Garcilazo-Reyes Ytel

Alentorn Agusti

Duran-Pena Alberto

Hoang-Xuan Khê
email: khe.hoang-xuan@aphp.fr

Houillier Caroline

MD Khê Hoang-Xuan

Treatment of Primary Central Nervous System Lymphoma in immunocompetent patients

Keywords: Primary Central Nervous System lymphoma chemotherapy, radiation therapy, Methotrexate, autologous stem cell transplantation, immunotherapy, rituximab, ibrutinib, imids

Purpose of review:

This review focus on the findings of recent randomized prospective trials evaluating new therapeutic options for primary central nervous system lymphoma (PCNSL) in first line treatment and on the most promising novel agents.

Recent findings:

The current standard treatment of newly diagnosed PCNSL has long been depending on high dose methotrexate (HD-MTX) based polychemotherapy followed by whole brain radiotherapy (WBRT).

Recent randomized trials have provided evidence that high dose chemotherapy with ASCT is a valuable alternative option to WBRT as consolidation after induction HD-MTX based chemotherapy. For the elderly, cumulative studies confirm that chemotherapy alone as initial treatment is the best approach in this frail population in order to reduce chemoradiation neurotoxicity. If the role of rituximab needs to be further investigated, novel agents such as imids and ibrutinib have showed promising drugs to be incorporated in innovative combination treatment.

Summary:

The role of WBRT, at least at conventional dose, is declining in first line treatment.in favor of intensive consolidation chemotherapy with or without ASCT and possibly maintenance chemotherapy in the elderly. Despite their rarity, it has been shown that ambitious randomized trials in PCNSL are feasible thanks to collaborative networks.

Introduction

PCNSLs are rare non-Hodgkin lymphomas of the diffuse large B-cell (DLBC) type that involve the brain, eyes, leptomeninges, or spinal cord, without any systemic lymphoma. Because of the multifocal and infiltrative nature of PCNSL, its well-known chemosensitivity and radiosensitivity, and the lack of randomized trials addressing specifically the interest of cytoreductive surgery [START_REF] Weller | Surgery for primary CNS lymphoma? Challenging a paradigm[END_REF] [START_REF] Labak | Surgical Resection for Primary Central Nervous System Lymphoma: A Systematic Review[END_REF], the role of surgery is widely limited to a stereotactic biopsy for establishing a histopathologic diagnosis [START_REF] Hoang-Xuan | Diagnosis and treatment of primary CNS lymphoma in immunocompetent patients: guidelines from the European Association for Neuro-Oncology[END_REF]. The current standard treatment of newly diagnosed PCNSL has long been depending on high dose methotrexate (HD-MTX) based polychemotherapy followed by WBRT [START_REF] Hoang-Xuan | Diagnosis and treatment of primary CNS lymphoma in immunocompetent patients: guidelines from the European Association for Neuro-Oncology[END_REF][START_REF] Deangelis | Combined modality therapy for primary CNS lymphoma[END_REF]. However, despite a high rate of remission after first line treatment, relapses remain frequent and the overall outcome is poor. In addition, the patients, especially the elderly, are exposed to a high risk of treatment-related neurocognitive dysfunctions and deleterious impact on quality of life [START_REF] Van Der Meulen | Cognitive functioning and health-related quality of life in patients with newly diagnosed primary CNS lymphoma: a systematic review[END_REF]. In order to optimize treatment, several approaches have been proposed such as immunochemotherapy with rituximab, high dose chemotherapy consolidation regimens with autologous stem cell transplantation (HCT-ASCT), reduced dose WBRT in order to minimize the delayed neurotoxicity of combined treatment, maintenance chemotherapy, especially for fragile patients who would not be eligible for WBRT or ASCT. Here, we reviewed recent published and ongoing controlled clinical trials addressing these issues. We also focused on the most promising new agents that would contribute to improve the management of PCNSL.

Induction immunochemotherapy with rituximab in first line treatment

Induction chemotherapy aims to obtain rapidly the highest complete response (CR) rate before consolidation.

If HD-MTX is considered as the standard drug for PCNSL treatment, a polychemotherapy is recommended in order to increase objective response rate and to circumvent chemoresistance. Drugs crossing the blood brain barrier, such as procarbazine, temozolomide, ifosfamide, etoposide, carmustine, lomustine,thiotepa, cytarabine, have been the most frequently used in combination with HD-MTX in PCNSL. In addition, cumulative evidence suggesting that immunotherapy with anti-CD20 rituximab might improve outcome as it does in systemic DLBC lymphomas despite its poor CNS penetration, has led to its incorporation into many induction immunochemotherapy regimens. Hence, several single arm phase II trials have reported encouraging results combining MTX, rituximab and alkylating agents with post-induction CR rates of 60-66%, and 2-year progression free survival (PFS) ranging from 57 to 79% according to subsequent consolidation treatment [START_REF] Omuro | R-MPV followed by high-dose chemotherapy with TBC and autologous stem-cell transplant for newly diagnosed primary CNS lymphoma[END_REF][START_REF] Morris | Rituximab, methotrexate, procarbazine, and vincristine followed by consolidation reduced-dose whole-brain radiotherapy and cytarabine in newly diagnosed primary CNS lymphoma: final results and long-term outcome[END_REF][START_REF] Rubenstein | Intensive chemotherapy and immunotherapy in patients with newly diagnosed primary CNS lymphoma: CALGB 50202 (Alliance 50202)[END_REF][START_REF] Swinnen | Phase II study of rituximab given in conjunction with standard chemotherapy in primary central nervous system lymphoma (PCNSL): a trial of the ECOG-ACRIN cancer research group (E1F05)[END_REF]. However, trials evaluating induction (immuno)chemotherapy combinations with control group are scarce. The international IELSG32 trial is a two sequential randomized phase II study, which randomly assigned 227 patients in three induction chemotherapy arms. The chemotherapy regimens included: (i) HD-MTX and cytarabine only as control group [START_REF] Ferreri | High-dose cytarabine plus high-dose methotrexate versus high-dose methotrexate alone in patients with primary CNS lymphoma: a randomised phase 2 trial[END_REF], (ii) the same regimen combined with rituximab, or (iii) the same regimen combined with rituximab and thiotepa (named MATRix schedule).

Patients with responsive or stable disease underwent a second randomization to consolidation with WBRT versus HCT-ASCT. The results of the first randomization demonstrated that the addition of rituximab alone and thiotepa-rituximab to MTX-cytarabine increased CR rates (CR rate: 31% and 49% respectively) compared with the control arm (CR rate: 23%). Although the trial was not designed for comparison, the CR rate increased significantly only when rituximab was combined with thiotepa over the control group, addition of rituximab alone was associated with a significant higher objective response rate (ORR: CR + Partial Response, PR) compared with the control arm (ORR: 73% versus 53%). Interestingly, the addition of thiotepa to rituximab further improved ORR rate (86%) and outcome (hazard ratio [HR] for overall survival 0・41, 95% CI 0・25-1・68) over the control group [START_REF] Ferreri | Chemoimmunotherapy with methotrexate, cytarabine, thiotepa, and rituximab (MATRix regimen) in patients with primary CNS lymphoma: results of the first randomisation of the International Extranodal Lymphoma Study Group-32 (IELSG32) phase 2 trial[END_REF]. However, efficacy of rituximab in PCNSL could not be confirmed in the HOVON 105/ALLG NHL 24 randomized phase III trial (conducted in the Netherlands, Australia, and New Zealand), which randomly assigned 200 patients with newly diagnosed PCNSL to receive rituximab in addition to HD-MTX based induction chemotherapy (including carmustine, etoposide) or the induction chemotherapy alone. After induction, all responding patients received consolidation chemotherapy with cytarabine, and only those aged younger than 60 years received additional WBRT. The authors failed to find any improvement with rituximab in terms of event-free survival (EFS), which was the primary endpoint ( to younger patients, a possible interaction with treatment has been raised. However, this was an unplanned post-hoc analysis that has to be interpreted with caution. Taking into account these two latter prospective studies with opposite conclusions, the identification of the patients who would benefit from rituximab warrant to be further investigated by clinical trials specifically dedicated to this issue and by age group.

Consolidation strategies in first line treatment

The role of WBRT as consolidation after HD-MTX based induction polychemotherapy has been challenged by cumulative studies in the recent years [START_REF] Hoang-Xuan | Diagnosis and treatment of primary CNS lymphoma in immunocompetent patients: guidelines from the European Association for Neuro-Oncology[END_REF]13], thus encouraging the evaluation of alternative strategies. The rationale behind the use of HCT-ASCT in PCNSL patients resides in the administration of maximum tolerable doses of cytostatic drugs, to reach therapeutic concentrations in the CNS to eradicate microscopic residual disease, overcoming drug resistance mediated by blood brain barrier. HCT-ASCT, has showed its efficacy and feasibility in patients with relapsed PCNSL [START_REF] Soussain | Intensive chemotherapy followed by hematopoietic stem-cell rescue for refractory and recurrent primary CNS and intraocular lymphoma: Société Française de Greffe de Moëlle Osseuse-Thérapie Cellulaire[END_REF][START_REF] Kasenda | High-dose chemotherapy with autologous haematopoietic stem cell support for relapsed or refractory primary CNS lymphoma: a prospective multicentre trial by the German Cooperative PCNSL study group[END_REF]. Prospective studies have reported encouraging results with this approach as consolidation in first line treatment using different conditioning regimens [START_REF] Omuro | R-MPV followed by high-dose chemotherapy with TBC and autologous stem-cell transplant for newly diagnosed primary CNS lymphoma[END_REF][START_REF] Alnahhas | Autologous Stem-Cell Transplantation for Primary Central Nervous System Lymphoma: Systematic Review and Meta-analysis[END_REF][START_REF] Illerhaus | High-dose chemotherapy with autologous haemopoietic stem cell transplantation for newly diagnosed primary CNS lymphoma: a prospective, single-arm, phase 2 trial[END_REF][START_REF] Cho | The role of upfront autologous stem cell transplantation in high-risk younger patients with primary central nervous system lymphoma[END_REF].

Although comparison between conditioning regimens is difficult in the absence of controlled study, high-dose thiotepa-based conditioning regimens (carmustine-thiotepa, thiotepa-cyclophosphamide-busulfan) seem the most efficient whereas results with BEAM regimen appeared disappointing [START_REF] Abrey | Intensive methotrexate and cytarabine followed by high-dose chemotherapy with autologous stem-cell rescue in patients with newly diagnosed primary CNS lymphoma: an intent-to-treat analysis[END_REF]. Comparison of the high dose chemotherapy with ASCT approach with the chemo-radiotherapy combination as first line treatment has been investigated by two phase II randomized trials with PFS at 2 years as primary endpoint and with prospective psychometric testing follow-up [START_REF] Houillier | Radiotherapy or Autologous Stem-Cell Transplantation for Primary CNS Lymphoma in Patients 60 Years of Age and Younger: Results of the Intergroup ANOCEF-GOELAMS Randomized Phase II PRECIS Study[END_REF][START_REF] Ferreri | Whole-brain radiotherapy or autologous stem-cell transplantation as consolidation strategies after high-dose methotrexate-based chemoimmunotherapy in patients with primary CNS lymphoma: results of the second randomisation of the International Extranodal Lymphoma Study Group-32 phase 2 trial[END_REF].

