Alexandre Corazza
email: alexandre.corazza@creatis.insa-lyon.fr

Pauline Muleki-Seya
email: pauline.muleki@creatis.insa-lyon.fr

Abderrahmane Walid Aissani
email: walid.aissani@sorbonne-universite.fr

Olivier Couture
email: olivier.couture@sorbonne-universite.fr

Adrian Basarab
email: adrian.basarab@creatis.insa-lyon.fr

Barbara Nicolas
email: barbara.nicolas@creatis.insa-lyon.fr

Microbubble detection with adaptive beamforming for Ultrasound Localization Microscopy

Keywords:

Ultrasound Localisation Microscopy (ULM) is an imaging framework which consists of following ultrasound contrast agents, microbubbles, in time, on ultrasound images. The three main steps of ULM are: detecting microbubbles by reducing tissue signal, localizing them with subwavelength precision and tracking their trajectories. ULM performances were evaluated in different studies throughout metrics such as localisation accuracy or capacity to filter the tissues. In parallel, adaptive beamforming offers narrower Point Spread Function (PSF) and/or better tissue filtering than delay-and-sum method classically used within ULM. In this paper, the ability of adaptive beamformers to enhance ULM performances is evaluated, with a particular focus on the trade-off between acquisition time and bubble concentration to achieve super-resolution results.

I. INTRODUCTION

ULM is a super-resolution imaging method used to build microvascular map. It has already been applied, for example, on rat [START_REF] Couture | Ultrasound Localization Microscopy and Super-Resolution: A State of the Art[END_REF] and human [START_REF] Demené | Transcranial ultrafast ultrasound localization microscopy of brain vasculature in patients[END_REF] brain, to study its ability to detect or prevent stroke and to better understand brain diseases such as Alzheimer's and Parkinson's. It can also be used to detect tumors [START_REF] Lin | Super resolution contrast ultrasound imaging: Analysis of imaging resolution and application to imaging tumor angiogenesis[END_REF] [START_REF] Lin | 3-d ultrasound localization microscopy for identifying microvascular morphology features of tumor angiogenesis at a resolution beyond the diffraction limit of conventional ultrasound[END_REF] and to evaluate anticancer therapy effects [5] [6]. However, ULM has a limitation due to the trade-off between acquisition time and number of tracked microbubbles (MBs) to map the vascular network. To mitigate this trade-off, this paper explores the possibility of limiting the number of undetected MB based on adaptive beamforming. To sustain the motivation of this work, ULM framework is displayed in Fig. 1a. First, from images beamformed with delay-andsum (DAS) algorithm tissues are filtered with a Singular Value Decomposition (SVD) [START_REF] Demené | Spatiotemporal Clutter Filtering of Ultrafast Ultrasound Data Highly Increases Doppler and fUltrasound Sensitivity[END_REF] to enable MB detection. The step of MB isolation consists in keeping only non-overlapping MBs, requiring to correctly localize their centers. Finally, tracking their trajectories in vessels allows maping the microvascular network. The steps of tissue filtering and MB isolation lead to an information loss as the first one attenuates relatively slow MBs [START_REF] Brown | Investigation of microbubble detection methods for super-resolution imaging of microvasculature[END_REF] and the second one removes the overlapping MBs [START_REF] Couture | Ultrasound Localization Microscopy and Super-Resolution: A State of the Art[END_REF]. Consequently, the choice of the beamforming method could have an important impact on the rest of the ULM framework. For example, it is well-known that adaptive beamformers such as the minimum variance one, also called Capon beamformer, provide a better resolved Point Spread Function (PSF) [START_REF] Asl | Contrast enhancement and robustness improvement of adaptive ultrasound imaging using forward-backward minimum variance beamforming[END_REF]. Due to the improved spatial resolution, MBs that naturally overlap on DAS images, could be separated, and the information loss at the isolation step could be reduced, resulting into more complete vessel map reconstruction, as illustrated in Fig. 1b.

DAS

Other beamforming algorithms like pDAS [START_REF] Polichetti | A nonlinear beamformer based on p-th root compression-application to plane wave ultrasound imaging[END_REF] and iMAP [START_REF] Chernyakova | IMAP Beamforming for High-Quality High Frame Rate Imaging[END_REF] have been shown to attenuate speckle compared to DAS, representing thus good candidates for ULM. In this paper, the influence of these adaptive beamformers is evaluated on simulated and experimental chicken embryo data.

II. MATERIAL AND METHOD

A. Simulated and in vivo datasets

The simulated dataset, provided by the Performance Assessment of Localization Algorithms (PALA) toolbox 1 [START_REF] Heiles | Performance benchmarking of microbubble-localization algorithms for ultrasound localization microscopy[END_REF], corresponds to moving MBs at various velocities and trajectories. The simulation main parameters are given in Tab. I. To enhance the simulation realism, an immobile residual speckle has been added. The ground truth of the MBs positions is available in the toolbox to evaluate detection metrics such as True Positive (TP), False Negative (FN) and False Positive (FP).

The in vivo dataset has been acquired on a chicken embryo with a Verasonics linear probe in plane wave mode. A specific area with bifurcations, which is interesting in the case of ULM, is chosen. Parameters of acquisition and beamforming are given in Tab. I.

B. Beamforming methods

During the acquisition, the emitted plane wave is returned as echoes by scatterers in the environment to image. The first step is to rephase each received echo to isolate the energy along the corresponding backscattered wave. According to the DAS, the second step is to sum the rephased signals, with an eventual weighting vector, to get the corresponding pixel intensity [START_REF] Perrot | So you think you can das? a viewpoint on delay-and-sum beamforming[END_REF]. Adaptive beamforming processes in the same way except for the weighting, which is adaptive and computed from the rephased signals. In this paper, in addition to DAS, three different beamformers are studied in the context of ULM.

• The Capon beamforming [START_REF] Stoica | Spectral Analysis of Signals[END_REF] [15] computes a weighting vector that minimizes the variance of the rephased signal to attenuate eventual disturbing source. In practice, this calculation rule leads to a thinner PSF. • The pDAS beamforming [START_REF] Polichetti | A nonlinear beamformer based on p-th root compression-application to plane wave ultrasound imaging[END_REF] is a generalization of the FD-MAS beamforming [START_REF] Matrone | Filtered delay multiply and sum beamforming in plane-wave ultrasound imaging: Tests on simulated and experimental data[END_REF]. The weighting vector computation is based on the rephased signal autocorrelation.

The motivation is to isolate the constant component whose autocorrelation is higher than noise or speckle component. A parameter p defines the autocorrelation order. In the following, the method is referred to as 2pDAS for p = 2 and 3pDAS for p = 3.

1 available at https://zenodo.org/record/4343435

• The iMAP beamformer [START_REF] Chernyakova | IMAP Beamforming for High-Quality High Frame Rate Imaging[END_REF] considers the rephased signals as the sum of the constant backscattered amplitude and a random noise supposed Gaussian. The objective is to find the mean and the standard deviation of the theoretical Gaussian distribution that maximizes its resemblance with the values of the rephased vector. The effect of this beamformer is thus to increase the constant component relatively to the noise level. In practice, to estimate the Gaussian mean and variance, the algorithm is iterative but only 1 or 2 iterations are enough to obtain good results.

In the following, this method is denoted as 1iMAP for 1 iteration and as 2iMAP for 2 iterations.

C. Ultrasound Localization Microscopy method

The algorithm used to perform ULM is the one provided in the PALA toolbox. The localization method chosen is based on the radial symmetry [START_REF] Parthasarathy | Rapid, accurate particle tracking by calculation of radial symmetry centers[END_REF], since it presents a good ratio between performance and computational cost.

The values of the hyperparameters are given in Table II. For the in vivo dataset, the SVD threshold was chosen by identifying tissue, MB and noise curve pattern on the singular values distribution as explained in [START_REF] Baranger | Adaptive Spatiotemporal SVD Clutter Filtering for Ultrafast Doppler Imaging Using Similarity of Spatial Singular Vectors[END_REF].

III. RESULTS AND DISCUSSION

A. Results on simulated dataset

The raw data resulting from this simulation have been used to reconstruct the images using the different beamformers introduced in the previous section. One image resulting from each beamformer is plotted in Fig. 2, highlighting the characteristics and in particular the potential benefits for ULM of each algorithm. Due to the available ground truth, it is possible to count the detected MBs (TP), missed ones (FN) and the false alarm (FP). A TP is counted if a MB is detected by the algorithm in a radius of λ/4 around the ground truth and a FN is counted if there is no detection in this range. The FP corresponds to detections where there is no simulated MB at a distance of λ/4. Fig. 3 regroups the three metrics for each beamformer. One can see that Capon and 2iMAP allow to detect around 85, 000 more MBs and 50, 000 less false alarm compared to DAS. The pDAS beamformer also helps to detect more MBs, at the cost of more false alarm compared to DAS. This is due to high side-lobes on pDAS images, as it can be seen in Fig. 2, which turn into false MB detections. The 3pDAS beamformer attenuates these side-lobes and thus decreases these errors. Finally, the 1iMAP is only slightly better than DAS, which can be explained by the fact that its iterative process is initalized by DAS.

Fig. 3: Detection metrics for each beamformer

This improved MB detections performance due to adaptive beamformers, in particular Capon and 2iMAP, can be explained by two linked phenomenon. The first one is a better spatial resolution in the lateral and axial directions, due to a thinner PSF. Indeed, it can be seen in Fig. 4 that the distance between localized MBs and ground truth present a thinner distributions, especially for the 2iMAP beamformer, in both lateral and axial directions. The second one is the ability to separate MBs that are overlapped with the DAS. This can be seen in Fig. 5 where the adaptive beamformers (except 1iMAP, for the reason mentioned above) allow an accurate reconstruction of the bifurcation thanks to more individual PSF detected.

B. Results on in vivo

Fig. 6 shows US images of a specific area of chicken embryo with injected microbubbles, highlighting the benefits of adaptive beamforming on experimental data.

