Marco Lorenzi
email: marco.lorenzi@inria.fr

Andre Altmann

Boris Gutman

Selina Wray

Charles Arber

Derrek P Hibar

Neda Jahanshad

Jonathan M Schott

Daniel C Alexander

Paul M Thompson

Sebastien Ourselin

Susceptibility of brain atrophy to TRIB3 in Alzheimer's disease: evidence from functional prioritization in imaging-genetics

Keywords: GWA, imaging-genetics, genotype, phenotype, Alzheimer's disease, bioinformatics

In this study we employ a novel experimental imaging-genetics approach for investigating the genetic underpinnings of brain atrophy in Alzheimer's disease. We successfully combined state-of-art imaging-genetics methods and experimental gene expression data to uncover novel biology in brain atrophy.

The novel experimental paradigm highlighted a significant role of TRIB3 (tribbles pseudokinase 3) in modulating the typical pattern of Alzheimer's brain pathology.

This result corroborates through rigorous data-driven statistical methods evidence emerging from previous studies about the role of TRIB3 in modulating known mechanisms of neurodegeneration, such as neuronal death, cellular homeostasis, and interaction with established genes causing autosomal dominant Alzheimer's disease: APP and PSEN1. The developed integrated statistical-experimental methodology could serve as a roadmap for investigations in other disorders.

Abstract

The joint modelling of brain imaging information and genetic data is a promising research avenue to highlight the functional role of genes in determining the pathophysiological mechanisms of Alzheimer's disease (AD). However, since genome-wide association (GWA) studies are essentially limited to the exploration of statistical correlations between genetic variants and phenotype, the validation and interpretation of the findings is usually non trivial and prone to false positives.

To address this issue, in this work we investigate the genetic functional mechanisms underlying brain atrophy in AD by studying the involvement of candidate variants in known genetic regulatory functions. This approach, here termed functional prioritization, aims at testing the sets of gene-variants identified by high-dimensional multivariate statistical modelling with respect to known biological processes, in order to introduce a biology-driven validation scheme. When applied to the ADNI cohort, the functional prioritization allowed identifying a link between TRIB3 (tribbles pseudokinase 3) and the stereotypical pattern of grey matter loss in AD, which was confirmed in an independent validation sample, and that provides novel evidence about the relation between this gene and known mechanisms of neurodegeneration. \body Introduction Alzheimer's disease (AD) is a devastating neurodegenerative disorder and its aetiology still remains largely concealed. In the anticipation of increasing prevalence of AD and other dementias, there is an urgent need for improving the understanding of the disease processes that underlie neurodegeneration. Whilst the knowledge about the genetic and environmental risks underpinning AD is steadily advancing, our understanding of how these factors interact to lead to the complex pathophysiology that results in dementia is less understood.

Advances in imaging technologies have led to non-or minimally-invasive imaging biomarkers that capture various aspects of the disease process including amyloid deposition [START_REF] Rabinovici | Amyloid imaging in aging and dementia: testing the amyloid hypothesis in vivo[END_REF], tau pathology [START_REF] Villemagne | In vivo tau imaging: obstacles and progress[END_REF], functional decline [START_REF] Mosconi | Preclinical detection of Alzheimer's disease using FDG-PET, with or without amyloid imaging[END_REF] and neuronal loss [START_REF] Frisoni | The clinical use of structural MRI in Alzheimer disease[END_REF].

Combining such imaging information with genetic measurements -so called imaging-genetics -provides the means for investigating the effect of genetic variation on underlying biological mechanisms [START_REF] Bigos | Neuroimaging Genetics: Principles and Practices[END_REF].

Genome-wide association studies (GWAS) query millions of single nucleotide polymorphisms (SNPs) individually for their association with either case-control status [START_REF] Lambert | Meta-analysis of 74,046 individuals identifies 11 new susceptibility loci for Alzheimer's disease[END_REF] or disease-specific quantitative phenotypes, e.g., in the case of AD, regional brain volumes [START_REF] Potkin | Hippocampal atrophy as a quantitative trait in a genome-wide association study identifying novel susceptibility genes for Alzheimer's disease[END_REF] or brain amyloid burden [START_REF] Ramanan | APOE and BCHE as modulators of cerebral amyloid deposition: a florbetapir PET genome-wide association study[END_REF]. Mass univariate analysis of genetic data is still the predominant method, in virtue of its ease-of-use and well-established theoretical framework, albeit suffering from significant limitations including the requirement for multiple testing, redundancies introduced by linkage disequilibrium (LD) and the lack of analysis of epistatic effects (e.g., SNP-SNP interactions), which have to be explicitly modeled and searched for exhaustively [START_REF] Kam-Thong | GPU-based linear regression for detection of epistasis[END_REF]. Moreover, more than one quantitative phenotype can be derived from the available imaging data, e.g., dozens or hundreds of regional brain volumes, or hundreds of thousands of voxellevel metrics [START_REF] Stein | Voxelwise genome-wide association study (vGWAS)[END_REF]. This potentially large number of genotype-phenotypes features of interest generally complicates the problem of reliably detecting statistical associations, and thus hampers the identification of disease-relevant genetic markers by purely statistical means.

Limitations of classical mass-univariate statistical methods have in recent years been overcome by employing multivariate approaches to data analysis in the context of neuroscience studies [START_REF] Schrouff | PRoNTo: pattern recognition for neuroimaging toolbox[END_REF] and GWAS [START_REF] Szymczak | Machine learning in genome-wide association studies[END_REF]. Likewise, in imaging-genetics meaningful genotype-phenotype interactions [START_REF] Liu | A review of multivariate analyses in imaging genetics[END_REF] are captured by simultaneously modeling sets of genetic variants that are jointly associated with a given imaging phenotype [START_REF] Floch | Significant correlation between a set of genetic polymorphisms and a functional brain network revealed by feature selection and sparse Partial Least Squares[END_REF][START_REF] Vounou | Discovering genetic associations with high-dimensional neuroimaging phenotypes: a sparse reduced-rank regression approach[END_REF][START_REF] Silver | Identification of gene pathways implicated in Alzheimer's disease using longitudinal imaging phenotypes with sparse regression[END_REF][START_REF] Liu | Combining fMRI and SNP data to investigate connections between brain function and genetics using parallel ICA[END_REF]. Multivariate GWAS have the potential to shed light on the complex genotype-phenotype relationship, and may thus highlight novel links between brain physiology and molecular and biological functions. However, although these methods have proven their ability to identify meaningful SNP combinations associated to brain imaging features, the interpretation and validation of the statistical findings remain very challenging tasks. These problems relate directly to the understanding of the functional role of sets of genetic variants, and to the difficulty of replicating the statistical results in unseen cohorts.