The IELSG32 trial cited above randomly assigned, in its second randomization stage, 118 eligible patients out of 227 patients after induction chemotherapy to receive WBRT (36 Gy with 1.8 Gy / fraction, with the addition of a 9 Gy tumor-bed boost in patients in partial response) or ASCT (using a carmustine-thiotepa conditioning regimen). In the PRECIS trial conducted by the ANOCEF-GOELAMS intergroup, 97 eligible patients out of 140 patients enrolled in the study who have received an induction MTX based immunochemotherapy (rituximab, MTX, carmustine, etoposide, cytarabine), were assigned to receive WBRT (40 Gy with 2 Gy / fraction) or ASCT (using thiotepa-cyclophosphamide-busulfan). Both trials met the predetermined efficacy threshold in both arms and confirmed the efficacy of WBRT and ASCT as consolidation. In addition, they demonstrated a better preservation of cognitive functions after ASCT, while, as expected, a higher hematological toxicity than in those who received WBRT. Treatment-related death occurred with ASCT only (3% in IELSG32 and 11% in PRECIS). Although both trials were not designed to allow direct comparison of the consolidation therapies , the IELSG32 trial, reported no significant differences in 2-year PFS between WBRT and ASCT, while in the PRECIS trial, the efficacy endpoints tended to favor the ASCT arm with a 2-year PFS rates of 63% (95% CI 49-81) and 87% (95% CI 77-98) in the WBRT and ASCT arms, respectively. Despite common objectives and endpoints, the IELSG32 and PRECIS trials differed by several relevant aspects, including their designs, treatment protocols and patient selection.

Particularly, in the PRECIS trial the upper age limit was lower (<60 years), the randomization was done at trial registration, the induction chemotherapy regimen was homogeneous, the WBRT total dose was higher and the conditioning regimen could be considered as more intensive. Altogether, the two latter randomized trials provide evidence to support the role of ASCT as a valuable alternative option to WBRT, at least at conventional dose. However, longer follow-up is needed to evaluate more precisely the potential delayed consequences on neurocognition and quality of life of the ASCT consolidation [START_REF] Houillier | Radiotherapy or Autologous Stem-Cell Transplantation for Primary CNS Lymphoma in Patients 60 Years of Age and Younger: Results of the Intergroup ANOCEF-GOELAMS Randomized Phase II PRECIS Study[END_REF][START_REF] Ferreri | Whole-brain radiotherapy or autologous stem-cell transplantation as consolidation strategies after high-dose methotrexate-based chemoimmunotherapy in patients with primary CNS lymphoma: results of the second randomisation of the International Extranodal Lymphoma Study Group-32 phase 2 trial[END_REF].

The MSKCC has reported encouraging results both in terms of efficacy and neurotoxicity in a prospective single arm study using a low-dose WBRT (23•4 Gy in 13 fractions) as consolidation following an induction immunochemotherapy including high-dose MTX, procarbazine, rituximab, and cytarabine [START_REF] Morris | Rituximab, methotrexate, procarbazine, and vincristine followed by consolidation reduced-dose whole-brain radiotherapy and cytarabine in newly diagnosed primary CNS lymphoma: final results and long-term outcome[END_REF]. This approach is currently evaluated in a randomized phase II trial (RTOG-1114) comparing the MSKCC regimen with or without reduced-dose WBRT has been conducted (NCT01399372). The trial is now completed, and the results are awaited. On the basis of the efficacy of an induction regimen combining rituximab, HD-MTX, and temozolomide (RMT), followed by consolidation with a non myeloablative chemotherapy comprising highdose etoposide and cytarabine [22,[START_REF] Birsen | Efficacy and safety of high-dose etoposide cytarabine as consolidation following rituximab methotrexate temozolomide induction in newly diagnosed primary central nervous system lymphoma in immunocompetent patients[END_REF], the CALGB group is conducting a randomized phase II (NCT01511562) in which patients receive RMT induction chemotherapy followed by consolidation with high dose etoposide-cytarabine or thiotepa-carmustine followed by ASCT.

Treatment of the elderly

Treatment of the elderly, who constitute the majority of PCNSL immunocompetent patients, is challenging as they represent a highly vulnerable population. Given the high risk of severe neurotoxicity following chemoradiation therapy. There is nowadays a wide agreement to consider HD-MTX-based chemotherapy with deferral or elimination of WBRT as the treatment of choice [START_REF] Hoang-Xuan | Diagnosis and treatment of primary CNS lymphoma in immunocompetent patients: guidelines from the European Association for Neuro-Oncology[END_REF][START_REF] Hoang-Xuan | Chemotherapy alone as initial treatment for primary CNS lymphoma in patients older than 60 years: a multicenter phase II study (26952) of the European Organization for Research and Treatment of Cancer Brain Tumor Group[END_REF][START_REF] Fritsch | High-dose methotrexate-based immuno-chemotherapy for elderly primary CNS lymphoma patients (PRIMAIN study)[END_REF][START_REF] Gavrilovic | Long-term follow-up of high-dose methotrexate-based therapy with and without whole brain irradiation for newly diagnosed primary CNS lymphoma[END_REF]. Controlled trials dedicated to this age group are scarce. To date the only one, is randomized phase II trial devoted to patients aged over 60 treated with either MPV-A regimen (MTX, procarbazine, vincristine, cytarabine) or MTX plus temozolomide without consolidation WBRT has been conducted by the ANOCEF-GOELAMS intergroup [START_REF] Omuro | Methotrexate and temozolomide versus methotrexate, procarbazine, vincristine, and cytarabine for primary CNS lymphoma in an elderly population: an intergroup ANOCEF-GOELAMS randomised phase 2 trial[END_REF]. Both chemotherapy regimens met the predetermined efficacy threshold confirming prospectively their efficacy.

MPV-A treated patients showed better outcomes in terms of CR rate, median PFS, and OS, compared with MTX plus temozolomide, although these differences did not reach level of significance. Both regimens were associated with manageable toxicity and psychometric and quality of life follow-up showed significant improvements over time, confirming the value of this approach in the elderly. However, in spite of high objective response rates remission were short-lasting and the OS were poor. Maintenance treatment is a potential valuable alternative strategy to prolong disease control. An ongoing phase III trial conducted by the French LOC network address this question (NCT02313389). Patients who have achieved a CR after an induction chemotherapy (rituximab, MPV-A) are randomly assigned to receive a maintenance chemotherapy combining rituximab, MTX and temozolomide versus observation. In selected elderly PCNSL patients, consolidation with high-dose chemotherapy with ASCT [START_REF] Schorb | High-dose thiotepa-based chemotherapy with autologous stem cell support in elderly patients with primary central nervous system lymphoma: a European retrospective study[END_REF] or with high-dose cytarabine [START_REF] Houillier | Rituximab, methotrexate, procarbazine, vincristine and intensified cytarabine consolidation for primary central nervous system lymphoma (PCNSL) in the elderly: a LOC network study[END_REF] using chemotherapy regimens adapted to age have been showed to be feasible in retrospective studies and warrant to be further investigated in controlled prospective trials.

New agents: biotherapies

With the current management of PCNSL, about one third of patients are refractory to first-line treatment and the majority of the patients will eventually relapse. The prognosis is poor after salvage therapy, overall, the median PFS and OS after recurrence were 2.2 months (range, 0-29.6) and 3.5 months (0-29.6), respectively, in a large population-based study, elderly remaining the group with the worse outcome [START_REF] Langner-Lemercier | Primary CNS lymphoma at first relapse/progression: characteristics, management, and outcome of 256 patients from the French LOC network[END_REF]. To date, there is no standard treatment however, HCT-ASCT is the best available option in selected candidates for refractory/relapsing PCNSL, with 2-year PFS of 62% (35%-85%), median PFS up to 25.8 months and 2-year OS of 63% (51% -74%) [START_REF] Kasenda | High-dose chemotherapy with autologous haematopoietic stem cell support for relapsed or refractory primary CNS lymphoma: a prospective multicentre trial by the German Cooperative PCNSL study group[END_REF] [START_REF] Soussain | Intensive chemotherapy followed by hematopoietic stem-cell rescue for refractory and recurrent primary CNS and intraocular lymphoma: Société Française de Greffe de Moëlle Osseuse-Thérapie Cellulaire[END_REF]. New active agents are needed to improve salvage treatment but also to strengthen the first line chemotherapy regimens. Promising results have been reported with ibrutinib and imids.

Ibrutinib

Ibrutinib is a selective inhibitor of Bruton tyrosine kinase (BTK), targeting B cell receptor (BCR) signaling which is particularly active in PCNSL with recurrent mutations altering BCR subunit CD79B and MYD88.

These mutations have been found in PCNSL at higher rate than in other extracerebral DLBCL for which it has been shown an efficacy of ibrutinib. Ibrutinib has been investigated in PCNSL as single agent in three clinical trials with promising efficacy [START_REF] Grommes | Ibrutinib Unmasks Critical Role of Bruton Tyrosine Kinase in Primary CNS Lymphoma[END_REF][START_REF] Lionakis | Inhibition of B Cell Receptor Signaling by Ibrutinib in Primary CNS Lymphoma[END_REF][START_REF] Soussain | Study of Ibrutinib in Patients With Relapsed or Refractory Primary Central Nervous Lymphoma or Intraocular Lymphoma. Results of the primary end point of the LOC phase II study from the LYSA and the French LOC network[END_REF]. Grommes et al reported the results of a phase I study of ibrutinib given at escalating dose to up to 840mg daily in patients with refractory and relapsing primary or secondary CNS lymphomas. Response was observed in 77 % of 13 patients with PCNSL with a PFS of 4.6 months [START_REF] Grommes | Ibrutinib Unmasks Critical Role of Bruton Tyrosine Kinase in Primary CNS Lymphoma[END_REF].

The LOC network has conducted a phase II trial enrolling 52 patients with refractory and relapsed PCNSL (including primary vitreoretinal lymphoma) using 560mg daily dosed ibrutinib (NCT02542514). Intent to treat response rate was observed in 52% of cases after 2 cycles, with a PFS of 4.8 months and OS: 19 months [START_REF] Soussain | Study of Ibrutinib in Patients With Relapsed or Refractory Primary Central Nervous Lymphoma or Intraocular Lymphoma. Results of the primary end point of the LOC phase II study from the LYSA and the French LOC network[END_REF]. Lionakis et al in a phase I of the NCI, reported a partial response rate of 83% two weeks after ibrutinib introduction, in a series of 18 patients suffering from newly diagnosed and relapsing PCNSL [START_REF] Lionakis | Inhibition of B Cell Receptor Signaling by Ibrutinib in Primary CNS Lymphoma[END_REF].