The results in Fig. 7 show that Capon is equivalent to DAS. However, pDAS and iMAP allow slow bubble detection in chicken embryo experiment. In particular, one can see bright areas with pDAS and iMAP, which correspond to vessels perpendicular to the imaging plane. From the ultrasound probe perspective, these bubbles are almost stationary. This is due to tissue filtering based on SVD that attenuates slow MBs. The pDAS and iMAP beamformers help to increase the relative intensity of these MBs to make them still detectable even after SVD filtering. This represents an important advantage to reconstruct capillaries (e.g., in tumors) with ULM, where bubbles are relatively slow. However, the adaptive beamformers present missed detections on in vivo data. Thus, in that case, the adaptive beamforming allows to build a complementary ULM map with slow MBs but not a more complete one.

IV. CONCLUSION

In this paper, it has been demonstrated through a simulation study that adaptive beamforming allows to detect more individual MBs and to localize them more precisely in both axial and lateral directions. The main consequence is a better reconstruction of a bifurcation.

Furthermore, the influence of adaptive beamforming in ULM is studied on an in vivo dataset of chicken embryo. This result highlighted the fact that the adaptive beamformers best filtering the tissues allow to detect slow MBs, which is very important as they are usually strongly attenuated by the tissue filtering. However, there is no significant difference between DAS and Capon in the experimental study. A further work to highlight the benefits of Capon would be to apply it on high concentration data with bifurcations to evaluate the trade-off between MB concentration and acquisition time.

  Fig. 1: ULM framework

Fig. 2 :

 2 Fig. 2: Simulated image beamformed with the different beamformers considered (zoom on MBs)

Fig. 4 :Fig. 5 :

 45 Fig. 4: MB localization error distribution for each beamformer

Fig. 6 :

 6 Fig. 6: Chicken embryo data beamformed with several beamformers (zoom on MBs) after SVD filtering

Fig. 7 :

 7 Fig. 7: MB density map on chicken embryo data. All images are normalized by the maximum value of the DAS result.

TABLE I :

 I Acquisition parameters for each dataset

	Parameter	Simulated dataset In vivo dataset
	US frequency	7.8MHz	7.8MHz
	Wavelength λ	197µm	197µm
	Pixel size	λ/2	λ/2
	Framerate	500Hz	400Hz
	Acquisition time	40s	60s

TABLE II :

 II ULM hyperparameters for each dataset

	Parameter	Simulated dataset In vivo dataset
	ROI size	3 pixels	3 pixels
	Number of particles to detect	40 per frame	20 per frame
	SVD cutoff	No SVD	3
	Max linking distance	2	1
	Minimum track length	15	20
	Density map resolution	λ/10	λ/10

ACKNOWLEDGMENTS

This work was supported by the LABEX CELYA (ANR-10-LABX-0060) and LABEX PRIMES (ANR-11-LABX-0063) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). We would like to acknowledge the authors of the PALA toolbox for having made publicly available the ULM Matlab codes and ultrasound datasets.


Alexandre Corazza

Pauline Muleki-Seya

Arthur Chavignon

Olivier Couture

Adrian Basarab

Barbara Nicolas

Adaptive beamforming combined with

Introduction

O Ultrasound Localisation Microscopy (ULM) is a non-invasive method for vascular microstructure imaging which allows to detect abnormalities related to tumors [1],

strokes [2] or brain diseases such as Alzheimer's or Parkinson's [3].

O ULM main steps [4]: O Standard detectors are based on microbubble (MB) intensity [6] or normalized cross-correlation (NCC) [7] to initialize the red regions of interest on Fig. 1(b). MB with intensity lower than the noise level are not detected with the first method and PSF variations alter the NCC performances. Recently, we proposed a new MB detection method based on decision theory to overcome these limits [8].

O The influence of beamforming on ULM with the MB identification method based on decision theory is studied on a rat brain dataset from the PALA toolbox [4].

Method

O Adaptive beamformers selected for high resolution and speckle attenuation:

• Capon: variance minimization [9],
• pDAS: auto-correlation approximation [10],

• iMAP: signal modeled as the sum of a constant component and a random Gaussian noise. Constant component extracted with a maximum a posteriori estimator [11].

O MB identification method based on decision theory [8]:

• intensity and PSF shape independent,

• pixel signal along time dimension modeled as the sum of Gaussian noise and peak corresponding to MB passage,

• adaptive threshold η i,j to isolate peak for each pixel (i, j), depending on a false alarm rate α 0 , noise mean m i,j and standard deviation σ i,j (see Eq. ( 1)).

x i,j (t)

H 1 ≷ H 0 σ i,j √ 2 erf -1 (1 -2α 0 ) + m i,j ∆ = η i,j (1)

Results

O Beamformed images (Fig. 2) → as expected, thinner PSF with Capon, attenuation of noise and speckle with pDAS and iMAP.

O Threshold maps (Fig. 3) → better resolved and new low threshold area with pDAS and iMAP.

O Vascular network maps (Fig. 4) → quite similar but better-detected vessels with pDAS and iMAP.

O Track length statistics (Fig. 5) → equivalent tracking performances.

O Fourier Ring Correlation (Fig. 6) → slight degradation of resolution with adaptive beamformers probably due to noise detection, but not observed on the final images. O In perspective, evaluate these adaptive beamformers on other datasets to generalize this conclusion.

Figure 1 :

 1 Figure 1: Ultrasound Localization Microscopy main steps O Beamforming method highly influence the aspect of ultrasound (US) images: it

Figure 5 :Figure 6 :O

 56 Figure 2(a): DAS


Romain Cazé
email: romain.caze@univ-lille.fr

Alexandra Tran-Van-Minh

Boris S Gutkin
email: boris.gutkin@ens.fr

David A Digregorio
email: david.digregorio@pasteur.fr

Romain D Caz

Demonstration that sublinear dendrites enable linearly non-separable computations

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Dendritic filtering influences the shape and amplitude of postsynaptic potentials depending on the synaptic conductance, dendritic morphology, synapse location and the expression of voltage-gated channels [START_REF] Tran-Van-Minh | Contribution of sublinear and supralinear dendritic integration to neuronal computations[END_REF] . Dendritic properties also influence how multiple synaptic potentials sum, either linearly (if the response amplitude equals the arithmetic sum of the individual synaptic responses), sub-linearly (response amplitude below the sum of the individual responses), or supra-linearly (response amplitude above their sum) [START_REF] Polsky | Computational subunits in thin dendrites of pyramidal cells[END_REF] . This dendrite-specific arithmetic can greatly enhance a neuron's computational abilities [START_REF] Poirazi | Pyramidal Neuron as Two-Layer Neural Network[END_REF] and is thought to be prominent in human neurons [START_REF] Gidon | Dendritic action potentials and computation in human layer 2/3 cortical neurons[END_REF] . Supra-linear summation is thought to underlie active whisker sensation [START_REF] Xu | Nonlinear dendritic integration of sensory and motor input during an active sensing task[END_REF] , generate orientation selectivity [START_REF] Wilson | Orientation selectivity and the functional clustering of synaptic inputs in primary visual cortex[END_REF] , grid cell activity [START_REF] Schmidt-Hieber | Synaptic integrative mechanisms for spatial cognition[END_REF] , and sensory perception [START_REF] Takahashi | Active cortical dendrites modulate perception[END_REF] . In contrast, little is known about the computational advantages imparted by sub-linear dendritic integration [START_REF] Abrahamsson | Thin Dendrites of Cerebellar Interneurons Confer Sublinear Synaptic Integration and a Gradient of Short-Term Plasticity[END_REF][START_REF] Hu | Dendritic Mechanisms Underlying Rapid Synaptic Activation of Fast-Spiking Hippocampal Interneurons[END_REF] . Recent computational studies suggest that sub-linear integration in cortical fast-spiking interneurons could contribute to memory encoding [START_REF] Tzilivaki | Challenging the point neuron dogma: FS basket cells as 2-stage nonlinear integrators[END_REF] .

Our previous theoretical work showed a single dendritic non-linearity (either sub-or supralinear) significantly expands the number of functions a neuron can implement [START_REF] Cazé | Passive Dendrites Enable Single Neurons to Compute Linearly Non-separable Functions[END_REF] .For example, for 8 excitatory uncorrelated inputs, a neuron with a sufficient number of non-linear dendrites (either sub our supralinear) can implement 10 17 more computations (see methods in [START_REF] Cazé | Spiking and saturating dendrites differentially expand single neuron computation capacity[END_REF] for details ). These additional computations are, by definition, a part of the class of linearly non-separable computations (LNSCs). It is interesting to note that passive sublinear dendrites are able to expand the neurons computational capacity on the par with active dendritic nonlinearities, albeit under different synaptic placement conditions (see below).

While LNSCs cannot be implemented by a point neuron model, a neuron with sublinear dendrites can robustly implement an LNSC called the feature binding problem (FBP) (Fig 1). The FBP computation allows a neuron to represent multiple distinct objects, each comprised of independent features. An example of a FBP is given in Figure 1 where the goal is to detect a yellow circle or a green triangle separately by giving an output of 1, but not respond to a yellow triangle or a green circle (Fig 1A). This distinction cannot be done by linearly separating the inputs based on their summed amplitudes. We note that mathematically speaking, aside for the specific feature combinations that must yeild 1 or 0, for the FBP example we consider, there are two feature combinations that do not require specific responses (i.e. two colors or two shapes can give either 0 or 1). Because FBPs can be implemented with only excitatory synapses, we used glutamate uncaging at single synapses to demonstrate this FBP experimentally.

