Emna Amdouni
email: emna.amdouni@univ-lyon2.fr

Bernard Gibaud
email: bernard.gibaud@univ-rennes1.fr

Semantic Representation of Neuroimaging Observations: Proof of Concept Based on the VASARI Terminology

Keywords: medical domain ontology, knowledge representation, ontology reuse and alignment

The main objective of this work is to facilitate the identification, sharing and reasoning about cerebral tumors observations via the formalization of their semantic meanings in order to facilitate their exploitation in both the clinical practice and research. We have focused our analysis on the VASARI terminology as a proof of concept, but we are convinced that our work can be useful in other biomedical imaging contexts. In this paper, we propose (1) a methodology, a domain ontology and an annotation tool for providing unambiguous formal definitions of neuroimaging data, (2) an experimental work on the REMBRANDT dataset to demonstrate the added value of our work over existing methods, namely DICOM SR and the AIM model.

BACKGROUND AND SIGNIFICANCE

In literature, an ontology is defined as "a formal and an explicit specification of a shared conceptualization" [START_REF] Gruber | A translation approach to portable ontology specifications[END_REF]. Ontologies define the formal semantics of vocabularies by specifying axioms, expressed in a logic-based language, that constrain and structure relationships between terms. The main purpose of ontologies is to enable knowledge integration and semantic data querying. In the medical field, semantic web technologies are used to standardize, formalize and share the medical data (coming form both the clinical and research context) is very important [START_REF] Scheuermann | Toward an ontological treatment of disease and diagnosis[END_REF][START_REF] Seifert | Semantic annotation of medical images[END_REF]Oberkampf et al., 2012). In this paper, we focused our interest on the domain of cerebral tumors. In oncology clinical practice, neuroimaging features/phenotypes play an important role; in particular they help clinicians in making their diagnosis, selecting the appropriate treatment and monitoring the therapeutic response to an intervention as for example the Response Evaluation Criteria in Solid Tumors (RECIST) [START_REF] Eisenhauer | New response evaluation criteria in solid tumours: revised recist guideline (version 1.1)[END_REF]. Many radiologypathology correlation studies have been conducted on cerebral tumors and show that some neuroimaging features are associated to genetic alterations and gene expression [START_REF] Gutman | Mr imaging predictors of molecular profile and survival: multi-institutional study of the tcga glioblastoma data set[END_REF][START_REF] Grams | Multimodal imaging to delineate tumor heterogeneity in cerebral gliomas[END_REF]. Therefore, suitable management of neu-roimaging phenotypes is needed to facilitate their use and reuse in multiple studies regarding imaging biomarkers [START_REF] Levy | Informatics methods to enable sharing of quantitative imaging research data[END_REF][START_REF] Möller | Radsem: Semantic annotation and retrieval for medical images[END_REF][START_REF] Esr | Medical imaging in personalised medicine: a white paper of the research committee of the european society of radiology (esr)[END_REF]Rubin et al., 2014a).

Currently, neuroimaging features can be recorded and stored in a formalized format such as the DICOM (Digital Imaging and Communications in Medicine) SR (Structured Report) [START_REF] Clunie | DICOM structured reporting[END_REF][START_REF] Clunie | DICOM structured reporting and cancer clinical trials results[END_REF] and the Annotation and Imaging Markup (AIM) model [START_REF] Channin | The caBIG annotation and image markup project[END_REF]: the DICOM SR formalizes the representation of radiological observations by introducing a set of rules that constrain concepts organization and a vocabulary (i.e. codes and associated code meanings) covering the domain of imaging observations. DICOM SR includes measurements and qualitative assessments, their relationships with image evidence and with the clinical interpretation of the clinician. The AIM model is an information model and an XML-based file format to describe the minimal information necessary to record image annotations. This information model has introduced the most relevant entities used in image annotation.

These standard formats enable the description of the content of medical images. Unfortunately, they are not suitable to support logic-based reasoning; these formats are based on coded terms and most of them have no semantic axioms to specify their meanings and the relationships between them. As a consequence, only searches based on keywords can be handled on decision making tools that exploit these stan-dard formats. Rubin et al., Levy MA and many others researchers have promoted the use of formal ontologies [START_REF] Rubin | A semantic image annotation model to enable integrative translational research[END_REF][START_REF] Levy | Semantic reasoning with image annotations for tumor assessment[END_REF][START_REF] Kahn | Informatics in radiology: an information model of the dicom standard[END_REF][START_REF] Van Soest | Towards a semantic pacs: using semantic web technology to represent imaging data[END_REF] for automatic reasoning on these data models and overcome the current limitations listed above.

This work is based on the assumption that the use of semantic web technologies, in particular ontologies as well as reasoning capabilities, can make the meaning of neuroimaging assessments more explicit and facilitate their advanced exploitation and interpretation. We are convinced that this approach can be beneficiary to the whole domain of neuroimaging, and beyond to the whole domain of biomedical imaging. However, this work focuses on a limited domain, namely the domain covered by the VASARI terminology (for Visually Accessible Rembrandt Images terminology)1 , used as a proof of a concept.

The VASARI terminology is a controlled vocabulary that describes thirty observations of high grade cerebral gliomas (glioblastoma multiform or GBM) in conventional Magnetic Resonance Imaging (MRI) images. Its main objective consists in standardizing brain tumors description and facilitating their interpretation by neuro-radiologists. The VASARI terminology was developed by experts in neuro-radiology who have considered the majority of possible assessments based on MRI. The validation of this corpus of imaging features was realized by eight experienced neuro-radiologists from distinct institutions.

Our work has three main contributions. First, making the meaning of VASARI features explicit via the design and the implementation of a specialized ontology, called VASARI ontology. Second, providing a semantic annotation tool that automatically translates VASARI features into instances of the VASARI ontology. This tool was applied to a VASARI corpus called REMBRANDT data set (Repository of Molecular Brain Neoplasia Data) [START_REF] Madhavan | Rembrandt: helping personalized medicine become a reality through integrative translational research[END_REF]. Third, performing semantic queries and reasoning tasks on these data to show how this semantic description of VASARI features can facilitate the interpretation of the content of medical images.

The remaining of this article is organized as follows: in Section Material and Methods, we describe the methodology for the design of the VASARI ontology. Section Results provides, first, an overview of the architecture and development details of both the developed ontology and the semantic annotation tool. Second, it demonstrates how we can automatically store and semantically manipulate RDF (Resource Description Framework) data of the REMBRANDT data set. In Section Discussion, we explain some modeling choices that we have made regarding ontology design and implementation, list accomplished work and enumerate remaining problems.

MATERIAL AND METHODS

Design of the VASARI ontology

The VASARI ontology was designed according to the realism-based approach proposed by Ceusters and Smith [START_REF] Ceusters | Tracking referents in electronic health records[END_REF][START_REF] Smith | From concepts to clinical reality: an essay on the benchmarking of biomedical terminologies[END_REF][START_REF] Smith | Ontological realism: A methodology for coordinated evolution of scientific ontologies[END_REF]. Our modeling methodology is composed of five main steps that can be outlined as follows. First, we analyzed for each VASARI feature Fi the meaning of the studied aspect and sorted its possible configurations to establish the list of possible values allowed for each criterion. Second, we identified and described the key real entities that are involved in each criterion. Third, we related entities to existing ontologies, most of which coming from the OBO foundry and aligned onto the Basic Formal Ontology [START_REF] Bittner | Normalizing medical ontologies using basic formal ontology[END_REF][START_REF] Smith | Basic formal ontology for bioinformatics[END_REF]. When needed new ontology classes were specified. Fourth, we specified and defined the axioms characterizing these entities and relations between them. Finally, we made sure that all possible configurations for each feature Fi can be modeled in a formal way.

In our work, we described the thirty VASARI features but this paper focuses on seven of them, namely: lesion location, lesion side, enhancement quality, proportion nCET (non contrast enhanced tumor), cortical involvement, extent of resection of enhancing tumor and lesion size (see Table 1).