We approach this technical bottleneck by leveraging multivariate approaches to explore high-dimensional datasets and to generate hypotheses, which are subsequently tested in downstream experiments. High-quality databases of matched genotype and gene expression measurements such as GTEx 1 [START_REF] Carithers | A Novel Approach to High-Quality Postmortem Tissue Procurement: The GTEx Project[END_REF] and BRAINEAC 2 [START_REF] Trabzuni | Quality control parameters on a large dataset of regionally dissected human control brains for whole genome expression studies[END_REF] facilitate the quantification of effects of SNPs on gene expression in numerous tissues, including various brain tissues. Typically, these databases are used to detail the effect of a genetic variant at the very end of an analysis pipeline and to garner evidence for molecular mechanisms of the genetic locus. However, functional information in 'convenience' databases can also be used at an earlier stage in the analysis in order to prioritize a few candidate hypotheses with a clear functional mechanism (e.g., expression quantitative trait loci; eQTL) for the validation phase and thus limit the multiple testing burden.

In this work we apply this novel investigative approach to study the genetic functional mechanisms underlying brain atrophy in AD. The framework is comprised of two steps: i) Statistical discovery. Candidate genetic variants are initially identified through data-driven multivariate statistical analysis of the matched imaging and genetics data. This is achieved by modeling the joint covariation between 1.1 million SNPs and the cortical and subcortical atrophy represented by 327,684 cortical and 27,120 subcortical thickness values of 639 individuals (either healthy older controls or patients with AD) from the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort;

ii) Functional prioritization. The candidate genetic variants are subsequently screened for functional relevance by querying high-dimensional gene expression databases such as GTEx.

The resulting small set of genetic loci, which are shown to modify gene expression, is then validated in an independent sample of 553 individuals from ADNI diagnosed with mild cognitive impairment (MCI), a proportion of whom progressed to AD.

Compared to previous approaches our work (i) analyses the whole genome and whole brain in a hypothesis free fashion, i.e., without preselecting SNPs or brain regions and (ii) uses a functional prioritization step in order to select genetic loci for validation in an independent cohort.

Starting from the initial ~1.1 million SNPs, the multivariate statistical analysis allowed the identification of a relatively small number of genetic loci that are statistically associated with the typical pattern of AD brain pathology. The subsequent functional prioritization step ultimately identified a significant role of TRIB3 (tribbles pseudokinase 3), a gene showing important connections to known mechanisms of neurodegenerative diseases. Indeed, although a role for TRIB3 in dementia has not been extensively explored, there are several aspects of TRIB3 function that have relevance to mechanisms related to neuronal death, cellular homeostasis, and of interaction with established AD genes, such as APP and PSEN1.

This study ultimately offers an illustration of the potential of effectively combining multivariate statistical modeling in imaging-genetics with recent instruments available from computational biology, to lead to novel insights on the pathophysiology of neurodegeneration.

Results

Model training and estimated components

Figures 2 and3 show the relevant areas of the identified joint genetic and phenotype variation, respectively, for the first three PLS components through stability selection.

The components were very robust (100% reproducible) during the stability selection procedure (Supplementary Methods). The fourth and fifth components did not present any relevant locations (i.e., all bins have p<0.95) after stability selection for both the genetic modality and for the imaging modality.

Genetic components

The circular Manhattan plot (Circos v0.96 [START_REF] Krzywinski | Circos: an information aesthetic for comparative genomics[END_REF]) of Figure 2 shows the PLS weights and the selection frequency for the PLS genotype components, describing the importance of the genetic loci associated to cortical thickness variation for component 1, 2 and 3. The plot shows the probability of a given genetic bin of size 10kb of being relevant in the PLS model, i.e., to contain a SNP that is ranked in the top 10% of the absolute weights of the genotype component. Spatially contiguous loci generally show similar importance values, which is caused by LD of these regions. The genes close to the important loci are listed in the innermost circle depending on their genomic position.

In the genetic components 1 through 3 a total of 118 bins exceeded the selection frequency threshold (61, 50, 7 for component 1,2 and 3, respectively). From these bins 402 (196, 181 and 25) influential SNPs were extracted and annotated with 98 genes through the computational VEP analysis. The extended APOE locus comprising APOE and TOMM40 was selected as the highest scoring region in component 1. A total of 3,956 candidate SNP-gene pairs were considered for the GTEx-based eQTL analysis in six tissues. However, a few genes did not show sufficient expression levels in some tissues and these combinations were excluded from the analysis, resulting in 1,598 unique SNP-gene-tissue tests, of those 104 were significant at the Bonferroni corrected p-value threshold (p=3.1e-5) (Table S1) linking to 14 genes (Table S2; The independent validation of those 14 genes in the MCI cohort confirmed TRIB3 (p=0.0034) (Table 2). Three additional genes were (close to) nominal significance: TM2D1 (p=0.053), LAMC1 (p=0.062), and RP11-181K3.4 (p=0.053) (Table 2). Of note the top eQTL SNP for TRIB3 rs4813620 received a p=0.06175 in stage I of a large AD GWAS [START_REF] Lambert | Meta-analysis of 74,046 individuals identifies 11 new susceptibility loci for Alzheimer's disease[END_REF]. However, rs62191440, a SNP in strong LD with rs4813620 (D'=0.8469; r2=0.6559) in the European population [START_REF] Machiela | LDlink: a web-based application for exploring population-specific haplotype structure and linking correlated alleles of possible functional variants[END_REF], received a p-value of 0.00601 (Figure S6) and also constitutes an eQTL for TRIB3 in various tissues in GTEx including brain tissues cortex and caudate ganglia (Figure S7). Interestingly, when estimating the PLS components on the sub-cohort of 279 training individuals with positive CSF amyloid (Table 1) we identified compatible validation results on the independent testing MCI group. Within this setting, TRIB3 still leads to marginally significant differences (p=0.0134) between progressing and stable MCI, although not significant after correction for multiple comparison (Table S3).

Morphometric components

Figure 3 shows the PLS phenotype components 1 through 3 (top), as well as the associated selection frequency describing the loci of brain atrophy associated with genetic variation (bottom). The selection frequency colors indicate the probability of each cortical mesh points of being relevant in the PLS model, i.e., to be ranked among the top 10% of the absolute weights of the phenotype component.

The first component is mainly associated to the thinning of the cortical mantle, and is localized in temporal and posterior cingulate cortices (Figure 3). The relevant areas at the subcortical level are primarily associated with amygdalae and thalami. The second component is mostly associated to the thinning of the subcortical areas (hippocampi and amygdalae), and to the cortical thinning of the temporal areas at the cortical level.

The third component is similar to component 2, and describes a sub-cortical thickness pattern prevalent in hippocampi, amygdalae, and thalami. At the cortical level, the component is associated with the thinning of frontal cortices, and to isolated spots located in the parahippocampal gyrus.

Discussion

In this work we modeled high-dimensional genome-wide SNP data and brain-wide cortical thickness data via joint multivariate statistical modeling and functional prioritization of genes through bioinformatics annotation and a large eQTL database.