Figure 1. The Feature Binding Problem: A linearly inseparable computation and its implementation in a scatter sensitive neuron.(A) A truth table describing the FBP of two objects with two features each. First column describes presynaptic activity: response of a dendrite is active:1 or not:1. The ntegration column "Int." describes how a neuron dendrites which implement this computation should integrate inputs. Here we define that the a dendrite saturates at 1. Hence for two clustered inputs the response of the dendrite is 1+0, for scattered it is the arithmetic sum 1+1. The output "Out." column shows if a neuron spikes:1 or not:0. We omit some inputs because whatever the response to them this computation would still be a LNSC (see Methods for more details). (B) FBP dendritic implementation: both dendrites must be saturated (saturation threshold of 1 in the square) to trigger neuron's spiking (threshold of 2 in the circle). Because Circle+Green and Triangle+Yellow inputs target the same dendrite, the resulting integration fails to reach the depolarization does not reach the threshold at the soma necessary for the spike. Yet for the two objects the inputs are scattered, both dendrites are saturated and the soma surpasses its threshold. (C) indicates that features activating the same dendrites do not reach threshold and cannot generate a spike, but those features scattered onto the two dendrites generate a somatic spike.

To implement the FBP, supralinear integration requires that the correct feature conjunction for an object cluster on a dendritic section, while feature conjunction that should lead to an absence of response must scatter over the dendritic tree. In contrast, sublinear integration requires the opposite [START_REF] Tran-Van-Minh | Contribution of sublinear and supralinear dendritic integration to neuronal computations[END_REF][START_REF] Cazé | Passive Dendrites Enable Single Neurons to Compute Linearly Non-separable Functions[END_REF] : object related conjunctions that should fire the neuron should scattered on different dendritic segments (or dendrites), irrelevant conjuctions should not scatter. Thus the case where scattered inputs fire the cell and clustered inputs do not is essential for solving the FBP using sublinear dendrites (Fig 1C). Here we used glutamate uncaging and biophysical modeling to show that the sublinear dendrites of cerebellar molecular layer interneurons render them scatter-sensitive, thereby enabling them to implement the FBP.

Results

Cerebellar stellate cells are scatter sensitive

Dendrites of cerebellar stellate cells are thin and integrate synaptic conductances passively [START_REF] Abrahamsson | Thin Dendrites of Cerebellar Interneurons Confer Sublinear Synaptic Integration and a Gradient of Short-Term Plasticity[END_REF] . The high-impedance dendrites generate large local depolarization upon excitatory synaptic activation that reduce the driving force for synaptic currents, resulting in a sublinear summation of postsynaptic potentials when activating multiple synapses [START_REF] Tran-Van-Minh | Differential Dendritic Integration of Synaptic Potentials and Calcium in Cerebellar Interneurons[END_REF] . Therefore, when synapses on the same sublinear dendrite are activated simultaneously, they "interact" and thus sum less effectively than if synapses were activated on two different dendrites, due to a lack of effective electrical interaction. In other words, the somatic depolarization is larger and more sensitive to synapse activation patterns that are "scattered" across the dendritic tree.

We used scanning two-photon glutamate uncaging [START_REF] Tran-Van-Minh | Differential Dendritic Integration of Synaptic Potentials and Calcium in Cerebellar Interneurons[END_REF][START_REF] Tran-Van-Minh | Two-Photon Neurotransmitter Uncaging for the Study of Dendritic Integration[END_REF] in parasagittal cerebellar brain slices to test the hypothesis that neurons with sublinear dendrites generate larger excitatory potentials when synaptic activation is distributed across dendrites rather than synaptic activation within a dendrite (Fig 2). We identified stellate cells by patching somata located in the outer third of the molecular layer. To mimic clustered activation, we uncaged glutamate using 0.2 ms 720 nm laser pulses in four locations within putative stellate cell dendritic trees in any one trial (slices were superfused wth 2 mM MNI-glutamate) and recorded uncaging-evoked excitatory postsynaptic potentials (uEPSPs) using somatic current clamp patch recordings. Current was injected into the soma to maintain a resting potential near -70mV. Either all uncaging locations were clustered in the same dendrite, or two uncaging locations were placed on two different primary dendrites (see Fig 2A). We used pairs of uncaging sites to increase the local depolarization. Compound subthreshold uEPSPs were generated from four sites ranging from 4-22 mV across all experiments (Fig 2C ). We observed that compound uEPSPs evoked on the same dendritic branch were systematically smaller than their linear sum, as expected for sublinear integration (Fig 2B ,C). However, compound uEPSPs generated from uncaging locations scattered onto two different dendrites were not significantly different than their linear sum 2/12 and thus consistent with scatter-sensitive subthreshold PSPs. Because of the inertia of galvanometer mirrors, we could more easily perform simultaneous activation of three dendrites if one was stimulated using an extracellular electrode (see Methods). Results were similar for the activation of effectively six uncaging sites across three dendrites (Fig 2D -F). These results confirm that compound synaptic potentials in neurons with sublinear dendrites were larger if the inputs were scattered across dendrites rather than clustered on a single dendrite. Unlike most studies that focus on the characterization of subthreshold dendritic operations, we set out to verify that the scatter-sensitive subthreshold behavior of stellate cell dendrites also translated into scatter-sensitive spiking probability. We applied the same uncaging protocol described for Fig 2, but adjusted the holding current to maintain the resting potential around -60 mV, to facilitate spiking. Indeed, we found that uncaging locations that were located on the same dendrite produced a significantly lower spiking probability than when uncaging locations were on separate dendrites (Fig 3). These data demonstrate that stellate cells are more likely to fire when inputs are distributed over their dendritic tree than when they cluster on specific dendrites. We also extended this study to three-branch stimulation as described above and observed a robust increased firing probability if the stimulation was distributed across the dendrites (Fig 3C , D, andE). Thus, the neuronal computation (as represented by somatic spiking) of cerebellar stellate cells is scatter-sensitive. It remains to be demonstrated that the FBP can be computed by the neuron with scatter-sensitive spike production.

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Since we established that stellate cells are scatter-sensitive, we next examined whether such scatter sensitivity would confer them the ability to perform linearly non-separable computations. Specifically, we set out to show they could implement the FBP (see Fig 4). Glutamate was uncaged at four distinct locations in six different patterns. There were four scattered cases (uncaging sites on different dendrites) and two clustered cases (uncaging sites on the same dendrite). To observe an FBP we examined whether a neuron remained silent (no action potential) in the two clustered cases and fired in two scattered cases with non-overlapping uncaging sites. Let us consider each uncaging location as a synaptic input encoding an object's feature, then combinations of uncaging locations that trigger a somatic spike effectively encode the object. If we observed that the neuron fires for specific combinations of non-overlapping uncaging sites and stays silent for others, then we can claim that it implements the FBP. To give a proof-of-principle demonstration, we chose to label each uncaging location with a unique symbol shape or color: triangle or a circle shape, and green vs. yellow color. Given such labeling, we would conclude that the feature binding problem was correctly implemented if a green triangle and yellow circle were encoded by the soma. In our experiments, we observed multiple trials in which the results were consistent with the FBP, while in others they were not (either scattered synaptic activation did not produce a spike or the clustered case did) (see Fig 4 lower right, red shading). The cell shown in Figure 4 implemented the FBP in nearly half of the trials (n=15), i.e. it fired for two objects with two specific disjoint features (e.g. green triangle or yellow circle) and stayed silent for two other objects made up of other disjoint feature combinations (the green circle and yellow triangle). We also observed, in this cell, trials where a false positive spike was generated (red shading Fig 4). Because of the costly experimental setup we managed to perform suprathreshold experiments only on four cells, where we stimulated a couple of dendrites. Two cells were capable of implementing the FBP 50% of the time. To strengthen this experimental work and explain cases where cells fail to implement the FBP we used a realistic biophysical model. Colored spots indicate the uncaging locations, on this cell we uncaged glutamate in four locations, each pair corresponds to one feature (Purple:"Green" on branch 1, "Triangle" on branch 2; Teal:"Yellow" on branch 2, "Circle" on branch 1). The color code is in the top of panel B.and indicates the two objects to be encoded (yellow circle, green triangle). (B) Examples of somatic voltage traces of the same stellate cell in two distinct trials. In the top trial, the neuron computes a feature binding problem, and in the bottom trial it fails to do it because of a false positive (red case). We discarded the two cases when inputs are coming from the shape or the color inputs only as they do not affect the result.

Understanding why scatter sensitive neurons could compute (or not) the feature binding problem

To understand better the origin of the failed FBP trials, we implemented a biophysical model of a cerebellar stellate cell. We built a multi-compartment model with a realistic dendritic tree morphology (using a reconstruction of cerebellar stellate cell [START_REF] Scorcioni | Measure: a web-accessible tool for the analysis, comparison and search of digital reconstructions of neuronal morphologies[END_REF] ) that was capable of reproducing the uEPSP amplitudes observed in the subthreshold protocol(see Fig 5, 4 pS peak synaptic conductance). The dendrites were modeled as passive and showed sublinear EPSP summation with clustered inputs and more linear summation with inputs scattered on different dendrites (Fig 5A andB). We considered two principal factors that could underlie trial-to-trial variability as well as cell variability in the ability to implement the FBP: EPSP size relative to the threshold and membrane fluctuations. To correctly implement the FBP, the voltage differential from rest to threshold must be such that the single uEPSP and the sublinear compound uEPSP (two-site activation within the same dendrite) are subthreshold, but the linearly summed uEPSPs (two-site activation on different dendrites) are suprathreshold. We thus varied the resting membrane voltage and examined if simulated compound uEPSPs (adjusted to 10 pS per site to ensure spikes) produced false positive or negative spikes (compare Fig 5 to Fig 4). For the depolarized resting membrane potential of -64mV the model reaches the threshold not only in all the scattered stimulation cases but also in one of the clustered cases creating a false positive. When , we used the first 300 ms without spike and measure the mean voltage in 2 ms timebins) follows a normal like distribution (µ=-68.5 mV, σ =0.9 mV). We reproduced this distribution using the same mean and standard deviation using a normal distribution (light blue superimposed). (E) Probability of implementing the FBP for different resting membrane potentials and noise levels (SD), calculated from 1000 simulations for each condition.

the membrane potential was decreased to -68mV the neuron reached the threshold only in the scattered case, thus correctly implementing the FBP. Finally, if the resting membrane potential was set too low (-72mV), the neuron spiked only in one of the scattered cases. Together, these three simulations exemplify that variations in the resting membrane voltage can influence the successful computation of the FBP. Thus, the EPSP size relative to the threshold must be tuned correctly to implement the FBP.

