Keywords: Patient-reported outcomes (PROs), health policies, clinical trials, methodology, patient experience measurement, patient organizations

The aim of this synthesized literature review is to provide an overview of patient-reported outcomes (PROs), a term we use to refer to both health outcomes reported directly by patients, and the tools used for their collection and measurement. Developed from the 2000s onwards, PROs have multiplied as their uses have diversified. We review approximately 50 articles authored by clinical researchers, public health physicians, and to a lesser extent, health economists, as well as approximately 10 practice guidelines distributed by public agencies, research consortia, and think tanks that develop PROs. The overview begins with descriptions of a few historical milestones that reveal the decisive role played by the FDA in the use of PROs when reviewing new treatments tested in clinical trials. These descriptions are followed by a formal definition of PROs that has now been adopted by most of the parties involved. The review continues with a focus on the different categories of PROs developed over the last two decades, well beyond the framework of clinical trials alone. Finally, it addresses recent debates on the capacity of PROs to collect and measure patient experiences, the methodological issues involved in the design of these tools, and in particular, the participation of patient organizations in the construction of PROs that better reflect the specific concerns of the people affected.

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Synthesis of the literature on patient-reported outcomes (2010-2019) *

The aim of this synthesized literature review is to provide an overview of patient-reported outcomes (PROs), a term we use to refer to both health outcomes reported directly by patients, and the tools used for their collection and measurement. Since their institutionalization in the 2000s, PROs have multiplied, as have the public agencies, research consortia, and think tanks that develop PROs and publish guidelines for best practices. Patient organizations are also involved in the production and use of PROs, often in collaboration with expert groups. Over the last two decades, a constellation of instruments has been developed, each of which has been assigned its own label and designed for a particular use. The aim of this synthesis is to provide an overview of these instruments and related discussions.

The literature on PROs has been authored primarily by clinical researchers, public health physicians, and to a lesser extent, health economists. This synthesis is based on a selection of approximately 50 articles, as well as approximately 10 practice guidelines and working group reports. This synthesis is composed of three parts. The first part describes a series of historical milestones in the development of PROs, highlighting the decisive role played by the FDA in proposing the use of PROs in the clinical assessment of new treatments tested in clinical trials and in establishing a definition of PROs that has now been adopted by most of the parties involved. The second part describes the different categories of PROs that have been developed over the last two decades and which today extend beyond the scope of clinical trials alone. The third part examines more recent debates on the capacity of PROs to collect and measure the actual experiences of patients, and the involvement of patient organizations in the construction of PROs that better reflect the concerns of the people affected. The main findings are summarized at the end of each section or sub-section. The corpus of literature on which this synthesis is based is included at the end of this document.

PROs originated from two sets of initiatives aimed at (i) measuring the effects of health policies, and (ii) evaluating the effectiveness of new drugs in clinical trials and pharmacovigilance.

I.1/ Assessing the effects of health policies on patients' quality of life [START_REF] Benamouzig | Mesures de qualité de vie en santé[END_REF] provided historical background on the measurement of the effects of health policies. In France, as in other countries, these measurement tools were initially developed as part of post-war national planning efforts and privileged the views of scientific experts. From the 1970s onwards, the views of individuals were gradually integrated, a phenomenon that was accentuated in the 1980s as health expenditures were increasingly rationalized. This consideration of individuals' points of view was based on the observation that, in addition to the possible clinical effects of health policies, it was necessary to assess the impacts of these policies on people's health-related quality of life (HRQoL), a criterion now considered important for the effective allocation of resources. This approach was advocated by RAND, an expert organization that advises the U.S. federal government, in a study commissioned in 1971 on the impacts of alternative forms of health insurance schemes on health status. In the United Kingdom, economist Alan Williams and psychiatrist Rachel Rosser also developed the famous quality-adjusted life year (QALY) indicator to assess therapeutic innovations with a view to their possible funding by the NHS. The British National Institute for Clinical Excellence (NICE), which was established in 1999 and is responsible for what is known as Health Technology Assessment, bases its recommendations on this indicator of the utility of new treatments by incorporating the subjective preferences of individuals. France has not adopted this utilitarian approach and favors a strictly medical assessment.

These initiatives highlight two components of the historical landscape within which PROs have developed. The first component addresses the issue of the value and usefulness of health policies, or more narrowly, of new treatments for patients. This question has been the subject of many debates and has led different consortia to propose clarifications. For example, the International Consortium for Health Outcomes Measurement (ICHOM) proposed the following definition of "value-based healthcare" in 2018:

Value is defined as the outcomes that patients experience relative to the cost of delivering those outcomes. Value-based health care, or VBHC, is health care that delivers the best possible outcomes to patients for the lowest possible cost. We believe that choice and competition in health care should be based on value. By restructuring care-delivery around outcomes, and promoting superior outcomes with financial incentives, health care systems will improve quality and curb inefficiencies. This will benefit every stakeholder across the health care spectrum. Utility is the (perceived) capacity of an item to satisfy needs or wants. In health economics, utilities measure the intensity of patient preferences. For example, the importance of various factors to patients, such as symptoms, pain, and psychological health. The impact of new treatments on these factors, and therefore on quality of life (QoL), can then be calculated. This is a common approach used by health technology assessment (HTA) agencies that advise whether or not treatments should be funded (for example) by government health services. (EUPATI, 2016) The notions of "value-based healthcare" and utility are therefore based on a vision of healthcare strategies as part of a market in which patients behave like economic agents who have preferences, are able to articulate their needs, and consequently are able to identify therapies that best meet their expectations and advise funding authorities accordingly.

The second component of these initiatives to measure the effects of health policies is that they are based on questionnaire surveys of patients. Two generic questionnaires, as opposed to pathology-specific questionnaires, constitute references for the community of experts and decision-makers.

The first questionnaire is the EQ-5D, which was developed between 1987 and 1991 by EuroQol Group, a multidisciplinary and international group of researchers (EuroQol Group, 1990). Patients who complete the EQ-5D rate five different dimensions of their health-mobility, selfcare, usual activities, pain and discomfort, anxiety, and depression-on a scale of 1 to 5 [START_REF] Desomer | Use of patient-reported outcome and experience measures in patient care and policy[END_REF], and rate their overall health status on a scale of 0 (worst possible health) to 100 (best possible health). This type of generic tool contributes to cost-benefit analyses [START_REF] Devlin | EQ-5D and the EuroQol Group: Past, present and future[END_REF] and is widely used by NICE, the UK's health technology assessment agency, to inform decision-making about health products and technologies [START_REF] Haywood | Using PROMs in healthcare: Who should be in the driving seat-policy makers, health professionals, methodologists or patients? The Patient-Patient-Centered Outcomes Research[END_REF].

The second questionnaire is the SF-36 developed based on the RAND Medical Outcomes Study (1987)(1988)(1989). The SF-36 is commonly used in health-related quality of life studies. RAND Health Care provides three versions of a free questionnaire (12, 20, or 36 items) covering, for example, physical functioning (measuring physical limitations and capacities, mobility), compliance, sleep, sexuality, mental health, etc. [START_REF] Gregory | The role of patient-reported outcomes in women's health[END_REF]. The SF-36 yields separate scores for physical and mental health, rather than an overall health score [START_REF] Devlin | Getting the most out of PROMs: Putting health outcomes at the heart of NHS decision-making. King's Fund[END_REF]. The instrument has been translated into many languages and has given rise to many adaptations.

These two questionnaires have two characteristics in common: (i) they ask patients to evaluate standardized items selected by medical experts to measure health-related quality of life; and (ii) they translate evaluations into quantitative indicators that make it possible to compare patients' assessments of different care strategies. Patients are thus considered to be producers of data considered relevant by experts.

Linking PROs with measurements of the effects of health policies is part of a movement that can be described as "evidence-based policy," which is motivated by a concern for better allocation of resources and based on patients' reports of the quality of life provided (or not) by different care strategies.

I.2/ Assessment of the therapeutic benefits of treatments tested in clinical trials

The second set of initiatives from which PROs have developed relates to the assessment of the efficacy of new drugs in clinical trials and pharmacovigilance. These initiatives introduce patient reports on the benefits of treatments into such evaluations, both pre-and postmarketing.