The specific contribution of ibrutinib on the final outcome is difficult to analyze, as a wide chemotherapy combination (DA-TEDDi-R) was rapidly added to ibrutinib. In this latter study, several unexpected cases of severe pulmonary and CNS aspergillosis, were reported raising the possible role of the treatment combination that could have exacerbated the ibrutinib induced fungal immune surveillance impairment. More recently, Grommes et al. showed in a phase 1b clinical trial that the sequential combination of ibrutinib (at dose of 560 or 840 mg) with HD-MTX and rituximab followed by maintenance ibrutinib in patients with refractory/relapsing CNS lymphoma was active and well tolerated [START_REF] Grommes | Phase 1b trial of an ibrutinib-based combination therapy in recurrent/refractory CNS lymphoma[END_REF], laying the bases for future comparative trials evaluating ibrutinib based combination treatment.

Imids

Imids including lenalidomide and pomalidomide are thalidomide-derived agents with antiproliferative and immunomodulatory properties which have shown antilymphoma activity, likely in the activated B cell (ABC) subtype of DLBCL. Lenalidomide as single agent has been used in patients with relapsing PCNSL, with 2 patients achieving a CR in a small retrospective cohort [START_REF] Houillier | Lenalidomide monotherapy as salvage treatment for recurrent primary CNS lymphoma[END_REF]. The activity was confirmed in a phase I with 9 objective response out of 14 relapsed/refractory PCNSL treated with lenalidomide monotherapy (15 mg on a 21day cycle) [START_REF] Rubenstein | Phase 1 investigation of lenalidomide/rituximab plus outcomes of lenalidomide maintenance in relapsed CNS lymphoma[END_REF]. A phase II study conducted by the LOC network and the LYSA evaluated lenalidomide (20 mg on a 21day cycle) in combination with rituximab in 50 relapsed /refractory PCNSL and primary vitreoretinal lymphoma (PVRL) and found an ORR of 35 %. Responding patients were proposed a maintenance with lenalidomide alone and the median PFS and OS were 7.8 and 17.7 months respectively [START_REF] Ghesquieres | Lenalidomide in Combination with Intravenous Rituximab (REVRI) in Relapsed/Refractory Primary CNS Lymphoma or Primary Intraocular Lymphoma: a Multicenter Prospective "Proof of Concept" Phase II Study of the French Oculo-Cerebral Lymphoma (LOC) Network and the Lymphoma Study Association (LYSA)[END_REF]. Pomalidomide is a third-generation imid that has shown a good CNS penetration [START_REF] Li | Pomalidomide Shows Significant Therapeutic Activity against CNS Lymphoma with a Major Impact on the Tumor Microenvironment in Murine Models[END_REF]. In a phase I study, Tun et al. assessed the efficacy of pomalidomide with dexamethasone in relapsed/refractory PCNSL and PVRL patients [START_REF] Tun | Phase 1 study of pomalidomide and dexamethasone for relapsed/refractory primary CNS or vitreoretinal lymphoma[END_REF]. The ORR reported was 48% and a median PFS of 5.3 months and 9 months for responders. In regard of their good safety profiles, imids would be potential interesting agents to improve response rates by incorporating induction regimens but also in the setting of maintenance treatment. Indeed, encouraging results with prolonged PFS and OS have been reported in a small cohort of 13 elderly patients (median age: 77 years; range 70-86), who have been treated with low dose lenalidomide (5-10 mg/day on a 21day cycle) after achieving an objective response to a HD-MTX based chemotherapy as induction [START_REF] Vu | Low-dose lenalidomide maintenance after induction therapy in older patients with primary central nervous system lymphoma[END_REF].

Conclusion

The management of patients suffering from PCNSL has been substantially improved in the past decade as a result of better knowledge of treatment strategies. The role of WBRT as consolidation is clearly declining in favor of high dose chemotherapy approaches with or without ASCT; and, for the elderly, there is now a large consensus to avoid its use in first line treatment in order to reduce the risk of neurotoxicity. Further efforts should focus on increasing the remission rate and prolonging their duration with a curative aim. In this setting, the role of rituximab remains unclear and further studies are needed to identify the patients who will benefit from this treatment. Hope come clearly from new targeted agents and immunomodulatory therapies which have shown promising results and already incorporated in innovative combination treatment evaluated in ongoing trials. Prospective trials evaluating the role of immune therapy with checkpoint inhibitors and anti CD19 CAR T cells in PCNSL are also awaited [START_REF] Nayak | PD-1 blockade with nivolumab in relapsed/refractory primary central nervous system and testicular lymphoma[END_REF][START_REF] Abramson | Anti-CD19 CAR T Cells in CNS Diffuse Large-B-Cell Lymphoma[END_REF]. Despite their rarity, it has been shown that ambitious randomized trials in PCNSL are feasible thanks to collaborative networks at the national and international level. Lessons from previous trials pointed out the importance to build adequate and robust designs for the future trials to allow firm conclusions. Elderly, representing a growing population that requires a specific management, should be investigated likely in dedicated trials.

  [HR] 1•00; 95% CI 0•70-1•43), of PFS (HR : 0•77; 95% CI 0•52-1•13), overall survival (OS) (HR:0•93; 95% CI :0•59-1•44) and post induction chemotherapy CR rate (30% versus 36%) compared to chemotherapy alone. Surprisingly, in a subgroup analysis by age, patients aged < 60 years seemed to benefit from addition of rituximab in terms of PFS (HR 0•48; 95% CI: 0•26-0•88), EFS (HR: 0•56; 95%CI 0•31-1•01), and OS (HR 0•59; 95%CI: 0•28-1•24) [12]. As WBRT consolidation was proposed only


Théo Cavalieri
email: theo.cavalieri@univ-lemans.fr

Jean Boulvert

Logan Schwan

Gwénaël Gabard

Vicent Romero-Garcìa

Jean-Philippe Groby

Marie Escouflaire

Jacky Mardjono

Acoustic wave propagation in effective graded fully-anisotropic fluid layers

Keywords: acoustic control, anisotropic fluid, heterogeneous fluid, graded porous layer, absorption

This work deals with the modeling of sound wave propagation in anisotropic and heterogeneous media. The scattering problem considered in this work involves an infinite layer of finite thickness containing an anisotropic fluid whose properties can vary along the depth of the layer. The specular transmission and reflection of an acoustic plane wave by such a layer is modeled through the state vector formalism for the acoustic fields. This is solved using three different numerical techniques, namely the transfer matrix method, Peano series and the transfer Green's function.

These three methods are compared to demonstrate the convergence of the numerical solutions. Moreover, the implemented numerical procedures allow to retrieve the internal acoustic fields and show their dependency along with the fluid's anisotropic properties. Results are then presented to illustrate the changes in absorption that can be achieved by tuning the anisotropy of the fluid as well as the variation of these properties across the depth of the layer. The results presented are in very good agreement across the different methods. Given that many porous materials can be modeled as equivalent fluids, the results presented show the potential offered by such numerical techniques, and can further give more insight on inhomogeneous anisotropic porous materials.

I. INTRODUCTION

Acoustic treatments involving porous materials are commonly used for sound absorption purposes. The recent development of additive manufacturing provides more control on the micro-structures of these porous materials. Hence, the anisotropic and graded properties of such microstructures influence the wave propagation in the medium, which is numerically described. A rigid-frame porous medium is usually modeled as an equivalent fluid, that can display anisotropic and heterogeneous frequency dependent effective properties. One way to describe these effective properties is the well-known Johnson-Champoux-Allard-Lafarge (JCAL) model 1 which provides the thermal and viscous dynamic permeabilities of the propagation medium. For a periodic porous material, formed by a repetition of a unit cell, the JCAL model can rely on homogenized properties of this unit cell calculated using the method of multiple scales 2 . Since the viscous dissipation has been shown to be directiondependent [START_REF] Van Der Kelen | Identification of the full anisotropic flow resistivity tensor for multiple glass wool and melamine foam samples[END_REF][START_REF] Tarnow | Measured anisotropic air flow resistivity and sound attenuation of glass wool[END_REF][START_REF] Tarnow | Compressibility of air in fibrous materials[END_REF] in anisotropic media, the same considerations are used in the current paper.

Recent work [START_REF] Nennig | A transverse isotropic equivalent fluid model combining both limp and rigid frame behaviors for fibrous materials[END_REF] have shown that anisotropic materials can have different apparent sound speed depending on the direction of propagation, coupling viscous and inertial regimes. This is especially visible at grazing angles of incidence, and can be exploited for absorption considering a diffuse field where all incidences are accounted for. The derivation of the equations has been done recently to retrieve the effective properties of an anisotropic homogeneous material [START_REF] Terroir | General method to retrieve all effective acoustic properties of fully-anisotropic fluid materials in three dimensional space[END_REF] , and is recalled in the section regarding wave propagation.

The present work focuses on the modeling and analysis of inhomogeneous anisotropic materials. The scattering problem considered here involves an infinite layer of finite thickness containing an anisotropic fluid whose properties can vary across the depth of the layer. The transmission and reflection of an acoustic plane wave by such a layer is modeled through the state vector formalism, which is solved using three different techniques. First, the layer is assumed piece-wise constant and the standard transfer matrix method (TMM) [START_REF] Brouard | A general method of modelling sound propagation in layered media[END_REF] is employed. The other two methods are applicable to continuously graded media. The Peano Series (PS) has previously been used for graded [START_REF] Geslain | An application of the Peano series expansion to predict sound propagation in materials with continuous pore stratification[END_REF][START_REF] Gautier | Propagation of acoustic waves in a one-dimensional macroscopically inhomogeneous poroelastic material[END_REF][START_REF] Baron | Matricant Peano series development to study elastic waves propagation in continuously varying properties materials[END_REF] and anisotropic materials [START_REF] Shuvalov | General formalism for plane guided waves in transversely inhomogeneous anisotropic plates[END_REF] , and wave-splitting techniques for continuously graded media [START_REF] De Ryck | Acoustic wave propagation and internal fields in rigid frame macroscopically inhomogeneous porous media[END_REF][START_REF] De Ryck | Acoustic wave propagation in a macroscopically inhomogeneous porous medium saturated by a fluid[END_REF][START_REF] Lundstedt | Comparison between Frequency Domain and Time Domain Methods for Parameter Reconstruction on Nonuniform Dispersive Transmission Lines[END_REF][START_REF] Norgren | General scheme for electromagnetic reflection and transmission for composite structures of complex materials[END_REF][START_REF] Forslund | Electromagnetic Scattering from an Inhomogeneous Grating Using a Wave-Splitting Approach[END_REF][START_REF] Borzdov | Frequency domain wave-splitting techniques for plane stratified bianisotropic media[END_REF] . In addition, the internal fields and dissipation rate of energy are estimated [START_REF] Krueger | A green's function approach to the determination of internal fields[END_REF] and shown to be dependent on the fluid's effective properties. Other solution procedures can however be applied to approximate such propagation problem, as Euler or Runge-Kutta iterative schemes, which are commonly used for linear systems [START_REF] De Ryck | Acoustic wave propagation in a macroscopically inhomogeneous porous medium saturated by a fluid[END_REF] .

The article is organized as follows, we first introduce the equivalent fluid model and the propagation problem considered in this work. The different numerical approaches are then presented, so as to solve for the acoustic fields inside the layer. Numerical results of the scattering coefficients on such anisotropic graded material are presented for all the methods considered, which show good agreement. Finally, further insight is provided into the dissipation rate within the anisotropic material and in the role played by the orientation of the micro-structure.