We also recognized that membrane potential fluctuations could generate false positives and false negatives. We, therefore, modeled the voltage fluctuations using a Gaussian noise distribution that matched experimental observations (mode at -68.4 mV with a standard deviation equal to 0.9 mV vs. resting potential mean for the cell in (Fig 6) was -68.5 mV with an SD of 0.8 mV (Fig 5D )). We, therefore, systematically varied the noise level around this experimental value as well as varying the resting membrane potential of the model from -72mV and -64mV (Fig 5E). To calculate the FBP probability we performed 1000 trials for each simulation condition. As expected from above, when the resting membrane potential is too high the neuron generated false positive spikes, and when it is too low, the neuron generated false negative errors. The simulations indicated an optimum around a resting membrane potential of -68mV, but the FBP probability degraded within increasing membrane potential fluctuations.

We were able to show that by adjusting the synaptic conductance in the model to match the uEPSP amplitudes for each individual uncaging site, as well as the membrane potential fluctuations, we could reproduce the probability of implementing the FBP (around 50%) as in the cell shown in Fig 4 . We, therefore, conclude that scatter-sensitive neurons can perform the

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FBP, but the relative amplitude of the EPSP versus the voltage-to-threshold and the membrane fluctuations need to be tuned to reliably compute the FBP.

Benchmarking that a neuron can solve the feature boning problem

Based on the analysis above, we can now demonstrate that a cerebellar stellate cell can indeed perform the FBP even in noisy experimental conditions, as we can see the cell (Fig 6A -C uEPSP is larger than the first. The third input with a high value guarantees that the neuron will fire in the third scattered case (20+3pS) while the sum is lower in the second scattered case (10+7pS) keeping the neuron silent in this situation. Thus this model could reproduce the observation (Fig 6A)

We wondered what were the reasons for the much more restricted implementation of the FBP as opposed to a more robust scatter-sensitivity we observed in Fig XX . One reason for failures several of the cells was that the responses at the different stimulation locations were not even: one location gave much larger somatic voltage responses that fired the cell for almost all the trials. Second was that at least one cell did not fire spikes at all and others did not produce enough spikes to access the FBP implementation.

Ideally, the FBP would be implemented in a neuron where every EPSP would be equal for every stimulation point, as in a synaptic democracy scenario [START_REF] Magee | Somatic epsp amplitude is independent of synapse location in hippocampal pyramidal neurons[END_REF] . In summary, scatter sensitivity is a necessary, but not sufficient condition for a sublinear dendritic implementation of the FBP.

Furthermore, Fig 6D explains why the neuron fails to perform the FBP only in certain trials. In this panel we plotted the membrane voltage of the cell just before the second stimulation (10ms before), and we colored each point depending on the cell activity (spikes:red, silence:green). We see that that resting potential cases where a neuron gave a false positive spike, the membrane resting potential was too high, and lead to consistent failure to implement the FBP. While for negatives, the resting potential was too low. We also conclude that it is possible to predict when the neuron implement (or not) the FBP. In summary, as we predicted from our modelling analysis above, the resting potential fluctuations combined with membrane noise lead to the FBP implementation failures.

Discussion

It is well known that dendritic nonlinearities can theoretically increase the computational capacity of neurons because they enable multi-layered information processing. In particular, while there has been fast-growing theoretical literature arguing for universal computing power of dendritic neurons [START_REF] Poirazi | Pyramidal Neuron as Two-Layer Neural Network[END_REF][START_REF] Tzilivaki | Challenging the point neuron dogma: FS basket cells as 2-stage nonlinear integrators[END_REF][START_REF] Cazé | Passive Dendrites Enable Single Neurons to Compute Linearly Non-separable Functions[END_REF][START_REF] Ujfalussy | Global and Multiplexed Dendritic Computations under In Vivo-like Conditions[END_REF] (bolstered by experimental results on subthreshold dendritic integration 1, 2, 4, 5 and the potential role of dendritic processes in neuronal tuning properties [START_REF] Takahashi | Active cortical dendrites modulate perception[END_REF][START_REF] Smith | Dendritic spikes enhance stimulus selectivity in cortical neurons in vivo[END_REF][START_REF] Palmer | NMDA spikes enhance action potential generation during sensory input[END_REF][START_REF] Fischer | Dendritic Mechanisms for In Vivo Neural Computations and Behavior[END_REF], experimental validation of an actual implementation of LNSC by a neuron endowed with nonlinear dendrites, to our knowledge, has not been performed. In this study, we demonstrated using multi-point glutamate uncaging that the sublinear dendritic integration of cerebellar stellate cells leads to larger EPSPs and spiking probabilities when synaptic activation is spread across dendrites (scatter-sensitive) as compared to when the synapses are activated within the same dendritic branch. We also showed that stellate cells can implement the feature binding problem (as previously predicted in [START_REF] Cazé | Passive Dendrites Enable Single Neurons to Compute Linearly Non-separable Functions[END_REF] ). Unlike a LNSC like the XOR, the FBP can be computed using only excitatory synapses. This singular property enabled our demonstration as the XOR would have required a mixture of caged neurotransmitters or a non-monotone neuronal transfer function absent from stellate cell. Moreover, the FBP is of particular interest since neurons implementing it are able to bind multiple feature combinations together into an object [START_REF] Malsburg | The what and why of binding: The modeler's perspective[END_REF][START_REF] Yu | The Binding Problem 2.0: beyond perceptual features[END_REF] . Finally, modeling dendritic integration of the thin passive dendrites of cerebellar stellate cells allowed us to identify the biophysical conditions necessary to perform this benchmark.

We have shown here that in order to implement the FBP using excitatory synapses and sublinear dendrites, the two features of a common object must innervate two different dendrites such that their compound EPSP, upon simultaneous activation, is maximized and generates the large spike probability. Otherwise, if two synapses are simultaneously activated within the same dendritic compartment, and their summed local depolarization is large enough to decrease the driving force for ionic currents, the net somatic depolarization will be smaller than the arithmetic sum. Thus clustered synaptic activation produces less depolarization than when the synapses are electronically independent. For a neuron to bind two (or more) features of an object, the features must be distributed across the dendritic tree to maximize the spike probability associated with the object, a computation termed "scatter-sensitive". However, an important condition is that the scattered activation produces a somatic spike, whereas the equivalent clustered activation must be subthreshold for spike generation. This fine-tuning requires a specific relation between the single synapse EPSP amplitude, the number of synapses associated with the different features, and the difference between the resting membrane potential and the spike threshold. EPSPs that are too strong generate false positives, whereas EPSPs that are too weak generate false negatives spiking representations of objects (Fig 5). Stronger background membrane potential fluctuations will also generate more false positives and negatives on a trial-to-trial basis (see Fig 4 and Fig 6). Synaptic In conclusion, to show that a scatter sensitive neuron can implement a LNSC you need to have strong and almost equal uEPSP and a well controlled resting membrane voltage.

In this study, we emphasized scatter-sensitivity of the neuron as a key factor for the implementation of linearly non-separable computations as it is possible both in active and passive dendrites. Passive thin dendrites have high input impedances and are good candidates for large local depolarizations that generate sublinear summation. Activation of voltage-gated potassium conductances can also generate sublinear integration [START_REF] Hu | Dendritic Mechanisms Underlying Rapid Synaptic Activation of Fast-Spiking Hippocampal Interneurons[END_REF] . Moreover, it is possible that for small numbers of active synapses, their compound EPSP can be large enough to decrease the driving force locally in the dendrite, but still too small to activate nonlinear conductances [START_REF] Losonczy | Integrative properties of radial oblique dendrites in hippocampal CA1 pyramidal neurons[END_REF] . In that window of synaptic depolarization, a scatter-sensitive computation can be performed. Moreover, for

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dendrites that exhibit robust calcium spikes [START_REF] Abrahamsson | Thin Dendrites of Cerebellar Interneurons Confer Sublinear Synaptic Integration and a Gradient of Short-Term Plasticity[END_REF] , once the dendritic spike has been generated, additional synaptic depolarization is ineffective in increasing spike probability. Synaptic contacts scattered onto other dendrites must be activated to generate additional somatic depolarization and increased spike probability. Thus both interneurons and principal neurons could exhibit scatter sensitivity and thus use sublinear summation to implement a LNSC [START_REF] Tzilivaki | Challenging the point neuron dogma: FS basket cells as 2-stage nonlinear integrators[END_REF] , albeit under specific regimes of synaptic and intrinsic cell membrane parameters. Given that scatter sensitivity responses on passive cable properties of dendritic trees, and is not catastrophically deteriorated by active dendritic processes (albeit under different synaptic and intrinsic regimes), it might be a widely generic property of information processing in wide classes of neurons.

Methods

Animals and slice preparation

Animal experiments were performed in accordance with the guidelines of Institut Pasteur, France, and all protocols were approved by the Ethics Committee 89 of Institut Pasteur (CETEA; approval DHA180006). Results of this study are reported in accordance with ARRIVE guidelines (https://arriveguidelines.org).

Cerebellar acute slices were prepared from CB6F1 mice (F1 cross of BalbC and C57Bl/6J) of postnatal day P60 to 90. The mice were killed by rapid decapitation (no anesthetic was used), after which the brains were quickly removed and placed in an ice-cold solution containing (in mM): 2.5 KCl, 0.5 CaCl2, 4 MgCl2, 1.25 NaH2PO4, 24 NaHCO3, 25 glucose, 230 sucrose, and 0.5 ascorbic acid bubbled with 95% O2 and 5% CO2. Parasagittal slices (20 0µm thick) were prepared from the dissected cerebellar vermis using a Leica VT1200S vibratome. After preparation, the slices were incubated at 32 degree Celsius for 30 minutes in the following solution (in mM): 85 NaCl, 2.5 KCl, 0.5 CaCl2, 4 MgCl2, 1.25 NaH2PO4, 24 NaHCO3, 25 glucose, 75 sucrose and 0.5 ascorbic acid. Slices were then transferred to an external recording solution containing (in mM): 125 NaCl, 2.5 KCl, 2 CaCl2, 1 MgCl2, 1.25 NaH2PO4, 25 NaHCO3, 25 glucose and 0.5 ascorbic acid, bubbled with 95% O2 and 5% CO2, and maintained at room temperature for up to 7 hours.