After a deep analysis of the meaning of the VASARI features and the identification of the different entities that they involve, we have proceeded with their formal description. This step was not a trivial task given that we faced several modeling problems summarized in Table 2 and more detailed in [START_REF] Amdouni | Concept-based versus realism-based approach to represent neuroimaging observations[END_REF]. Modeling problems concern: negative findings (MP1) [START_REF] Ceusters | Referent tracking: The problem of negative findings[END_REF], spatial knowledge (MP2) [START_REF] Bennett | A vocabulary of topological and containment relations for a practical biological ontology[END_REF] and complex entities representation (MP3).

We have used the version 2 of the Basic Formal Ontology (BFO) as a foundation for the VASARI ontology, thus facilitating the integration of specialized ontologies that come from the Open Biological and Biomedical Ontologies (OBO) foundry [START_REF] Smith | The OBO Foundry: coordinated evolution of ontologies to support biomedical data integration[END_REF]. In particular, we reused the following ontologies: the Foundational Model of Anatomy (FMA) unidimensional, largest diameter in centimeters [START_REF] Smith | Towards a reference terminology for ontology research and development in the biomedical domain[END_REF], the Information Artifact Ontology (IAO) [START_REF] Ceusters | An information artifact ontology perspective on data collections and associated representational artifacts[END_REF], the Phenotypic Quality Ontology (PATO) [START_REF] Mungall | Interpreting patient data using medical background knowledge[END_REF], the Open Biomedical Investigations (OBI) [START_REF] Brinkman | Modeling biomedical experimental processes with OBI[END_REF], the Ontology for General Medical Sciences (OGMS) [START_REF] Scheuermann | Toward an ontological treatment of disease and diagnosis[END_REF], the Unit Ontology (UO) [START_REF] Gkoutos | The units ontology: a tool for integrating units of measurement in science[END_REF] and the Relation ontology (RO) (Smith et al., 2005a); in our work we have considered that RO relations are integrated under the BFO 2 ontology. Note that ontologies acronyms will be used in the rest of the paper.

Design of the experimental work

In our experimental work, we have developed a semantic annotation software of VASARI data using the VASARI ontology. This software enables the user to transform the informal description of the 30 VASARI features into a formal one. This software was applied to a corpus of VASARI data called the REM-BRANDT repository. The resulting semantic data set was used to evaluate the added value of our work; especially, we performed some reasoning tasks by formulating semantic queries as well as some consistency tests to detect inconsistent assertions. Negative findings are expressed by the use of negative qualifiers as for example none or expressions as indeterminate, not applicable, without etc.

Non-existence of an entity or a quality/disposition. Examples: C1:Johns cerebral tumor is without an enhancing region. C2:Johns cerebral tumor is not edematous. Or Johns cerebral tumor is not infiltrative. MP2: How to ensure a faithful representation of the studied pathological structure and describe how its components are situated in space?

Containment is denoted by natural language expressions like within, portion of, comprise of whereas overlapping is denoted by the term invasion. The proximity of a given entity to another one is expressed with terms such as surrounding and adjacency, and separation is denoted by terms like not contiguous and separated.

Spatial location of existing entities, entities that are related to each other, entities that are separated from each other, entities that are adjacent to each other, etc. Examples: Johns cerebral tumor epicenter is in the parietal lobe. A cerebral tumor has part a cerebral tumor margin. MP3: How to encode complex entities as for example derived measurements (proportions of volume measurements, length measurements, etc.), and associate them to their corresponding clinical findings?

Volume proportions: 0%, <5%, 6-33%, 34-67%, 68-95%, >95%, 100%. Or, two-dimensional length (x,y) that represents cross-sectional diameters; scores are between <0.5 cm and >8cm.

The representation of the extent of the resection of a given cerebral tumor component (nCET, necrotic, etc.). Examples: 35% of Johns cerebral tumor is enhanced, Johns cerebral tumor of size 1cm2cm.

Presentation of the REMBRANDT repository

The REMBRANDT repository is freely accessible on this link16. The ultimate objective of the REM-BRANDT data set is to facilitate the discovery of significant correlations between clinical and genomic information in order to provide patients with more personalized treatments in the clinical context. The REMBRANDT data set contains 30 VASARI features labeled by 3 radiologists that concern 34 patients with GBM tumors. Features values are stored in an Excel document where each spreadsheet contains evaluations asserted by a radiologist.

Implementation details

We have designed the VASARI ontology in the Ontology Web Language 2 (OWL2) format using the version 5 of the Prot ég é tool [START_REF] Tudorache | Webprotégé: A collaborative ontology editor and knowledge acquisition tool for the web[END_REF].

To extract modules from the relevant OBO ontologies we used the Ontofox web interface [START_REF] Smith | The OBO Foundry: coordinated evolution of ontologies to support biomedical data integration[END_REF]. Our semantic annotation tool was developed with the JAVA language and created using the Net-Beans IDE 8.0.2 programming environment. To design the semantic annotation software, we used the version 2.8.3 of the JENA35 semantic web programming framework and the version 2.3.2 of the JENA-Pellet reasoner engine (external engine of the JENA API) [START_REF] Sirin | Pellet: A practical owl-dl reasoner[END_REF] to perform automatic reasoning tasks. To execute some SPARQL queries, we have used the CORESE tool 3.2 2 . Note that instance data are serialized in the RDF/XML format.

RESULTS

The VASARI ontology

The VASARI ontology imports eight ontology modules and contains around 570 OWL classes and 120 properties. Figure 1 shows that the four major semantic aspects that constitute the VASARI domain, namely: pathological structures, anatomical localization, qualities and dispositions, and measurements. In this section, classes are represented in Italic and relationships between them in Bold.

In our proposed ontology, a vasari:CerebralTumor is a vasari:CerebralPathologicalStructure. Different regions of the cerebral tumor are introduced with the entity vasari:CerebralTumorComponent that is defined as a vasari:CerebralPathologicalStructure and bfo:continuant part at some time some vasari:CerebralTumor. In our semantic model and as it is defined in the VASARI terminology, we considered that a vasari:CerebralTumor can be composed of four basic components that characterize the brain tissue abnormality: vasari:EnhancingCerebralTumorComponent, vasari:NonEnhancingCerebralTumorComponent, vasari:NecroticCerebralTumorComponent and vasari:CerebralEdemaComponent.

The following paragraphs describe how the specific domains requirements mentioned in the Material and Methods Section were addressed in the VASARI ontology.

Modeling Problem 1: In order to respect the basic principles of realist ontology, no instance should be created when no concrete entity exist in reality. The solution that we proposed uses an equivalentclass axiom (condition if and only if involving some negative somevaluesfrom assertion). Thus, classes are defined as follows: As asserted in BFO, C1 bfo:part of continuant at some time C2 means that for every particular c1, if c1 instance of C1 then there is some c2 such that c2 instance of C2 and c1 bfo:part of continuant at some time c2, C1 bfo:located in at some time C2 asserts that for every c1 if c1 instance of C1, then there is some c2 instance of C2 and c1 bfo:located in at some time c2.

In our ontology, we used the relation bfo:located in at some time, for example to associate a particular vasari:CerebralTumorEpicenter to its specific vasari:LobeOfCerebralHemisphere and the relation bfo:has continuant part at some time to define that the vasari:EdematousCerebralTumor [definition] is a vasari:CerebralTumor and (bfo:has continuant part at some time some vasari:CerebralEdemaComponent). vasari:CerebralTumor and (ro:adjacent to some vasari:CerebralCortex).

• Separation relation: We used the relational quality vasari:ContiguousWithCerebralTumor with the logical negation operator (not) to qualify and identify cerebral component that are separated from the cerebral tumor, as for example:

vasari:SatelliteLesion [definition]

vasari:CerebralPathologicalStructure and (not (bfo:has quality at some time some vasari:ContiguousWithCerebralTumor)) and (bfo:has disposition at some time some vasari:DispositionToBeEnhancing).

• Separation relation: We used the relational quality vasari:ContiguousWithCerebralTumor with the logical negation operator (not) to qualify and identify cerebral component that are separated from the cerebral tumor, as for example:

vasari:SatelliteLesion [definition] vasari:CerebralPathologicalStructure and (not (bfo:has quality at some time some vasari:ContiguousWithCerebralTumor)) and (bfo:has disposition at some time some vasari:DispositionToBeEnhancing).

Modeling Problem 3: The representation of the extent of the resection of an enhancing cerebral tumor component appears to be simple data to represent, but in reality it involves hidden information that are not explicit in the definition of the feature. To model this kind of feature, we consider that the vasari:EnhancingCerebralTumorComponent will not preserve its identity after and before the surgery. Thus, we identified two distinct entities: vasari:EnhancingCerebralTumorComponentBefore-

Surgery

[definition] is a vasari:EnhancingCerebralTumorComponent and (bfo:part of continuant at some time some vasari:EnhancingCerebralTumorComponent) and (bfo:is specified input of some vasari:ResectionOfEnhancingCerebralTumorComponent). vasari:EnhancingCerebralTumorCompone-ntAfterSurgery

[definition] is a vasari:EnhancingCerebralTumorComponent and (bfo:part of continuant at some time some vasari:EnhancingCerebralTumorComponentBefore-Surgery) and (bfo:is specified output of some vasari:ResectionOfEnhancingCerebralTumorComponent).

We considered that the measured quality, i. vasari:volumeMeasurementDatum and (bfo:is about some vasari:enhancingCerebralTumorComponentBeforeSurgery). The interpretation of extreme values of F26 will be as follows:

• %0 means that the enhancing tumor component is totally preserved and that the measured volume value before the surgery is the measured volume value after the surgery.

• %100 means that the enhancing cerebral tumor component is totally resected, thus the cerebral tumor component is classified as a vasari:NonEnhancingCerebralTumorComponen-tAfterSurgery.

Semantic annotation software of VASARI data

The annotation software begins by reading as an input the set of imaging features values of the REMBRANDT repository and the VASARI ontology schema. Then, to semantically annotate the data the software realizes four main tasks. First, it instantiates the VASARI ontology based on the VASARI labeled values. Second, it describes imaging features by creating RDF triples that establish semantic links between instances. Third, it adds these triples as statements in an RDF graph. Fourth, it serializes data in the RDF/XML grammar records the RDF graph in memory or in a JENA triple database (TDB). Note that the software stores separately the schema and the instance data (denoted by the terms Tbox and Abox in the following paragraph). It returns the generated RDF graph of the whole REMBRANDT dataset in 1.06 s ( 0.47s per radiologist).

Semantic exploitation of the VASARI annotation data

The developed software bases its reasoning on an inferred model generated with a reasoner. The information stored in the inferred graph is contained in a knowledge base (KB) that can be exploited in two ways: 1) accessed via SPARQL queries to retrieve data based on their semantics 2) checked via consistency tests. Querying a knowledge base: Let us consider this example to illustrate inference capabilities and demonstrate how the semantic format enables the exploitation of the anatomical knowledge coming from the FMA ontology. We suppose that a given KB is composed of an Abox that contains the following assertions: (A1) cte instance of CerebralTumorEpicenter, (A2) tl instance of Tempo-ralLobe, (A3) rch instance of RightCerebralHemisphere, (A4) cte bfo:located in at some time tl, (A5) tl regional part of rch.

A Tbox that contains: (T1) RightTemporalLobe [equivalentClass] Tempo-ralLobe and regional part of some RightCerebral-Hemisphere, (T2) regional part of [equivalentProperty] part of continuant at some time.

Based on the assertions of the Abox and on the (T1) axiom we can deduce that: (A6) tl instance of RightTemporalLobe (see Figure 3). Us-ing (T2), ( T3) and (A6), we can infer: (A7) cte bfo:located in at some time rtl (see figure 2). Figure 3 presents an example of SPARQL query that retrieves the location of cerebral tumors (?lobe, ?cerebral hemisphere) and their corresponding length measurements (?long axis value, ?perpendicular long axis value). The lower part of the figure presents the results returned by the CORESE semantic query tool.

Validation of a knowledge base: The pellet JENA reasoner enables the detection of conflicts in the knowledge content; thus we have exploited this capacity to perform a global check across the KB and looked for inconsistencies between the radiologists assertions. For example lets suppose that (A1) ct instance of CerebralTumor and that one radiologist said that (A2) ct is a HemorrhagicCerebralTumor however, another radiologist said that (A3) ct is a NonHemorrhagicCerebralTumor. Reasoning on this knowledge base is impossible given because the two classes HemorrhagicCerebralTumor and NonHemor-rhagicCerebralTumor are defined as disjoint classes in the Tbox; this means that they cannot share the same set of instances (i.e., ct). As a consequence, a classification error should occur when the reasoner performs inference tasks.

The result of a consistency checking is provided via the object ValidityReport of the JENA API. This data structure encapsulates all detected inconsistent axioms and assertions. To generate explanations about inconsistencies, we have used the method explainconsistency(). The output generated after the execution of this method consists on the listing of the set of all involved axioms; Figure 4 depicts an example of inconsistency that is caused by the assignment of two different length measures to the same cerebral tumor. This multiple attribution violates the owl:functionalProperty axiom of the property iao:has measurement value that is declared as functional.

DISCUSSION

In our work, we followed the realism-based approach to describe the neuroimaging reality on the side of the patient which appeared to us the most relevant methodology in the context of the biomedical research; the realism-based approach is being adopted by a growing community of researchers in the medical context. Actually, medical terminologies such as the DICOM SR and the AIM model do not refer to concrete existing phenomena on the side of the patient, but they only code medical statements in a To follow this modeling perspective, we have used two foundational and realism-based ontologies; namely the BFO ontology to describe existing entities and relationships between them. The use of BFO ontology has facilitated the integration of heterogeneous knowledge from different ontologies that are specialized in anatomy, quality phenotypes, measurements, etc.

The developed ontology answers to some challenging points that are highlighted in many papers [START_REF] Ceusters | Referent tracking: The problem of negative findings[END_REF][START_REF] Cimino | In defense of the desiderata[END_REF][START_REF] Levy | Informatics methods to enable sharing of quantitative imaging research data[END_REF] mainly: 1) the formalization of the description of neuroimaging information via the use of specialized ontologies; we can cite the example of the FMA ontology that allowed the description of some clinical statements or the BFO and RO ontologies that helped us in the description of foundational (i.e., is a, part of) and spatial relations (i.e., location, adjacent to) between pathological structures, 2) the representation of negative neuroimaging observations via the use of OWL axioms and 3) the representation of complex entities was made more explicit by referring to the involved concrete entities; but we have faced some difficulties to represent mathematical expressions with the IAO ontology, thus we think that it will be interesting to extend it to cover this kind of information that is needed in the definition of biomedical experiments.

It is important to note that our approach is not limited to the translation of VASARI features resulting from the subjective assessment of MRI images by human neuro-radiologists. In contrast, it would express its full value if it were implemented as a complement to an automated or semi-automated image analysis system [START_REF] Velazquez | Fully automatic gbm segmentation in the tcgagbm dataset: Prognosis and correlation with vasari features[END_REF]. For example systems that are described in these papers [START_REF] Rubin | Automated tracking of quantitative assessments of tumor burden in clinical trials[END_REF][START_REF] Porz | Multi-modal glioblastoma segmentation: man versus machine[END_REF] enable to segment the various parts of the tumor, and to automatically determine their anatomical environment (e.g. what anatomical structures they are contained in, or they overlap or they are adjacent to). Such mereotopological properties could be directly translated in semantic form using the relationship discussed above. Similarly, the volume measurements and the derived proportions could be generated automatically and with a better accuracy than through the current subjective assessments. VASARI features could be derived from the detailed image-based observations and measurements rather precede them, and our model provides the conceptual basis to make such enrichment of image processing systems.

The Radiology Reading Room of the Future [START_REF] Gillies | Radiomics: images are more than pictures, they are data[END_REF] will entail a reading room where in practicing radiologists interact with picture archiving and communication system software to identify, segment, and extract features from regions of interest. If prior studies obtained in the same patient are available, the previous regions of interest will be automatically identified by the reading software. As part of the reading, the extracted size, shape, location, and textural features will be automatically uploaded to a shared database and algorithmically compared with prior images to enable more precise diagnoses.

The first limit of our proposal is that it is implemented in OWL and thus it does not generate tempo-ralized instances [START_REF] Smith | Towards a reference terminology for ontology research and development in the biomedical domain[END_REF]. We think that taking into consideration the temporal aspect in the representation of neuroimaging features is needed especially in longitudinal imaging studies to, for example, evaluate cancer treatment response. In this context, we recommend to select a logic-based language that is capable to represent n-ary relationships. The second limit is intrinsic to the problem of logical contradiction that is due to the fact that radiologists describe what they observe based on their thoughts and experiences. As a consequence they may describe differently the reality and produce different clinical records about the identified entities. To resolve the disagreement in interpretation many medical systems require preserving in data entry a single correct value for the evaluated feature to facilitate the aggregation of data. According to Rector et al., electronic medical records should allow the presence of conflicting statements, multiple measurements, etc. to faithfully reflect the reality of clinical practice. Thus, they propose three types of foundational information models to describe (a) the medical records, (b) the state of the patient and (c) clinical care [START_REF] Rector | Foundations for an electronic medical record[END_REF] and they consider that a meta-language should be used to separate between what can be said and what actually occurs, and avoid the problem of inconsistency. Smith et al. have mentioned that even the adoption of a meta-language cannot remove errors because medical dialogues are also subject to error [START_REF] Smith | Towards a reference terminology for ontology research and development in the biomedical domain[END_REF]. In our work, we have stored (a) observations in separate data sets and we have not included (b and c) the meta-observation level.

The experimental work regarding the VASARI ontology shows that the semantic representation of neuroimaging features can enhance search operations; e.g. the exploitation of the VASARI ontology with the DL reasoner can resort the list of cerebral tumor epicenters that are located in the right temporal lobe by retrieving cerebral tumor epicenters that are located in the temporal lobe and the right hemisphere. Certainly, such classification task cannot be obtained with non semantic representations such as DICOM SR and the AIM model. We believe that our work can be reused in other image-based reasoning contexts as for example, RECIST criteria that base the tumor classification task (i.e. measurable and non-measurable lesions) on the knowledge of the location of the lesion and the calculation of its length. Added to the reasoning task, the consistency checking functionality offered by OWL reasoners can detect inconsistent statements that can be caused by inappropriate or erroneous diagnosis or treatment, in the clinical context, until now DICOM SR and the AIM model do not offer this semantic capability.

CONCLUSION

We believe that neuroimaging data should be held in a structured format that makes their meanings explicit to the systems and thus facilitate their comprehension as well as management. Semantic data about imaging features (measurement values, qualities, lesion components, lesion localization, etc.) are important (1) to support the clinical research on the development of new imaging biomarkers by combining clinical data with information coming from different medical domains (2) to improve the quality of the clinical healthcare that tend to provide personalized treatments to patients via the use of clinical guidelines that are based on evaluation criteria. In this paper, we employed the VASARI terminology as a proof of concept for the demonstration of the feasibility and the importance of making RDF and OWL data available to describe cerebral tumors observations and determining the key concepts and relationships that are central in their evaluation. Our work can be easily expanded to answer to other use cases; thanks to the modular aspect of the ontology and to the OWL language that is self-descriptive (concepts are textually and formally described in the ontology to guide users) and extendable.

Figure 1 :

 1 Figure 1: The basic pattern of the main classes in the VASARI ontology

  e. the volume, is the same, but the measured volume values are distinct: vasari

Figure 2 :

 2 Figure 2: Illustrative example of semantic exploitation of anatomical knowledge from the FMA ontology (protg tool); instances names are automatically generated with our developed annotation tool, the ID of the patient 900 00 1961 is included to refer to existing entities on the side of the patient.

Figure 3 :

 3 Figure 3: Execution result to a SPARQL query on observations of the radiologist1 in the REMBRANDT repository (demonstration with the CORESE tool). FMA 61823 denotes the LobeOfCerebralHemisphere, FMA 61817 denotes the Cerebral-Hemisphere and BFO 0000171 denotes the relation bfo:located in at some time.

Figure 4 :

 4 Figure 4: Example of a validation output: detection of a logical contradiction, IAO 000004 denotes the relation iao:has measurement value and paldmd 900 00 1961 refers to the measurement value of the perpendicular longest axis of the patient 900 00 1961.

Table 1 :

 1 Selected subset of the VASARI features defined in the VASARI terminology

	Feature	Feature definition	feature
	F1.Lesion location	Location of lesion geographic epi-	frontal, parietal, temporal,
		center; the largest component of the	occipital, corpus callosum,
		tumor either contrast enhancing or	thalamus
		non contrast enhancing.
	F2.Lesion side	Side of lesion epicenter.	right, central, bilateral
	F4.Enhancement	Qualitative degree of contrast	n/a, none, mild, marked
	quality	enhancement is defined as having
		all or portions of the tumor that
		demonstrate significantly higher
		signal on the post contrast T1W
		images compared to pre contrast
		T1W images.
	F6.Proportion nCET	What proportion of the entire tumor	n/a, 0%, >5%, 6-33%,
		is non enhancing? Non enhancing	34-67%, 68-95%, >95%,
		tumor is defined as regions of T2W	100%, indeterminate.
		hyper intensity that are associated
		with mass effect and architectural
		distortion, including blurring of the
		gray-white interface.
	F20.Cortical involve-	Non-enhancing o enhancing tumor	no, yes
	ment	extending to the cortical mantle, or
		cortex is no longer distinguishable
		relative to subjacent tumor.
	F26.Extent of resec-	Using the first postoperative scan
	tion of enhancing tu-	(contrast enhancing MR imaging)
	mor	assessed for tumor residual esti-
		mating the proportion of enhanc-
		ing tumor. Total resection com-
		ponent should be scored to 100%,
		subtotal resection of enhancing tis-
		sue should be scored accordingly.

n/a, 0%, >5%, 6-33%, 34-67%, 68-95%, >95%, 100%, indeterminate F29.Lesion size Largest perpendicular (x-y) cross section diameter of T2 signal abnormality (longest dimension X perpendicular) measured on single sectional image only.

Table 2 :

 2 Modeling problems

	Modeling problem	VASARI expressions	Use cases and examples
	MP1:	How to
	represent	negative
	neuroimaging obser-
	vations that indicate
	the non-existence of
	a dependent contin-
	uant (category C1)
	or an independent
	continuant (category
	C2): bfo:Quality or
	bfo:Disposition?

•

  Overlapping vs adjacency relation: We employed the spatial relation ro:adjacent to to express that two continuants do not share a common spatial region and we defined the relation vasari:overlaps to represent the case of overlapping.

