Cristina M Pedrero-Prieto

Alicia Flores-Cuadrado

Daniel Saiz-Sánchez

Isabel Úbeda-Bañón

Javier Frontiñán-Rubio

Francisco Alcain

Lourdes Mateos-Hernandez

Jose De

La Fuente

Mario Duran-Prado

Margarita Villar

Francisco J Alcaín

Lourdes Mateos-Hernández

José De La Fuente

Mario Durán-Prado

Alino Martínez-Marcos

Juan R Peinado
email: juanramon.peinado@uclm.es

Human amyloid-β enriched extracts: evaluation of in vitro and in vivo internalization and molecular characterization

Keywords: Alzheimer's disease, Amyloid-β, Prion-like hypothesis, Amyloid-β internalization, Proteomics

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

Background

Alzheimer's disease (AD) is the main cause of dementia worldwide [START_REF] Scheltens | Alzheimer's disease[END_REF][START_REF] Masters | Alzheimer's disease[END_REF]. From a neuropathological point of view, Alzheimer's disease (AD) is characterized by the deposition of insoluble forms of amyloid-β (Aβ) in the brain parenchyma and abnormal hyperphosphorylation of tau protein, forming, respectively, plaques and neurofibrillary tangles [START_REF] Selkoe | Cell biology of protein misfolding: The examples of Alzheimer´s and Parkinson´s diseases[END_REF]. Even though these pathological features are well-known, the etiology of the disease is still unknown. Together with the accepted amyloid hypothesis [START_REF] Pearson | Physiological roles for amyloid beta peptides[END_REF][START_REF] Shirwany | The amyloid beta ion channel hypothesis of Alzheimer's disease[END_REF], the prion-like hypothesis is gaining strength to explain the etiology of neurodegenerative diseases characterized by proteinopathies-such as AD [START_REF] Walker | The Prion-Like Properties of Amyloid-beta Assemblies: Implications for Alzheimer's Disease[END_REF], whose initial stages reportedly begin in the mesial temporal structures [START_REF] Braak | Staging of Alzheimer disease-associated neurofibrillary pathology using paraffin sections and immunocytochemistry[END_REF]. This hypothesis is based on the capacity of Aβ to induce abnormal folding of native adjacent proteins and cell-to-cell propagation of Aβ and tau, resembling a prion-like seeding and spreading mechanism [START_REF] Eisele | Propagation of Ass pathology: hypotheses, discoveries, and yet unresolved questions from experimental and human brain studies[END_REF]. This idea is supported by the fact that inoculation of human brain extracts obtained either from patients with AD [START_REF] Morales | De novo induction of amyloid-beta deposition in vivo[END_REF][START_REF] Kane | Evidence for seeding of b-amyloid by intracerebral infusion of Alzheimer brain extracts in β-amyloid precursor protein transgenic mice[END_REF][START_REF] Meyer-Luehmann | Exogenous induction of cerebral -amyloidogenesis is governed by agent and host[END_REF] or from APP23 mice [START_REF] Watts | Bioluminescence imaging of Aβ deposition in bigenic mouse models of Alzheimer's disease[END_REF] into transgenic mice [START_REF] Morales | De novo induction of amyloid-beta deposition in vivo[END_REF][START_REF] Kane | Evidence for seeding of b-amyloid by intracerebral infusion of Alzheimer brain extracts in β-amyloid precursor protein transgenic mice[END_REF][START_REF] Meyer-Luehmann | Exogenous induction of cerebral -amyloidogenesis is governed by agent and host[END_REF][START_REF] Watts | Bioluminescence imaging of Aβ deposition in bigenic mouse models of Alzheimer's disease[END_REF] or marmosets (Callithrix jacchus) [START_REF] Ridley | Very long term studies of the seeding of beta-amyloidosis in primates[END_REF] induces the development of diffuse plaques far from the injection site [START_REF] Morales | De novo induction of amyloid-beta deposition in vivo[END_REF][START_REF] Kane | Evidence for seeding of b-amyloid by intracerebral infusion of Alzheimer brain extracts in β-amyloid precursor protein transgenic mice[END_REF].

Prion-like spreading of AD appears to follow a threestep process. First, after injection of AD extracts, the seeds (mostly oligomers and protofibrils) are internalized by using a variety of mechanisms [START_REF] Wesen | Endocytic uptake of monomeric amyloid-beta peptides is clathrin-and dynamin-independent and results in selective accumulation of Abeta(1-42) compared to Abeta(1-40)[END_REF]. Second, internalized seeds nucleate the fibrillation of native monomers in the cytoplasm of the recipient cell, and a positive feedback loop starts [START_REF] Guo | Cell-to-cell transmission of pathogenic proteins in neurodegenerative diseases[END_REF]. Finally, cell-to-cell transmission of cytosolic protein aggregates starts after their release into the extracellular space in their "naked" form [START_REF] Guo | Cell-to-cell transmission of pathogenic proteins in neurodegenerative diseases[END_REF]. Different proteomic analyses have been performed using Aβ-enriched extracts [START_REF] Adav | Dementia-linked amyloidosis is associated with brain protein deamidation as revealed by proteomic profiling of human brain tissues[END_REF][START_REF] Izco | Optimized protocol for amyloid-beta extraction from the brain[END_REF][START_REF] Roher | Purification, ultrastructure, and chemical analysis of Alzheimer disease amyloid plaque core protein[END_REF][START_REF] Diner | Enrichment of detergent-insoluble protein aggregates from human postmortem brain[END_REF][START_REF] Tsuji | Analysis of brain proteins in Alzheimer's disease using high-resolution two-dimensional gel electrophoresis[END_REF][START_REF] Tsuji | Analysis of the proteomic profiling of brain tissue in Alzheimer's disease[END_REF][START_REF] Rostagno | Isolation and biochemical characterization of amyloid plaques and paired helical filaments[END_REF] and micro-dissected plaques coupled with LC-MS/MS [START_REF] Hadley | Determining composition of micron-scale protein deposits in neurodegenerative disease by spatially targeted optical microproteomics[END_REF][START_REF] Hondius | Profiling the human hippocampal proteome at all pathologic stages of Alzheimer's disease[END_REF][START_REF] Liao | Proteomic characterization of postmortem amyloid plaques isolated by laser capture microdissection[END_REF][START_REF] Drummond | Proteomic differences in amyloid plaques in rapidly progressive and sporadic Alzheimer's disease[END_REF], in order to identify additional components which may be relevant to both transmissibility and seeding process. Usually, AD brain extracts are inoculated directly into the brain of APP23 [START_REF] Kane | Evidence for seeding of b-amyloid by intracerebral infusion of Alzheimer brain extracts in β-amyloid precursor protein transgenic mice[END_REF][START_REF] Meyer-Luehmann | Exogenous induction of cerebral -amyloidogenesis is governed by agent and host[END_REF] or tg2576 transgenic mice [START_REF] Morales | De novo induction of amyloid-beta deposition in vivo[END_REF] to evaluate the prion-like hypothesis. To our knowledge, none of the published studies has assessed the possibility of injection of fractions enriched with Aβ plaques. This study proposes a method that strongly enriches Aβ aggregates from human AD samples while retaining their ability to internalize Aβ in vitro and in vivo. Proteomic characterization of these extracts revealed the presence of several proteins either over-or underrepresented in AD-enriched fractions, which may contribute to plaque integrity and/or Aβ internalization.

Materials and methods

Human brain samples

Human tissue blocks were provided by biobanks IDI-BAPS (Barcelona), BT-CIEN (Madrid), and BIOBANC-MUR (Murcia). Experimental procedures were approved by the Ethical Committee for Clinical Research of the Ciudad Real University Hospital. Twelve human brain samples containing the olfactory cortex, amygdala, and hippocampus were used (five diagnosed AD cases, six cases with no AD diagnosis, and one case with incidental plaques but no AD diagnosis; Additional file 1: Table S1). The exact locations of the brain sections used in this study are shown in Additional file 2: Figure S1.

Enrichment of Aβ plaque-containing fractions from human brains

To obtain Aβ-enriched fractions, we used two samples from human brains with no AD diagnosis, two cases diagnosed as AD (stage VI), and one case with incidental Aβ plaques but no AD diagnosis (Additional file 1: Table S1). Approximately 10 g from each sample was cut into 1-cm 3 blocks and homogenized in lysis buffer (20 mM Tris pH 7.4, 100 mM NaCl and 5 mM CaCl 2 ) supplemented with protease inhibitor. Homogenization was performed on a mechanical homogenizer on ice. The homogenates were incubated on ice with DNase I. An efficient enrichment of Aβ plaques from the human brain was achieved using a protocol based on four centrifugation steps using Triton X (1%) and SDS (1.75%) followed by acetone precipitation (Additional file 2: Figure S2A). This protocol was applied to two human brain samples with no evidence of AD pathology (non-AD; n = 2), samples from two AD patients (AD; n = 2), and also one sample from a patient with diffuse plaques but no evidence of AD (DP; n = 1), for comparison. An overview of the process is shown in Additional file 2: Figure S2A. The resulting precipitate was resuspended in Hank's solution and stored at -20 °C.

Determination of the efficacy of Aβ enrichment

The Aβ 1-42 content (the major component of Aβ plaques in the brain parenchyma) of the fractions was examined with dot blot (Additional file 2: Figure S2B-C) and western blot (Fig. 1A). Dot blot was carried out with 1 μl of each fraction resulting from the enrichment procedure, which was set on PVDF membranes. PVDF membranes were dried during 2 h at 60 °C and blocked with 5% BSA (VWR, Solon; OH, USA) in TTBS (200 mM Tris-HCl pH 8.8, 6 mM NaCl and 1% Tween20) for 1 h at room temperature. Membranes were blotted with Aβ 1-42 (1:5000) and tau (1:1000) antibodies. For western blot, all the protein extracts were quantified using bicinchoninic acid assay (BCA; Sigma Aldrich). Sixty micrograms of protein for each sample (all supernatants and pellet) was prepared using 12.5-μL sample buffer (Bio-Rad), 2.5-μL reducing buffer (Bio-Rad), and deionized water, and boiled for 5 min. Samples were electrophoresed on Criterion™ XT Precast Gel 12% Bis-Tris (Bio-Rad) with XT MES running buffer (Bio-Rad) at 180 V for 45 min. The proteins were transferred to a PVDF membrane (Bio-Rad) for 50 min at 0.25 mA constant in transfer buffer (50 mM Tris-HCL, pH 8.8, 192 mM glycine, 0.02% SDS and 20% methanol). Membranes were stained with ponceau red and destained with 1% acetic acid and blocked in 5% BSA in TTBS for 1 h at room temperature and then incubated with Aβ 1-42 antibody (1:1000; 2.5% BSA in TTBS) overnight at 4 °C. After secondary antibody incubation, the membranes were washed with TTBS and developed with Clarity Western ECL substrate according to the manufacturer's directions. To evaluate the effectiveness of the enrichment Aβ 1-42 , western blot results were compared with Coomassie blue staining of 20 μg of all the fractions by quantifying the ratio with ImageJ.

