MD Sophie Robin

MD Marjory Jolicoeur

MD Samuel Palumbo

MD Thomas Zilli

MD PhD Gilles Crehange

MD Olivier De Hertogh

MD Talar Derashodian

MD Paul Sargos

MD Carl Salembier

MD, PhD Stéphane Supiot

PhD Corina Udrescu

Olivier Chapet
email: olivier.chapet@chu-lyon.fr

Pr Olivier Chapet

Prostate Bed Delineation Guidelines for Postoperative Radiation Therapy: On Behalf Of The Francophone Group of Urological Radiation Therapy

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

INTRODUCTION

Radical prostatectomy (RP) is one of the standard treatments for localized prostate cancer [START_REF] Hamdy | 10-year outcomes after monitoring, surgery, or radiotherapy for localized prostate cancer[END_REF]. However, approximately one third of patients experience a biological recurrence within the decade following surgery [START_REF] Cornford | Eau-estro-siog guidelines on prostate cancer. Part ii: Treatment of relapsing, metastatic, and castration-resistant prostate cancer[END_REF][START_REF] Pisansky | Adjuvant and salvage radiation therapy after prostatectomy: Astro/aua guideline amendment, executive summary 2018[END_REF].

Salvage radiotherapy is recommended for the management of biochemical relapse after RP [START_REF] Cornford | Eau-estro-siog guidelines on prostate cancer. Part ii: Treatment of relapsing, metastatic, and castration-resistant prostate cancer[END_REF][START_REF] Pisansky | Adjuvant and salvage radiation therapy after prostatectomy: Astro/aua guideline amendment, executive summary 2018[END_REF][START_REF] Carrie | Short-term androgen deprivation therapy combined with radiotherapy as salvage treatment after radical prostatectomy for prostate cancer (getug-afu 16): A 112-month follow-up of a phase 3, randomised trial[END_REF][START_REF] Shipley | Radiation with or without antiandrogen therapy in recurrent prostate cancer[END_REF]. The clinical target volume (CTV) for post-operative radiotherapy is the prostate bed (PB), sometimes extended to the pelvic lymph nodes [START_REF] Pollack | Short term androgen deprivation therapy without or with pelvic lymph node treatment added to prostate bed only salvage radiotherapy: The nrg oncology/rtog 0534[END_REF]. However, after surgery, the delineation of the CTV is complex and subject to large intra-and interobserver variations [START_REF] Latorzeff | Delineation of the prostate bed: The "invisible target" is still an issue?[END_REF]. Four guidelines are already available, in order to assist the radiation oncologist with the delineation of the PB [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF][START_REF] Poortmans | Guidelines for target volume definition in post-operative radiotherapy for prostate cancer, on behalf of the eortc radiation oncology group[END_REF][START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF][START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF]. Nevertheless, these guidelines differ in several major points, such as the borders of the PB at the apex or at the base, limiting therefore an overall contouring agreement among the radiation oncology community. Moreover, use of modern imaging techniques like multiparametric magnetic resonance imaging (mpMRI) and more recently prostate-specific membrane antigen (PSMA) PET/CT have been implemented in the restaging workflow of relapsing prostate cancer, with a clear impact on treatment volume delineation [START_REF] Amzalag | Target definition in salvage radiotherapy for recurrent prostate cancer: The role of advanced molecular imaging[END_REF][13][START_REF] Bhargava | Imaging biochemical recurrence after prostatectomy: Where are we headed?[END_REF].

The GFRU identified the need to generate new recommendations for PB delineation and a consensual atlas based on simple and reproducible anatomical landmarks, easy to be identified on planning computed tomography (CT) datasets.

MATERIALS AND METHODS

A group of 10 GFRU prostate radiation oncologists' experts (4 from France, 3 from Belgium, 1 from Switzerland, and 2 from Quebec-Canada) worked together for the definition of the PB, following a four-step procedure:

Step 1: PB delineation guidelines review Four existing guidelines for PB-CTV delineation were analyzed: the European Organization for Research and Treatment of Cancer (EORTC) [START_REF] Poortmans | Guidelines for target volume definition in post-operative radiotherapy for prostate cancer, on behalf of the eortc radiation oncology group[END_REF]; the Faculty of Radiation Oncology Genito-Urinary Group (FROGG) [START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF]; the Radiation Therapy Oncology Group (RTOG) [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF]; and the Princess Margaret Hospital (PMH) [START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF] consensus guidelines. For the definition of each anatomical boundary of the PB, the four guidelines were compared and variations in PB definition were identified (Table 1).

Step 2: Literature review

The methodology used in this study was based on a critical, not systematic, review of the literature of the last three decades up to March 2020, on PubMed, to collect surgical, radiological, anatomical and/or histological information likely to help finding an accurate and converging definition of the delineation limits of the PB differing between the four guidelines.

Step 3: Magnetic resonance imaging (MRI)-based analysis of PB boundaries

For each boundary of the PB delineation, the GFRU group performed an analysis of 50 prostate T2-MRI series. Twenty-five patients have already had a prostatectomy and 25 different patients had an intact prostate gland.

Step 4: Consensus on PB definition and CT image

Based on the analysis of these four guidelines, the review of the literature and the analysis of the MRI acquisitions, a final consensus on limits for PB-CTV definition was reached among the 10 GFRU experts and a CT image atlas was proposed (maximum thickness of 3 mm for the continuous CT scan slices with an injection of contrast agent).

The final consensus on these guidelines was established among the panelists after several meetings conducted from 2016 to prepare the GFRU contouring workshops.

RESULTS

INFERIOR LIMIT

Existing guidelines

Two landmark structures are commonly used to define the inferior limit of the PB-CTV delineation: the vesico-urethral anastomosis (VUA) with an additional margin below it [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF][START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF][START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF] and the penile bulb [START_REF] Poortmans | Guidelines for target volume definition in post-operative radiotherapy for prostate cancer, on behalf of the eortc radiation oncology group[END_REF][START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF][START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF]. The recommended limit to define the PB-CTV apex ranges on the different guidelines between 5 and 12 mm below the VUA. The distance from the cranial part of the penile bulb to the inferior limit of the PB-CTV also ranges from a minimum of one CT slice (thickness not defined) up to15 mm. Urethrography has been used to define the prostate apex by providing a clear visualization of the penile urethra to the point where it enters the urogenital diaphragm [START_REF] Schild | The role of retrograde urethrography in the planning of prostate cancer radiotherapy[END_REF]. The penile bulb, an easily identifiable soft tissue structure, lying immediately below the urogenital diaphragm of the pelvic floor, can be used as a surrogate landmark for the prostate apex [START_REF] Li | Using ct imaging to delineate the prostatic apex for radiation treatment planning[END_REF][START_REF] Plants | Bulb of penis as a marker for prostatic apex in external beam radiotherapy of prostate cancer[END_REF]. Studies correlating the penile bulb location with the prostate apex, suggest an average distance between the two structures of 15 mm based on the MRI imaging [START_REF] Plants | Bulb of penis as a marker for prostatic apex in external beam radiotherapy of prostate cancer[END_REF]. Incorporation of this average distance into treatment planning has been associated with satisfactory target coverage of the apical region of the prostate [START_REF] Milosevic | Magnetic resonance imaging (mri) for localization of the prostatic apex: Comparison to computed tomography (ct) and urethrography[END_REF].

Lock et al. compared on 10 patients the relative accuracy of urethrogram or penile bulb delineation as surrogate markers for the prostate apex [START_REF] Lock | The utility of penile bulb contouring to localise the prostate apex as compared to urethrography[END_REF]. The authors showed that the penile bulb can be used to identify the prostate apex, and that the measurements between the penile bulb and the apex are consistent between patients and through the course of treatment. Penile bulb can be reliably contoured between observers, ensuring a localization of the prostate apex comparable to urethrography [START_REF] Lock | The utility of penile bulb contouring to localise the prostate apex as compared to urethrography[END_REF].

MRI analysis

Apex-penile bulb distance

The distance between the prostate apex and the penile bulb measured on the 25 prostate T2-MRI acquisitions was on average 6.7 mm (range, 4.7-11 mm) (Figure 1). All the measurements were inferior to 15 mm in contrast with the results of the literature [START_REF] Plants | Bulb of penis as a marker for prostatic apex in external beam radiotherapy of prostate cancer[END_REF]. Using the EORTC definition (where the apex was localized at 15 mm from the penile bulb) [START_REF] Poortmans | Guidelines for target volume definition in post-operative radiotherapy for prostate cancer, on behalf of the eortc radiation oncology group[END_REF], the PB-CTV would not be correctly covered at the apex for all the 25 patients. For the three other guidelines [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF][START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF][START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF], the first slice of PB-CTV corresponds to the first slice above the penile bulb. Assuming that the slice thickness of the planning CT does not exceed 5 mm, the PB-CTV apex would be correctly covered for all cases analyzed.

VUA-penile bulb distance

The distance between the VUA and the penile bulb was measured on the 25 postoperative T2-MRI acquisitions (Figure 1). This distance ranged from 10.3 mm to 27 mm, with an average of 18.4 mm. In the PMH, FROGG, and RTOG guidelines, the inferior limit of the PB-CTV is defined at 8 mm, 5-6 mm, and 8-12 mm below the VUA, respectively [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF][START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF][START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF]. According to these three guidelines, on the 25 post-operative T2-MRI series, the most inferior slice of the PB-CTV delineation would be on average 9.6 mm (range, 2.3-19 mm), 12.1 mm (range, 4.8-21.5 mm), and 7.6 mm (range, 0.3-17 mm) above the penile bulb, respectively (Figure 2). In the present analysis on the 25 postoperative MRI acquisitions, major discrepancies compared to existing guidelines were demonstrated.