In the United States, RAND played an important role in the development of a "science of health outcomes measurement" in the 1980s. Pharmacological researchers also began to consider quality of life as a relevant outcome to be measured in the assessment of new drugs around the same time. Likewise, the FDA was asking sponsors of new oncology products to consider quality of life measures formulated in terms of symptoms and functioning based on the idea that traditional objective measures, such as tumor response, do not always reflect the benefits perceived by patients. In 1985, a medical journal published the results of a clinical trial in which quality of life was used as the primary endpoint for the first time; specifically, the researchers measured the "tolerability" of the product rather than its efficacy [START_REF] Johnson | Food and Drug Administration requirements for approval of new anticancer drugs[END_REF]. In response to the frenzy that this publication generated in the industry, the FDA established a working group and consulted with interested professionals to formulate principles to inform the use of PROs and provide a framework for product evaluation. This led to the development of guidelines which have been amended over the years. In 2000, these guidelines defined a PRO, thereby distinguishing it from a quality of life measurement. This definition was updated in 2009 and adopted by the European Medicines Agency (EMA) and the academic world:

A PRO is any report of the status of a patient's health condition that comes directly from the patient, without interpretation of the patient's response by a clinician or anyone else. The outcome can be measured in absolute terms (e.g., severity of a symptom, sign, or state of a disease) or as a change from a previous measure. In clinical trials, a PRO instrument can be used to measure the effect of a medical intervention on one or more concepts (i.e., the thing being measured, such as a symptom or group of symptoms, effects on a particular function or group of functions, or a group of symptoms or functions shown to measure the severity of a health condition). (FDA, 2009) This definition indicates the key characteristics of PROs: the concept refers to significant therapeutic benefits to be measured in clinical trials; the symptom refers to "subjective evidence of a disease, condition or treatment-related effect that can only be perceived and known by the patient;" the sign refers to "objective evidence of a disease, condition or treatment-related effect," "usually observed and interpreted by the clinician," but which the patient can "notice" and "report."

The notion of PRO was introduced in the 2000s, as part of the assessment of experimental treatments tested in clinical trials. In addition to measures of quality of life, PROs include elements related to manifestations of a disease and the effects of a treatment as perceived by patients. Since then, PROs have gained momentum and have become the subject of extensive discussion.

The development of PROs from the 2000s onwards has manifested in several ways. First, many institutional actors, researchers in biomedicine, economics, and health management, think tanks, and patient organizations have produced PROs, organized themselves into consortia and working groups to discuss them, and published practice recommendations. Second, as PROs have multiplied, new uses beyond the scope of clinical trials have emerged, and researchers have explored their application to a broad and diverse set of other contexts.

Reflecting on the design of PROs, the FasterCures think tank notably proposed a workshop in 2017 entitled "Patient-Reported Outcomes: Design with the End in Mind" [START_REF] Grossman | Patient-reported outcomes: Design with the end in mind[END_REF].

Based on the literature, we can distinguish four ways of categorizing PROs and their uses, and the specific questions that each type of PRO raises.

concept: the thing being measured, such as a symptom or group of symptoms, effects on a particular function or group of functions, or a group of symptoms or functions shown to measure the severity of a health condition

In clinical trials, a PRO instrument can be used to measure the effect of a medical intervention on one or more concepts. PRO concepts represent aspects of how patients function or feel related to a health condition or its treatment.

item: an individual question, statement, or task (and its standardized response options) that is evaluated by the patient to address a particular concept (FDA, 2009) II.1/ Categorizing PROs according to the levels at which they are used

A/ The macroeconomic or system level

PROs can be used to monitor the health of the population, to design and evaluate public health policies (prevention, health promotion, measurement of health disparities, etc.), and to inform decisions about the reimbursement of care-related expenses, the contracting of health services and pay-for-performance. According to [START_REF] Desomer | Use of patient-reported outcome and experience measures in patient care and policy[END_REF], what increases the value of PROs is the possibility of linking them to monitoring data in clinical registries, or data related to health care expenses and length of hospital stays. Such links make it possible to cross-reference different medical and economic data and to study the correlations between, for example, clinical data collected by health care professionals and compiled in registries, and PROs.

B/ The institutional or service level

PROs can be used to pilot quality improvement initiatives. Aggregate data can be used to evaluate and compare provider performance (benchmarking and feedback), identify quality issues that remain under-treated, and inform the general public with the aim of promoting informed patient choice [START_REF] Desomer | Use of patient-reported outcome and experience measures in patient care and policy[END_REF]. This type of use has developed mainly in the United Kingdom. However, critics have argued that this type of analysis fails to clearly demonstrate links between PROs and quality of care. Extensive effort has been directed toward measuring quality of care, mainly in terms of assessing health care services according to criteria such as safety, responsiveness, or efficiency. This type of criticism illustrates how difficult it is to convince experts of the validity of non-traditional criteria for both assessing the quality of health care services and informing the organization of such services.

C/ Clinical practice level or individual level

PROs can be used to refine a diagnosis [START_REF] Desomer | Use of patient-reported outcome and experience measures in patient care and policy[END_REF], as a support for shared decisionmaking between caregiver and patient [START_REF] Mckenna | Measuring patient-reported outcomes: Moving beyond misplaced common sense to hard science[END_REF], to engage the patient in health management [START_REF] Snyder | Implementing patient-reported outcomes assessment in clinical practice: A review of the options and considerations[END_REF], and to report problems that would not otherwise be addressed, such as anxiety and depression, and problems with physical, social, or emotional functioning [START_REF] Aaronson | User's guide to implementing patient-reported outcomes assessment in clinical practice[END_REF][START_REF] Greenhalgh | The applications of PROs in clinical practice: What are they, do they work, and why?[END_REF]. PROs also can be used to facilitate patient-centered discussions in multidisciplinary team meetings [START_REF] Aaronson | User's guide to implementing patient-reported outcomes assessment in clinical practice[END_REF][START_REF] Desomer | Use of patient-reported outcome and experience measures in patient care and policy[END_REF][START_REF] Greenhalgh | The applications of PROs in clinical practice: What are they, do they work, and why?[END_REF][START_REF] Snyder | Implementing patient-reported outcomes assessment in clinical practice: A review of the options and considerations[END_REF]. Notably, although PROs allow for the identification and discussion of problems encountered by patients during consultations, they have little impact on how clinicians subsequently manage these problems.1

II.2/ Categorizing PROs according to their intended objectives

A/ Measuring the effects of an experimental treatment in a clinical trial

When clinical trials involve treatments for which there are no objective outcome measurements (degree of morbidity, biomarkers of symptoms, etc.) and for which results can only be observed subjectively in terms of patient impacts, PROs can be used as primary outcome measures. PROs are also used to complement primary outcomes (e.g., survival rates, biomarkers), as they reflect outcomes that are important to patients and may reveal relationships between symptoms and other indicators such as quality of life [START_REF] Weldring | Patient-reported outcomes (PROs) and patient-reported outcome measures (PROMs)[END_REF].

B/ Identifying treatment side effects

Patient-reported outcomes of adverse events (PRO-AEs) are used to identify treatment side effects. The Patient-Reported Outcomes Safety Event Reporting (PROSPER) Consortium was established to improve drug safety by adopting an approach that fully integrates the patient's perspective according to a "patient-centered model of care." The consortium has developed recommendations and guidelines to promote the development of PRO-AEs, and more broadly, devices for capturing and analyzing patient-reported data. According to the consortium, the benefit of patient reporting is that patients respond earlier than health professionals, perceive the impacts and severity of drug reactions differently, and provide more detailed descriptions of the circumstances surrounding drug use, including cases of prescribing errors or unintended use. The aim is to obtain "real-world" data to improve the assessment of the benefits and risks of pharmaceutical therapies [START_REF] Banerjee | Patient-reported outcome measures in safety event reporting: PROSPER Consortium guidance[END_REF].

C/ Early detection of alerts reported by patients regarding their health status

Research has been undertaken to assess health care service responses to PRO-alerts, urgent updates provided by patients regarding their health status. One of the conclusions of this research is that research nurses, data managers/coordinators, trial managers, or chief/principal investigators who become aware of these alerts when processing PRO data are very often uncertain about how to respond. Moreover, these alerts generally are not processed in real time. The results of the STAR study, presented by oncologist Ethan Basch at the annual conference of the American Society for Clinical Oncology in 2017, have generated interest among members of the medical press [START_REF] Dean | The patient is speaking": Discovering the patient voice in ophthalmology[END_REF][START_REF] Marino | Rôle et utilisation des patient reported outcomes (PROs) dans la prise en charge des patients en oncologie[END_REF]. The study reveals the effects of routine electronic reporting by cancer patients on their health status and healthrelated quality of life. The electronic reporting system was able to notify a nurse who would contact the patient, answer questions, and suggest a solution or consult with a team physician if necessary.

D/ Collecting patient-reported data for clinical research

The fourth objective of collecting patient-reported data for clinical research is greatly facilitated by information and communication technologies and is part of efforts to harness the power of "big data" in the field of health.

Patient-reported information (PRI) is presented as an alternative to PROs. Unlike traditional PROs, the novelty lies in the fact that information can be collected and disseminated using social networking platforms [START_REF] Baldwin | Patient-reported outcomes, patientreported information: From randomized controlled trials to the social web and beyond[END_REF].

Patient-generated health data (PGHD) are recorded and transmitted by patients to teams of researcher-clinicians using smart phones, digital platforms, and other technologies. PGHD have five characteristics: (i) patients (or trusted third parties, if the patients cannot do so) record and transmit these data, not caregivers; (ii) data are collected outside clinical settings; (iii) data are longitudinal, and it is possible to obtain repeated measurements over time; (iv) the frequency of collection may be very high; and (v) depending on the parameter of interest, the data flow can be quasi-continuous over long observation periods [START_REF] Wood | Emerging uses of patient generated health data in clinical research[END_REF].

II.3/ Categorizing PROs according to their degree of generality

The literature distinguishes between two types of PROs: generic PROs and specific PROs.

A/ Generic PROs

Generic PROs are assessed using a specific set of questions, regardless of patients' health status. The aim is that health status (and changes in health status, in cases where generic PROs are measured before and after treatment or several times during treatment) can be compared between patients or population groups, or between care sectors. Generic PROs measure the impacts of health status on life in general, quality of life, and quality of life relative to certain dimensions such as physical functioning. The lack of robustness of comparisons conducted on the basis of generic PROs, as well as the obsolete nature of certain items (which sometimes date back several decades) are highlighted [START_REF] Mckenna | Measuring patient-reported outcomes: Moving beyond misplaced common sense to hard science[END_REF]. To address these shortcomings, an item-banking approach can be adopted whereby parts of questionnaires designed to assess generic PROs are replaced with domain-relevant items [START_REF] Mckenna | Measuring patient-reported outcomes: Moving beyond misplaced common sense to hard science[END_REF].

B/ Condition-specific or disease-specific PROs

Condition-specific or disease-specific PROs relate to a particular disease (diabetes), group of diseases (cancer), body part (the knee), function (visual, auditory, etc.), or focus of care (pain). Questions relate to the severity of the condition and are therefore tailored to the people affected. For this reason, they are not used in population health surveys. Items are designed based on qualitative interviews with affected patients and tested with new patient populations to assess their validity. A well-designed measurement tool only includes questions that are relevant, meaningful and acceptable to patients. Research shows that disease-specific PROs are more likely to show differences between competing therapies [START_REF] Desomer | Use of patient-reported outcome and experience measures in patient care and policy[END_REF][START_REF] Devlin | Getting the most out of PROMs: Putting health outcomes at the heart of NHS decision-making. King's Fund[END_REF].

The different types of PROs and their uses, which have multiplied since the 2000s, show: (i) the progressive institutionalization of PROs at different levels of decision-making (i.e., the health system, health services, medical practices), and for different activities (i.e., clinical trials, pharmacovigilance, patient feedback on their health status, clinical research); (ii) a variety of methods for collecting PROs and the nature of the data collected (e.g., standardized questionnaires with items defined by experts, data collected through digital self-tracking equipment, qualitative interviews with patients, information disseminated by patients via social networks); and (iii) necessary adjustments to practices and the organization of care to ensure PROs are adequately considered (e.g., the organization of responses to PRO-alerts). Beyond the specific concerns raised by each PRO, a cross-cutting question has emerged in recent years: To what extent do PROs accurately reflect patients' experiences with diseases or treatments?

Although PROs are being designed and applied in an increasing number of contexts, experts have expressed reservations since their inception. Specifically, PROs reveal patients' subjective perceptions and do not constitute reliable data for objectively assessing health conditions and the effects of health policies or treatments on health For this reason, a number of consortia have been established to develop PRO design methodologies that neutralize these subjective biases by offering standardized and validated questionnaires and graduated scales on which patients can objectively assess their perceptions. [START_REF] Mckenna | Measuring patient-reported outcomes: Moving beyond misplaced common sense to hard science[END_REF], a Research Director at an organization specializing in PROs (Galen Research Ltd., Manchester), emphasized that when developing PROs, "common sense" is insufficient; scientific expertise is required, as PROs must be designed in a way that enables qualitative information to be quantified. This is also why certain experts consider PGHD, which are collected and transmitted by patients via digital self-tracking equipment, to be much more reliable than traditional PROs based on subjective patient reports. This question of the subjectivity of PROs is the focus of ongoing discussions and reflections by organizations and actors involved in their production and use [START_REF] Shapiro | Patient-generated health data-white paper[END_REF].

Mirroring the issue of the subjectivity of patients' reports, a second topic of discussion has emerged in recent years regarding the relevance of the questions patients are asked. Such discussions have been motivated by the development of "patient-centered healthcare" and by the increased participation of patients in health issues, which is seen as both an ethical and democratic imperative. Concerns over the relevance of questions point to possible discrepancies between the PRO items developed by medical experts and the experiences of patients, which may not necessarily correspond to these items. This has led to the development of a set of tools known as patient-reported experience measurements (PREMs), and of principles and recommendations for the design and use of these tools. It has also led to the involvement of patient organizations in the construction of such tools.

III.1/ How can patients' experiences be taken into account?

A number of experts have noted a discrepancy between the questions patients are asked and their experiences of a disease or treatment. For example, together with his colleagues, Dr. Ethan Basch, Director of the Cancer Outcomes Research Program and Professor of Medicine and Public Health at the UNC Lineberger Comprehensive Cancer Center in North Carolina, found that the side effects observed during phase 1 of a clinical trial measuring the toxicity of an experimental treatment were not included in the Common Terminology Criteria for Adverse Events (CTCAE) of the National Cancer Institute (NCI). As they began to record symptoms in patients, they discovered that patients were detecting more symptoms than clinicians, and doing so much earlier [START_REF] Basch | Symptom monitoring with patient-reported outcomes during routine cancer treatment: A randomized controlled trial[END_REF]. [START_REF] Basch | Assuring the patient-centeredness of patientreported outcomes: Content validity in medical product development and comparative effectiveness research[END_REF] discussed the example of a pain item that was originally designed for use by clinicians and was included in a PRO without undergoing a qualitative assessment involving direct patient participation. The terms on the pain scale below are problematic because they merge different registers-that is, the words typically are not used together to draw comparisons (e.g., mild, discomforting, and horrible). Moreover, the distinctions between, for example, mild and discomforting or horrible and excruciating are not explicit. They concluded that the ability of this item to assess patients' experiences of pain associated with both disease and treatment is compromised.

How strong is your pain? In light of these findings, the solution recommended by several experts and regulatory authorities such as the FDA and certain PRO research and production consortia is to encourage direct patient participation in the development of the items. For example, the FDA's "Patient Focused Drug Development Efforts" program publishes guidelines for collecting data about patient experiences. The agency also offers workshops to review what it calls clinical outcome assessments (COA) which include PROs and real-world evidence (RWE)2 [START_REF] Treadwell | Clinical outcome assessments: Nothing about me without me[END_REF]. The PROSPER Consortium has published a report indicating that PROs should include not only patient reports collected by clinicians using validated instruments, but also the full range of voluntary patient reports.

For now, it seems as though these recommendations are being disregarded. Wiering, de Boer, and Delnoij (2017) investigated patient participation in the development of PROs by examining 189 studies. Patient participation was not documented a quarter of the studies, particularly older ones. When it was documented, patients were involved mainly in question development (58%) and comprehension testing (51%). In contrast, patient involvement in identifying outcomes to be measured ("concepts of interest," in the FDA's terminology) was very low (11%). Patients were involved in all aspects of PRO development in only 7% of cases [START_REF] Wiering | Patient involvement in the development of patientreported outcome measures: A scoping review[END_REF]. Even more instructive, when standards for the use of PROs in randomized controlled trials were set by the International Society for Quality of Life Research (ISOQOL), the issue of patient involvement was rejected during the review process. [START_REF] Dean | The patient is speaking": Discovering the patient voice in ophthalmology[END_REF] suggested that change could only come from learning how to listen to patients, both as representatives on the various committees and as researchers, policy makers, and industrialists.