II. PROPAGATION IN GRADED ANISOTROPIC FLUID LAYERS

In this section the propagation of a plane wave through an anisotropic, heterogeneous equivalent fluid is described. We set the reference in the Cartesian coordinate system R 0 = layer, denoted Ω, is a slab of finite thickness L and infinite extent in the (0, x ⊥ ) plane, as illustrated in Fig. 1. The subscript ⊥ denotes the restriction of a vector to the (O, x ⊥ ) plane with x ⊥ = {x 1 , x 2 }. The domain Ω is delimited by the plane boundaries at x 3 = 0 and x 3 = L denoted Γ 0 and Γ L respectively. We solve for the sound field in this layer Ω in the linear harmonic regime using the time convention e -iωt where ω is the angular frequency.

The effective bulk modulus and density of the anisotropic heterogeneous fluid are denoted B(x 3 , ω) and ρ(x 3 , ω). Note that these quantities are complex-valued, frequency dependent and can vary along the x 3 direction, moreover, while the bulk modulus of the medium is scalar, the density is a second order tensor accounting for anisotropic phenomena. The pressure p and velocity v induced by the acoustic field in Ω are governed by the following linear equations for mass conservation and momentum conservation

iωρ(x 3 , ω)v(x, ω) = ∇p(x, ω) , (1a) iωB -1 (x 3 , ω)p(x, ω) = ∇ • v(x, ω) . ( 1b
)
58

The exterior of the domain Ω is denoted Ω 0 and contains an homogeneous isotropic fluid, taken to be air in this case. The density of air is ρ 0 = 1.213 kg.m -3 and its bulk modulus B 0 = γP 0 with γ = 1.4 the ratio of specific heat and P 0 = 101 325 Pa the atmospheric pressure. The sound field in the exterior domain Ω 0 satisfies

iωρ 0 v(x, ω) = ∇p(x, ω) , (2a)
iωB -1 0 p(x, ω) = ∇ • v(x, ω) . ( 2b
)
While the density of the isotropic fluid in Ω 0 is described by the scalar ρ 0 , the anisotropy of the fluid in the layer Ω is described by the tensor density ρ. This tensor accounts for the fact that the properties of the waves in Ω depend on the direction of propagation. The density tensor ρ is diagonal in the special case where its principal directions are aligned with the coordinate system R 0 . But in the general case it is full, symmetric and can be written

ρ = R            ρ 11 0 0 0 ρ 22 0 0 0 ρ 33            R Ω R T , (3)
with R the complete rotation matrix accounting for the yaw, pitch and roll angles, respectively (u 1 , u 2 , u 3 ) along (e 1 , e 2 , e 3 ). For the sake of simplicity and since the particle velocity depends on the inverse of the density tensor, the second-order tensor H = ρ -1 remains symmetric and will be used instead of ρ in the remainder of this work.

In the upper region of Ω 0 , x 3 ≥ L, we define an incident plane wave with unit amplitude:

p i (x, ω) = e ik 1 x 1 +ik 2 x 2 -ik 3 (x 3 -L) ,
where the components of the wave-vector k i are given by

k 1 = -k 0 cos(θ) cos(ψ), (4)
k 2 = -k 0 cos(θ) sin(ψ), (5)
k 3 = k 0 sin(θ), (6)
with ψ and θ the polar and elevation angles, respectively. k 0 = ω/c 0 is the free-field acoustic wave-number.

The presence of the anisotropic layer Ω gives rise to a reflected wave p r in the upper region of Ω 0 and to a transmitted wave p t in the lower region of Ω 0 , x 3 ≤ 0. These are written

p r (x, ω) = Re ik ⊥ •x ⊥ +ik 3 (x 3 -L) , (7)
p t (x, ω) = T e ik ⊥ •x ⊥ -ik 3 x 3 , (8)
where R and T are the specular coefficients of reflection and transmission and

k ⊥ = {k 1 , k 2 } and x ⊥ = {x 1 , x 2 }.
As the incident wave could physically come from x 3 < 0, it is important to be explicit about the scattering coefficients which are R± and T ± , depending on the sign of wave incidence. The system being reciprocal we reach T = T + = T -, whereas the distinction has to be made for the reflection since the heterogeneity of the medium can be non-symmetric. Without any specific considerations about the effective properties of the medium, R+ = Rin the inhomogeneous case. For the sake of simplicity and as reversing the layer Ω between its interfaces is equivalent to propagating in the opposite direction, we use the notation R = R+ when the incident waves comes from the upper region x 3 ≥ L.

However, the solution procedures developed further are valuable for all scattering coefficients.

The incident plane wave p i also induces a sound field in the anisotropic and graded layer Ω. Given that (i) the properties of this layer are independent of x 1 and x 2 and (ii) the incident field has an harmonic spatial dependence e ik ⊥ •x ⊥ , it is clear that the wave field in the layer Ω retains the same harmonic spatial dependence:

p(x, ω) = p(x 3 )e ik ⊥ •x ⊥ , (9a) v(x, ω) = v(x 3 )e ik ⊥ •x ⊥ . (9b) (9c) 83
The derivation of the governing equations Eqs. (1) has recently been done for retrieval techniques and applied to fully-anisotropic porous materials [START_REF] Terroir | General method to retrieve all effective acoustic properties of fully-anisotropic fluid materials in three dimensional space[END_REF] . The process is recalled as follows, and leads to the state-vector equation for pressure and normal particle velocity.

From the conservation equations Eqs. ( 1), the transverse and normal components of the fields are expanded,

iωv ⊥ = iH ⊥ • k ⊥ p + H 33 q ∂p ∂x 3 , (10a) iωH -1 33 v 3 = ik ⊥ • q p + ∂p ∂x 3 , (10b) iωB -1 p = ik ⊥ • v ⊥ + ∂v 3 ∂x 3 , (10c)
where we have again used the notation v ⊥ = {v 1 , v 2 }. We have also introduced the coupling

vector q = {H 13 /H 33 , H 23 /H 33 } and the 2 × 2 matrix H ⊥ = H mn ∀ (m, n) ∈ {1, 2} 2 . From
Eqs. (10a) and (10c) we get

iωB -1 p = ik ⊥ • i(H ⊥ • k ⊥ ) p iω + H 33 iω q ∂p ∂x 3 + ∂v 3 ∂x 3 . ( 11
)
Together with the momentum conservation in Eq. (10b), leads to

iωB -1 p = H 33 (k ⊥ • q) 2 p iω -k ⊥ • (H ⊥ • k ⊥ ) p iω + i(k ⊥ • q)v 3 + ∂v 3 ∂x 3 , (12)
where after rearranging the pressure terms, emerges the equivalent bulk modulus:

B -1 eq = B -1 + H 33 (k ⊥ • q) 2 -k ⊥ • (H ⊥ • k ⊥ ) /ω 2 . ( 13
)
Yields the following equation of mass conservation, where B eq relates the compressibility effects of the equivalent fluid, accounting for anisotropic dependencies and oblique consid-

erations, iωB -1 eq p = ik ⊥ • qv 3 + ∂v 3 ∂x 3 , (14)
and with Eq. 10b, they characterize the sound field in the layer Ω, with equivalent density

H -1
33 and bulk modulus B eq . They can be written using a state-vector formulation

dW dx 3 = A(x 3 )W , (15)
where we have introduced the state vector W = {p, v 3 } T (with T the non-conjugate transpose), and the matrix

A(x 3 ) =       -ik ⊥ • q iωH -1 33 iωB -1 eq -ik ⊥ • q       . ( 16
)
At the interfaces Γ 0 and Γ L between the anisotropic layer and the surrounding fluid, the continuity of pressure and normal velocity is imposed as boundary conditions. As a consequence, the state vector at both interfaces reads

W L =            1 + R Z -1 e ( R -1)            and W 0 =            T -Z -1 e T            , (17)
with Z e = Z 0 / sin(θ) the apparent impedance of the air in domain Ω 0 with respect to the unit outward normal vector n = e 3 at interface Γ L . Note that in the case where the layer is rigidly backed (absorption problem), the boundary term at Γ 0 simplifies to W 0 = {p(0), 0} T since the Neumann condition involves zero normal velocity on the rigid layer backing.

III. SOLUTION PROCEDURES

The state-vector Eq. ( 15) can be solved using a variety of numerical techniques. In this section three different methods are presented. The well-known TMM is first described, then two other approaches are presented for continuously graded media.

The heterogeneous fluid layer Ω can be approximated by a succession of N homogeneous layers. The propagation of the waves through each homogeneous layer can be solved exactly using the TMM 8 . This approximation is accurate provided that the thickness of each homogeneous layer is small compared to the wavelength. We introduce the start-and end-points of the successive homogeneous layers as x

(i)
3 so that x = L. The state vectors on either sides of the ith homogeneous layer can be related as follows

W x (i+1) 3 = M x (i+1) 3 , x (i) 3 W x (i) 3 , ( 18
)
where M is the matricant which can be written in terms of the constant matrix A i associated with the ith homogeneous layer:

A i = A x (i+1) 3 + x (i) 3 2 . ( 19
)
To do so we first diagonalize this matrix by writing A i = V -1 i λ i V i with λ i the diagonal matrix of eigenvalues and V i the matrix of eigenvectors. The state-vector formulation Eq. ( 15) in the ith layer can be transformed into two decoupled ordinary differential equations:

d dx 3 (V i W) = λ i (V i W) . (20)
These can be readily solved to obtain the matricant:

M x (i+1) 3 , x (i) 3 = V -1 i       e λ 1 l i 0 0 e λ 2 l i       V i , (21)
with

l i = x (i+1) 3 -x (i)
3 . This expression can be directly written as a matrix exponential 20 :

M x (i+1) 3
, x

(i) 3 = exp(A i l i ) . (22)
The overall transfer matrix M relating the state vectors at the two interfaces Γ 0 and Γ L is defined as the product of the matricants of all the homogeneous layers:

W L = MW 0 , M = N -1 i=0 e A i l i . ( 23
)
The discretization of domain Ω is chosen to be linear across N = 40 positions, and will serve as comparison with two different methods which follow.

B. Peano Series

Another approach to solve Eq. ( 15) is to use the PS which have previously been used for continuously graded isotropic materials [START_REF] Geslain | An application of the Peano series expansion to predict sound propagation in materials with continuous pore stratification[END_REF] . In the homogeneous case, i.e. when A is constant, the PS can be shown to be equivalent to the product of matrix exponentials in Eq. ( 23). In the present case of x 3 dependent properties, the matrix A does not commute with itself for different values of x 3 , so ∀(x 3 , x 3 ) ∈ [0, L] 2 , x 3 = x 3 , [A(x 3 )A(x 3 ) -A(x 3 )A(x 3 )] = 0 and the matricant is no longer defined by matrix exponentials, but rather by the Peano series.