GFRU analysis

Identification of the VUA is not easy on CT imaging because of the postsurgical rearrangements and requires the use of an intravenous injection of contrast. Moreover, according with the measures above, there is some variability in the distance between the VUA and the penile bulb on post-prostatectomy MRI. Consequently, the current definitions of the apex based on VUA (PMH, FROGG and RTOG) could be inappropriate to systematically cover the inferior limit of the PB-CTV as it has already been shown by Manji et al. [START_REF] Manji | Target volume definition for post prostatectomy radiotherapy: Do the consensus guidelines correctly define the inferior border of the ctv?[END_REF].

The penile bulb is a structure easily identified on the CT imaging even without contrast injection and its position remains stable after RP. By starting the delineation of PB-CTV 5 mm above the penile bulb, the apical part of the PB-CTV was correctly covered on all 25 analyzed prostate MRI acquisitions.

GFRU definition

At its most inferior part the PB_CTV lies between the inferior limit located 5mm above the penile bulb. The posterior limit is represented by the anterior wall of the rectum or of the anal canal. The lateral and anterior limits are the pelvic muscles or the insertion of the corpora cavernosa (Figure 4A). These limits are in correlation with the other guidelines.

MIDDLE SECTION

Existing guidelines

The four guidelines propose very similar limits to delineate the middle section of the PB-CTV: the pubic symphysis anteriorly, the levator ani or the obturator internus muscles laterally, and the anterior rectal wall posteriorly [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF][START_REF] Poortmans | Guidelines for target volume definition in post-operative radiotherapy for prostate cancer, on behalf of the eortc radiation oncology group[END_REF][START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF][START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF]. A small variation is proposed by the RTOG and FROGG guidelines [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF][START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF], which suggest that the posterior limit of the PB-CTV needs to be concave on both side of the rectum to better include the rectoprostatic angles [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF][START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF].

Analysis of the literature

Nevoux et al. performed a quantitative tissue analysis of prostate cancer foci in an

unselected series of 96 cysto-prostatectomy specimens [START_REF] Nevoux | Quantitative tissue analyses of prostate cancer foci in an unselected cystoprostatectomy series[END_REF]. They showed that 75% of the tumors are located in the peripheral zone [START_REF] Nevoux | Quantitative tissue analyses of prostate cancer foci in an unselected cystoprostatectomy series[END_REF]. In the middle part of the prostate, the tumors of more than 0.5 cc are mainly located in the peripheral zone and more specifically in the two posterolateral areas [START_REF] Nevoux | Quantitative tissue analyses of prostate cancer foci in an unselected cystoprostatectomy series[END_REF]. When target volumes were delineated using the RTOG guideline, the CTV coverage was marginal in the posterolateral regions near to the rectum and the mesorectal fascia [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF]. In another series analyzing 121 surgical specimens, the extracapsular extension occurred postero-laterally along the neurovascular bundle in all analyzed cases [START_REF] Chao | Clinicopathologic analysis of extracapsular extension in prostate cancer: Should the clinical target volume be expanded posterolaterally to account for microscopic extension[END_REF]. These results clearly support the need to have a concave delineation of the posterior limit of the PB-CTV on both sides of the rectum.

MRI analysis

A specific analysis of the available T2-MRI series was not found to be relevant for the delineation of the middle section of the PB-CTV.

GFRU analysis

Anteriorly and laterally, the four guidelines converge on similar recommendations based on the anatomical definition of the structures surrounding the prostate. Posteriorly, the anterior rectal wall represents the limit. Based on the review of the literature, the two posterolateral recto-prostatic angles need to be included in the PB-CTV volume.

GFRU definition

In the middle section, the posterior limit of the PB-CTV is the anterior border of the rectum including the posterolateral angles on both sides of the rectum of 5 mm. The experts considered that it is a reasonable compromise to cover the risk of relapse and to limit the irradiation of the rectal wall. The lateral limits are the internal borders of the levator ani or of the obturator internus muscles. The muscles should not be included in the PB-CTV. The anterior limit is represented by the posterior border of the pubic symphysis (Figure 4B,C).

ANTERIOR UPPER LIMIT

Existing guidelines

Based on the EORTC guidelines [START_REF] Poortmans | Guidelines for target volume definition in post-operative radiotherapy for prostate cancer, on behalf of the eortc radiation oncology group[END_REF], the anterior upper limit of the PB-CTV should include "the VUA and the urethral axis". In the PMH and RTOG guidelines, this limit is represented by the top of the edge of the pubic bone [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF][START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF]. In the FROGG guidelines [START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF], from the lower border of the PB-CTV to 3cm superior, the anterior border of the PB-CTV is the posterior aspect of the symphysis pubis. In these last three guidelines [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF][START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF][START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF], at least 1.5 cm of the bladder neck must be included in the delineation (up to 2 cm in the RTOG guideline) [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF].

Analysis of the literature

Based on the Nevoux et al. study [START_REF] Nevoux | Quantitative tissue analyses of prostate cancer foci in an unselected cystoprostatectomy series[END_REF], no significant tumor (> 0.1cc) is generally found on the pathological RP specimen in the upper anterior third of the prostate.

MRI analysis data based on the guidelines

On the 25 prostate MRI acquisitions, the length of contact between the prostate and the pubic bone was measured and the ratio between the length of this contact and the total length of the pubic bone was calculated. The ratio varied from one patient to another from 17% to 90%. However, in 80% of cases, this percentage was inferior to 66% (Figure 3).

GFRU analysis

In a study by Freitag et al., 119 patients with biochemical recurrence after RP were restaged both with hybrid 68 Ga-PSMA-11-PET/CTlow-dose and PET/MRI including a multiparametric MRI (mpMRI) protocol of the PB [START_REF] Freitag | Local recurrence of prostate cancer after radical prostatectomy is at risk to be missed in 68 Ga-PSMA-11-PET of PET/CT and PET/MRI: comparison with mpMRI integrated in simultaneous PET/MRI[END_REF]. The authors observed that the detection rate of local recurrences using the PET-component was significantly influenced by the proximity to the bladder, with the risk to miss relapses due to the 68 Ga-PSMA residual urinary radioactivity [START_REF] Freitag | Local recurrence of prostate cancer after radical prostatectomy is at risk to be missed in 68 Ga-PSMA-11-PET of PET/CT and PET/MRI: comparison with mpMRI integrated in simultaneous PET/MRI[END_REF]. These findings were confirmed by another study by Achard et al. suggesting the added value of mpMRI imaging for the detection of PB recurrences compared to standard whole body hybrid 18 F-choline PET/MRI protocols [START_REF] Achard | Recurrent prostate cancer after radical prostatectomy: restaging performance of 18F-choline hybrid PET/MRI[END_REF]. Compared to PET, mpMRI was able to detect more local relapses (17 vs 14 patients over 58 analyzed), mostly located in the anastomotic region, the bladder neck and the SV bed [START_REF] Achard | Recurrent prostate cancer after radical prostatectomy: restaging performance of 18F-choline hybrid PET/MRI[END_REF].

In a systematic literature review concerning the current role of mpMRI in the detection of locoregional recurrence, Barchetti et al. reported that after RP, the most common site of local recurrence is the vesico-urethral anastomosis around the urinary bladder and/or membranous urethra [START_REF] Barchetti | Multiparametric MRI for recurrent prostate cancer post radical prostatectomy and postradiation therapy[END_REF]. Other common sites of local recurrence are retrovesical (between the urinary bladder and rectum), within retained SVs, at the anterior or lateral surgical margins of the prostatectomy bed (e.g., abutting the levator ani muscles) and at the resection site of the vas deferens [START_REF] Barchetti | Multiparametric MRI for recurrent prostate cancer post radical prostatectomy and postradiation therapy[END_REF]. Similar results were observed by Zilli et al. in a series of 171 prostate cancer patients relapsing after RP and restaged with an endorectal MRI before salvage radiotherapy [START_REF] Zilli | Results of dose-adapted salvage radiotherapy after radical prostatectomy based on an endorectal MRI target definition model[END_REF]. Among the 131 patients with a positive MRI imaging, the perianastomotic (35.9%) and the bladder neck region (33.6%) were the most common sites of local recurrence, followed by penile bulb (19%) and the SV bed (3.8%) [START_REF] Zilli | Results of dose-adapted salvage radiotherapy after radical prostatectomy based on an endorectal MRI target definition model[END_REF].

Based on the above studies, on the Nevoux et al. study [START_REF] Nevoux | Quantitative tissue analyses of prostate cancer foci in an unselected cystoprostatectomy series[END_REF] and the analysis on the 25 MRI acquisitions, the use of the top of the edge of the pubic bone as upper anterior limit of the PB-CTV seems to be a quite generous landmark. An upper limit located at 2/3 of the pelvic bone (closer to the FROGG definition [START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF]) appears a reasonable solution to cover the area at risk of relapse and to limit the volume of bladder included in the high-dose volume. In the three guidelines [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF][START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF][START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF], a length of 1.5 cm of the bladder neck has to be included in the PB-CTV. This rule is necessary to cover the VUA and the interface between the prostate and the bladder. In the FROGG guideline [START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF], the PB-CTV must be extended by at least 3 cm from the lower slice of delineation. This minimal length is reasonable according to the size of the prostate and the necessity to cover at least 1.5 cm of bladder neck.

Analysis of the literature

In several studies on MRI analysis, the rate of involvement of the bottom of the SV is very low, ranging between 0% and 13%. In the Samaratunga et al. study, 16% of the SV invasions were located in the distal third of the SV [START_REF] Samaratunga | Distal seminal vesicle invasion by prostate adenocarcinoma does not occur in isolation of proximal seminal vesicle invasion or lymphovascular infiltration[END_REF]. Kestin et al. measured the length of cancer involvement from the prostate to the SV junction [START_REF] Kestin | Treatment of prostate cancer with radiotherapy: Should the entire seminal vesicles be included in the clinical target volume?[END_REF]. On the 81 pathologic specimens analyzed in this study, the risk of SV involvement beyond 2 cm was approximately 1% [START_REF] Kestin | Treatment of prostate cancer with radiotherapy: Should the entire seminal vesicles be included in the clinical target volume?[END_REF]. In another study on 71 patients treated with RP, 12 patients (17%) had a SV involvement but none of them had a pathological involvement of the last 1 cm of the SV [START_REF] Korman | Radical prostatectomy: Is complete resection of the seminal vesicles really necessary?[END_REF].