Slice electrophysiology and imaging

Whole-cell current-clamp recordings were performed from stellate cells (SCs) (33 • C -36 • C) located in the outer third of the molecular layer, using a Multiclamp 700B amplifier (Molecular Devices), and fire-polished thick-walled glass patch-electrodes (tip resistances of 4-6 MΩ). The pipettes were backfilled with an internal solution containing (in mM): 110 K-MeSO3, 40 HEPES, 1 EGTA, 4.5 MgCl2, 0.49 CaCl2, 10 Na-pyruvic acid, 0.3 NaGTP, 4 NaATP, 10 Tris phosphocreatine and 0.04 Alexa Fluor 594 and adjusted to 305 mOsm and pH 7.3. Synaptic responses were filtered at 10 kHz, and digitized at 100 kHz using an analogue-to-digital converter (model NI USB 6259, National Instruments, USA) and acquired with NClamp (www.neuromatic.thinkrandom.com), running in the Igor Pro environment (Wavemetrics). Current was injected to maintain the membrane potential between -70mV and -90mV (after correcting for liquid junction potentials, calculated to be -7 mV using JPCalcW (Barry, 1994; J. Neurosci. Method., 51: 107-116)), and series resistance was compensated by balancing the bridge and compensating pipette capacitance.

Unless otherwise stated, the external solution included 10 µM SR-95531 to block GABAA receptors to avoid confounding results due to partial blockade of GABAA receptors by MNI glutamate, and 50 µM D-AP5 to avoid stimulation of extra-synaptic NMDA receptors.

A pulsed Ti:Sapphire laser (DeepSee, Spectra-Physics) beam tuned at 810 nm was scanned on the preparation using an Ultima microscope (Bruker Fluorescence Microscopy) mounted on an Olympus BX61WI microscope and equipped with a 60x (1.1 NA) water-immersion objective. Simultaneous two-photon fluorescence and Dodt contrast imaging (Luigs and Neumann, Germany) were used to position extracellular stimulating electrodes and uncaging points along spatially isolated dendrites of Alexa Fluor-594-filled SCs, using a transmitted light PMT mounted after the Dodt tube to acquire a laser-illuminated contrast image simultaneously with the 2PLSM image. Alexa Fluor 594 fluorescence was filtered using 640/100 nm bandpass filters (Chroma) and detected using side-on multi-alkali PMTs (3896, Hamamatsu Photonics). In addition to the light collected through the objective, the transmitted infrared light was collected through a 1.4 NA oil-immersion condenser (Olympus), and reflected on a set of substage photomultiplier tubes (PMTs). Chemicals D-AP5 (D-(-)-2-Amino-5-phosphonopentanoic acid) and SR 95531 (2-(3-Carboxypropyl)-3-amino-6-(4 methoxyphenyl) pyridazinium bromide) were purchased from Abcam, UK. MNI-glutamate (4 methoxy-7-nitroindolinyl caged L-glutamate) was purchased from Tocris Bioscience, UK. Alexa Fluor 594 was from Life Technologies, USA. All other chemicals were purchased from Sigma-Aldrich, France.

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Glutamate uncaging MNI-glutamate was bath applied at a final concentration of 2 mM in ACSF, and recycled. The solution was kept protected from light and any lamps used for ambient light and microscope trans-illumination used during approach of the patch-clamp electrode were covered with a UV yellow filter to prevent undesired photolysis of MNI-glutamate. The preparation was illuminated through a second set of galvanometer-based scan mirrors, allowing independent and rapid positioning of the photolysis beam. The photolysis laser was either a 1P laser at 405 nm diode laser (Omicron) or a pulsed Ti:Sapphire laser (DeepSee, Spectra-Physics) tuned at 720nm. The outputs of the two lasers were independently modulated to combine uncaging of MNI-glutamate and imaging morphology. The imaging laser beam was modulated using a Pockels cell (350-50-BK 02, Conoptics, Danbury, CT). For 2P uncaging, the intensity and duration (200-300 µs) of the photolysis pulse was modulated using an acousto-optic modulator (MT110-B50A1.5-IR-Hk, AA Opto-Electronic, France). For 1P uncaging, the intensity and duration of the photolysis pulse were. A telescope placed on the path of each uncaging beam (Thorlabs) was used to adjust the convergence angle to both backfill the objective and match the focal plane of the two-photon excitation for imaging. Parfocality of the two beams was verified using bleached spots on a microscope slide coated with fluorescent ink. Photolysis laser powers, estimated at the exit of the objective were <1 mW for 1P uncaging and <20 mW for 2P uncaging. We uncaged near simultaneously at up to 6 spots, each 3-6 µm apart, by rapidly switching the focal spot to each new location along the dendrite at 200 µs intervals. For multi-dendrites stimulation, the minimum displacement time of uncaging mirrors between two uncaging locations constrained the distance between the stimulated dendrites (typically in the order of 100-150 µm between the most distant uncaging locations).

Distribution of the resting membrane voltage

The voltage membrane is sampled at 1kHz as we would we be incapable to obseve spiking at a lower sample rate. We looked at all the 15 trials and used the first 100ms to plot an histogram of the voltage distribution. We have overlapped surrogate data (n=150000 points) generated from a normal distribution using the observed µ=68.48 and σ =0.90. We have used a visual verification to test the normality of the distribution as usual statistical test (Shapiro wilk or Kolmogorov) were not adapted for the extended number of data points and as we approximated the distribution as a normal. Table 1. The FBP truth table organised depending on the number of 1s in the input vectors (the In row). For input vectors with less than two 1s the neuron should stay silent, and if it has more than two 1s the neuron should fire. When there are two 1s, the neuron should fire for two disjoint conjunctions and stay silent for two of other disjoint conjunctions. This guarantees that the FBP is a LNSC. In the two other cases the neuron could fire or not (meaning of ?)

Formal definition of the FBP

The definition of the FBP in Tab.1 ensures that FBP is positive (thefore monotone) and linearly non-separable. In another article, we prove using a constructive proof that that a neuron with a sufficient number of sub or supra-linear subunit could compute all positive functions [START_REF] Cazé | Spiking and saturating dendrites differentially expand single neuron computation capacity[END_REF] . While for eight variables there are 2730166 threshold positive computations [START_REF] Muroga | Enumeration of threshold functions of eight variables[END_REF] the total number of positive computations is non (the 8th dedekind number). This gives the ratio of 10 [START_REF] Scorcioni | Measure: a web-accessible tool for the analysis, comparison and search of digital reconstructions of neuronal morphologies[END_REF] It is important to note here that the FBP is a monotone function, contrary to the XOR, therefore it enables our demonstration without using a mixture of excitatory and inhibitory caged neurotransmitter, as cerebellar stellate dendrites behave in a monotone way.

We may have wanted to study a more "complex " FBP with more features or objects. However, the number of dendrites necessary to compute them could have grown rapidly. We studied this scaling in [START_REF] Cazé | Spiking and saturating dendrites differentially expand single neuron computation capacity[END_REF] , and here we focus on the simplest FBP (2 objects and 4 features). This choice is motivated by experimental constraints.

For instance, we could have defined a FBP with four features per object. Let us imagine that such feature dimensions are: size, color, texture, shape. For such FBP, we need to define four cases: two where the neuron fires for a small-greenstripy-triangle (object 1) or for a large-yellow-dotted-circle (object 2) and two where the neuron should stay silent, e.g. for a large-green-stripy-triangle or a small-yellow-dotted-circle. In this case, you need a neuron with a minimum of four dendrites to scatter the features of each object on them, and to prevent spiking you need then to cluster the sizes and another set of features on two different branches (like big and green on one branch and small and yellow on another). Note that such clustering does not need to be exquisitely precise, but sufficient such that these non-spiking conjunctions would saturate the dendritic response and not cause a spike. Since our goal in this manuscript was to provide an experimental demonstration that a dendritic neuron can implement the FBP, we would need to set up an experiment with 4 stimulated dendrites with 4 uncaging locations each. This is beyond experimental capabilities. Hence we focused on the 2-feature-object case.

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Figure 2 .

 2 Figure 2. Scattered inputs sum more linearly than clustered inputs. (A, C) 2PLSM image of a cerebellar stellate cell filled with Alexa Fluor 594. Colored spots indicate dendritic locations stimulated using glutamate uncaging (branches 1 and 2, A and C) or electrical stimulation (branch 3, C). (B, D) Example traces of somatic current-clamp recordings in response to stimulation of a group of clustered (left) of scattered (right) inputs (blue traces), and traces obtained as the sum of EPSPs recorded in response to stimulation of individual locations (black traces). (E, F) Peak amplitudes of observed and expected EPSPs in response to stimulation of clustered or scattered inputs.Note that in panel F while the difference between the expected and observed voltage responses are not statistically significant for the number of neurons recorded, we allow the possibility that this may change with a larger number of cells.Note that lines connect responses of a single cell on a single clustered vs scattered trials.

Figure 3 .

 3 Figure 3. Multi-branch glutamate uncaging reveals a higher firing probability for scattered versus clustered stimulation. (A) 2PLSM image of a cerebellar stellate cell filled with Alexa Fluor 594. Colored spots indicate locations stimulated using glutamate uncaging (branch 1 and 2) or electrical stimulation (branch 3). (B-C) Example traces of somatic current-clamp recordings of EPSPs and action potentials in response to stimulation of a group of clustered (left) or scattered (right) inputs on 2 (B) or 3 (C) branches. (D-E) Spike probabilities in response to clustered:orange and scattered:grey synaptic inputs.