Quantification of Aβ 1-42 contents in the enriched fraction

Quantification of the Aβ contents in the final enriched fraction was done by dot blot and ELISA after sonicating the samples. ELISA was performed using an Aβ42 Human ELISA Kit (Invitrogen; Vienna, Austria) following the manufacturer's instructions. The samples were sonicated (Branson Ultrasonics™ Sonifier™ SFX150) for 1 min. Dot blot was performed as described previously using different dilutions of the extract and dilutions of the synthetic Aβ 1-42 peptide with known concentrations.

Scanning electron microscopy (SEM)

The presence of aggregates in the Aβ-enriched extracts was confirmed by SEM after sonication. The homogenates were diluted in methanol and centrifuged at 16100g for 10 min at 4 °C, twice. The resulting pellets were resuspended in pure methanol, then deposited in silicon and left to dry. Samples were metallized with gold chips and observed using a Zeiss GeminiSEM 500 scanning electron microscope.

In vitro Aβ 1-42 internalization into endothelial cells

Internalization of Aβ 1-42 from enriched extracts was examined in vitro. As endothelial cells are the first to interact with the circulating Aβ, we used for these studies the endothelial cell line bEnd.3 (ATCC CRL-2299). Cells were cultured in DMEM containing 10% fetal bovine serum (FBS) and 1% antibiotic/antimycotic, at 37 °C and 5% CO 2 . They were then seeded in eight-well μ-Slides (Ibidi, Martinsried, Germany) and incubated with AD and non-AD extracts. After 48 h, cells were fixed and permeabilized in 4% paraformaldehyde (PFA). To analyze Aβ incorporation, cells were sequentially incubated with Aβ 1-42 antibody (1 h) and AlexaFluor® 488conjugated anti-mouse antibody (1 h). Cells were costained with 1 μg/ml Hoechst and ActinRed™ 555 and examined using an LSM 800 confocal microscope (Zeiss; Jena, Germany) with a × 63 objective.

In vivo microinjection of Aβ-enriched fractions

In vivo experiments were carried out with female C57BL/6J mice (000654, The Jackson Laboratory, USA). Three different experimental groups were established: saline microinjection (n = 6), human non-AD extract microinjection (n = 6), and human AD Aβ-enriched extract microinjection (n = 6). Animals were anesthetized using vaporized isoflurane. The animals were placed in a Kopf (Tujunga, CA) stereotaxic apparatus, and the skull trepanned at the injection spot into the dorsal part of the left anterior olfactory nucleus (AONd, coordinates from Bregma [START_REF] Paxinos | The mouse brain in stereotaxic coordinates[END_REF] were AP = + 2.8 mm, L = 1 mm, and depth = -2.75 mm, from the dura mater). This structure was chosen because it is preferentially vulnerable and directly involved in Aβ aggregation [START_REF] Ubeda-Banon | alpha-Synucleinopathy in the human olfactory system in Parkinson's disease: involvement of calcium-binding proteinand substance P-positive cells[END_REF][START_REF] Saiz-Sanchez | Interneurons in the human olfactory system in Alzheimer's disease[END_REF]. Next, saline, 6 μg/μl of human non-AD and 6 μg/μl of human Aβ 1-42enriched extracts (all extracts were previously tagged with AlexaFluor® 488 nm [green] labeling dye [Molecular Probes]) were injected in a constant infusion (0.2 μl/ min) for 10 min using a microsyringe (10 μL Neuros Model 1701 RN, point style 4, SYR, Hamilton Co., Nevada, USA). Animals were kept on the stereotaxic apparatus for additional 5 min to favor the diffusion of the extract before removing the syringe. The animals were housed on a standard 12/12 h light/dark cycle, at 21 °C with food and water ad libitum. All the animal research procedures described herein were in agreement with European (Directive 2010/63/EU) and Spanish (RD 53/ 2013) legislation on the protection of animals used for scientific purposes. All experiments described were approved by the Ethical Committee for Animal Research of the University of Castilla-La Mancha (SAF2016-75768-R).

Isolation of mouse brain for immunostaining

Four months after injection, animals were anesthetized with a mixture of ketamine hydrochloride (1.5 mL/kg, 75 mg/kg, Ketolar, Madrid, Spain) and xylazine (0.5 mL/ kg, 10 mg/kg, Xilagesic, Calier, Barcelona, Spain) and perfused with saline solution followed by 4% w/v paraformaldehyde fixative (phosphate-buffered; 0.1 M sodium phosphate, pH 7.2). Brains were post-fixed in 4% w/v paraformaldehyde, cryo-protected in 30% w/v sucrose, and coronally sectioned (50 μm) employing a freeze sliding microtome. To visualize the injection site, sections were counterstained with DAPI. To study the extracts injected into the AONd, saline, human non-AD extracts, and human Aβ 1-42 -enriched extracts were tagged with AlexaFluor® 488 nm (green) dye, following the manufacturer's instructions. Immunofluorescence labeling against Iba-1 (1:1000) and AlexaFluor® 568 nm (1: 200) was performed in order to detect microglia.

Label-free proteomics of human brain extracts

For proteomics analysis, two AD samples, two non-AD samples, and one corresponding to a patient with preamyloid diffuse plaques but without evidence of AD were used (all samples were enriched as described in the previous section). The protein extracts (150 μg per sample) were concentrated on gel and analyzed by reverse phase liquid chromatography-tandem mass spectrometry (RP-LC-MS/MS) using an Easy-nLC II system coupled to a linear ion trap mass spectrometer model LTQ (Thermo Scientific) as previously described [START_REF] Villar | Integrated metabolomics, transcriptomics and proteomics identifies metabolic pathways affected by Anaplasma phagocytophilum infection in tick cells[END_REF]. The MS/MS raw files were searched against the Uniprot-Human proteome database (70,931 entries in January 2019) (http://www.uniprot.org) using the SEQUEST algorithm (Proteome Discoverer 1.4, Thermo Scientific). The following constraints were used for the searches: tryptic cleavage after Arg and Lys, up to two missed cleavage sites, and tolerances of 1 Da for precursor ions and 0.8 Da for MS/MS fragment ions and the searches were performed allowing optional Met oxidation and Cys carbamidomethylation. A false discovery rate (FDR < 0.01) and at least two peptides per protein was considered as a condition for successful peptide assignments. For the semiquantitative analysis of proteins, the total number of peptide-spectrum matches (PSMs) for each protein was normalized against the total number of PSMs in each sample and compared between AD and non-AD samples using the chi-square test (p < 0.05).

Gene ontology analysis study was carried out with the proteomic profiles obtained for both AD and non-ADenriched extracts to identify overrepresentation profiles.

To that end, we use GOrilla (http://cbl-gorilla.cs.technion.ac.il; [START_REF] Eden | GOrilla: a tool for discovery and visualization of enriched GO terms in ranked gene lists[END_REF]), a bioinformatics tool previously used in several studies (i.e., [START_REF] Witztum | Hierarchical partitioning of metazoan protein conservation profiles provides new functional insights[END_REF]). As a background, we used the most recent database of a global quantitative analysis of the human brain proteome in Alzheimer's disease, extracted from [START_REF] Ping | Global quantitative analysis of the human brain proteome in Alzheimer's and Parkinson's disease[END_REF] (16,559 recognized proteins in GOrilla; database updated June 2019). We set p value to 10 -6 in order to avoid unreliable data. Gene ontology was investigated at three levels: biological process, biological function, and biological component.

Immunofluorescence and immunohistochemical procedures

Immunofluorescence analysis was performed in 4% phosphate-buffered formaldehyde-fixed samples. Afterwards, all blocks were post-fixed in fresh 4% phosphatebuffered paraformaldehyde for 45 days. Coronal sections of the amygdala, olfactory cortex, and hippocampus (50 μm) were obtained using a freezing sliding microtome Microm HM 450. For these experiments, a total of six antibodies against Aβ 1-42 , RNF213, COL6A, ANXA5, CNTN1, and GFAP were used (Additional file 1: Table S2). Tissue antigenicity was unmasked by boiling the tissue under pressure for 2 min in citrate buffer. Sections were immersed in formic acid for 3 min and rinsed in phosphate buffer. Endogenous peroxidase activity was inhibited by a 30-min bath in 1% H 2 O 2 in phosphatebuffered saline. Blocking consisted of 5% NDS+ 0.3% Triton X-100 in PBS. Sections were incubated overnight at 4 °C with primary antibodies containing 0.3% Triton X-100 and 5% normal serum in phosphate-buffered saline. Controls included omitting primary or secondary antibodies. Sections were counterstained using DAPI (Santa Cruz Biotechnology; Inc.; Sc-3598) or Nissl and coverslipped with PVA-DABCO or DPX after dehydrating. Human tissue autofluorescence was not reduced. Images were captured using an LSM 800 confocal microscope and analyzed using ZEN software.

Results

Detergent-centrifugation method allows efficient enrichment of insoluble Aβ 1-42

The presence of Aβ 1-42 in the five samples during the different steps was monitored by dot blot [Additional file 2: Figure S2B (non-AD1, AD1 and DP) and Additional file 2: Figure S2C (non-AD2 and AD2)]. As expected, the results showed no Aβ 1-42 in the non-AD samples. The SDS 1.75% supernatants (S3-S4) showed immunostaining both in AD and DP samples, suggesting that part of the soluble Aβ 1-42 was diluted using this concentration of SDS. In AD samples, the pellet from the last step was extremely difficult to reconstitute and showed a strong Aβ 1-42 signal (probably corresponding to the Aβ plaques). Interestingly, the DP samples did not show reactivity in the insoluble fraction (Additional file 2: Figure S2B), and tau protein was mainly eliminated in the second wash with SDS (Additional file 2: Figure S2D). A 4-kDa band was observed with strong immunoreactivity against Aβ 1-42 in the last fraction of the AD and DP samples (Fig. 1A), probably corresponding to monomeric Aβ 1-42 . Aβ 1-42 dimers, trimers, and oligomers appeared only in the AD samples (Fig. 1A, right), indicating that AD and DP experience different aggregation strengths.

