PhD) Manager, RCU, PASET-RSIF, ICIPE Osiru Moses

Everlyn Nguku

ICIPE Paset-Rsif

ICIPE Oremo Paset-Rsif

Caroline

Icipe Tambo

Erick Gankam

Cheo Ambe

Koli Margaret

Garnier Esthere

Giraud Grégory

Brulé Gaëlle

Mainguy Gaell

Type: One organisation ☐ | Alliance ⌧ 'PHD PROGRAMS IN AFRICA: THE ARROWS, THE TARGETS AND THE ARCHERS'

The research ecosystem in sub-Saharan Africa is changing. Organised around new centres of scientific excellence, the sub-continent is building a research agenda aimed toward major development challenges and the achievement of the sustainable development goals. Thus, strengthening doctoral programs and their beneficiaries becomes crucial in supporting this transformation. However, great challenges remain in the designing and implementation of impactful scholarship programs to accompany the creation of African scientific communities of excellence. Stakeholders suffer from a lack of investment in research infrastructure and its operators as well as the absence of sufficient qualified supervisory staff. An increase in the student population and heavy dependence on international partnerships accentuates these challenges. In this context, five doctoral support programs operators in sub-Saharan Africa (ICIPE, IRD, LPI and UNU) offer an inventory of the challenges associated with regional doctoral support. We offer a field vision, based on experience supporting over 1,500 doctoral students in Sub-Saharan Africa. We propose an approach that addresses SDG 4 -Quality Education and 9 -Industry, Innovation and Infrastructures (mainly objectives 4.b and 9.5) and demonstrate how these programs have become vectors in building sustainable solutions to development challenges in Africa. This proposal aims to draw up the archetype of an impactful regional doctoral program in Sub-Saharan African that also ensures the well-being of the students involved.

Introduction

Sub-Saharan Africa is increasing its scientific production and its investment in higher education. The subcontinent's scientific production (number of published articles) doubled its contribution to the world scientific research from 0.44% to 0.72% during 2003-2012 1 , regional investment in research and development as a share of GDP is increasing 2 , the African student population is booming, notably within its doctoral student's body (3% of the world population of doctoral students) [START_REF] Bernard | CAMPUS France : Les doctorants à l'international : Tendances de la mobilité doctorale en France et dans le monde[END_REF] . Public decision-makers and socio-economic actors are becoming aware of the role that science and innovation have in the development of the continent's human capital. The support of a competent workforce through Higher Education is key to meeting the continent's major development challenges and to achieving sustainable development goals. In this context, funding doctoral programs is crucial to the strengthening of a critical mass of qualified academic and specialised staff. Highly qualified individuals are fundamental to meet the demands of the socio-economic sector, reducing brain drain and strengthening the pan-African scientific pools of excellence.

It is fundamental for Africa to increase PhD programs on the continent and to continue to engage in partnerships that increase the number of PhD holders in Africa (Kigali Communique, 2014 4 ). SDG 4, especially indicator 4.b emphasises this objective 5 . International funding flows for scholarships in Sub-Saharan Africa have increased by 120% between 2010 and 2019 6 . SDG indicator 9.5 calls states to encourage innovation and substantially increase the number of researchers 7 . Globally, the number of researchers per million inhabitants stands at 1,198 (in 2017). Europe & Northern America have an above world average with 3,707 researchers per million inhabitants, while it is as low as 99 in sub-Saharan Africa 8 .

Volume of official development assistance flows for scholarships by sector and type of study, constant USD in Sub-Saharan Africa 9

Although many African countries have regulated and enhanced doctoral training, the quality and support of PhD programs in sub-Saharan Africa remains challenging. African research infrastructures stay underfunded, many qualified staff migrate and student flow is increasing 10 . African research is dependent on international collaboration and funding, few pan-African scientific networks of excellence exist, and collaborations with industrial partners are rare and sometimes challenging. Meanwhile, the PhD holds the key to the creation of a highly-skilled workforce that will contribute to the knowledge economy. Strengthening PhD programs and students through African universities and innovative international cooperation will enhance educational standards and research capacity, as a lever of innovation for development.

Distribution of tertiary education scholarships for sub-Saharan

The arrows: a focus on PhD students

In 2020, contributors to this note were responsible for 471 PhD students 12 , and 1,507 since their creation 13 . PhD students are the future of African research 14 . Their well-being and capacity building are integral to the mission of doctoral program designers.

PhD students well-being

Doing a PhD is a stimulating, but also a challenging and stressful experience. Many stress factors affect PhD students: research project elaboration, integration in a research environment and into various networks, relationships with the supervisor(s) and with peers, growing competition, the quest for funding, scientific writing, solitude, lack of self-confidence, precariousness, uncertain future, cultural background, education system, mobility in a new environment etc. These factors directly affect the thesis quality and the way that stakeholders deal with them determine the impact of such experiences.

PhD programs may offer a professional and financial environment adapted to the needs of a doctoral thesis. Gratification mechanisms generally provide a living allowance or grant, and a series of services to scholarship holders, such as insurance, reimbursement of registration fees, etc. Determining the adapted student's allowance is key to achieving the right balance between student well-being and its insertion in its research environment. These amounts must be regularly revised to consider inflation and the local ecosystem. A PhD student should not be gratified more than a local early career researcher. Programs must also adapt to tuition funding. We observe a general rise in tuition and great differences between thematic and universities.

The difference in the cost of living between countries of intervention and Northern countries represents a challenge for South/North mobility. Gratification models need to adapt, but sometimes-poorly cover transition periods (new housing, initial purchases, etc.). Third parties, such as supervisors, family or friends must sometimes intervene to make up for the income gap.

In many African countries, gender gaps exist when it comes to women's enrolment and completion of PhD studies. This subsequently affects recruitment into university teaching and research positions. On average, women comprise 30% of Africa's researchers 15 . Female student well-being can be addressed through a gender-inclusive framework, especially for engagement of women researchers and paying attention to their specific needs. This has implications for successful completion rates and eliminating gender disparities in higher education and beyond.

PhD students' skills and capacity building

The most in-demand skills are creativity, persuasion, collaboration, adaptability and emotional intelligence 16 . These skills are completely interdisciplinary. Many students at African universities are technically strong in their own subject matter areas, but struggle to compete in work environments. Soft skills and transversal skills such as scientific communication, research methods, scientific paper writing, monitoring/evaluation and grant writing, are critical for career growth. The delivery of such skills emphasises a combined approach with research skills for PhD researchers to practically apply e.g. through entrepreneurship, consulting, the opportunity for supervision, teaching or potentially leading their own projects. More and more, these skills are accessible through online courses (MOOC, SPOC).

Higher education internationalisation (and the Covid 19 pandemics) forces African actors to develop new tools for collaboration. Reliant on digital technology, they remain used in a heterogeneous way and sometimes create inequalities of use in academic populations. As a result, access to the Internet is essential, yet it remains expensive and low quality in a majority of African universities. Moreover, the pandemic has shown that physical interaction, travel and access to funds may be curtailed. In future, PhD programs may face challenges with limited opportunities for on-ground/physical data collection because of pandemics and political unrest.

Like many arrows launched simultaneously by an archer, thousands of African doctoral students are launched towards doctorate degrees. As we just saw, equipping them with skills and ensuring their well-being will allow them to go far in their careers. Evidently, these doctoral students each have an individual path, a history, and free will. Still, where are these arrows headed?

The multiple targets of PhD programs

Doctoral programs aim at different targets. Firstly, the employability of doctoral students so that they can integrate into the job market once they have obtained their degree, either in the academic, entrepreneurial, private, public or NGO sectors remains a priority. Secondly, they aim to respond, through their scientific production, to the challenges of sustainable development (SDGs). opportunity and education backlogs. Until the turn of the century, primary education funding was favoured above higher education. This approach contributed to the decrease of high-level human capital training, and the erosion of research infrastructures. Little data exists on the destinations and employment characteristics of international African doctoral graduates after completion of their studies, especially in the poorest countries. Although, employment remains at the heart of doctoral students' preoccupations.

Strengthening the relations between research programs and the associated socio-economic sector, through events, workshops, summer schools, thesis committees or thesis subject cocreation is crucial. Alumni networks are emerging with a range of services, job offers, postdoctoral fellowships, training, networking, etc. involving socio-economic partners. Post PhD progression framework can be designed for example in collaboration with industry, funders, civil society, innovators and beyond.

Entrepreneurial momentum is rising amongst the PhD students. Empirical observations within the doctoral population suggest that the creation of start-ups based on doctoral work is now a valid alternative to employment in academia or industry. Entrepreneurship can contribute to local ownership and wider utilisation of research outputs and technology acquisition.

Sustainable development, SDGs and interdisciplinarity

The problem-solving approach is critical to the PhD program conceptualisation. There is a need to ensure that research directly responds to the needs of African communities and impacts on development. Borrowing and adapting existing technology to the specific needs of the continent will support leapfrogging 18 .

But how can we concretely nurture interdisciplinarity? This is addressed by various mechanisms: firstly, by selecting priority areas for the program to focus on that are aligned to the needs of the continent; secondly developing cooperation between institutions with different research focus coming together for cooperation; thirdly, creating an environment and events behind interdisciplinary programs. Those events -intercultural and intersectoral-can be workshops or summer schools 19 that build capacities through innovative andragogical approaches. They focus on capacity building knowledge objectives, such as being able to: ➢ Focus on an important scientific question and to define the means to approach it from different disciplines; ➢ Zoom out (have a broader view) and zoom in (be precise and define the key experiments); ➢ Think and express ideas more clearly; Employability and the SDGs can be two different targets. How can we achieve several targets at the same time? We must ensure the employability of graduates in a job market that does not always care about the major issues of sustainable development. This represents an important challenge that must be addressed by doctoral programs. Our challenge is to align these targets so that an arrow can hit them both.

The archer: a stable and solid framework

Symbolically, the archer is the one who selects and launches the arrow. He/she must therefore implement all the measures to make the doctorate a success. This includes the general doctoral regulation framework, the doctoral supervision and the way the doctoral program is designed.

In partnership with multilateral organisations (European Union, World Bank…), the African Union is promoting a new framework for research and innovation policy. The Science, Technology and Innovation Strategy for Africa (STISA-202420 ) aims to mobilise African research toward the wellbeing and improved quality of life of African citizens as articulated in the African Union Agenda 206321 . Despite this general framework, regional doctoral fellowship programs tend to be limited in comparison to those promoting North/South collaboration. Doctoral programs are dependent on strong and reliable postgraduate education. It is expected that poor graduate programs within African Universities will lead to poor doctoral programs. These challenges force African academia to respond more directly to the needs of the socioeconomic sector. To reach this goal, a multi-actor research program (ideally involving public, private and civil society actors) can partly answer that question. In practice, including actors outside of academia within the PhD experience faces many challenges. Few mechanisms exist in Sub-Saharan Africa toward the facilitation and the co-construction of thesis programs between academic actors and industrial actors (CIFRE fellowship in France for example). In general, the academic and industrial worlds tend to evolve apart from each other. Incentive programs are being developed to break academia/industry silos, aiming at changing the ways researchers do research and encouraging economic actors to mobilise local expertise (ex: FONSTI in Côte d'Ivoire…).

PhD mentoring: thesis supervision

PhD mentoring is challenging in two ways: the lack of critical mass among staff able to supervise doctoral students and the supervision quality. Regarding the first point, some supervisors will mentor a large number of students, which will have a direct impact on the quality of supervision. Some thesis scholarship programs reward supervision, some do not. This question remains open and may have consequences on the number of students by supervisor. What happens when a supervisor mentors five, six or more PhD students? How viable is this situation, regarding the availability of supervisors for students? This challenge is most prevalent in interdisciplinary thesis subjects. In this case, supervisors are about twice as many because the interdisciplinary nature demands double supervision of theses for the sharing of experience and facilitates as much as possible the interactions between supervisors.

Regarding the supervision quality, seemingly inadequate supervision and mentorship support by African university supervisors exist. Consequently, doctoral students can easily lose contact with one of the supervisors in case of co-supervision. Training courses exist, and allow the acquisition of very important scientific and pedagogical (hard and soft) skills specific to doctoral supervision, such as:

➢ creating a thesis subject while thinking about its employability;

➢ managing a bibliography;

➢ creating hypothesis;

➢ reading and decoding a scientific article;

➢ scientific writing to increase chances of being published;

➢ how to avoid predatory journals;

➢ managing conflicts;

➢ setting milestones throughout the thesis;

➢ providing constructive feedback;

➢ thinking about employability throughout the thesis;

➢ helping your doctoral student stay motivated;

➢ communicating; ➢ managing fieldwork;

➢ supporting the autonomy and empowerment of the doctoral student;

➢ managing data;

➢ scientific ethics… Furthermore, regarding international mobility, the role of supervisors is important, as they provide much help upon arrival with the resettlement. Supervisors who are supportive at crucial moments in the thesis process allow for PhD's greater empowerment, autonomy, and quality of production. Conversely, students who are left to their own devices are more likely to quit, waste time, and lose motivation.

PhD programs: a challenging design

The mission of thesis program operators is multifaceted. They are the architects who have to think about how to involve each partner institution in every country to ensure their sense of ownership. Indeed, from the very beginning, it was very important that all program partners be involved in defining a clear, verifiable and realistic scope and schedule for the PhD program. This includes clarifying milestones and deliverables at every stage of the program, defining a transparent selection process to attract the best African students (in Africa and beyond, within the diaspora), as well as the funding available for program activities. Program designers have to facilitate the mobility for both students and thesis supervisors, which enables the exchange of knowledge and experience among researchers from institutions in the global north and south.

Through this journey, the importance of access to relevant resources, transversal skills acquisition, as well as published academic literature is evident to ensure successful completion and PhD research. Funding for open access publication of PhD research outputs also proves to be important in ensuring widespread, unrestricted access to research results and recommendations. Conference participation also enables researchers to present their work to wider international audiences and receive initial feedback on their research. This implies a permanently integrated approach for interdisciplinary research and practice while taking care of the students' well-being, caring for their future regarding the professional and cultural challenges they will face. As stable and solid the program might be, it paradoxically implies strong agility to adapt to:

-unexpected challenges (political unrest, strikes, pandemics); -onboard new and well-selected key partners joining the program; and -find ways of eliminating bottlenecks and bureaucracy.

It is, therefore, necessary to constantly zoom in and out so as not to lose sight of the major development issues, nor of the day-to-day lives of doctoral students, who individually live a unique and challenging experience.

Recommendations

The ideal doctoral program provides doctoral students with the means to conduct research, experiment, publish, grow, develop, build key skills, create a multi-actors network, defend their thesis in good conditions, travel, work in the field, find answers, find work, produce knowledge, and contribute to the achievement of the SDGs. All this in a setting where they are guided, educated, cared for, can take a variety of courses, and benefit from high-quality thesis supervision.

In order to achieve this ideal, we suggest better interactions between universities and doctoral schools in Africa, to harmonise practices in the sub-Saharan region at different levels:

1. Develop regulation practices (easing mobility, thesis defence criteria, co-supervision); 2. Promote soft skills training that will improve the employability of doctoral students (related to 21st-century skills 22 and the skills tree 23 ); essentially off the beaten track. Moreover, we consider that the supervisors should not lead more than three other theses at the same time to ensure good availability, and training in thesis supervision should be systematised. Regarding the lack of critical mass of supervisors; should PhD programs prepare future supervisors? One idea would be to encourage mentoring of master's students by doctoral students to introduce transmission and mentoring. Another idea is that capacity for PhD mentorship and training could be significantly enhanced, where there was access to collaborations both across countries and within.

Regarding student well-being, we need to rethink the grant system to support quality of mobility and social inclusion (women with children, visa process, health care, arrival allowance, accommodation, and any facilitation upon arrival) for PhD students to avoid additional stress. This implies an efficient and trusting partnership with the host institute and preparation and training of local operators. The emergence of gender-based violence mitigation mechanisms and policies within universities is not enough. We need to think about dedicated grants adapted to women's mobility that can adapt to local socio-economic and cultural differences.

Moreover, student well-being should be addressed through regular meetings between a designated authority (thesis committee) and students where each student gives a non-technical summary of the PhD progress and raises any issues and challenges faced. Follow-ups and recommendations do not just focus on thesis content, but on the broader experience of students during their PhD. In the same frame, regular PhD colloquia should be organised between the students and the supervisors to provide constructive feedback on the progress of their PhD research. In the case of international cooperation, the project management team and the supervisors should hold regular coordination meetings to assess the progress of the project and explore opportunities for collaboration. We may also systematically assess the well-being of students through questionnaires or semi-directed interviews, which leads to PhD program regular adjustments.

We recommend the creation and support of alumni networks with a wide range of services, job offers, post-doctoral fellowships, training, networking, etc. that would be designed with socioeconomic partners. Such networks can create new spaces for exchange and understanding of the expectations and needs of the private sector and NGOs, through conferences or workshops. Partnerships are a key component for successful PhD programs. We need to make sure that any partner (North and South) is aware and agrees about the scientific scope (interdisciplinary, problem-solving, coherent with the employability, and aiming at SDGs). They provide something additional that strengthens the collaboration. Partnerships may not include only academic partners such as universities, but also need to include socio-economic actors who will help us to develop tomorrow's tools. Facilitating the co-construction of thesis subjects between academic actors and the socio-economic sector will improve employability and technology transfer. In the broader partnership approach, we encourage all stakeholders (universities, funders, public and private actors…) to shift the power balance toward Africa in order to end North/South unequal partnerships.

A new paradigm based on scientific excellence and ethical partnership will allow us to design African solutions for Africa. PhD Sandwich programmes between institutions should be promoted since it provides a sustainable alternative to conduct PhD with joint resources (infrastructure, laboratory, joint supervision…). Such international cooperation fosters collaboration beyond the PhD programme. It provides opportunities for institutions with no PhD programme or with no potential to issue a PhD certificate. This approach helps to develop research programmes through the sharing of infrastructure and expertise between heterogeneous but complementary partners. At the regional level, we encourage African governments and multilateral organisations involved in the development of science and innovation in Africa (African Unions, European Union, World Bank, French Development Agency, foundations…) to strengthen their support toward doctoral support. This support can take two forms:

1. Provide additional funding toward South/South/North impactful doctoral programs; and; 2. Encourage the creation of gateways between academia and socio-economic actors (incentives for multi-actor research programs and events, support science-based entrepreneurship…).