Our study ultimately identified a link between TRIB3 (tribbles pseudokinase 3) and the stereotypical pattern of grey matter loss in AD (cortical thinning in temporal and posterior cingulate regions and subcortical atrophy). TRIB3 is a pseudokinase which acts as a regulator of several signaling pathways. For example it can interact directly with Akt and inhibit the pro-survival pro-survival Akt pathway [START_REF] Du | TRB3: a tribbles homolog that inhibits Akt/PKB activation by insulin in liver[END_REF]. TRIB3 expression is induced during neuronal cell death [START_REF] Zareen | A feed-forward loop involving Trib3, Akt and FoxO mediates death of NGF-deprived neurons[END_REF] and recently increased levels of the TRIB3 protein were found in dopaminergic neurons of the substantia nigra pars compacta in patients with Parkinson's disease [START_REF] Aimé | Trib3 Is elevated in Parkinson's disease and mediates death in Parkinson's disease models[END_REF]. TRIB3 expression is stress induced and increases in response to nerve growth factor (NGF) deprivation; endoplasmatic reticulum (ER) stress, and amino acid deprivation [START_REF] Zareen | A feed-forward loop involving Trib3, Akt and FoxO mediates death of NGF-deprived neurons[END_REF]. Although a role for TRIB3 in dementia has not been extensively explored, there are several aspects of TRIB3 function that have relevance to known mechanisms of neurodegenerative disease. TRIB3 can interact directly with P62 to modulate autophagic flux [START_REF] Hua | TRB3 links insulin/IGF to tumour promotion by interacting with p62 and impeding autophagic/proteasomal degradations[END_REF], an important process in maintaining cellular homeostasis that is known to be disrupted in neurodegeneration [START_REF] Menzies | Compromised autophagy and neurodegenerative diseases[END_REF]. Knockdown of TRIB3 modulates PSEN1 stability [START_REF] Hua | TRB3 links insulin/IGF to tumour promotion by interacting with p62 and impeding autophagic/proteasomal degradations[END_REF] and a yeast two-hybrid screen identified progranulin as a direct interaction partner of TRIB3 [START_REF] Zhou | E3 ubiquitin ligase SIAH1 mediates ubiquitination and degradation of TRB3[END_REF]. Intriguingly, it has recently been demonstrated that TRIB3 induces both apoptosis and autophagy in Aβ-induced neuronal death, and silencing of TRIB3 was strongly neuroprotective [START_REF] Saleem | Tribbles Pseudokinase 3 Induces Both Apoptosis and Autophagy in Amyloid-β induced Neuronal Death[END_REF]. These links warrant further investigation for a functional role of TRIB3 in neuronal death in dementia.

These earlier findings align with our eQTL analysis where carriers of the minor allele show increased TRIB3 expression (Figure S5), which potentially lowers the threshold to TRIB3 mediated neuronal cell death. TRIB3 expression was modulated by the identified SNP in various other tissues including the caudate (Figure S7), a region affected in PD and Huntington's disease. A recent study of Trib3 expression in mice concluded that "Trib3 has a pathophysiological role in diabetes" [START_REF] Zhang | Skeletal Muscle TRIB3 Mediates Glucose Toxicity in Diabetes and High Fat Diet-Induced Insulin Resistance[END_REF]; diabetes itself is a known risk factor for dementia [START_REF] Sims-Robinson | How does diabetes accelerate Alzheimer disease pathology?[END_REF] perhaps through shared metabolic processes with AD [START_REF] Ribe | Insulin signalling in Alzheimer′s disease and diabetes: from epidemiology to molecular links[END_REF]. Interestingly, one of the three SNPs (rs1555318) selected in the PLS model and attributed to TRIB3 showed a strong association with type-2 diabetes in stage 1 of a large GWAS (p=4.4e-4; Figure S8) [START_REF] Morris | Large-scale association analysis provides insights into the genetic architecture and pathophysiology of type 2 diabetes[END_REF]. Other GWAS showed links between TRIB3 and information processing speed (p=1.7e-7) [START_REF] Luciano | Whole genome association scan for genetic polymorphisms influencing information processing speed[END_REF] and AD (p=0.006; [START_REF] Lambert | Meta-analysis of 74,046 individuals identifies 11 new susceptibility loci for Alzheimer's disease[END_REF]). An earlier genetic study on AD in Swedish men found an association in TRIB3 as well (p=0.044; [START_REF] Giedraitis | Genetic analysis of Alzheimer's disease in the Uppsala Longitudinal Study of Adult Men[END_REF]), which was replicated in a Canadian cohort (p<0.001 ; [START_REF] Li | Candidate single-nucleotide polymorphisms from a genomewide association study of Alzheimer disease[END_REF]).

Lastly, TRIB3 was reported to physically interact with APP [START_REF] Oláh | Interactions of Pathological Hallmark Proteins: Tubulin Polymerization Promoting Protein/p25, β-Amyloid, AND α-Synuclein[END_REF] and it shares numerous functional annotations for biological processes regarding lipid metabolism with APOE.

The functional prioritization component of the analysis successfully reduced the set of candidate genetic variants for the independent validation, however, this prioritization has a shortcoming: it hypothesizes that identified SNPs alter the expression of a nearby gene. Although, this scheme led to the identification of TRIB3 in the cortical thickness phenotype, it did miss a long-established AD risk gene: APOE. SNPs belonging to APOE (rs429358 and rs7412) were selected as highest scoring SNPs in component 1. However, none of them was detected as an eQTL and thus APOE was excluded from the downstream analysis. Other types of functional prioritizations based on exonic function prediction may have retained APOE and other genes in the pipeline. However, SNPs data typically features only a few non-synonymous exonic variants and their high frequency (MAF >5%) renders them unlikely to receive significant 'damaging' scores in these predictions. Thus, for this scenario the use of these function predictions would be limited.

The list of genes we identified contains other interesting candidates. For instance, IL10RA (interleukin 10 receptor subunit alpha) is a receptor for interleukin 10 (IL10), a cytokine that controls inflammatory response [START_REF] Li | Contextual regulation of inflammation: a duet by transforming growth factor-β and interleukin-10[END_REF]. Carriers of the minor allele show increased IL10RA expression (Figure S5) and Il10ra expression is increased in affected brain regions with increasing age and presence of AD pathology in transgenic mouse models of AD (MOUSEAC; [START_REF] Matarin | A genome-wide gene-expression analysis and database in transgenic mice during development of amyloid or tau pathology[END_REF] Figure S9). Moreover, a link between downregulation of IL10RA and TRIB3 in TRIB3-silenced HepG2 cells was reported in [START_REF] Hua | TRB3 links insulin/IGF to tumour promotion by interacting with p62 and impeding autophagic/proteasomal degradations[END_REF], along with increased abundance of Presenilin 1, ApoE3, and Clusterin. Finally, blocking IL10 response was recently suggested as a therapeutic mechanism in AD [START_REF] Guillot-Sestier | Il10 deficiency rebalances innate immunity to mitigate Alzheimer-like pathology[END_REF]. A gene that showed a statistical trend in the validation sample was TM2D1 (TM2 domain containing 1), which is a beta-amyloid binding protein and may be involved in beta-amyloid-induced apoptosis [START_REF] Kajkowski | β-Amyloid peptide-induced apoptosis regulated by a novel protein containing a G protein activation module[END_REF]. Further, MEF2A (Myocyte Enhancer Factor 2A), like APOE, was filtered out by the functional prioritization. However, MEF2A is a paralog of MEF2C, which is an established AD gene [START_REF] Lambert | Meta-analysis of 74,046 individuals identifies 11 new susceptibility loci for Alzheimer's disease[END_REF].

Noteworthy, bins covering MEF2C only barely missed the selection threshold in component 2 for further analysis (max p=0.926; Figure 2).

Methodological Considerations

The experimental setting proposed in this study is based on the investigation of potential genetic candidates in the AD and healthy training population, and on their testing in the MCI cohort. This experimental choice was motivated by clinical and practical considerations.

From the clinical point of view, although we cannot exclude that the imaging-genetics association patterns could be modulated by state-specific factors throughout the development of the disease [START_REF] Stage | The effect of the top 20 Alzheimer disease risk genes on gray-matter density and FDG PET brain metabolism[END_REF], the heterogeneity of the MCI label is likely to lead to the inclusion in the discovery dataset of individuals with non-AD pathologies. Thus, including MCIs in the discovery cohort bears the risk of diluting the gene finding (especially considering the relatively low sample size of the study cohort). Likewise, GWAS in AD carried out to date focus on comparing CT and AD. Moreover, the paradigm proposed in this study is rather conservative since it explores associations present throughout the progression of the pathology, i.e., associations were discovered by comparing CT and AD subjects and validated on disease progression in the intermediate MCI cohort. This consideration, while being more conservative, may play in favor of the robustness of the reported results. From a practical point of view, the proposed scheme allowed the validation of the model on a clinically relevant testing cohort by taking advantage of the full sample available in the ADNI dataset.

Splitting the available AD and CT subjects into discovery and validation cohort, would have dramatically reduced the sample size, thus increasing the uncertainty of the PLS findings.

Concerning the number of components analyzed in the PLS model, we limited the study to the exploration of the first five eigen-modes. As shown in the experimental results, the stability of PLS parameters of the high-order components was generally quite low and did not lead to any significant results after permutation testing. For this reason, we believe that extending the analysis to higher-order components (e.g., components six to ten) would not change the proposed analysis and subsequent results.

The relevance assessment procedure proposed in this study relies on the choice of statistical significance thresholds, such as the 10% cutoff on the magnitude of the PLS weights, and p<0.05 for the selection frequency over the 1,000,000 folds. These thresholds were not optimized to maximize specific statistical outcome (e.g. the ratio between true and false positives). Indeed, the optimization of these parameters may lead to important methodological issues such as overfitting and selection bias [START_REF] Mendelson | Selection bias in the reported performances of AD classification pipelines[END_REF], and ultimately lead to poor generalization of the statistical findings. This is particularly true in the challenging setting proposed in this work, characterized by large dimensions and low sample size. For this reason, we chose to use standard cutoffs for significance assessment as a compromise between minimizing this important source of bias while still identifying meaningful genotype and phenotype features. Furthermore, we believe that the ultimate approach to assess the validity of the findings is through testing on genuinely independent data, such as on the MCI cohort proposed in this study.

Conclusions

This study illustrates the potential of effectively combining multivariate statistical modeling in imaging-genetics with recent instruments available from computational biology, to lead to novel insights on the disease pathophysiology. Thanks to the evergrowing data-driven knowledge based on the vast quantities of information now available to the research community, the paradigm proposed in this study may represent a promising avenue for linking imaging-genetics findings to the current knowledge on functional genetics mechanisms involved in neurodegeneration.

Materials and methods

Study Participants

Data used in the preparation of this article were obtained from the ADNI database (http://adni.loni.usc.edu). The ADNI was launched in 2003 as a public-private partnership, led by Principal Investigator Michael W. Weiner, MD. The primary goal of ADNI is to test whether serial magnetic resonance imaging, positron emission tomography, other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of MCI and early AD. For up-to-date information, see www.adni-info.org. This research mainly involves further processing of previously collected personal data. We have explicit authorization for the use of the ADNI dataset, and we have signed the relevant papers guaranteeing that we abide to the ethics standards. The ADNI protocol details on page 30-31 the informed consent for imaging data (section d.5.d) and the procedures to maintain confidentiality of the data (section D.5.e).

We selected genotype and phenotype data available in the ADNI-1/GO/2 datasets for 1,192 subjects. Summary socio-demographic, clinical and genetic information are available in Table 1. At time of study entry subjects were diagnosed as healthy individuals (N=401), MCI (N=553) or AD (N=238). A total of 212 (38.3%) MCI patients subsequently converted to AD over the course of the study (6 years). All participants were non-Hispanic Caucasian, with a prevalence of males across the considered groups. AD and MCI groups show significant cognitive decline measured by MMSE and ADAS-COG as compared to the healthy individuals (p<1e-2, two sample t-test for group-wise comparison). There was also a significant increase of individuals with pathological levels of Aβ 1-42 in the CSF (Aβ 1-42 <192pg/ml) across the clinical groups, with proportions ranging from 43% for healthy individuals to 93% for AD patients (p<1e-2). Similarly, we observed a higher prevalence of APOE4 carriers in AD and progressing MCI individuals when compared to healthy and MCI stable groups.

In what follows, the 639 healthy and AD subjects form the discovery set, while the MCI converters and non-converters form the independent validation set.

Data processing

The imaging phenotype comprised the baseline brain cortical thickness maps estimated with FreeSurfer 5.3 [43] and the bilateral radial thickness maps for hippocampi, amygdalae, thalami, caudate, putamen, globus pallidus and nucleus accumbens. In detail, radial thickness of each subcortical surface model was based on the distance to a medial curve. We fit the medial curve using curve evolution individually for each shape [START_REF] Gutman | Shape matching with medial curves and 1-D group-wise registration[END_REF]. Surfaces are then registered parametrically to achieve point-to-point correspondence by matching curvature and medial curve-based features [START_REF] Gutman | A family of fast Spherical registration algorithms for cortical shapes[END_REF][START_REF] Roshchupkin | Heritability of the shape of subcortical brain structures in the general population[END_REF]. The procedure resembles the cortical surface registration on the sphere performed in FreeSurfer. Finally, the full imaging component comprises 327,684 cortical and 27,120 subcortical features per subject. SNP genotype data (Illumina Human610-Quad BeadChip for ADNI-1, and Illumina Human Omni Express for ADNI-GO/2) was downloaded from the ADNI website and preprocessed with PLINK [START_REF] Purcell | PLINK: a tool set for whole-genome association and population-based linkage analyses. The American Journal of Human Genetics[END_REF]. Standard quality control (QC) parameters were used to filter SNPs: minor allele frequency (MAF) < 0.01, genotype call rate <95% and Hardy-Weinberg equilibrium (HWE) p-value < 1x10 -6 . Finally, genotyped SNPs passing QC were used to impute SNPs in the HapMap III reference panel. Imputed SNPs underwent a separate QC regarding minor allele frequency (MAF > 0.01) and imputation quality (imputation R-squared > 0.3) in order to exclude poorly imputed SNPs. For the analysis the individuals' minor allele counts for each of the resulting 1,167,126 SNPs in the 22 autosomes were used.

Statistical Discovery

The joint relationship between the genetic and imaging modalities was investigated through partial least squares (PLS) modeling [START_REF] Wold | Estimation of principal components and related models by iterative least squares[END_REF][START_REF] Martens | Multivariate calibration[END_REF][START_REF] Mcintosh | Partial least squares analysis of neuroimaging data: applications and advances[END_REF][START_REF] Mcintosh | Spatial pattern analysis of functional brain images using partial least squares[END_REF][START_REF] Worsley | An overview and some new developments in the statistical analysis of PET and fMRI data[END_REF][START_REF] Lorenzi | Secure multivariate large-scale multi-centric analysis through online learning: an imaging genetics case study[END_REF]. Among the several PLS versions proposed in the literature we focus on the symmetric formulation of PLS computed through the singular value decomposition (SVD) of the cross covariance matrix (Figure S1) [START_REF] Mcintosh | Spatial pattern analysis of functional brain images using partial least squares[END_REF][START_REF] Worsley | An overview and some new developments in the statistical analysis of PET and fMRI data[END_REF][START_REF] Friston | Functional connectivity: the principal-component analysis of large (PET) data sets[END_REF]. Within this setting, the aim of PLS is to estimate the latent components that maximize the global covariance between the two input modalities. Each input feature receives a weight in the latent component that represents its relative importance for describing the global joint multimodal relationship. Analyzing these weights helps identifying SNPs that are linked to the patterns of cortical thinning in the brain.

In this study we applied a robust approach for the stable estimation and interpretation of PLS weights in genome-wide genotyping data, aimed at promoting sparsity (i.e., selecting only few features for simplified interpretation) and regularity (by aggregating SNPs within the same genetic neighborhood). This is achieved through a stability selection procedure in which the reproducibility and robustness of the PLS parameters is assessed through a split-half cross-validation based scheme on 1,000,000 repetitions of the models on randomly sampled subgroups (Figure 1 and supplementary Methods).

By considering a pre-defined partition of each chromosome into contiguous loci of size 10kb, the procedure leads to the estimation of a confidence measure taking values ranged between 0.0 and 1.0 indicating the probability of each genetic loci to contain highly reproducible PLS weights, and therefore serving as a measure of importance of the genomic location (Figure 2).

A similar procedure was employed to assess the importance of the phenotype component (Figure 1). However, no regional binning was employed (Figure 3).

The procedure was applied to assess the parameter reproducibility of the first five PLS modes; subsequent analyses were performed only on components with relevant genetic and brain regions (i.e., reproducible PLS weights with selection frequency >95%). PLS components and probability measures will be made available at the author's website. selected due to links between AD and obesity, type-2 diabetes and metabolic disease [START_REF] Luchsinger | Oxidative Stress, Reactive Metabolites, Inflammation, and RAGE -Building a Bridge from Alzheimer's Disease to Diabetes and Vice Versa[END_REF][START_REF] Ferreira | Inflammation, defective insulin signaling, and neuronal dysfunction in Alzheimer's disease[END_REF]. Finally, transformed fibroblasts (N=272) were included as a general-purpose cell line. P-values were corrected for multiple testing using the Bonferroni method.

Model validation in independent MCI subjects

The genes that were found to be under expression control by the identified SNPs were validated for their capacity to predict clinical conversion in MCI subjects. To this end, for each identified gene we applied the PLS weights estimated on the discovery set on the validation set, with the genetic component restricted to SNPs +/-20kb of the gene borders. The identified latent projections (i.e., a weighted sum of SNPs) results in one score per subject per gene. For each gene the association of the projection score with

Figure

  Figure S5): CAPN9, CRYL1, FAM135B, IL10RA, IP6K3, ITGA1, KIN, LAMC1,

  conversion status was assessed by statistically comparing the scores distribution between healthy individuals and AD patients, and between MCI converters and nonconverters (Kruskal-Wallis non parametric test for two sample comparison, Bonferroni correction for multiple comparisons).

Figure 1 .

 1 Figure 1. Cross-validation scheme for the assessment of the genetic loci of maximal

Figure 2 .

 2 Figure 2. PLS genotype component: the outer circular plots show the probability of a

Acknowledgment

SO receives funding from the EPSRC (EP/H046410/1, EP/J020990/1, EP/K005278), the MRC (MR/J01107X/1), the EU-FP7 project VPH-DARE@IT (FP7-ICT-2011-9-601055), the NIHR Biomedical Research Unit (Dementia) at UCL and the National Institute for Health Research University College London Hospitals Biomedical Research Centre (NIHR BRC UCLH/UCL High Impact Initiative-BW.mn.BRC10269). EPSRC grants EP/J020990/01 and EP/M020533/1 support DA and SO's work on this topic. ML, DA, JS, and SO also received support from the European Union's Horizon 2020 research and innovation programme under grant agreement No 666992 (EuroPOND) for this work. JMS acknowledges the support of the National Institute for Health Research University College London Hospitals Biomedical Research Centre, Wolfson Foundation, EPSRC (EP/J020990/1), MRC (MR/L023784/1), ARUK (ARUK-Network 2012-6-ICE; ARUK-PG2017-1946; ARUK-PG2017-1946), Brain Research Trust (UCC14191) and European Union's Horizon 2020 research and innovation programme (Grant 666992). AA holds an MRC eMedLab Medical Bioinformatics Career Development Fellowship. SW and CA are supported by the NIHR Queen Square Biomedical Research Unit in Dementia and Alzheimer's Research UK, and by the National Institute for Health Research University College London Hospitals Biomedical Research Centre. Contribution to this work by BG and PT was funded by the National Institutes of Health "Big Data to Knowledge" (BD2K) award (NIH U54 EB020403, PI: Thompson). Data collection and sharing for this project was funded by the Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer's Association; Alzheimer's Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck &

Gene identification

We analyzed the 10kb bins (genetic loci) with the selection frequency exceeding 0.95, i.e., bins selected in 95% or more of the 1,000,000 replications. Within these bins we then identified the influential SNPs: a SNP was declared influential if it was associated with the weights of greatest magnitude in the PLS components estimated on the full data sample, i.e., SNPs with absolute weights exceeding the 99 th quantile of all weights in the component. These weights are the ones contributing to the high selection frequency in the split-half procedure, and are representative of the significant variation modeled in the data. Focusing on the features associated with these weights allows us to restrict the functional prioritization on a SNPs subset of reduced dimensionality, by focusing only on the most representative elements.

In order to link SNPs to corresponding genes we used the Ensembl Variant Effect Predictor (VEP) for GRCh37 (date accessed: 17 th October 2016) [START_REF] Aken | The Ensembl gene annotation system. Database (Oxford)[END_REF] with the GENCODE gene annotation. SNPs tagged as 'regulatory' were manually investigated and annotated with the nearby genes.

Functional prioritization

All SNPs successfully annotated with a gene were subjected to functional prioritization through expression quantitative trait loci (eQTL) analysis based on the Genotype-Tissue-Expression project (GTEx) data. The sample size in GTEx for relevant brain tissues in AD was rather small (e.g., N=81 for hippocampus).

Therefore, we added five more tissues with large samples sizes that were more distantly relevant to AD: nerve tibial (N=256) was added as a proxy for nervous tissue; whole blood (N=338) and artery tibial (N=285) were included to cover bloodbased changes and effects on blood vessels [START_REF] Kimbrough | Vascular amyloidosis impairs the gliovascular unit in a mouse model of Alzheimer's disease[END_REF]

Conflict of Interest

The authors do not report any conflict of interest.


Naohiko Shimizu
email: nshimizu@keyaki.cc.u-tokai.ac.jp

Junichi Akita
email: akita@is.t.kanazawa-u.ac.jp

Marie-Minerve Louërat

Haralampos-G Stratigopoulos

Jean-Paul Chaput

Dimitri Galayko

Open Source Hardware and EDA Tools for Analog/Mixed-Signal Design and Prototyping

The paper aims at stimulating a discussion on the prospect and potentiality of open source electronic design automation tools and open source hardware. We discuss the benefits and motivation, as well as the expected difficulties and shortcomings. Finally, we provide a representative list of efforts as of today specifically for analog and mixed-signal circuits and systems design and prototyping.

I. INTRODUCTION

Electronic Design Automation (EDA) tools aiming to perform modeling, design, simulation, verification, design-fortest, etc., of electronic circuits and systems are commercialized and, thereby, "un-democratized", in the sense that licenses come at a price that is prohibitive for individuals and in many cases for Universities and small and medium size enterprises as well. Even if access to EDA tools is granted, the subsequent circuit fabrication and hardware prototyping steps are also very costly and cannot be easily afforded either.

In light of this reality, as of today there have been many attempts towards open source EDA tools (OSEDA) and open source hardware (OSHW), turning electronic circuits and systems design from being a "privilege" to being accessible at a personal scale [START_REF] Stallman | Free hardware and free hardware designs[END_REF]. Open source in this context means that the source code of EDA tools and netlist, layout, benchmark suites, etc., of a hardware design, are made publicly available and are freely distributed with no discrimination against persons or groups, and, thereby, they can not only be used freely, but can also be modified and enhanced with new features for the specific needs of a project [START_REF] Ayass | CERN Open Hardware Licence[END_REF]. Furthermore, a first version of OSEDA or OSHW can continuously evolve through the work of additional, multiple, and independent contributors in a collaborative spirit.

OSEDA can be considered as part of the free open software movement [START_REF] Stallman | The gnu manifesto[END_REF] and OSHW can be considered as part of the worldwide makers movement or a technology-based extension of the Do-It-Yourself (DIY) movement [START_REF] Anderson | Makers: The New Industrial Revolution[END_REF], [START_REF] Verhaegen | The open source EDA tool chain for the Chips4Makers project. Is an ASIC made with fully open source tool chain possible ? Is it affordable[END_REF].

One of the first pioneers of OSEDA was University of California, Berkeley, proposing a variety of tools for circuit design [START_REF]EDA tools[END_REF]. Perhaps the most popular OSHW nowadays is Arduino [8], which offers the possibility of fast hardware prototyping without requiring the user to have a strong background in electronics and programming. Historically, OSEDA and OSHW have been developed more intensively for digital circuits compared to their analog counterparts [START_REF] Verhaegen | The open source EDA tool chain for the Chips4Makers project. Is an ASIC made with fully open source tool chain possible ? Is it affordable[END_REF]. For example, Alliance [START_REF] Greiner | Alliance: A complete set of CAD tools for teaching VLSI design[END_REF], [START_REF]Alliance, A Free VLSI/CAD System[END_REF], which is a tool for digital integrated circuit design allowing the automated synthesis of a circuit from Registered Transfer Level (RTL) description to Graphic Database System (GDSII) description, was proposed in the early 90s. An excellent and comprehensive review of OSEDA and OSHW efforts, as well as existing project repositories (for example, see [11]- [START_REF] Katz | Open Hardware License OHL v2.0[END_REF]), can be found in [START_REF] Barriga | Visiting open source harware: A survey of opportunities[END_REF]. The ongoing project "Open!" is studying the current practices in open source project development [START_REF] Bonvoisin | OPEN! Methods and tools for communitybased product development[END_REF].

In this paper, we provide some representative examples of existing and under development OSEDA and OSHW specifically for analog and mixed-signal (AMS) circuit design and prototyping. Due to space limitations the list is not meant to be complete. Section II discusses the benefits from widely adopting OSEDA and OSHW which explains the growing interest of the designers community. Section III discusses the difficulties for OSEDA and OSHW to become a reality and common practice. Section IV provides the examples and Section V concludes the paper.

II. MOTIVATION FOR OSHW AND OSEDA

OSHW and OSEDA will greatly increase the number of individuals (i.e. makers, passionates of electronics, curious, etc.) who can perform designs. It will also allow small and medium size enterprises that do not necessarily have the capital to purchase licenses of proprietary tools and hardware platforms to perform designs. The larger pool of designers created by OSHW and OSEDA implies that innovation will be brought up at a faster pace. There will be more innovation and higher productivity through reuse especially on what it concerns application-specific integrated circuits, thus allowing the development of new products and applications. As a result, OSHW and OSEDA can facilitate the proliferation of electronic circuits, extending their deployment in a broader range of applications.

OSHW and OSEDA will be valuable for supporting teaching activities on electronics at Universities even in countries and continents that have limited financial means. Students anywhere in the world will be able to put their hands on actual designs, learn, experiment, and even make silicon demonstrators. OSHW and OSEDA can be used even in secondary education such that students get exposure to electronic design and design automation at a very early stage.

OSEDA will bring down drastically the cost of designing an integrated circuit. This not only reduces the final product cost, but also allows the design companies to invest the amount that would be spent otherwise to purchase licenses of proprietary tools for other purposes, such as performing more design iterations, fabricating more prototypes, and adding more features into the design that often are overlooked due to cost factors, i.e. built-in test infrastructure, security, reliability, self-repair, fault tolerance, etc.

Since the number of designers increases and the cost of design drops, there will be more designs that reach a silicon implementation, thus overall there will be more clients for the foundries. Apart from the economic benefit, this will sustain a high volume manufacturing of devices in a current technology for a longer period. Therefore, the investment on a foundry, which is typically in the order of tens of billions of U.S. dollars, will amortize itself faster and, in general, the phenomenon of rapid technology obsolesce will slow down. In addition, we may observe the sustainability of foundries in several countries, thus partially alleviating security and trust concerns, such as IC/IP piracy, counterfeiting, overproduction, etc., that are due to outsourcing and the globalization of the manufacturing chain of electronic components.

OSEDA may motivate or even force in the end foundries to freely distribute their process design kits (PDK). This will circumvent complications that designers often experience with the signing of the Non Disclosure Agreement (NDA). For example, often in the case of academic projects the foundry demands the ownership of the design.

OSHW and OSEDA will also facilitate the creation of benchmark circuits that can be used for demonstrating and comparing concepts. It is often the case that for a given problem numerous solutions are proposed in the literature, but it is impossible to perform a quantitative comparison because the underlying case studies in each paper, i.e. circuit, topology, technology, etc., are different. Benchmarks can help evaluating and comparing solutions on common grounds, thus offering more credibility to published papers and avoiding the flood of literature. Benchmarks can help also practitioners selecting much faster the best solution for a given application.

EDA companies tend to decompose the tool for performing and completing successfully a design into several individual tools, each requiring a different license. OSEDA could target an all-in-one tool or combine OSEDA tools with licensed tools.

Using proprietary tools for which the source code is not available introduces various trustworthiness and security threats. In particular, there are various vulnerable points that can be exploited by a knowledgeable adversary to introduce Hardware Trojans. Hardware Trojans are malicious modifications in an IC aiming at covertly leaking secret information, such as cipher keys in a cryptoprocessor, degrading the reliability and performance, rendering the IC completely malfunctional, or bringing the IC at a denial of service state. OSEDA can offer full transparency for the user who, in turn, will have full control over the design. Assuming a chip designed entirely with OSEDA and a trusted foundry, the Hardware Trojans threat is eradicated.

It is commonly accepted that the benefits from OSHW would be greater if it is supported by publicly available documentation regarding the EDA tools that were employed to develop the OSHW [START_REF] Bonvoisin | What is the Source of Open Source Hardware?[END_REF]. OSEDA is a key factor to reach this goal.

OSHW and OSEDA are based on the principle that anyone can be a user of a released version and a contributor in a future version. The different versions can also be traced back to understand the evolution. In this regards, OSHW and OSEDA become automatically world heritage that is by default preserved indefinitely and can further evolve at any chosen time even after a long period of silence [16].

III. DIFFICULTIES AND CHALLENGES FOR OSHW & OSEDA TO BECOME REALITY

If a large number of chip designers start relying on OSEDA, then EDA companies will face financial losses and this may bring them out of business resulting in significant job cuts. A new business model will be needed, perhaps a support-oriented business model. Nevertheless, as explained above, OSEDA are expected also to create jobs and even new markets, thus the job cuts in the EDA industry may be counterbalanced.

Continuous and quick maintenance and debugging of OSEDA is not guaranteed. Typically, a group of core developers makes public a first version of the tool and stays active for some time processing demands for fixing bugs in reasonable time. However, core developers may at some point withdraw, retire, loose interest, etc., thus the maintenance and debugging risk to be slowed down or totally discontinued. Users then may loose interest in the tool if bugs cannot be fixed or new features cannot be added, and the tool may eventually become obsolete.

OSHW and OSEDA must be extensively validated and verified before usage. The presence of errors and bugs may result in erroneous, lower-performance, and non-manufacturable designs. Ideally, many potential users should play the role of testers to validate and verify the beta versions. However, this is not guaranteed, thus reducing the confidence of the end users and affecting the spreading and popularity of OSHW and OSEDA.

It is unclear if foundries will accept to openly share their PDKs in the context of OSEDA. This is especially true for advanced technology nodes where confidentiality rises. Thus, OSHW and OSEDA in the end may be only linked to old and obsolete technology nodes without offering the possibility of performing state-of-the-art designs.

Academia is typically behind the development OSHW and OSEDA, but securing sufficient funding to develop OSHW and OSEDA is not straightforward. It is unclear which bodies (i.e. universities, governments, donors, etc.) will accept to provide generous funding to boost the development of OSHW and OSEDA and whether this funding will be uninterrupted.

Many developers despite being in favor of OSEDA and actually having this goal at the initial stages of the development, in the end they choose rather to pursue a technology transfer or the creation of a start-up since the economic incentive becomes too high. In general, the success of OSHW and OSEDA will largely depend on devoted and knowledgeable volunteers and passionates and on the rise of a spirit of open source consciousness in the design and EDA communities.

IV. EXAMPLES OF OSEDA AND OSHW FOR AMS CIRCUIT DESIGN AND PROTOTYPING

A. MakeLSI: Project MakeLSI: Project is a project aiming at realizing an open source Large Scale Integration (LSI) design and fabrication community [START_REF] Akita | Open Source LSI design & Fabrication Project for Distributed IP Development[END_REF]. The project started using the FAIS Semiconductor Center [START_REF]Semiconductor Center[END_REF], which is a commonly operated LSI fabrication facility in Kitakyushu, Japan. FAIS offers a 2µm, two-metal layer CMOS technology, with a simple and clear lambda-based design rule. Using the PDK does not require signing a NDA and, in addition, the users are free to share and distribute their circuit designs. Finally, the cost to fabricate a wafer is affordable and suitable for training and educational purposes and even for hobbyists. The project employs two OSEDA tools for physical design, which are accompanied with tutorials so as to guide the user in the first steps of the design. The first OSEDA tool is Wgex and is used for layout design with combined circuit extraction and Design Rule Checking (DRC) [START_REF] Asada | Wgex[END_REF]. The second OSEDA tool is Glade and is used for generating and verifying schematics and layout with built-in DRC and Layout Versus Schematic (LVS) [20]. Figs. 1a and1b show screenshots from these two tools.

The project is running for four years now and in total four fabrication runs have been performed using the FAIS technology. In each fabrication run, several circuits were designed by the members of the project, including analog, radio frequency (RF), and digital circuits, as well as sensors. Fig. 2 shows the microphotographs of two example circuits.

The project now also targets using the 0.6µm technology provided by Phenitec Semiconductor Corp., Japan. Although using this process requires a strict NDA for design rule disclosure, the project tried to avoid this by using directly the design rules of the FAIS 2µm technology with a shrinking factor of ×0.3. Some information has still to be provided by Phenitec Semiconductor Corp., such as contact and via size. MOSFET spice parameters were also fitted from measured fabricated devices, in order to generate the MOSFET simulation model and circumvent relying on the model included in the actual PDK. The MOSFET parameter extraction is performed by the OSEDA tool PyEDA [START_REF] Drake | Python library for electronic design automation[END_REF].

In order to design the digital part of mixed-signal circuits, the project selected the Alliance OSEDA tool chain [START_REF]Alliance, A Free VLSI/CAD System[END_REF] and its included standard cell library. Alliance is a complete set of OSEDA tools based on symbolic unit λ, starting at RTL level and going all the way down to layout and GDSII. Alliance has a special layout tuning mechanism to migrate a symbolic layout into a real one. Therefore, the layout component dimensions generated with Alliance are not constrained to be multiple of λ, unlike other λ-based rule existing tools. This feature makes Alliance to be compatible with a wide range of technologies. The project has successfully fabricated LSI chips with Alliance using the 180nm ROHM technology [START_REF] Hosokawa | The Layout Design Method for Rohm 0.18um Process Using Open Source EDA Tool-set and lambda rule based cell library Corresponding to Deep Sub-micron Process[END_REF] and the 0.6µm Phenitec Semiconductor Corp. technology. Fig. 3 shows the design flow and a microphotograph of a fabricated chip [START_REF] Shimizu | Development of VLSI design Flow with FOSS EDA and NDA Free Design Rules[END_REF], [START_REF] Shimizu | Development of NDA free VLSI design Flow for 0.6µm Commercial Fabrication[END_REF]. C. Analog circuit sizing Oceane [START_REF] Porte | Oceane: Software tool for analog design and education[END_REF] is an OSEDA tool dedicated to the electrical sizing of analog circuits. Oceane provides a library of parametrized topologies of several analog functions, i.e. Operational Transconductance Amplifier (OTA), operational amplifier, comparator, voltage regulator, filters, switch, etc. The user has to select a technology, a topology, and set the values of the target performances. Oceane provides the sized topology in the form of a spice netlist [START_REF]nsgpice[END_REF], [START_REF]The SPICE page[END_REF] and estimates of the performances, together with a set of benchmarks compliant with spice simulation so as to validate the estimated performances. The user can also perform statistical analysis to reach a centered design that will have a high fabrication yield.

D. Field-programmable analog array (FPAA)

FPAA is the analog equivalent of the field-programmable digital array (FPGA) and is perhaps the most popular OSHW platform for rapid and flexible AMS circuit design and prototyping [START_REF] Malcher | Analog Reconfigurable Circuits[END_REF], [START_REF] George | A Programmable and Configurable Mixed-Mode FPAA SoC[END_REF]. FPAA can enable configurable and programmable analog and digital computation and interfacing.

E. Benchmarks for analog test

Mentor Graphics and ams AG recently made available a set of benchmark AMS circuits with the aim to facilitate the development of fault models, design-for-test techniques, and test generation techniques, as well as their comparison based on fault coverage metrics and fault simulation times [START_REF] Sunter | A/MS benchmark circuits for comparing fault simulation, DFT, and test generation methods[END_REF], [START_REF]Benchmarks for analog test[END_REF]. The list of benchmark circuits includes an operational amplifier, a high-speed comparator, a power-on reset circuit, a charge-pump phase locked loop (PLL), and a 8-bit digitalto-analog converter (DAC). It is hoped that this set of benchmarks will boost the development of alternative, low-cost test techniques for AMS circuits, similarly to what happened for digital circuits following the publishing of digital benchmark circuits [START_REF] Brglez | Accelerated ATPG and fault grading via testability analysis[END_REF], [START_REF] Brglez | Combinational profiles of sequential benchmark circuits[END_REF].

F. SystemC AMS extensions

Virtual Prototyping (VP) is used for the design space exploration and verification of complex and heterogeneous embedded systems [START_REF] Oetjens | Safety Evaluation of Automotive Electronics Using Virtual Prototypes: State of the Art and Reasearch Challenges[END_REF]. SystemC is a hardware description language for rapid VP of digital systems. In the framework of the European Project Catrene/BREAMS [START_REF] Scotti | Beyond Dreams: Design Refinement of Embedded Analogue and Mixed-Signal Systems[END_REF], the AMS extensions of SystemC [START_REF]Accellera Systems Initiative[END_REF] have been standardized by the Accellera consortium [START_REF] Barnasconi | SystemC AMS extensions Users Guide, Version 1.0, Accellera systems initiative[END_REF] under the OSCI [START_REF]SystemC Open Source Licence v3.3[END_REF] licence. In 2016, a new version of the Language Reference Manual [START_REF] Barnasconi | SystemC AMS Extensions 2.0 Language Reference Manual, Accellera systems initiative[END_REF] has been standardized by Accellera Systems Initiative [START_REF]SystemC AMS Extensions[END_REF] under the Apache licence [START_REF]the APACHE software foundation[END_REF], as well as by the IEEE consortium [START_REF][END_REF]. Version 2.1 of the simulator proof of concept has been recently released by COSEDA [START_REF] Einwich | SystemC AMS PoC2.1 Library[END_REF] compliant with the IEEE standard 1666.1 under the Apache 2.0 licence. SystemC AMS adds the Timed Data Flow (TDF) model of computation to SystemC, that handles analog signals sampled in time. The TDF model of computation is inspired by the Synchronous Data Flow model [START_REF] Ptolemaeus | System Design, Modeling, and Simulation using Ptolemy II. Ptolemy.org[END_REF]. TDF models can interact with SystemC models thanks to converter ports. The SystemC AMS TDF model of computation is fully compliant with the discrete event simulator of SystemC [START_REF] Andrade | Pre-Simulation Formal Analysis of Synchronization Issues between Discrete Event and Timed Data Flow Models of Computation[END_REF], therefore mixedsignal system VP can be performed within the same simulation environment [START_REF] Porras | Principles and implementation of a generic synchronization interface between SystemC AMS models of computation for the virtual prototyping of multi-disciplinary systems[END_REF], [START_REF] Ben Aoun | Principles and Realization of a Virtual Prototyping Environment for Composable Heterogeneous Systems[END_REF].

G. Place & Route

Coriolis [START_REF]Coriolis, Digital Place & Route[END_REF] is perhaps the only Place & Route EDA tool to be released as Free Open Source Software (FOSS) under the GPL licence [50]. The ongoing work of the Coriolis team is to extend its features to analog and mixed-signal circuits and systems [START_REF] Lao | Semi-automated analog placement based on margin tolerances[END_REF]. It is now possible to take a netlist sized with Oceane and design the layout with Coriolis. H. Layout viewer and editor KLayout is a GDS and OASIS file viewer and editor [START_REF] Koefferlein | KLayout[END_REF]. It comes with a comprehensive documentation. It allows the drawing of any shape required by a technology process.

I. OSHW in health applications

echOpen [START_REF] Echopen | ECHOSTETHOSCOPY[END_REF] is an open and collaborative project and community, led by a multidisciplinary core of experts and senior professionals with the aim of designing a functional low-cost and open source echo-stethoscope (ultrasound probe) connected to a smartphone, allowing the radical transformation of diagnostic orientation in hospitals, general medicine and medically underserved areas.

V. CONCLUSION We argued about the several benefits that OSEDA and OSHW can offer and pointed to the several difficulties that need to be overcome towards this goal. We also shed light on today's status of OSEDA and OSHW specifically for AMS circuit and system design and prototyping. While several OSEDA and OSHW exist and can be used to perform a low-cost design, it will require a larger collective effort to make OSEDA and OSHW trustful and useful in the context of practical and robust designs.

Fig. 1 .

 1 Fig. 1. OSEDA tools used in "MakeLSI: Project".

Fig. 2 .

 2 Fig. 2. Microphotograph of chips fabricated in the framework of the "MakeLSI: Project".

Fig. 3 .

 3 Fig. 3. NDA free design method and the generated chip layout B. Electrical simulators Ngspice [25] is one of the most popular mixed-signal circuit simulation tools. Its code is based on three open source software packages, namely Spice3f5 [26], Cider1b1 [27], and Xspice. It is an ongoing project that stared 15 years go, growing continuously with the help of new contributions suggestions, and reports from users.

  Fig 4 shows the netlist of a simple OTA sized with Oceane and the corresponding layout designed with Coriolis.

Fig. 4 .

 4 Fig. 4. OTA sized with Oceane and its layout with Coriolis.

ACKNOWLEDGMENT

The authors would like to thank Jacky Porte for his work on the Oceane software and Luca Alloatti for the interesting discussions that inspired this paper.