MRI analysis

The distance between the distal part of the SV and the top of the pubic bone is used in the RTOG guidelines [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF]. This definition is by far the easiest to apply. In the 25 prostate MRI acquisitions, the distance between the extremity of the SV and the top of the pubic symphysis was measured on average at 26.4 mm [range, 3-56.2 mm]. This distance was less than 4 cm and 3 cm in 84% and 76% of the cases, respectively.

GFRU analysis

The vas deferens arises from the testicle, following the epididymal canal and it ends at the confluence of the SV and the ejaculatory duct. The union between the vas deferens and the neck of the SV forms the ejaculatory duct at the base of the prostate.

Using the vas deferens to define the upper border of the SV bed might present some limitations:

1-The vas deferens is not always visible on the planning CT.

2-The surgical section of vas deferens may vary from a surgery (and surgeon) to another.

3-The vas deferens may retract upward and backward after RP.

For these reasons, vas deferens may not be the most appropriate anatomical landmark to define the upper limit of the delineation of the SV bed. According to the analysis of the 25 MRI acquisitions and the review of the literature, the RTOG definition [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF] based on the top of pubic bone (+ 3cm) seems accurate, and highly reproducible.

GFRU definition

If SV are pathologically involved (Figure 4F, I, J):

The superior limit of delineation of the SV bed is defined at 3 cm above the top of the pubic symphysis. This limit can be extended up to 4 cm in case of involvement of the last third of the SV on the histopathological specimen. The posterior limit is the anterior border of the mesorectum. The GFRU recommends the inclusion of the posterior third of the bladder wall (with a thickness of 1cm) to better encompass the the SV bed. The lateral limits are the internal obturator muscles. 4E,G,H): In order to cover the prostate-SV junction, the superior border of the SV bed is maintained to the first 1 cm above the pubic symphysis, keeping the same anterior, posterior and lateral limits used in case of SV involvement. consideration the site of post-RP relapse combined with surgical and anatomical data [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF].

If SV are not pathologically involved (Figure

In the Malone et al. study [START_REF] Malone | Postoperative radiotherapy for prostate cancer: A comparison of four consensus guidelines and dosimetric evaluation of 3d-crt versus tomotherapy imrt[END_REF], the four consensus guidelines were compared in 20 patients in terms of treatment volumes and organs at risk irradiation. The PB-CTV differed significantly between the four guidelines, allowing a potential impact on longterm clinical outcome and treatment-related toxicity [START_REF] Malone | Postoperative radiotherapy for prostate cancer: A comparison of four consensus guidelines and dosimetric evaluation of 3d-crt versus tomotherapy imrt[END_REF]. The PB-CTV volume defined using the EORTC guidelines was significantly smaller than the CTVs defined using the other recommendations, with a more limited coverage of the PB in the anterior and superior directions [START_REF] Malone | Postoperative radiotherapy for prostate cancer: A comparison of four consensus guidelines and dosimetric evaluation of 3d-crt versus tomotherapy imrt[END_REF]. In another study, Ost et al. analyzed the inter-observer variability in contouring the PB-CTV according to the EORTC guidelines [START_REF] Ost | Delineation of the postprostatectomy prostate bed using computed tomography: Interobserver variability following the eortc delineation guidelines[END_REF]. They showed only a moderate observer agreement for both the PB-CTV (mean kappa, 0.49; range, 0.35-0.62) and the SV bed (mean kappa, 0.42; range, 0.22-0.59) [START_REF] Ost | Delineation of the postprostatectomy prostate bed using computed tomography: Interobserver variability following the eortc delineation guidelines[END_REF].

Taking into consideration limitations and divergences of the existing guidelines, the GFRU defined the need for a new guideline and atlas, able to limit the inter-observer variations with well-defined anatomical limits easily identified by any physician.

Why a guideline based on CT imaging?

Matching postoperative MRI and CT may be challenging due to anatomical variations in the PB shape between the two exams. Based on these considerations, the GFRU experts' panel estimates that a guideline based on only one single imaging modality is more adapted to homogenize contouring of the PB-CTV among the radiation oncology community. As observed by Barkati et al. using the RTOG guidelines, defining the PB-CTV based on CT imaging resulted in a statistically significant lower interobserver variability (mean dice similarity coefficient: 0.76) compared to a MRI-based contouring (mean dice similarity coefficient: 0.66) [START_REF] Barkati | Magnetic resonance imaging for prostate bed radiotherapy planning: An inter-and intra-observer variability study[END_REF]. The increasing use of mpMRI for restaging and radiotherapy planning, along with the diffusion among the radiation oncology community of educational platforms for contouring, are both expected to reduce this interobserver variability in PB definition.

What are the interests of this new guideline?

We applied a three-step methodology was applied based on the analysis of the existing guidelines and their discordances, on a review of the literature, and on the study of 50 MRI datasets. This guideline, written by experts in the field of prostate radiotherapy, is based on simple anatomical structures easy to be identified on a planning CT: the penile bulb, the bladder, the rectum, the mesorectum, the pubic symphysis, and the pelvic muscles. Anatomical boundaries more difficult to be identified on CT imaging or associated with a variable position in the pelvis (such vas deferens or the VUA) were avoided.

We acknowledge that a stronger methodology based on a systematic review of the literature, a larger panel of experts including specialists from other disciplines, and integration of agreement measures among the panelists, would have provided more robustness to our guidelines. However, a validation analysis of our consensus guidelines is actually ongoing using the available datasets from three contouring workshops organized annually from 2017 by the GFRU.

CONCLUSIONS

New recommendations for PB-CTV delineation based on simple anatomical boundaries and available as a CT image atlas are proposed by the GFRU for [START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF], Faculty of Radiation Oncology Genito-Urinary Group (FROGG) [START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF], and Radiation Therapy Oncology Group (RTOG) [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF] guidelines. [START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF] 8mm below the vesicourethral anastomosis or the top of the penile bulb.

-Caudal boundary : Posterior edge of the symphysis pubis up to the top of the symphysis pubis.

-Cranial boundary : The posterior 1.5 cm of the bladder wall.

-Cranial boundary : The sacro-recto-genitopubic fascia, lateral to the neurovascular structures. At the cranial aspect of the CTV, it is not necessary to extend to the obturator muscle.

-Caudal boundary : the medial border of the levator ani and obturator internus.

-Cranial boundary : the mesorectal fascia.

-Caudal boundary : the anterior border of the rectal wall and levator ani.

The superior surgical clips (if present) or 5mm above the inferior border of the vas deferens. Retained seminal vesicles were included when pathologically involved. FROGG [START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF] 5-6mm below the vesicourethral anastomosis but should extended lower to include all surgical clips inferiorly. When the anastomosis is not clearly defined, the inferior border will be the slice above the penile bulb.

-From the lower border of the CTV to 3cm superior, the anterior border of the CTV is the posterior aspect of the symphysis pubis.

-More superiorly, the anterior border of the CTV encompasses the posterior 1.5cm of the bladder. -If SV are pathologically involved :

The superior limit of delineation of the SV bed is defined at 3 cm above the top of the pubic symphysis. This limit can be extended up to 4 cm in case of involvement of the last third of the SV on the histopathological specimen. The GFRU recommends the inclusion of the posterior third of the bladder wall (with a thickness of 1cm) to better encompass the the SV bed.

-If SV are not pathologically involved :

The superior border of the SV bed is reduced to the first 1 cm above the pubic symphysis, keeping the same anterior, posterior and lateral limits used in case of SV involvement.

Figure 1 .

 1 Figure 1. Average distance with range (in mm) between the penile bulb and the apex on

Figure 2 .

 2 Figure 2. Average distance with range (in mm) between the inferior border of the

Figure 3 .

 3 Figure 3. Ratio of the length (in mm) of the prostate in contact with the pubic bone (PBo)

Figure 4 .

 4 Figure 4. Computed tomography-based atlas for prostate bed clinical target delineation

GFRU 5 mm

 5 above the PB. The posterior limit is the anterior wall of the rectum or of the anal canal. The lateral and anterior limits are the pelvic muscles or the insertion of the corpus cavernosum. Delineation of the upper anterior limit of the PB-CTV must fulfill three criteria : -At least 1.5 cm of the bladder neck must be included in the PB-CTV.-The PB-CTV must cover the posterior border of the pubic bone on at least 2/3 of its length.-At least 3 cm are necessary between the lower and upper slices of delineation of the PB-CTV along the pubic bone. When the three rules criteria are fulfilled, the anterior delineation of the CTV along the pubic bone is discontinued.Internal borders of the levator ani or obturator internus muscles. The muscles are not included in the volume of delineation.The anterior border of the rectum including the posterolateral angles in both sides of the rectum in 5 mm.

Table 1 .

 1 Consensus guidelines for post-operative prostate bed clinical target delineation.

		Inferior border	Anterior border	Lateral border	Posterior border	Superior border
	EORTC [9]	Including the apex. 15 mm cranially from the penile bulb.	Including the anastomosis and the urethral axis.	Up to the neurovascular bundles (if removed : up to the ilio-obturatic muscles).	Up to but not including the outer rectal wall. Cranially including the most posterior part of the bladder neck	Include the bladder neck. For patients with invasion of the seminal vesicles, the prostate bed including the apex and the original location of the seminal vesicles.
	PMH

postoperative prostate radiotherapy. Improvement in uniformity in PB-CTV definition and treatment homogeneity in the context of clinical trials are expected. Further validation of these consensus guidelines is ongoing based on the data of several contouring workshops organized by the GFRU with radiation oncologists from France, Belgium, Switzerland, and Morocco.

GFRU definition

Delineation of the upper anterior limit of the PB-CTV must fulfill three criteria (Figure 4D,E

SEMINAL VESICLES BED

Existing guidelines

In the EORTC guidelines [START_REF] Poortmans | Guidelines for target volume definition in post-operative radiotherapy for prostate cancer, on behalf of the eortc radiation oncology group[END_REF], delineation of the seminal vesicles (SV) bed is recommended only in case of SV invasion on the surgical specimen. The PB-CTV includes the original location of the SV. In the PMH guidelines [START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF], the PB-CTV is delineated up to the vas deferens (5 mm above the inferior border of the vas deferens) and must include all the surgical clips. The FROGG guidelines use the same limits but specify that residual SV must be included in the volume [START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF]. Lastly, in the RTOG guidelines the PB is delineated up to the vas deferens, or 3 to 4 cm above the top of the pubic symphysis and includes SV remnants if pathologically involved [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF].

Considering the minimal risk of pathological involvement of the bottom part of the SV, the superior border limit of the SV bed can be reduced in order to respect the dose constraints to the rectum and the bladder.

DISCUSSION

Based on the existing literature, postoperative RT for prostate cancer is associated with a large interobserver variability in the PB-CTV contouring [START_REF] Foppiano | Airo pros 01-04 multi-centric study in contouring ctv for conformal radiotherapy after radicalprostatectomy[END_REF]. Systematic errors in PB-CTV definition may impact the final dosimetry and treatment delivery by translating into possible underdosage of the target and/or overdosage of the healthy tissues [START_REF] Foppiano | Airo pros 01-04 multi-centric study in contouring ctv for conformal radiotherapy after radicalprostatectomy[END_REF].

International guidelines have been developed to assist radiation oncologists in standardizing the contouring process and potentially reducing its variability [START_REF] Michalski | Development of rtog consensus guidelines for the definition of the clinical target volume for postoperative conformal radiation therapy for prostate cancer[END_REF][START_REF] Poortmans | Guidelines for target volume definition in post-operative radiotherapy for prostate cancer, on behalf of the eortc radiation oncology group[END_REF][START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF][START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF].

Why is a new guideline necessary?

The present GFRU analysis of the existing guidelines shows some large variations in the limits of delineation of the PB-CTV which may induce significant variations in the doses delivered to the target and to the organs at risk [START_REF] Croke | Postoperative radiotherapy in prostate cancer: The case of the missing target[END_REF]. Differences in methodology used for defining the PB-CTV in the four guidelines can explain this variability. The EORTC guidelines do not provide a precise description of the methodology used [START_REF] Poortmans | Guidelines for target volume definition in post-operative radiotherapy for prostate cancer, on behalf of the eortc radiation oncology group[END_REF]. The PMH guidelines have been generated evaluating data based on the topography of the post-RP relapses, as well as based on radiological anatomy and surgical findings [START_REF] Wiltshire | Anatomic boundaries of the clinical target volume (prostate bed) after radical prostatectomy[END_REF].

The FROGG guidelines are the result of an expert's debate on the PMH contouring atlas [START_REF] Sidhom | Post-prostatectomy radiation therapy: Consensus guidelines of the australian and new zealand radiation oncology genito-urinary group[END_REF]. The RTOG atlas uses an algorithm to determine the PB-CTV borders taking into


Barbara Lafarge

Sébastien Grondel

Christophe Delebarre

Octavian Curea

Claude Richard

Linear electromagnetic energy harvester system embedded on a vehicle suspension: From modeling to performance analysis

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

1 Abstract-Although linear electromagnetic energy harvester (LEH) is a promising technique for converting energy in a vehicle suspension, due to the large displacements, one of the main drawbacks of the solutions inside the vehicle is still their size and complexity. To address this issue, this paper focuses on the design and fabrication of a fully embedded LEH without any modification of the suspension initial structure. After a determination of the electrical, mechanical and electromechanical parameters using a Finite Element analysis, the dynamic efficiency is highlighted with a global Bond Graph model. This formalism is well adapted to simulate energy transfers inside multiphysic systems and to reduce the computational time, whereas the finite element model is not exploitable for a complete suspension simulation. In order to validate the Bond Graph simulation results, an embedded prototype has been built and tested in a laboratory environment. The embedded LEH system delivers around 10 watts for a solicitation of linear velocity of 1m/s which is sufficient to power a classical electronic circuit which is in good correlation with the measured ones and significant power has been obtained. Index Terms-Energy harvesting, car suspension, electromagnetic harvesters, Bond Graph modeling.

I. NOMENCLATURE magnetic induction, damping of the shock absorber or the suspension, / electromotive force, measured energy for a full cycle, integral of the magnetic force for a full cycle, damper force, generated force by the external tooth, magnetic force, _ magnetic force for coil according to the index i, !" total magnetic force, # mean force for a full cycle, tire force, $ = 1 '( 3 index i indicates the number of considered coils, *$ + $(+, -./$.0, $1'2 current in the coils, 3 4 BG storage element I represents the inductance 5 67 _ of each coil respectively 8 9 # stiffness of the suspension, / 8 tire stiffness, / 5 67 coil inductance, : 5 67 _ coil inductance according to the index i, : ; [START_REF] Wang | Modelling, testing and analysis of a regenerative hydraulic shock absorber system[END_REF] sprung mass, kg ; [START_REF] Zhang | A high-efficiency energy regenerative shock absorber using supercapacitors for renewable energy applications in range extended electric vehicle[END_REF] mass is shared between the sprung mass and the unsprung mass of the suspension, kg ; [START_REF] Wang | Modelling, testing and analysis of a regenerative hydraulic shock absorber system[END_REF] unsprung mass, kg ;<= power exchange between the electrical and mechanical subsystems of each coil is represented by the modulated gyrator ;<= whose the modulation ratio corresponds to the non-linear function / >? 1'2@ 67 number of the turns contained in a coil, *$ + $(+, -./$.0, A maximum power for a full cycle, B / non-linear term, *$ + $(+, -./$.0, / non-linear term according to the index i, *$ + $(+, -./$.0, C Bond Graph (BG) dissipative element R represents the resistance C 67 _ of each coil respectively C 67 resistance of the coil, Ω C 67 _ resistance of the coil according to the index i, Ω C 7 resistance of the load, Ω 1 '2 voltage at the outputs of the electromagnetic element and of the load circuit, ?E linear velocity according to the mechanical variable used on BG, / ? 1'2 displacement imposed on the shock absorber, ? F 1 '2 unsprung mass displacement, ?E F 1 '2 unsprung mass translation velocity, / ? G 1 '2 sprung mass displacement, ?E G 1'2 sprung mass translation velocity, / ? 1'2 displacement of the electromagnetic harvester with respect to the magnet, ?E 1'2 translation velocity, / Greek ΔI travel distance for a half cycle machine, Δ'

travel time for a full cycle machine, J electromagnetic efficiency, *$ + $(+, + 67 _ number of turns in a coil according to the index $, *$ + $(+, -./$.0, K magnetic induction flux circulating in a coil, B0

II. INTRODUCTION

ODAY energy efficiency is a major concern in the automotive industry which leads also several researches to be developed on energy harvesting in vehicle suspension. In the literature, electro-mechanical conversion applied to vehicle may be realized using different kinds of harvesters [START_REF] Abdelkareem | Vibration energy harvesting in automotive suspension system: A detailed review[END_REF][START_REF] Lafarge | A validated simulation of energy harvesting with piezoelectric cantilever beams on a vehicle suspension using Bond Graph approach[END_REF]: electromagnetic, electrostatic, piezoelectric, Peltier effect and photovoltaic. In theory, mechanical energy conversion can be performed on all links and on all flexible and rigid elements of the suspension [START_REF] Lafarge | From functional analysis to energy harvesting system design: application to car suspension[END_REF] but the choice regarding the location of the energy harvester and the conversion technology has therefore to be made according to the amplitude of the available movement without disturbing mechanical behavior of the system. As in a car, a portion of the energy dissipated in the form of heat relies directly on the piston movement in the damper's body of the suspension, the authors have decided to focus on converting the dissipated energy in traditional hydraulic shock absorbers.

Several types of energy harvester have already been fixed or embedded into the body of a shock absorber. These solutions can be grouped into two categories [START_REF] Abdelkareem | Vibration energy harvesting in automotive suspension system: A detailed review[END_REF]: the linear harvesters (direct energy harvesters) and the rotary harvesters (indirect energy harvesters). As seen in Fig. 1, all techniques convert large displacements with more or less important energy levels and across different operability frequency ranges. However, although some of the rotary harvesters can be more compact and have higher energy density than the linear ones [START_REF] Abdelkareem | Vibration energy harvesting in automotive suspension system: A detailed review[END_REF], their structure is usually more complex. This is obvious for the following systems: the mechanical based transmission as ball screw mechanism [START_REF] Kawamoto | Modeling of electromagnetic damper for automobile suspension[END_REF], the simple [START_REF] Li | Energy-harvesting shock absorber with a mechanical motion rectifier[END_REF][START_REF] Li | Electromagnetic energy-harvesting shock absorbers: design, modeling, and road tests[END_REF] or double [START_REF] Zhang | A high-efficiency energy regenerative shock absorber using supercapacitors for renewable energy applications in range extended electric vehicle[END_REF] rack-pinion mechanism, the hydraulic regenerative shock absorber [START_REF] Zhang | Study on a novel hydraulic pumping regenerative suspension for vehicles[END_REF][START_REF] Wang | Modelling, testing and analysis of a regenerative hydraulic shock absorber system[END_REF][START_REF] Zhang | Electro-hydraulic damper for energy harvesting suspension: Modelling, prototyping and experimental validation[END_REF] and the electromagnetic rotary damper [START_REF] Audit | Innovative of the year: Audit eRot[END_REF] respectively. This complexity leads to a rise of both costs and structure modifications of the shock absorber or the automotive suspension.

Furthermore, the linear electromagnetic solution [START_REF] Gupta | Design of electromagnetic shock absorbers[END_REF][START_REF] Longxin | Structure and Performance Analysis of Regenerative Electromagnetic Shock Absorber[END_REF][START_REF] Zhen | Structure and Magnetic Field Analysis of Regenerative Electromagnetic Shock Absorber[END_REF][START_REF] Lin | Simulation and performance evaluation of hydraulic transmission electromagnetic energy-regenerative active suspension[END_REF][START_REF] Zuo | Design and characterization of an electromagnetic energy harvester for vehicle suspensions[END_REF][START_REF] Gysen | Active electromagnetic suspension for improved vehicle dynamics[END_REF] and the spring mass system one [START_REF] Wei | A novel approach to energy harvesting from vehicle suspension system: Half-vehicle model[END_REF] are the easiest to integrate comparing with other techniques such as the no-electromagnetic rotary type [START_REF] Audit | Innovative of the year: Audit eRot[END_REF] and the linear type hydraulic system [START_REF] Ebrahimi | Feasibility study of an electromagnetic shock absorber with position sensing capability[END_REF][START_REF] Ebrahimi | Design of a hybrid electromagnetic/hydraulic damper for automotive suspension systems[END_REF]. Among these solutions, the most accomplished ones is the electromagnetic linear system [START_REF] Gysen | Active electromagnetic suspension for improved vehicle dynamics[END_REF] which has been already successfully tested on the laboratory environment or road. Since the surface of magnetic circuit and the number of coils are optimized for the entire distance of the energy harvester movement, it allows output power at low speed. Consequently, this solution becomes increasingly attractive because of its high energy conversion efficiency, design simplicity, fast response, strong controllability and efficient capability in the energy recovery. Nevertheless, the main drawback of the current linear energy harvesters is still their size since this kind of structure provides at this time no place for the hydraulic part of a classic vehicle shock absorber. O. Curea is with ESTIA Recherche, 64210 Bidart, France (e-mail: o.curea@estia.fr).

C. Richard is with LGEF Laboratory, INSA, University of Lyon, France (e-mail: claude.richard@insa-lyon.fr). T Fig. 1. Performances of energy harvester system embedded in a car suspension In response to this problem, the authors have decided in this paper to design a new linear electromagnetic energy harvester directly embedded on a real shock absorber. Such a development requires solving many technological and scientific key issues. The first one deals with the choice of used materials to obtain an optimal energy conversion without changing the overall original structure of the suspension. A second one is a compromise to find between a maximum power harvesting while reducing at the same time as much as possible the magnetic force fluctuations due to the tooth of the magnetic circuit. The last challenge concerns the precise characterization of the non-linear electromagnetic coupling coefficient which is essential for the energy conversion.

In the section II, this paper presents the proposed design for the linear electromagnetic energy harvester embedded in the vehicle suspension. This system is composed of several subsystems: the car suspension, the linear electromagnetic energy harvester and the restitution electronic circuit. Taking care about the design, the analysis of the main parameters is done in the section III. In particular, the electronic, mechanical and electromechanical parameters are determined using a Finite Element analysis. In section IV, a Bond Graph (BG) model is developed to simulate the dynamic and power efficiency of the linear electromagnetic harvester. Simulations are then compared with the experimental results measured on a prototype.

III. SYSTEM DESCRIPTION

A. Technical description

The instrumented suspension can be divided into several subsystems (see Fig. 2): the first subsystem corresponds to the suspension itself, the second one to the electromagnetic harvester and the last one to the electrical circuit for managing and storage of the electrical energy. In this study, the energy harvester is embedded between the vehicle body (sprung mass) and the wheel (unsprung mass). This choice is motivated by the fact that the upper part of the rod outside the damper near the coil spring, despite a reduced space, is a region of high potential energy. The mechanical stresses applied to the suspension system are the input movements induced by the road profile.

In order to facilitate the integration of the harvester without disturbing the other mechanical elements, the permanent magnets are placed inside the rod and the coils in the shock absorber body. In addition, the orientation of the magnets is such that adjacent magnets oppose each other to act as magnetic flux guides around the coils. Finally, a magnetic circuit surrounding the coils is designed to optimize the passage of this magnetic field. This magnetic circuit is usually made of ferromagnetic material through which the magnetic induction flux flows (see Fig. 4).

B. Theoretical study

The linear electromagnetic energy harvester can be divided also into two subsystems (Fig. 3-a). The first one describes the transformation of the mechanical energy into electrical energy, whereas the second one corresponds to the electrical circuit coupled to this conversion for the electrical energy recovery. In this case, the voltage at the outputs of the electromagnetic element and of the load circuit are equal to 1'2. [START_REF] Arroyo | Comparison of electromagnetic and piezoelectric vibration energy harvesters: Model and experiments[END_REF] and (b) equivalent electrical circuit representing the linear electromagnetic harvester [START_REF] Arroyo | Comparison of electromagnetic and piezoelectric vibration energy harvesters: Model and experiments[END_REF] In order to take into account the energy source characteristics, it is also necessary to add a mass-spring-damper type representation in parallel with the mechanical energy conversion subsystem (Fig. 3-a). This part which mechanically includes the energy transformation, symbolizes the physical structure in which the active components, i.e. the electromagnetic harvester and the magnet are located. It is represented using damping of the shock absorber, inertia ; 7 and stiffness 8 9 # elements. Here the mass ; 7 is shared between the sprung mass and the unsprung mass of the suspension. When a mechanical stress is applied to the shock absorber, this results in the displacement ? 1'2 of the electromagnetic harvester with respect to the magnet. ? L 1t2 here corresponds to the displacement imposed on the shock absorber.

If we focus on the electromagnetic harvester, it can be modeled using the equivalent electrical circuit shown in Fig. 3-b. It consists of a voltage source >? 1'2@ proportional to the translation velocity ?E 1'2 and an electromagnetic coefficient depending on this translation, in series with the inductance of the coil 5 67 and its resistance C 67 . Therefore, we assume as the electromotive force ( ) and the position (? ) is a composion of function and ? expressed as N o? P1'2 = >? 1'2@. Using the equivalent circuits, we can easily deduce both a mechanical equation (1.a) and an electrical one (1.b) [START_REF] Munaz | A study of an electromagnetic energy harvester using multi-pole magnet[END_REF]:

Q R R R S R R R T ; 7 *²? 1'2 *'² = ; 7 *²? 1'2 *'² V *? 1'2 *' V ⋯ 8 9 # ? 1'2 V / >? 1'2@ $1'2 >? 1'2@ = 1C 67 V C 7 2$1'2 V 5 67 *$1'2 *'
>? 1'2@ = / >? 1'2@ *? *' >? 1'2@ = / >? 1'2@ $1'2 11. .2 11. 02 11. Y2 11. *2 where C 7 corresponds to the load resistance.

The movement ? 1'2 = ? G 1'2 Z ? F 1'2 of the sprung mass ? G 1'2 relativity to the unsprung mass ? F 1'2 induces a translation of the shock absorber body containing the coils with respect to the stack of permanent magnets located in the rod as shown in Fig. 10. This results in a current in the coils $1'2 and therefore a voltage 1'2 measurable at the linear electromagnetic harvester output. At the end, the electric energy can be stored or directly used to simulate the function of a real electrical load.

Nevertheless, it should be noted that this system presents a non-linear effect because the magnetic force

>? 1'2@(1.d)
belonging to the mechanical equation (1.a) and the electromotive force >? 1'2@ (1.c) of the electrical equation are both functions of a non-linear term / >? 1'2@ which depends on the position ? 1'2. / >? 1'2@ is the mechanical-electrical coupling term. A key issue for the design of the electromagnetic harvester is to be able to characterize these functions, therefore it is essential to describe more precisely the structure of the electromagnetic harvester. As shown in Fig. 4-a, the electromagnetic structure is axisymmetric. Compared to the structure shown in Fig. 3-a, Fig. 4-a takes into account several layers of coils and magnets [START_REF] Kwon | Electromagnetic energy harvester with repulsively stacked multilayer magnets for low frequency vibrations[END_REF] to increase the energy performance of the system. Let us now present the relevant equations arising from such a system. According to Lenz-Faraday's law [START_REF] Donoso | Magnet fall inside a conductive pipe: motion and the role of the pipe wall thickness[END_REF], the electromotive force depends on the distribution of the magnetic induction flux K circulating in the coil:

>? 1'2@ = Z 67 *K >? 1'2@
*'

(2) with 67 the number of the turns contained in a coil.

It is clear from the literature that this calculation of magnetic induction fluxes strongly depends on the chosen configuration and is fundamentally non-linear. Some authors have recently worked to solve analytically this problem [START_REF] Kwon | Electromagnetic energy harvester with repulsively stacked multilayer magnets for low frequency vibrations[END_REF] and [START_REF] Soliman | A wideband vibration-based energy harvester[END_REF][START_REF] Mann | On the performance and resonant frequency of electromagnetic induction energy harvesters[END_REF][START_REF] Dallago | Analytical model of a vibrating electromagnetic harvester considering nonlinear effects[END_REF][START_REF] Priya | Energy harvesting technologies[END_REF]. Nevertheless, the disadvantage is that it requires to determine experimentally all the parameters, which is not always possible.

In our case, we propose another approach. As a main assumption, we consider that the magnetic induction flux seen by each turn is the same and is described by equation ( 3):

K >? 1'2@ = [ 1? 1'22*\ 67 9 6 7#
(3) Since the distribution of the magnetic induction as function of the space and time for the chosen configuration remains very complex, its computation is obtained using the finite element method (see section III).

Note that the index $ indicates the number of considered coils (we consider three coils). We obtain the following expression (4):

>? 1'2@ = Z 67 _ *K >? 1'2@ *' (4)
In order to express equation ( 4) as a function of the mechanical-electrical coupling term / >? 1'2@, we can rewrite this expression as follows, with the derivative of the composite function:

>? 1'2@ = Z 67 _ *K >? 1'2@
*? *? *'

(5) Thus, we obtain:

>? 1'2@ = / > ? 1'2@ *? *' (6)
Knowing that each coil is characterized by an inductance 5 67 _ and a resistance C 67 _ , it is possible to deduce the expression of the output voltage 1'2 of each coils using the Kirchhoff laws [START_REF] Sinha | Electromagnetic suspension: dynamics and control[END_REF] for coils connected in parallel, as shown in Fig. 5-a.

1'2 = Z5 67 _ *$ 1'2 *' Z C 67 _ $ 1'2 V >? 1'2@ (7)
The coils can be connected to the external electrical circuit in two ways, either in series or in parallel. A series connection gives a high output voltage with a low current across a load, while conversely, a parallel connection induces a low voltage with a higher output current. Consequently, the power is identical for these two configurations and only the voltage/current proportions vary. In our case study, the authors have chosen the parallel configuration as shown in Fig. 5-a to obtain a high current with respect to the voltage. The power recovered across a resistance C 7 for coils in parallel is as followed: Fig. 5-b illustrates the normalized power variation (output power divided by its maximum) with regard to the normalized value of the load resistor (value of the load resistor divided by the equivalent resistance of the coils). The output power is maximized by a load resistor that matches the value of the equivalent resistance of the coils. In this case, the same power will be dissipated on the coil and load resistance and it is obvious that electrical efficiency cannot exceed 50%. For a different resistor, the output power decreases. If the value of the resistor is lower, the current increases, but more power will be dissipated on the coils and if the value is higher, the output current decreases and the power lost on the coils will be lower. However, output power losses do not exceed 5% for a variation of the normalized resistance from 0.73 to 1.38.

A1'2 = C 7 $1'2 G (8) with $1'2 the sum of current crossed the coils. $1'2 = ] $ 1'2 ^ _F (9) (a) (b)
To obtain experimentally the maximum power, the technical solution are to measure directly the current and voltage across the load resistance or for more precision to use a Maximum Power Point Tracking (MPPT) algorithm with its associated converter. The last technique is used commonly to maximize power extraction under all conditions [START_REF] Kumar | A review of conventional and advanced MPPT algorithms for wind energy systems[END_REF].

With the help of the fundamental principle of dynamics which describes the relative movement of magnets with respect to coils caused by the excitation imposed by the road through the unsprung mass [START_REF] Priya | Energy harvesting technologies[END_REF][START_REF] Kaźmierski | Energy harvesting systems: Principles, modeling and applications[END_REF], it is possible to achieve the expression below:

9 `a`1 2 `= 9 `Na `1 2ba c 1 2P `V Na `1 2ba c 1 2P V 8 9 # N? G 1'2Z? F 1'2P V ! > ? 1'2@ (10)
It remains then to determine the magnetic force for each coil d >? 1'2@ corresponding to the term / >? 1'2@ $ 1'2. It is obtained from a power balance on the electromagnetic system such as:

d 1? 1'22 *? 1'2 *' = 1? 1'22$ 1'2 (11)
It is then possible to replace the electromotive force by its expression given in equation ( 2) and thus by coil, one obtains:

d 1? 1'22 *? 1'2 *' = Z 67 _ *K >? 1'2@ *' $ 1'2 (12)
By generalizing the equation ( 12) for all the coils and taken into account the generated force by the external tooth noted effeg >? 1'2@ we can deduce that:

h c > ? 1'2@ V `> ? 1'2@ V i > ? 1'2@ V I' tooth > ? 1'2@k a l 1 2 = Z m 67 c n c Na l 1 2P $ F 1'2 V 67 ` n `Na l 1 2P $ G 1'2 V 67 i n i Na l 1 2P $ ^1'2 Z I' tooth > ? 1'2@o
(13) Note that we have added the complementary term corresponding to the tooth which will be measured at very slow speed. This term can then be rewritten as follows: Hence the total magnetic force !" N? , 'P can be deduced from the following relationship:

c >? 1'2@ V `>? 1'2@ V i >? 1'2@ V effeg >? 1'2@ = Z m 67 c n c Na l 1 2P a l $ F 1'2 V 67 ` n `Na l 1 2P a l $ G 1'2 V 67 i n i Na l 1 2P a l $ ^1'2 Z effeg >? 1'2@o (14)
! 1'2 = / F >? 1'2@ $ F 1'2 V / G >? 1'2@ $ G 1'2 V / ^>? 1'2@ $ ^1'2 V effeg >? 1'2@ (15)
The key issue hereafter is to maximize the harvester power at the output of the electromagnetic harvester without degrading the dynamic shock absorber behavior. A compromise on both the geometry and the location of the electromagnetic harvester has to be found in order to increase the energy conversion.

Using equation ( 4), a flux optimization of the magnetic induction can be obtained by adjusting both the geometry, i.e. the size of the coils and the configuration of the magnetic circuit. Furthermore, the electromagnetic coupling term, seen in expressions ( 6) and [START_REF] Lin | Simulation and performance evaluation of hydraulic transmission electromagnetic energy-regenerative active suspension[END_REF], is a non-linear one and requires a thorough characterization. Another key issue is the electromagnetic harvester location which plays a main role in energy recovery. Indeed, the higher the displacement speed applied to the harvester is, the greater the obtained energy levels are as shown in equation [START_REF] Abdelkareem | Vibration energy harvesting in automotive suspension system: A detailed review[END_REF]. Notice that the maximum energy level remains however limited because of the material magnetic saturation and the actually available space inside the rod. Consequently, the harvester mechanical structure as well as its electrical part would have to be adapted to the characteristics of the energy source.

IV. PARAMETERS ANALYSIS

A. Parameter's definition

When designing the electromagnetic energy harvester, a first key issue is that its integration does not interfere with the car damper linear movement whereas a second key issue is that it also not brings major changes in the suspension laws. We will see in the section III-B that the tooth forces have a negative impact on it, so the design aim will be to reduce the circuit magnetic's dentition phenomena to +/-20N. This value is acceptable because it is less than 10% of the shock absorber's damping force and may be decreased in future works. To achieve this range of strength, several techniques can be proposed: either one can modify the magnetic circuit and the elements location of the electromagnetic harvester or move the magnets away from the magnetic circuit. The chosen solution (Fig. 4-b) is to adapt the elements location of the electromagnetic harvester and to redraw the magnetic circuit surrounding the coils as shown in Fig. 4-a and Fig. 6. The designed damper is therefore much easily inserted into the actual suspension system of the vehicle. The key parameters are summarized in Table I.

B. Finite Element Method (FEM) simulation

To determine the magnetic forces generated by each of the three coils as well as by the tooth of the magnetic circuit, such as the external cages whose position is given in Fig. 6, it is first necessary to analyze the derivative of the flux evolution of magnetic induction computed with a static FEM analysis (see Fig. 7-a). Fig. 6. New magnetic circuit topology integrated into a shock absorber considering the magnetic forces reduction More precisely, this first step leads us to characterize the nonlinear coefficients / F >? 1'2@, / G >? 1'2@ and / ^>? 1'2@ corresponding to the magnetic circuit portions surrounding the coils (Fig. 7-b) since they are directly dependent on the derivation calculation of the magnetic induction flux as underlined in the expression (4). Notice that their value summarized in Table II as example for a given velocity can be used as an input variable in the BG model as shown in section IV. It is supposed in this case that the magnetic fields induced by the coil current are small compared to the magnet coercive field so that they do not modify significantly the global magnetic flux.

TABLE II PARAMETERS INTEGRATED IN

In a second step, the generated magnetic forces (Fig. 7-d) are deduced from the currents present in the coils (Fig 7-c) as shown in equation [START_REF] Gupta | Design of electromagnetic shock absorbers[END_REF]. Finally, the total magnetic force (Fig. 7-e) is the sum of these generated magnetic forces and the tooth force of the magnetic circuit.

C. Comparison between simulations and test results in a static mode

The tests carried out on the prototype are intended to understand the involved phenomena on the one hand and to validate the static finite element simulations on the other hand. It is question of being able to quantify the value of magnet attraction forces/magnetic circuit without any coil as well as to observe the different parameters influence [START_REF] Kwon | Electromagnetic energy harvester with repulsively stacked multilayer magnets for low frequency vibrations[END_REF][START_REF] Priya | Energy harvesting technologies[END_REF] on its intensity.

As shown on Fig. 8, this part is the first phase of the study of finding the right location for the magnetic circuit. The prototype tested in this section is a simplified version of the energy harvester, since only the magnets, the spacers and the magnetic circuit surrounding the coils are present. The coils are not present. More precisely, the prototype consists of a part of the magnetic circuit which corresponds to a simple disc in translation with the rod containing magnets separated by spacers (see Fig. 8-a) without coil. This configuration was specially developed in order to minimize the effects of frictional forces due to fluids, sealing elements, such as lip seals and O-rings, and the mechanical friction between elements, as well as the electromotive force. Therefore, frictions between the elements of the electromagnetic harvester are reduced at their minimum in order to measure only the magnetic forces induced by the magnetic circuit structuring, i.e. the tooth effect.

In practice, this means that the shock absorber prototype including a simplified circuit magnetic (Fig. 8-a and8-c) is installed on a hydraulic test bench shown in Fig. 8-b. Furthermore, only the lower part of the shock absorber is set in motion which corresponds to ? 1'2 while the upper part remains static.

Then, a BC302 strain gauge used as force sensor is fixed on the shock absorber (Fig. 8-a) to deduce with a better precision than the S-beam load cell the forces acting on the system. In this configuration, the weight of the discs has no effect on the measurement system. The force sensor has been calibrated to cancel the weight of the rod. Moreover, the conventional interface of the test bench has been modified (Fig. 8-b) to vary the position of the rod containing the magnets with respect to the teeth, millimeter by millimeter at a very low speed of 0.001m/s. The speed is as low as possible. We assume a quasi-static movement. In this measurement, there is no current. This approach allows the measurement of the magnetic instantaneous force.

The magnets and the steel parts in the rod and intercalated between them have a height of 8mm and 4mm respectively, while the thickness of the disc representing part of the magnetic circuit leading the flux lines is equal to 3mm. Note that the middle position of the magnetic circuit is indicated on the upper part of Fig. 9. After analysis of the results, it can be observed that the measured magnetic forces vary mostly sinusoidally with an amplitude of +/-10N for a single disc (Fig. 9). However, it is necessary to have two discs of the same thickness to properly conduct magnetic field lines around a coil. As expected, the additional disc increases considerably the magnetic forces. The obtained result confirms that the magnetic induction flux varies sinusoidally as a function of its position in the magnetic circuit.

The experimental results obtained are then compared to the FEM simulation ones. As expected, the comparison is in good keeping. Indeed, the difference between the results is less than 6.75% (Table III) which validates the simulation. It should be also noticed that various topological configurations of the magnetic circuit have been also tested which demonstrated that it was possible to increase or decrease this magnetic force just by changing the position and adding steel discs.

V. DYNAMIC EFFICIENCY OF THE ELECTROMAGNETIC ENERGY HARVESTER

A. Bond Graph model of the electromagnetic energy harvester embedded on the shock absorber

In order to analyze the dynamic efficiency of the electromagnetic harvester, the BG method is proposed since it allows taking into account both the mechanical behavior of the suspension as well as the electromagnetic harvesting and at the same time characterizing the power exchanges inside the system. The first step is therefore to establish the word BG of the global system (see Fig. 10). This word BG is deduced from Fig. 2 and represents the suspension system divided into subsystems helping to have a general overview of the topic. The input and output of each subsystem define power variables represented by a half arrow. Variables used for this studied system are the mechanical variables 1 (/Y , 5$+ ./ -,(Y$'?2 = 1 , ?E 2 and the electrical ones 1 (,'.x , y// +'2 = 1 , $2.

The second step lies in finding the BG model of each subsystem. As the BG subsystems of the road suspension system as well as the power storage and restitution circuit have been lengthy developed in [START_REF] Lafarge | A validated simulation of energy harvesting with piezoelectric cantilever beams on a vehicle suspension using Bond Graph approach[END_REF], only the electromagnetic harvester subsystem will be detailed here. To determine its BG model, the equations ( 6), ( 7) and ( 14) of the electromagnetic conversion system are used. In this case, the BG dissipative element R and the BG storage element 4 represent the resistance C 67 d and the inductance 5 67 d of each coil respectively.

Shock absorber

Unsprung mass of the suspension

Tire

Road

?E 1'2 ?E F 1'2 ?E F 1'2 1'2 1'2 1'2

Sprung mass of the suspension

?E G 1'2 1'2 Electromagnetic harvester 1'2 ?E ' = ?E G ' -?E F ' 1'2 ?E ' Electromagnetic harvester External load 1'2 ?E ' = ?E G ' -?E F ' 1'2 ?E ' V1'2 i ' (a) (b)
Fig. 12. Electromagnetic harvester prototype embedded on a shock absorber and mounted on a hydraulic test bench

The power exchange between the electrical and mechanical subsystems of each coil is represented by the modulated gyrator ;<= whose modulation ratio corresponds to the non-linear function / 1? 1'22. The index $ indicates the highlighted coil. The 0 junction results directly from the Kirchhoff's current law whereas the 1 junction reflects the Kirchhoff's voltage law in each coil. Note that the generated force by external tooth effeg 1? 1'22 is evaluated from experiments, and is required for the computation of the global magnetic force. The resulting BG model of this subsystem is shown in the Fig. 11.

B. Energy harvesting validation in a laboratory environment

In order to demonstrate the validity of the approach in a real case, the electromagnetic shock absorber prototype (Fig. 4-b) is mounted on a hydraulic bench (Fig. 12). Note that the movement of the hydraulic bench does not exceed 49mm and is imposed through a linear velocity. Contrarily to previous experiments, the tests are carried out in dynamics. Fig. 13 presents the curves of the voltage and the power measured and simulated on the same optimal load (C 7 = 46.5Ω) for two different velocities: 0.75m/s and 1m/s respectively. As expected, the results of the simulation and experiments are in good correlation, since the interval error between the measured and simulated results is less than 6% (Table IV). The obtained maximum amplitudes of the voltages and the power are equal to 15V and 4W for a solicitation of 0.75m/s respectively while they reach 20V and 7W for a solicitation of 1m/s. Another significant result is the sinusoidal variation of the voltages and powers curves which validates our initial assumption that the flux inside the coils varies sinusoidally.

Figure 14 represents the variation of the magnetic forces for two different velocities. When the velocity is equal to 0.75m/s, the variation of the magnetic forces is approximately 18N (Fig. 14-a) while it increases slightly for a velocity of 1m/s (Fig. 14b). This variation of the magnetic force is added to the friction forces present in the shock absorber.

The Table V summarizes all the results. The observed maximum differences between the experiments and the FEM and BG simulations methods are equal to 26.2% and 33.3% respectively. As showed by [START_REF] Kwon | Electromagnetic energy harvester with repulsively stacked multilayer magnets for low frequency vibrations[END_REF], it could be possible to develop more precise computations but this will undoubtedly require to develop an experimental device to accurately estimate the magnetic induction flux variation. Although, this difference stays important, it allows however to quantitatively estimate generally the magnetic force generated by the magnetic circuit.

Furthermore, all these results are physically coherent as demonstrated below. Let us consider first the measured energy ( 16) for a complete cycle:

= [ *I 6a6 = 2 | # | ∆I (16)
at V = 0.75m/s and V = 1m/s which is equal to 2.17J and 2.64J respectively and second the cycle time [START_REF] Gysen | Active electromagnetic suspension for improved vehicle dynamics[END_REF]:

∆' = 2 * ∆I (17)
equal to 0.1261s and 0.0945s for 0.75m/s and 1m/s respectively, then the combination of these expressions leads to the generated power [START_REF] Wei | A novel approach to energy harvesting from vehicle suspension system: Half-vehicle model[END_REF]. (18) The maximum power for a complete cycle is then equal to 17.25W and 28W for 0.75m/s and 1m/s respectively, a part of this energy is converted in electrical energy, which is consistent with the results of Table IV. Note that represents the integral of the magnetic force i.e. 23N at 0.75m/s (Fig. 14-a) and 28N at 1m/s (Fig. 14-b) whereas ∆x = 47. [START_REF] Dallago | Analytical model of a vibrating electromagnetic harvester considering nonlinear effects[END_REF] is the travel distance for a half cycle.

These first results are encouraging since the energy available at the output of the proposed electromagnetic energy harvester of the order of 10 Watts appears sufficient to power a classical electronic circuit. Moreover, magnetic forces remain important but have been largely reduced.

C. Simulation of the global model

In order to demonstrate the validity of the approach, simulation tests have been performed with the whole energy harvester system embedded in a vehicle model. Moreover, two different situations have been experimented: the first situation corresponds to drive through a speed bump at 30km/h, whereas the second one coincides with driving test at 20km/h on a road of A-B class and E-F class respectively.

Table VI summarizes all the mechanical parameters injected on the vehicle system. The analysis of the simulated harvester power signals demonstrated that the energy is significant on a long period and could be used to supply sensors. Fig. 15 illustrates the voltage and power simulated as function of the time measured through the optimal load resistance (C 7 ). The maximal output voltage range obtained is close to 22.26V with a maximal output power of 10.67W during the speed bump excitation. The average power value is 4.4mW. To know the energy distribution in the global system, it is relevant to study its evolution in all the subsystems (Fig. 16 and17). The simulated injected energy to the suspension parts by the road is 208J. The energy is then decomposed in three different ones. The main part is dissipated through friction in the car damper (

) and in the electromagnetic energy harvester (C 67 and C 7 ). In parallel, less quantity is stored in potential energy (8 and 8 9 # ) and in kinetic energy (; 9 and ; 9 ). Figure 16 illustrates the total energy, i.e. the injected, dissipated and stored (potential and kinetic) energy as function of the time, in the mechanical parts of the suspension. The obtained responses reflect the behavior of the dual-mass for the mechanical domain. Between 0.2s and 0.26s, the car goes up to the speed bump and goes down from 0.4s to 0.47s. After 0.47s, there is no variation of the road height. Indeed Figure 16 shows that the 8 stored energy increases first between 0.2s and 0.236s which means that the injected energy is stored in the first mechanical part closest to the road, then the 8 9 # stored energy in second time between 0.222s and 0.3s. The energy begins to dissipate in at 0.225s. As the injected energy is stopped to increase at 0.24s and that all this energy is transferred to all mechanical elements, the stored and dissipated energy drop. This behavior is reproduced when the car goes down. When the car goes down, the injected energy is constant and tends towards 207.6J. After a long time of 12s, the injected energy is totally dissipated in and the system converges to a stable state. The kinetic energy (; 9 and ; 9 ) and the potential energy (8 and 8 9 # ) cancel after several fluctuations due to the storage and then the restoration of energy.

It was also possible to simulate the injected and dissipated energy in the electromagnetic energy harvester (see Fig. 17). The injected energy is mainly dissipated both in the coils (C 67 ) (i.e. 70.75% of the injected energy) and in the load (C 7 ) (29.24% of the injected energy). From these curves, it was also possible to determine the electromagnetic efficiency which is equal to J = 0.2924.

When the external load value coincides with the coils equivalent resistance, an optimal repartition of the energy in the system should be obtained and this repartition would correspond to 50% for all the coils and 50% in the load. However, the phase difference between the coils as shown in Fig. 17 From the Fig. 18-a, it can be noted that the magnetic force is in the order of 2N. Therefore, the suspension dynamic behavior is relatively undisturbed for this class road and this car speed. As shown in Fig. 18-b, the simulated injected energy to the electromagnetic harvester by the suspension is equal to 81.71mJ. Once again, the mechanical energy is mainly dissipated in the coils (C 67 ) and in the load (C 7 ) with 67.67% and 32.33% of the injected energy by the suspension respectively.

The E-F class coincides with a very poor surface with holes in the road pavement. The magnitude voltages and power are logically higher than in the previous case. The maximal power and the average power values are equal to 36.32W and 1.67W respectively. The magnetic force is also high with a maximal amplitude of 22.12N, but this force is low in comparison with the original suspension forces. Indeed, the suspension dynamic behavior is slighty disturbed due to the electromagnetic energy harvesters presence with a disturbance in order to 1% all over the vehicle. As shown in Fig. 19-b, the injected energy to the electromagnetic harvester by the suspension is equal to 28.86J. Once again, the mechanical energy is mainly dissipated in the coils (C 67 ) in the load (C 7 ) with 71.10% and 28.92% of the injected energy by the suspension respectively.

When comparing the dissipated energies in the resistive load in the A-B and E-F class of the road pavement, a significant variation of 99.68% is observed. This result is coherent on roads from excellent to poor pavement. To conclude, according to the road classification, it is possible to supply either continuously or alternatively an auxiliary control circuit.

VI. CONCLUSION

In this paper, the study has been focused on the design and fabrication of a fully embedded linear electromagnetic harvester without changing the initial structure of the suspension. To enable an optimum design, it has been however necessary to propose a modeling method sufficient robust to evaluate the efficiency of the system.

In order to evaluate the electrical, mechanical and electromechanical parameter, a static finite element analysis has been first performed in a first step whereas in the second step, these linear and nonlinear parameters have been injected in a dynamic BG model to evaluate the efficiency of the system. Dynamic tests have been then successfully performed and compared with simulation results for a solicitation of linear velocity of 0.75m/s and 1m/s. Obtained results are very promising since the embedded linear electromagnetic harvester system delivers around 10 watts which is enough to power a classical electronic circuit. In comparison with the performances of energy harvester systems embedded in a car suspension in Fig. 1, our harvester system delivers results close to the harvesters cited in references [START_REF] Kawamoto | Modeling of electromagnetic damper for automobile suspension[END_REF], [START_REF] Audit | Innovative of the year: Audit eRot[END_REF] and [START_REF] Gysen | Active electromagnetic suspension for improved vehicle dynamics[END_REF] with the particularity of being embedded in a classic car shock absorber without modifying the structure of the car.

In addition, a simulation of the complete system has been proposed with an analysis allowing extracting injected, stored and dissipated powers in both mechanical and electrical domains and for all subsystems as function of time and for the case of a speed bump solicitation. To our knowledge, this is the first time that a complete modeling (i.e. composed of the car suspension, the electromagnetic energy harvester and the restitution circuit) is proposed.

In view of an energy balance, significant average power is obtained since the simulated results give 4.4mW for a speed bump solicitation, and 5.3mW and 1.67W on a road of A-B class and E-F class respectively with an electromagnetic efficiency equal to J = 0.2924.

Future work is now in progress to test this system in real time on a car driven on a road.

B.

  Lafarge is with Université de technologie de Compiègne, Laboratoire ROBERVAL -FRE UTC -CNRS 2012 (e-mail: barbara.lafarge@uct.fr).S. Grondel and C. Delebarre are with Univ. Polytechnique Hauts-de-France, CNRS, Univ. Lille, ISEN, Centrale Lille, UMR 8520 -IEMN -Institut d'Électronique de Microélectronique et de Nanotechnologie, DOAE -Département d'Opto-Acousto-Électronique, F-59313 Valenciennes, France (sebastien.grondel@uphf.fr and christophe.delebarre@uphf.fr).

Fig. 2 .

 2 Fig. 2. Suspension system with the energy harvester embedded on the shock absorber

Fig. 3 .

 3 Fig. 3. (a) Energy extraction circuit[START_REF] Arroyo | Comparison of electromagnetic and piezoelectric vibration energy harvesters: Model and experiments[END_REF] and (b) equivalent electrical circuit representing the linear electromagnetic harvester[START_REF] Arroyo | Comparison of electromagnetic and piezoelectric vibration energy harvesters: Model and experiments[END_REF]

Fig. 4 .

 4 Fig. 4. Cross sectional view of the electromagnetic energy harvester (a) and the prototype embedded in the shock absorber (b)

Fig. 5 .

 5 Fig. 5. (a) Electrical circuit representative of the coils in parallel connection connected with a resistive load C 7 , and (b) the variation of output power according to load resistor value

Fig. 7 .

 7 Fig. 7. (a) FEM Magnetic induction flux seen by each of the coils and in the so-called "upper zone" (see the Fig. 6), (b) computation of the non-linear term / 1? 1'22 for each of the coils and (c) current evolution, (d) simulated magnetic forces for each coil and (e) resulting total magnetic force

Fig. 8 .Fig. 9 .

 89 Fig. 8. Equipment for tests (a) and (b): the hydraulic test bench, cross view of the shock absorber (c) and the strain gauge sensor

Fig. 11 .

 11 Fig. 11. Word Bond Graph of the suspension system with the electromagnetic harvester embedded on the shock absorber

Fig. 11 .

 11 Fig. 11. Bond Graph model of the electromagnetic harvester

Fig. 13 .

 13 Fig. 13. Instantaneous power and voltage curves for a load resistance value of 46.5Ω and a linear velocity of (a) 0.75m/s, (b) 1m/s

Fig. 17 .

 17 Fig.[START_REF] Gysen | Active electromagnetic suspension for improved vehicle dynamics[END_REF]. Evolution of the injected energy by the electromagnetic system (in black) and total dissipated energy (in red) for the electromagnetic energy harvester subsystem

Fig. 18 .

 18 Fig.[START_REF] Wei | A novel approach to energy harvesting from vehicle suspension system: Half-vehicle model[END_REF]. Simulated voltages and powers with a load resistance value of 46.5Ω in case of driving through a class A-B road with a car speed of 20km/h (a) and evolution of the total injected energy (in black) and total dissipated energy (in red) for the electromagnetic energy harvester (b)

Fig. 19 .

 19 Fig.[START_REF] Ebrahimi | Feasibility study of an electromagnetic shock absorber with position sensing capability[END_REF]. Simulated voltages and powers with a load resistance value of 46.5Ω in case of driving through a class E-F road with a car speed of 20km/h (a) and evolution of the total injected energy (in black) and total dissipated energy (in red) for the electromagnetic energy harvester (b)

TABLE I MATERIAL

 I AND ELECTROMAGNETIC PARAMETERS OF THE TESTED ENERGY RECOVERY SYSTEM

		Parameters	Values	Unity
	C 67 _F + 67 _F	Coil's resistance n°1 Number of turns of the coil n°1	145.6 1820	Ω N/A
	C 67 _G + 67 _G	Coil's resistance n°2 Number of turns of the coil n°2	144.9 1806	Ω N/A
	C 67 _^ + 67 _^	Coil's resistance n°3 Number of turns of the coil n°3	148.1 1840	Ω N/A
	C 7 5 67 c,` i	External load resistance Coil's inductance n°1, 2 or 3	46.5 104.4	Ω mH

  FEM AND BG) AND EXPERIENCE FOR DIFFERENT SPEEDS IMPOSED AT THE INPUT OF THE MODEL

					TABLE IV
			RESULTS OF SIMULATIONS AND EXPERIENCES FOR DIFFERENT IMPOSED VELOCITIES
			Maximal peak voltage [V] from prototype		Maximal peak power [W] from prototype
	Velocity [m/s]	FEM n°4	BG	experiment	gap FEM/exp [%]	gap BG/ exp [%]	FEM n°4	BG	experiment	gap FEM/exp [%]	gap BG/ exp [%]
	0.75m/s	15.15V	15.1V	15V	1%	0.66%	4.21W	4.2W	4W	5.25%	5%	(b)
			FIG. 14. TOTAL FORCES MEASURED FOR A LINEAR SPEED OF (A) 0.75M/S (B) OF 1M/S
	1m/s	20.1V	19.9V	20V	0.5%	1.5%	7.2W	7.15W	7W	2.85%	2.14%
					TABLE V
	RESULTS OF SIMULATIONS (Velocity [m/s]		Magnetic force [N] from prototype
			FEM n°4	BG	experiment	gap FEM/exp [%]	gap BG/exp [%]
	0.75m/s		31N		28N	42N		26.2%	33.3%
	1m/s		38N		34N	50N		24%	32%
												(a)

  Fig.[START_REF] Lin | Simulation and performance evaluation of hydraulic transmission electromagnetic energy-regenerative active suspension[END_REF]. Simulated voltages and powers with a load resistance value of 46.5Ω in case of driving through a speed bump with a car speed of 30km/h Fig.16. Evolution of the total injected energy (in black), total kinetic energy (in cyan), total potential energy (in blue) and total dissipated energy (in red) for the suspension subsystem

		TABLE VI
	MECHANICAL PARAMETERS OF THE VEHICLE SYSTEM [32]
	Symbol	Parameters	Values	Units
	; 9 8 9 #	Sprung mass Suspension stiffness Suspension damping	897.2 66824.4 1190	kg N/m Ns/m
	; 9 8	Unsprung mass Tire stiffness	87.15 101115	kg N/m