Figure 4 .

 4 Figure 4. Cerebellar stellate cells might implement the feature binding problem (FBP). (A) 2PLSM image of a cerebellar stellate cell filled with Alexa Fluor 594.Colored spots indicate the uncaging locations, on this cell we uncaged glutamate in four locations, each pair corresponds to one feature (Purple:"Green" on branch 1, "Triangle" on branch 2; Teal:"Yellow" on branch 2, "Circle" on branch 1). The color code is in the top of panel B.and indicates the two objects to be encoded (yellow circle, green triangle). (B) Examples of somatic voltage traces of the same stellate cell in two distinct trials. In the top trial, the neuron computes a feature binding problem, and in the bottom trial it fails to do it because of a false positive (red case). We discarded the two cases when inputs are coming from the shape or the color inputs only as they do not affect the result.

4 / 12 Figure 5 .

 4125 Figure 5. Simulations exploring synaptic and cell parameters necessary to perform FBP(A) Morphologically detailed model of a cerebellar stellate cell, with colored circles indicating input locations corresponding to the two combinations of features (teal:yellow+circle;purple:green+triangle. (B) compound uEPSPs were simulated by placing two 4 pS synaptic conductance (max value) with a τ = 1ms time constant on the same (clustered) or different dendrites (scattered). (C) Membrane potential responses for compound uEPSP responses when stimulating pairs of uncaging locations as indicated in the diagram.The dashed line is the the threshold for spike generation. Note that only a resting membrane potential of -68 mV allows for a correct implementation of the FBP, the two other voltages lead to errors in the FBP implementation-being due to respectively a false positive (extraneous spike) and a false negative (absence of a spike). (D) Histogram of the experimental voltage distribution of the voltage (black, we used the first 300 ms without spike and measure the mean voltage in 2 ms timebins) follows a normal like distribution (µ=-68.5 mV, σ =0.9 mV). We reproduced this distribution using the same mean and standard deviation using a normal distribution (light blue superimposed). (E) Probability of implementing the FBP for different resting membrane potentials and noise levels (SD), calculated from 1000 simulations for each condition.

  top) can perform the FBP in approximately 50 percent of the trials as is also shown by our model (Fig 6A-C bottom). As we see in our simulations, like the real cell our model also fails to implement the FBP in certain trials because its resting membrane voltage fluctuate randomly (Fig 6B). We note that the model further matches the error trials in the neuron giving spurious spikes at the inputs encoding the yellow triangle (Fig 6C). This enabled us to computationally reproduce the variation observed experimentally (Fig 6C) and observe the neuron implementing the FBP in seven trials over fifteen, thereby matching the experimentally observed variability in FBP implementation. More generally, out of the 13 neurons we subjected to this protocol, we observed two cells that robustly implemented the FBP with a probability of approx 0.5 (cell shown 7/15 trials, cell not shown 6/11 trials).

Figure 6 .

 6 Figure 6. Model simulations reproduce measured FBP probability. (A) Top, somatic voltage trace recorded experimentally of one cell in one trial. Bottom: voltage trace predicted by our model. Importantly, in both cases the neuron implement the FBP (B) Voltage distribution used in our simulation during a 300ms period without stimulation (histogram using 2ms timebins). Note the similarity with panel D from the previous figure. (C) Top, the obtained experimental result from the cell in Fig. 4 with all trials plotted. Trials in black are those in which the FBP was correctly implemented. Bottom, are 15 simulated trials showing a similar FBP probability. (D) Value of the membrane voltage 10ms before the second stimulation episode (red arrow in panel (C)), coloured in green when the neuron stay silent and in red when the neuron spikes

Scientific Report manuscript revision (18/07/2023)

Acknowledgements

B.S.G. would like to acknowledge the support from the Basic Science Program Basic Research Program at the National Research University Higher School of Economics (HSE University). This work was partially supported by the ANR projects "CerebComp" and "InTempCode".

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Data availability statement

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Biophysical model

All simulations were performed with Brian 2 [START_REF] Stimberg | an intuitive and efficient neural simulator[END_REF] and we used a detailed reconstruction from [START_REF] Scorcioni | Measure: a web-accessible tool for the analysis, comparison and search of digital reconstructions of neuronal morphologies[END_REF] . The code needed to reproduce the last figure is available under an open-source licence. We used a conductance-based model with the reconstructed dendritic arbor. The axial resistance between compartments equals 150Ω. Every compartment contained the following passive currents:

V is the membrane potentials, C m = 1 µF cm -2 is the membrane capacitance, g L is the leak capacitance equal to 5e -5siemens which is equivalent to a R i = 20000Ω input resistance. The synaptic current I s is described by

with E s being the synaptic reversal potential and g s the synaptic conductance. This conductance jumps up instantaneously for each incoming input and decays exponentially with time constant τ s = 1 ms otherwise:

The neuron "spikes" when it reaches -50mV from below and we signal a spike using a vertical bar. We set the resting membrane voltage to -68mV.

Simulations to match the experimental observation

In Fig 6 we used the same biophysical model as described above with four synaptic conductances placed as indicated (Fig 6A )  with peak amplitudes of Br1 teal:7 pS, purple:3 pS; Br2 teal:20 pS, and purple:10 pS exponentially decaying with a 1 ms time constant, to match as close as possible the experimental data (uEPSP amplitude or spike probability). The two first stimulation points have a weaker value than the two last as the second uEPSP is larger than the first. The third input with a high value guarantees that the neuron will fire in the third scattered case (20+3pS) while the sum is lower in the second scattered case (10+7pS) keeping the neuron silent in this situation.

To mimic the observed variation in the membrane resting voltage we used two conductances based processes, one inhibitory and one excitatory of 0.2pS targeting the soma. To create randomly distributed membrane voltage in the model we used the following procedure. We randomly picked 400 integers between 0 and 2000 each with the same probability. Of these 200 corresponded to the times at which an excitatory synapse activates (with the reversal potential of 0mV) and the other 200 to the activation times of an inhibitory synapse (reversal potential -140mV). Both of these surrogate synapses target the soma and have a conductance strengths of 0.2nS. Each synapse was modeled as an instantaneous increase preceding an exponential decay with a 1ms time constant. The goal was to obtain a resting potential distribution that matched the experimentally observed one (see Fig 6A).

The python code to entirely reproduce the two last figures and subpanels is available on zenodo [START_REF] Caze | Demonstration that sublinear dendrites enable linearly non-separable computations[END_REF] .

Author contributions statement Without surprise the further we were the larger was the difference (as close-by synaptic inputs interact via the soma). Surprisingly we found that after a certain distance this difference decreases. This is because dendritic filtering decrease the effect of both clustered and scattered stimulation on the soma. It leads to a decreased difference between the two types of stimulation.

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Louis Lebreton
email: louis.lebreton@chu-bordeaux.fr

Margaux Gaschignard

Claire Guibet

Delphine Lamireau

Sandrine Roche

Emmanuel Richard

Cecile Ged

Samir Mesli

Lebreton Louis

| Gaschignard

Guibet Claire

| Lamireau

| Roche Sandrine

| Richard Emmanuel

Ged Cécile

Mesli Samir

| Redonnet-Vernhet
email: isabelle.redonnet-vernhet@chu-bordeaux.fr

Lebreton

Jerry Vockley

Lebreton Orcid

Louis

Roche Sandrine

Richard Emmanuel

Infantile primary carnitine deficiency: A severe cardiac presentation unresponsive to

Keywords:

scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

tially suspected as intracranial hypertension, the clinical condition evolved rapidly and caused a reversible cardiac arrest with profound hypoglycemia. Despite carnitine supplementation, she succumbed from cardiac arrhythmia and multivisceral failure 4 days after admission. The genetic analyses showed a PCD with biallelic pathogenic variants of SLC22A5 gene. The case report is notable for the severity of the cardiac damage possibly favored by maternal carnitine deficiency during pregnancy. The analysis of previously published PCD cases highlights (i) the importance of having large access to emergency biochemical tests for early therapeutic care although the disease has unpredictable severity and (ii) the fact that the clinical outcome remains unpredictable if carnitine treatment is initiated late.

K E Y W O R D S

cardiomyopathy, children, fatty oxidation, primary carnitine deficiency

| INTRODUCTION

Primary carnitine deficiency (PCD) is an autosomal recessive metabolic-inherited disease of the carnitine cycle (OMIM no. 212140) caused by a carnitine transporter OCTN2 (organic cation transporter protein) [START_REF] Longo | Carnitine transport and fatty acid oxidation[END_REF] defect that results in defective fatty acid oxidation. The incidence of PCD varies according to populations as shown by neonatal screening programs with a frequency of 1/20 000-1/70 000 in Europe, [START_REF] Olpin | Systemic primary carnitine deficiency; Orphanet encyclopedia[END_REF] 1/40 000 in Japan, [START_REF] Koizumi | Genetic epidemiology of the carnitine transporter OCTN2 gene in a Japanese population and phenotypic characterization in Japanese pedigrees with primary systemic carnitine deficiency[END_REF] 1/140 000 in United States, [START_REF] Therrell | Inborn errors of metabolism identified via newborn screening: ten-year incidence data and costs of nutritional interventions for research agenda planning[END_REF] and 1/300 in Faroe Islands [START_REF] Lund | Carnitine transporter and holocarboxylase synthetase deficiencies in The Faroe Islands[END_REF] due to a founder effect.

Localized in the cytoplasmic membrane, OCTN2 is encoded by the SLC22A5 gene (solute carrier family 22 member 5) located on chromosome 5q31.1. Carnitine is an essential water-soluble molecule for the transfer of long-chain fatty acids across the inner mitochondrial membrane with subsequent β-oxidation. Defects in the OCTN2 carnitine transporter result in urinary carnitine wasting, low serum carnitine levels, and intracellular carnitine deficiency. Since their supplied energy mainly comes from fatty acids beta-oxidation, myocardium and skeletal muscles are particularly sensitive to carnitine deficiency.