Doctoral programs must prepare students to become international professionals and fulfilled researchers, with the final objective of achieving the SDGs. It is necessary to support doctoral programs that encourage African universities to join or consolidate international standards of excellence. It requires different types of resources: financial on the one hand, but also to move the lines in terms of pedagogical innovation, considering the expectations of the economic sector and keeping in mind the challenges of sustainable development. The operators of doctoral programs must be resolutely inclusive. The academic and private sectors, NGOs, scientists, donors and students must be brought to the table before, during and after the implementation of doctoral programs. We are getting closer, but we are not here yet.

Introduction

  The arrows: a focus on PhD students PhD students well-being PhD students' skills and capacity building The multiple targets of PhD programs Employability Sustainable development, SDGs and interdisciplinarity The archer: a stable and solid framework PhD mentoring: thesis supervision PhD programs: a challenging design Recommendations References

  African students offered by the largest 50 providers, by degree type, 2019 11 : 9 UNESCO -Global and thematic indicators for the SDG 4 by Country (2010-2021) -Tab 583 http://data.uis.unesco.org/ 10 Meyer J-B., Pilon M., et Ravalihasy A, « Les effectifs étudiants en Afrique au XXIe siècle : évolution passée et exercice de prospective », Working Paper du Ceped, n°48, Ceped (UMR 196 Université de Paris IRD, ERL 1244 Inserm), Paris, Septembre 2020. 11 Source: Education Sub Saharan Africa (2020). GEM StatLink: http://bit.ly/opportunity represented by the WHEC 2022, five operators of doctoral programs in sub-Saharan Africa have come together to propose this contribution. Its objective is to share practices and reflect on the major challenges of doctoral support in Africa. ICIPE (PASET Program), the United Nations University, the IRD (ARTS and ACE Partner programs) and the Learning Planet Institute offer this contribution to open a discussion. Using the metaphor of an archer, its arrow and targets, we will conclude our discussion by sharing recommendations on a successful and impactful doctoral program in Sub-Saharan Africa.

  12 IRS (ARTS): 130; ACE-Partners: 40; FIRE doctoral school (LPI): 120; ICIPE: 173; UNU: 8, total of 471 PhD students. 13 IRD (ARTS): 800; ACE-Partner: 40; FIRE doctoral school (LPI): 475; ICIPE 184; UNU: 8, total of 1507 PhD students since the beginning of the program. 14 Except for the 40 PhD students of FIRE doctoral school, all programs are mainly dedicated to African PhD students.

Employability

  Africa is expected to host the largest and youngest workforce by 2050 17 . This demographic pressure exists in a context of low economic development, lack of human skill and employment 15 UNESCO -Global and thematic indicators for the SDG 9. Indicator 9.5 http://uis.unesco.org/en/news/new-uisdata-sdg-9-5-research-and-development-rd 16 B. Durette et al., The core competencies of PhDs, Studies in Higher Education 41(8):1355-1370, 2016 B. Anderson, The Most In-Demand Hard and Soft Skills of 2020, LinkedIn Business Solutions, January 9, 2020 17 https://population.un.org/wpp/Download/Probabilistic/Population/

➢

  Gain confidence in proposing, exploring, developing ideas; ➢ Discuss, reject or accept ideas; ➢ Learn to take constructive scientific criticisms; ➢ Learn to write a research proposal with scientists from other domains; ➢ Discuss scientific questions thoroughly; and 18 https://openknowledge.worldbank.org/handle/10986/28440 19 Example: https://www.ird.fr/4e-ecole-dete-des-odd-une-edition-dediee-lapproche-one-health-linterface-entrebiodiversite-et ➢ Interact with people from different backgrounds and cultures.

3 .

 3 Develop access to a quality Internet network and to publications (open science), which requires massive investments and funding; and 4. Enhance the quality of doctoral supervision through the training of supervisors. Those aspects have a direct and long-term impact on the research quality. Regarding the last point about the quality of doctoral supervision, we advise taking no more than one interdisciplinary project proposed per supervisor each year, because these are theses that are 22 Determinants of 21st-Century Skills and 21st-Century Digital Skills for Workers: A Systematic Literature Review -Ester van Laar, Alexander J. A. M. van Deursen, Jan A. G. M. van Dijk, … First Published January 24, 2020 23 B. Durette et al., The core competencies of PhDs, Studies in Higher Education 41(8):1355-1370, 2016

https://au.int/sites/default/files/newsevents/workingdocuments/33178-wd-stisa-english_-_final.pdf

https://media.africaportal.org/documents/Competences_techniques_essentielles_French.pdf

This contribution is intended for decision-makers (public and private) and national and international donors committed to strengthening research funding in sub-Saharan Africa through doctoral programs.


Thanh Trung Nguyen
email: thanh-trung.nguyen@g2elab.grenoble-inp.fr

Gérard Meunier

Jean-Michel Guichon

Olivier Chadebec

T-T Nguyen

J-M Guichon

An Integral Formulation for the Computation of 3D Eddy Current Using Facet Elements

Keywords: Approximation methods, eddy currents, Integral equation method

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

I. INTRODUCTION

Facet elements have been developed to model magnetostatic problems for the finite element method [START_REF] Le Menach | Determination and utilization of the source field in 3-D magnetostatic problems[END_REF] and for the integral equations method [START_REF] Vishnevsky | Modeling magnetization using Whitney facet elements[END_REF], [START_REF] Vishnevsky | Boundary integral computation of electric fields in multielectrode galvanic systems using normally continuous elements[END_REF]. Using the facet interpolation, different unknown can be approximated, such as the current in [START_REF] Le Menach | Determination and utilization of the source field in 3-D magnetostatic problems[END_REF], [START_REF] Vishnevsky | Boundary integral computation of electric fields in multielectrode galvanic systems using normally continuous elements[END_REF] and the magnetization in [START_REF] Vishnevsky | Modeling magnetization using Whitney facet elements[END_REF]. This approach seems very powerful as it allows both incorporating different geometrical structures and lumped elements of electrical network within a unified integral formulation.

The PEEC method (Partial Element Equivalent Circuit) is mainly used for the modeling of complex interconnection and can be applied to a large range of devices where the air region is dominant [START_REF] Ruehli | Equivalent circuit models for three dimensional multiconductor systems[END_REF]. However, the classical PEEC method does not enable the 3D modeling of conductive.

This paper proposes a genaralisation of the classical inductive PEEC formulation using facet elements. An equivalent electrical circuit, whose branches are the facets and the nodes of these branches are the centroid of elements of mesh, is proposed.

II. THE INTEGRAL FORMULATION

A. Problem description

Eddy current in conductive materials fit the classical PEEC formulation which is derived from the equation governing the total electric field at a point r inside the conductors:

V d r 4 j C 0 C grad J J - = Ω π µ ω + σ ∫ Ω (1)
where Ω C is conductive region, J is the current density, V is the scalar electric potential, σ is the material conductivity, µ 0 is the vacuum permeability, and ω is the excitation pulse.

B. System assembly

With facet elements interpolation, the current density is described as follows:

∑ = f I . w J f
where w f is shape function and I f is flux across the fth facet. The normal component of w f is conserved.

Applying the Galerkine method to (1), a system of linear equations is obtained:

{ } { } b f b U I ]. Z [ = (2) with [Z b ] = [R] + jω.[L]
where:

C f g fg .d R C Ω σ = ∫ Ω w w C C f g 0 fg d .d r 4 L C C Ω Ω π µ = ∫ ∫ Ω Ω ' w w ' and Ω - = ∫ Ω V.d U C g g b

grad . w

Matrix [Z b ] can be seen as the impedance matrix of the electrical equivalent circuit generated, [R] is matrix of the resistance terms, and [L] is matrix of the mutual inductance terms. To avoid the singularity problem of [L], we assume that the face to face interaction of the element onto itself equal to zero. We consider now the following equality:

Ω - Ω = Ω ∫ ∫ ∫ Ω Ω Ω d ).V div( d .V) div( V.d
II I d ).V div( d .V) i Ω - Γ = ∫ ∫ Ω Γ
where n is the outward normal vector on the boundary. The first term (I) vanishes inside the domain because w g .n is conserved and on the boundary, since the current is tangential. Moreover, (I) allows imposing V on a surface boundary.

The second term (II

): v 1 ) ( div ± = g w
(v is volume of element). We het then: The sign ( ± ) depends on the orientation of facet. For example, in Fig. 1, the facet g is oriented from the element a to the element b.