With regard to learning how to listen to patients, the question arises of how to acquire a better understanding of their experiences. Some authors have called for reflection on the use of qualitative research methodologies applied in sociology and anthropology (i.e., in-depth interviews, focus groups, observations, use of visual aids) to be implemented in the initial phases of studies [START_REF] Dean | The patient is speaking": Discovering the patient voice in ophthalmology[END_REF]. Others have suggested interviewing patients about specific experiences rather than assessing their satisfaction [START_REF] Nilsson | Patient-reported outcomes in the Swedish National Quality Registers[END_REF]. Still others have suggested that a distinction should be made between classic PROs and what they call patient-centered PROs (PC-PROs): patients report information in both cases, but the difference lies in what information is reported [START_REF] Tractenberg | Maintaining primacy of the patient perspective in the development of patient-centered patient reported outcomes[END_REF]. A PC-PRO, the authors explained, "explicitly maintains the primacy of the patient's, vs. the clinician's or researcher's, perspective on the patient's health status, condition, or experience" (Tractenberg et al. 2017, p. 3). They detailed the iterative process they implemented to build PC-PROs in partnership with interested parties (i.e., experts representing the target population, caregivers, clinicians, and researchers). The process begins by compiling an initial list of signs and symptoms based on a literature review and discussions with patients, researchers, and clinicians; this list, which is amended throughout the process, is designed as a working tool. Focus groups are organized with both patients and clinicians. Particular attention is paid to maintain alignment with the perspectives of patients and clinicians on what to measure and how to measure it independently, with the ultimate goal of integrating the patient experience as captured by all participants in the design of PC-PROs [START_REF] Tractenberg | Maintaining primacy of the patient perspective in the development of patient-centered patient reported outcomes[END_REF].

PROs have been designed to collect patients' responses to questions developed by experts to augment knowledge of the effects of treatments or health policies on people's lives.

Considerable effort has been made to standardize questions and validate the answers in order to neutralize the subjective nature of patient reports. Recently, there has been important reflection not so much on the quality of the answers, but on the relevance of the questions, and the idea is beginning to spread that PROs should be designed to collect patients' experience of a disease or treatment without preconceived orientations. Initiatives have been taken in this direction, contributing to the emergence of PREMs.

III.2/ The role of patient organizations in the development of PROs

As the literature demonstrates, experts are advocating that patients should be involved in the development of PROs. From this perspective, patient associations are well-positioned to facilitate this process, given their role in collecting and shaping the experiences of patients. Some experts have recognized this unique capacity of patient associations. For example, Nicklin and his colleagues at the University of the West of England, Bristol, have developed an approach to capture the fatigue experience of rheumatoid arthritis patients:

Patients have an understanding of fatigue and its effect on their everyday life that only they can describe. Therefore, an understanding of the lived experience of rheumatoid arthritis (RA) fatigue could be gained through listening to patients (experts) and applied to the development of PROMs [patient-reported outcome measures], which will then capture issues relevant to patients. [START_REF] Nicklin | Collaboration with patients in the design of patient-reported outcome measures: Capturing the experience of fatigue in rheumatoid arthritis[END_REF](Nicklin et al., , p. 1553)).

According to these researchers, not only do commonly-used tools use different vocabularies, which makes comparisons difficult, but more importantly, they only measure the severity of symptoms (e.g., fatigue) and not the perceived impacts of these symptoms on the ability to cope, which may be equally (if not more) important to patients. They have established a partnership between researchers and an organization of patients affected with RA, and a list of terms used by patients to describe fatigue during qualitative interviews has been gradually established and refined. [START_REF] Morel | Measuring what matters to rare disease patients-reflections on the work by the IRDiRC taskforce on patient-centered outcome measures[END_REF], members of the IRDiRC (International Rare Diseases Research Consortium), considered it essential to produce knowledge on rare diseases, which are often poorly known or incompletely described, or described in ways that do not accurately reflect patients' experiences. In addition to qualitative interviews and focus groups, they recommended the use of patient diaries to design PROs that are more relevant to patients:

It is important to invest in a careful description of the clinical manifestations, disease course, clinical outcomes and -importantly -of the disease impact on patients' daily life and of the patients' chief complaints and expectations from future therapies. A comprehensive understanding of patient disease burden is key to later support the assessment and selection of the outcome measures that are most relevant to patients. Because a rare disease affects every aspect of their daily life, patients and their caregivers become experts of the rare condition and of the important outcomes of diseases that need to be addressed. It is thus critically important to partner with and listen to them. (Morel & Cano, 2017, p. 3) In order to effectively incorporate patients' experiences into PROs, it is recommended that core outcome sets (COSs) be identified, i.e., the essential outcomes that patients expect from new drugs or care strategies [START_REF] Dean | The patient is speaking": Discovering the patient voice in ophthalmology[END_REF][START_REF] Mills | Patient-centered outcome measures initiatives in the field of rare diseases[END_REF].

Patient organizations are launching initiatives as well. For example, the Michael J. Fox Foundation for Parkinson's Research collected data directly from patients and caregivers about their daily experiences with Parkinson's disease using Apple's ResearchKit and a digital platform [START_REF] Grossman | Patient-reported outcomes: Design with the end in mind[END_REF]. Initiatives are multiplying, such as the Duchenne Parent Project's outcome measurement initiative, the Patient Reported Outcomes Burdens and Experiences on Hemophilia, the Dravet syndrome internet platform, and the survey on the perspectives and priorities of patients with spinal muscular atrophy conducted by SMA Europe and Cure SMA [START_REF] Morel | Measuring what matters to rare disease patients-reflections on the work by the IRDiRC taskforce on patient-centered outcome measures[END_REF].

PROs in the field of rare diseases deserve a special mention. In the context of orphan drug development, the EMA requires clinical trial documentation to include a pre-specified PRO endpoint in addition to other clinical efficacy endpoints, and suggests the use of Health-Related Quality of Life (HRQoL) questionnaires. An examination of the Summaries of Product Characteristics (SmPCs) of orphan drugs approved by the EMA from 2012 to 2016 revealed that only 27% of these documents mention the use of PROs, compared to more than 45% for documents relating to non-orphan drugs [START_REF] Jaroslawski | Patient-reported outcome claims in European and United States orphan drug approvals[END_REF]. The same trend can be observed for FDA-approved orphan drugs. The authors offered an explanation for this phenomenon: in order to speed up the availability of orphan drugs, less evidence is provided for marketing authorization; therefore, pharmaceutical companies look for less data during the product development process, including data that PROs can provide. Benjamin and colleagues (2017) provided a different explanation: given the rarity of the diseases, the fact that many of them affect young children, and the wide heterogeneity of clinical situations, specific PROs must be developed for each disease or group of diseases (e.g., rare metabolic diseases), which are currently very few in number. In their report on how to proceed with the development of PROs in the field of rare diseases, they advocated:

• The introduction of observer-reported outcomes (ObsROs) which a third party could provide if the patient is unable to do so, either because the individual is too severely affected or because the individual is a child;

• The mobilization of patients' associations during the upstream phases of the construction of PROs; • The development of PROs that would provide information on three sets of phenomena:

o The natural history of diseases, based on the collection of patients' and families' experiences, as well as data from disease registries (some of which are set up by patient associations), literature reviews, satisfaction surveys among the people concerned, etc.;

o The therapeutic benefits of treatments from patients' perspectives, focusing on the common benefits sought by the population of people concerned, especially those sought in the short term. Patient-reported benefits could then be used as "surrogate outcomes" in the evaluation of drug efficacy in order to overcome the difficulties of conducting randomized double-blind clinical trials in the case of rare diseases.

o The construction of specific aggregation methods for the data collected and/or the adaptation of methods used in generic PROs such as SF-36 or EQ-5D, in order to account for data heterogeneity. For example, the EuroQoL group has just developed a child-friendly version of the EQ-5D. Likewise, Basch and Bennett (2014) described a multi-attribute questionnaire whereby a numerical value is used to weight the most sought-after attributes in the subject studied. Such a questionnaire was designed to aggregate data collected on a drug called Ruxolitinib which was approved in 2011 by the FDA and EMA for patients with myelofibrosis.

Finally, it should be noted that in the field of rare diseases, patient organizations have launched initiatives to self-test medications, the results of which have been measured using patient reports. The best-known case is the amyotrophic lateral sclerosis (ALS) lithium study conducted on the online platform PatientsLikeMe3 [START_REF] Stefanou | Patient-led research in amyotrophic lateral sclerosis: Quo vadis?[END_REF]. It was initiated by two patients with advanced ALS living in Brazil and the United States, both of whom died before the end of the study. ALS patients, 149 according to Vayena and colleagues [START_REF] Streuli | The promising revolution of participant-led research in rare neurological diseases. Potential benefits and pitfalls[END_REF][START_REF] Vayena | Research led by participants: A new social contract for a new kind of research[END_REF] or 160 according to [START_REF] Wicks | Patient, study thyself[END_REF], were contacted via the platform and decided to take lithium to test the results of a small study that suggested positive effects in terms of slowing disease progression and alleviating symptoms. The ALS PatientsLikeMe study took place over eight months and was published in Nature Biotechnology. Its findings that lithium had no effect were later confirmed by standard clinical trials [START_REF] Streuli | The promising revolution of participant-led research in rare neurological diseases. Potential benefits and pitfalls[END_REF][START_REF] Vayena | Research led by participants: A new social contract for a new kind of research[END_REF][START_REF] Wicks | Patient, study thyself[END_REF]. However, the authors acknowledged the limitations of this type of self-experimentation, which raises a series of questions about the control of these trials, the lack of assistance when needed, and the risks faced by individuals. These initiatives also open up a debate regarding how "classical" research can be linked to what is called "patient-led research" in the literature.

The involvement of patient organizations in the development and use of PROs is an important step in the development of tools that collect not only patient reports on questions developed by experts, but also information about patients' experiences and their own assessments of what counts in new care strategies or treatments. The articulation of these PREMs or PC-PROs relative to classic PROs is currently an ongoing project, which will undoubtedly require work on a case-by-case basis.

PROs are data collected from patients about their own health status, particularly their healthrelated quality of life. It was in the context of the evaluation of new treatments tested in clinical trials that the FDA proposed the first formal definition of PROs in the 2000s. Since then, PROs have been used for a variety of purposes ranging from pharmacovigilance to alerts from patients on changes in their state of health, and from the collection of physiological data via individual digital devices and health platforms for clinical research to the development of medico-economic indicators to inform decisions on the management of health products by national authorities.

The subjective nature of patient reports has been the subject of intense reflections within communities of experts, and has led to methodological research aimed at standardizing the questions asked, developing graduated scales of response, and testing and validating the tools with different populations of concerned individuals. Another element of discussion relates to the conditions for the development of disease-specific PROs or particular dimensions of patients' health status (e.g., pain, fatigue, etc.).

Recently, a new question has arisen regarding the ability of PROs to truly reflect patients' experiences. Indeed, PROs ask questions related to subjects that experts consider important in their practices, but which are not necessarily relevant to patients. To address this issue, partnerships have been established with patient organizations to develop qualitative surveys that reveal the therapeutic benefits patients expect from a new drug in light of their experiences with the disease, or the problems that, from their point of view, impact their quality of life. These initiatives mainly concern chronic and rare diseases, and address issues such as the variety of symptoms or the expression of pain and fatigue.

To sum up, although PROs are now part of the health landscape, the literature shows that their development and articulation with other real-life data require a substantial amount of collaborative work and framing, and that concerns about their use remain, especially in France where few have developed expertise with PROs, unlike in the United States and the United Kingdom. In particular, the use of PROs in clinical practice is still very tentative, probably because it would require changing patient care practices and the organization of care.

(

  UMR 9217) a été créé en 2012. Il rassemble : • les équipes de recherche de MINES ParisTech en économie (CERNA), gestion (CGS) et sociologie (CSI), • celles du Département Sciences Economiques et Sociales (DSES) de Télécom ParisTech, • ainsi que le Centre de recherche en gestion (CRG) de l'École polytechnique, soit plus de 200 personnes dont une soixantaine d'enseignants chercheurs permanents.

(

  UMR 9217) was founded in 2012. It brings together: • the MINES ParisTech economics, management, and sociology research teams (from CERNA, CGS and CSI), • the Department of Economics and Social Science (DSES) at Télécom ParisTech, and • the Management Research Center (CRG) at Ecole Polytechnique.

  (PPI) item of the McGill Pain Questionnaire

The International Society for Quality of Life Research publishes a "User's Guide to Implementing Patient-Reported Outcomes Assessment in Clinical Practice"(Aaronson et al.,

2011).

The FDA defines real world data (RWD) as care information that comes from multiple sources generally outside the typical clinical research setting, such as electronic medical records, complaint and billing data, product and disease registries, or data collected through personal equipment and health-related applications.

PatientsLikeMe is an exchange platform for communities of patients, including patients suffering from chronic and rare diseases.


Antoine Van Der Laan

Valérie Boyer

Romain Epherre

Claude Estournès
email: estournes@chimie.ups-tlse.fr

V Boyer\

C Estoumès

Simple method for the identification of electrical and thermal contact resistances in spark plasma sintering

Keywords:

teaching and research institutions in France or abroad, or from public or private research centers.

Simple method for the identification of electrical and thermal contact resistances in spark plasma sintering

Introduction

Spark plasma sintering (SPS) is a powder consolidation technique that can produce fully dense materials within minutes and at lower production costs compared to other conventional techniques [START_REF] Grassa | Electric current activated/assisted sintering (ECAS): a review of patents 1906-2008[END_REF]. The application of uniaxial pressure combined with a pulsed direct current allows the sintering of powders or porous materials such as ceramics, refractory metals, or intermetallics at a temperature lower than their melting temperature [START_REF] Guillon | Field-assisted sintering technology /spark plasma sintering: mechanisms, materials, and technology developments[END_REF][START_REF] Orrù | Consolidation/synthesis of materials by electric current activated/assisted sintering[END_REF]. Compared to conventional sintering, the SPS allows to lower the consolidation temperature as well as the processing time. One of the benefits is to keep a fine microstructure throughout the process, which can enhance the mechanical properties of the material [START_REF] Olevsky | Fundamental aspects of spark plasma sintering: 1. Experimental analysis of scalability[END_REF][START_REF] Chaim | Sintering and densification of nanocrystalline ceramic oxide powders: a review[END_REF][START_REF] Chaim | Densification and preservation of ceramic nanocrystalline character by spark plasma sintering[END_REF].

Since the 2000s the number of publications regarding numerical modeling of SPS has significantly increased because it can offer several benefits and possibilities [START_REF] Munir | Electric current activation of sintering: a review of the pulsed electric current sintering process[END_REF]. One is the determination of the tempera ture and the current that goes through the SPS column ( comprised of the electrodes, spacers, punches, die and sample) [START_REF] Orrù | Consolidation/synthesis of materials by electric current activated/assisted sintering[END_REF]. After a thorough calibration, it allows a better understanding of the mechanisms involved and the mode! can then be used as a predictive tool for other experi ments. Such a tool would then help reducing thermal gradients in the sample, which would lead to more homogeneous densification and microstructure.

Severa! authors have identified the electrical and thermal contact resistances (ECR and TCR respectively) as crucial parameters to obtain a good thermo-electrical model of the process [START_REF] Zavaliangos | Temperature evolution during field activated sintering[END_REF]- [START_REF] Manière | Pulse analysis and electric contact measurements in spark plasma sintering[END_REF]. Those resistances can be found at each interface between each part of the SPS apparatus (tooling parts and sample). A theoretical expression of the ECR and TCR could be used [START_REF] Wang | FEM analysis of the temperature and stress distribution in spark plasma sintering[END_REF][START_REF] Cincotti | Modeling of SPS apparatus: temperature, current and strain distribution with no powders[END_REF], but is difficult to implement in the mode! due to the presence of parameters like the lateral pressure or the specific sur face area of the contact that cannot be determined experimentally. Thus, they are usually evaluated empirically and are only valid for a specific machine, configuration, or material. A formulation developed with a certain configuration of the SPS apparatus are usually not transposable to another machine or material. Therefore, the objective of this study is to develop a simple approach based on an optimization algorithm to determine the ECR and TCR of an SPS apparatus. With this method, an accurate electrothermal mode! of the sintering of a material by SPS can be obtained with only one experimental trial. Furthermore, the contact resistances numerically identified can then be used for any complex configuration provided that the same tooling (die and punches) and experimental conditions (pressure and heating rate) are employed. The benefits of this method are its ease of use as well as its versatility in terms of materials, which are not only limited to ceramics. To validate the mode! and demonstrate its feasibility, it is first calibrated on three different configurations of alumina samples and one titanium aluminide pellet. Then, the contact resistances optimized on simple pellets are tested on more complex bi-material configurations to show the effi ciency of the approach. https:/ / doi.org/10.1 O 16/j .j eurceramsoc. 2020. 08. 073

Materials and methods

Ail the sintering experiments were performed on the SPS machine Dr. Sinter 2080 (Japan) located at the Plateforme Nationale CNRS de Frit tage Flash (University of Toulouse III -Paul Sabatier).

The graphite used for the dies, spacers and punches was provided by Toyo Tanso©. For ail experiments, a 200 µm graphite foil (PERMA FOIL®Toyo Tanso) was placed to cover the inside wall of the die, as well as at the interfaces between the punches/sample and spacers/electrodes. A graphite felt is placed ail around the outside wall of the die to mini mize the heat loss during the experiment. The two different materials used, were one ultra-pure alumina (99.9 %, spray-dried granulates with an average crystallite size of 150 nm and a mean granulate size of 35 µm, from Nanoe) and a titanium aluminide powder (Ti-4822-9, with an average grain size of 75.4 µm, from Praxair).

Two different sets of experiments were performed in this work. The first one is conducted to calibrate the thermo-electrical model and the second one to test its efficiency on more complex configurations. The first set of experiments consists in the sintering of 3 mm thick pellets of alumina and TiAl inside dies of different diameters (i.e. 8, 20 and 36 mm). The different setups are illustrated Fig. 1. For the 8 mm setup, T shaped punches were used for the stability of the assembly. The second set of experiment, on which the model will be tested consists in three different configurations illustrated Fig. 2. The first configuration con sists in the sintering of a bi-material pellet composed of a pre-sintered alumina pellet on top of a TiAl powder. For the three configurations, the alumina part was pressed and then sintered at 1000 °C for 1 h in a Nabertherm© oven up to a 50 % density. The goal ofthis step is to pre sintered the alumina so that it acquires a minimal mechanical strength. This allows its manipulation and facilitates the setting up of the bi material samples. The second set-up is composed of a 15 mm diameter TiAl pellet (in powder form) enclosed in a pre-sintered alumina part (which is composed of two pieces as illustrated Fig. 2b). The last configuration is a TiAl star-shaped object placed under an alumina counter-part. This set-up relies on the patented sintering technique developed in the work of C.Manière et al. [START_REF] Manière | Spark plasma sintering and complex shapes: the deforrned interfaces approach[END_REF] that allows the fabrica tion of complex shapes by SPS. The counter-part is first pressed in a 36 mm die with a suitable punch and then pre-sintered. The TiAl powder is then introduced in the counter-part and the whole assembly is then sintered.

For ail configurations, the current delivered by the SPS generator, during ail the thermal cycle is acquired by the SPS machine. It is

(a) 20nun l 11 ,,;a 0 i---\ -: • -_ -- 80mm (b) 20mm
important to note that the current measured by the SPS machine cor responds to the average value of the current. The actual current responsible for Joule heating of the apparatus corresponds to the root mean squared (rms) value of the current [START_REF] Cincotti | Modeling of SPS apparatus: temperature, current and strain distribution with no powders[END_REF][START_REF] Pavia | Electro-thermal measurements and finite element method simulations of a spark plasma sintering device[END_REF]. To switch from the average to the rms value of the current the same corrective factor as A. Pavia et al. [START_REF] Pavia | Electro-thermal measurements and finite element method simulations of a spark plasma sintering device[END_REF] was used since it was determined on the same SPS machine. For the experimental validation, the choice bas been made to work with the current and not the voltage, since the SPS machine used in this study is a current generator and not a voltage generator. A previous study of the machine has showed that a precise current measurement is easier [START_REF] Pavia | Electro-thermal measurements and finite element method simulations of a spark plasma sintering device[END_REF]. However, depending on the machine, in some cases it is better to work with the voltage instead of the current [START_REF] Gucci | Refined SPS Modeling Based on Calibrated Current and Voltage Measurements[END_REF].

For the first set of experiments, the temperature was measured at three different locations in the die (as illustrated Fig. 3 (a)) with K thermocouples. One is placed in a hole located in the outside wall of the die (1.5 mm in diameter and 3 mm in depth) to measure the control temperature, which is used by the SPS machine for the current regula tion. For each configuration, the two other thermocouples are placed inside the powder sample. One in the middle and one located 1 mm away from the inside wall of the die (Fig. 3 (b) and (c)), through holes drilled across the die walls. The three thermocouples are placed 120 ° away from each other, as showed Fig. 3 (a). These two measurements are used to fit the thermo-electrical model.

For the second set of experiments, besides the control temperature being measured in the die (like the previous one), the temperature was also measured in the TiAl powder and the pre-sintered alumina. For the bi-material pellet, the temperature was measured at the center of each pellet (Fig. 3 (d)). For the TiAl pellet enclosed in the alumina, the temperature was measured in the center of the TiAl and 5 mm away from the inside wall of the die (Fig. 3 (e)). For the last configuration the temperature was taken in the middle of the star-shaped TiAl and 3 mm away from the inside wall of the die (Fig. 3 (f)).

For each experiment, the pressure is applied linearly from O to 25 MPa in 3 min. The higher the applied pressure is, the lower the contact resistance is. However, since holes were drilled across the die wall, an important pressure is more likely to break it. Then, the pressure is held for the rest of the experiment. For the calibration trials, after the pres sure build-up, the setpoint temperature (measured on the die outside wall) is set to increase at a rate of 100 °C/min from room temperature up to 1200 °c, the thermocouple upper use limit. For the three complex configurations, the pressure was linearly applied during the first five minutes of temperature rise. Ail experiments where stopped whenever one of the thermocouples used as reached the 1200 °C. The regulation of the set-point temperature is obtained through PID regulation on the root mean square of the current delivered during the SPS experiment [START_REF] Manière | Proportional integral derivative, modeling and ways of stabilization for the spark plasma sintering process[END_REF]. Thanks to a good PID regulation, the measured temperature (as well as the calculated one) accurately follows the set-point temperature. Thus, to facilitate easy reading of the results, the temperature of the outside wall of the die will not be showed in the results.

22,5mm

Theory/calculation

All the computational work was done on Comsol Multiphysics© software. The SPS process was modeled using a finite element analysis considering only the thermal and electrical aspects of the process. The model used for the FEM calculations is 2D-axisymetric and the geometry was treated as a union. For each simulation, in addition to the materials parameters, the input variable is the setpoint temperature taken on the outside wall of the die (heating ramp oflO0 °C/min up to 1200 °C) while the output parameters are the Current and Temperatures (at the border and center of the sample). Even though powder was used for the ex periments, the sintering aspect of the process was neglected. A pre liminary unpublished study has showed that the creep and sintering considerations have a very limited effect on the calculated temperature and current (only a difference of less than 1 o/o is introduced).

Thenno-electrical simulation

During the SPS, most of the heat is generated by Joule heating when the current flows through the colurnn. The constitutive thermal and electrical equations, as well as their coupling, has been widely studied in the literature [START_REF] Orrù | Consolidation/synthesis of materials by electric current activated/assisted sintering[END_REF][START_REF] Anselmi-Tamburini | Fundamental investigations on the spark plasma sintering/synthesis process: Il. Modeling of current and temperature distributions[END_REF]. The general heat equation applied to a volume V with a surface S can be written as follow:

Where p is the density, C p the specific heat, T the temperature and k the thermal conductivity. This equation is usually paired with the charge conservation equation [START_REF] Anselmi-Tamburini | Fundamental investigations on the spark plasma sintering/synthesis process: Il. Modeling of current and temperature distributions[END_REF]:

'ï!J =0 (2)
The coupling between the thermal and the electrical aspect of the problem is achieved by the second term on the right-hand side ofEq. (1), which describes Joule heating. It depends on the electrical field Ê and the current density J as follow:

qe = Ê.J (3)
The boundary conditions are contained in the last term ofEq. [START_REF] Grassa | Electric current activated/assisted sintering (ECAS): a review of patents 1906-2008[END_REF]. q,, CÏ conv • CÏ r et ci e , are respectively the thermal conduction, convection and radiation and the heat transfer induced by imperfect contacts between the bodies of the SPS column. The last one will be developed later in this paper. The heat is radiated to the surroundings from the surface of each component, whereas the cooling of the two electrodes is obtained by convection using a water cooling circuit:

(4)
Where cr, is the Stefan-Boltzman constant, e the emissivity and hc the convection coefficient. Te is the emission surface temperature, Ta the chamber temperature, T 5 the electrode surface temperature and T w the water cooling temperature.

The convection coefficient is set at 200 W/(m 2 .K) and the emissivity of the electrodes, the graphite tooling and the graphite felt are 0.71, 0.8 and 0.3 respectively [START_REF] Manière | Spark plasma sintering : couplage entre les approches modélisation[END_REF]. The electrical and thermal properties of graphite, Inconel, alumina and TiAI used in the simulation of the process are summed up in Table 1 [START_REF] Manière | Finite element modeling of the electro-thermal contacts in the spark plasma sintering process[END_REF]. The porosity dependence of the prop erties for the alumina and titanium aluminide was the same as in the work of R.Orrù et al. [START_REF] Orrù | Consolidation/synthesis of materials by electric current activated/assisted sintering[END_REF]. As a first approximation the porosity was assumed constant and equal to the compacted bulk density of the powders, which are 50 % for the alumina and 65 % for the titanium aluminide. Furthermore, it is important to note that compared to bulk graphite, which is isotropie [START_REF] Tanso | Isotropie Graphite[END_REF], the electrical and thermal conductivity of the graphite foi! are respectively about 40 and 140 times superior parallel to the surface according to the producer Toyo Tanso©.

Theory on contact resistances

Thermal and electrical contact resistances (TCR and ECR respec tively ), are induced by imperfect contacts between two interfaces. In an ideal situation, when two objects are in contact, the current can flow freely through the interface from one element to the other. Thus, there is neither current nor temperature discontinuities at the interface. How ever, in a real contact, only a fraction of the surface allows the current flow due to surface asperities. This is called the specific surface area. It leads to a discontinuity of the electrical potential and the temperature. Though, it is easier to work with the expression of the electric and thermal fluxes at the interface since it is difficult to experimentally determine the specific surface area.

{ f = OE g (V1 -V2) IÎc = h 8 (T1 -T2) (5)
Where OE g and hg are the electrical and thermal contact conductance, and Vx and Tx are the electrical potential and the temperature on both sides (x = 1 & 2) of the interface.

kg-'. r')

m- All the contact resistances that were considered in the mode! are summed up in Fig. 4. For all the horizontal contacts: electrode/spacer, spacer/spacer, spacer/punch and punch/sample, the values of the electrical and thermal resistances used were the ones developed by C. Manière et al. [START_REF] Manière | Contact resistances in spark plasma sintering: from in-situ and ex-situ determinations to an extended mode! for the scale up of the process[END_REF]. However, it has been showed that the impact of the contact resistances on the final electrothermal simulation is negligible at high pressures (>10 MPa) [START_REF] Anselmi-Tamburini | Fundamental investigations on the spark plasma sintering/synthesis process: Il. Modeling of current and temperature distributions[END_REF][START_REF] Diatta | Numerical modeling of spark plasma sintering-Discussion ondensification[END_REF]. Thus, even if it does not fully correspond to the actual values of the resistances, it would only have a negligible impact on the outcome of the simulation.

The crucial parameters in the thermo-electrical mode! are therefore, the vertical TCR and ECR punch/die and sample/die. The graphite foi! placed on the inside wall of the die greatly influences the electro-thermal behavior of the SPS column. A great amount of current flows through it which leads to a localized heating of the foi! due to the TCR between the graphite foi! and the die, punches and sample [START_REF] Manière | Finite element modeling of the electro-thermal contacts in the spark plasma sintering process[END_REF]. Thus, the contact resistances were considered on both side of the graphite foi!. Those re sistances, directly linked to the pressure between the two objects in contact, are very difficult to evaluate experimentally. However, vertical contact resistances in the SPS have been studied in the literature. First, they were considered as constants with temperature and pressure [START_REF] Zavaliangos | Temperature evolution during field activated sintering[END_REF][START_REF] Achenani | Finite element modeling of spark plasma sintering: application to the reduction of temperature inhomogeneities, case of alumina[END_REF]. However, the contact pressure varies over the SPS trial as the temper ature increases and thus as the materials creep. Then, a temperature and pressure dependence were introduced in the expression of the ECR and the TCR [START_REF] Wang | FEM analysis of the temperature and stress distribution in spark plasma sintering[END_REF][START_REF] Cincotti | Modeling of SPS apparatus: temperature, current and strain distribution with no powders[END_REF]. However, most of the time those expressions are difficult to implement in the mode! due to the presence of unknown parameters that cannot be determined experimentally. Thus, the ex pressions of the ECR and TCR can be determined empirically while keeping a temperature dependence [START_REF] Wei | Experimental investigation of electric contact resistance in spark plasma sintering tooling setup[END_REF][START_REF] Manière | Pulse analysis and electric contact measurements in spark plasma sintering[END_REF]. Nevertheless, those ex pressions only correspond to a specific SPS configuration or material. To have a good grasp on the issue, the evolution of the current and tem peratures in alumina samples with sizes of 8, 20 and 36 mm was modelled using the ECR and TCR determined by C. Manière et al. [START_REF] Manière | Contact resistances in spark plasma sintering: from in-situ and ex-situ determinations to an extended mode! for the scale up of the process[END_REF]:

{ ECRpunch/die (O.m 2 ) = dpap(l, 7(.10-3 -9 � : � � 0 � 7 :))Fe TCRpunch/die (m 2 .K/W) =d pap 80+50 T-SO Fr (6)
Where dp ap is the thickness of the graphite foi!, and F, and Fr are dimension dependent factors. Fig. 5, Fig. 6, Fig. 7 illustrate the difference between the experi mental and calculated data. In their work those resistances where also determined with alumina samples and on the same machine used for this study. However, C. Manière et al. [START_REF] Manière | Contact resistances in spark plasma sintering: from in-situ and ex-situ determinations to an extended mode! for the scale up of the process[END_REF] work was performed on samples sizes of 10, 20 and 30 mm in diameter, with homothetic dies configu rations, which is not the case in the present study.

Detennination of the ECR and TCR

The significant difference with the experimental data shows that the expression developed by C. Manière et al. [START_REF] Manière | Contact resistances in spark plasma sintering: from in-situ and ex-situ determinations to an extended mode! for the scale up of the process[END_REF] only corresponds to a certain type of configuration, specific to a die, spacer, punch and sample size. Since a general formulation for the contact resistance has not been found yet, it is important to develop an effective way to determine the vertical ECR and TCR in any configuration.

Looking at the expressions of the TCR and ECR Eq. ( 6), it appears that they are both decreasing function with temperature. However, the ECR is a linear function, which is an issue above 1500 °c because the resis tance becomes negative. For the scope of this study, a new form of the TCR and ECR was introduced. For both expressions, a decreasing exponential fonction was chosen as follow:

{ ECR � Q.m 2 )
= a e exp(b e .T) TCR (m .K/W) = arexp(br.T) [START_REF] Munir | Electric current activation of sintering: a review of the pulsed electric current sintering process[END_REF] The a,,, b e , ar and br are parameters to be determined and ECR and TCR are strictly positive. The benefit of this expression is that given the right couple of parameters a and b, it can approximate the two types of fonction seen previously, as illustrated Fig. 8.

First, only the sample of alumina is considered. Due to its low elec trical conductivity it is assumed that no current flows between the graphite and the sample. Thus, only the ECR punch/die, and the TCR punch/die and sample/die need to be determined, which means there are six parameters to be found. A Nelder-Mead algorithm with bounded variables was used to calculate those six parameters [START_REF] Nelder | A simplex method for fonction minimization[END_REF][START_REF] Luersen | Globalized nelder-mead method for engineering optimization[END_REF]. This al gorithm is used to minimize a least square fonction, which compares the calculated values to the experimental ones. The data used for the opti mization are the evolutions of the current and the temperatures at the center and the border of the sample. The initial guess for the parameters, required by the algorithm, was chosen according to the approximated values found in the literature [START_REF] Manière | Contact resistances in spark plasma sintering: from in-situ and ex-situ determinations to an extended mode! for the scale up of the process[END_REF]. Then, the ECR punch/die is

Results and discussion

The end goal of this study is to obtain an accurate thermo-electrical model of the sintering of complex shapes by SPS. The principle of the method developed in this work is to optimize the ECR and TCR on simple shapes (that requires few experimental tests). This needs to be done on both materials that are used in the complex shapes configuration, because the ECR and TCR might differ from one material to another. Then, the optimized ECR and TCR are used to predict the thermo electrical behavior of complex shape configurations. For example, with only one experimental trial on a 36 mm alumina pellet and one on a 36 mm titanium aluminide pellet, it is possible to obtain an accurate electrothermal model of any complex configuration using the same materials, configuration (with identical die, punches and spacer sizes) and experimental conditions (pressure, heating rate).

Calibration results for the alumina samples

The comparison between the experimental and the calculated values of the current and the temperatures with the new expression of the ECR and TCR are plotted Fig. 9, Fig. 10, Fig. 11. The experimental and calculated voltage was also added in Fig. 9 but to facilitate easy reading of the results, only the current will be shown for the rest of the study. In the same way as the current, the calculated voltage was obtained using a corrective factor determined by A. Pa via et al. [START_REF] Pavia | Electro-thermal measurements and finite element method simulations of a spark plasma sintering device[END_REF]. This factor allows to model the actual voltage measured outside the power source by the SPS machine. The experimental measurements show that the 20 mm alumina sample reach a lower temperature than the two other config urations. This could be due to the ratio internai diameter/thickness of • 600 700

the die that is not homothetic compared to the two other configurations.

For ail three configurations (diameters of 8, 20 and 36 mm), there is a good agreement with the experimental value, which is much better than the one showed in Fig. 5, Fig. 6 and Fig. 7. The evolution of the current, the voltage and the border temperature are well simulated by the mode!.

As for the temperature in the middle of the samples, the mode! is a bit Jess effective, but the results are still acceptable and give a good approximation of the experimental values. This shows the efficiency of this method thanks to its dual identification through both current and temperature. Thus, only one experiment is needed to assess the contact resistance, and therefore the thermo-electrical behavior of the SPS apparatus.