Clinical manifestations of PCD vary widely from infant sudden death to asymptomatic adult forms. [START_REF] Magoulas | Systemic primary carnitine deficiency: an overview of clinical manifestations, diagnosis, and management[END_REF] Between 3 months and 2 years of age the metabolic presentation is more frequent [START_REF] Longo | Disorders of carnitine transport and the carnitine cycle[END_REF] with hypoketotic hypoglycemic episodes, hepatic encephalopathy, lethargy, hyperammonemia, hepatomegaly, and elevated transaminases. Seizures, triggered by fasting or febrile episodes, can leave neurological sequelae that will result in mental retardation or learning difficulties. Lack of treatment can lead to cerebral edema, seizures, coma, and death. Patients with PCD can develop dilated cardiomyopathy, usually between 1 and 7 years of age, sometimes associated with proximal myopathy giving rise to muscle weakness and amyotrophy [START_REF] Longo | Disorders of carnitine transport and the carnitine cycle[END_REF][START_REF] Di San | Cardiomyopathy and carnitine deficiency[END_REF][START_REF] Shibbani | Primary carnitine deficiency: novel mutations and insights into the cardiac phenotype[END_REF][START_REF] Fu | Primary carnitine deficiency and cardiomyopathy[END_REF] Adult patients with PCD are in most cases asymtomatic [START_REF] Crefcoeur | Clinical characteristics of primary carnitine deficiency: A structured review using a case-by-case approach[END_REF] or present with minor symptoms as muscle weakness. However, adults are at risk of sudden death from cardiac arrhythmia. [START_REF] Mazzini | Primary carnitine deficiency and sudden death: in vivo evidence of myocardial lipid peroxidation and sulfonylation of sarcoendoplasmic reticulum calcium ATPase 2[END_REF][START_REF] Rijlaarsdam | Ventricular fibrillation without overt cardiomyopathy as first presentation of organic cation transporter 2-deficiency in adolescence[END_REF][START_REF] Rasmussen | Primary carnitine deficiency and pivalic acid exposure causing encephalopathy and fatal cardiac events[END_REF][START_REF] Schimmenti | Expanded newborn screening identifies maternal primary carnitine deficiency[END_REF][START_REF] De Biase | Primary carnitine deficiency presents atypically with long QT syndrome: A case report[END_REF][START_REF] Rasmussen | Primary carnitine deficiency in The Faroe Islands: health and cardiac status in 76 adult patients diagnosed by screening[END_REF] Asymptomatic mothers with PCD were identified through their baby's newborn screen by extremely low free carnitine levels reflecting the mother's condition. [START_REF] Schimmenti | Expanded newborn screening identifies maternal primary carnitine deficiency[END_REF][START_REF] Li | Molecular spectrum of SLC22A5 (OCTN2) gene mutations detected in 143 subjects evaluated for systemic carnitine deficiency[END_REF][START_REF] El-Hattab | Maternal systemic primary carnitine deficiency uncovered by newborn screening: clinical, biochemical, and molecular aspects[END_REF] PCD outcome partly depends on early diagnosis and carnitine supplementation. [START_REF] Magoulas | Systemic primary carnitine deficiency: an overview of clinical manifestations, diagnosis, and management[END_REF] Herein, we present the case of an 18-week-old female child diagnosed with PCD during a severe and fatal episode of metabolic and cardiac decompensation.

| CASE REPORT

| Clinical and biochemical presentation

An 18 week-old female child was admitted at the pediatric emergency of Bordeaux University Hospital presenting hypotonia, moaning, diarrhea and vomiting. Second child from nonconsanguineous parents, she was born at term with normal weight and she has presented since birth many unexplained crying episodes that became more frequent in the last weeks. She had weight gain difficulties from the first weeks of life in the context of exclusive breastfeeding then switched to artificial milk. The progressive occurrence of diarrhea and vomiting with lethargic episodes led the parents to bring their child to the pediatric emergency department.

On admission to hospital, hemodynamics showed a heart rate of 140 bpm interspersed with episodes of bradycardia and arterial hypertension, deep respiration (respiratory rate = 40) with normal oxygen saturation. Hepatomegaly was found by abdominal palpation of a 3 cm liver span. Neurological exam showed Glasgow scores ranging from 11 to 15, fluctuating consciousness, generalized hypotonia, no signs of focusing, no apparent motor deficiency, and normotensive fontanel. She had no fever.

Mannitol administration was quickly started (1 g/kg) to prevent intracranial hypertension. In addition, antibiotic prophylaxis (Ceftriaxone and Gentamicin) and hydratation (NaCl 0.9%) were set up.

No abnormalities were identified on brain computed tomography scan and on thoracic x-ray.

Biochemical testing (Table 1) highlighted metabolic acidosis with hyperlactatemia, hepatic cytolysis, hyperammonemia, cardiac, and hepatic functions. Hematology and other common parameters were in the normal range, no infectious agent was detected, blood glucose was not tested at admission. Thus, 3 h after admission she was transferred to an intensive care unit. On arrival, the child had seizures with generalized hypertonia and was recovered from cardiorespiratory arrest through an intensive care management. At that time, capillary blood glucose level was 0.18 g/L, treated by 10% glucose infusion at the dose of 8 mg glucose/kg/d.

Immediately after recovering from cardiorespiratory arrest a bolus of carnitine (200 mg/kg) and a bolus of sodium benzoate (250 mg/kg/4 h) were administered.

The biological follow-up showed a majoration of hyperammonemia (354 μmol/L) further treated, after metabolic advice, by carglumic acid (Carbaglu ® ; 50 mg/ kg/6 h) and a second bolus of sodium benzoate (200 mg/ kg). The ammonia level dropped to 121 μmol/L 3 h after that treatment and to 72 μmol/L after 5 h. Additionally, an exclusive carbohydrate diet was started and a treatment with carnitine at 50 mg/kg/d was instaured.

Left ventricular enlargement as well as severe cardiac failure (ejection fraction 25%-30%) were shown by cardiac ultrasound, requiring transfer to a specialized cardiac care unit 1 day after admission. Results from the inherited metabolic diseases department were available 3 days after admission. First, an elevated medium and long-chain dicarboxylic aciduria was found in the chromatography of urinary organic acids (OA), in good agreement with a long chain fatty acids betaoxidation defect. Then the deeply decreased free blood carnitine (0.5 μmol/L; normal range: 33-44 μmol/L) and total blood carnitine (1.36 μmol/L; normal range: 59-80 μmol/L) levels raised the suspicion of PCD. Consequently carnitine treatment was increased from 50 to 200 mg/kg/d at Day 3.

In summary, the doses of carnitine injected were a bolus of 200 mg/kg after cardiac recovery (Day 1), then 50 mg/kg (Days 1 and 2), and 200 mg/kg (Day 3 and 4).

Unfortunately, despite high doses of carnitine, she presented severe episodes of arrhythmia with long QRS complex and supraventricular tachycardia (200/300 bpm), an oedematous syndrome and finally a multisystemic failure leading to death 4 days after hospital admission.

| Genetic analysis and family testing

The diagnosis of PCD was further confirmed by SLC22A5 gene analysis (reference transcript NM_003060.4). Two heterozygous variants were found and classified as pathogenic, an already described [START_REF] Rose | Genotype-phenotype correlation in primary carnitine deficiency[END_REF] maternally inherited missense c.839C > T (p.Ser280Phe) variant, and a paternally inherited nonsense c.1006C > T (p.Arg336*) variant.

In contrast to the patient, carnitine testing and molecular study performed in the parents and the 3-year-old brother showed low levels of free and total carnitine in good agreement with an herozygous status (Table 2).

| MATERIALS AND METHODS

| Carnitine and acylcarnitine analysis

Acylcarnitines, total and free carnitine quantifications were performed by electrospray tandem mass spectrometry (Waters Quattro micro™) from dried blood spots using the nonderivatized kit MassChrom ® Amino Acids and Acylcarnitines (Chromsystems).

| Urine OA profile

Urine OA detection and quantification were performed by gas chromatography-mass spectrometry Clarus 500™ (Perkin Elmer) after liquid/liquid extraction in ethyl acetate and derivatization by (N,O-Bis[trimethylsilyl] trifluoroacetamide).

| Genetic analyses

Genomic DNA was extracted from peripheral blood by automated method (TECAN freedom EVO). The SLC22A5 exons and flanking regions (±25 bp) were amplified using a polymerase chain reaction-based method designed through Ampliseq designer (Thermofisher). The library was prepared using Ion AmpliSeq Library kit 2.0-96LV and Ion CHEF (Ion Torrent by Thermo Fisher Scientific); the sequencing was performed with Ion S5XL (Ion Torrent by Thermo Fisher Scientific); the bioinformatic worflow utilized Tor-rentSuite for base calling, alignment and variant calling steps; the biological interpretation was conducted following the ACMG classification. The Ampliseq design also contained other genes to ruled out other betaoxydation defects: ACADVL, CPT1A, CPT2, ETFA, ETFB, SLC25A20, HADHA, HADHB, ACAD9, ACADS, and ACADM.

Sanger sequencing was performed for relatives with targeted analysis of the Exons 5 and 6 of SLC22A5 (NM_003060.4) gene, using an 3500xl genetic analyzer (Applied Biosystems).

| DISCUSSION

We reported a severe case of PCD decompensation in an 18-week-old female infant. Initially, a few days before admission, the infant presented gastrointestinal disorders. First, metabolic evaluation evidenced cardiac, renal and hepatic involvement, metabolic acidosis, and hyperammonemia. The condition worsened rapidly after admission with seizures followed by cardiorespiratory arrest. After recovery, dilated cardiomyopathy with left ventricular insufficiency was evidenced which rapidly caused malignant arrhythmia resistant to drug treatment and cardioversion. Despite implementation of high doses of oral carnitine, irreversible multivisceral failure led to the decision to discontinue supportive care.