Estimation of Aβ 1-42 enrichment (Fig. 1B) was attempted by comparing western blot and Coomassie blue staining (Additional file 2: Figure S2E). In AD samples, the concentration of Aβ 1-42 increased according to the ratio western blot/Coomassie blue staining (Fig. 1B, left). In the DP sample, the ratio did not change (Fig. 1B, right). In order to accurately quantify Aβ 1-42 concentration, a human Aβ 1-42 ELISA (Invitrogen; Fig. 1C) was performed. Despite the sensitivity of the kit, non-AD samples did not show immunoreactivity against Aβ 1-42 . It is especially relevant that although AD samples contained 50 ng/mL (AD1) and 210 ng/mL (AD2) of Aβ 1-42 , the DP sample showed a higher concentration of Aβ 1-42 (over 0.8 μg/ml). This result is completely opposite to that obtained with western blot and dot blot. To quantify Aβ concentration in the extracts, dot blot with diluted concentrations of the Aβ-enriched fractions and known dilutions of synthetic Aβ 1-42 [START_REF] Gouwens | Amyloid-beta42 protofibrils are internalized by microglia more extensively than monomers[END_REF] (Sigma Aldrich; Fig. 1D) was carried out. The results indicated a concentration of Aβ 1-42 in the sample ranging from 0.1 to 0.5 μg/μL. Although we are aware that neither of the methods developed so far for insoluble Aβ 1-42 quantification are accurate, the examination of our samples by electron microscopy revealed the presence of aggregates (with the presence of fibrils) in AD (Fig. 1E, a-d) and DP (Fig. 1E, e-f ) sonicated extracts, which were not observed in non-AD samples (Fig. 1E, g-h).

Aβ internalization from the enriched fractions into cultured microvascular endothelial cells

Our Aβ plaque enrichment protocol was aimed at maintaining the plaque integrity and to preserve its prion-like properties. Therefore, we first evaluated the in vitro incorporation Aβ 1-42 internalization into bEnd.3 cells were tested by adding AD-enriched extracts (a volume corresponding to approximately 1 μg of Aβ 1-42 according to dot blot quantification) to the cell culture. Figure 2 shows immunofluorescence against the Aβ 1-42 antibody and ActinRed™ 555 labeling after 48-h incubation with non-AD extracts (Fig. 2a) and Aβ-enriched extracts from AD1 (Fig. 2b,c) and AD2 (Fig. 2d,e). This strategy allowed us to visualize internalized Aβ 1-42 in vesicle-like structures using confocal z-stacks (Fig. 2b-e). Additional file 3: Video S1. shows different angles of the Aβ 1-42 internalized in the cell from Fig. 2b.

In vivo injection of Aβ plaque-enriched extracts in mouse brain and Aβ 1-42 internalization

Aβ-enriched extracts tagged with AlexaFluor® 488 nm (green) were injected into the dorsal part of the anterior olfactory nucleus. Labeled saline injections (images not shown) did not reveal any fluorescence near the injection site. Inoculation with the extracts obtained non-AD sample allowed for the identification of the injection site, but no fluorescence was detected inside the cells (Fig. 3a,b). In contrast, the fluorescence of the sections 4 months after inoculation of Aβ 1-42 -containing extracts could be observed inside the cells closer to the injection location (Fig. 3c,d). Internalization of human Aβ extracts (green) in microglia was also examined using Iba-1 antibody (red; Fig. 3e). Figure 3f shows an Iba-1-positive cell within the z-stack.

Proteomic characterization of Aβ-enriched extracts

Next, the enriched fraction containing insoluble Aβ was characterized in order to identify possible protein components bound to the Aβ plaque that had not been observed in the non-AD extracts. To that end, proteomic analysis on enriched extracts of two AD and two non-AD samples was performed. Specifically, 149 and 133 proteins were identified in AD-enriched samples, and 144 and 131 in non-AD samples (Additional file 4: Table S3.) In AD samples, six of these proteins were overrepresented and three proteins were underrepresented (Table 1). Proteins that were exclusively detected in AD or non-AD extracts were also examined (Table 2; 1% FDR, target-decoy database approach). A total of 34 proteins were identified at least in one of the two AD samples, while 12 proteins were identified in the non-AD extracts, which probably correspond to proteins that decrease in AD-enriched extracts. Several proteins previously related to AD were identified as overrepresented in the Aβ-enriched fraction [APOE [START_REF] Kim | The role of apolipoprotein E in Alzheimer's disease[END_REF], ANXA2 [START_REF] Eberhad | Alterations of Annexin expression in pathological neuronal and glial reactions[END_REF], or MAPT [START_REF] Zhang | Meta-analysis of the association between variants in MAPT and neurodegenerative diseases[END_REF]]. The rest of the identified proteins are shown in Table 2.

GO enrichment analysis was carried out with the proteins observed in the enriched samples of both AD and non-AD, using whole brain proteome as background. This study retrieved significant results when biological process was inquired (Additional file 2: Figure S3). Thus, negative regulation of wound healing and homeostasis were identified an AD while cell morphogenesis and cell junction assembly appeared in the non-AD samples.

Distribution of the proteins in the amygdala and olfactory cortex sections GFAP, ANXA5, and COL6A expression was evaluated by immunofluorescence. Since proteomics had been performed in regions containing mostly amygdala (see Additional file 2: Figure S1), immunohistochemical experiments were performed in the same regions using additional AD samples. Furthermore, several of the proteins in the olfactory cortex area were also examined in order to evaluate whether the changes induced in AD could also be observed in this section of the brain-since olfactory deficits usually precede the clinical onset of cognitive and memory deficits in AD pathology [START_REF] Vasavada | Olfactory cortex degeneration in alzheimer's disease and mild cognitive impairment[END_REF]. GFAP expression was examined as a control of the enrichment process, since it has been previously shown to co-localize with the Aβ plaque in AD [START_REF] Kamphuis | Glial fibrillary acidic protein isoform expression in plaque related astrogliosis in Alzheimer's disease[END_REF]. The results indicated that although there was co-localization between Aβ 1-42 and GFAP, GFAP immunolabeling in AD could be observed in all the tissue (Fig. 4A). ANXA5 was also overrepresented in Aβ 1-42 extracts.

Immunostaining was higher in AD samples than in non-AD samples in both the amygdala (Fig. 4B) and the olfactory cortex (Additional file 2: Figure S4A). However, in contrast with GFAP, the ANXA5 signal increase was especially noticeable surrounding the plaques in human AD brain samples. As for COL6A, which was highly represented in non-AD samples, it also showed reduced immunostaining in AD samples (Fig. 4C).

Finally, a triple immunofluorescence was carried out in amygdala with Aβ 1-42 (Fig. 5a,b,red) and two of the proteins observed exclusively in AD samples (RNF213; Fig. 5c,d, green) and non-AD samples (CNTN1; Fig. 5e,f,purple) . It is especially relevant that CNTN1 expression in non-AD samples was strong and widespread when compared to AD samples (Fig. 5e,f). On the other hand, RNF213 immunostaining (which, as expected, appears in the nuclei of the cells) seems to be overexpressed in AD samples. Together with the Aβ 1-42 fluorescence (Fig. 5g,h), a noteworthy increase in RNF213 intensity (twofold increase) could be appreciated when the nuclei were located into Aβ plaques (arrow). Similar experiments performed in the olfactory cortex of AD patients revealed that CNTN1 was also abundant in non-AD samples in this section of the brain (Additional file 2: Figure S4B) while RNF213 appeared strongly associated within the limits of the Aβ plaque (Additional file 2: Figure S4B).

Discussion

Aβ enrichment from AD patients and pre-amyloid diffuse plaques

Several laboratories have developed protocols to extract Aβ and other components from AD plaques [17, 19, 22, 40] although those with higher success rates (70-99% formic acid; [START_REF] Rostagno | Isolation and biochemical characterization of amyloid plaques and paired helical filaments[END_REF]) involve aggressive treatments of the Aβ plaque and solubilize the core structure of amyloid fibrils [START_REF] Rostagno | Isolation and biochemical characterization of amyloid plaques and paired helical filaments[END_REF]. In this study, we aimed at preserving as much fibrillar structures as possible and therefore we used a four-step enrichment protocol based on detergent centrifugations. We avoided the combination of detergent extraction with high molarity urea or guanidinium salts as it may result in increased solubilization of fibrillar structures [START_REF] Jimenez | Disruption of amyloid plaques integrity affects the soluble oligomers content from Alzheimer disease brains[END_REF]. We also avoided sonication during the process as it has been shown that it produces the redistribution of Aβ species from plaques to more soluble fractions [START_REF] Jimenez | Disruption of amyloid plaques integrity affects the soluble oligomers content from Alzheimer disease brains[END_REF].

In AD, Aβ aggregates start as pre-amyloid diffuse plaques [START_REF] Davies | Is the "preamyloid" of diffuse plaques in Alzheimer's disease really nonfibrillar?[END_REF] that contain smaller amounts of Aβ and are not as organized into fibrils as in more advanced stages. In this study, a strong precipitate was observed in Aβenriched samples of stage VI AD patients, and dimers and oligomers remained in western blot experiments. The presence of such insoluble material was not observed in non-AD samples and barely observed in the extract from the patient with diffuse plaques. Nevertheless, in order to obtain accurate information of the soluble Aβ that was present in each enriched extract used for the different experiments, we avoided the use of formic acid or guanidinium salts for ELISA. Quantification in such conditions uncovered the presence of five to ten times higher Aβ 1-42 in DP than in AD. In this sense, it has been shown that ELISA usually works fine with soluble Aβ but not with insoluble Aβ aggregates as it underestimates the concentration of total Aβ 1-42 of the Aβ plaque [START_REF] Esparza | Soluble amyloid-beta aggregates from human Alzheimer's disease brains[END_REF]. Taking into consideration the solubility of Aβ in the AD samples, it was not possible to ascertain their Aβ 1-42 concentration, and only dot blot analysis (which has previously been used for this purpose) [START_REF] Gouwens | Amyloid-beta42 protofibrils are internalized by microglia more extensively than monomers[END_REF] gave an approximated concentration of 0.5 μg/μl of Aβ in the final pellet. Although we are aware that the presence of insoluble material may introduce some bias in the process of protein quantification, as far as we know, this concentration constitutes the highest Aβ enrichment tested to date in vivo and in vitro.

Labeled extracts from Aβ-enriched fractions are internalized in vitro and in vivo

This study provides the first evidence that AD-enriched extracts, but not non-AD extracts, are efficiently incorporated into the cells surrounding the injection site 4 months post-injection, which constitutes the first step toward Aβ transmissibility. Additional labeling with Iba-1 demonstrates that among the cells that incorporate labeled extracts of AD patients in vivo there are glial cells (microglia). This fact has been previously described in vitro [START_REF] Gouwens | Amyloid-beta42 protofibrils are internalized by microglia more extensively than monomers[END_REF], where it was proposed that Aβ 1-42 protofibrils were more efficiently internalized by microglia than monomers [START_REF] Gouwens | Amyloid-beta42 protofibrils are internalized by microglia more extensively than monomers[END_REF]. In fact, microglia might play a crucial role in AD [START_REF] Salter | Microglia emerge as central players in brain disease[END_REF]. We cannot assure that the long-lived component of the extracts incorporated into Iba-1positive cells is exclusively Aβ 1-42 as we labeled whole Aβ 1-42 -enriched extracts. In fact, there exists the possibility that the observed fluorescence corresponds to additional labeled proteins that are not enriched in control extracts, as these extracts are not internalized. In this sense, previous experiments injecting preparations of soluble or fibrillar synthetic Aβ 40 , Aβ 42 , or a mixture of both [START_REF] Meyer-Luehmann | Exogenous induction of cerebral -amyloidogenesis is governed by agent and host[END_REF] and Aβ 1-40 , Aβ 1-42 , and Aβ 40-1 synthetic Aβ peptides [START_REF] Ridley | Very long term studies of the seeding of beta-amyloidosis in primates[END_REF] did not generate such a prion-like effect as AD brain extracts, suggesting that these extracts may contain unique features important for the internalization and transmission of the seeding. Also, further attempts to initiate the aggregation of Aβ in vivo with synthetic peptides in combination with several of the components known to be associated with the Aβ plaque, such as ApoE [START_REF] Meyer-Luehmann | Exogenous induction of cerebral -amyloidogenesis is governed by agent and host[END_REF], did not reach success reinforcing the idea that other plaque components should be participating in this phenomenon. This is especially relevant, and we are Table 1 Proteins overrepresented in Aβ-enriched fraction and proteins overrepresented in non-AD samples. The MS/MS raw files were examined against the universal protein database UniProt (70,931 entries in January 2019) (http://www.uniprot.org), using the SEQUEST algorithm (Proteome Discoverer 1.4, Thermo Fisher Scientific). Fold of change; P value < 0.05. PSM peptide-spectrum matches, x ̄average, ND-AD not detected in Alzheimer extracts, ND-non-AD not detected in control extracts currently undergoing further experiments to identify the nature of the incorporated proteins. In addition, our study also found that cultured endothelial cells, as the primary components of the blood-brain barrier, uptake Aβ extracts from Aβ-enriched fractions in what may constitute the pathway for Aβ to reach the bloodstream.

Proteomics analysis identified components that were over-and underrepresented in plaque-containing AD extracts

Previous studies [START_REF] Kamphuis | Glial fibrillary acidic protein isoform expression in plaque related astrogliosis in Alzheimer's disease[END_REF][START_REF] Hol | Neuronal expression of GFAP in patients with Alzheimer pathology and identification of novel GFAP splice forms[END_REF] have related a hyper-reactivity of the GFAP protein to Aβ deposition. In this study, the GFAP signal was found to be intense in the amygdala of AD patients, corroborating those findings. Two members of the annexin family were also enriched in AD extracts. One of them, annexin A5 (ANXA5), has been proposed as an AD biomarker since its plasma levels, commonly used to detect apoptotic cells, are significantly higher in AD patients [START_REF] Sohma | Evaluation of annexin A5 as a biomarker for Alzheimer's disease and dementia with Lewy bodies[END_REF][START_REF] Yamaguchi | Investigation of annexin A5 as a biomarker for Alzheimer's disease using neuronal cell culture and mouse model[END_REF]. Intense ANXA5 immunoreactive spots were observed in an AD transgenic mouse model [START_REF] Yamaguchi | Investigation of annexin A5 as a biomarker for Alzheimer's disease using neuronal cell culture and mouse model[END_REF]. Our study shows for the first time that the ANXA5 signal is especially intense several micrometers around the plaque. In this sense, GO enrichment analysis revealed overrepresentation of two biological processes in AD extracts, where ANXA5, together with ANXA2, APOE, and CD9 proteins take part: negative regulation of wound healing and homeostasis. These biological processes are not found in non-AD extracts and enhance the potential importance of these four proteins for systemic inflammation, or other processes that lead to the brain homeostasis collapse in advanced Alzheimer's disease stages [START_REF] Frere | Alzheimer's disease: from firing instability to homeostasis network collapse[END_REF].

It is especially intriguing that the presence of HIST1H2BK among the most significant proteins is overrepresented in Aβ-enriched extracts. This fact has been observed for histone H3 previously in full extracts off AD by iTRAQ [START_REF] Minjarez | Identification of proteins that are differentially expressed in brains with Alzheimer's disease using iTRAQ labeling and tandem mass spectrometry[END_REF] and in laser proteomics of the plaques for histone H4 [START_REF] Liao | Proteomic characterization of postmortem amyloid plaques isolated by laser capture microdissection[END_REF]. Search for ligands of b-APP using ligand blotting showed strong affinity for histones specially H4 [START_REF] Potempska | Interaction between the β-amyloid peptide precursor and histones[END_REF], and although we do not know whether histones bind or not to APP-derived peptides, their consistent finding in proteomic studies points toward a deep histone-amyloid plaque relation. This fact is especially relevant and deserves a deeper analysis, even more if we take into account that extracellular histones induce inflammation and other toxic effects [START_REF] Xu | Extracellular histones are major mediators of death in sepsis[END_REF][START_REF] Chen | Release and activity of histone in diseases[END_REF]. It is also relevant the result that suggests that fibronectin is reduced in AD extracts vs non-AD as major changes in the molecular composition of the vascular basement membranes (BM) are observed in acute and chronic neuropathological settings [START_REF] Thomsen | The vascular basement membrane in the healthy and pathological brain[END_REF]. Other proteins of the extracellular matrix (ECM) intimately related with the BM such as fibrinogen or laminin A5 are more abundant in non-AD extracts while no differences were found on tubulins or vimentin between non-AD and AD samples. Therefore, the dissimilar distribution of these structural components of the BM and the ECM between AD and non-AD extracts reflects alteration of the BM that occurs in AD [START_REF] Morris | The cerebrovascular basement membrane: role in the clearance of beta-amyloid and cerebral amyloid angiopathy[END_REF].

It also shows that the alpha-3 subunit of type VI collagen decreases in patients with AD. Collagen VI is an extracellular matrix protein which, according to previous studies [START_REF] Cheng | Collagen VI protects neurons against Abeta toxicity[END_REF], protects neurons from the toxicity of Aβ peptides. Consequently, brains with collagen VI deficiency can be expected to show greater vulnerability to apoptosis, due to alterations in oxidative stress triggered by Aβ deposits [START_REF] Cescon | Lack of collagen VI promotes neurodegeneration by impairing autophagy and inducing apoptosis during aging[END_REF]. This protein could be a promising focus for future treatments.

On the other hand, one of the most interesting proteins observed exclusively in both samples of Aβenriched extracts is the E3 ubiquitin-protein ligase RNF213 [START_REF] Bai | Distinctive RNA expression profiles in blood associated with Alzheimer disease after accounting for white matter hyperintensities[END_REF]. RNA expression of the gene encoding this protein was found in genomic microarrays from AD patients [START_REF] Bai | Distinctive RNA expression profiles in blood associated with Alzheimer disease after accounting for white matter hyperintensities[END_REF]. Recent studies suggest that RNF213 plays an important role in cerebral blood flow maintenance under ischemic conditions by affecting angiogenesis [START_REF] Morimoto | Dysregulation of RNF213 promotes cerebral hypoperfusion[END_REF], processes whose alteration usually precede development of amyloid plaques in AD patients and AD animal models [START_REF] Farkas | Cerebral microvascular pathology in aging and Alzheimer's disease[END_REF]. Immunoreactivity is mostly observed in the nucleus (increased in those located inside the plaque), although, in the olfactory cortex, the protein is also found within the plaque. The distribution of RNF213 immunostaining reveals a potential direct Aβ plaque biomarker. Contrary to RNF213, CNTN1 was highly expressed in non-AD, as opposed to AD, samples. The contactin family has been known to interact with the extracellular domain of amyloid precursor protein (APP). For instance, contactin-2 regulates APP cleavage by secretases, a process important for neurotoxic Aβ liberation and production of the APP intracellular domain [START_REF] Medway | Using in silico LD clumping and meta-analysis of genome-wide datasets as a complementary tool to investigate and validate new candidate biomarkers in Alzheimer's disease[END_REF]. Also, it is implied in synaptic plasticity [START_REF] Gulisano | Role of the adhesion molecule F3/Contactin in synaptic plasticity and memory[END_REF]. It is interesting that a number of specific calcium binding (ANXA2, ANXA5, and FN1; [START_REF] Gabel | Phosphorylation cycling of Annexin A2 Tyr23 is critical for calciumregulated exocytosis in neuroendocrine cells[END_REF][START_REF] Huber | The calcium binding sites in human annexin V by crystal structure analysis at 2.0 A resolution Implications for membrane binding and calcium channel activity[END_REF][START_REF] Amphlett | The binding of calcium to human fibronectin[END_REF]) or calcium-sensitive (COL6A3 [START_REF] Quill | Calcium channel blockade reduces mechanical strain-induced extracellular matrix gene response in lamina cribrosa cells[END_REF]) proteins are differentially enriched in proteomics of both AD and non-AD extracts. This fact may be related to the importance that calcium plays in the progression of AD ( [START_REF] Wang | Calcium Dysregulation in Alzheimer's Disease: A Target for New Drug Development[END_REF]) where calcium increases are associated with increased production of Aβ and also with reductions in macroautophagy-a clearance pathway for intracellular aggregates- [START_REF] Penke | β-Amyloid and the Pathomechanisms of Alzheimer's Disease: A Comprehensive View[END_REF].

Conclusions

In conclusion, the obtained enriched Aβ fractions of human AD brains retain their ability to be internalized in vitro by cultured cells, but also the intracellular detection in vivo of the labeled extracts was marked after 4 months post-inoculation. Therefore, the enriched Aβ extract allows for easy traceability by immunofluorescence as the increased concentration of Aβ plaques amplifies the cell exposure to Aβ. We have deeply characterized the components of Aβ-enriched fractions identifying several proteins with dissimilar distribution between AD and non-AD extracts and investigating the distribution of the most representative findings in amygdala and olfactory cortex. These unique characteristics in terms of Aβ enrichment and extract characterization made these extracts the finest tool to further investigate seeding and transmissibility of the proposed prion-like hypothesis of AD.

Fig. 1

 1 Fig. 1 Quantification and evaluation of the Aβ-enriched extracts. a Western blot of AD sample 1 (AD1) and diffuse plaque sample (DP) using Aβ 1-42 antibody. The last fraction enriched in Aβ plaques is shown boxed in order to identify Aβ monomer (4-kDa band), dimers, and multimers. b Ratio between western blot signal and Coomassie blue staining that reflects Aβ enrichment in the fractions. c ELISA of Aβ 1-42 carried out with non-AD (non-AD1 and non-AD2), AD (AD1 and AD2), and DP samples. c Dot blot on the enriched extracts (P4) of the samples previously analyzed with western blot and ELISA. SEM images of AD1 extracts (a, b), AD2 extracts (c, d), DP extracts (e, f), and non-AD extracts (g, h). Scale bars: a, c, e, g, 1 μm and b, d, f, h, 200 nm

Fig. 2

 2 Fig. 2 Immunofluorescence against Aβ 1-42 in ActinRed™ 555-labeled endothelial cells (bEnd.3) after 48-h incubation with the enriched extracts. a Non-AD extracts. b, c Two representative cells after incubation with AD1-enriched extracts. d, e Two representative cells after incubation with AD2-enriched extracts. Zstacks are shown on the top and right sides of each image. Pictures were acquired using a confocal microscope with a × 63 objective. Scale bars a-d = 10 μm

Fig. 3

 3 Fig. 3 Microinjection and internalization of Aβ 1-42 in the dorsal anterior olfactory nucleus. Images show the region where the AlexaFluor 488labeled extracts were injected. Human non-AD extracts (a, b) and human Aβ 1-42 -enriched extracts (c, d). Nuclei are shown in blue (DAPI), and labeled extracts appear in green. Images e and f correspond to the tissue of samples injected with labeled extracts (green) together with Iba-1 labeling (red). Z-stack images are also shown. Scale bars a, c = 130 μm, b = 20 μm, d = 40 μm, e = 10 μm, f = 3 μm. AO anterior olfatory nucleus (D, dorsal; L, lateral; M, medial; V, ventral)

Fig. 4

 4 Fig. 4 Double immunofluorescence against Aβ 1-42, and GFAP (A), Aβ 1-42 and ANXA5 (B) and Aβ 1-42 and COL6A (C). Confocal images of amygdala sections of human AD samples and non-AD samples, used to study the distribution of GFAP (green, A), ANXA5 (green, B), or COL6A (green, C). Immunostaining against Aβ 1-42 (red, a-b) was also included to identify the Aβ plaques. Nuclei are labeled in blue with DAPI. Calibration bars 50 μm

Fig. 5

 5 Fig. 5 Triple immunofluorescence against Aβ 1-42, RNF213, and CNTN1. Confocal images showing a triple-immunofluorescence against Aβ 1-42 (a, b), RNF213 (c, d), and CNTN1 (e, f) in coronal sections of non-AD (a, c, e, and g) and AD human brain (b, d, f, and h). Calibration bar a-h 50 μm. Yellow arrowheads indicate the highly RNF213 immunofluorescence identified nuclei

Table 2

 2 Proteins found exclusively in AD extracts and proteins found exclusively in non-AD extracts

	Symbol	Entrez gene name

Table 2

 2 Proteins found exclusively in AD extracts and proteins found exclusively in non-AD extracts (Continued)

	Symbol	Entrez gene name

Acknowledgements

We are indebted to the IDIBAPS, BTCIEN, and BIOBANC-MUR Biobanks for the sample and data procurement. We thank Sara Fairén and Calum Ross for the English edition of this manuscript.

Funding

Sponsored by the Spanish Ministry of Economy and Competitiveness-FEDER (grant # SAF2016-75768-R) to AMM, MINECO-RETOS (AEI-FEDER) to MDP, and the Autonomous Government of Castilla-La Mancha/FEDER (grant no. SBPLY/ 17/180501/000430) to AMM and DSS.

Availability of data and materials

The data generated during in this study is included in this article and its additional files.

Additional files

Additional file 1: Table S1. Data of patients used in the present study. AD, Alzheimer disease; non-AD, non-Alzheimer disease; M, Male; F, Female; y, years; P, Proteomic study; E, ELISA; D, dot blot; I, immunofluorescence. *Human brain tissue used for the optimization of the enrichment protocol. Table S2. Antibodies used in the present study. (PPTX 47 kb) Additional file 2: Figure S1. Schemes showing the medial view of the brain and the corresponding levels: A) Coronal sections of olfactory (B) and amygdaloid (C) areas analyzed [Bregma -5.8 and -6.7 mm respectively, according to [START_REF] Mai | Atlas of the human brain[END_REF]]. The corresponding tissue blocks (D, E) and Nissl-stained, mosaic-reconstructed sections (F, G) are also illustrated. Calibration bars 1 cm. A: amygdala; aic: anterior limb of internal capsule; AONc: anterior olfactory nucleus, cortical part; C: claustrum; cc: corpus callosum; Cd: caudate nucleus; HiH: hippocampal head; ic: internal capsule; LV: lateral ventricle; OlfA: olfactory area; Pir: piriform cortex; PHG: parahippocampal gyrus; Pu: putamen; SG: straight gyrus; TLV: temporal horn of lateral ventricle; un: uncus; Ent: Entorhinal cortex; PRC: perirhinal cortex. CMPP performed the protocol for amyloid β enrichment and in vitro research, she also performed all dot blots, western blots, ELISA and SDS-PAGE, and prepared the tables and figures. AFC, DSS and IUB did the in vivo experiments and prepared tissue for immunohistochemistry. LMH and MV, performed the proteomic study. JFR, MDP and AFC provided technical assistance. CMPP, MV, JRP, and MDP contributed to the analysis of the results (in vitro, in vivo and proteomic results). CMPP, JRP, and AMM wrote the original draft of the manuscript. FJA, JF, and MDP reviewed, and edited the manuscript. We want to thank Patricia Villanueva for technical assistance. All authors read and approved the final manuscript.

Authors' information NA

Ethics approval and consent to participate Animal procedures strictly followed the Institutional Animal Care and Use Committee guidelines approved protocols at the University of Castilla La-Mancha.

Consent for publication

All authors read and approved the final manuscript.

Competing interests

The authors declare that they have no competing interests.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Jonathan Mamou
email: jmamou@riversideresearch.org

Thomas Pellegrini

Denis Kouamé

Adrian Basarab
email: basarab@irit.fr

A Convolutional Neural Network for 250-MHz Quantitative Acoustic-microscopy Resolution Enhancement

Quantitative acoustic microscopy (QAM) permits the formation of quantitative two-dimensional (2D) maps of acoustic and mechanical properties of soft tissues at microscopic resolution. The 2D maps formed using our custom SAM systems employing a 250-MHz and a 500-MHz single-element transducer have a nominal resolution of 7 µm and 4µm, respectively. In a previous study, the potential of single-image super-resolution (SR) image post-processing to enhance the spatial resolution of 2D SAM maps was demonstrated using a forward model accounting for blur, decimation, and noise. However, results obtained when the SR method was applied to soft tissue data were not entirely satisfactory because of the limitation of the convolution model considered and by the difficulty of estimating the system point spread function and designing the appropriate regularization term. Therefore, in this study, a machine learning approach based on convolutional neural networks was implemented. For training, data acquired on the same samples at 250 and 500 MHz were used. The resulting trained network was tested on 2D impedance maps (2DZMs) of human lymph nodes acquired from breast-cancer patients. Visual inspection of the reconstructed enhanced 2DZMs were found similar to the 2DZMs obtained at 500 MHz which were used as ground truth. In addition, the enhanced 250-MHz 2DZMs obtained from the proposed method yielded better peak signal to noise ratio and normalized mean square error than those obtained with the previous SR method. This improvement was also demonstrated by the statistical analyses. This pioneering work could significantly reduce challenges and costs associated with current very high-frequency SAM systems while providing enhanced spatial resolution.

INTRODUCTION

Quantitative acoustic microscopy (QAM) uses very high frequency ultrasound (> 100 MHz) to form quantitative, two-dimensional (2D) maps of acoustic and mechanical properties of soft tissues at resolutions better than 10 µm [START_REF] Lemons | Acoustic microscopy: biomedical applications[END_REF]. SAM systems use a single-element transducer and the spatial resolution of the resulting 2D maps is approximately equal to the wavelength at the center frequency of the transducer. For instance, our custom SAM systems, which employ a 250-MHz [START_REF] Rohrbach | Fineresolution maps of acoustic properties at 250 mhz of unstained fixed murine retinal layers[END_REF] or a 500-MHz [START_REF] Rohrbach | A novel quantitative 500 mhz acoustic-microscopy system for ophthalmologic tissues[END_REF] single-element transducer, the resulting 2D acoustic impedance (Z) maps (2DZMs) have a nominal in plane spacial resolution of 7 µm, and 4µm, respectively. Nevertheless, the design and use of the 500-MHz system is challenging. Therefore, while increasing the transducer frequency improves resolution, it often comes with increased costs associated with the transducer and the necessary electronics (i.e., pulser, amplifier, A/D conversion, precise motor stages). In addition, experimental difficulties also arise (e.g., sensitivity to nm scale vibrations and temperature). Therefore, in a previous study, the potential of single-image super-resolution (SR) reconstruction to enhance 2DZM resolution obtained using our 250-MHz SAM system was investigated [START_REF] Basarab | Enhancement of 250-mhz quantitative acousticmicroscopy data using a single-image super-resolution method[END_REF]. The forward image degradation model in [START_REF] Basarab | Enhancement of 250-mhz quantitative acousticmicroscopy data using a single-image super-resolution method[END_REF] linked the non-observed high-resolution (HR) image to the 250-MHz 2D impedance map (2DZM) through two operators (2D convolution with the imaging system point spread function (PSF) and spatial subsampling) and additive white Gaussian noise. To invert this model, a reconstructionbased approach was used by minimizing the HR image total variation, i.e., assuming it is piece-wise constant [START_REF] Zhao | Fast single image super-resolution using a new analytical solution for ℓ 2 -ℓ 2 problems[END_REF]. While encouraging results were obtained in [START_REF] Basarab | Enhancement of 250-mhz quantitative acousticmicroscopy data using a single-image super-resolution method[END_REF] on simulated and experimental phantom data, results were less satisfactory, when the SR method was applied to experimental data acquired from soft tissues. This outcome can be explained by several factors. First, the considered image formation model (e.g., spatially-invariant PSF) may not be sufficient to explain the complex physical phenomena occurring in QAM. Second, the parameters of the model (e.g., the PSF and the noise variance), known in simulations, must be estimated in practical situations increasing drastically the complexity of the inverse problem. Finally, the data-independent regularization function (e.g., total variation) strongly influences the results and making an appropriate choice is challenging. Therefore, in the present study, a deep learning based approach is proposed to improve the flexibility relating the low-resolution 2DZMs to their high-resolution counterpart by learning their relationship from training data instead of imposing a predefined model. Specifically, a U-Net like convolutional neural network (CNN) was trained to learn the relationship between 250 and 500-MHz 2DZMs in order to enhance 250-MHz previously unseen 2DZMs at test time. This kind of architecture has gained popularity in recent years, in particular in the fields of biomedical image segmentation [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] and image SR [START_REF] Hatvani | Deep learning-based super-resolution applied to dental computed tomography[END_REF]. The objective of this study is to adapt and test this CNN for SAM, which, to the best of our knowledge, is the first attempt of using machine learning in 2D acoustic map reconstruction from SAM data.

MATERIAL AND METHODS

Experimental SAM data

Experimental data were acquired at 250-MHz and 500-MHz from the same areas of 6-µm thick sections of cancerous human lymph nodes. (The protocol was approved by the Internal Review Board of Kuakini Medical Center in Honolulu, HI, where the samples were prepared.) Briefly, the ultrasound transducer performed a twodimensional raster scan of the sample. Data were first collected using the 500-MHz transducer with 1-µm steps immediately followed by the 250-MHz transducer with 2-µm steps. At each scan location from both scans, an RF signal is digitized with 12-bit accuracy at 2.5 GHz [START_REF] Rohrbach | Fineresolution maps of acoustic properties at 250 mhz of unstained fixed murine retinal layers[END_REF][START_REF] Rohrbach | A novel quantitative 500 mhz acoustic-microscopy system for ophthalmologic tissues[END_REF]. The two 3D block of RF data (2D vs time) are then processed using an auto-regressive algorithm [START_REF] Rohrbach | Autoregressive signal processing applied to high-frequency acoustic microscopy of soft tissues[END_REF] to yield 2D maps of impedance, speed of sound, and acoustic attenuation. In total, QAM data were acquired at both frequencies from 15 samples of an average area of approximately 2 by 2 mm. Without loss of generality, we focused in this study, both within the training and testing phases, on 2DZMs.

U-net convolutional neural network

U-nets are a special type of fully convolutional neural networks (CNN) that have two particularities: their architecture is symmetric and they include skip connections. U-nets are encoder-decoderlike networks: an input image is processed through a number of stacked convolution-pooling blocks to obtain a new data representation (i.e, encoder or contracting/downsampling path) that is then processed by transposed convolution blocks (the decoder or expanding/upsampling path).

The specific U-net architecture used in the present study is depicted in Figure 1. The encoder is composed of four successive convolution (3 × 3 filters, [32, 64, 128, 256] maps, respectively) and downsampling layers (2 × 2 max-pooling). The output of these layers is of dimension 25 × 25 × 256 (see bottom of Fig. 1). The decoder part of the model is symmetric except that transposed convolution layers are used to upsample the activation maps to progressively obtain the same dimensions as the input patch. These upsampling convolutions are depicted as vertical green arrays in Fig 1 . Blue horizontal arrows represent standard convolution layers. The grey arrows indicate the skip connections, i.e., the activations of the samelevel encoder layers (left part) are concatenated to the current acti-vations before being processed by two conv-pooling layers at each level. The final network output is of the same dimension as the input patch. (All the convolution layers use the leaky Rectifier Linear Unit (leaky-ReLU) activation function: f (x) = max(αx, x) with α = 0.01 [START_REF] Maas | Rectifier nonlinearities improve neural network acoustic models[END_REF].)

The skip connections intend to provide local information to the global information during upsampling [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF]. The U-net design was chosen for its efficiency in image segmentation and image SR due to these skip connections: first, these connections enable passing low-level details to deeper layers, second, they facilitate the training process by back-propagating the gradients more easily through the entire network. Furthermore, such a network can be trained end-toend from a limited amount of images and was shown to outperform standard CNNs without skip connections. For instance, U-nets were used by the winners of the 2015 ISBI challenge for segmentation of neuronal structures in electron microscopic stacks [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF]. (The Tensorflow deep learning library1 was used to run the U-net experiments.)

Training: A set of approximately 5600 200 × 200-pixel (i.e., 0.4 by 0.4 mm) patches were generated from thirteen 250 MHz 2DZMs together with the ground-truth patches from the corresponding coregistered 500 MHz 2DZMs. To do so, a 10% (20 pixels) overlap was used to extract patches. Training mini-batches were made of eight patches drawn randomly from the training set. A smooth absolute error function (ℓ1 smooth loss) was used, because it is less sensitive to outliers than ℓ2 or standard ℓ1 losses, and also prevents exploding gradients. The learning rate adaptive optimizer Adam was used with a starting learning rate of 1e-4 [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF]. The total training time on a 1080 Ti NVidia GPU was 40 hours to perform 10 5 steps (number of processed mini-batches). No development subset was used so that no specific learning termination criterion was applied except that of the total number of steps. Several values were tested and no further gain was observed for longer duration. Due to the limited amount of experimental data in this initial study, Fig. 3. Zoomed-in Fig. 2 from the white rectangle in Fig. 2a. a leave-one-out learning procedure (i.e., where a single full 2DZM is left apart for testing) was used.

Testing: At test time, in order to reconstruct an entire enchanced 2DZMs instead of a 0.4 by 0.4 mm patch, overlapping patches (this time 50% overlap, equivalent to 100 pixels) were processed through the network and output patches were concatenated to form the final enhanced entire 2DZM.

Performance quantification

In addition to qualitative visual comparison between enhanced 2DZMs and corresponding 500-MHZ 2DZMs, the results were also quantitatively analyzed using two standard metrics: the normalized root mean square error (NRMSE) and the peak signal-to-noise ratio (PSNR) defined as follows:

NRMSE = x -x 2 x 2 , PSNR = 10 log 10 N h max(x) 2 x -x 2 ,
where the vectors x and x are the 2DZMs reconstructed from data acquired at 500 MHz and the one obtained by postprocessing using either the proposed machine-learning based method or the previous SR approach in [START_REF] Basarab | Enhancement of 250-mhz quantitative acousticmicroscopy data using a single-image super-resolution method[END_REF], respectively. Note that all the parameters of the method in [START_REF] Basarab | Enhancement of 250-mhz quantitative acousticmicroscopy data using a single-image super-resolution method[END_REF] (e.g., PSF, balance between total variation and data fidelity terms) were manually tuned to optimize the NRMSE and the PSNR. The statistical distribution of the images were also evaluated through first and second order statistics and Rayleigh fitting.

RESULTS

Figures 2a and 2b

display illustrative 2DZMs of a section obtained from a lymph node of a breast-cancer patient using the 500-MHz SAM system and the 250-MHz SAM system, respectively. Figures 2c and2d show the resulting 2DZMs obtained using the previous SR method and the proposed method applied to Fig. 2b, respectively. These 2DZMs were not part of the CNN training subset and left out for testing purposes. For further visual inspection at finer scales, Figure 3 displays the zoomed in region (white rectangle) of Fig. 2 in the same format.

Visual inspection of Fig. 2c and 2d reveals novel fine details not previously seen in Fig. 2b, but the spatial resolution improvement seems far better in Fig. 2d obtained with the methods presented herein. See for example, the area within the small red circle where more detailed structures are visible, in particular in the background (i.e., low Z) regions and also in the high Z values regions as expected from better resolution images.

These observations are also confirmed by the comparison of Fig. 2c and2d with Fig. 2a which also reveals the superiority of the proposed approach. Specifically, Fig. 2d is more similar to Fig. 2a. For example, the area within the red squares are similar even though the 500-MHz 2DZMs contains a lot of fine structures.

Another striking feature of the proposed method is its potential ability to properly account for dispersion. Physics predict that speed of sound and therefore Z is a slightly increasing function of frequency. Dispersion is likely responsible for the slightly larger Z values obtained at 500 MHz (Fig. 2a) compared to those obtained at 250 MHz (Fig. 2b). The previous SR approach is completely incapable of taking that phenomenon into account because it was not integrated in its model, whereas in the proposed approach the network was able to learn and account for dispersion on its own. This finding is even more visible in Fig. 4 which shows the estimated probability density functions (PDFs) of Z for all the 2DZMs of Fig. 4. The peak of the PDFs are nearly identical of the enhanced 2DZM and the 500-MHz 2DZM. They are also nearly identical for the SR 2DZM and the 250-MHz 2DZM.These observations are consistent Fig. 4. Estimated probability density functions of Z for all four 2DZMs of Fig. 3 with the first row of Table 1 displaying the actual mean of the four PDFs.

Overall, all the above findings are also confirmed by the computed metrics. The SR approach, in spite of its ability of producing a sharper 2DZM than the native 250-MHz 2DZM, produced worst PSNR and NRMSE values than the original 2DZM, as shown in Table 2. This may be explained by the fact that the model considered (decimation, convolution and Gaussian noise) is not sufficient to explain the entire quality gap between the 250 and 500-MHz 2DZMs. Learning this model from the data, as proposed in this study through a convolutional neural network, allows to improve the PSNR and the NRMSE and to get closer to the high-resolution (500-MHz) 2DZMs than the native low-resolution (250-MHz) 2DZM. Moreover, although not perfectly matched, the PDFs of the 2DZMs shown in Fig. 4d demonstrate that the statistical properties of the proposed 2DZM image are closer to that of the 2DZM at 500 MHz than those of the SR 2DZM and the native 2DZM at 250 MHz. The visual impression of the histograms in Fig. 4 is confirmed by computing the maximum likelihood estimate of the Rayleigh distribution parameter and the 95% confidence interval of the parameter (Table 1). These results confirm the best statistical matching between the proposed 2DZM and the one computed from the 500-MHz high resolution data.

CONCLUSIONS

SAM can provide invaluable new information about the acoustical and mechanical properties of tissue at microscopic scale. Ultimately, the required spatial resolution is driven by each specific investigation, but the most usual way to reach finer resolution is the use of a higher center frequency transducer. SAM systems at frequencies greater than 250 MHz are challenging and expensive because precise motor stages are necessary, fast electronics are needed to excite, amplify, and digitize RF signals, vibrations must be mitigated, and temperature control becomes critically important. In this study, a fundamentally different approach was investigated to improve spatial resolution of SAM data thereby avoiding aforementioned challenges. Specifically, a machine-learning method based on U-net CNNs was implemented and trained on SAM data acquired from samples scanned using two SAM systems operating at 250 and 500-MHz. Results indicated that this approach can provide a significant resolution enhancement as well as take into account complex physical phenomena (e.g., dispersion). The machine-learning method was also found to be superior than a previous SR approach based on the standard model including blurring, decimation and Gaussian noise and using total variation to stabilize the solution. The proposed method could revolutionize SAM technology by significantly lowering costs, mitigating experimental challenges, while improving spatial resolution.

Fig. 1 .

 1 Fig. 1. U-net architecture. The colored arrows represent different layer operations: convolution (conv) and transposed convolutions (up-conv), max-pooling and concatenation (skip connections, in grey). The numbers on top of the rectangles denote the numbers of channels or activation maps, and width/height dimensions are indicated vertically on each map block.

Fig. 2 .

 2 Fig. 2. Illustrative 2DZMs: a) Original at 500-MHz , b) Original at 250-MHz, c) SR approach applied to b), d) proposed machine-learning approach applied to b).

Table 1 .

 1 Mean, standard deviation, and Rayleigh PDF fit obtained on the PDF of the four 2DZMs of Fig.3.

		2DZM at 500 MHz 2DZM at 250 MHz	SR 2DZM	Proposed 2DZM
	Mean (MRayl)	1.6054	1.5889	1.5889	1.6021
	Standard deviation (MRayl)	0.0406	0.0391	0.0449	0.0329
	Rayleigh parameter	1.1355	1.1238	1.1240	1.1331
	95% confidence interval	[1.1323 1.1387]	[1.1207 1.1270]	[1.1208 1.1272] [1.1299 1.1363]

Table 2 .

 2 Numerical results on experimental 2DZM data.

		2DZM at 250 MHz SR 2DZM Proposed 2DZM
	NRMSE	0.0297	0.0326	0.0286
	PSNR [dB]	32.2296	32.1680	32.5662

https://www.tensorflow.org/


Oleg Michailovich

Adrian Basarab

Denis Kouame

ITERATIVE RECONSTRUCTION OF MEDICAL ULTRASOUND IMAGES USING SPECTRALLY CONSTRAINED PHASE UPDATES

Keywords: Medical ultrasound, blind deconvolution, alternating minimization, all-pass filtering

Image deconvolution is a standard numerical procedure used in medical ultrasound imaging for improving the resolution and contrast of diagnostic sonograms. However, due to the intrinsic bandlimitedness of ultrasound scanners and the adverse effect of measurement noises, image deconvolution is known to be exceedingly sensitive to the errors incurred during inference of the point spread function (PSF) that characterizes the imaging system in use. In this case, even the slightest errors in specification of the PSF are likely to result in significant artifacts, rendering the reconstructed images worthless. To address the aforementioned problem, this paper describes a new method for blind deconvolution of ultrasound images, in which the errors due to inaccuracies in specification of the PSF are eliminated concurrently with estimation of tissue reflectivity directly from its associated radio-frequency data. A principal derivation and justification of the proposed method are supported by experimental results which demonstrate the effectiveness and viability of the new technique.

INTRODUCTION

The last few decades have witnessed significant developments in medical ultrasound technology, which nowadays features a wide spectrum of devices, ranging from high-end clinical sonographs to lightweight pocket-sized scanners particularly optimized for point-of-care application. Without doubt, the operational means of implementation of ultrasound imaging will continue their advance for many years to come, bringing about faster scanners with progressively improving functionality. This being said, however, the physical principles of ultrasound imaging harbour some principal limitations which seem to be impossible to rectify through the sophistication of hardware design alone. In particular, the intrinsic bandlimitedness of ultrasound scanners along with the coherent nature of ultrasound image formation remain responsible for the familiar limitations of this imaging modality in terms of its effective spatial resolution and contrast. These limitations, on the other hand, can be alleviated by post-processing means, among which image deconvolution is arguably the most traditional method of choice [START_REF] Dalitz | Point spread functions and deconvolution of ultrasonic images[END_REF].

In medical ultrasound imaging, adopting the convolution model of image formation requires one to exercise some precautions, since, strictly speaking, this model can only be applied under certain assumptions, collectively known as the first Born approximation [START_REF] Newton | Scattering Theory of Waves and Particles[END_REF]. Even though the conditions of this approximation are nearly met in soft biological tissues, applying the convolution model to an entire image is rarely advised in view of the spatial variability of the PSF. Indeed, more often than not, the effect of dispersive attenuation along with the non-uniformity of acoustic focusing make the PSF vary across the image domain [START_REF] Florea | An axially variant kernel imaging model applied to ultrasound image reconstruction[END_REF]. This being said, however, the above variability has been observed to be relatively slow in most practical scenarios, which makes it possible to apply the convolution model to localized segments of an ultrasound scan 1 . For this reason, the discussion below will be restricted to one of such segments, associated with a spatially invariable, yet generally unknown PSF.

In medical ultrasound, the problem of blind deconvolution -deconvolution with an unknown PSF -has been addressed through a variety of different methods. In their majority, these methods can be divided into two general subgroups, depending on the way the uncertainty in the definition of PSF is dealt with. Specifically, one approach is to recover an estimate of the PSF first, followed by image reconstruction by means of "non-blind" deconvolution [START_REF] Taxt | Restoration of medical ultrasound images using two-dimensional homomorphic deconvolution[END_REF][START_REF] Michailovich | A novel approach to the 2-D blind deconvolution problem in medical ultrasound[END_REF]. Such methods frequently offer the possibility of fast implementation, accompanied by some credible convergence guarantees. On the downside, the methods usually depend on somewhat strict assumptions on the nature of the PSF, which has a negative effect on the range of their practical applicability. In contrast, an alternative approach aims at recovering the PSF concurrently with the process of image reconstruction [START_REF] Yu | A blind deconvolution approach to ultrasound imaging[END_REF]. While considerably more general in comparison to the previous subgroup of approaches, these methods usually come with weaker guaranties of convergence to globally optimal solutions, which undermines their value for diagnostic applications.

In an attempt to consolidate the strong features of the two methodologies mentioned above, a "hybrid" approach to the problem of blind deconvolution was discussed in [START_REF] Michailovich | Blind deconvolution of medical ultrasound images: A parametric inverse filtering approach[END_REF]. The key idea underlying this approach is to deconvolve ultrasound images using only partial information about the PSF, such as, for instance, its power spectrum. The "hybrid" algorithm was derived based on an explicit formulation, aiming at estimation of an optimal inverse filter, whose application to the data image would yield the desired reconstruction. The results produced by the "hybrid" deconvolution have been demonstrated to match closely those of Wiener filtering. However, similarly to the latter case, the linearity of inverse filtering always confines its action to the scanner's passband, taking its toll on the quality of image reconstruction in terms of residual blur and Gibb's like artifacts.

The main goal of this work has been to alleviate the aforementioned drawback of "hybrid" deconvolution through its formulation as an implicit inverse problem. We show that the proposed method leads to solution of a familiar reconstruction problem, augmented with an analytical update of the spectral phase of the PSF. The effectiveness and practical value of the new method are demonstrated through experiments with reallife data.

PROPOSED METHODOLOGY

As usual, we begin with establishing some necessary nomenclature and notations, starting with an image formation model of the form

g = f * h + η, (1)
where g denotes an N × M (quasi-)stationary segment of a radio-frequency (RF) image contaminated by a noise term η, while h and f stand for the PSF and tissue reflectivity function associated with the given segment, respectively. Note that model ( 1) can be equally applied to in-phase/quadrature (IQ) data, which might offer a substantial reduction in the number of computations due to subsampling (albeit at the expense of complex arithmetics). In this work, both analytical derivations and data processing were carried out in the IQ domain, with appropriate interpretation of the variables in [START_REF] Dalitz | Point spread functions and deconvolution of ultrasonic images[END_REF].

In blind deconvolution, only the measured data g is assumed to be known, with both f and h treated as unknowns. However, it is usually possible to make some reasonable assumptions regarding either the functional or statistical nature of the latter. Such assumptions are usually "encoded" in the action of properly defined real-valued functionals ϕ and ψ which attain relatively small values for all admissible f and h, correspondingly. In this case, the problem of blind deconvolution can be formulated as an optimization problem of the form

min f,h (1/2) f * h -g 2 F + ϕ(f ) + ψ(h) , (2)
with • F denoting the Frobenius matrix norm. Subsequently, the optimal values of f and h can be found by means of al-ternating minimization (AM), which recursively updates one of the variables while keeping the other variable "frozen" and visa versa. It is important to emphasize, however, that the cost function in ( 2) is not jointly convex in f and h, even when the regularization functionals ϕ and ψ are. Consequently, the minimization routine is not guaranteed to converge to a globally optimal solution, in general. The idea of "hybrid" deconvolution can be used to substantially constrain the space of admissible solutions of (2), thus largely improving one's chances to attain the global optimizer. In particular, let's assume for a moment that the IQ image g is now available along with partial information on the PSF, namely, the magnitude ĥ of its Discrete Fourier Transform (DFT) F : h → ĥ. In this case, the optimization problem (2) can be reformulated in a constrained form as

min f,h (1/2) f * h -g 2 F + ϕ(f ) , (3)
s.t. |F(h)| = ĥ.
As before, this optimization problem can be solved by means of AM, which will alternate between sequential updates of f and h according to

f ← arg min f (1/2) f * h -g 2 F + ϕ(f ) , (4)
h ← arg min h f * h -g 2 F , s.t. |F(h)| = ĥ. (5)
Assuming the functional ϕ to be convex, problem (4) admits an efficient solution in terms of its associated proximal operator defined as

prox ϕ (y) = arg inf x (1/2) y -x 2 F + ϕ(x) . (6)
Thus, for example, a global minimizer of (4) can be obtained as the stationary point of iterations produced by the proximal gradient method (PGM) according to [START_REF] Beck | A fast iterative shrinkagethresholding algorithm for linear inverse problems[END_REF]

f t+1 = prox ϕ f t + h * (g -f t * h) , (7)
with h[n, m] = h * [-n, -m] and assuming h to be normalized so that ĥ ∞ ≤ 1, with ĥ = F(h). Moreover, there exist several ways to significantly increase the rate of convergence of PGM, which makes it a particularly favourable choice in practical computations [START_REF] Beck | A fast iterative shrinkagethresholding algorithm for linear inverse problems[END_REF].

The second update given by ( 5) requires a less traditional approach. To solve this problem efficiently, we use Parseval's theorem to reformulating it in terms of minimization with respect to the DFT ĥ of h, leading to

min ĥ f • ĥ -ĝ 2 F , s.t. | ĥ| = ĥ, (8)
with the • symbol denoting element-wise multiplication. In addition, the fact that ĥ = ĥ • û, with û = exp(∡ ĥ), allows further simplifications, effectively leading to a minimization with respect to û, i.e.,

min û ( f • ĥ) • û -ĝ 2 F , (9)
over the space of all all-pass (AP) filters û. Consequently, the resulting optimization problem can be interpreted as a filter design problem looking for an all-pass filter û, with its phase response ∡û matching as close as possible the DFT phase given by ∡ĝ -∡ f or, equivalently, by ∡(ĝ • f * ).

The current arsenal of filter design algorithms is vast. For the purpose of this work, the design procedure of [START_REF] Pei | Eigenfilter design of 1-D and 2-D IIR digital all-pass filters[END_REF] has been found to be especially useful. In what follows, we describe a modified version of this procedure, adapted for processing of complex-valued signals. In particular, let r be an (N 1 + 1) × (N 2 + 1) array of complex numbers and let rZ (z 1 , z 2 ) be a two-dimensional z-transform defined by

rZ (z 1 , z 2 ) = N1 n1=0 N2 n2=0 r n1,n2 z -1 1 z -1 2 . ( 10
)
It can then be easily verified that

ûZ (z 1 , z 2 ) = z -N1 1 z -N2 2 rZ (z -1 1 , z -1 2 ) rZ (z 1 , z 2 ) (11)
defines the transfer function of an AP system of order L, with L = max{N 1 , N 2 }. Furthermore, restricting (z 1 , z 2 ) to the unit sphere (thus reducing rZ (z 1 , z 2 ) and ûZ (z 1 , z 2 ) to their associated DFTs r(ω 1 , ω 2 ) and û(ω 1 , ω 2 )) suggests that the phases of r and û are related according to

∡r(ω 1 , ω 2 ) = -(1/2) N 1 ω 1 + N 2 ω 2 + ∡û(ω 1 , ω 2 ) , ( 12
)
thereby making it possible to design the AP filter û in terms of r. Specifically, denoting by r ℜ and r ℑ the real and imaginary parts of r, respectively, it is straightforward to verify that [START_REF] Huber | Robust statistics[END_REF] suggests that

N1 n1=0 N2 n2=0 r ℜ n1,n2 S ∡r n1,n2 (ω 1 , ω 2 ) + r ℑ n1,n2 C ∡r n1,n2 (ω 1 , ω 2 ) = 0, (13) with S ∡r n1,n2 (ω 1 , ω 2 ) = sin(ω 1 n 1 + ω 2 n 2 + ∡r(ω 1 , ω 2 )) and C ∡r n1,n2 (ω 1 , ω 2 ) = -cos(ω 1 n 1 + ω 2 n 2 + ∡r(ω 1 , ω 2 )).
The above equation can be expressed in a more compact form by stacking the vectorized versions of r ℜ and r ℑ into a column vector r = [vec(r ℜ ) T , vec(r ℑ ) T ] T , while letting A(ω 1 , ω 2 ) be a row vector of function-valued components defined by the basis functions S ∡r n1,n2 (ω 1 , ω 2 ) and C ∡r n1,n2 (ω 1 , ω 2 ), arranged in congruence with the order of the elements of r. Then, in the new notations, (13) becomes

A(ω 1 , ω 2 ) r = 0, ∀(ω 1 , ω 2 ). (14)
In practice, ∡r(ω 1 , ω 2 ) is computed using (12), upon replacing ∡û(ω 1 , ω 2 ) with the desired phase response, i.e., ∡(ĝ• f * ). The latter is usually too noisy to be modelled with reasonably small values of L, which makes the equality in (14) practically unattainable. It is nevertheless possible, however, to solve the equation in a least-square sense by first computing a matrix R according to

R = π -π π -π A(ω 1 , ω 2 ) T A(ω 1 , ω 2 ) dω 1 dω 2 , (15)
and then minimizing r T R r subject to energy normalization r 2 = 1. By the well-known Rayleigh's principle, this problem is solved by the eigenvector of R corresponding to the smallest eigenvalue of the matrix.

Once available, the optimal r can be reshaped into a complex array r to compute the phase of the AP filter û, which can, in turn, be used to compute an updated value of the PSF as h = F -1 ( ĥ • û). Subsequently, the latter can be passed back into (4), commencing a new cycle of the AM procedure. It has been observed that up to five iterations of AM initiated with ĥ = ĥ are usually sufficient for its convergence.

EXPERIMENTAL RESULTS

Additional assumptions

Before presenting the experimental results, the nature of the regularization functional ϕ in (3) needs to be specified. Usually, ϕ is chosen to reflect one's a priori beliefs on the statistical behaviour of tissue reflectivity, which, in turn, depends on the echogenicity of insonified tissue. For instance, diffuse scattering is conventionally associated with Gaussian statistics, in which case setting ϕ(f ) = f 2 F would be an apt choice. On the other hand, the behaviour of specular reflections adheres more naturally to Laplacian statistics, leading to ϕ(f ) = f 1 . Practical sonograms, however, can rarely be described exclusively by one of these two statistical models. In this case, the Huber model [START_REF] Huber | Robust statistics[END_REF] have been observed to be a propitious "middle round", allowing characterization of complex echogenicity patterns based on a single stochastic model. The Huber regularization suggests ϕ to be defined as

ϕ(f ) = γ N -1 n=0 M -1 m=0 |f n,m | 2 , |f n,m | ≤ a 2a|f n,m | -a 2 , |f n,m | > a , (16)
where γ > 0 is a user-defined regularization parameter, while a > 0 sets a dividing line between a Gaussian and Laplacian behaviour of the values of tissue reflectivity. In this work, we used γ = 0.002 and a = 0.05.

The final missing piece in the description of the proposed method is the estimation of ĥ. Fortunately, an accurate estimate of ĥ is easy to find by means of homomorphic denoising of [START_REF] Michailovich | A novel approach to the 2-D blind deconvolution problem in medical ultrasound[END_REF], which was used in the current work as well.

Reconstruction of in vivo scans

The proposed blind deconvolution method has been tested using in vivo data acquired from healthy volunteers using a Siemens Sonoline Antares TM scanner equipped with the Axius Direct Ultrasound Research Interface (URI). The acquired RF images were subjected to a standard demodulation procedure, followed by antialiasing filter and downsampling so that the effective sampling rate of the resulting IQ images was approximately equal to twice its critical value (in both the axial and lateral directions). Subplot A of Fig. 1 depicts a segment of a typical abdominal image from the experimental dataset. Note that the chosen image is characterized by a range of diverse features, including both specular reflection and diffuse scattering.

Subplot B of Fig. 1, on the other hand, shows the same image after the application of the proposed deconvolution algorithm. To obtain this result, a total number of AM iterations was set to five, with N 1 = N 2 = 3. It deserves noting that the whole reconstruction procedure (including the deconvolution of the 4480×384 RF image, filtering, estimation of ĥ, and the AM iterations) took only 0.55 sec on a standard 2.6 GHz Intel Core i7 via straightforward MATLAB implementation without GPU acceleration. Hence, the computational efficiency of the proposed method can be regarded as reasonable.

One can see that the procedure of blind deconvolution results in a noticeable increase in spatial image resolution and improved contrast. Moreover, the proposed method seems to produce neither "clipping" nor Gibbs-like artifacts typical for ℓ 1 -and ℓ 2 -norm regularizations, respectively. The absence of "ringing" effects and residual blur around sharp image details is likely to indicate proper recovery of the PSF phase.

CONCLUSIONS

In this paper, a novel approach to the problem of blind deconvolution of medical ultrasound images has been proposed. In its core, the method belongs to the family of "hybrid" deconvolution techniques, which estimate tissue reflectivity based on only partial information on the PSF, and, in particular, its power spectrum. As opposed to earlier works in the same direction, the proposed method relies on an implicit formulation, which allows recovering the spectral information beyond the transducer passband. The results obtained in a preliminary experimental study indicate a promising potential of the method, thus warranting its further development and testing.

Fig. 1 .

 1 Fig. 1. Subplot (A): Original image, Subplot (B) Reconstruction by means of the proposed algorithm.

Partitioning the entire image domain into 3-4 sectors along the axial and lateral directions usually works well for most commercial scanners in both cardiac and abdominal settings.