Using this formalism, the matricant M defined by Eq. ( 23) is written as an infinite series of integrals [START_REF] Borzdov | Frequency domain wave-splitting techniques for plane stratified bianisotropic media[END_REF][START_REF] Pease | Methods of Matrix Algebra[END_REF] :

M(0, x 3 ) = I d + x 3 0 A(ξ)dξ + x 3 0 A(ξ) ξ 0 A(ξ 1 )dξdξ 1 + . . . . (24)
In practice this is calculated through the use of the following recurrence relations [START_REF] Baron | Matricant Peano series development to study elastic waves propagation in continuously varying properties materials[END_REF] ,

           M {0} (0, L) = I d M {n} (0, L) = I d + L 0 A(x 3 )M {n-1} (x 3 )dx 3 (25)
and the state vector relation at both interfaces now reads,

W L = lim n→∞ M {n} (0, L)W 0 . (26)
An approximate solution is obtained by truncating this infinite series. In fact, unlike the TMM where the matricant of the system is assembled piece by piece, each term of the integral series accounts for the whole domain 0 < x 3 < L. The integral itself is estimated by the trapezoidal method at each iteration, using the same unit spacing L/N . Hence, any additional term of the truncated series tends to refine the solution given by this method.

The recurrence relation is chosen to be expanded up to 50 terms, a sufficient number for the series to converge.

C. Wave-Splitting, Transfer Green Functions

The wave-splitting method relies on the separation of the overall acoustic field into forward and backward propagative waves [START_REF] De Ryck | Acoustic wave propagation in a macroscopically inhomogeneous porous medium saturated by a fluid[END_REF][START_REF] Borzdov | Frequency domain wave-splitting techniques for plane stratified bianisotropic media[END_REF] . Since the effective properties of the medium are inhomogeneous along x 3 , the wave-splitting applied in the current paper is not related to Ω, but rather with respect to the domain Ω 0 [START_REF] Lundstedt | Comparison between Frequency Domain and Time Domain Methods for Parameter Reconstruction on Nonuniform Dispersive Transmission Lines[END_REF][START_REF] Norgren | General scheme for electromagnetic reflection and transmission for composite structures of complex materials[END_REF] . The wave-splitting matrix is independent of the graded parameters (tensorial density ρ and equivalent bulk modulus B eq ), which ensures the split fields to be continuous across any x 3 -plane in the medium Ω [START_REF] Forslund | Electromagnetic Scattering from an Inhomogeneous Grating Using a Wave-Splitting Approach[END_REF] . These are defined as s ± = (p ± Z e v • n)/2 where the ± sign indicates the direction of propagation relative to the unit vector n. Although they only have a physical sense in Ω 0 according to the wavesplitting transformation, the associated change of basis remains valid. It is then possible to

S(x 3 , ω) = ZW(x 3 , ω) , with Z = 1 2       1 Z e 1 -Z e       . ( 27
)
Introducing this definition in the state vector formulation Eq. ( 15), it is straightforward to obtain:

d dx 3 S = B(x 3 )S , (28)
with

B(x 3 ) = ZA(x 3 )Z -1 =       U + U - -U --U +       -i(k ⊥ • q)I d , (29)
I d being the identity matrix, and

U ± (x 3 , ω) = iω 2 Z e B -1 eq (x 3 , ω) ± H -1 33 (x 3 , ω)Z -1 e .
The differential equations Eq. ( 28) can be solved using the transfer Green's functions (TGF) [START_REF] Krueger | A green's function approach to the determination of internal fields[END_REF] method by writing the forward and backward internal fields in terms of the transmitted wave s -(0, ω) as follows:

s ± (x 3 , ω) = G ± (x 3 , ω)s -(0, ω) ,
where G ± denote the two Green's functions. They are solutions of the following differential

equations dG dx 3 = BG , (30)
with G = {G + , G -}.

In the case of an absorption problem (rigid backing at Γ 0 ) the boundary condition for the Green functions Eq. ( 30) reads G 0 = {1, 1} as a total specular reflection. In the case of a transmission problem, we must have a total transmission at the interface Γ 0 , corresponding to G 0 = {1, 0}. The fluid layer heterogeneity being of macroscopic scale (the order of L), the spatial discretization is easily achieved. The continuous graded properties along x 3 in the domain Ω are split linearly into N = 40 positions. The differential system of equations, Eq. ( 30) is solved numerically.

IV. RESULTS AND DISCUSSIONS

This section deals with the numerical validation of the proposed models. The scattering coefficients are retrieved with all three different methods and applied to an heterogeneous anisotropic porous material.

A. Scattering coefficients

With the TMM and the PS the reflection and transmission coefficients are readily available as part of the solution procedures. From the relation W L = MW 0 from Eq. ( 23) one can derive the following expressions for these coefficients:

T = 2Z -1 e [Z -1 e Tr(M) -Z -2 e M 12 -M 21 ] -1 , (31a) R = M 11 T -Z -1 e M 12 T -1 , (31b)
where Tr(M) is the trace of the square matrix M and M ij are the coefficients of the matrix.

Note that R and T are functions of the angular frequency ω and the incidence angles (the polar and elevation angles ψ and θ, respectively).

For the wave-splitting method, the reflection and transmission coefficients are recovered from the solutions for the Green's functions G + and G -as follows [START_REF] De Ryck | Acoustic wave propagation in a macroscopically inhomogeneous porous medium saturated by a fluid[END_REF][START_REF] Forslund | Electromagnetic Scattering from an Inhomogeneous Grating Using a Wave-Splitting Approach[END_REF][START_REF] Borzdov | Frequency domain wave-splitting techniques for plane stratified bianisotropic media[END_REF] :

T = 1/G -(0) , (32a)
R = G + (L)/G -(L) . ( 32b
)
To quantify the acoustic dissipation inside the layer Ω we calculate the absorption coefficient. As mentioned earlier, as the scattering coefficients depend from the direction of incidence, the absorption coefficient follows the same dependency,

α ± (ω) = 1 -| R± (ω)| 2 -| T (ω)| 2 .
It will vary between 0 and 1 and can also be calculated when the layer is rigidly backed so T = 0. The different computing methods have been compared to the transfer matrix method. For a similar spatial sampling (linear with N = 40) the relative error between each method is below 0.2% and the average computation time per frequency is t tgf ≈ 0.21s for Green's functions (and mainly depends on absolute and relative tolerances of the numerical integration), while t ps ≈ 0.05s for 50 terms of Peano Series and t tmm ≤ 0.01s for TMM.

These results are obtained by averaging the computing time over 100 frequency points, the overall comparison for the three different methods can also be done in parallel. Moreover, other numerical differentiation procedures can be set up to reach the scattering coefficients, such as Runge-Kutta schemes 14 .

B. Porous material

The anisotropic fluid layer considered as an example in the present work is a periodic porous material. The unit cell that is periodically distributed to form this periodic material is a rigid cube of length c from which an ellipsoid with semi-axes of different lengths is carved out, see Fig 2(c). The effective properties of this unit cell are obtained using the multiple-scale method outlined in Ref. 2 and 7. The resulting parameters of the JCAL model 1 are listed in Table I as functions of the unit cell size c and in the coordinate system R 0 . Some of these parameters are scalar quantities (porosity φ, characteristic thermal length Λ and static thermal permeability K 0 ) while others are tensorial (high-frequency tortuosity τ ∞ , characteristic viscous length Λ and static viscous permeability K 0 ).

To obtain an inhomogeneous material the unit cell size c is varied along the x 3 direction.

As a consequence the effective JCAL parameters will also vary along this direction. The profile chosen as an example in this work is the 'ramp' shown in Fig. 2(a). The unit cell size c is varied continuously from 0.1 mm at the base of the layer (x 3 = 0) to 2 mm at the top of the layer (x 3 = L). This profile was chosen to achieve an impedance matching between the exterior domain and the porous material. The layer thickness is L = 50 mm and achieves perfect absorption at the frequency f 0 = 2500 Hz.

C. Influence of wave incidence

We begin by considering the case of a plane wave at oblique incidence with where c is small). Concerning the dependence of α with the elevation angle θ, the system tends towards total reflection for grazing incidences and the anisotropic properties of the fluid layer are clearly visible, as shown in Figs.

k i = (k 1 , k 2 ,
3(e) and 3(f).

D. Effects of anisotropic coupling

In the results above the unit cell has been aligned with the coordinate system, as shown in Fig. 3. To illustrate the effects of the anisotropy of the material, one can rotate the unit cell using the expression given in Eq. ( 3). This is shown in Fig. 4 for the absorption coefficient α. Depending on the rotation components (u 1 , u 2 , u 3 ) involved in the density tensor, the acoustic behavior of the fluid layer is significantly impacted, especially at high frequencies.

To provide further insight into the losses occurring within the layer, we derive the balance of acoustic energy in an anisotropic fluid. From the governing Eq. ( 1) in Ω, one can derive,

iωv * ρv -v * • ∇p = 0 , (33a) iωB -1 |p| 2 -p∇ • v = 0 , (33b)
where we have introduced the conjugated transposed velocity v * and the conjugated pressure p. As depicted in Eq.( 3), the density tensor is complex and symmetric and emerges from the dynamic viscous permeability of the medium Ω. It can be split into its complex components from the Toeplitz decomposition 21 so, ρ = ρ R + iρ I with ρ R = (ρ + ρ * )/2 and ρ I = (ρ -ρ * )/2i. In the general case of a non-symmetric ρ tensor, both Hermitian matrices ρ R and ρ I remain complex-valued, however, in our case of symmetric tensor density, ρ R and ρ I are real. Taking the sum of both of the equations (33) yields,

1 2 (iω) v * (ρ R + iρ I )v + B -1 |p| 2 = 1 2 (v * • ∇p + p∇ • v) , (34)
which after expansion of the complex terms and reads,

1 2 ω iv * ρ R v -v * ρ I v + iB -1 |p| 2 = 1 2 (v * • ∇p + p∇ • v) . (35)
Now considering the real part of this equality, it yields to the time average of the acoustic instantaneous intensity 22 , as the products v * ρ R v and v * ρ I v are real-valued, As depicted in Eq. ( 35), the estimated dissipation rate directly depend on the rotations applied to the density tensor. Figures 4(c) and 4(d) display the estimated dissipation inside the domain Ω, at frequency f 0 . As previously, the dependence on the rotation angles (u 1 , u 2 ) affects the losses in the fluid, hence on the absorption properties. We notice that most of the energy losses in the domain are localized where the pore size becomes small, which is correlated to the total pressure profile in Fig. 3(d).

1 2 ω v * ρ I v + Im{B -1 }|p| 2 = - 1 2 Re {v * • ∇p + p∇ • v} , (36)

E. Diffuse field absorption

Instead of a single wave with a specific incidence angle, one can also consider a diffuse field where all wave directions are present, but uncorrelated with the same intensity. The corresponding absorption coefficient accounts for the absorption averaged over all possible angles of incidence:

α dif (ω) = 1 2π π 0 π 0 α(ω, θ, ψ) cos(θ) dθdψ , (39)
with (θ, ψ) ∈ [0, π] 2 and frequency ω. The averaging process is done accounting for the solid angle associated to each direction of incidence, which induces the weight cos(θ). This diffuse field absorption coefficient is shown in Fig. 5 as a function of frequency using 400 plane wave direction to compute the average. As pictured in Fig. 5, the graded anisotropic materials is able to provide good diffuse absorption over a wide range of frequencies. However its absorption is limited at low frequencies. Unlike the absorption of the plane wave at normal incidence which is perfect around 2500Hz (see Fig. 3), the diffuse field case is unable to reach a perfect absorption. This is explained by the contributions of the plane waves with grazing incidence which can only be partially absorbed. But as oblique incidences weight a lot in this considerations, the anisotropic properties firmly impact the diffuse field absorption coefficient.

FIG. 5. Diffuse field absorption coefficient as a function of frequency.

V. CONCLUSIONS

In this work, the propagation of acoustic waves through a graded layer of anisotropic fluid has been modeled to calculate the transmission and reflection coefficients. This approach is applicable to a wide range of porous materials that are described by their effective bulk modulus and density tensor, and in this case is developed for non-symmetric heterogeneous systems. Three different numerical techniques have been presented and compared to solve for the sound field in such a layer. Two of the solution procedures account for the continuous macro-modulated effective properties of the anisotropic medium, and altogether show excellent agreement with the more traditional TMM approach. In addition, the knowledge of the pressure and velocity fields inside the anisotropic fluid provides useful insight into the losses occurring within the layer.

The dependence of the absorption coefficient with frequency (over the range 100Hz -5kHz), angles of incidence and orientation of the micro-structure has been discussed in detail. All the results demonstrates the complex interplay between these parameters and the fact that the anisotropy plays a significant role in the absorption achieved by this kind of materials. The absorption of a diffuse field was also considered.

The use of anisotropic and heterogeneous materials drastically enhances the potential for efficient acoustic control in scattering and absorption problems. The next step on this topic would be to perform a full optimization of both the anisotropy and the heterogeneity of a porous layer, so as to maximize the acoustic absorption in specific applications.

FIG. 1 .

 1 FIG. 1. [Color online] Schematic representation of the propagation problem in Ω 0 and Ω. A fluid

FIG. 2 .

 2 FIG. 2. [Color online] (a) Variation of the unit cell size c along the depth of the porous material

  k 3 ). Results are shown for an absorption problem, when the layer is rigidly backed at Γ 0 . Fig.3(a) shows the absorption coefficient as a function of frequency between 100 Hz and 5 kHz. The second axis spans the values of elevation angle, while the polar angle of incidence is ψ = 0 in Fig.3(a) and ψ = π/2 in Fig.3(b). While the absorption is limited at low frequency, this material is able to achieve a perfect absorption (α = 1) for a frequency close to f 0 = 2500 Hz. However, we can observe a notable change in the absorption depending on the polar angle of incidence. Fig.3(c) also shows that the three solution procedures presented here (namely the TMM, PS and TGF) are in excellent agreement over the whole range of frequencies. Fig.3(d)shows the evolution of the forward and backward components s ± (x 3 ) in the layer Ω for the frequency where the perfect absorption f 0 is achieved. It is clear that the magnitude of the backward wave s + (x 3 , ω) = (p + Z e v 3 )/2 vanishes on the upper side of the layer (x 3 = L), which is consistent with the fact that there are no reflected wave at this frequency. Also visible in Fig.3(d) is the strong absorption of the forward propagating component s -when it reaches the more resistive part of the porous layer (i.e.

FIG. 4 .

 4 FIG. 4. [Color online] Absorption coefficient at normal incidence as a function of the circular

TABLE I .

 I Homogenized JCAL parameters for the anisotropic unit cell with characteristic size c in the coordinate system R 0 .

		φ (1)	Λ (m)	K 0 (m 2 )	τ ∞ (1)	Λ (m)	K 0 (m 2 )
	Ω	0.7210	0.533 c	0.0214 2 c	-	-	-
	e 1	-	-	-	2.987	0.129 c	5.74 10 -4 2 c
	e 2	-	-	-	1.089	0.448 c	1.56 10 -2 2 c
	e 3	-	-	-	1.487	0.273 c	4.83 10 -3 2 c

ACKNOWLEDGMENTS

The authors gratefully acknowledge the support from ANR Chaire industrielle MACIA (ANR-16-CHIN-0002).

The left-hand side of this equation is the divergence of the Poynting vector P = pv * , since the porous layer is purely lossy, we expect this term to be strictly negative. This quantity is homogeneous to the dissipation rate of acoustic energy at each infinitesimal point x 3 ∈ Ω and is expressed in W.m -3 . Although, it is estimated as only dependent of the normal direction x 3 since the acoustic fields in Eq. ( 9) show an harmonic spatial dependence.

It highlights the role of the coupling vector q and its effect on the fully-anisotropic behavior of such medium. The total energy lost in the system can be retrieved by spatial integration between boundaries Γ 0 and Γ L . As all three components of the particle velocity are involved, the transverse part of v is derived from Eqs. (10a) and (10b).

Inside the domain Ω, the transverse components of particle velocity read

It is worth noting that even at normal incidence, with k ⊥ = (0, 0), the coupling still occurs from the term v 3 q. In order to illustrate this effect, Fig. 4 shows the absorption coefficient when the fluid is taken out of its principal directions. Also considering normal incidence and with R 0 ≡ R Ω , a sole rotation around e 3 cannot impact the acoustic properties of the fluid. First, the dependence on the rotation angle around e 1 is shown in Fig. 4


Isabelle Mosnier
email: isabelle.mosnier@aphp.fr

Ghizlene Lahlou

Jonathan Flament

Nathalie Mathias

Evelyne Ferrary

Olivier Sterkers

Daniele Bernardeschi

Yann Nguyen

Affiliations

Benefits of a contralateral routing of signal device for unilateral Naída CI cochlear implant recipients

Abstract

Purpose: Many bilaterally deaf adults are only able to receive one cochlear implant (CI), resulting in suboptimal listening performance, especially in challenging listening environments. Adding a contralateral routing of signal (CROS) device to a unilateral CI is one possibility to alleviate these challenges. This study examined the benefit of such a CROS device.

Methods: Thirteen adult subjects with at least 6 months of CI use, and no or limited benefit of a hearing instrument in the contralateral ear were included in the study. The perceived benefit of a CROS device in everyday listening environments was evaluated up to one year after initial fitting using several questionnaires. Speech intelligibility performance was determined using the French matrix sentence test in quiet and in two speech-in-noise setups and was followed for three months after CROS fitting.

Results: Subjects indicated high satisfaction with the practical usability of the CROS device and long-term device retention was high. Perceived benefits in everyday listening environments were reported. Formal speech intelligibility tests revealed statistically significant median improvements of 6.93 dB SPL (Wilcoxon Z = 2.380, p = 0.017) in quiet and up to 8.00 dB SNR (Wilcoxon Z = 2.366, p = 0.018) in noise. These benefits were accessible immediately without a need for prolonged acclimatization.

Conclusions: Subjective satisfaction and device retention as well as speech intelligibility benefits in quiet and in noise prove the CROS device to be a valuable addition to a unilateral CI in cases of bilateral deafness where bilateral implantation is not an option.

Introduction

Cochlear implantation has become the standard auditory rehabilitation for adults and children with bilateral severe to profound hearing loss. Although several studies show the benefits of bilateral cochlear implantation with respect to sound localisation and listening in noise [START_REF] Seta | Five-Year Hearing Outcomes in Bilateral Simultaneously Cochlear-Implanted Adult Patients[END_REF][START_REF] Laske | Subjective and objective results after bilateral cochlear implantation in adults[END_REF][START_REF] Mosnier | Speech performance and sound localization in a complex noisy environment in bilaterally implanted adult patients[END_REF][START_REF] Smulders | Comparison of Bilateral and Unilateral Cochlear Implantation in Adults: A Randomized Clinical Trial[END_REF][START_REF] Van Schoonhoven | The effectiveness of bilateral cochlear implants for severe-to-profound deafness in adults: a systematic review[END_REF], individual results vary and the few available cost-utility analysis in adult recipients reports provide insufficient evidence to draw definite conclusions [START_REF] Chen | Cost-utility analysis of bilateral cochlear implantation in adults: a health economic assessment from the perspective of a publicly funded program[END_REF][START_REF] Crathorne | A systematic review of the effectiveness and cost-effectiveness of bilateral multichannel cochlear implants in adults with severe-to-profound hearing loss[END_REF]. Consequentially, bilateral implantation, especially in adults, is currently not funded in many healthcare systems. Therefore, many bilaterally deaf adults receive only one cochlear implant (CI). Even if bilateral implantation is reimbursed in adults, medical reasons might prevent implantation of the second side. Additionally, patients may choose not to undergo a second CI surgery, for example because they are concerned about surgery risks or because they wish to preserve that ear for future treatment options.

Irrespective of the reason preventing the second implantation, these bilaterally deaf unilaterally implanted subjects will continue to experience limitations due to the head shadow effect. Audibility of sound sources located away from the implanted ear is reduced resulting for example in impaired speech intelligibility in noise and reduced awareness of the surrounding sounds.

To alleviate these difficulties, one treatment option is a contralateral routing of signal (CROS) device, consisting of a microphone placed on the non-hearing/ implanted ear. Signals from that side are picked up and transmitted to the hearing/implanted side.

While long established in the hearing aid community [START_REF] Ryu | Clinical effectiveness of wireless CROS (contralateral routing of offside signals) hearing aids[END_REF], CROS devices in combination with unilateral CIs have only recently been investigated [START_REF] Arora | The addition of a contralateral routing of signals microphone to a unilateral cochlear implant system. A prospective study in speech outcomes[END_REF][START_REF] Grewal | The role of a new contralateral routing of signal microphone in established unilateral cochlear implant recipients[END_REF][START_REF] Guevara | Assessment of the contralateral routing of signal system in unilateral cochlear implantation[END_REF][START_REF] Taal | Benefit of contralateral routing of signals for unilateral cochlear implant users[END_REF][START_REF] Van Loon | The addition of a contralateral microphone for unilateral cochlear implant users: not an alternative for bilateral cochlear implantation[END_REF][START_REF] Weder | Benefit of a contralateral routing of signal device for unilateral cochlear implant users[END_REF][START_REF] Wimmer | Directional Microphone Contralateral Routing of Signals in Cochlear Implant Users: A Within-Subjects Comparison[END_REF][START_REF] Dwyer | Contralateral Routing of Signal Yields Significant Speech in Noise Benefit for Unilateral Cochlear Implant Recipients[END_REF][START_REF] Ernst | Evaluation of a wireless Contralateral Routing of Signal (CROS) device with the Advanced Bionics Naída CI Q90 sound processor[END_REF][START_REF] Snapp | Application of wireless contralateral routing of signal in unilateral cochlear implant users with bilateral profound hearing loss[END_REF].

These studies consistently demonstrated a speech intelligibility benefit provided by the CROS device when the target speech source is located on the side of the non-implanted ear. When noise is located on the side of the nonimplanted ear, a decrease in speech intelligibility was observed, the degree of which varies depending on the exact test setup.

In addition to acute speech intelligibility testing, chronic data have been collected, with a maximum take home of two weeks. While Weder [START_REF] Weder | Benefit of a contralateral routing of signal device for unilateral cochlear implant users[END_REF] did not show a significant perceived improvement after chronic trials, a subjective benefit was observed in other studies on the Abbreviated Profile of Hearing Aid Benefit (APHAB, [START_REF] Cox | The abbreviated profile of hearing aid benefit[END_REF]) [START_REF] Grewal | The role of a new contralateral routing of signal microphone in established unilateral cochlear implant recipients[END_REF][START_REF] Guevara | Assessment of the contralateral routing of signal system in unilateral cochlear implantation[END_REF], in the Speech subscale of the abbreviated Speech Spatial and Qualities of Hearing Scale (SSQ12, [START_REF] Noble | A short form of the Speech, Spatial and Qualities of Hearing scale suitable for clinical use: the SSQ12[END_REF]) [START_REF] Dwyer | Contralateral Routing of Signal Yields Significant Speech in Noise Benefit for Unilateral Cochlear Implant Recipients[END_REF] and in the Spatial subscale of the Speech Spatial and Qualities of Hearing Scale (SSQ, [START_REF] Gatehouse | The Speech, Spatial and Qualities of Hearing Scale (SSQ)[END_REF]) [START_REF] Grewal | The role of a new contralateral routing of signal microphone in established unilateral cochlear implant recipients[END_REF]. However in the Guevara study which evaluated a CROS device with a wire connection [START_REF] Guevara | Assessment of the contralateral routing of signal system in unilateral cochlear implantation[END_REF], only two of the eight subjects were still using their CROS device after six months, citing difficulties in noisy environments and trouble with the connecting wire.

The Phonak Naída Link CROS device investigated in the current study provides a wireless solution, designed to improve wearing comfort. Additionally, the device carries a mute button to silence input from the CROS side in noisy listening environments. Both features have previously been reported as useful enhancements to the tested prototype devices [START_REF] Guevara | Assessment of the contralateral routing of signal system in unilateral cochlear implantation[END_REF][START_REF] Van Loon | The addition of a contralateral microphone for unilateral cochlear implant users: not an alternative for bilateral cochlear implantation[END_REF][START_REF] Weder | Benefit of a contralateral routing of signal device for unilateral cochlear implant users[END_REF]. The device can be used with the Advanced Bionics Naída CI Q70 and Q90 sound processors.

Our study focusses on the long-term evaluation of perceived everyday benefits of using the CROS device. Subjects were followed closely for 3 months after fitting of the CROS device using measures of real life benefit and subjective satisfaction as well as repeated speech intelligibility testing. A one-year followup questionnaire evaluated the long-term retention rate and satisfaction with the CROS device.

Materials and Methods

A prospective, single centre, within-subjects repeated-measures design was chosen for this study. ') v

Study Population

Thirteen adult subjects were identified from the clinic's database. All subjects were implanted with an Advanced Bionics CII or HiRes90k cochlear implant for at least six months and had used the Naída CI Q70 sound processor for at least three months prior to testing. Three subjects clinically used a hearing aid in the contralateral ear, with limited benefit (defined as < 20% monosyllabic words in quiet). Two subjects were implanted in the contralateral ear but did not use the second CI due perceived to lack of benefit. Detailed subject information is provided in table 1.

Device Fitting

The most recent Advanced Bionics sound processors, the Naída CI Q70 and Q90, have the ability to communicate wirelessly with another Naída CI processor, or with some Phonak hearing instrument models, including a CROS device. The Naída Link CROS device consists of a microphone, radio transmitter and battery worn on the unilateral CI recipient's non-implanted ear. The microphone signal from the CROS device is transmitted wirelessly to the Naída CI sound processor and mixed with the microphone signal from the implanted side with a mixing ratio of 50:50 before being coded by the sound processor.

In addition to the CROS device, a loaner Naída CI processor was used for the duration of the study. The loaner sound processor was fitted with each subject's clinical program, according to the clinic's standard fitting routine and no changes were made to the fitting parameters. The Advanced Bionics SoundWave 3.1 fitting software was used, which allows the activation of a HiBAN (Hearing Instrument Body Area Network) link between the CI processor and the Naída CROS device. The CROS device is an out-of-the-box solution and works automatically with the Naída CI processor without the need for any additional fitting. Subjects were counselled on use of the mute button which allows them to easily disable input from the CROS device in situations where it would enhance unwanted noise rather than speech.

Subjective evaluation

Three questionnaires were used to record each subject's self-assessment of their hearing abilities as well as their satisfaction with the CROS device:

1) The Abbreviated Profile of Hearing Aid Benefit (APHAB; [START_REF] Cox | The abbreviated profile of hearing aid benefit[END_REF]), a 24-item selfassessment inventory, requires subjects to report the amount of trouble they experience with communication in various everyday situations. The APHAB includes four subscales: Ease of communication (EC), Reverberation (RV), Background noise (BN), and Aversiveness (AV). Scores are given on a scale from A (I always experience this) to G (I never experience this). A percentage score from 1% to 99% is assigned to each category to yield a mean percentage for each subsection.

2) The abbreviated Speech Spatial Qualities Questionnaire (SSQ12, [START_REF] Noble | A short form of the Speech, Spatial and Qualities of Hearing scale suitable for clinical use: the SSQ12[END_REF]) requires subjects to rate their listening abilities on a Likert scale from 1 (not at all) to 10 (perfectly). The SSQ12 includes three sub scales relating to aspects of speech, spatial and other qualities of hearing.

3) An adapted version of the Auditory Performance and Satisfaction Scale for

Single-Sided Deafness (APS-SSD, [START_REF] Snapp | Application of wireless contralateral routing of signal in unilateral cochlear implant users with bilateral profound hearing loss[END_REF][START_REF] Schafer | Behavioral and Subjective Performance with Digital CROS/BiCROS Hearing Instruments[END_REF]) focuses on specific situations encountered in real life where a CROS device may be beneficial, grouped into three categories: hearing at home, hearing at work or school, and hearing in social situations. Each situation is rated on a scale from 0 (Can function fine) to 6 (Cannot function at all). It additionally contains a category on the satisfaction with and usability of the CROS device (see Electronic Supplementary Material).

Speech perception tests

Speech intelligibility was measured in quiet and noise in a sound treated room using the French Matrix test (Framatrix, Auritec, Hamburg, Germany, [START_REF] Jansen | Comparison of three types of French speech-in-noise tests: a multi-center study[END_REF]).

Subjects were asked to repeat semantically unpredictable sentences with a fixed structure: name, verb, number, common name, color. Prior to testing, at least one practice list of 20 sentences for testing in quiet, and two practice lists for testing in noise were presented to the subject to avoid training effects.

For testing in quiet, the speech recognition threshold (i.e. speech level required for 50% word intelligibility) was measured in dB SPL by adaptively adjusting the signal level. Speech was presented from -90° azimuth, on the CROS side. For testing in noise, the speech reception threshold (SRT; i.e. signalto-noise-ratio (SNR) required for 50% word intelligibility) was measured in dB SNR by adaptively adjusting the signal level while stationary speech-shaped noise was fixed at 65 dB. Noise was presented from + 90° azimuth on the CI side, while speech was presented either from -90° azimuth (CROS side) or from 0° azimuth (front). The two conditions were tested in random order. All loudspeakers were positioned at 1m distance from the subject's head. In all test conditions, subjects were tested with and without the CROS device in random order. Lower speech recognition thresholds as well as lower SRTs indicate better performance.

Measurement schedule

Subjects were invited to the clinic for four appointments. An overview of the study schedule is provided in table 2. At baseline, all subjects received a loaner Naída CI processor, fitted with their clinical everyday program(s), and the CROS device. Subjects were tested in quiet and noise with the Naída CI processor with and without the CROS device at the baseline, 1 month and 3 months appointments. The CROS device was removed at the 3 months appointment and subjects used the Naída CI processor only for a further two weeks. Subjects were asked to complete questionnaires at each visit regarding their recent listening configuration (Naída CI processor alone or with the CROS device). At the last visit, the loaner Naída CI processor and the CROS device were returned and subjects were given the option to receive the CROS device free of charge once the appropriate market certification was obtained. All subjects were provided with a CROS device after completing the study. After approximately 1 year, these subjects were provided with a follow-up questionnaire evaluating device retention as well as long-term satisfaction with the CROS.

Statistical analysis

Statistical analyses were performed using Statistica 12 software (TIBCO Software Inc., Palo Alto, USA) with a level of significance set at 0.05. Due to the low N, non-parametric analyses were chosen.

Speech perception tests

Significance of the CROS benefit (i.e. difference in performance between CI only and CI + CROS condition) was tested using the Wilcoxon signed rank statistic. Differences in performance over time as well as differences in CROS benefit over time were analysed using Friedman ANOVA followed by post-hoc Wilcoxon signed rank tests. Bonferroni corrections were applied where necessary.

Subjective evaluation

Analysis of the subjective feedback collected via questionnaires focused on the respective subscales. The two CI only timepoints (baseline and 3.5 months) and the two CI + CROS timepoints (1 month and 3 months) were combined and contrasted using Wilcoxon signed rank tests.

Results

Three of the 13 originally recruited subjects chose to withdraw from the study after the baseline or 1 month visit. Subject 11 withdrew from the study for personal reasons. Subjects 4 and 9 clinically used a HA in the contralateral ear and discontinued use of the CROS device in favour of their clinical HA.

Of remaining ten subjects, eight performed speech tests in quiet. The remaining two subjects were unable to perform the French matrix test. In noise, one further subject was unable to complete the matrix test at the baseline appointment resulting in seven complete datasets.

At baseline, 1, 3 and 3.5 months, questionnaires were completed by all ten subjects. At 1-year follow-up, questionnaires were returned by eight subjects.

Subjective evaluation

To analyze the subjective feedback, responses from the baseline and 3.5 months appointments and responses from the 1 month and 3 months appointments were combined to form two categories: CI only and CI + CROS.

The two categories were then compared regarding each questionnaire's respective subscales as well as one overall score for each questionnaire. These results are displayed in figure 1.

For the APHAB and SSQ12 questionnaires, no significant differences between the CI only and CI + CROS categories were found for any of the respective subscales or the overall scores. For the experience portion of the adapted APS-SSD questionnaire, significant differences were found for the 'Social' and 'General' subscales but not for the remaining two subscales or the overall score. Results of the Wilcoxon signed rank statistic for all questionnaires is summarized in table 3.

The satisfaction portion of the adapted APS-SSD questionnaire revealed high satisfaction with several aspects of the CROS device itself indicated by median ratings lower than 3 (figure 2a). Responses from eight subjects who provided answers at the 1 month, 3 months and 1 year appointments were combined for each item.

In addition, the average score across all items of the APS-SSD satisfaction portion was analyzed regarding changes across time (see figure 2b). No statistically significant difference in average satisfaction score was found between the different timepoints (1 month, 3 months and 1 year).

The questionnaire further revealed that the CROS device was used most of the time with median usage times of 11.5h (1 month), 11h (3 months) and 10.25h

(1 year). When asked for the preferred device configuration by the end of the study, nine out of the ten subjects who completed the study clearly preferred the CROS device while the remaining subject stated no preference. One year after the end of the study, only one out of eight responses reported a preference for the CI alone.