According to the review of Shibbani et al., [START_REF] Shibbani | Primary carnitine deficiency: novel mutations and insights into the cardiac phenotype[END_REF] cardiac involvement is very common in the PCD patients. Nevertheless, cardiac presentations are usually described after 1 year of life and hepatic presentations are the most frequent before 2 years of age. Thus, to our knowledge, only nine infant PCD cases presenting with cardiac involvement before 1 year of age were published (Table 3). These patients had signs of respiratory infection or metabolic decompensation and showed evidence of altered cardiac function during evaluation. For almost all of them, cardiac function was totally or partially recovered by carnitine therapy within a few months and further metabolic decompensation was prevented. Tang et al. [START_REF] Tang | Mutations of OCTN2, an organic cation/carnitine transporter, Lead to deficient cellular carnitine uptake in primary carnitine deficiency[END_REF] described the case of PCD twins who died at 6 months of life in a context of acute metabolic decompensation complicated by cardiac arrhythmias but in this particular case carnitine therapy was not provided.

Thus our case report is notable both for the severity of the cardiac damage by 18 weeks of age and for unresponsiveness to high doses of carnitine. Could the genotype, in association with other intrinsic or environmental factors, explain such a severe cardiac presentation in our patient?

This case had a compound heterozygous status combining a nonsense and a missense variant classified as pathogenic. The nonsense variant causes a loss of function and the missense variant p.S280F, located in cytoplasmic domain, was shown to alter cations transport by OCTN2 in CHO cells. [START_REF] Di San Filippo | Pharmacological rescue of carnitine transport in primary carnitine deficiency[END_REF] Both variants are rare in the gno-mAD population and phenotype-genotype correlations are not available for these variants. Biallelic nonsense variants are more present in symptomatic than in asymptomatic patients [START_REF] Rose | Genotype-phenotype correlation in primary carnitine deficiency[END_REF] and are associated with lower free carnitine levels [START_REF] Shibbani | Primary carnitine deficiency: novel mutations and insights into the cardiac phenotype[END_REF] than biallelic missense and mono-allelic nonsense variants. No clear relationship between severity and predicted functional consequences of missense variant was found. [START_REF] Shibbani | Primary carnitine deficiency: novel mutations and insights into the cardiac phenotype[END_REF][START_REF] Lamhonwah | Novel OCTN2 mutations: no genotype-phenotype correlations: early carnitine therapy prevents cardiomyopathy[END_REF] There is no correlation between genotype and cardiac or metabolic phenotype in PCD since different types of presentation have been observed within an individual family. [START_REF] Rose | Genotype-phenotype correlation in primary carnitine deficiency[END_REF][START_REF] Lamhonwah | Novel OCTN2 mutations: no genotype-phenotype correlations: early carnitine therapy prevents cardiomyopathy[END_REF][START_REF] Wang | Functional analysis of mutations in the OCTN2 transporter causing primary carnitine deficiency: Lack of genotype-phenotype correlation[END_REF][25] Moreover, we cannot exclude other factors, whether genetic, including nonexplored genes, or environmental, which may influence cardiac response to the lack of energetic supply caused by PCD. Such severe cardiac presentation may be explained by pre-existing cardiac susceptibility that could be explored by large-scale NGS sequencing. Thus, we did not find any other pathogenetic variant in the analyzed betaoxydation genes (cf Section 3).

In addition, analyses revealed no infectious diseases, and particularly no gastrointestinal infection that could promote a catabolic state and favor metabolic decompensation. Table 3 shows that some case reports had clinical manifestations of infectious diseases at the time of PCD disclosure.

In our case, the patient's heterozygous mother had very low levels of free and total carnitine in agreement with a secondary carnitine deficiency (Table 2). This could have negatively impacted the child's phenotype, by causing low tissue carnitine stores at birth. Normal or borderline low levels of plasma carnitine are described in heterozygous parents of affected children [START_REF] Lamhonwah | Novel OCTN2 mutations: no genotype-phenotype correlations: early carnitine therapy prevents cardiomyopathy[END_REF][START_REF] Scaglia | Defective urinary carnitine transport in heterozygotes for primary carnitine deficiency[END_REF] but most of the publications do not report parental and siblings carnitine levels. In heterozygotes for PCD, a low protein dietary intake (vegetarian diet) in association with a less effective renal carnitine reabsorption 26 could result in low levels of plasma and tissue carnitine, as exogenous carnitine constitutes about 75% of the carnitine pool.

The index case's older brother had also very low levels of free carnitine deficiency (6 μmol/L) the difference >5 μmol/L between free and total carnitine was consistent with heterozygous status. [START_REF] Mchugh | Clinical validation of cutoff target ranges in newborn screening of metabolic disorders by tandem mass spectrometry: A worldwide collaborative project[END_REF] Echocardiography and clinical examination at 2-year-old were normal. Genetic analysis confirmed the heterozygous carrier status. Only Exons 5 and 6 of SLC22A5 genes were analyzed for the relatives.

The occurrence in our case of sudden cardiac signs moving towards a rapidly fatal cardiovascular decompensation although high doses of carnitine treatment, and comparative literature show both that (i) under 1 year of age cardiovascular damages in PCD are very frequent and most of the time at subclinical level (ii) clinical outcome remains unpredictable if carnitine treatment is initiated late. These data reinforce the interest of neonatal screening in PCD, despite a low predictive positive value [START_REF] Schiergens | Newborn screening for carnitine transporter defect in Bavaria and the long-term follow-up of the identified newborns and mothers: assessing the benefit and possible harm based on 19 ½ years of experience[END_REF] and the decision to discontinue screening in some countries. [START_REF] Wilson | The decision to discontinue screening for carnitine uptake disorder in New Zealand[END_REF] Neonatal screening in PCD would allow newborns to be immediately treated with L-carnitine in order to avoid future fatal complications.

| CONCLUSION

The PCD case reported had an early fatal demise following metabolic and cardiac decompensation. The absence of striking clinical signs before admission delayed the appropriate management of the patient. Factors influencing the severity of the phenotype were not clearly identified. A secondary carnitine defect in the mother due to the association of poor diet and decreased renal reabsorption could be a part of the explanation. In case of new pregnancy, carnitine supplementation should be provided to the mother until the genetic testing results in foetus are obtain. The unresponsiveness to carnitine therapy in this severe case highlights the importance of expanding neonatal screening to PCD.

INFORMED CONSENT

All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2000 (5). Informed consent was obtained from all patients for being included in the study.Proof that informed consent was obtained must be available upon request.

ANIMAL RIGHTS

No animal in that study.

T A B L E 2

 2 Familial analysis: genetic outcome and carnitine levels

  Laboratory testing at entrance

	Parameter	Value	Normal range
	pH	7.27	7.32-7.43
	Bicarbonate	15.1 mmol/L	23-26 mmol/L
	Lactate	2.5 mmol/L	0.5-1.5 mmol/L
	Troponin	349 ng/L	<16 ng/L
	AST	997 UI/L	5-34 UI/L
	ALT	469 UI/L	6-55 UI/L
	Ammonia (venous)	227 μmol/L	18-72 μmol/L
	Creatine kinase	616 UI/L	29-168 UI/L
	Urea	8.6 mmol/L	1.2-6.0 mmol/L

T A B L E 1

Abbreviations: ALT, alanine transaminase; AST, aspartate transaminase.

  Review of infantile cardiac PCD cases reports (age of onset <1 year)

			Plasmatic		Cardiac function
			Free
			carnitine
		Clinical history	(NR: 33-43	Carnitine			Last follow-
	Age of onset	before diagnosis	μmol/L)	supplementation	Initial	Recovery	up	Reference
	8 months	Respiratory	10.7	50 mg/kg/d	EF = 34%, LVE EF 62%	4 months	Shibbani
		infection						et al. 9
								("Patient
								II-2")
	11 months	Cough and poor	8.8	50 mg/kg/d	EF = 28%, LVE EF 56%	12 months	Shibbani
		feeding						et al. 9
								("Patient
								VI-4")
	11 months	None	10.3	Unknown	EF = 47%, LVE EF 65%	12 months	Shibbani
								et al. 9
								("Patient
								IV-5")
	6 months	Encephalopathy,	0.72	150 mg/kg/d (first year)	LVE	Full recovery 17 months	Lamhonwah
		seizures		100 mg/kg/d (then)				et al. 23
	7 months	Breathing	1	Intravenous and	LVE	Full recovery 11 months	Rahbeeni
		shortness,		per os 100 mg/kg/d				et al. 30
		congestive heart
		failure
	6 months	Breathing shortness low	Unknown	Cardiac	Full recovery Unknown	Di san Filippo
					fibroelastosis			et al. 22
	5 months	Metabolic	<1	Unknown	unknown	Full recovery Unknown	Di san Filippo
		deterioration						et al. 22
		following
		gastroenteritis
	6 months	Acute metabolic	9	No	unknown	Fatal demise		Tang et al. 21
		derangement
	3 months	Episodes of cardiac	low a	variable dosing b	LVE	Full recovery 20 years	Cederbaum
		arrest with severe						et al. 31
		hypoglycemia						("Case 1")

T A B L E 3 Abbreviations: EF, ejection fraction; LVE, left ventricle enlargement; NR, normal range; PCD, primary carnitine deficiency. a In vitro testing. b Titrated to maintain plasma carnitine in the low to mid normal range.

AUTHOR CONTRIBUTIONS

Lebreton Louis: analysis and interpretation of data + drafting the article. Gaschignard Margaux: analysis and interpretation of data. Guibet Claire: analysis and interpretation of data (bibliographic research). Lamireau Delphine: revising the article critically for important intellectual content. Roche Sandrine: revising the article critically for important intellectual content. Richard Emmanuel: head of biochemistry department at Bordeaux University Hospital. Ged Cécile: revising the article critically for important intellectual content. Mesli Samir: revising the article critically for important intellectual content. Redonnet-Vernhet Isabelle: analysis and interpretation of data + revising the article critically for important intellectual content.

CONFLICT OF INTEREST

The author declares that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported.