Arnaud Coez
email: acoez@noos.fr

Ludovic Fillon

Ana Saitovitch

Caroline Rutten

Sandrine Marlin

Jennifer Boisgontier

Alice Vinçon-Leite

Hervé Lemaitre

David Grévent

Charles-Joris Roux

Volodia Dangouloff-Ros

Raphaël Levy

Eric Bizaguet

Isabelle Rouillon

Eréa Noël Garabédian

Françoise Denoyelle

Monica Zilbovicius

Natalie Loundon

Nathalie Boddaert

Arterial spin labeling brain MRI study to evaluate the impact of deafness on cerebral perfusion in 79 children before cochlear implantation

Keywords: deafness, children, hearing loss, cochlear implant results, oral intelligibility scores, MRI, arterial spin labeling, auditory cortex, brain development

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

Introduction

One in 1,000 newborns are identified with severe to profound hearing loss at birth [START_REF] Butcher | Prevalence of permanent childhood hearing loss detected at the universal newborn hearing screen: Systematic review and meta-analysis[END_REF]. Approximately 80% of prelingual deafness is due to genetic factors [START_REF] Marlin | GJB2 and GJB6 mutations: genotypic and phenotypic correlations in a large cohort of hearing-impaired patients[END_REF] with about a hundred identified gene abnormalities [START_REF] Ideura | Comprehensive analysis of syndromic hearing loss patients in Japan[END_REF] [START_REF] Bai | Identification of novel variants in MYO15A, OTOF, and RDX with hearing loss by next-generation sequencing[END_REF]. Phenotypic expression of these genetic mutations is variable, with a hearing loss ranging from mild to severe. Despite the use of hearing aid devices, persistent lack of audibility may require patients to develop skills other than using sounds to communicate, relying particularly on visual cues (lip reading, cued speech, sign language) or tactile cues.

Cochlear implants (CI) have proven to be a useful treatment option for individuals with severe to profound hearing loss and are part of the French National Authority for Health management guidelines (HAS 2012, https://www.has sante.fr/upload/docs/application/pdf/fiche_bon_usage_implants_cochleaires.pdf). It has been recognized that early implantation provides children with the best outcomes [START_REF] Simon | Guidelines (short version) of the French Society of Otorhinolaryngology (SFORL) on pediatric cochlear implant indications[END_REF]. Cochlear implantation is not recommended as an option for children over 5 years old, unless hearing loss is acquired or progressive [START_REF] Simon | Guidelines (short version) of the French Society of Otorhinolaryngology (SFORL) on pediatric cochlear implant indications[END_REF].

Improvement of auditory perception after CI was investigated by electrophysiological studies using the latency of the P1 cortical auditory evoked potential [START_REF] Dorman | Central auditory development: evidence from CAEP measurements in children fit with cochlear implants[END_REF]. Results

showed that if children experience less than 3 years of auditory deprivation before implantation, P1 latencies fall back into the normal range. Children who are implanted after the age of 7 years old, however, generally do not develop normal P1 latencies.

The development of other somatosensory modalities, such as lip reading [START_REF] Finney | Visual stimuli activate auditory cortex in the deaf[END_REF], sign language [START_REF] Macsweeney | The signing brain: the neurobiology of sign language[END_REF], vibrotactile stimulation [START_REF] Cardon | Somatosensory Cross-Modal Reorganization in Children With Cochlear Implants[END_REF], as well as the response to reinstated auditory input after cochlear implantation [START_REF] Kang | Neural changes associated with speech learning in deaf children following cochlear implantation[END_REF] in deaf patients has been investigated by functional neuroimaging studies over the last two decades. Results have shown differences in cerebral organization in adults with congenital deafness [START_REF] Finney | Visual stimuli activate auditory cortex in the deaf[END_REF], [START_REF] Macsweeney | The signing brain: the neurobiology of sign language[END_REF]. However, it is not clear whether these differences stem from the acquisition of non-verbal communication skills, from deafness, or from both. Few functional studies have focused on children candidates for cochlear implantation, mainly because of the challenges associated with brain imaging studies in children. In a study by Lee et al, brain metabolism in 33 deaf children (age = 6.3 ± 2.3 years, with less than 70 dB HL pure tone thresholds with their hearing aids) was examined preoperatively using FDG-PET and correlated with postoperative speech perception scores [START_REF] Lee | Cortical activity at rest predicts cochlear implantation outcome[END_REF]. Results showed that the degree of hypometabolism within the auditory cortex before implantation was positively correlated with oral intelligibility scores after implantation: patients obtaining higher scores were those presenting stronger hypometabolism before CI, suggesting that the auditory cortices would not have been recruited by other cortical functions and could respond effectively to the auditory input reinstated by cochlear implantation. The results from fMRI and rest metabolism studies [START_REF] Finney | Visual stimuli activate auditory cortex in the deaf[END_REF], [START_REF] Macsweeney | The signing brain: the neurobiology of sign language[END_REF], [START_REF] Cardon | Somatosensory Cross-Modal Reorganization in Children With Cochlear Implants[END_REF] indicate that deafness can lead to cross-modal plasticity: the auditory cortex became more responsive to non-auditory stimulation in deaf individuals [START_REF] Benetti | Functional selectivity for face processing in the temporal voice area of early deaf individuals[END_REF]. Nevertheless, the question remains of whether reorganization of auditory cortex in deaf individuals is due to the effects of auditory deprivation (bottom-up regulation) or the later acquisition of sign language (top-down regulation) [START_REF] Cardin | Differential activity in Heschl's gyrus between deaf and hearing individuals is due to auditory deprivation rather than language modality[END_REF].

Brain functional investigations using nuclear imaging methods remain limited in children for obvious methodological reasons. It is difficult to justify the use of radiotracers for imaging children before cochlear implantation. However, recent advances in neuroimaging allow to measure rest brain function using arterial spin labeling (ASL) MRI sequence. This technique uses magnetically labeled arterial blood water as a diffusible flow tracer. By labeling inflowing blood water proximal to the target imaging region, the perfusion signal is subsequently calculated by comparison with a separate image acquired using a control pulse without labeling blood flow to remove static background signal and control for magnetization transfer effects. Therefore, ASL-MRI non-invasively assesses brain perfusion and provides an absolute and quantifiable voxel-by-voxel measurement of rest cerebral blood flow (CBF)

without the administration of contrast material or exposure to ionizing radiation, [START_REF] Detre | Perfusion magnetic resonance imaging with continuous arterial spin labeling: methods and clinical applications in the central nervous system[END_REF], offering new opportunities to quantify cerebral blood flow at rest in neonates and children. We sought to investigate whole-brain cortical perfusion in deaf children compared to normally hearing controls in three age groups: younger than 2 years old; from 2 to 5 years old; and from 5 to 16 years old. In addition, in deaf children aged from 5 to 16 years old, we aimed to investigate a putative relationship between preoperative cortical perfusion and clinical outcome after cochlear implantation using oral intelligibility scores at arthrogryposis, facial cutaneous angioma or hemangioma or lymphangioma, morphological evaluation of upper-limit head circumference, sub-cutaneous cyst, feeding difficulties, abnormal eye-movements, benign nystagmus, benign eye-motion disorder, isolated strabism, neo-natal diabetes with no severe hypoglycemia) and presented strictly normal scans and no hearing loss verified by routine clinical follow up.

Participants were divided into 3 subgroups based on their age at time of MRI. A subgroup under 2 years of age was composed of 28 patients (median age = 0.9 years, range 0.5 to 2.0 years) and 33 controls (median age = 1.0 year, 0.5 to 2.0 years). A subgroup aged between 2 and 5 years of age was composed of 26 deaf patients (median age = 3.2 years, 2.1 to 4.6 years) and 20 controls (median age = 2.9 years, 2.0 to 5.0 years). A subgroup older than 5 years of age was composed of 25 deaf patients (median age = 9.0 years, 5.2 to 15.8 years) and 33 controls (median age = 10.1 years, 6.0 to 13.0 years).

All children, patients and controls, younger than 5 years of age received standard premedication before their MRI (pentobarbital, 5 mg / kg). The study design was approved by the local ethics committee, 61-NCK, 20190621163621.

Clinical description

All patients had bilateral hearing loss. In the studied population 60.8 % had a symmetric bilateral hearing loss and 39.2% had an asymmetric hearing loss with a right predominance in 77.4% of the cases. Seventy percent (70%) of patients were implanted on the right ear, 26%

were implanted on the left ear, 4% received bilateral cochlear implantation and one child had not been implanted yet. Concerning the etiology, 47% had a hearing loss (HL) of unknown etiology, 5% had congenital cytomegalovirus infection (cCMV), 18% had a connexin gene mutation, 26% had an inner ear malformation (two of which had SCL26A4 mutation), and 4% had an auditory neuropathy.

For children over 5 years old, speech perception was evaluated in free field, before and 12 months after cochlear implantation based on the mean intelligibility score obtained using open-set recognition of French Fournier disyllabic words (OSW) (for 5 out of 25 of deaf children, the OSW scores were unknown). Prior to CI, following hearing aid rehabilitation, oral communication was evaluated with a mean intelligibility score of 64.5 +/-32%. Twelve months after CI, mean intelligibility score was of 92 +/-11.5% (see Figure 1). There was no correlation between age and intelligibility scores either before or after cochlear implantation (see Figure 1). The hearing thresholds before cochlear implantation showed that patients had some auditory perception with hearing aids at low frequencies. Perceived frequencies were mainly low frequencies 250 Hz (36 dB HL) and high frequencies remained difficult to perceive (63 dB HL at 4 kHz). Cochlear implants significantly improved perception of frequencies between 500 Hz and 4 kHz in comparison to hearing aids (see Figure 2), improving the audibility of long-term average speech spectra [START_REF] Byrne | An international comparison of long-term average speech spectra[END_REF]. For 3 deaf children, perceived frequency values were unknown.

Data acquisition

All On the 3.0T scanner, 3D T1-weighted FSPGR images were acquired with the following parameters: 156 axial slices; TR = 6.9 ms; TE = 3 ms; resolution in plane = 1 x 1 mm; slice thickness = 1 mm; FA = 12°. For most deaf patients, Cube T1 images were acquired with these parameters: 374 sagittal slices; TR = 500 ms; TE = 11.2 ms; resolution in plane = 0.47 x 0.47 mm; slice thickness = 1 mm; FA = 90°. ASL perfusion images were obtained using the same parameters as on the 1.5T system.

Data preprocessing

For the data preprocessing, we used the quantification of the CBF and not only perfusion weighted images. The ASL sequence provided by General Electric Medical System included a proton-density image used for signal normalization during CBF quantification.

CBF images are produced by the processing console automatically and we can measure the ASL quantitatively.

All T1-weighted and ASL-MRI images were first visually checked for major artifacts: we performed a two-step quality control, the first one by an expert radiologist right after acquisition (NB) and the second one by an expert image processing engineer (LF) before preprocessing to discard images with artifacts, such as motion, aliasing, ghosting, spikes, low signal to noise ratio. Then, all images were analyzed using SPM12

(http://www.fil.ion.ucl.ac.uk/spm, London, UK).

Native 3D T1-weighted FSPGR and Cube T1 images were segmented into gray matter, white matter and cerebrospinal fluid using the CAT12 toolbox (http://www.neuro.unijena.de/cat/) within SPM12 and deformation fields between native space and MNI space were obtained. The MNI template used for segmentation has been adapted according to the age of the given subject: a pediatric template was created with "Template-O-Matic" toolbox (http://dbm.neuro.uni-jena.de/software/tom/) using the NIH Pediatric MRI Data Repository (n=404, age range 5-18 years) for children over 2 years old, and the Infant Brain Probability Templates [START_REF] Altaye | Infant brain probability templates for MRI segmentation and normalization[END_REF] for children under 2 years old.

For each child, the co-registration between the native CBF image and the native gray matter image was estimated. Then, the combination of the deformation fields and the estimated coregistration was applied to the CBF image to spatially normalize this image in the MNI space. The resulting image was checked for proper registration and smoothed with a Gaussian kernel of 10-mm full-width at half-maximum (FWHM). All spatially normalized images had the same resolution in plane (1.5 x 1.5 mm) and the same slice thickness (1.5 mm).

Statistical analysis Whole-brain voxel-based analysis

For each subgroup, comparisons between deaf children and normally hearing controls were performed to investigate voxel-wise cortical perfusion differences using a two-sample t-test design within the framework of the general linear model (GLM) in SPM12. Age and MRI field strength were considered as confounding covariates. A proportional scaling of the CBF images was applied and set to a grand mean scaled value of 50 mL/dL/min to minimize intersubject variability. Voxels included on an explicit binary mask were considered, corresponding to the cortical gray matter excluding the cerebellum.

Multiple regression analysis

An additional GLM analysis, using a multiple regression design, was applied to the smoothed CBF images spatially normalized in the subgroup of deaf children older than 5 years old, to investigate a putative relationship between preoperative cortical perfusion and clinical outcome after cochlear implantation. Oral intelligibility scores obtained 12 months after implantation were used as independent factors. Age and MRI field strength were considered as confounding covariates. Proportional scaling of the CBF images was also applied and set to a grand mean scaled value of 50 mL/dL/min in this analysis. All p-values were threshold at 0.05 and corrected for multiple comparisons with family-wise error correction (FWE).

Region-of-interest analysis

As a post-hoc analysis, a region of interest analysis was performed to investigate, in both groups, the evolution of rest CBF across age within temporal clusters identified in the wholebrain group comparison. Thus, the mean CBF from these clusters was extracted for all participants. The individual mean CBF values were normalized by the mean CBF measured within the cortical gray matter binary mask for each participant to obtain relative CBF. We used the residual values from the analysis as dependent variables, canceling out field strength effect using the ordinary least squares (OLS) model with the python stats models v0.9.0 module. P-values ≤ 0.05 were considered statistically significant.

Results

Whole-brain voxel-based comparisons

For children over 5 years old, whole-brain voxel-based comparison between rest CBF in deaf patients and normally hearing controls revealed significant bilateral decrease in rest CBF localized in the superior temporal and Heschl's regions in patients (p ≤ 0.05, FWE correction) (see Figure 3). This result appeared to be independent of the predominance of deafness, with no significant differences found between right-predominant and left-dominant deaf children.

This result was independent of the side of the predominant hearing loss. No significant cluster was There were no significant differences between groups for children between 2 and 5 years old and for children younger than 2 years old.

Multiple regression analysis

Clinical OSW scores were available for 20 out of 25 deaf children older than 5 years old.

Whole-brain voxel-based multiple regression analysis showed a significant negative regression between rest-CBF before implantation and OSW scores at 12 months after implantation localized in left inferior and mid-occipital regions: deaf children who presented higher OSW scores 12 months after implantation were those who had lower rest-CBF values in these regions prior to implantation (t = 6.63; z(score) = 4.53; p(FWE-corr) = 0.036; MNI coordinates: x = -33, y = -81, z = -8). There was no significant positive regression with OSW scores at 12 months after implantation. No significant positive or negative regression were found between rest-CBF and clinical OSW scores before implantation.

Region-of-interest analysis

The evolution of rest-CBF across age within temporal regions was significantly different in both groups (t = 4.14; p = 0.0001) (see Figure 4). While in normally hearing children rest-CBF increased with age (β = 0.0207 unit/year; t(161) = 5.67; p = 0.00001), in deaf children rest-CBF did not increase with age and remained stable over time (β = -0.0011 unit/year; t(161) = -0.29; p = 0.773).

In addition, further analyses comparing mean rest-CBF relative values in these regions for specific age groups, showed no significant differences between deaf children and normallyhearing controls for 0-2 and 2-4 years old groups and a significant difference for the others age groups: 4-6, 6-8, 8-10, 10-12 and 12-16 years groups (Figure 5).

Discussion

To our knowledge, this is the first study to use 3D ASL-MRI at different ages and stages of brain development in infants and children as part of their preoperative work-up for cochlear implantation. It gives us insight on the brain reorganization secondary to deafness and subsequent hearing restoration from hearing aids and cochlear implants.

Our results showed that, in comparison to normally hearing children of the same age, deaf children above 5 years old present a significantly decreased cerebral blood flow at rest within temporal regions bilaterally. This decrease is more pronounced on the right side independently of the side of deafness if single-sided. In addition, a significant increased rest-CBF was also observed within occipital regions in deaf children. Importantly, even if conventional hearing devices were systematically used in patients, abnormal cortical blood flow at rest is still observed, suggesting that, even in the context of partial auditory stimulation, a functional reorganization occurs with the temporal cortex becoming less functional and the visual cortex becoming over functional. Comparable results have been reported by [START_REF] Coez | Processing of voices in deafness rehabilitation by auditory brainstem implant[END_REF] in a PET study involving adults with acquired hearing loss after auditory brainstem implant with a low average score of postoperative intelligibility. When compared to controls, patients presented higher rest PET CBF in bilateral occipital brain areas (left: x=-18, y=-86, z=22; right: x=14, y=-84, z=26), and lower rest PET CBF in the left temporal areas (x=-58, y=-14, z=-2). The authors hypothesized that patients had developed and optimized their visual strategies to better perceive their environment.

Our results also showed that the degree of hyperperfusion within occipital regions regressed negatively with cochlear implant OSW scores in children older than 5 years old: deaf children who presented higher OSW scores obtained 12 months after CI were those who had lower rest CBF values in these regions prior to implantation. In normally hearing children, the role of the auditory cortical network in enabling processing of the acoustic cues required for language development is present very early in life and is quickly lost [START_REF] Dehaene-Lambertz | The Infancy of the Human Brain[END_REF]. Profoundly deaf individuals will not be able to develop a full phonological inventory of their native language despite conventional hearing aids [START_REF] Mccandliss | Success and failure in teaching the [r]-[l] contrast to Japanese adults: tests of a Hebbian model of plasticity and stabilization in spoken language perception[END_REF]. Here, even though we show that deaf children seem to use the available and operational somatosensory networks to establish ad-hoc communication (eg. visual networks if they have a deficient auditory cortical activity), we also show that over recruitment of this alternative network seems to disrupt rehabilitation of the function.

It is worth noticing that the OSW scores of most patients improved after cochlear implantation (Figure 1), especially if the pre-OSW score was under 80%, which suggests that, despite previous partial auditory stimulation, cortical temporal areas are still capable of analyzing and processing the new incoming high-frequency phonemes that ensure further language development. As showed in Figure 2 with speech outcomes at 1 year after implantation [START_REF] Han | Brain Plasticity Can Predict the Cochlear Implant Outcome in Adult-Onset Deafness[END_REF]. Here we corroborate these results in a pediatric population. Indeed, we describe not only a significantly decreased cerebral blood flow at rest within temporal regions bilaterally and significantly increased within left occipital regions, but we show that deaf children who undergo late cochlear implantation after hearing aid rehabilitation seem to develop sufficient language skills. These results reinforce the hypothesis that temporal regions remain relatively resistant to cross modal plasticity.

Our results showing differences in rest CBF across age within temporal regions between deaf and normally hearing children provides a better understanding of the developmental dynamics of deafness. Results from the whole brain group comparison showed no significant differences in rest CBF between deaf children and normally hearing children under 5 years old, suggesting that auditory deprivation does not immediately impact brain function at rest.

Results showing the evolution of rest CBF across age within temporal regions indicate that functional changes, characterized by increase in rest CBF occur in these areas and continue progressively throughout childhood in normally hearing children. In deaf children, however, no rest CBF evolution was observed with age, suggesting a lack of synaptic activity in auditory cortex in the context of auditory deprivation. Importantly, the analysis performed in separated age groups showed that mean rest CBF within the Heschl's gyri is comparable between deaf children and normally hearing controls between 0 and 4 years old, indicating equivalent brain neuronal activity. However, from this age on, significant differences are observed for all age groups (4-16 years old), which suggest that there might be a critical period around 4 years old where, in the context of auditory deprivation, typical brain maturation within the temporal cortices becomes significantly disturbed (Figure 5). This could be associated with the fact that synapse formation begins after birth and increases rapidly in the early postnatal period and the synapses that are not activated by sensory stimulation are lost [START_REF] Rakic | Concurrent overproduction of synapses in diverse regions of the primate cerebral cortex[END_REF]. Interestingly, it has been shown that the time point for synapses loss differs across brain regions, occurring at about 2 years old in occipital areas, 4 years old in temporal areas and between 5 and 10 years old in the prefrontal cortex [START_REF] Huttenlocher | Regional differences in synaptogenesis in human cerebral cortex[END_REF]. Previous electro-physiological studies using the P1-N1 complex of auditory evoked potentials corroborate this hypothesis, by describing a sensitive period for development of the primary auditory cortex in deaf children fitted with cochlear implants [START_REF] Sharma | Developmental and cross-modal plasticity in deafness: evidence from the P1 and N1 event related potentials in cochlear implanted children[END_REF]: children implanted above age 3.5 years show considerable variability in P1 and N1 development, indicating poor clinical outcome, in contrast to the early implanted children.

Contrary to previous rest metabolism PET studies in deaf children, in our study all deaf children older than 5 years old included had benefited from early rehabilitation with conventional hearing aids. They had progressive deafness, meeting the eligibility criteria for late cochlear implants, including significant residual hearing (mean threshold of aided hearing was around 40 dB HL; Figure 2) and spoken language skills. With hearing aids, all children presented functional verbal communication. Importantly, in the study of [START_REF] Lee | Cortical activity at rest predicts cochlear implantation outcome[END_REF], the best threshold of aided hearing was 70 dB HL, which might explain the negative correlation observed between age at implantation and oral intelligibility scores after cochlear implantation. In addition, even though some studies consider the impact of the "duration of auditory deprivation" [START_REF] Han | Brain Plasticity Can Predict the Cochlear Implant Outcome in Adult-Onset Deafness[END_REF], in our study this parameter was not relevant since all children benefited from early screening and early rehabilitation by the use of hearing aids.

It is important to notice that rest CBF results presented in this study, obtained using ASL-MRI, strongly agree with FDG-PET results, indicating the robustness of these measures. The discrepancies in the neuroimaging literature in the field might be partially explained by heterogeneity of etiologies. Indeed, certain genetic causes of hearing loss can make any attempt at cochlear implant rehabilitation unsuccessful, as the neural system cannot withstand the additional current load [START_REF] Delmaghani | Hypervulnerability to Sound Exposure through Impaired Adaptive Proliferation of Peroxisomes[END_REF]. In our sample, even though some patients had an identified genetic cause of deafness and despite the genetic screening recommendations, about 50% of etiologies unfortunately remained unknown. Interestingly, a preliminary study indicates that there were no notable differences between patients with connexin 26 gene mutations and patients with hearing loss from other genetic causes of unknown etiology (unpublished data). In a prospective study, we will address brain perfusion differences and cochlear implant benefit in sub-groups of different etiologies of genetic deafness. Another possible methodological limitation of this study was the use of pentobarbital in the group under 5 years old even if deaf patients and controls received the same premedication. Nevertheless, many recent studies reported no effects of pentobarbital on the regional distribution of CBF (Veselis et al., 2004[START_REF] Carsin-Vu | Measurement of pediatric regional cerebral blood flow from 6 months to 15 years of age in a clinical population[END_REF]) [START_REF] Greicius | Persistent default-mode network connectivity during light sedation[END_REF]. Moreover, other PET activation studies using the same sedation with pentobarbital found hyperperfusion in temporal regions [START_REF] Boddaert | Perception of complex sounds in autism: abnormal auditory cortical processing in children[END_REF] or hypoperfusion at rest when comparing groups of normally hearing, autistic versus non autistic children [START_REF] Zilbovicius | Temporal lobe dysfunction in childhood autism: a PET study. Positron emission tomography[END_REF]. DiFrancesco et al. ( 2013) performed a study on BOLD fMRI in infants under sedation: Comparing the Impact of Pentobarbital and Propofol on Auditory and Language Activation. They compared activation profiles in response to passive story-listening stimulation. Nembutal, had robust activation of primary and secondary sensory cortices. They concluded that clinical fMRI of sedated infants could be performed [START_REF] Difrancesco | BOLD fMRI in infants under sedation: Comparing the impact of pentobarbital and propofol on auditory and language activation[END_REF]. We hypothesized that this limited effect of pentobarbital was similar using ASL-MRI.

We also admit that the sequence parameters are not optimized for the different ages and field strengths across the study and therefore this may have influenced absolute measurement of CBF. Nevertheless, it could also be discussed as a limitation of our study that the scanner noise could have been cause an effect on perfusion. Although the scanner noise is reduced to 60 dB by earplugs it is possible that the noise partly cause a difference between hearing impaired children and hearing children especially since the sedation with pentobarbital may play a role. Pentobarbital may reduce the perception of the scanner noise also in hearing children and may lead to the lack of the difference between hearing impaired and hearing children.

OSW scores appeared to be of limited value to evaluate the effectiveness of CI, especially in the groups under 5 years old. Better outcome measures, such as listening effort including verbal response times to repeating back words [START_REF] Coez | Audiométrie vocale chronométrée: le temps de réaction pour répéter un mot, indicateur de l'effort attentionnel fourni[END_REF], pupillometry [START_REF] Steel | Correction: Binaural Fusion and Listening Effort in Children Who Use Bilateral Cochlear Implants: A Psychoacoustic and Pupillometric Study[END_REF]) [START_REF] Aminihajibashi | Individual differences in resting-state pupil size: Evidence for association between working memory capacity and pupil size variability[END_REF] or electrophysiology [START_REF] Anderson | Pre-operative Brain Imaging Using Functional Near-Infrared Spectroscopy Helps Predict Cochlear Implant Outcome in Deaf Adults[END_REF][START_REF] De Schonen | Visual cortical activity before and after cochlear implantation: A follow up ERP prospective study in deaf children[END_REF] could improve the evaluation of cochlear implant effectiveness. Associated with these measures, rest-CBF investigations using ASL-MRI could help develop a useful prognostic tool to predict cochlear implant benefit.

Conclusion

This study provides insight into brain perfusion changes associated with deafness and subsequent auditory rehabilitation in children. A decrease rest-CBF in the auditory cortex is observed in children older than 5 years old and not in younger children, suggesting and motivating early cochlear implantation to maximize implant outcomes. These perfusion abnormalities seem to occur progressively and become significant around 4 years old, compared to typically hearing children. It would be interesting to undertake additional research in the early years of life in deaf children to fine-tune the analysis of early brain development and further determine critical periods in auditory brain development.

Figure 1: OSW scores before (red) and 12 months after cochlear implantation (green) for patients above 5 years old. After cochlear implants, mean intelligibility scores were statistically better (92 +/-11.5 %) than before (64.5 +/-32 %) (p<0,001). There were no correlations between age and the intelligibility scores either before (β = -1.16 unit/year; t(18) = -0.539; p = 0.597) or after cochlear implantation (β = -0.08 unit/year; t(18) = -0.097; p = 0.924). Figure 5: Comparison of the mean rest-CBF relative values in temporal clusters identified in the whole-brain group comparison between normally-hearing children (orange) and deaf children (blue) for specific age groups. No significant differences for groups above 4 years: 0-2 years (t = 1.12; p = 0.266) and 2-4 years (t = -1.23; p = 0.226). However, we found significant differences for all groups after 4 years: 4-6 years (t = 5.82; p = 0.0003), 6-8 years (t = 7.46; p = 0.0001), 8-10 years (t = 2.74; p = 0.018), 10-12 years (t = 3.99; p = 0.002) and 12-16 years (t = 2.28, p = 0.047).

  images were acquired in the Department of Pediatric Radiology of Necker Children's Hospital (Paris, France) with a standard routine protocol including T1, T2 and ASL weighted sequences. Before June 2015, data from 33 of the 79 children candidates for cochlear implantation and 41 of the 86 controls were acquired on a 1.5 Tesla MRI scanner (Signa HDxt General Electric (GE) Medical System). After June 2015, data from 46 of the 79 children candidates for cochlear implantation and 45 of the 86 controls were acquired on a Discovery 3.0 Tesla MRI scanner (MR750 General Electric Medical System). We used normal-hearing earplugs for children, which attenuates the noise from 90 dB(A) to 60 dB(A). On the 1.5T scanner, 3D T1-weighted Fast Spoiled Gradient Echo (FSPGR) images were acquired with the following parameters: 240 axial slices; repetition time (TR) = 16.4 ms; echo time (TE) = 7.2 ms; resolution in plane = 0.47 x 0.47 mm; slice thickness = 1.2 mm; flip angle (FA) = 13°. ASL perfusion images were performed with a 3D pseudo continuous arterial spin labeling (3D pcASL) sequence using a fast spin echo acquisition with spiral filling of the K space (TR/TE = 4453/10.96 ms; 8 spiral arms x 512 sampling points; Freq = 512; postlabeling delay (PLD) = 1025 ms; FA = 155°; matrix size = 128 x 128; resolution in plane = 1.875 x 1.875 mm; slice thickness = 4 mm; field of view = 24 x 24 cm; bandwidth = 62.50; Imaging Options EDR, Fast, Spiral, Phase 8 Freq, NEX 3.00, Auto Shim On; 40 contiguous axial slices and duration time ≈ 4 minutes. Labeling duration is 1500 ms.

  found using two-sample t-test comparison between right-predominant and left-predominant deaf children. Furthermore, no significant effect of the predominance of deafness was found on relative mean CBF from the Heschl ROI (ANOVA; F(2, 17) = 0.34; p = 0.718), with age and MRI field strength as confounding covariates. Decrease in rest CBF was more pronounced in the right hemisphere (t = 6.42; z(score) = 5.51; p(FWE-corr) < 0.001; MNI coordinates: x = 45, y = -21, z = 10) than in the left hemisphere (t = 5.19; z(score) = 4.65; p(FWE-corr) = 0.015; MNI coordinates: x = -42, y = -24, z = 8). In addition, a significant bilateral increase in rest CBF was observed in the left (t = 5.12; z(score) = 4.61; p(FWE-corr) = 0.018; MNI coordinates: x = -33, y = -82, z = 2) and right (t = 4.80; z(score) = 4.36; p(FWE-corr) = 0.048; MNI coordinates: x = 27, y = -72, z = 24) occipital regions.

  , partial auditory stimulation prior to implantation reinforces postoperative speech performance. Even though postoperative ASL MR imaging is not feasible, our results lead us to suspect a change in brain activity at rest favoring auditory cortex over visual cortex. In a previous study comparing brain metabolism at rest using FDG-PET from post-lingually deaf adults to normally hearing controls before cochlear implant surgery, Han and colleagues described that bilateral temporal lobe hypometabolism(right: x=54, y=-14, z=6; left: x=-46, y=-24, z=16) and bilateral occipital hypermetabolism(right: x=18, y=-94, z=-4; left: x=-14, y=-94, z=-8) negatively correlated

Figure 2 :

 2 Figure2: Mean auditory thresholds (dB HL), with error bars corresponding to the 68% confidence interval (standard error), for the group of deaf children older than 5 years old before cochlear implantation without hearing aids (HA) (blue), with hearing aids (orange) and after cochlear implantation (green) at different frequencies: 250 Hz, 500 Hz, 1000 Hz, 2000 Hz and 4000 Hz. The side with the best tonal audiometric thresholds has been reported on the figure. Speech auditory perception improved with the use of hearing devices. Although performance was similar with hearing aids and cochlear implant at the frequency of 250 Hz (p=0,11), it was significantly better with the cochlear implant at frequencies of 500 Hz(p<0,05), 1000Hz (p<0,05) and 2000 Hz (p<0,05) and 4000 Hz (p<0,001). The long term average speech spectrum energy is reported in gray: (250Hz: -46 dB HL; 500Hz: -52 dB HL; 1000 Hz: -46 dB HL; 2000 Hz: -44 dB HL; 4000 Hz: -48 dB HL). HL thresholds over the speech spectrum did not allow speech perception.

Figure 3 :

 3 Figure 3: Whole brain voxel-by-voxel SPM analyses comparing deaf children and normallyhearing children older than 5 years old. A) Significant rest-CBF decrease in temporal regions, more pronounced in the right hemisphere (t = 6.42; z(score) = 5.51; p(FWE-corr) < 0.001; MNI coordinates: x = 45, y = -21, z = 10) than in the left hemisphere (t = 5.19; z(score) = 4.65; p(FWE-corr) = 0.015; MNI coordinates: x = -42, y = -24, z = 8). B) Significant rest-CBF increase in left (t = 5.12; z(score) = 4.61; p(FWE-corr) = 0.018; MNI coordinates: x = -33, y = -82, z = 2) and right (t = 4.80; z(score) = 4.36; p(FWE-corr) = 0.048; MNI coordinates: x = 27, y = -72, z = 24) occipital regions. Images were selected for illustrative purposes.

Figure 4 :

 4 Figure 4: Significant difference in age-related changes of the rest-CBF relative values in temporal regions for normally-hearing children (orange) and deaf children (blue) between 0 and 16 years (t = 4.09; p = 0.0001). The rest-CBF relative values are presented in arbitrary units.


Dragos Horvath
email: dhorvath@unistra.fr

Gilles Marcou

Alexandre Varnek
email: varnek@unistra.fr

Generative Topographic Mapping in Drug Design

Keywords: Generative Topographic Mapping, Chemography, Chemical Space Analysis, Quantitative Structure-Activity Relationships, Virtual Screening AD -Applicability Domain, DNN -Deep Neural Network, GTM -Generative Topographic Mapping, LLh-LogLikelihood, [Q]SAR -[Quantitative] Structure-Activity Relationships, PC(A) -Principal Component (Analysis), R -Responsibility vector, RBF -Radial Basis Function, SOM -Self-Organizing Map, VS -Virtual Screening

This is a review article of Generative Topographic Mapping (GTM) -a non-linear dimensionality reduction technique producing generative 2D maps of high-dimensional vector spaces -and its specific applications in Drug Design (chemical space cartography, compound library design and analysis, virtual screening, pharmacological profiling, de novo drug design, conformational space & docking interaction cartography, etc.) Written by chemoinformaticians for potential users among medicinal chemists and biologists, the article purposely avoids all underlying mathematics. First, the GTM concept is intuitively explained, based on the strong analogies with the rather popular Self-Organizing Maps (SOMs), which are well established library analysis tools. GTM is basically a fuzzy-logics-based generalization of SOMs. The second part of the review, some of published GTM applications in drug design are briefly revisited.

Introduction.

Computer-aided management of chemical information exploits the "chemical space" (CS) defined by a molecular descriptor vector, which positions molecules in this framework [START_REF] Oprea | Chemography: the art of navigating in chemical space[END_REF]. It assumes "Neighborhood Behavior" (NB) compliance [START_REF] Papadatos | Analysis of Neighborhood Behavior in Lead Optimization and Array Design[END_REF][START_REF] Patterson | Neighborhood Behavior: A Useful Concept for Validation of "Molecular Diversity" Descriptors[END_REF] -molecules with similar descriptors should have similar properties. Beyond abstract and often conflicting similarity scoring [START_REF] Willett | Chemical Similarity Searching[END_REF], humans best understand neighborhoods on 2D maps. Chemography is a domain of chemoinformatics dedicated to "flattening out" the CS. Knowing that even Earth planisphere projections cannot avoid significant artefacts, squeezing thousands of CS dimensions into a plane seems bound to fail. Yet, some loss in NB compliance is acceptable in exchange of an intuitive representation. From this perspective, even Principal Component Analysis, PCA [START_REF] Dunteman | Principal Components Analysis[END_REF] provides acceptable compromises [START_REF] Reymond | The enumeration of chemical space[END_REF]. Many non-linear dimensionality reduction approaches were designed [START_REF] Agrafiotis | Stochastic proximity embedding[END_REF][START_REF] Agrafiotis | Multidimensional scaling and visualization of large molecular similarity tables[END_REF][START_REF] Gaspar | Visualization of a Multidimensional Descriptor Space[END_REF], the most popular [START_REF] Schneider | Ligand-based Combinatorial Design of Selective Purinergic Receptor (A2A) Antagonists Using Self-Organizing Maps[END_REF][START_REF] De Sousa | Data Visualization and Analysis Using Kohonen Self-Organizing Maps[END_REF] being the Kohonen Self-Organizing Maps (SOM) [START_REF] Kohonen | Self-Organizing Maps[END_REF][START_REF] Kohonen | Self-Organization and Associative Memory[END_REF]. This is a hybrid of a clustering and a mapping procedure. "Code vectors" pointing towards "nodes" -centroids of dense clusters -represent the neighboring molecules. The "winning" node closest to a molecule will claim it as its resident. Then, code vectors are mapped onto a 2D grid in a topology-preserving way. Compounds residing in a node are no longer distinguishable.

Enough nodes are needed to avoid "squeezing" relevant subfamilies together. A wellparameterized SOM may be NB-compliant and may even serve as property predictor: the property of a node resident is taken as the mean over co-resident training set members. Such model cannot reproduce the influence of small structure variations on the predicted property: unless structure is changed enough to "force" the molecule into another node, the prediction will not change at all. This is a fundamental limitation to NB compliance of SOMs.

Fuzzy logics may solve this shortcoming. Consider the statement "molecule M resides in node N" within a fuzzy-logics framework. Its truth value is a real 0<RN(M)<1. RW(M), the largest over all N corresponds to the winning node W of the SOM. The sum of all RN(M) -further on referred to as the Responsibility vector R -over all nodes equals one. Any small structural change impacts R levels, and smoothly modifies predicted properties.

Although based on different mathematics, Generative Topographic Maps (GTMs) [START_REF] Bishop | Developments of the generative topographic mapping[END_REF][START_REF] Bishop | GTM: The Generative Topographic Mapping[END_REF] behave like fuzzy SOMs. "Nodes" are grid points on a flexible manifold, like a "rubber sheet" inserted in the descriptor space and bent in such a way as to maximize coverage of the molecule population in dense CS zones. Association of each molecule to the grid points is done by means of a set of Gaussian Radial Basis Functions (RBFs) constructing a probability density model in descriptor space. Note that other popular approaches such as PCA and t-SNE [START_REF] Maaten | Accelerating t-SNE using tree-based algorithms[END_REF] return only (x,y) latent space coordinates of the items -monitoring of local distributions based on the latent space coordinates is not implicitly supported by these approaches. Or, the latter feature is paramount to supporting predictive property landscapes.

GTMs inherit advantages of SOMs:

• they generate 2D maps of customizable topology,

• they allow an Applicability Domain assessment (distance to node/manifold -the so-called LogLikelihood parameter LLh) • they provide an implicit clustering scheme based on compound-to-node mapping.

GTMs depend on user-defined control parameters -foremost, the number of RBFs controlling manifold flexibility. How then to choose parameters in order to obtain good maps? [START_REF] Gaspar | Generative Topographic Mapping Approach to Chemical Space Analysis[END_REF][START_REF] Gaspar | Chemical Data Visualization and Analysis with Incremental Generative Topographic Mapping: Big Data Challenge[END_REF][START_REF] Gaspar | GTM-Based QSAR Models and Their Applicability Domains[END_REF][START_REF] Gaspar | Generative topographic mapping-based classification models and their applicability domain: application to the biopharmaceutics Drug Disposition Classification System (BDDCS)[END_REF][START_REF] Kireeva | Generative Topographic Mapping (GTM): Universal Tool for Data Visualization, Structure-Activity Modeling and Dataset Comparison[END_REF]. A good map is a predictive map! Their predictive propensity may serve as fitness score and GTMs may be evolved to become CS representations with validated Virtual Screening (VS) abilities.

Moreover, a same GTM may host any number of different property landscapes, and hence be predictive with respect to an entire panel [START_REF] Sidorov | Mappability of drug-like space: towards a polypharmacologically competent map of drug-relevant compounds[END_REF][START_REF] Lin | Multi-task generative topographic mapping in virtual screening[END_REF] of activities. GTMs provide a unifying framework in which compound libraries are represented by the cumulated responsibilities of their members. This makes tedious comparison of large libraries as easy as the similarity scoring of two molecules [START_REF] Gaspar | Chemical Data Visualization and Analysis with Incremental Generative Topographic Mapping: Big Data Challenge[END_REF]. Visualization -coupled, if needed, with "zooming" by hierarchical GTM [START_REF] Tino | Hierarchical GTM: constructing localized nonlinear projection manifolds in a principled way[END_REF] -is a tool of choice for the analysis of diversity holes [START_REF] Lin | Diversifying chemical libraries with generative topographic mapping[END_REF]. This article revisits key aspects of GTM technology. First, a brief recall of methodology is given.

Next, GTM-based visualization is intimately linked with the creation of property landscapes, which are at the core of GTM-based predictive models. Predictive propensity serves to select map architectures of maximal relevance for a specific problem, or for a vast panel of different properties -dedicated versus universal maps. Eventually, maps are applied to address specific problems, from drug design to library comparison, to the guidance of de novo compound design.

Generative Topographic Mapping -Principles

GTM was introduced by Bishop, Svensen & Williams [START_REF] Bishop | Developments of the generative topographic mapping[END_REF][START_REF] Bishop | GTM: The Generative Topographic Mapping[END_REF]. Figure 1 outlines the steps of GTM construction. More technical details can be found in the joint Supplementary Information document. A GTM consists of a (typically squared) grid of nodes covering the 2D latent space [START_REF] Gaspar | Generative Topographic Mapping Approach to Chemical Space Analysis[END_REF][START_REF] Horvath | Generative Topographic Mapping Approach to Chemical Space Analysis[END_REF].

Nodes are mapped to manifold points embedded in the D-dimensional CS. The considered manifold (rubber sheet) is flexible, and its degrees of freedom are adjusted such as to maximize the coverage of the molecules (items) present in the CS. Items used for manifold fitting -the Frame Set (FS) of compounds, Figure 1.1 -span the targeted CS. Extrapolation beyond the external FS "borders" is, like in geography, of very limited reliability.

Unsupervised Manifold Fitting

Manifold fitting is unsupervised, e.g. oblivious to molecular properties of FS members. The goal is to find the rubber sheet geometry passing though the vicinity of as many as possible of the FS items, be they active, inactive, not tested -or not even synthesized (enabling cartography of virtual CS). Compound closeness to the manifold is termed LogLikelihood (LLh). Optimization of LLh is typically performed by gradient-based methods, starting from a flat manifold aligned on the two first principal components (PCs) of FS descriptors, as in Figure 1.3. Following gradients, this initial planar surface is "twisted" such as to bring it closer to FS items (Figure 1.4). This is prone to get stuck in local minima and might benefit from more aggressive sampling heuristics [START_REF] Choi | Generative topographic mapping by deterministic annealing[END_REF]. Manifold flexibility is user-tunable, being controlled by the number of considered RBFs: the more RBFs allowed, the easier it will be for the algorithm to mimic highly irregular, nonlinear surfaces. Large FSs imply long computing times and potential memory problems, so that alternative approaches such as incremental [START_REF] Gaspar | Chemical Data Visualization and Analysis with Incremental Generative Topographic Mapping: Big Data Challenge[END_REF] algorithms were designed.

Assessing Neighborhood Behavior: GTM Classification & Regression Models and their

Applicability Criteria

After the manifold was optimized, (new) items can be projected thereon (Figure 1.5), herewith obtaining their responsibility vectors. "Exotic" external compounds, remote from manifold, are identified by low LLh values and discarded. This is a safeguard against attempting to map areas the GTM was not designed to cover, i.e. out of Applicability Domain (AD).

Compounds within AD and having measured properties or categorical labels are then used to "color" the manifold, i.e. to train a property [START_REF] Gaspar | GTM-Based QSAR Models and Their Applicability Domains[END_REF] or category [START_REF] Gaspar | Generative topographic mapping-based classification models and their applicability domain: application to the biopharmaceutics Drug Disposition Classification System (BDDCS)[END_REF] landscape. The similarity principle states that close analogues within a CS sphere centered on a reference compound of property P will likely have property values close to P. Or, one may conceive P as a local characteristic of the CS -like a physical field filling the entire space, not only points where its "sources" (here -the reference compounds) are located. Responsibilities R correspond to the relative intensities of the "field" contributed by the reference compound of property P to each of the map nodes. Structure-activity (SA) information is herewith "disembodied" from its original providers (the training molecules) and transferred to the GTM nodes. Each node is "colored" by a property value obtained as the responsibility-weighed (R-weighed) mean of the properties of its residents or will be assigned the label of the winning class most popular amongst residents. In fuzzy class landscapes for binary classification, real-value node colors correspond to the relative populations of node residents of each class.

There are two criteria of node trustworthiness. The first is the cumulated responsibility of node residents, i.e. the node density. Nodes with cumulated responsibilities below some user-chosen threshold are terra incognita -any predictions based on them is not trustworthy.

The second is the coherence of the property data contributing to a node, i.e. the spread (Rweighed standard deviations) of the resident properties -showing that some map zones may be more NB-compliant than others. Do not use low coherence zones for prediction.

Landscape construction is nothing but responsibility-mediated transfer of structure-property information from the training set onto the nodes. Prediction represents the inverse-first, the compound is projected, and the predicted property is taken as the R-weighed mean of node properties. Actually, compound "positions" as real-value (x,y) coordinates on the map (Figure 1.6, blue arrows) are R-weighted means of node (x,y). The GTM acts like a "transfer agent" of structure-activity information "received" from training compounds and "passed on" to molecules to be predicted. Therefore, computational cost does not depend on training set size, unlike in k-Nearest Neighbors methods.

Landscape predictive propensity can be quantified by cross-validation or external prediction. But landscapes can also be visualized and interactively explored, a plus over all black-box machinelearned models. In Kohonen-style rendering, only the nodes and their properties are plotted. This is a natural choice in multi-class classification landscapes, with nodes colored by winning class.

In continuous landscapes density and color at a map point (x,y) are interpolated from neighboring node values. Supervised Manifold Selection -Dedicated, Multitask and Universal Maps LLh optimization drives manifold fitting as defined by map hyperparameters -grid size, number of RBFs, RBF width and regularization parameter, choice of the FS, but most of all the nature of descriptors picked to define CS. The question of optimal combination of hyperparameters leading to a most useful manifold arises.

Dedicated Maps

A dedicated map is selected such as to maximize the landscape predictive power for a specific property P, represented by its training set (typically also used as FS). At current hyperparameters, the quality of the resulting P landscape is monitored by some cross-validation criterion C (a determination coefficient Q 2 for regression, the Balanced Accuracy BA for classification problems). How to best browse through the hyperparameter space in quest of maximal C depends on the number of available descriptor space options -Genetic Algorithms (GAs) are well suited [START_REF] Horvath | An Evolutionary Optimizer of libsvm Models[END_REF].

When lacking experimental data for molecules to map, prediction propensity-based C may be replaced by technical map quality criteria -penalties for empty nodes, homogeneity of FS distribution (Shannon entropy), etc.

Multitask Maps

A GTM may support not one, but many different predictive landscapes, associated to different properties: the mean quality score <C> over these may be a selection criterion per se. The various landscapes may correspond to related properties, for example a "same" endpoint (antimalarial activity) measured according to distinct protocols [START_REF] Sidorov | AntiMalarial Mode of Action (AMMA) Database: Data Selection, Verification and Chemical Space Analysis[END_REF], making data fusion impossible. It is however possible to search a GTM manifold able to host independent predictive landscape for each of these antimalarial activity scores. Visualizing landscapes on such multitask GTMs immediately highlights zones where two distinct properties are correlated, anticorrelated or not correlated -a first step towards understanding why.

In Figure 2, a multitask GTM supports active/inactive fuzzy class landscapes for two kinases. By projecting a large library and picking members within the appropriate zone(s), one may propose selective (or promiscuous) focused libraries. shows activity with respect to B but was not extensively explored for A. Zone 2 is one of A-specific ligands, by contrast to the rather B-specific zone 4. Last but not least, zone 3 is a "promiscuity" area.

The interest of multitask GTMs is not limited to the emergence of this common reference framework for visualizing landscapes. The selection of a consensual manifold being simultaneously NB-compliant with respect to the tracked properties is a genuine act of multitask learning. The simple fact of selecting, out of the pool of considered descriptor types, the precise molecular descriptor enabling such a simultaneous NB-compliance is of great value [START_REF] Lin | Multi-task generative topographic mapping in virtual screening[END_REF].

Universal Maps

Manifolds challenged to provide predictive models for all the exploitable targets within structure-activity "big data" from public databases such as ChEMBL were termed universal maps [START_REF] Sidorov | Mappability of drug-like space: towards a polypharmacologically competent map of drug-relevant compounds[END_REF][START_REF] Casciuc | Virtual Screening with Generative Topographic Maps: How Many Maps Are Required?[END_REF]. These are multitask GTMs standing out by the very large number of covered biologically unrelated transmembrane receptors, kinases, cytochromes, oxidoreductase, etc. It is not trivial to assume that a single set of descriptors may be NB-compliant with respect to all these targets, dimensionality reduction notwithstanding, yet several ISIDA fragmentation schemes [START_REF] Ruggiu | Isida Property-labelled Fragment Descriptors[END_REF][START_REF] Varnek | Isida -Platform for virtual screening based on fragment and pharmacophoric descriptors[END_REF] performed unexpectedly well. The best map accommodates highly predictive activity class landscapes (cross-validated BA >0.7) for 536 of the 618 considered targets, and virtually all (609/618) landscapes have BA >0.6 (clearly better than random BA=0.5). The seven "top" universal maps are close in terms of the average predictive propensity, while predictivity of any target may significantly vary from one to another. The combination of the different universal maps offers a kaleidoscopic view of CS from several perspectives: connectivity, topological pharmacophores, etc. Consensus predictions from the seven maps are more robust than output of any single map [START_REF] Casciuc | Virtual Screening with Generative Topographic Maps: How Many Maps Are Required?[END_REF].

A dedicated map is likely to outperform universal maps for its assigned target, because it has the freedom to pick the absolutely best descriptor for it. Universal maps favor compromise description spaces with overall acceptable NB compliance. They are tools of choice for analysis of (very) large and diverse libraries and serve as pharmacological profile predictors (see §3.4).

Chemography and Property Prediction -Practical Applications of GTM in Compound Design.

The following is a brief review of GTM usage in drug discovery. Other applications, for example mapping of conformational space [START_REF] Horvath | Generative Topographic Mapping of the Docking Conformational Space[END_REF][START_REF] Horvath | Monitoring of the Conformational Space of Dipeptides by Generative Topographic Mapping[END_REF][START_REF] Horvath | Generative Topographic Mapping of Conformational Space[END_REF], applications in materials science [START_REF] Higuchi | Prediction of the Glass-Transition Temperatures of Linear Homo/Heteropolymers and Cross-Linked Epoxy Resins[END_REF][START_REF] Marcou | In Silico Design, Virtual Screening and Synthesis of Novel Electrolytic Solvents[END_REF], chemical reactivity analysis and prediction [START_REF] Glavatskikh | Predictive Models for Kinetic Parameters of Cycloaddition Reactions[END_REF][START_REF] Glavatskikh | Visualization and Analysis of Complex Reaction Data: The Case of Tautomeric Equilibria[END_REF] and in chemical engineering [START_REF] Escobar | Combined generative topographic mapping and graph theory unsupervised approach for nonlinear fault identification[END_REF] will not be discussed here.

GTM as Library Comparison Tool

The cumulated R vector of the members of a compound library is a descriptor of the library. It can be used to estimate its Shannon entropy, high if library homogeneously covers the CS; low if focused on narrow CS areas. Libraries can be compared in terms of cumulated R vector similarity scores, representing the degree of "overlap" of libraries in CS [START_REF] Gaspar | Chemical Data Visualization and Analysis with Incremental Generative Topographic Mapping: Big Data Challenge[END_REF][START_REF] Lin | Mapping of the Available Chemical Space versus the Chemical Universe of Lead-Like Compounds[END_REF][START_REF] Volochnyuk | Evolution of commercially available compounds for HTS[END_REF]. This is very cost-effective: it merely requires the N+N' compounds of the two libraries to be mapped, instead of N×N' pairwise comparisons in initial descriptor space. Comparison of property landscapes is even more instructive. These can be generated for calculable molecular properties, such as size, number of aromatic rings, number of chiral centers, predicted lipophilicity. The approach [START_REF] Lin | Mapping of the Available Chemical Space versus the Chemical Universe of Lead-Like Compounds[END_REF] was perfectly suited to compare >10M real "fragment-like" compounds (of ≤ 17 heavy atoms) from public databases to a core of 10M fragment-like structures extracted from 166 billionstrong GBD-17 library [START_REF] Visini | Fragment Database FDB-17[END_REF][START_REF] Ruddigkeit | Enumeration of 166 Billion Organic Small Molecules in the Chemical Universe Database GDB-17[END_REF] of feasible compounds. The real-world bias in favor of aromatic ring-rich molecules and against chiral compounds can be directly read from property landscapes.

Library Analysis with GTM

GTM-based library visualization typically provides a global "satellite view". However, details reaching out to individual compounds can be highlighted, either by hierarchical zooming [START_REF] Tino | Hierarchical GTM: constructing localized nonlinear projection manifolds in a principled way[END_REF][START_REF] Lin | Diversifying chemical libraries with generative topographic mapping[END_REF] or by using alternative chemoinformatics approaches to analyze zone-specific sublibraries. These include scaffold analysis [START_REF] Kayastha | Privileged Structural Motif Detection and Analysis Using Generative Topographic Maps[END_REF][START_REF] Klimenko | Chemical Space Mapping and Structure-Activity Analysis of the ChEMBL Antiviral Compound Set[END_REF], Maximal Common Substructure (MCS) detection [START_REF] Lin | Diversifying chemical libraries with generative topographic mapping[END_REF], or alternative "detail-friendly" representations of compounds within the sublibrary -for example molecular networks [START_REF] Kayastha | From bird's eye views to molecular communities: two-layered visualization of structure-activity relationships in large compound data sets[END_REF][START_REF] Stumpfe | Exploring Activity Cliffs in Medicinal Chemistry[END_REF]. MCS patterns that are underrepresented in a corporate library but occur in commercially available compounds have been evidenced after "breaking up" the large libraries into GTM zone-specific sets, small enough for an effective MCS search [START_REF] Lin | Diversifying chemical libraries with generative topographic mapping[END_REF].

GTMs are very flexible with respect to possible definitions of map "zones of interest".

Responsibility Patterns (RPs) define subsets of molecules which project in the same way on the map. Compounds with R vectors rounding up to a same RP correspond to cell-based clusters in R vector space and were shown to share significant common structural patterns. Interestingly, these patterns may differ in terms of "resolution". Some RPs are characterized by a common scaffold, while others are even more specific: common substituted scaffold. Below scaffold-level resolution are RPs corresponding to pools of closely related scaffolds (like N heterocycles with varying positions of N atoms). Some RPs are characterized by even less stringent rules assimilable to a topological pharmacophore, for example (aromatic ring)-variable size linker-cationic group. By analogy to the concept of "privileged scaffold" it is possible to define privileged RPs seen to preferentially occur within active molecules. This approach is more "open-minded" -it may "privilege" whatever best describes a local cluster: scaffold, family of scaffolds, topological pharmacophore, etc. The analysis of ChEMBL following these lines proposed a coherent way to look at target-specific structural requirements, sometimes matching and sometimes completing the human scaffold-centric viewpoint [START_REF] Kayastha | Privileged Structural Motif Detection and Analysis Using Generative Topographic Maps[END_REF]. This kind of analysis was successful for both protein binding affinity and more complex biological activities (antiviral activity [START_REF] Orlov | Getting to Know the Neighbours with GTM: The Case of Antiviral Compounds[END_REF], notably).