		As de-
	scribed in Table 1, F20 evaluates the location
	of the cerebral tumor regarding the cerebral
	cortex. To describe these different situations
	and ensure a correct classification of the cerebral
	tumor, we have defined the following classes:
	vasari:CerebralTumorInvadingBrainCortex
	[definition]	vasari:CerebralTumor	and
	(vasari:overlaps some vasari:CerebralCortex),

Table 3 :

 3 Alignment of ontologies to represent VASARI features

	VASARI fea-	Main involved classes	Main involved relations
	ture
	F1:lesion lo-	vasari:CerebralTumorEpicenter,	bfo:located in at some time
	cation	fma:LobeOfCerebralHemisphere,	fma:regional part of
		fma:Brainstem, fma:Cerebellum
	F2:lesion side vasari:CerebralTumorEpicenter,	bfo:located in at some time
		fma:CerebralHemisphere,
		fma:MedianSagittalPlane
	F4:enhancem-	pato:Volume,	iao:is quality measurement of,
	ent quality	vasari:CerebralTumorComponent,	bfo:is specified input of,
		vasari:VolumeMeasurementDatum,	bfo:is specified output of,
		obi:ValueSpecification	bfo:is about
	F5: propor-	pato:Volume,	iao:is quality measurement of,
	tion nCET	vasari:CerebralTumorComponent,	bfo:is specified input of,
		vasari:VolumeMeasurementDatum,	bfo:is specified output of,
		obi:ValueSpecification	bfo:is about
	F20:cortical	vasari:CerebralTumor,	vasari:overlaps ro:adjacent to
	involvement	fma:CerebralCortex
	F26:extent	pato:Volume,	iao:is quality measurement of,
	of resection	vasari:VolumeMeasurementDatum,	bfo:has measurement unit label,
	of enhancing	uo:VolumeUnit,	iao:has measurement value,
	tumor	vasari:RatioValueSpecification,	bfo:is about,
		vasari:ProportionOfEnhancingAndRemo-	obi:is specified input of,
		vedTumor,	obi:is specified output of,
		vasari:EnhancingCerebralTumor-	vasari:has specified denominator -
		Component,	value,
		vasari:ResectionOfEnhancingCerebralTu-	vasari:has specified nominator -
		morComponent	value, ro:derives from
	F29 and F30:	obi:LengthMeasurementDatum,	iao:is quality meausrement of,
	lesion size	uo:LengthUnit, pato:Quality	iao:has measurement value,
			iao:has measurement unit label,
			iao:is about
	formal way. The adoption of the realism-based ap-
	proach enabled us to provide a faithful representation
	of imaging features by considering both the univer-
	sals level (e.g. cerebral tumor concept) and instances
	of universals level (e.g. Davids cerebral tumor).

https://wiki.cancerimagingarchive.net/ display/Public/VASARI+Research+Project


Yan Zhang

Chris R Bowen

Sylvain Deville

Ice-templated poly(vinylidene fluoride) ferroelectrets

Keywords: porous polymer, ferroelectret, aligned porosity, piezoelectric coefficient, ice templating

Ferroelectrets are piezoelectrically-active polymer foams that can convert externally applied loads into electric charge. Existing processing routes used to create pores of the desired geometry and degree of alignment appropriate for ferroelectrets are based on complex mechanical stretching and chemical dissolution steps. As a simple, cost effective and environmentally friendly approach, freeze casting is able to produce aligned pores with almost all types of the materials, including polymers. In this work, we present the first demonstration of freeze casting to create polymeric ferroelectrets. The pore morphology, phase analysis, relative permittivity and direct piezoelectric charge coefficient (d33) of porous poly(vinylidene fluoride (PVDF) ferroelectrets with porosity volume fractions ranging from 24% to 78% were analysed. The long-range alignment of pore channels produced during directional freezing was shown to be beneficial in forming a highly polarised structure after breakdown of air in the pore channels via corona poling. This new method opens a way to create tailored pores and voids in ferroelectret materials for transducer applications related to sensors and vibration energy harvesting.

Introduction

Piezoelectric materials manifest themselves by the generation of a charge when subjected to mechanical loads.

The direct piezoelectric effect can be used to sense dynamic pressure, acceleration, or change in force and there is also potential for scavenging energy from motion in the surrounding environment [START_REF] Bowen | Piezoelectric and ferroelectric materials and structures for energy harvesting applications[END_REF]. Ferroelectric materials are a sub-class of piezoelectric materials and exhibit piezoelectric properties as a result of a remnant polarisation due to the presence of aligned domains, which have been of interest in sensor and energy harvesting applications [START_REF] Zhang | Control of electro-chemical processes using energy harvesting materials and devices[END_REF]. In order to evaluate the performance of such materials, relevant figures of merit such as 𝑑 𝑖𝑗 2 /𝜀 33 𝜎 for piezoelectric energy harvesting, while the piezoelectric voltage coefficient, such as g33=d33/𝜀 33 𝜎 for sensor applications have been widely used, where dij is the piezoelectric charge coefficient, and

𝜀 33
𝜎 is the permittivity of the material at constant stress. These figures of merit indicate that a low permittivity, and high piezoelectric activity are beneficial for sensor and energy during harvesting applications. Ferroelectric ceramics often exhibit high figures of merit for high sensor sensitivity or high energy capability, but they are relatively high density and exhibit poor mechanical flexibility. Ferroelectric polymers exhibit a relatively low piezoelectric activity, but they have a low permittivity, are lightweight and exhibit flexibility which is important for flexible electronics, wearables and stretchable electronics [START_REF] Kim | A robust polymer microcable structure for flexible devices[END_REF].

As an alternative to ferroelectric materials, ferroelectrets are a class of piezoelectrically-active foam manufactured from a non-polar porous polymer whereby gas, such as air, within the pore space can be subjected to electrical breakdown when subjected to a high electric field during a poling process. This process results in opposing electric charges being deposited on the upper and lower surfaces of the pores [START_REF] Bauer | Ferroelectrets: Soft Electroactive Foams for Transducers[END_REF]. As a result of a poling process, a dipole-like structure is formed where the dipole moment can be changed by applying a mechanical stress, thereby leading to a piezoelectric response. The piezoelectric d33 charge coefficient, a measure of the charge generated per unit force, can be an order of magnitude greater than those found in conventional ferroelectric polymers, such as polyvinylidene fluoride (PVDF) and can be comparable or even greater than ferroelectric ceramics [START_REF] Luo | Energy harvesting study on single and multilayer ferroelectret foams under compressive force[END_REF][START_REF] Ghosh | Yb 3+ assisted self-polarized PVDF based ferroelectretic nanogenerator: A facile strategy of highly efficient mechanical energy harvester fabrication[END_REF] while maintaining a high compliance due to their polymeric nature. For example, for sensing applications a ferroelectret polymer exhibited a g33, a measure of the electric field per unit stress, that was 10-150 times higher than ferroelectric PVDF and over a thousand times higher than that of lead zirconate titanate (PZT), due to their high d33 values (e.g. 25-700 pC/N for porous polypropylene) and low permittivity (e.g. 𝜀 33 𝜎 =1.12-1.23 for porous polypropylene). [START_REF] Bovtun | Ferroelectret non-contact ultrasonic transducers[END_REF][START_REF] Heywang | Piezoelectricity[END_REF] Ferroelectret polymers with an average pore diameter of 0.9 µm or a pore height of 4.5 µm and pore width of 1.55 µm were also demonstrated to produce 44.9 nW [9] and 4.35 mW [START_REF] Mahanty | An effective flexible wireless energy harvester/sensor based on porous electret piezoelectric polymer[END_REF] for energy harvesting applications. Therefore, ferroelectrets have gained much interest in low-level mechanical energy harvesting [START_REF] Hillenbrand | Electret transducer for vibration-based energy harvesting[END_REF] and sensing [START_REF] Bauer | Ferroelectrets: Soft Electroactive Foams for Transducers[END_REF] based on their relatively high piezoelectric coefficient and low permittivity.

long and only a few μm in height [START_REF] Kachroudi | Air-spaced PDMS piezo-electret cantilevers for vibration energy harvesting[END_REF][START_REF] Zhong | Surface charge selfrecovering electret film for wearable energy conversion in a harsh environment[END_REF]. Such a morphology is beneficial due to the relatively low elastic stiffness of such an anisotropic pore structure in the polarisation direction [START_REF] Wegener | Piezoelectric Polyethylene Terephthalate (PETP) Foams -Specifically Designed and Prepared Ferroelectret Films[END_REF][START_REF] Mellinger | Thermal and Temporal Stability of Ferroelectret Films Made from Cellular Polypropylene/Air Composites[END_REF]. Micron-size pores are desirable to achieve micro-discharges within pores, which are interpreted in terms of Paschen breakdown [START_REF] Qiu | Influence of gas pressure in the voids during charging on the piezoelectricity of ferroelectrets[END_REF];

and large electric fields are required in very small pores. As a result, the majority of existing processing routes have focused on creating cellular or lens-shaped microstructures for ferroelectrets. Current processing routes include biaxial stretching of polymers with embedded foreign particles followed by chemically dissolution of the embedded foreign particles [START_REF] Ghosh | Self-poled Efficient Flexible "Ferroelectretic" Nanogenerator: A New Class of Piezoelectric Energy Harvester[END_REF][START_REF] Mahanty | An effective flexible wireless energy harvester/sensor based on porous electret piezoelectric polymer[END_REF], or the injection of the polymer by high-pressure gas to further modify the pore size and shape [START_REF] Anton | Piezoelectret foam-based vibration energy harvesting[END_REF][START_REF] Wu | Cellular Polypropylene Piezoelectret for Human Body Energy Harvesting and Health Monitoring[END_REF].

Freeze casting, also termed the ice-templating method [START_REF] Deville | Freezing Colloids: Observations, Principles, Control, and Use[END_REF], is an effective and facile technique to prepare materials with tailored pore morphology and anisotropic porosity. This approach involves freezing a colloidal suspension under a unidirectional gradient temperature, followed by sublimation of the solvent. The aligned pore channels formed parallel to the freezing direction are direct replica of the solvent after solidification.

Freeze casting has potential to be a cost effective and environmentally friendly approach, and it is feasible to tailor pore characteristics and form aligned pores in almost all types of materials: ceramics, polymers, metals and their composites [START_REF] Deville | Freezing Colloids: Observations, Principles, Control, and Use[END_REF]. To date, more than 30 different types of polymers with straight, aligned and elongated pore channels have been formed by freeze casting for catalysis, separation, biomedical and thermal insulation applications. [START_REF] Deville | Freezing Colloids: Observations, Principles, Control, and Use[END_REF] However, there has been no report to date on the freeze casting of polymers to create polymeric ferroelectrets.

In this work we used freeze casting of PVDF to produce a porous ferroelectret material. PVDF is a classical ferroelectric polymer which is partially crystalline and has the dipole moment perpendicular to the polymer chain, especially when the polar all-trans β-phase is dominant [START_REF] Hasegawa | Crystal Structures of Three Crystalline Forms of Poly(vinylidene fluoride)[END_REF]. Copolymers of the materials have been employed to achieve a higher crystallinity for improved ferroelectric properties; these include poly(vinylidene fluoride-trifluoroethylene) (PVDF-TrFE) and poly(vinylidene fluoride-hexafluoropropylene) (PVDF-HFP) [START_REF] Nunes-Pereira | Poly(vinylidene fluoride) and copolymers as porous membranes for tissue engineering applications[END_REF][START_REF] Moussaif | Miscibility of poly(vinylidene fluoride) and poly(methyl methacrylate-co-zinc polyacrylate) ionomers[END_REF].

PVDF has been selected since freeze casting has been previously employed to form a PVDF microporous membrane with pore sizes ˂ 10 µm whose Young's modulus and water flux ability were explored [START_REF] Mu | Fabrication of microporous membranes by a feasible freeze method[END_REF], but no piezoelectric properties were reported. Here we have examined the fabrication of the optimised pore structure in PVDF formed by freeze casting, with proof of its ferroelectret nature and corresponding piezoelectric response. A range of polymer solutions at different polymer loading levels were assessed for freeze casting and the microstructure, phase identity, direct d33 piezoelectric charge coefficients and permittivity of the polymers were examined in detail.

Experimental

Poly(vinylidene fluoride) (PVDF, 6010) powders were used from Solef® (Belgium) and used in the as-received condition. A schematic of the freeze casting process applied to PVDF is shown in Fig. 1. PVDF powders with different weight fractions of 0.2, 0.4, 0.6, 0.8, 1 and 1.2 g were dissolved in 10 g solvent of dimethyl sulfoxide (DMSO, anhydrous≥99.9%, freezing point of 19°C, Sigma-Aldrich) and stirred at 60˚C for overnight to achieve homogenous solutions; see Fig. 1(A). Other widely used polar solvents (e.g. N-methyl-2-pyrrolidone/NMP, dimethylformamide/DMF, dimethylacetamide/DMAc) with lower melting points of -20 to -61˚C were not suitable for the demoulding step at room temperature. The prepared PVDF/DMSO solutions were then poured into polydimethylsiloxane (PDMS) mould with a diameter of 20 mm and height of 10 mm. The bottom face of the mould was held on the surface of liquid N2 and the top face of the mould held at an ambient temperature of ~20˚C to unidirectionally freeze the solution. In a conventional freeze casting process [START_REF] Deville | Freezing as a path to build complex composites[END_REF], freeze drying is undertaken at low temperature and pressure in order to sublimate the solvent from a solid to a gas. In this work, freeze drying of the frozen PVDF/DMSO was not chosen since DMSO has the potential to contaminate not only the vacuum pump [START_REF]How to Freeze Dry the 6 Most Challenging Samples[END_REF], but has an unpleasant sulfur smell [START_REF] Boral | Cellular cryopreservation in blood banking[END_REF] with potential health risks during sublimation of the solvent [START_REF] Hebling | Cytotoxicity of dimethyl sulfoxide (DMSO) in direct contact with odontoblast-like cells[END_REF]. After freezing, the samples were therefore demoulded and immediately immersed into water to dissolve and remove the solidified DMSO, which was repeated 7-8 times to ensure fully remove the DMSO. The samples were then dried in an oven at 40˚C for 24hrs to eliminate the remaining water (Fig. 1B). The dried samples were then frozen in liquid N2, followed by cutting to a thickness of ~1.5 mm parallel to the freeze-cast direction using a sharp blade (Fig. 1C). Materials were cut parallel to the freezing direction to pole the pores that were aligned and elongated in the direction normal to the polarisation direction. Corona poling was conducted by applying a DC voltage of 26.8 kV for 30 min at ambient temperature (Fig. 1D). All samples were silver electroded (RS Components, Product No 186-3600, UK) on both sides normal to the freeze-cast direction for piezoelectric and dielectric characterisation.

The microstructure of the samples was examined by scanning electron microscopy (SEM, JSM6480LV, Tokyo, Japan). The bulk density of the sintered specimens was measured using Archimedes' principle. The piezoelectric strain coefficient (d33) was measured using a Berlincourt Piezometer (PM25, Take Control, UK) 0.5-6 days after corona poling. To confirm that the measured d33 values originate from the piezoelectric effect, the sample orientation was reversed to ensure the piezoelectric coefficient changes from a positive to negative polarity. The relative permittivity (ε) and dielectric loss (tan δ) were measured in the frequency rage of 1 to 10 6 Hz with an oscillating voltage of 1 Vrms using an Agilent Technology 4192A impedance analyzer.

Fourier transform infrared spectra (FT-IR) of the materials were recorded using a Perkin Elmer Spectrum 100 with a diamond universal ATR attachment. The phase structure of the ceramics was examined by X-ray diffraction (BRUKER D8-Advance, USA) with Cu radiation with 2θ ranging from 10˚ to 60˚.

Results

Microstructural observations of the freeze cast porous PVDF materials, phase analysis, dielectric spectroscopy and piezoelectric properties of the poled freeze-cast materials are now described.

Microstructure

Figure 2 A-F show the porous structure of PVDF prepared from the solutions with weight ratios of PVDF/DMSO from 0.2/10 to 1.2/10. At a ratio of 0.2/10 with the minimum PVDF content, adjacent pore channels with a pore size less than 5 µm were formed that were overlapped, see Fig. 2A. A further increase in the weight ratios from 0.4/10 (Fig. 2B) to 0.8/10 (Fig. 2D) led to the formation of more aligned pore channels along the freezecast direction, and the pore size normal to the freeze-cast direction decreased from 25 ± 3 µm in the 0.4/10 sample to 20 ± 2 µm in the 0.8/10 sample (Fig. 2D). At low magnification aligned pores can be observed on the upper sample surface, where in Fig. 3A mm-scale length pores can be seen in the freeze-cast PVDF with a ratio of 0.4/10. A similar low magnification side view, see inset of Fig. 3B, reveals the lens-shaped pore morphology.

Compared to commercially available ferroelectrets [START_REF] Anton | Piezoelectret foam-based vibration energy harvesting[END_REF], the freeze-cast polymers had a larger pore length with similar pore shape and pore size which might facilitate the generation and deposition of plasma charges on the inner pore surface under the action of a high electric field during the poling process. A further increase in the amount of PVDF to a ratio of 1.0/10 (Fig. 2E) and 1.0/10 (Fig. 2F) resulted in an overlapped pore morphology (Fig. 2E) with the formation of more rounded pores, as in Fig. 2F, rather than an aligned structure; this is similar to the structure of ice-templated ceramics when the solid loading is too high [START_REF] Deville | Ice-templated porous alumina structures[END_REF].

In general, larger pores are formed from the PVDF/DMSO solution at low PVDF concentrations during directional freezing, since the porous structure is a replica of DMSO crystals. However, for a low PVDF content of 0.2/10, the capillary force [START_REF] Zhang | Mesoporous piezoelectric polymer composite films with tunable mechanical modulus for harvesting energy from liquid pressure fluctuation[END_REF] formed by water during evaporation during drying leads to shrinkage of the pore channels, thereby making the adjacent pore channels overlap, as shown in Fig. 2A. With an increase of PVDF concentration, there is a reduced effect of the capillary force on pore deformation (Fig. 2B-D) for the 0.4/10 to 0.8/10 samples, due to the lower amount of water left in the samples. However, if PVDF concentration is too high there is a loss of directionality and smaller equi-axed pores were formed; this is possibly due to the high viscosity of the solution during freeze casting [START_REF] Zhang | Effects of rheological properties on ice-templated porous hydroxyapatite ceramics[END_REF], (Fig 2E -F).

Phase analysis

Figure 4 shows the FT-IR and XRD spectra of the freeze cast porous PVDF with different weight ratios of PVDF/DMSO. The FT-IR transmittance spectra are shown in the 550-1500 cm -1 (Fig. 4A), and 800-900 cm -1 (Fig. 3B) ranges. No characteristic peak for either the α-or β-phase was found in all freeze cast samples. Some peaks could be attributed to both β-and γ-phases, namely 1176 cm -1 (Fig. 4A) and 840 cm -1 (Fig. 4B) [START_REF] Cai | A critical analysis of the a, b and g phases in poly(vinylidene fluoride) using FTIR[END_REF][START_REF] He | Enhanced β Crystalline Phase in Poly(vinylidene fluoride) via the Incorporation of Graphene Oxide Sheets assisted by Supercritical CO2 Treatment[END_REF].

However, the representative peak at 1234 cm -1 can be exclusively used to identify the γ-phase characteristic band [START_REF] Martins | Electroactive phases of poly(vinylidene fluoride): Determination, processing and applications[END_REF][START_REF] Jia | Enhanced electroactive and mechanical properties of poly(vinylidene fluoride) by controlling crystallization and interfacial interactions with low loading polydopamine coated BaTiO3[END_REF], which is uniquely assigned to the γ-crystalline form [START_REF] Ramasundaram | Preferential formation of electroactive crystalline phases in poly(vinylidene fluoride)/organically modified silicate nanocomposites[END_REF][START_REF] Abolhasani | A facile method to enhance ferroelectric properties in PVDF nanocomposites[END_REF]. A small peak at 811 cm -1 was also observed, and is also a peak exclusively attributed to the γ-phase [START_REF] Cai | A critical analysis of the a, b and g phases in poly(vinylidene fluoride) using FTIR[END_REF]. Fig. 4C and Fig. 4D show the X-ray diffraction of the polymers with different weight ratios of PVDF/DMSO. A typical semi-crystalline peak appeared in the XRD curves indicating the semi-crystalline nature of the materials for all weight ratios of PVDF/DMSO. All PVDF samples exhibited peaks centred at a diffraction angle of 20.04˚ (110) [START_REF] Martins | Electroactive phases of poly(vinylidene fluoride): Determination, processing and applications[END_REF] which further confirmed the γ-phase crystal polymorph was dominant in the final materials. Therefore both infrared spectroscopy and XRD spectra in Fig. 4 indicate that the γ-phase was the predominant crystalline presence in the porous PVDF for all PVDF/DMSO weight ratios, which is in agreement with previous conclusions that γphase usually was normally obtained from the DMSO solvent [START_REF] Benz | The Role of Solution Phase Water on the Deposition of Thin Films of Poly(vinylidene fluoride)[END_REF][START_REF] Martin | Solid-state-processing of δ-PVDF[END_REF], regardless of the preparation temperature [START_REF] Park | Micropatterning of semicrystalline poly(vinylidene fluoride) (PVDF) solutions[END_REF][START_REF] Satapathy | Effect of annealing on phase transition in poly(vinylidene fluoride) films prepared using polar solvent[END_REF].

Piezoelectric and frequency dependent dielectric properties

Figure 5 A-D shows the porosity variation and piezoelectric performance of the poled porous PVDF with weight ratios of PVDF/DMSO ranging from 0.2/10 to 1.2/10. The apparent porosity increased from 35 vol.% for 0.2/10 sample to reach the maximum value of 78 vol.% 0.4/10, followed by a decrease to 24 vol.% for 1.2/10 (Fig. 5A). The higher porosity level of the aligned porous structure may provide more space to retain the plasma charges for piezoelectric activity. As the PVDF/DMSO weight ratio increased from 0.2/10 to 0.8/10, the d33 values increased from 41 ± 1 pC/N for 0.2/10 to 264 ± 2 pC/N for 0.4/10; this was followed by a decrease in d33 for ratios higher than 0.6/10; see Fig. 5B. The d33 values obtained for these materials were comparable with ferroelectrets prepared from stretching and gas injection methods [START_REF] Luo | Energy harvesting study on single and multilayer ferroelectret foams under compressive force[END_REF][START_REF] Ghosh | Yb 3+ assisted self-polarized PVDF based ferroelectretic nanogenerator: A facile strategy of highly efficient mechanical energy harvester fabrication[END_REF][START_REF] Zhenhua | An electromechanical model of ferroelectret for energy harvesting[END_REF], and a commercial ferroelectret with a reported values of 25 pC/N to 200 pC/N [START_REF]Screen printable electroactive ferroelectret film[END_REF]. In addition, Fig. 5B clearly shows the almost equal in magnitude and opposite charge accumulations at the two-opposing poled-sides in terms of negatively-poled and positively-poled in all the porous PVDF samples, indicating the piezoelectric origin of measured electrical charge from the applied force.

It is known that among the five crystalline polymorphs in PVDF, namely α, β, γ, δ and ε, the α and ε phases are non-polar with no electroactive response [START_REF] Ruan | Properties and Applications of the β Phase Poly(vinylidene fluoride)[END_REF], while the ferroelectric properties are related to the polar phases of β, γ, and δ. β-PVDF is the most desired phase for ferroelectric applications since it exhibits the highest piezoelectric properties of the available PVDF polymorphs, with β-rich PVDF exhibiting a d33 ~ -30 pC/N [START_REF] Khaled | A review of piezoelectric polymers as functional materials for electromechanical transducers[END_REF], compared to a lower d33 ~ -7 pC/N [START_REF] Lopes | Nucleation of the Electroactive γ Phase and Enhancement of the Optical Transparency in Low Filler Content Poly(vinylidene)/Clay Nanocomposites[END_REF] in γ-rich PVDF due to the smaller dipole moment. Therefore, the ferroelectric γ-phase in the freeze cast materials in this work (Fig. 4), is unlikely to be the main contributor to the high piezoelectric response of the freeze cast porous PVDF since the d33 values are typically well in excess of 7 pC/N. This indicates that the porous semi-crystallized PVDF fabricated by ice-templating were piezoelectric, due to the formation of the dipole-like structure via applying a high electric field normal to the freezing direction and pore direction. This is in contrast to electret materials where charge flow is produced by either the change in a dielectric gap or the variation of the overlapping area [START_REF] Kai | A three-dimensional electret-based micro power generator for low-level ambient vibrational energy harvesting[END_REF]. Therefore, it can be concluded that the freeze-cast PVDF for all the weight ratios were ferroelectret in nature and, as shown in Fig. 5C. After applying a high poling electric field normal to the freezing direction, the air inside the aligned pore channel were subject to electrical breakdown, thereby depositing the opposite charges on the surface of the pore channel to form the dipole-like structure. Due to the high compliance of the porous polymer material, the polarisation and dipole moment is changed on application of a mechanical stress, thereby leading to an electro-mechanical response.

Since the piezoelectric properties the ferroelectret originate from charged pores, it is of interest to evaluate their surface potential decay with time. The piezoelectric coefficient (d33) of all samples decreased rapidly from 0.5 to 6 days followed by a slow reduction in d33 values from 5 to 6 days measured after corona poling, as shown in Fig. 5D. Normally the surface potential, or d33 values, fall rapidly in the first week for ferroelectrets based on polydimethylsiloxane (PDMS) [START_REF] Achraf | Micro-structured PDMS piezoelectric enhancement through charging conditions[END_REF], PDMS/Polyvinyl alcohol (PVA) [START_REF] Shi | PDMS/PVA composite ferroelectret for improved energy harvesting performance[END_REF], ethylene vinyl acetate copolymer (EVA) / biaxially oriented polypropylene (BOPP) [START_REF] Zhong | Surface charge selfrecovering electret film for wearable energy conversion in a harsh environment[END_REF], and fluorinated ethylene propylene (FEP)/polytetrafluoroethylene (PTFE) [START_REF] Wang | Sandwiched Composite Fluorocarbon Film for Flexible Electret Generator[END_REF], then reach a more stable value, which can last for at least six weeks using porous polyethylene terephthalate (PET)/ethylene vinyl acetate copolymer (EVA) [START_REF] Zhong | Flexible PET/EVA-based piezoelectret generator for energy harvesting in harsh environments[END_REF]. High charge capturing ability and low elastic modulus of the porous polymer have been considered as the main reasons for the stabilisation of the piezoelectric response in the ambient atmosphere with time [START_REF] Zhong | Flexible PET/EVA-based piezoelectret generator for energy harvesting in harsh environments[END_REF]. In addition, the polymer nature and electrical properties, the ratio between the width and length of the elongated pore channel, and the thickness of the sample also play a crucial role in the change in piezoelectric performances of ferroelectrets with time. Figure 6 shows the dielectric properties of the porous PVDF measured from 1 Hz to 1MHz with different weight ratios ranging from 0.2/10 to 1.2/10, respectively. The relative permittivity of all the porous PVDF samples exhibited a frequency dependence at low frequency (~30 Hz) and a more frequency independent behaviour at higher frequencies (> 1 kHz, Fig. 6A), which is a common behaviour for disordered materials and which obeys the universal law of dielectric response [START_REF] Jonscher | The 'universal' dielectric response[END_REF]. The low frequency dispersion in permittivity is likely to be due to a small amount of conductivity in the sample [START_REF] Almond | Anomalous Power Law Dispersions in ac Conductivity and Permittivity Shown to be Characteristics of Microstructural Electrical Networks[END_REF] and this observation agrees with the higher dielectric loss (loss tangent) in the materials at low frequency (Fig. 6B). If the permittivity at the same frequency of 1 kHz is examined for all the samples (inset of Fig. 6A), the relative permittivity initially decreased from 3.0 at 0.2/10 until it reached a minimum of 1.5 at a weight ratio of 0.4/10, it then increased to 3.5, as the ratio increased to 1.2/10. Based on the microstructural observations, Fig. 2, and porosity results in Tab.1, the increase in porosity of PVDF from 35% to 78% as the weight ratios increased from 0.2/10 to 0.4/10 led to a reduction in permittivity of the porous PVDF and the subsequent increase relative permittivity was a result of the porosity decrease from 64% to 24% as the weight ratios increased from 0.6/10 to 1.2/10 (Fig. 6A). The dielectric loss (Fig. 6B) also revealed that at the same frequency the change of the dielectric loss varied in accordance with the change of the relative permittivity and porosity; see inset of

Conclusions

In contrast to conventional processing methods to prepare ferroelectret materials with a cellular pore morphology, we have developed a new strategy to fabricate PVDF ferroelectret materials using an icetemplating method. The ferroelectret polymers are foams with charged pores and have the potential to be used in flexible wearable electronics, sensors and energy harvesters. The generated internal quasi-permanent macro-dipoles in the pore void can be induced by Paschen breakdown by application of a high electric field, where leads to piezoelectric properties. The ice-templated porous PVDF polymers formed by this new processing route exhibited elongated pore channels which were beneficial to achieve a high ferroelectret response. A maximum piezoelectric d33 coefficient of ~264 pC/N was obtained for a porous ferroelectret PVDF with a pore size of 25 µm, which is significantly higher than a d33 of 30 pC/N for dense -phase ferroelectric PVDF films. In conclusion, this is the first demonstration of freeze casting in terms of its reliability and stability in the formation of ferroelectret polymers with highly aligned pore structures. Future avenues can include further optimisation of pore geometry or exploitation of the technique on polymer systems with longer charge and thermal stability, along with energy generation and sensor performance for practical flexible transducer applications.

Figure 1 :

 1 Figure 1: Schematic of porous polymer obtained from freeze casting. (A) formation of PVDF/DMSO solution, (B) the freeze casting process, (C) sample sectioning parallel to freezing direction after solvent removal, (D) corona poling of sectioned PVDF.

Figure 2 :

 2 Figure 2: Scanning electron micrographs of porous freeze cast PVDF with increasing weight ratios of PVDF/DMSO. (A) 0.2/10, (B) 0.4/10, (C) 0.6/10, (D) 0.8/10, (E) 1.0/10, (F) 1.2/10.

Figure 3 :

 3 Figure 3: Scanning electron micrographs of (A) the mm-scale pore length and (B) the prism/lens pore morphology of the freeze-cast PVDF with the weight ratio of 0.4/10.

Figure 4 :

 4 Figure 4: (A) FTIR and (B) XRD spectra of porous PVDF with different weight ratios of PVDF/DMSO, (C) and (D) are FTIR and XRD spectra in the range of 800-900 cm -1 and 16-25˚, respectively.

Figure 5 :

 5 Figure 5: (A) porosity, (B) piezoelectric coefficient (d33), (C) schematic of the plasma discharges on the surface and (D) aging performance of the porous PVDF with different weight ratios of PVDF/DMSO.

  Fig. 6A at 1 kHz. The combination of low permittivity and high piezoelectric activity can lead to high sensor sensitivity due to high g33 (=d33/𝜀 33 𝜎 ) coefficients, e.g. 19.9 Vm/N of 0.4/10 porous PVDF at 1 kHz compared with that of 0.067 Vm/N in the piezoelectric porous lead zirconate titanate (PZT) ceramic [53].

Figure 6 :

 6 Figure 6: (A) Relative permittivity and (B) dielectric loss of the porous PVDF with different weight ratios of PVDF/DMSO.

Acknowledgements Dr. Y. Zhang acknowledges support from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant, Agreement No. 703950 (H2020-MSCA-IF-2015-EF-703950-HEAPPs). Prof. C. R. Bowen, would like to acknowledge the funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 320963 on Novel Energy Materials, Engineering Science and Integrated Systems (NEMESIS). The authors are thankful for the helpful advice and inspiring discussions with Mr Sujoy Kumar Ghosh from Jadavpur University, India.