To make sure the Nelder-Mead algorithm converged to an adequate solution, a mapping of the error with the experimental current values was plotted for the different (a e , b e ) couples the algorithm explored. The mapping was also completed with a Monte-Carlo algorithm, which calculated the same error but chose random (a., b e ) couples within the bounds fixed. Fig. 12 shows that the algorithm converged to the best solution within the bounds. The evolution of the ECR punch/ die and TCR punch/ die and sample/ die are plotted in Fig. 13. The fact that there is no obvious relationship between the parameters can be explained by the non-homothetic rela tion between the three configurations. If the expressions here only depend on the temperature, the influence of the pressure and the specific surface area is implicitly contained in those equations. If the uniaxial pressure is identical for the three configurations, the lateral pressure on the die differs, and thus the contact resistances are different.

Calibration results with the TiAl samples

The contact resistance assesses the ability of an interface to let the current flow or conduct temperature. Hence, the ECR and TCR punch/ die will be considered as identical for an alumina sample and a TiAI one. Actually, there could be a slight difference since the two sample do not have the same dilation coefficient. The TiAl tend to apply a higher pressure on the die due to its higher dilation coefficient. Thus, the lateral pressure at the interface between the punch and the die could be slightly lower with a TiAI sample, but this effect is neglected in this work.

For the alumina sample, the ECR sample/die was neglected because of its insolating properties. This assumption is no more valid for a conductive sample like a TiAl powder. The same optimization strategy was used to determine the ECR and TCR sample/die (the ECR and TCR punch/die were the one identified with the alumina sample). Fig. 14 shows the comparison between the experimental and calculated values of the current flow and the temperature at the center and the border of the TiAI sample with the optimized ECR and TCR. The evolution of the current and the border temperature can be well approximated by the mode!. As for the center temperature, the experimental values show a fast increase in the temperature range of 500-750 °C. One explanation could be the percolation of the TiAI powder which makes the thermal conductivity of the sample suddenly increase. Thus, one way to improve the mode! would be to consider the effect of the porosity evolution on the materials properties. However, even if the simulation is not able to replicate this phenomenon, the agreement with the experimental values is still acceptable. Testing the mode! on complex shapes One of the objectives of this study is the identification of the ECR and TCR for both alumina and TiAI in order to be able to predict the thermo electrical behavior of the sintering of complex shapes by SPS. The un known here is the contact resistance at the interface between the alumina and the TiAI. However, the ECR alumina/TiAI can be neglected due to the insulating aspect of alumina. Also, as mentioned before, the horizontal ECR and TCR have a limited impact on the final calculations of the mode!. Thus, for the rest of the study, the ECR alumina/TiAI will be neglected and the TCR alumina/TiAI will have the same order of magnitude has the punch/sample TCR. Fig. 15, Fig. 16, Fig. 17 show the evolution of current and temper atures for the three complex configurations. The temperatures calcula tions are in a good agreement with the experimental data, but it appears that there is a slight gap between the calculated and experimental current values. This gap might be explained by the pressure application method. For the calibration experiments, the uniaxial pressure was applied before the increase in temperature whereas for the three com plex configurations the pressure was applied during the first five mi nutes of temperature rise. It appears that it can significantly affect the evolution of the current during the SPS trial. Moreover, the creep of the different materials involved can affect the lateral pressure and thus the contact resistances. The pressure dependence of the contact resistances was not considered in this study, but it is implicitly contained in the expressions of the ECR and TCR. Thus, those expressions are only valid for a specific set of experimental conditions (pressure, heating rate, tooling size, etc.), and a change in those conditions would require further experimental trials. In addition, aging and wear of the tooling (which were not considered in this work) could also affect the interface Û 1200 � 1000 _ § 800

Conclusions and future work

A new expression of the vertical ECR and TCR of the SPS column was developed. The contact resistances were obtained using an optimization algorithm, which allows the identification of unknown parameters by fitting experimental curves. The main benefit of this approach is that it requires only one instrumented experiment per configuration and ma terial. The calibration on different die sizes (8, 20 and 36 mm) led to a good simulation of the evolution of the current and sample temperature for both alumina and TiAI. Thus, this method can be used on any ma terial, and is not restricted to ceramics. The new expressions of the contact resistances were then tested on more complex configurations. In terms of temperature calculations, the mode! can accurately predict the thermal evolution of the TiAI and alumina parts for ail three configu rations. It shows the efficiency of this method, which allows to have a robust simulation from only two trials (one for the TiAI and one for the alumina).

The main benefit of this approach is that an accurate simulation of the electro-thermal behavior of the spark plasma sintering of different complex shapes can be obtained with a very limited number of experi ments on simple configurations. Thus, for a given complex shape (with a given diameter), only two instrumented experiments on simple shapes (pellets) with the same diameter are necessary. One with the material of the desired part and the other with the material of the counter-part. The ECR and TCR are then optimized and implemented in the final mode!.

However, if the temperatures calculated by the mode! reflect well the experimental data, there is a slight gap between the calculated and experimental current. This gap can be explained by the pressure appli cation mode. A progressive applied pressure can modify the current density in the SPS column, and thus the contact resistances. Therefore, it shows that the pressure has a significant role in the determination of the contact resistances. However, it is possible to determine the contact pressure with the finite element analysis. The next step is then to implement the pressure dependence in the contact resistance expres sions, through the realization of experiments at different pressures. The contact pressure dependence of the ECR and TCR can then lead to equations working for any SPS configuration.

Fig. 1 .

 1 Fig. 1. Cross section of the three calibration configurations of the SPS column with die sizes of (a) 8 mm, (b) 20 mm and (c) 36 mm.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Cross section of the three complex configuration -(a) bi-material alumina/TiAI pellet, (b) TiAl pellet encapsulated in alumina and (c) TiAl star-shaped object with an alumina counter-part.

Fig. 4 .

 4 Fig. 4. Location of the contact resistances along the SPS column.

  Current de!ivered tlu:ough the SPS co!umn -36mm alumina sample --C.Manière et al. 700 600 Fi g . S. Evolution of the current through the SPS column for 8 mm (a), 20 mm (b) and 36 mm (c) diameter alumina samples.Center temperature of the 8mm alumina sample -CJ,1anière et al.

Fi g . 6 .

 6 Evolution of the temperature at the center of alumina pellets with a 8 mm (a), 20 mm (b) and 36 mm (c) diameter.

Fig. 7 .

 7 Fig. 7. Evolution of the temperature 1 mm away from the side of alumina pellets with a 8 mm (a), 20 mm (b) and 36 mm (c) diameter.

Example ofTCR obtained with the new fonnulation 2 5 2000Fig. 8 .

 258 Fig. 8. Illustration of the different functions that can be obtained with the new formulation of contact resistance.

( a )■Fig. 9 .Fig. 10 .

 a910 Fig. 9. Evolution of the voltage and the current through the SPS column for 8 mm (a), 20 mm (b) and 36 mm (c) die sizes.

Fig. 11 .

 11 Fig. 11. Temperature 1 mm away from the border of alumina samples with a size of 8 mm (a), 20 mm (b) and 36 mm (c).

5 ae

 5 Cumulated error on the experimental current -7.5 -7.0 -6.5 -6.0 -5.5 -5.0 -4.

Fig. 12 .

 12 Fig. 12. Illustration of the cumulated error between the experimental and calculated values for several aefb e couples.

  606

Fig. 13 .

 13 Fig. 13. Evolution of the TCR punch/die, sample/die and the ECR punch/die for different sizes of alumina samples.

Fig. 14 .

 14 Fig. 14. Evolution of the temperature at the center (a), the border (b) and the current (c) of the sintering of a 36 mm TiAI pellet.

Fig. 17 .

 17 Fig. 17. Evolution of the temperature of the TiAl star-shaped object (a) and the alumina counter-part (b) and the current (c) through the SPS column for the star shaped object configuration.

Table 1 Physical properties of inconel, graphite, alumina and TiAI.

 1

	Material	Heat capacity (J.	Thermal conductivity (W.	Electrical resistivity (Q.m)	Density (kg. m-3 )

Acknowledgements

The SPS experiments were performed at the Plateforme Nationale CNRS de Frittage-Flash (PNF2/CNRS Toulouse). This work was sup ported by the Association Nationale Recherche Technologie (ANRT) as part of the CIFRE (Industrial Agreement of Formation by Research) contract 11 °2017 /1026; and the Programme Opérationnel FEDER-FSE Midi-Pyrénées et Garonne 2014-2020 as part of the CERAPRINT proj ect 11 °17014462.

Declarations of Competing Interest

None.

and thus the contact resistances. To improve the model, further inves tigation has to be done to extrapolate the pressure influence on the contact resistances.

However, it appears that using the ECR and TCR calculated previ ously with the alumina and TiAI pellets give a pretty accurate evolution of the thermo-electrical behavior of the SPS experiments with complex configurations. It also shows that the expressions of the ECR and TCR are robust with different configurations. With only two experiments, it is possible to predict accurately predict the evolution of the current and temperature for multiple configurations.