) ( grad . w g b a V - V V.d C ± = Ω ∫ Ω with ∫ Ω Ω = a a V.d V a

C. Resolution of the electrical circuit

It is not possible to solve directly the system of linear equations (2), because equations are not independent The current density has to satisfy the several conditions. In the conductive region Ω C : div J = 0 [START_REF] Vishnevsky | Boundary integral computation of electric fields in multielectrode galvanic systems using normally continuous elements[END_REF] and on its boundary

C Ω ∂ n.J = 0 (4)
The current flux is represented by the facets. The facets are considered as the branches of an electrical circuit. The conditions of ( 3) and (4) will be ensured when applying a loop analysis.

By using the independent loops search proposed in [START_REF] Nguyen | An independent loops search algorithm for solving inductive PEEC large problems[END_REF], we can write a new system of linear equations where the unknowns are the currents flowing in the loops : In order to validate the proposed formulation and to show its performances, we consider an example with a multiply connected region. The results will be compared to those obtained with FLUX [6], a commercial Finie Element Method (FEM) program.

{ } { } { } { }
In this example, we compute the eddy currents in a conductive disk with a hole ( σ = 6e+7 S/m) which is placed genrated by a loop conductor (Fig. 2). This conductor is fed by a current source. In this case, with the presence of current source, the equations in system (2) need to be adapted. We must add a mutual term: We focus on the computed eddy current distribution and loss in the disk (Fig. 3 and Tab.1). The new formulation has been modelled in the case of a skin depth such as δ/∆R ≈ 0.2. The accuracy is very similar to FEM 3D and the solution has a small relative error compared to the FEM 2D. Moreover, the convergence of the results is quickly reached with the new formulation. We can obtain it with a smaller number of elements in the disk than the FEM 3D.

{ } { } { } b S f b U I ]. Mu [ I ]. Z [ = + (

IV. CONCLUSION

In this paper, we have presented an eddy currents volume integral formulation using facet elements in nonmagnetic conductors. The formulation produces very similar results in the comparison with the FEM and allows the treatment of multiply connected domains. In the future, we can improve this formulation by using matrix compression techniques in order to save memory and to reduce the computation time. Moreover, we will to improve the accuracy by using analytical correction to treat the singularity of the mutual inductance terms.

Fig. 1 .

 1 Fig.1. Orientation of facet

  b ] is a complex branch impedance matrix, [Z m ] is a complex loop-based impedance matrix, {I m } is a vector of independent loop-based currents, [M] is the incidence matrix (branch -fundamental independent loop matrix) where the value of each element can be -1, 0 or 1, {U s } is the vector of source voltages (most of the time is equal to 0), and the size of {I m } is the number of fundamental loops. Once the problem is solved, we can obtain the currents flowing on each branch by the following relationship: {I b } = [M t ].{I m } III. NUMERICAL EXAMPLE

Fig. 2 .

 2 Fig.2. Geometry considered

  6) where {I S } is current flowing in the conductor and [Mu] is the matrix of mutual inductance between the circuit loop and each facet element: t 0k is unit vector defining the current direction. Note that for the case {U b } = {0}, (6) becomes: we have a the system of linear equations to solve as follows:

Fig. 3 .

 3 Fig.3. Eddy current distribution in the disk considered (δ/∆R ≈ 0.2)

Rs


Douglas Martins Araujo

Jean-Louis Coulomb

Olivier Chadebec

A Hybrid Boundary Element Method-Reluctance Network Method for Open Boundary 3D Non Linear Problems

Keywords: Actuators, boundary element method, coupling of numerical techniques, magnetostatics, reluctance network method

published or not. The documents may come

I. INTRODUCTION

Based on the principle of equivalent magnetic circuits, Network Reluctance Method (NRM) is an approach enabling a very quick evaluation of electromagnetic quantities in devices [START_REF] Du Peloux | Automatic generation of sizing static models based on reluctance networks for the optimization of electromagnetic devices[END_REF]. Although easy to implement, NRM results can be somewhat inaccurate in a first step especially if significant flux leakages are associated to the device. Thus, the network can be improved by comparing the results with those from the FEM model and rebuilding a more representative NRM. Unfortunately, the development of such an approach can be very extensive.

Tools based on Finite Element Method (FEM) provide to the user effective representation of the device. Compared to NRM, the geometric and physical properties are both precisely and quickly described. On the one hand, the FEM can solve a wide range of problems; on the other hand, resolution times can be prohibitive for an actuators presizing step. This question is more meaningful in a context of optimization with a large number of parameters.

A method combining fast computation time and quite good accuracy would be very appropriate during the presizing process. This paper proposes a new hybrid method combining the Boundary Element Method (BEM), for the surrounding region (the air), and NRM, for magnetic regions in order to combine their respective advantages. This approach has been already presented for 2D applications [START_REF] Araujo | A Hybrid Method BEM-NRM for Magnetostatics Problems[END_REF]. The novelty here is its extension to 3D problems.

II. BOUNDARY ELEMENT METHOD (BEM) FOR AIR

Let us consider the third Green's identity applied in the air region to the scalar magnetic potential φ . We have:

( ) ( ) dC G G c e C ∫       ∂ φ ∂ - ∂ ∂ φ = φ n n x x 0 0 , (1)
where ( )

0 x φ
represents the magnetic scalar potential at x 0 point , G is the 1/r Green's function, C e is the boundary of magnetic regions, n its external normal and c is the solid angle subtend by the boundary C e .

We consider a constant distribution for the potential and its normal derivative on the border (0-order shape function). Thanks to a point matching approach at centroid of each element, c i is identically equal to 1/2 and we get a very simple discretized expression of (1) in matrix forme:

0 = + BEM BEM Q T U H , (2)
where U BEM and Q BEM are vectors of dimension N and T and H matrices are associated to following expressions, [START_REF] Meunier | Hybrid finite element boundary element solutions for three dimensional scalar potential problems[END_REF]:

dC G T j C i ij ∫ = , dC G c H j C i ij ij ∫ ∂ ∂ - = n , (3)
where c ij is null if i≠j and equals 1/2 if i=j. T is an invertible matrix, thus we can write a relation linking the flux to the potential on the boundary:

BEM BEM BEM U P Q = , (4)
( )H

T P BEM inv - = .
(5) Let us notice that the matrix P BEM is a fully populated matrix.

III. RELUCTANCE NETWORK METHOD (RNM) FOR MAGNETIC MATERIAL

We decompose the magnetic domain into bricks and we introduce a reluctance network inside each of them. This network can optionally contain sources of magnetomotive force F kt .

F u u q + - = , (6)
where P kt is the permeance of a flux tube and can be calculated from its permeability µ kt , its length L kt and its cross section S kt . By isolating the central potential in the equation and considering the flux conservation, we get for each face number kt:

( ) ( ) kt T 1 t kt T 1 t kt kt kt T 1 t kt T 1 t kt kt kt kt P P P F F P P u u q                         + +             - = ∑ ∑ ∑ ∑ = = = = . (7)
Magnetomotive force F kt can be computed according to Ampere's law by assuming a uniform inductor field into a subset of the domain bricks. More details about the technique will be provided in the full paper.

IV. COUPLING BOTH METHODS

It remains now to couple both methods. Equation ( 7) can be rewritten as follows, [START_REF] Araujo | A Hybrid Method BEM-NRM for Magnetostatics Problems[END_REF]:

NRM NRM NRM NRMborder F U P Q + = , ( 8
) where PNRM represents the permeance matrix, UNRM the potentials, QNRMborder the flux flowing through the border of the device, and FNRM the magnetomotive forces created by sources. Let us notice that PNRM is a sparse matrix and have more unknowns than equation.

Thanks to ( 4) and (8), we can easily eliminate external flux unknowns and build a matrix representing the BEM-NRM coupling:

NRM NRM NRM BEM F U P = - , (9)
where PNEM-NRM is built using PBEM and PNRM matrix.

The nonlinear ferromagnetic material is represented by an initial permeability and a saturation level. We use the fixed point method to solve the nonlinear system. Once the problem has been solved, the Maxwell stress tensor approach is used to compute forces.

V. RESULTS AND COMPARISONS

In this section, we present the comparisons between a FEM model and the BEM-NRM model of an actuator represented by Fig. 2. In order to present the comparison, we have to consider the variation of the air gap thickness. Fig. 2 presents the force errors computed with BEM-NRM as a function of the air gap thickness in comparison with a FEM reference computed by Flux® [4], with a very dense mesh. FEM 2, FEM 3 and FEM 4 represent others FEM solutions using different mesh size.

The idea is to study the evolution of the accuracy and the computation time. The error is divided by a reference value of force in order to get a relative one. It is shown that with FEM we can not decrease drastically the mesh size. Otherwise, the quality of the result becomes poor (see results of FEM 4).

Relative Error

Inaccuracies for the BEM-NRM appear when the gap becomes too small. It can be certainly explained by the use of zero order shape functions. However, our new method remains very efficient if we consider its speed comparing to the quality of its results (see results of BEM-NRM 1 associated to 52 degrees of freedom).

VI. CONCLUSION

With our new method a very low number of elements and a very low computation time are needed to get an accurate result. Getting an equivalent accuracy with a FEM necessitates much more time.

Fig. 1 .

 1 Fig. 1. Introducing NRM in the brick of the magnetic domain Let us suppose a magnetic region m Ω , discretized by K bricks. Each brick k contains T flux tubes connecting the central potential u k0 to the potentials of facets u kt . q kt is the flow through the facet t of the brick k. The following relation can be written:

Fig. 2 .

 2 Fig. 2. 3D U-shaped actuator modeling

3 Fig. 3 .

 33 Fig. 3. Relative error as a function of gap

  Twenty different positions are computed for each problem. Computation times and number of degrees of freedom are presented on the table I.


Anthony Carpentier
email: anthony.carpentier@g2elab.grenoble-inp.fr

Nicolas Galopin

Olivier Chadebec

Gérard Meunier

Modeling of Magneto-Mechanical Coupling with Magnetic Volume Integral and Mechanical Finite Element Methods

Keywords: magneto-mechanical coupling, integral method, finite element method

published or not. The documents may come   L'archive ouverte pluridisciplinaire

I. Introduction

The modeling of magneto-mechanical devices using magnetic and deformable materials involves the resolution of the magnetostatic and mechanical equations. The first problem is an open boundary problem for the magnetic field whereas the second is restricted to the solid domain. A classical method to solve numerically such problems is the finite element method [START_REF] Galopin | Finite Element Modeling of Magnetoelectric Sensors[END_REF]. However, for devices with a huge volume of free space compared to the active structure or high size ratio between the geometric objects (like MEMS), problems of accuracy could be present [START_REF] Rakotoarison | Formal Sensitivity Computation of Magnetic Moment Method[END_REF].

Integral formulations of the magnetostatic field problems are particularly advantageous for the numerical solution of open boundary problems which include magnetic materials since only the active regions containing these materials need to be discretized. So, a volume integral method is used to solve the magnetostatic problem.

To realize the magneto-mechanical coupling, the knowledge of the magnetic forces distribution is necessary. A local application of the virtual work principle adapted to the integral formulations is used. A finite element method is then used to solve the mechanical problem in the solid domain.

This paper presents in the first part the magnetostatic and mechanical formulations. The second part is dedicated to the magneto-mechanical coupling. A numerical example is given.

II. Formulations

A. Magnetostatic problem

Let us consider the following magnetostatic problem. A three dimensional simply connected region Ω f is filled with a isotropic magnetic material with the known linear magnetic susceptibility χ. Primary sources of magnetic field in which currents flows are associated to the region Ω j . Both region, Ω f and Ω j , are disposed in free space Ω 0 so that these regions do not overlap, Ω = Ω f ∪ Ω j ∪ Ω 0 . The linear magnetic behavior law is defined by:

M (r) = χH (r) , (1)
where M(r) is the magnetization and H(r) the magnetic field at point of coordinates r. At any point of Ω, the magnetic field is the sum of the reduced magnetic field created by the magnetic material H red (r) and the magnetic source field created by currents flows H 0 (r).

The simply connected region Ω f containing no current sources, the following volume integral equation [START_REF] Han | Integral Equation Method Using Total Scalar Potential for the Simulation of Linear or Nonlinear 3D Magnetostatic Field with Open Boundary[END_REF] [4] using the total scalar potential Φ is considered:

Φ (r) + 1 4π Ω f χ ∇Φ (r ) • (r -r ) |r -r | 3 dΩ = Φ 0 (r) , (2)
where Φ 0 is the scalar potential whose the magnetic field produced by sources can be derived. A collocation method at mesh nodes is used to solve (2).

B. Mechanical problem

Let us consider the following quasi-static mechanical problem. A three dimensional region Ω m is filled with isotropic linear elastic material with the known stiffness tensor [C]. We note Γ m the boundary between the region Ω m and the free space. The behavior law is defined by:

σ = [C]ε, ( 3
)
where σ is the stress tensor and ε the strain tensor. The local application of the equilibrium equations for a quasi-static mechanical problem leads to the relation:

divσ + f = 0, ( 4
)
where f is the volume force density applied to the mechanical system. According to the small perturbation hypothesis, the strain tensor can be written as:

ε(u) = 1 2 (∇u + ∇ t u), (5)
where u is the displacement field. Two boundary conditions can be imposed on Γ m . We note Γ u and Γ σ the parts of Γ m associated respectively to the conditions on the displacement and the stress with respect to Γ σ ∪ Γ u = Γ m and Γ σ ∩ Γ u = ∅. These conditions are defined by:

u = u 0 on Γ u , (6) σ • n = f Γ on Γ σ , ( 7
)
where n is the outward unit normal vector. The weak formulation associated to the mechanical problem is:

Ω m ε(u)[C]ε(v) dΩ = Ω m f • v dΩ + Γ m f Γ • v dΓ ∀v,( 8
)
where v is a displacement field verifying the boundary condition [START_REF] Carpentier | Comparison of Magnetic Force Computation with a Volume Integral Method[END_REF]. A finite element method is used to solve (8).

III. Magneto-mechanical Coupling This paper considers magneto-mechanical coupling without magnetostriction effect. The force of magnetic origin acting on the solid becomes a source term in (4). The following section presents a method to compute this local magnetic force from an integral formulation.

A. Local magnetic force computation

According to the virtual work principle, the magnetic forces are deduced from the variation of magnetic co-energy, keeping constant the current I during a virtual displacement [START_REF] Coulomb | A methodology for the determination of global electromechanical quantities from a finite element analysis and its application to the evaluation of magnetic forces, torques and stiffness[END_REF]:

F = ∂W co ∂u I , ( 9
)
where I is the electric current, W co the magnetic co-energy, F the magnetic force and u a displacement of the system.

Applying this principle at the element level, the nodal magnetic force distribution is obtained by taking the partial derivative of magnetic co-energy with respect to nodal displacements. The nodal magnetic forces F n can then be express as [START_REF] Carpentier | Comparison of Magnetic Force Computation with a Volume Integral Method[END_REF]:

2F n = ∂Ω ∂un M • B 0 dΩ + Ω M • ∂B 0 ∂u n dΩ + Ω ∂M ∂u n • B 0 dΩ. ( 10
)
The computation of each term of (10) will be presented in the full paper.

B. Application

Let us consider a cantilever beam with a linear and isotropic magnetic behavior (1) and a isotropic linear elastic behavior [START_REF] Han | Integral Equation Method Using Total Scalar Potential for the Simulation of Linear or Nonlinear 3D Magnetostatic Field with Open Boundary[END_REF]. Two positions for the coil, (a) and (b) (Fig. 1), are considered. The volume integral method (2) is used to solve the magnetostatic problem. The computed magnetic fields are presented in Fig. 2a. The virtual work principle (10) is applied to compute the nodal local magnetic forces which are presented in Fig. 2b. These computed local magnetic forces are validated by an application of the virtual work principle with a finite element approach. The cases (a) and (b) are equivalent to a beam problem with respectively bending and traction stresses. We suppose that the magnetic force is the unique volume force density acting on the beam. After discretization, the corresponding source term in (8) is directly the previous computed nodal magnetic forces. The mechanical problem is then solved and the computed Von Mises stress and displacement fields are presented in Fig. 2c and Fig. 2d.

C. Conclusion

A magneto-mechanical coupling problem is solved with a volume integral method for the magnetic part and a finite element method for the mechnical part. The volume integral method allows to not mesh the free space and is well suited to compute the energies. These last are used thanks to the virtual work principle to compute the magnetic force density which becomes a source term in the mechanical formulation. The same mesh could be used for magnetostatic and mechanical problems. A futur work can be the investigation of the nonlinear case including a material magneto-mechanical coupling.

Figure 1 :

 1 Figure 1: Description of the application.

  (a) Computed magnetic fields. (b) Computed nodal magnetic forces. (c) Computed Von Mises stresses. (d) Computed displacements (200 and 2e 5 amplification factors).

Figure 2 :

 2 Figure 2: Results of the beam application.C. ConclusionA magneto-mechanical coupling problem is solved with a volume integral method for the magnetic part and a finite element method for the mechnical part. The volume integral method allows to not mesh the free space and is well suited to compute the energies. These last are used thanks to the virtual work principle to compute the magnetic force density which becomes a source term in the mechanical formulation. The same mesh could be used for magnetostatic and mechanical problems. A futur work can be the investigation of the nonlinear case including a material magneto-mechanical coupling.


Matthew P Gibbins

Katja Müller

Maya Glover

Jasmine Liu

Elyzana D Putrianti

Karolis Bauza

Arturo Reyes-Sandoval

Kai Matuschewski

Olivier Silvie

Clemence R Hafalla

Julius Clemence

R Hafalla

The importance of the immunodominant CD8+ T cell epitope of Plasmodium berghei circumsporozoite protein in parasite-and vaccine-induced protection

The circumsporozoite protein (CSP) builds up the surface coat of sporozoites and is the leading malaria pre-erythrocytic-stage vaccine candidate. CSP has been shown to induce robust CD8+ T cell responses that are capable of eliminating developing parasites in hepatocytes resulting in protective immunity. In this study, we characterised the importance of the immunodominant CSP-derived epitope, SYIPSAEKI, of Plasmodium berghei in both sporozoite-and vaccineinduced protection in murine infection models. In BALB/c mice, where SYIPSAEKI is efficiently presented in the context of the major histocompatibility complex class I (MHC-I) molecule H-2-K d , we established that epitope-specific CD8+ T cell responses contribute to parasite killing following sporozoite immunisation. Yet, sterile protection was achieved in the absence of this epitope substantiating the concept that other antigens can be sufficient for parasite-induced protective immunity. Furthermore, we demonstrated that SYIPSAEKI-specific CD8+ T cell responses elicited by viral-vectored CSP-expressing vaccines effectively targeted parasites in hepatocytes. The resulting sterile protection strictly relied on the expression of SYIPSAEKI. In C57BL/6 mice, which are unable to present the immunodominant epitope, CSP-based vaccines did not confer complete protection, despite the induction of high levels of CSPspecific antibodies. These findings underscore the significance of CSP in protection against malaria pre-erythrocytic stages and demonstrate that a significant proportion of the protection against the parasite is mediated by CD8+ T cells specific for the immunodominant CSP-derived epitope.

INTRODUCTION

Malaria is caused by a protozoan parasite of the genus Plasmodium and remains a major global health challenge in tropical and subtropical countries [START_REF]World Malaria Report 2017 World Health Organisation[END_REF]. A vaccine that diminishes the burden of disease and prevents malaria transmission remains a decisive goal for malaria elimination programmes. As a gold standard in malaria vaccination, multiple immunisations of g-radiation-attenuated Plasmodium sporozoites (RAS) can completely protect against wildtype (WT) sporozoite challenge [START_REF] Nussenzweig | Protective immunity produced by the injection of x-irradiated sporozoites of Plasmodium berghei[END_REF][START_REF] Hoffman | Protection of humans against malaria by immunization with radiation-attenuated Plasmodium falciparum sporozoites[END_REF][START_REF] Seder | Protection against malaria by intravenous immunization with a nonreplicating sporozoite vaccine[END_REF]. This parasite-induced protection targets the developing exo-erythrocytic forms in hepatocytes, also called liver stages, and completely abrogates blood stage infection. Antibodies and T cells have been implicated as important mechanisms of parasite-induced protection (reviewed in ( 5)), and CD8+ T cells are the prime mediators of cellmediated protective immunity, as exemplified in murine [START_REF] Doolan | The complexity of protective immunity against liver-stage malaria[END_REF][START_REF] Schmidt | Memory CD8 T cell responses exceeding a large but definable threshold provide long-term immunity to malaria[END_REF] and non-human primate [START_REF] Weiss | Protective CD8+ T lymphocytes in primates immunized with malaria sporozoites[END_REF] infection models.

The circumsporozoite protein (CSP), the major surface coat protein of the malaria sporozoite, has been at the forefront of vaccination studies -being the basis of RTS,S/AS01, the most progressed malaria vaccine candidate to date [START_REF] Sctp | Efficacy and safety of RTS,S/AS01 malaria vaccine with or without a booster dose in infants and children in Africa: final results of a phase 3, individually randomised, controlled trial[END_REF]. Immunisation of BALB/c mice with Plasmodium berghei (Pb) or P. yoelii (Py) RAS evokes immunodominant major histocompatibility complex class I (MHC-I) H-2-K d -restricted CD8 + T cell responses [START_REF] Schofield | Gamma interferon, CD8+ T cells and antibodies required for immunity to malaria sporozoites[END_REF][START_REF] Weiss | CD8+ T cells (cytotoxic/suppressors) are required for protection in mice immunized with malaria sporozoites[END_REF] against distinct CSP epitopes: SYIPSAEKI for Pb [START_REF] Romero | Cloned cytotoxic T cells recognize an epitope in the circumsporozoite protein and protect against malaria[END_REF] and SYVPSAEQI for Py [START_REF] Weiss | Cytotoxic T cells recognize a peptide from the circumsporozoite protein on malaria-infected hepatocytes[END_REF]. Indeed, the measurement of responses to these epitopes has become the standard in fundamental immunological studies in BALB/c mice and their role in parasite-induced protection from sporozoite challenge has been repeatedly demonstrated [START_REF] Doolan | The complexity of protective immunity against liver-stage malaria[END_REF][START_REF] Romero | Cloned cytotoxic T cells recognize an epitope in the circumsporozoite protein and protect against malaria[END_REF][START_REF] Rodrigues | CD8+ cytolytic T cell clones derived against the Plasmodium yoelii circumsporozoite protein protect against malaria[END_REF]. Furthermore, numerous vaccination studies involving different viral-vectored CSP-or CSP epitope-expressing vaccines -used alone or in combination as part of prime-boost regimens -have corroborated that CSP is a highly protective antigen in the BALB/c infection model [START_REF] Li | Priming with recombinant influenza virus followed by administration of recombinant vaccinia virus induces CD8+ T-cell-mediated protective immunity against malaria[END_REF][START_REF] Rodrigues | Single immunizing dose of recombinant adenovirus efficiently induces CD8+ T cell-mediated protective immunity against malaria[END_REF][START_REF] Bruna-Romero | Complete, long-lasting protection against malaria of mice primed and boosted with two distinct viral vectors expressing the same plasmodial antigen[END_REF][START_REF] Gilbert | Enhanced CD8 T cell immunogenicity and protective efficacy in a mouse malaria model using a recombinant adenoviral vaccine in heterologous prime-boost immunisation regimes[END_REF][START_REF] Gonzalez-Aseguinolaza | Induction of protective immunity against malaria by priming-boosting immunization with recombinant cold-adapted influenza and modified vaccinia Ankara viruses expressing a CD8+-T-cell epitope derived from the circumsporozoite protein of Plasmodium yoelii[END_REF][START_REF] Reyes-Sandoval | Single-dose immunogenicity and protective efficacy of simian adenoviral vectors against Plasmodium berghei[END_REF][START_REF] Reyes-Sandoval | Prime-boost immunization with adenoviral and modified vaccinia virus Ankara vectors enhances the durability and polyfunctionality of protective malaria CD8+ T-cell responses[END_REF]. In these studies, elevated levels of either SYIPSAEKI-or SYVPSAEQI-specific CD8+ T cell responses correlated with protection.

Nonetheless, several studies have interrogated and contested the immunological relevance of CSP with regard to parasite-induced protection in contrast to vaccine-induced protection.

These studies emanated from observations that in naturally exposed humans T cell responses to CSP are scarce [START_REF] Dodoo | Measuring naturally acquired immune responses to candidate malaria vaccine antigens in Ghanaian adults[END_REF]. In murine malaria models, multiple immunisations are required to elicit CD8+ T cell-dependent protective immunity in various mouse strains, particularly where no other strongly immunogenic CSP-derived CD8+ T cell epitopes have been identified [START_REF] Schmidt | Extreme CD8 T cell requirements for anti-malarial liver-stage immunity following immunization with radiation attenuated sporozoites[END_REF].

Furthermore, in PyCSP-transgenic BALB/c mice that are tolerant to PyCSP, complete protection can be achieved by Py RAS immunisation [START_REF] Kumar | The circumsporozoite protein is an immunodominant protective antigen in irradiated sporozoites[END_REF]. In good agreement, BALB/c mice immunised with Pb WT parasites are completely protected when challenged with transgenic Pb parasites where the endogenous CSP has been swapped with the P. falciparum CSP [START_REF] Gruner | Sterile protection against malaria is independent of immune responses to the circumsporozoite protein[END_REF].

Taken together, these studies indicate that immune responses to CSP are dispensable for protection, and that other antigens are important to elicit protective immunity.

In this study, we have extended previous work on the entire CSP by dissecting the relevance of a single CSP-derived immunodominant epitope in parasite-and vaccine-induced protection.

As the most stringent model system, we utilised transgenic Pb parasites lacking SYIPSAEKI for immunisation and challenge experiments in BALB/c mice. In addition, we have highlighted the level of protection achieved by CSP-based vaccines in mice expressing the relevant (BALB/c) or irrelevant (C57BL/6) MHC-I needed to present the CSP-derived immunodominant epitope.

RESULTS

Sporozoite-induced SYIPSAEKI-specific CD8+ T cell responses contribute to parasite killing but are dispensable for the development of sterile immunity.

First, we interrogated the role that SYIPSAEKI, the H-2-K d -restricted immunodominant epitope of PbCSP, plays in protective immunity induced after live attenuated sporozoite immunisation. weeks after immunisation, the mice were challenged with PbWT sporozoites and protection was determined by measuring the parasite loads in the liver 40 hours later (Fig. 1B andC). A significant reduction in parasite load -up to four orders of magnitude difference as compared to naïve mice -was observed in mice immunised with PbWT RAS and challenged with PbWT parasites. In contrast, protection was reduced only by approximately two orders of magnitude (after one immunisation) or three orders of magnitude (after two immunisations) in mice immunised with PbCSP SIINFEKL RAS (Fig. 1B andC). These results highlight the notion that within PbCSP, the SYIPSAEKI epitope has a critical and immunodominant contribution to protecting BALB/c mice after one or two immunisations with RAS.

However, multiple immunisations with RAS are required to induce sterile protection. To establish whether the development of sterile immunity is dependent on SYIPSAEKI-specific CD8+ T cell responses, BALB/c mice were immunised thrice with PbCSP SIINFEKL RAS one week apart; two weeks after the last immunisation, mice were challenged with PbWT sporozoites (Fig. 1C). All mice were protected from blood stage infection compared to the naïve controls, implying that SYIPSAEKI-specific CD8+ T cell responses are not necessary for the development of sterile immunity. Next, we probed the requirement for SYIPSAEKI presentation in protection elicited by viralvectored CSP-expressing vaccines administered in a prime-boost regimen. Priming with adenovirus (Ad) carrying a foreign antigen and boosting with orthopoxvirus modified vaccinia Ankara (MVA) expressing the same antigen has consistently been shown to induce strong CD8+ T cell responses with high levels of protective efficacy against intracellular pathogens including malaria pre-erythrocytic stages [START_REF] Gilbert | Enhanced CD8 T cell immunogenicity and protective efficacy in a mouse malaria model using a recombinant adenoviral vaccine in heterologous prime-boost immunisation regimes[END_REF][START_REF] Reyes-Sandoval | Prime-boost immunization with adenoviral and modified vaccinia virus Ankara vectors enhances the durability and polyfunctionality of protective malaria CD8+ T-cell responses[END_REF].

Chimpanzee adenovirus serotype 63 (AdCh63) and MVA vaccines expressing PbCSP were used to vaccinate BALB/c mice with a two-week resting period between priming and boosting (Fig. 2A). Two weeks after boosting, whole blood was collected and restimulated ex vivo with SYIPSAEKI peptide. The frequencies of IFN-g secreting CD8+ T cells were enumerated by flow cytometry (Fig. 2B) and Ad-MVA PbCSP-vaccinated mice elicited ~12% SYIPSAEKIspecific circulating CD8+ T cells (Fig. 2C), which is consistent with the level of epitope-specific CD8+ T cells induced by similar, previously published, viral vectored prime-boost regimens [START_REF] Gonzalez-Aseguinolaza | Induction of protective immunity against malaria by priming-boosting immunization with recombinant cold-adapted influenza and modified vaccinia Ankara viruses expressing a CD8+-T-cell epitope derived from the circumsporozoite protein of Plasmodium yoelii[END_REF][START_REF] Reyes-Sandoval | Prime-boost immunization with adenoviral and modified vaccinia virus Ankara vectors enhances the durability and polyfunctionality of protective malaria CD8+ T-cell responses[END_REF]. Serum samples were also collected from the vaccinated animals and were used in an immunofluorescence assay against air-dried Pb sporozoites (Fig. 2D). Ad-MVA PbCSPvaccinated BALB/c mice induced high anti-CSP antibody tires (1:10 4 ). These data indicate that Ad-MVA PbCSP vaccination elicit both high frequencies of SYPSAEKI-specific CD8+ T cells and high titres of CSP-specific antibodies.

Two weeks after boosting, Ad-MVA PbCSP-vaccinated mice were challenged with PbWT or PbCSP SIINFEKL parasites. Protection was assessed by two complementary assays; (i) determination of the reduction of parasite load in the liver (Fig. 2E) and (ii) induction of sterile protection (Fig. 2F). Strikingly, parasite load in the liver of Ad-MVA PbCSP-vaccinated mice was not significantly reduced compared to non-vaccinated mice when challenged with PbCSP SIINFEKL sporozoites, in marked contrast to challenge with PbWT sporozoites. In perfect agreement, vaccinated mice challenged with PbCSP SIINFEKL sporozoites were patent for parasitaemia by day 5, whereas vaccinated mice challenged with PbWT sporozoites remained completely protected. These results denote that vaccine-induced effector SYIPSEAKI-specific CD8+ T responses efficiently target parasites expressing the cognate epitope. Parasites lacking the SYIPSAEKI epitope are not eliminated despite high levels of CSP-specific antibodies evoked by vaccination in this experimental system.

CSP-based vaccines do not elicit protective immunity in C57BL/6 mice.

To further investigate the requirement of SYIPSAEKI as the indispensable protective epitope of CSP, mice unable to present this epitope were vaccinated with the PbCSP prime-boost regimen with an interval of two weeks between vaccines, followed by challenge with either PbWT or PbCSP SIINFEKL parasites (Fig 3A). C57BL/6 mice were used because SYIPSAEKI is an H-2-K d restricted epitope, and this mouse strain does not express the relevant MHC-I allele.

Thus, SYIPSAEKI would fail to be presented by infected hepatocytes. As before, blood and serum were derived two weeks after boost. As expected, SYIPSAEKI-specific CD8+ T cells (Fig. 3B) were not detectable in Ad-MVA PbCSP-vaccinated C57BL/6 mice (Fig. 3C), but strong anti-CSP antibody titres (1:10 4 ) were elicited (Fig. 3D). Ad-MVA CSP-vaccinated C57BL/6 mice challenged with either PbWT or PbCSP SIINFEKL parasites had comparable parasite load in the liver (Fig. 3E), indicative of full liver stage development in all groups.

DISCUSSION

Our findings lend full support to the notion that CSP is an immunodominant sporozoite-derived antigen [START_REF] Kumar | The circumsporozoite protein is an immunodominant protective antigen in irradiated sporozoites[END_REF]. A single epitope, SYIPSAEKI, is the immunodominant CD8+ T cell epitope of CSP, and we show that it is responsible for the antigen's protective capacity against parasites in the liver in the BALB/c model. Following RAS immunisation, CD8+ T cell responses to SYIPSAEKI contribute to the reduction in parasite load in the liver following sporozoite challenge, as shown herein. When RAS-immunised mice are challenged with PbCSP SIINFEKL , transgenic parasites lacking SYIPSAEKI, reduced anti-Plasmodium activity in the liver is observed. Nonetheless, complete protection is achievable in the absence of SYIPSAEKIspecific CD8+ T cell responses, demonstrating that responses to other, yet unidentified, H-2-K d -restricted epitopes contribute to parasite killing. It is conceivable that these epitopes are encoded by the hundreds of other Plasmodium genes expressed in malaria pre-erythrocytic stages, some of which might be shared with blood stage antigens [START_REF] Muller | Evidence of cross-stage CD8+ T cell epitopes in malaria pre-erythrocytic and blood stage infections[END_REF].

Our findings also emphasise the importance of SYIPSAEKI-specific CD8+ T cell responses for promoting protective immunity when using CSP-based viral vaccines in the BALB/c model. These vaccines are aimed at generating high levels of epitope-specific memory CD8+ T cells but rely on the expression of relevant MHC-I in the vaccinated host and the presence of the cognate epitope in the parasite used for challenge [START_REF] Silvie | Tissue-specific cellular immune responses to malaria preerythrocytic stages[END_REF]. Notably, despite high levels of antibodies against whole sporozoites elicited following Ad-MVA PbCSP vaccination, sterile protection was not achieved following challenge of C57BL/6 mice. These mice cannot present SYIPSAEKI, fully supporting the notion that the protective efficacy of CSP strictly depends on the expression of the immunodominant epitope. These findings were independently corroborated by the lack of protection in mice, either BALB/c or C57BL/6, immunised with transgenic sporozoites lacking SYIPSAEKI.

Together, these results have important implications for the development of next generation malaria vaccines. We have demonstrated the significance of a single epitope of CSP in mediating protective CD8+ T cell responses while also recapitulating that protection can be achieved in the absence of responses to the entire CSP antigen [START_REF] Kumar | The circumsporozoite protein is an immunodominant protective antigen in irradiated sporozoites[END_REF][START_REF] Gruner | Sterile protection against malaria is independent of immune responses to the circumsporozoite protein[END_REF]. In BALB/c mice, SYIPSAEKI-specific CD8+ T cell responses offered protection. However, to achieve complete sterile protection either multiple sporozoite immunisations or viral vaccines, which induced large populations of SYIPSAEKI-specific CD8+ T cells, were required. Multiple immunisations likely induced a broad range of immune responses and multiple high-dose immunisations with RAS in humans have been shown to induce dose-dependent anti-sporozoite CD8+ T cell responses in addition to dose dependent anti-sporozoite antibody and CD4+ T cell responses (4). It will be important in the future to determine how the magnitude of SYIPSAEKI-specific CD8+ T cell responses modulates, after consecutive immunisations, but also the breadth of responses to other CSP epitopes (B and T cell) and their effect on protection compared to other antigens. In line with this, our findings also show that protection can be achieved in the absence of responses to immunodominant epitopes, leading us to suggest that future preerythrocytic malaria vaccine research should not only focus on inducing strong CD8+ T cell responses against one or multiple antigens but should try to target a broad array of antigens and cover diverse MHC to offer the best protection possible. The identification of novel antigens and epitopes that contribute to protection in H-2-K d -restricted BALB/c mice, and ultimately in human populations with broad MHC haplotypes, will aid this development. In C57BL/6 mice pre-erythrocytic immunity is mounted irrespective of CSP-specific CD8+ T cell responses, and recent genome-wide epitope profiling returned multiple sporozoite antigens and epitopes [START_REF] Hafalla | Identification of targets of CD8(+) T cell responses to malaria liver stages by genome-wide epitope profiling[END_REF][START_REF] Lau | CD8+ T cells from a novel T cell receptor transgenic mouse induce liver-stage immunity that can be boosted by blood-stage infection in rodent malaria[END_REF][START_REF] Pichugin | Identification of a Novel CD8 T Cell Epitope Derived from Plasmodium berghei Protective Liver-Stage Antigen[END_REF]. RTS,S/AS01, the leading subunit malaria vaccine based on CSP, seems to offer some protection against P. falciparum re-infection [START_REF] Sctp | Efficacy and safety of RTS,S/AS01 malaria vaccine with or without a booster dose in infants and children in Africa: final results of a phase 3, individually randomised, controlled trial[END_REF]. Partial and short-lived protection is likely primarily mediated by the action of transitory anti-sporozoite antibodies [START_REF] Olotu | Efficacy of RTS,S/AS01E malaria vaccine and exploratory analysis on anti-circumsporozoite antibody titres and protection in children aged 5-17 months in Kenya and Tanzania: a randomised controlled trial[END_REF][START_REF] White | Immunogenicity of the RTS,S/AS01 malaria vaccine and implications for duration of vaccine efficacy: secondary analysis of data from a phase 3 randomised controlled trial[END_REF][START_REF] Kester | Randomized, double-blind, phase 2a trial of falciparum malaria vaccines RTS,S/AS01B and RTS,S/AS02A in malaria-naive adults: safety, efficacy, and immunologic associates of protection[END_REF].

Strikingly, peripheral blood CD8+ T cell responses were not identified to provide a role following sporozoite challenge in this candidate vaccine. Together with previous findings [START_REF] Schmidt | Memory CD8 T cell responses exceeding a large but definable threshold provide long-term immunity to malaria[END_REF][START_REF] Bruna-Romero | Complete, long-lasting protection against malaria of mice primed and boosted with two distinct viral vectors expressing the same plasmodial antigen[END_REF][START_REF] Gonzalez-Aseguinolaza | Induction of protective immunity against malaria by priming-boosting immunization with recombinant cold-adapted influenza and modified vaccinia Ankara viruses expressing a CD8+-T-cell epitope derived from the circumsporozoite protein of Plasmodium yoelii[END_REF][START_REF] Kumar | The circumsporozoite protein is an immunodominant protective antigen in irradiated sporozoites[END_REF] our data underscore efforts to improve the most advanced candidate malaria vaccine, RTS,S/AS01, by eliciting CD8+ T cells against CSP or other immunodominant antigens.

in endotoxin-free PBS at a concentration of 10 5 viral particles for AdPbCSP for the prime immunisation and 10 6 viral particles MVAPbCSP for the boost immunisation.

Immunofluorescent antibody assay. 10,000 sporozoites were spotted onto epoxy coated glass slides with marked rings (Medco), dried at room temperature and stored at -20°C.

Thawed slides were fixed in acetone, dried and rehydrated with PBS before incubation in 10% FCS supplemented DMEM (Gibco) for 1 hour at 37°C in a humid chamber. Serum at concentrations 1:10 3 , 1:3.3x10 3 , 1:10 4 , 1:3.3x10 4 , 1:10 5 (and, additionally, 1:3.3x10 5 and 1:10 6 for C57BL/6 serum) were added to the ring wells and incubated for 1 hour at 37°C in a humid chamber. Slides were washed and stained with a mouse anti-CSP (38) primary antibody.

Hoechst33342 was added as the nuclear stain together with a respective fluorescently labelled anti-mouse secondary antibody for a further one-hour incubation. Slides were washed and mounted with 'Fluoromount-G' (Southern Biotech) and analysed by fluorescent microscopy (Zeiss Axio Observer).

Quantification of SYIPSAEKI-specific CD8+ T cell responses. Spleens were harvested and lymphocytes were derived by passing spleens through 40µm cell strainers (Corning).

Peripheral blood was drawn from the tail vein and collected in Na + heparin capillary tubes (Brand) and assayed in 96-well flat bottom plates (Corning). Red blood cells were lysed using PharmLyse (BD) and lymphocytes were resuspended in 10% FCS, 2% Penicillin-Streptomycin and 1% L-glutamine supplemented RPMI 1640 (Gibco). Splenocytes were counted using a 40x dilution with Trypan Blue (ThermoFisher Scientific) and a Neubauer 'Improved' haemocytometer (Biochrom). 2x10 6 splenocytes and the lysed blood samples were prepared in 96 well plates and incubated with a final concentration of 10µg/ml of SYIPSAEKI peptide in in the presence of Brefeldin A (eBioScience) for 5-6 hours at 37°C and 5% CO 2 . For staining of cell surface markers and intracellular cytokines, cells were incubated for 1 hour at 4°C for each staining. Cells were stained for CD8 (53-6.7) and CD11a (M17/4) (eBiosience). Splenic cells were fixed with 4% paraformaldehyde and peripheral blood cells were fixed with 1%

For

  this purpose, PbCSP SIINFEKL radiation-attenuated sporozoites (RAS), where the SYPSAEKI sequence has been replaced with the H-2-K b -restricted epitope of ovalbumin, SIINFEKL ((26), Müller and Gibbins et al., unpublished) were used to immunise H-2-K d -expressing BALB/c mice. To date, there are no other reported strongly immunogenic H-2-K d -restricted PbCSP epitopes identified. Removal of SYPSAEKI, by replacement with an irrelevant epitope, in the PbCSP SIINFEKL parasites allows unequivocal assignment of critical roles of this immunodominant PbCSP-derived epitope in protection elicited by live sporozoite immunisations. Two weeks after immunisation, the frequencies of IFN-g-producing SYIPSAEKI-specific CD8+ T cell responses in the spleen after gating for CD11a expression (an activation marker commonly used to identify antigen-experienced cells (27)) were measured by flow cytometry (Fig. 1A). As expected, PbCSP SIINFEKL RAS parasites elicited no SYIPSAEKI-specific CD8+ T cell responses in BALB/c mice. To ascertain whether SYIPSAEKI contributes to parasite-induced protection, BALB/c mice were immunised once (Fig 1B) or twice (Fig 1C) with either PbWT or PbCSP SIINFEKL RAS. Two

FIG 1

 1 FIG[START_REF]World Malaria Report 2017 World Health Organisation[END_REF] SYIPSAEKI is dispensable for RAS immunisation but predominates protection with

203FIG. 2

 2 FIG. 2 Prime-boost vaccination with viral vectored CSP-expressing vaccines induces strong

FIG 3

 3 FIG[START_REF] Hoffman | Protection of humans against malaria by immunization with radiation-attenuated Plasmodium falciparum sporozoites[END_REF] Prime-boost vaccination with CSP expressing viruses does not protect C57BL/6 mice,

ACKNOWLEDGEMENTS J.C.R.H. was funded by grants from The Royal Society (University Research Fellowship UF0762736/UF120026 and Project Grant RG130034) and the National Centre for the Replacement, Refinement & Reduction of Animals in Research (Project Grant NC/L000601/1). O.S. was funded in part by the Laboratoire d'Excellence ParaFrap (ANR-11-LABX-0024). K.Matuschewski was supported by the Max Planck Society and grants from the European Commission (EviMalaR Network of Excellence #34), the Chica and Heinz Schaller Foundation, and the Alliance Berlin Canberra "Crossing Boundaries: Molecular Interactions in Malaria", which is co-funded by a grant from the Deutsche Forschungsgemeinschaft (DFG) for the International Research Training Group (IRTG) 2290 and the Australian National University. A.R-S., a Jenner Investigator and an Oxford Martin Fellow, was funded by a Wellcome Trust Career Development Fellowship (Grant 097395/Z/11/Z). We would like to thank the Jenner Institute's Viral Vector Core Facility for the viral vectored vaccines. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

 [START_REF] O'hara | Clinical assessment of a recombinant simian adenovirus ChAd63: a potent new vaccine vector[END_REF][START_REF] Reyes-Sandoval | CD8+ T effector memory cells protect against liver-stage malaria[END_REF]. The viral vectors were administered intramuscularly paraformaldehyde before staining for IFN-g (XMG1.2) (eBioscience) in the presence of Perm/Wash buffer (BD) for intracellular staining. Data was acquired by flow cytometry using an LSRFortessa or LSRII (BD) and analysed using Flowjo9.5.2 (Tree Star, Inc.).

Quantification of parasite load in the liver. Livers were harvested 40-42 hours after sporozoite challenge and total RNA was extracted following homogenisation using TRIzol (ThermoFisher Scientific). cDNA was generated using the RETROScript Kit (Ambion).

Quantitative real-time PCR was performed using the StepOnePlus Real-Time PCR System and Power SYBR Green PCR Master Mix (Applied Biosystems). Relative liver parasite levels were quantified using the ΔΔCt method comparing levels of P. berghei 18S rRNA using specific primers and normalised to levels of mouse GAPDH mRNA [START_REF] Muller | The Puf-family RNA-binding protein Puf2 controls sporozoite conversion to liver stages in the malaria parasite[END_REF].

Assessment of parasitaemia.