GTM-driven Virtual Screening (VS)

In our hands, GTM landscape-driven VS performed robustly [START_REF] Lin | Multi-task generative topographic mapping in virtual screening[END_REF][START_REF] Casciuc | Virtual Screening with Generative Topographic Maps: How Many Maps Are Required?[END_REF], though was not unexpectedly outperformed by similarity screening, or by machine-learned models using initial descriptors. The selection [START_REF] Casciuc | Pros and cons of virtual screening based on public "Big Data": In silico mining for new bromodomain inhibitors[END_REF] of a 3K pool of likely to bind Bromodomain BRD4 binders out of the Enamine compound pool is to our knowledge the only prospective, experiment-backed up VS using GTM landscapes amongst other machine-learned models, and docking. The modest enrichment factor in BRD4 actives (×2.7) over an analogous random screening campaign can be traced back to the low correlation between public activity data used to create the GTM landscapes (activity classes based on ChEMBL-reported IC50 values) and the differential calorimetry data by which the hit rate was calculated. Yet, "big data" and activity landscapes are not needed for successful discovery of actives on GTMs. It is straightforward to rephrase the similarity principle "similar molecules have similar properties" as "molecules of a same RP have similar properties". The hypothesis that molecules of a same RP have similar properties is weaker than actual NB compliance in full-blown descriptor space but helps to quickly prune obviously dissimilar candidates. RPs privilegedly populated by anti-(flavo-and entero-)viral compounds were highlighted [START_REF] Orlov | Getting to Know the Neighbours with GTM: The Case of Antiviral Compounds[END_REF], and commercial compounds within privileged RPs were similarity-scored against reference antivirals within same RP, herewith avoiding number-crunching of >10 12 Tanimoto scores of >1000-dimensional vectors between each InterBioScreen candidate compound and each reference antiviral.

Candidates closest to their references were actually tested with an excellent hit rate: 23 out of 44 had antiviral activities within or below micromolar.

Polypharmacological profiling with Universal GTMs

As the GTM is a common frame for all the (precomputed) activity landscapes, in Silico polypharmacological profiling of millions of compounds (prediction of a compound×target profile matrix, reporting the likelihood to be active of each compound for almost 800 targets) can be achieved in hours. Relying on several universal maps significantly improves the consensus prediction. This profiling tool (Figure 3) covering 749 distinct biological activities is freely accessible at the Laboratory of Chemoinformatics of Strasbourg (http://infochim.ustrasbg.fr/webserv/VSEngine.html, under "QSAR-based Property Predictions"). Its strength is that training sets of individual activities are independent (testing every compound on each target is not required). Alternatively, with such a complete matrix, "Stargate" GTM [START_REF] Gaspar | Stargate GTM: Bridging Descriptor and Activity Spaces[END_REF] may "connect" descriptor space and activity profile space (or any other vector space), a distinct paradigm of multitasking GTM.

Targets are the 749 most data-rich proteins with reported dose-response data in ChEMBL v.24.

Dose-response values were converted to Active/Inactive labels and each target-specific compound series generated fuzzy binary class landscapes, on each of the seven universal maps.

"Pure" landscapes only include compounds that were actually tested on the target. They cover target-specific zones -compounds of other chemotypes would project into terra incognita and be considered out of AD. "Decoy" landscapes depict the confirmed actives against confirmed inactives supplemented by 5% of remaining ChEMBL compounds (considered inactive). "Pure" and "decoy" landscapes typically tend to return converging predictions, but also might complement each other, in several possible ways. Figure 3: Sample html output of consensus "hits" discovered in the GTM-predicted polypharmacological profiling against 749 major single protein targets covered by ChEMBL (http://infochim.ustrasbg.fr/webserv/VSEngine.html). Each of the 14 landscapes of a target ("pure" and "decoy" × 7 universal maps) returns a fuzzy class score within [START_REF] Oprea | Chemography: the art of navigating in chemical space[END_REF][START_REF] Papadatos | Analysis of Neighborhood Behavior in Lead Optimization and Array Design[END_REF] (1 → inactive, 2 → active, 1.5 → in-between, undecidable). The mean and standard deviation of scores is taken over only those landscapes for which the compound passes AD criteria. If the mean value exceeds 1.5 plus the standard deviation, the compound is a "virtual hit" for the target, and its structure, the concerned target and final scores ("mean" and "corrected mean" = mean -standard deviation) are output

De Novo compound design with GTMs.

Deep Neural Networks [START_REF] Thomas | Application of Generative Autoencoder in De Novo Molecular Design[END_REF][START_REF] Barzilay | Junction Tree Variational Autoencoder for Molecular Graph Generation[END_REF] (DNNs) based on an autoencoder/decoder architectures can reversibly translate brute molecule representations (SMILES, graphs) to a latent vector of few hundred real numbers. This latent vector is a molecular descriptor "designed" by Artificial

Intelligence and contains all the information needed to reconstruct the structure -which is precisely the role of the decoder. By finding the structure associated to every point of the latent space, decoders are an elegant solution for the "hard" part of the inverse QSAR [START_REF] Miyao | Inverse QSPR/QSAR Analysis for Chemical Structure Generation (from y to x)[END_REF][START_REF] Baskin | Solving the inverse problem of structure-property relations for the case of topological indexes[END_REF] problem: "What structure is associated to given descriptor values?" For the other, "easy" subproblem of inverse QSAR -"What are the descriptor values that correspond to the desired property?" -GTMs provide an elegant answer (Figure 4). "Active" nodes can be traced back to descriptor space, and vectors in their immediate neighborhood can be generated by some normally distributed random perturbation. In order to use GTMs in focused de novo compound design, the following steps are required, after calibration of the autoencoder/decoder DNN.

• Build and validate a latent vector space-based GTM following to the universal map paradigm.

• Select SAR data sets for predictive landscape building. In our proof-of-concept study [START_REF] Sattarov | De Novo Molecular Design by Combining Deep Autoencoder Recurrent Neural Networks with Generative Topographic Mapping[END_REF], actives and tested inactives on the Adenosine receptor A2a were taken from ChEMBL.

• Select "interesting" nodes associated to targeted property values. Here, nodes with a high density of active residents were selected. Other criteria could apply -recall Figure 2.

• Generate normally distributed vectors in the neighborhood of selected node(s). Use the decoder to unveil their associated SMILES strings and apply chemical consistency check and synthesizability index estimators to rank new molecules by practical interest.

• Alternatively, use a Genetic Algorithm for unconstrained browsing thru latent vector space.

Decode the visited point and assess synthesizability. Discard if not satisfactory. Otherwise, enter new structure into the Darwinian selection process, with its A2a activity (read from the landscape) as fitness.

Both sampling strategies above were operational in discovering novel structures that seem feasible and which dock well into the A2a active site (awaiting experimental testing, docking was used as "orthogonal" validation).

Conclusions

This review article targeting a non-linear dimensionality reduction technique, GTM, visited virtually all key aspects of chemoinformatics: the similarity principle, chemography, QSAR and machine learning, VS, library design, de novo compound design. This convincingly illustrates its multivalence. No application is GTM-specific: SOMs were tools of choice for library comparison. However, the fuzzy-logics based GTM allows for genuine property prediction. On SOMs, the node level is intrinsically the highest-resolution cluster level the method can provide.

On GTMs, the number of possible responsibility patterns is virtually infinite -allowing for a much finer clustering resolution.

Property landscapes can be plotted in the plane of the two main principal components -but the non-linearity of GTM provides a significant competitive edge. Should a distribution really be "flat", GTM is seamlessly able to mimic PCA -no risk taking in preferring GTM.

Figure 1 :

 1 Figure 1: Key steps of GTM construction

Figure 2 :

 2 Figure 2: The ability to deploy distinct property landscapes on a same multitask GTM allows the intuitive discovery of CS zones of interest. Color coding represents the local percentage of active residents. Zone 1shows activity with respect to B but was not extensively explored for A. Zone 2 is one of A-specific ligands, by contrast to the rather B-specific zone 4. Last but not least, zone 3 is a "promiscuity" area.

Figure 4 :

 4 Figure 4: Principle of GTM-driven navigation in the Encoder/Decoder latent space, towards the discovery of novel species of desired properties

GTM-based models provide intuitive AD criteria, derived from mapping and landscape building.

They are thus compliant with every request of "good QSAR practice". Their predictive propensity is robust but not outstanding. Instead, they are outstanding in terms of a feature that is altogether absent in "black-box" machine-learned models: the ability to visualize and intuitively compare property landscapes stemming from a common multitask or universal manifold. Support for multiple predictive models, rendered within a common reference frame, is a key advantage of GTMs.