maps would not be enough to capture every brain texture detail. The last points of Fig. 15 indicates that with a sufficient number of parameters, beginning with only 3 feature maps was completely equivalent to beginning with more than 3.

Complexity and performances

In Fig. 16, we observe the influence of the depth of neural network on the Dice score. For almost all experiments, there is improvement with depth up to 7 convolutional layers and then a plateau. Almost all architectures converge to a mean Dice score around 0.6-0.7. This convergence seems to appear roughly from 5-7 convolutions.

The best Dice score is obtained with 7 convolutions (4 levels) with architecture beginning with 6 feature maps.

For two experiments, there is a collapse of performance with depth.

Fig. 17 demonstrates similar results for the number of learnable parameters. The convergence of performance is easier to see in this plot. This convergence seems to appear with approximately 100,000 learnable parameters, and our best Dice scores are with approximately 270,000 learnable parameters. The experiment with two convolutions per level delivers a better performance than others with the same number of parameters but rapidly collapses.

Sensitivity and precision

As described in 3.3, the predictor has to compromise between its sensitivity (its aptitude to detect the maximum correct voxels) and its precision (its ability to detect only true lesion voxels).

Figure 18: Sensitivity depending on the number of convolutional layers (A). Precision depending on the number of convolutional layers (B). Sensitivity of segmentation is far less improved than precision with bigger models.

Fig. 18A presents the sensitivity of all our architecture versions. It appears that sensitivity seems to converge at approximately 0.6. Some architectures reach the same sensitivity with only three convolutional layers.

Fig. 18B, the predictors seem to converge to a precision of more than 0.8. However, these levels are only reached after at least five convolutional layers. Furthermore, increasing model complexity benefits more to precision than to sensitivity.

These experiments indicate that:

• Reaching top level sensitivity requires fewer convolutional layers than with precision.

• Tested CNNs tend to be more precise than sensitive.

Segmentation visualization

Segmentation visualization can help find indices on the true nature of algorithm segmentation. In this part, only a 2 -dimensional slice of segmentation for one test exam is presented, although the algorithm generates 3-dimensional segmentation.

On FLAIR images, lesions appear as hyper intensities. On the example images in Fig. 19 and 20, there are periventricular lesions. The presence and number of this type of lesion is taken into account in the McDonald criteria [START_REF] Thompson | Diagnosis of multiple sclerosis: 2017 revisions of the mcdonald criteria[END_REF]. In the figures below, we can visually compare the mean segmentation maps performed by different architectures.

In Fig. 19, the segmentation of each version of the reference architecture is shown. All segmentation maps are similar, but this is not the case for the two leveled version. The latter is the shallowest version with the smallest number of learnable parameters. This version tends to segment any hyper-intensity with fewer considerations for more intense texture of the healthy cortex. In Fig. 20, it is quite clear that the best segmentation versions of each architecture type are very similar.

Globally the same hyper-intensities are detected by the best versions, whatever the architecture.

We also observe, that for each CNN prediction, segmentation maps are similar in both predictions, although ground truth maps are different. Segmentation 2 tends to highlight slightly more voxels than segmentation 1.

The segmentation predictions seem here to slightly overestimate lesions near the right occipital right horn of the lateral ventricle (in the bottom left part of images). In our training set, and for MS in general, periventricular lesions are much more represented than other types of lesions and some are very large. It is possible that, regarding the training set, the CNNs tend to be more sensitive to hyper-intensities near the ventricles.

Assessment of design choices

Feature map size change

Our results tend to show that adding feature map size reductions in the encoding path as well as feature map size increases in the decoding path improves the CNN performances. In other words, the conventional encoder and decoder model is relevant for segmentation.

Empirically, we showed that learning this feature map size change with strided convolutions gave no improvements in our experimental setup. The couple max-pooling and up-sampling was in practice better. These transformations are predefined and do not need to be learned, and this should simplify the learning process.

The max-pooling is commonly used in CNNs in general [START_REF] Zeiler | Stochastic pooling for regularization of deep convolutional neural networks[END_REF] and is known for creating position invariance. Max- pooling decreases the size of its inputs, reduces complexity and helps to have fast convergence, by selecting strong features bringing generalization improvements [START_REF] Nagi | Max-pooling convolutional neural networks for vision-based hand gesture recognition[END_REF]. Up-sampling transformations have been shown to avoid checkerboard artifacts compared to strided transposed convolution [START_REF] Isensee | Brain tumor segmentation and radiomics survival prediction: Contribution to the brats 2017 challenge[END_REF].

However, feature map size change is not the only design choice that makes U-nets so widely used for segmentation.

Skip-connections

One key element of U-net is the use of long skip-connections between the encoder and the decoder. Skip connections are known for helping gradient to flow in deep neural networks, to allow gain of performance even with a very deep architecture and a faster convergence [START_REF] Drozdzal | The importance of skip connections in biomedical image segmentation[END_REF][START_REF] Zagoruyko | Wide residual networks[END_REF].

Interestingly, in experiments, without feature map size change, skip connections are not needed. In addition, compared to plain architecture, they disturb segmentation. This can be explained by the fact that max-pooling is also known for causing overfitting [START_REF] Zeiler | Stochastic pooling for regularization of deep convolutional neural networks[END_REF][START_REF] Graham | Fractional max-pooling[END_REF]. In the specific case of U-net, skip-connections may resolve the overfitting issues. The previously described max-pooling gain can thus be obtained. (Fig. 17)

Complexity and performances

[29] [48] [49] ∼ 240k ∼ 270k ∼ 470k ∼ 29M < 75M

Table 3: Number of parameters of some other existing methods

It is interesting to notice that there seems to exist a minimum number of necessary layers or parameters to perform our specific task. According to our experiments, we obtained our best performances with approximately 270 000 parameters, which is not the lowest number of parameters, compared to other existing approaches (see Table 3). This limit seems much lower than what can be found in the very deep and complex models used in natural image classification. One can argue that this extremely low need of parameters derives from the fact that the task of segmenting MS lesions on FLAIR images is quite simple since the inputs are very similar to each other. With brain MR images and preprocessing, the problems of pose or lighting, common in natural images, are very limited or null here.

In their work, Bianchini et al. [START_REF] Bianchini | On the complexity of neural network classifiers: A comparison between shallow and deep architectures[END_REF] and Bengio et al. [START_REF] Bengio | Scaling learning algorithms towards ai[END_REF], indicate that deep neural networks implement more complex tasks with the same resources by augmenting depth. This phenomenon is regularly cited, such as in Zagoruyko et al. [START_REF] Zagoruyko | Wide residual networks[END_REF] and He et al. [START_REF] He | Deep residual learning for image recognition[END_REF] and explains that very deep neural networks are targeted for state-ofthe-art performances. Our empirical observations are in accord with this principle, since doubling convolutions for one level allows good performances to be delivered with only about 40,000 parameters (Fig. 12).

In some experiments, we also identified a descending of performances when complexity is too high, also observed by He et al. [START_REF] He | Deep residual learning for image recognition[END_REF]. This can be explained by the curse of dimensionality, as it is also applicable to the number of parameters [START_REF] Bengio | Scaling learning algorithms towards ai[END_REF], but also by the vanishing gradient as deeper architectures seem to lose performance more quickly than the shallower architectures with the same number of parameters.

For almost all experiments we identified a convergence of performances from a given complexity of the model with a plateau of performances. This phenomenon is interesting as it indicates that the best qualities of segmentation obtained in experiments is reached at a given complexity and augmenting it has not improved results significantly in our experiments. As suggested by He et al. [START_REF] He | Deep residual learning for image recognition[END_REF], with more complexity and additional regularizers to avoid fall of performance described in the paragraph above, a new plateau with better performances, closer to the radiologist analysis, could be reached.

Sensitivity and precision

We noticed that the shallower models can be sensitive but not precise. Precision is considerably improved with complexity than with sensitivity. Concerning MS lesion segmentation at least, it appears that this segmentation needs few convolutional layers to reach an acceptable level of sensitivity and precision comes with more depth according to our previous analysis [START_REF] Fenneteau | Learning a CNN on multiple sclerosis lesion segmentation with self-supervision[END_REF]. For all our experiments, neural networks seem to find a compromise between sensitivity and precision. They tend to prefer precision to sensitivity, even if the Dice score loss gives as much importance to both metrics. This indicates that with a sufficient number of convolutional layers, it is easier to increase precision than sensitivity.

Dealing with two ground truths

Each tested architecture version predicts two segmentation maps: one for each ground truth mask given with the data set. It appears that both segmentations for all predictors are almost the same. So, tested neural networks make their own consensus and are not able to reproduce the behavior of two different radiologists.

More complex neural networks could do so.

After observing and analyzing the above results, we decided to design and rigorously evaluate a last architecture by taking into account what we had learned.

Applying lessons in one shot

The main objective of the study was to design a minimum architecture in terms of complexity. The aim is to have the best compromise between performances and number of parameters. This is motivated by the fact that the simpler the model is, the simpler it is also to interpret.

The previous experiments give some insights for designing a compact U-net like architecture. We decided to design and test an architecture designed with the following specifications for our MPU-net:

• Skip-connections with max-pooling and up-sampling;

• Four levels with three convolutions per level;

• Beginning with 6 feature maps;

• Approximately 30,000 parameters, which is far less than 270, 000 but should deliver a good performance with high depth and reduce the risk of collapsing performances. By setting the number of the feature maps as presented in Table 4 we obtained an architecture with 33,332 learnable parameters and 21 convolutional layers in Fig. 21.

The MPU-net was trained by using the entire ISBI 2015 MS segmentation challenge training set with a random leave-one-subject-out-cross-validation, and was tested on the official testing set. The segmentation performed by the first radiologist was used as ground truth since it was observed to be the closest to the predictions in general, and that using both expert segmentations as ground truth would have produced two similar prediction maps. The segmentation of the test set was submitted and evaluated in the ISBI 2015 MS segmentation online leader-board [START_REF] Carass | Longitudinal multiple sclerosis lesion segmentation: resource and challenge[END_REF]. The online submissions are ranked using the website score weighted by different metrics.

The MPU-net segmentation obtained a score of 90.591 which is comparable to human level segmentation [START_REF] Carass | Longitudinal multiple sclerosis lesion segmentation: resource and challenge[END_REF]. Compared to the found publications also submitting to this challenge (see Table 5), we have achieved acceptable segmentation since we have only used the FLAIR sequence, trained without transfer learning and only on the given ISBI training data set, without artificial data augmentation, dropout [START_REF] Srivastava | Dropout: a simple way to prevent neural networks from overfitting[END_REF] or batch normalization [START_REF] Ioffe | Batch normalization: Accelerating deep network training by reducing internal covariate shift[END_REF] and without taking into account temporal data.

ISBI score Submission information

The segmentation prediction with the MPU-net runs easily on a laptop with 8 GB of memory and an Nvidia Quadro P1000 GPU and takes 12s per brain. In case of deployment in a clinical environment, the use of this architecture would not necessitate a big investment, thus facilitating the adoption of these type of techniques to help radiologists.

Conclusion

With the goal of finding a compact architecture for the segmentation of MS lesions, we performed an empirical study to determine the relevance of some of the choices assumed in the design of CNN architectures in medical imaging and more precisely in our specific segmentation task. This study focuses on a simple adaptation of the famous U-net and assesses the influence of modifications to give some insights about why and when this architecture is relevant.

It appears that, for this lesion segmentation task, there is a rather wide range of complexity of model in terms of number of parameters and number of convolutional layers showing almost the same performances. In other words, a compact model can be equivalent in performance with a more complex one for our specific task and this should also be the case for other tasks. Furthermore, a predictor that is too complex shows a decrease of performance. The minimum complexity of the model can give some insight on the complexity of a given task.

Since the classification of natural images is much more complex than brain lesion segmentation for machines, the minimum complexity of CNNs for our task is far lower that of state-of-the-art classification models, which have many millions of parameters. Also, by adding layers, tested CNNs tend to necessitate fewer parameters to learn.

In given experimental conditions, the use of max-pooling and up-sampling in encoder and decoder was the best method but only with the use of long skip-connections. These connections act as regularizers for avoiding loss of performance due to the complexity of the predictor.

Finally, thanks to all those observations, it has been possible to design a very light architecture for MS lesion segmentation, the MPU-net, that uses FLAIR images only. This architecture appears to deliver a good segmentation quality, comparable to that of the human even if its design and training are in fact very simple as it does not required complex engineering or regularizers and uses only 33,332 parameters.

As the power of a given CNN architecture is often not explained or partly explained in medical imaging, we aimed at defining the reasons for our choices of implementing a U-net like architecture. The present work is an attempt to present, clarify and explain the process of designing a CNN through the example of our specific interest in MS. This study can be extended to many points in this particular case but also to other tasks and domains.

In this work we have presented some of the reasons of the U-net architecture success. We showed that, for this task, with enough convolutional layers, very few parameters and feature maps are needed to reach human level analysis. Designing such efficient light architecture would simplify the use of artificial neural networks in hospitals by not requiring expensive servers. This could also help to explain CNN learned representations [START_REF] Samek | Towards explainable artificial intelligence[END_REF] in addition to other types of interpretability, and thus could increase trust [START_REF] Lipton | The mythos of model interpretability[END_REF] and lead to the adoption of deep learning methods in medical imaging.

Disclosures

Authors have no conflicts of interest to disclose.

Figure 1 :

 1 Figure 1: Patch size (in red) and lesion size (in green). Axial view at the left and sagittal view at right. Pictures are not taken from the same patients and are not in the same location

Figure 2 :

 2 Figure 2: A) Two leveled and B) three leveled versions of the reference architecture. The size of output feature maps is written vertically in blue at each level and the number of feature maps is written in red below them.

Figure 3 :

 3 Figure 3: The two leveled version of the reference architecture used in experiments.

  chitecture variation. For each version, it gives about 0.1 Dice score improvement, compared to architectures without size change. The feature map size change with convolution and transposed convolution is equivalent to the max-pooling / up-sampling only for the two last versions, with the cost of adding one convolutional layer.

Figure 4 :

 4 Figure 4: The two leveled version of the two strided convolution architecture.

Figure 5 :

 5 Figure 5: The two leveled version of the architecture without feature map size change.

Figure 6 :

 6 Figure 6: Feature map size change influence with confidence interval. Feature map size change improves segmentation. The couple max-pooling / up-sampling (reference) seems to have better performances with fewer convolutional layers than stride convolutions.

Figure 7 :

 7 Figure 7: The two leveled version of the architecture without skip-connections.

Figure 8 :

 8 Figure 8: The two leveled version of plain architecture.

Figure 9 :

 9 Figure 9: Skip connection study with confidence interval. Skip-connections avoid performance collapsing with feature map size change.

Figure 10 :

 10 Figure 10: The two leveled version of the two convolutions by level architecture.

Figure 11 :

 11 Figure 11: The effect of doubling the number of convolutional layers with confidence interval. Doubling convolutions rapidly lead to instability.

Figure 12 :

 12 Figure 12: The effect of doubling the number of convolutional layers on the number of parameters with confidence interval. Doubling convolution can reduce the number of required learnable parameters, but rapidly loss stability with increasing complexity.

Figure 13 :

 13 Figure 13: The two leveled version of the architecture beginning with 6 feature maps.

Figure 14 : 2 :

 142 Figure 14: The two leveled version of the architecture beginning with 9 feature maps.

Figure 16 :

 16 Figure 16: Dice mean of each experiment in function of the number of convolutional layers. Acceptable performances appear from 5 convolutional layers only, but adding more layers slightly improves then decreases the quality of segmentation.

Figure 17 :

 17 Figure 17: Dice mean of each experiment in function of the number of parameters to learn. Augmenting the number of parameters up to 300,000 for the given U-net like architectures is not necessary.

Figure 19 :

 19 Figure 19: Mean segmentation of all versions of the reference. From the three to five leveled versions, segmentation is similar. The two leveled version has more false positives.

Figure 20 :

 20 Figure 20: Mean segmentation of the best versions of all experiments. All segmentations of the best predictors are similar, and close to ground truth. However, none of them are perfectly matching ground truth.

Figure 21 :

 21 Figure 21: The proposed MPU-net architecture with 33,332 learnable parameters and 21 convolutional layers.

  al., including the registration and resampling steps. The original size of FLAIR images before preprocessing were 256 × 256 × 35; 70 voxels with voxel size of 0.8281 × 0.8281 × 4.4; 2.2 mm 3 .

Table 1 :

 1 Number of feature maps at each level.

	Level 1 Level 2 Level 3 Level 4 Level 5
	3	9	27	81	99

  Roy et al. Best tested architecture Valverde et al. Zhang et al. Aslani et al.

	[34]

Table 4 :

 4 Number of feature maps at each level.

	Level 1 Level 2 Level 3 Level 4
	6	7	8	9

Table 5 :

 5 Known published attempts to ISBI online MS lesion segmentation.

	Submission year

available at https://smart-stats-tools.org/lesion-challenge


Martin Blanchard

Matthieu Martin

Philippe Quétin

Philippe Delachartre
email: delachartre@creatis.insa-lyon.fr

Quantitative Comparison of 3D Freehand Ultrasound and MRI Images of the Neonatal Brain

Keywords: ultrasound, MRI, preterm neonates, brain imaging, brain structure comparison

Premature neonates' care can be improved by a quantitative evaluation of brain structures. In current clinical practice, first-line diagnosis is done qualitatively with 2D cranial ultrasonography (cUS) images. These patients would benefit from an evolution to a quantitative analysis based on 3D cUS. A way to obtain high quality 3D cUS images is to use a reconstruction algorithm based on the clinician acquisition motion. In this paper we assess the accuracy of such reconstruction by comparing brain structures between MRI and 3D renconstructed cUS. This comparison was performed based on manual contours, we obtained a mean Dice value of 0.72 ± 0.05 for thalami and ventricles and a mean volume error of 10 ± 5.7%. In addition, the contour interpolation method that we used significantly improved Dice and volume error compared to nearest neighbor approach.

I. INTRODUCTION

Preterm births represents 10% of mondial births (approximately 15 millions babies per year). These babies are prone to complications such as cerebral palsy or neurodevelopmental disorders [START_REF] Arpino | Preterm birth and neurodevelopmental outcome: a review[END_REF]. To estimate theses risks a qualitative neurological imaging checkup is routinely performed after birth with 2D freehand cranial ultrasonography (cUS). Magnetic Resonance Imaging (MRI) is also performed to look for White Matter Injuries (WMI) in the case of great perterms or if cUS reveals some abnormalities.

Advanced MRI sequences have been developed in order to get biomarkers of neurodevelopment but this kind of MRI is done only in few research centers. In any case, MRI flaws are its accessibility and the fact that it can underestimate severe cavitary lesions, as well as moderate lesions such as Punctuate White Matter Lesions (PWML) [START_REF] Martines-Biarge | MRI Based Preterm White Matter Injury Classification: The Importance of Sequential Imaging in Determining Severity of Injury[END_REF].

Moreover, technological progress in ultrasound has enabled an easier description of hyperechoic moderate lesions of the white matter (WM) such as gliotic nodules (suggesting presence of PWML) and to propose a new classification of WMI [START_REF] Agut | Preterm white matter injury: ultrasound diagnosis and classification[END_REF].

Our current proposition leans on a 3D cUS obtained by reconstruction after a 2D freehand cUS acquisition which enables the evolution to 3D quantitative cUS.

To get cUS volume, a 3D reconstruction algorithm was implemented by [START_REF] Martin | Automatic Segmentation of the Cerebral Ventricle in Neonates Using Deep Learning with 3D Reconstructed Freehand Ultrasound Imaging[END_REF]. This algorithm takes a pile of 2D cUS images as input and provide a 3D spatially coherent volume as output. As, this algorithm considered the doctor's movement as uniform during all the acquisition, there is a need to assess its efficiency by comparing the reconstructed brain structures with an acquisition from another modality. 3D cUS can also be achieved by tracking the probe like in [START_REF] Herickhoff | Low-cost Volumetric Ultrasound by Augmentation of 2D Systems: Design and Prototype[END_REF].

Comparisons between MRI and 3D cUS have already been made in the past but rarely on cerebral imaging. To the best of our knowledge, only one study by Boucher et al. [START_REF] Boucher | Computer-aided lateral ventricular and brain volume measurements in 3D ultrasound for assessing growth trajectories in newborns and neonates[END_REF] compared cUS and MRI contours but only for ventricles.

In this paper, we developed a pipeline to measure the similarity between several cerebral structure in 3D cUS and MRI: cerebral ventricles, thalami and corpus callosum. To the best of our knowledge, this has never been done for thalami and corpus callosum. Registration between cUS and MRI has already been implemented by Fuerst et al. [START_REF] Fuerst | Automatic ultrasound-MRI registration for neurosurgery using the 2D and 3D LC2 Metric[END_REF] but on whole volumes rather than contours of structures. Our study therefore differs because it does not try to fit MRI to US and vice versa but only to directly measure the difference between the cerebral structures in order to evaluate our reconstruction pipeline accuracy.

II. METHOD

A. Data Acquisition and data segmentation cUS data were acquired on two patients through the anterior fontanel with an Acuson Siemens 9L4 multi-D matrix transducer. In order to get 3D Us images, the pile of 2D images from the cUS exam was processed with the 3D reconstruction pipeline proposed in [START_REF] Martin | Automatic Segmentation of the Cerebral Ventricle in Neonates Using Deep Learning with 3D Reconstructed Freehand Ultrasound Imaging[END_REF]. On the same day, T1-weighted and T2-weighted MRI sequences were performed with a Philips 3T Ingenia. Pixel resolution of our images can be found on Table .1.

Cerebral ventricles and thalami were manually annotated by a paediatrician. These structures are of major interest in our study because PWMLs are alongside the ventricles [START_REF] Raybaud | The Premature Brain: Developmental and Lesional Anatomy[END_REF] and thalami volume has been proven to be negatively correlated with lesion load [START_REF] Tusor | Punctate White Matter Lesions Associated With Altered Brain Development And Adverse Motor Outcome In Preterm Infants[END_REF]. Because there were many slices in cUS (a mean of 235 slices per structure per volume, compared to 45 slices per structure per volume for MRI), the specialist only segments one among four images, which still took two 2 hours per structure on average. The cerebral structures were segmented on T1-weighed or T2-weighted MRI images, depending on which sequence they were visible.

The contours were used as inputs for the comparison pipeline proposed in this paper. An example of manual segmentation is given on Fig 1.

B. Comparison of the brain structures in US and MRI

To compare brain structures between 3D cUS and MRI we developped a pipeline which enable to obtain complete segmentation in the US volume and which to register the contours drawn in US and MRI images. The obtaining of full segmentation in 3D cUS volume is summarized in Fig. 2. The steps of this pipeline, which will be described more precisely in the next section, are:

C. Pipeline step description

Interpolation

In order to interpolate contours in all slices located between two manually segmented images, interpolated distance maps to the border of the contours were used.

Let Ω i be the set of points representing the manual segmentation of a given structure on a slice S i . Each point x map of the signed distance map m i associated to S i was calculated as follow :

x map = d(x, ∂Ω) if x ∈ Ω -d(x, ∂Ω) if x ∈ Ω (1)
where ∂Ω defines the boundary of Ω, Ω the complement of Ω and d is defined such that :

d(x, ∂Ω) = min y∈∂Ω d(x, y) (2)
Given an empty slice S i+k between two segmented slices S i and S i+e , the distance map m i+k , k ∈ [|0, e|], was calculated with equation 3 as follows:

m i+k = m i × e -k e + m i+e × k e . (3)
A threshold was finally applied to the distance maps, all negative values were put to 0 and all positive values to 1.

Registration

Given our two volumes respectively described by f (x, y, z) and g(x, y, z), we estimate the transformation Ψ(x, y, z, q)with q = (t x , t y , t z , Θ x , Θ y , Θ z ), parameters of the transformation -by minimizing the following square error given by equation 4:

H(q) = x,y,z [f (x, y, z) -g(Ψ(x, y, z, q))] 2 . ( 4
)
This loss was used because of the binary nature of the volume. H was minimised using gradient descent and q was initialized at q 0 = (0, 0, 0, 0, 0, 0). At each step k, the gradient ∇H(q k ) was computed, if it was under a threshold = 10 -6 , the minimisation was stopped, otherwise q k+1 was calculated as follows:

q k+1 = q k -α∇H(q k ).
(

) 5
with α = 0.001 the learning rate. The maximum number of iterations was set to M = 150.

Dice and volume calculation

To evaluate the accuracy of our pipeline, the difference between the segmentation in cUs and MRI volumes was measured with Dice, which is the gold-standard for measuring the similarities between 2 contours. Given two sets E and F representing segmentation, Dice was calculated as follows:

Dice(E, F ) = 2 × card(E ∩ F ) card(E) + card(F ) . ( 6
)
In addition, we calculated the structure volumes and the relative volume error between two structures:

SE(V M RI , V CU S ) = |V M RI -V CU S | V M RI . ( 7
)
Where |.| is the absolute value and V M RI and V cU S respectively correspond to the volume measured in MRI and cUS volumes. These volumes were calculated by multiplying the pixel volume by the number of pixel contained in the structure.

The pipeline was implemented with Python, using sim-pleITK [START_REF] Beare | Image Segmentation, Registration and Characterization in R with SimpleITK[END_REF].

III. RESULTS AND DISCUSSION

The similarity between cUS and MRI contours was measured on three cerebral structures: ventricles, thalami and corpus callosum. Table II presents A mean Dice of 0.72 ± 0.05 was obtained for thalami and ventricles, which is encouraging considering the low resolution of most of the MRI scans. A Dice of 0.44 was found in the case of the corpus callosum which was under our expectations but can be explained by an acceleration during the cUS acquisition which resulted in a misrepresent corpus callosum (Fig. 3). This shows the need for a probe tracking during acquisition. The Ventricle volume error was 5.3 ± 1.7% which is similar to the values reported by [START_REF] Boucher | Computer-aided lateral ventricular and brain volume measurements in 3D ultrasound for assessing growth trajectories in newborns and neonates[END_REF] and the mean Dice for this structure was 0.68 ± 0.03. Visual results can be seen on Fig. 4. Even if thalami volume error was very high, Dice was still very satisfying (0.8 ± 0.05). It is also important to note that thalami segmentation is very difficult and therefore can result in a higher volume error. Visual results can be seen on Fig. 5. In order to assess the accuracy of the proposed distance map method to interpolate the segmentation in cUS volumes, we tried the nearest neighbor interpolation as an alternative method. Comparison for the LV contours of Patient #1 are given in Table III. These results show that our interpolation method provides a better volume approximation and a better Dice. This means that it was better at reconstructing the contours in the empty slices.

Apart from thalami which presents great Dice results, performances of our pipeline were limited by the resolution and the number of slices in MRI volumes. Nevertheless, a decent Dice of 0.72 as well as a small volume error of 3 % were obtained in the case of LV for the MRI with the highest number of slices and the most isotropic voxels (T1-weighted MRI of Patient #1).

IV. CONCLUSION

In this study, we developed a pipeline to evaluate the similarities between 3D cUS and MRI contours of structures such as ventricles, corpus callosum and thalami. To the best of our knowledge this had never been done in the case of corpus callosum and thalami. The best Dice was obtained by the thalami and LV gave us a good Dice and the lowest volume error. These results are very encouraging for the use of 3D cUS as a high-resolution alternative imaging modality to cerebral MRI in the case of preterm babies.

In a future work, MRI acquisitions with a higher resolution will be performed and our database size will be increased. Moreover, we also plan to improve the 3D US reconstruction algorithm accuracy by tracking the probe speed and angle.

Fig. 1 .

 1 Fig. 1. Contours (Green: Thalami, Red: Ventricles, Yellow: Corpus Callosum) drawn on a) T1-weighted MRI, b) T2-weighted MRI, c) 3D cUS.

Fig. 2 . 4 )

 24 Fig. 2. Summary of our reconstruction pipeline.

  the Dice and Volume error results for two different patients, Patient #1 with T1 and T2weighted MRI and Patient #2 with only T2-weighted MRI.

Fig. 3 .

 3 Fig. 3. Comparison of corpus callosum from Patient #1 (Red: T1-weighted MRI ; Green: 3D cUS). Arrows point to the body of the corpus callosum to highlight the shape difference between cUS and MRI.

Fig. 4 .

 4 Fig. 4. Comparison of ventricles from Patient #1 (Red: T1-weighted MRI ; Green: cUS). Dice: 0.72 ; Volume Error: 3%.

Fig. 5 .

 5 Fig. 5. Comparison of thalami from Patient #1 (Red: T1-weighted MRI ; Green: cUS). Dice: 0.85 ; Volume Error: 18%.

TABLE I SUMMARY

 I

	#1	T1	0.75 x 0.84 x 0.75	319
	#1	T2	0.375 x 2.5 x 0.375	85
	#2	T2	1.031 x 1.1 x 1.031	43
	All	cUS	0.16 x 0.16 x 0.16	≈ 600

OF PIXEL RESOLUTION OF OUR SCANS (A: AXIAL ; S: SAGITTAL ; C: CORONAL). Patient Exam Resolution (AxSxC) (mm) Slices Number (A)

TABLE III DICE

 III AND VOLUME ERROR RESULTS FOR TWO DIFFERENT TYPES OF INTERPOLATIONS ON LV OF PATIENT #1

	Interpolation	Dice	Volume Error
	Nearest Neighbor	0.63	8%
	Distance Maps	0.72	3%

ACKNOWLEDGMENT

This work was performed within the framework of the LABEX CELYA (ANR-10-LABX-0060) and PRIMES (ANR-11-LABX-0063) of Universite de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). We would like to thank Dr. Borhane Slama, the innovation and clinical research commission president of CH Avignon, and the CH Avignon direction for their support to this research.


Tron C a , Lemaitre F a , Boisteau E b Le Sourd

Dr Camille Tron
email: camille.tron@chu-rennes.fr

When helping the minority of patients may hurt the majority: the case for DPD phenotyping and 5-fluorouracil therapeutic drug monitoring

    When helping the minority of patients may hurt the majority: The case for DPD phenotyping and 5-fluorouracil therapeutic drug monitoring C Tron, F Lemaitre, Emeric Boisteau, S Le Sourd,

Dear Editor, 5-fluorouracil (5-FU) is still the backbone in some cancer treatments particularly in digestive cancers.

The drug is associated with potential severe adverse events leading in some cases in substantial morbidity and mortality. As the drug is essentially catabolized through an enzymatic process mediated by dihydropyrimidine deshydrogenase (DPD), DPD deficiency is thought to be the main mechanism leading to 5-FU accumulation and toxicity [START_REF] Goirand | How can we best monitor 5-FU administration to maximize benefit to risk ratio?[END_REF]. Identifying patients with DPD deficiency and notably patients with complete deficiency, is then a relevant approach to limit the risk of severe adverse event.

Recently, the European Agency for Medicine has therefore recommended DPD deficiency screening prior a treatment with fluorouracil or one of these derivatives [START_REF]EMA recommendations on DPD testing prior to treatment with fluorouracil, capecitabine, tegafur and flucytosine[END_REF].

The rate for complete DPD deficiency in Caucasian population is estimated to up to 0.5% to 1%, while up to 9% of patients may have some kind of partial enzymatic deficiency [START_REF]EMA recommendations on DPD testing prior to treatment with fluorouracil, capecitabine, tegafur and flucytosine[END_REF]. Thus, considerable effort should be undertaken to recognize these patients before any initiation of 5-FU treatments. Genotyping approach allows identifying patients carriers of one the four most common allelic variants associated with a loss or a decrease of function of DPD. Although frequencies of the variants of interest are low, these pharmacogenetics tests could be useful in some cases to explain an enzymatic deficiency.

However, on a large cohort, genotyping was shown to be poorly predictive of DPD deficiency [START_REF] Pallet | A comprehensive population-based study comparing the phenotype and genotype in a pretherapeutic screen of dihydropyrimidine dehydrogenase deficiency[END_REF].

Actually, the phenotyping approach appears more appropriate to screen DPD deficiency. Because DPD catabolized uracil into its metabolite, dihydro-uracil, measuring uracil plasma level before any treatment initiation is the recommended phenotyping method aiming at preventing the drug toxicity at the first treatment cycle. In France, a concentration threshold of 16 ng/mL of uracil in plasma is proposed to categorize patients with potential partial DPD deficiency while a concentration above 150 ng/mL prohibits any 5-FU treatment. For patients with uracil plasma level between 16 and 150 ng/mL, caution is required and the treatment dosage may be decreased to prevent drug toxicity [START_REF] Ansm | Recherche de déficit en dihydropyrimidine déshydrogenase en vue de prévenir certaines toxicités sévères survenant sous traitement comportant des fluoropyrimidines[END_REF][START_REF] Loriot | Dihydropyrimidine déhydrogenase (DPD) deficiency screening and securing of fluoropyrimidine-based chemotherapies: Update and recommendations of the French GPCO-Unicancer and RNPGx networks[END_REF]. This situation can be frequent since a recent study reported that 15 % of the patient of its cohort (n= 526) had uracil concentration within this range [START_REF] Tafzi | Phenotyping of uracil and 5-fluorouracil metabolism using LC-MS/MS for prevention of toxicity and dose adjustment of fluoropyrimidines[END_REF]. As a result, an important part of patients treated with 5-FU receives a reduced drug dosage.

A c c e p t e d M a n u s c r i p t

However, it is known that there is a wide inter-individual variability of 5-FU exposure and that in digestive cancer, most of patients treated with 5-FU are underexposed to the drug even when treated with the standard regimen [START_REF] Beumer | Therapeutic Drug Monitoring in Oncology: International Association of Therapeutic Drug Monitoring and Clinical Toxicology Recommendations for 5-Fluorouracil Therapy[END_REF]. At usual dosage, around 50% of patients displays low drug exposure, when targeting a 5-FU area under the curve of drug concentrations (AUC) exposure of 20-30 ng.h/mL [START_REF] Beumer | Therapeutic Drug Monitoring in Oncology: International Association of Therapeutic Drug Monitoring and Clinical Toxicology Recommendations for 5-Fluorouracil Therapy[END_REF]. Consequently, the risk for low 5-FU exposure might be further increased due to the DPD phenotyping. It is of utmost importance since 5-FU exposure has been related to overall response rate in a randomized multicenter study conducted in metastatic colorectal cancer patients [START_REF] Gamelin | Individual Fluorouracil Dose Adjustment Based on Pharmacokinetic Follow-Up Compared With Conventional Dosage: Results of a Multicenter Randomized Trial of Patients With Metastatic Colorectal Cancer[END_REF].

The aim of the present study was to assess the relationship between DPD phenotype and the 5-FU exposure during the first treatment cycle.

We included in the analysis patients treated for digestive or head and neck cancers in Rennes University Hospital and the Eugène Marquis Anticancer Center, with a regimen including continuous infusion of 5FU. Data were collected from April 2019 to June 2020 based on the routine follow-up of patients. The study was approved by the local ethical committee (authorization n° 20.98). DPD phenotyping was performed by measuring uracil concentration in plasma (uracilemia) before the chemotherapy according to national recommendations [START_REF] Ansm | Recherche de déficit en dihydropyrimidine déshydrogenase en vue de prévenir certaines toxicités sévères survenant sous traitement comportant des fluoropyrimidines[END_REF][START_REF] Loriot | Dihydropyrimidine déhydrogenase (DPD) deficiency screening and securing of fluoropyrimidine-based chemotherapies: Update and recommendations of the French GPCO-Unicancer and RNPGx networks[END_REF]. Uracilemia was measured using a validated high performance liquid chromatography tandem mass spectrometry method in the Rennes University Hospital laboratory. At the first 5-FU cycle (C1), concentration of 5-FU in plasma was determined in a sample collected during the infusion (between 18h after the start of the infusion and 4h before the end) in order to measure 5-FU at steady state according to Adjei et al. [START_REF] Adjei | Comparative Pharmacokinetic Study of Continuous Venous Infusion Fluorouracil and Oral Fluorouracil With Eniluracil in Patients With Advanced Solid[END_REF]. Because 5-FU is very unstable ex-vivo in the blood sample (due to the remaining DPD metabolism), a DPD inhibitor was added in the sample immediately after blood withdrawal. Then, 5-FU was quantified by an immunoassay [START_REF] Beumer | Multicenter Evaluation of a Novel Nanoparticle Immunoassay for 5-Fluorouracil on the Olympus AU400 Analyzer[END_REF]. Genotype of DPYD (the gene encoding the DPD) was available when it was requested by clinicians for patients who consented to this analysis. The following demographic and therapeutic parameters were collected routinely and prospectively: age, sex, weight, chemotherapy regimen, dose of 5-FU continuous infusion at C1.

A c c e p t e d M a n u s c r i p t

A total of 42 patients were enrolled in the study. Their characteristics are reported in Table 1. No linear correlation was found between uracil concentration and 5-FU clearance or 5-FU exposure at C1 (Figure 1). Furthermore, sixty-six percent of patients had 5-FU AUC below the therapeutic threshold of 20-30 ng.h/mL at C1. The rate of underexposed patients according to DPD status revealed that 5-FU underexposure trended to be more frequent in patient with partial DPD deficiency than in patients without DPD deficiency (75% vs 57% in uracilemia ≥ 16 ng/mL and < 16 ng/mL respectively. p=0.28, F-test) (Figure 2). Besides, according to the recommendations, all patients with pretherapeutic uracilemia ≥ 16 ng/mL received a decreased dose of 5-FU at C1 (of at least -20%) compared to the protocol-specified dose. In patients without DPD deficiency, only 13% received a decreased dose at C1. Systematic screening of DPD deficiency before any 5-FU (or other fluoropyrimidine) based treatment is crucial to prevent rare but early and highly severe 5-FU related toxicities. In France, this screening is now mandatory by the phenotyping approach based on uracilemia. Indeed, several studies have shown that uracilemia was a surrogate marker of 5-FU early toxicity [START_REF] Loriot | Dihydropyrimidine déhydrogenase (DPD) deficiency screening and securing of fluoropyrimidine-based chemotherapies: Update and recommendations of the French GPCO-Unicancer and RNPGx networks[END_REF]. The range of uracil concentrations associated with partial DPD deficiency is wild (16-150 ng/mL) and to date, no algorithm is available to choose the appropriate starting 5-FU dose based on uracilemia. Thus, it is challenging for clinicians and laboratory scientists to accurately determine the magnitude of the dose decrease to apply at C1. Usually, an empirical reduction of 20 to 30 % of the standard dose is applied for patients with moderate increase of uracilemia (16-40 ng/mL). In the present work we reported that this strategy tended to worsen the proportion of patients underexposed to 5-FU especially when uracilemia was slightly high as the majority of DPD deficient patients from our cohort. Despite differences were not statistically significant, likely due to the small sample size of our cohort, we wanted to alert readers on the potential risk of 5-FU underexposure meaning that more than never patients would benefit of 5-FU plasma concentration measurement as early as C1. The recent work from Chamorey et al. supports this statement, since this team evidenced that patients with high DPD activity (so likely low 5-FU plasma exposure) had poorer overall survival, progression free survival and response rate [START_REF] Chamorey | DPD status and fluoropyrimidines-based treatment: high activity matters too[END_REF]. We admit that a limit of our work is the lack of data regarding patient toxicity A c c e p t e d M a n u s c r i p t at C1. Guidelines clearly state that if a dose reduction was applied at C1, the dose should be increased at the next cycle when the first cycle was well tolerated, in order to maximise the treatment efficacy [START_REF] Loriot | Dihydropyrimidine déhydrogenase (DPD) deficiency screening and securing of fluoropyrimidine-based chemotherapies: Update and recommendations of the French GPCO-Unicancer and RNPGx networks[END_REF]. However, it can be challenging and take several cycles to find the patient's optimal 5-FU dose in this context. It appears much more efficient to monitor 5-FU concentration in plasma at C1 and at the next cycle if needed, since a validated dosage algorithm is available to safely choose dose the increase leading to 5-FU therapeutic exposure [START_REF] Beumer | Multicenter Evaluation of a Novel Nanoparticle Immunoassay for 5-Fluorouracil on the Olympus AU400 Analyzer[END_REF]. Thus, therapeutic drug monitoring of 5-FU is a time saving approach, easy to implement in clinical practice and strongly recommended to optimized and individualized 5-FU dosages [START_REF] Beumer | Therapeutic Drug Monitoring in Oncology: International Association of Therapeutic Drug Monitoring and Clinical Toxicology Recommendations for 5-Fluorouracil Therapy[END_REF]. Hence, to our point of view, the required DPD phenotyping approach aiming at preventing toxicities in patients with deep DPD deficiency should be systematically associated with 5-FU exposure evaluation using therapeutic drug monitoring, otherwise it could be detrimental for the treatment efficacy in a significant proportion of patients who had no toxicity following the first cycle of 5-FU based chemotherapy.

5-FU clearance (mL/h)

Figure 1 :

 1 Figures legends: Figure 1: Relationship between uracilemia and 5-FU clearance (A) or exposure (B) at first cycle. p: p-value pearson correlation test. Clearance was calculated as follow : Dose 5FU continuous infusion (mg) / AUC 5-FU (mg.h/mL).5-FU: 5-fluorouracil; AUC: area under the curve of drug concentrations

Figure 2 :

 2 Figure 2: Percentage of patients with 5-FU AUC values below, within or above the therapeutic range at first cycle depending on the DPD activity status 5-FU: 5-fluorouracil; AUC: area under the curve of drug concentration; DPD: dihydropyrimidine deshydrogenase

A c c e p t e d M a n u s c r i p t

Table 1 : Patients characteristics (n=42)

 1

	(p: 0.24)
	Uracil concentration in plasma (ng/mL)

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.