Speech intelligibility

Median speech perception scores in quiet (Fig. 3) as well as the two noise scenarios SCROSNCI (Fig. 4a) and S0NCI (Fig. 4b) are presented in figures 3 and4 for the baseline, 1 month and 3 months appointments.

In quiet, the median differences in performance between the CI only and CI + CROS conditions were 6.93 dB SPL, 4.15 dB SPL and 3.38 dB SPL at the baseline, 1 month and 3 months appointments.

In SCROSNCI, the median differences in performance between the CI only and CI + CROS conditions were 6.15 dB SNR, 7.75 dB SNR and 8.00 dB SNR at the baseline, 1 month and 3 months appointments. In SCROSNCI, the median differences in performance between the CI only and CI + CROS conditions were 2.10 dB SNR, 2.00 dB SNR and 2.65 dB SNR at the baseline, 1 month and 3 months appointments. All differences were found to be statistically significant (Wilcoxon signed rank test, statistics reported in table 4).

Furthermore, Friedman analysis revealed that overall performance improved across the appointments for CI only in quiet (χ²(2) = 10.75, p = .005), for CI + CROS in quiet (χ²(2) = 7.75, p = .021), for CI only in SCROSNCI (χ²(2) = 8.00, p = . 018), for CI + CROS in SCROSNCI (χ²(2) = 7.14, p = .028) and for CI only in S0NCI (χ²(2) = 7.14, p = .028). Performance for CI + CROS in S0NCI (χ²(2) = 3.71, p = .

156) as well as the CROS benefit in quiet (χ²(2) = 1.35, p = .508), in SCROSNCI (χ²(2) = .28, p = .867) and in S0NCI (χ²(2) = 4.96, p = .084) remained stable across the appointments.

Discussion

Three subjects withdrew throughout the course of the study. Subject 11 withdrew for personal reasons and reported satisfaction with the CROS device. Subjects 4 and 9 stated higher satisfaction with their clinical HA as reason for their discontinuation. While both patients only achieve limited speech intelligibility with their HA alone (6% and 18% monosyllabic words in quiet), both patients receive a sizeable bimodal benefit of 23% and 30% respectively, suggesting that bimodal benefit rather than contralateral speech scores may be a more suitable criterion for CROS candidacy. Conversely, subject 3 who also received 30% bimodal benefit with the clinical HA reported high satisfaction with the CROS device compared to the clinical HA. This indicates that CROS candidacy and the acceptance of CROS in bimodal CI users depend to a large extend on personal factors and cannot be predicted by speech intelligibility with the HA or bimodal benefit alone. Since the Naída Link CROS device does not require personalized fitting and the Naída CI processor is easily activated for use with the CROS device, a trial phase with the CROS device could be realized within the clinical routine to determine the best rehabilitation option (CROS or HA) in bimodal CI users with limited bimodal benefit or limited contralateral speech intelligibility.

The subjective evaluation revealed few significant changes. Especially the validated, general questionnaires APHAB and SSQ12 proved not sensitive enough to capture CROS benefits by showing no significant changes in any of the subscales or the overall score. Considering that these questionnaires were designed for HA users and are not geared towards listening environments or situations where a CROS benefit can be expected, the lack of significance is not surprising, even though Grewal et al [START_REF] Grewal | The role of a new contralateral routing of signal microphone in established unilateral cochlear implant recipients[END_REF] and Guevara et al [START_REF] Guevara | Assessment of the contralateral routing of signal system in unilateral cochlear implantation[END_REF] were able to demonstrate a significant CROS benefit in the APHAB questionnaire and Grewal et al. [START_REF] Grewal | The role of a new contralateral routing of signal microphone in established unilateral cochlear implant recipients[END_REF] and Dwyer et al. [START_REF] Dwyer | Contralateral Routing of Signal Yields Significant Speech in Noise Benefit for Unilateral Cochlear Implant Recipients[END_REF] in the SSQ and SSQ12 respectively. The dedicated adapted APS-SSD questionnaire did show significant improvements in the 'Social' and 'General' subscale. The remaining subscales 'Home' and 'Work/School' as well as the overall score did not reveal significant changes, indicating that even dedicated questionnaires might not be sensitive enough to capture CROS benefits. Subjects were asked to fill in the questionnaires at each appointment independently without access to their previous ratings.

Providing subjects access to their previous responses, therefore enabling a comparative rating, may have improved the questionnaires sensitivity to subtle changes. The high preference for the CI + CROS configuration, immediately after the study as well as after one year, indicates the usefulness of and perceived benefit provided by the CROS device nonetheless.

The usefulness and perceived benefit despite the lack of significant improvements in the questionnaires is further supported by the free feedback provided by subjects. Several subjects indicated feeling more balanced with the CROS device, being more aware of surrounding sounds and missing the CROS immediately if the batteries run out. Notably, several subjects also indicated improved localisation abilities with the CROS device. While localisation performance with the CROS device was not investigated in this study, by design the device does not provide binaural auditory input and can therefore not be expected to enable or improve localisation abilities as confirmed by previous studies [START_REF] Weder | Benefit of a contralateral routing of signal device for unilateral cochlear implant users[END_REF][START_REF] Wimmer | Directional Microphone Contralateral Routing of Signals in Cochlear Implant Users: A Within-Subjects Comparison[END_REF]. We therefore suggest that subjects indicating improved localisation abilities rather refer to improved awareness of surrounding sounds, especially sounds originating towards the unimplanted ear. Speech intelligibility tests in quiet and in noise expectedly yielded good results in favourable conditions: median improvements of up to 6.9 dB and 8.0 dB with the CROS device when speech is presented from the CROS side in quiet an in noise respectively and up to 2.7 dB in noise when speech is presented from the front.

In many cases, direct comparison of these outcomes to previously published studies is precluded by the use of different speech materials as well as different test setups in the respective studies. While Wimmer et al. [START_REF] Wimmer | Directional Microphone Contralateral Routing of Signals in Cochlear Implant Users: A Within-Subjects Comparison[END_REF] used comparable speech material (German matrix sentence test [START_REF] Wagener | Entwicklung und Evaluation eines Satztests für die deutsche Sprache I: Design des Oldenburger Satztests[END_REF]), the CROS device tested consisted of a directional microphone rather than the omnidirectional microphone tested here, complicating direct comparisons.

Ernst et al. [START_REF] Ernst | Evaluation of a wireless Contralateral Routing of Signal (CROS) device with the Advanced Bionics Naída CI Q90 sound processor[END_REF] however used comparable speech material and included the SCROSNCI condition reported here allowing a direct comparison: their reported CROS benefit (median difference) of 7.23 dB s compares quite well to the 8.0 dB found here.

Unfavourable conditions where speech is presented from the CI side and noise from the CROS side or diffusely were not included in this evaluation. In these conditions, the CROS device adds additional noise and performance is expected to decrease as has previously been shown [START_REF] Arora | The addition of a contralateral routing of signals microphone to a unilateral cochlear implant system. A prospective study in speech outcomes[END_REF][START_REF] Taal | Benefit of contralateral routing of signals for unilateral cochlear implant users[END_REF][START_REF] Van Loon | The addition of a contralateral microphone for unilateral cochlear implant users: not an alternative for bilateral cochlear implantation[END_REF][START_REF] Dwyer | Contralateral Routing of Signal Yields Significant Speech in Noise Benefit for Unilateral Cochlear Implant Recipients[END_REF]. To avoid this performance decrease in unfavourable listening conditions, the CROS device tested here features a mute button which can be used to silence undesired input from the CROS side.

The overall performance increased significantly over time in almost all listening conditions. This could either indicate subjects' general speech intelligibility improving over time or the subjects becoming more familiar with the used speech test material. The subjects included in this study have used their CI for at least 10 months with an average CI use of 5 years and 3 months, leading us to exclude a general learning effect as the cause of the improved performance over time. The French matrix sentence test used in this study is not routinely used in the clinic, therefore most subjects were not familiar with this closed set speech material. Although the most pronounced improvement is seen during the first two test lists and therefore two practice lists are generally considered sufficient to avoid training effects, long-term training effects using closed-set speech material have been shown for the German matrix sentence test [START_REF] Schlueter | Normal and Time-Compressed Speech: How Does Learning Affect Speech Recognition Thresholds in Noise? Trends Hear[END_REF].

We therefore suggest a training/learning effect to have caused the overall performance improvement over time.

In contrast to the overall performance, CROS benefits remained stable over time in all listening conditions. No acclimatisation or learning was required, subjects benefitted from the CROS device immediately after fitting.

Conclusion

The Naída Link CROS device was designed as an addition to a unilateral CI in cases of bilateral deafness when bilateral implantation is not an option. It was shown to increase speech intelligibility for speech sources located toward the unimplanted side. Subjects reported satisfaction with the CROS device itself and perceived benefits in their everyday listening environments such as increased sound awareness. The high long-term retention rate further confirms the CROS device to be a valuable addition to a unilateral CI.

Compliance with ethical standards

Conflict of interest: The authors declare that they have no conflict of interest.

Ethical approval:

All study procedures were approved by the ethical committee, 'Comité de Protection des Personnes Sud-Est V' and the French competent authority, ANSM (Agence Nationale de Sécurité du Médicament et des produits de santé) and were conducted in accordance with the ethical standards defined by the Declaration of Helsinki. The study was registered as N° NCT03078920 at www.clinicaltrials.gov.

Informed consent: Informed consent was obtained from all individual participants included in the study.

Tables

Figure Captions

Fig. 1 Fig. 2 Fig. 3 Fig. 4

 1234 Fig. 1 Subject responses to the APHAB (a) and SSQ12 (b) questionnaires and the

Table 1

 1 Detailed subject demographics

	Subje ct	Ag e	Gen der	Etiology	Impl ant Side	Duration of CI experience (yrs/mos)	Contralateral HL (avg. PTA @ 0.5, 1, 2, 4kHz)	Regular eral HI use contralat	Note
	1	76 m	meningitis, otosclerosis	l	1/2	130	no
	2	65 f	meningitis	r	7/3	130	no
	3	62 m	Menière's disease	l	0/10	85	yes	HA, 0% WiQ
	4	69 m	congenital syphilis	l	0/10	92.5	yes	HA, 6% WiQ
	5	67 f	otosclerosis	r	6/4	123.75	no
	6	59 m	chronic otitis media	r	7/6	130	no
	7	55 f	familial	l	1/6	113.75	no
	8	56 f	hydrocephalus	r	1/1	130	yes	CI, non-user
	9	51 f	unknown	r	7/0	106.25	yes	HA, 18% WiQ
	10	22 f	unknown	l	6/8	130	no
	11	57 f	familial, otosclerosis	l	8/10	92.5	yes	CI, non-user
	12	50 f	auto-immune disease	l	11/1	96.25	no
	13	63 m	trauma, TB fracture	r	8/6	103.75	no
	HL = hearing loss, HI = hearing instrument, HA = hearing aid, TB = temporal bone, WiQ = contralateral
	monosyllabic word score in quiet (Lafon lists)
	Shaded rows indicate subjects who withdrew from the study

Table 2

 2 Study visits and procedures in chronological order

	Visit	Speech Test	Questionnaire
	baseline	Lafon quiet (screening)	SSQ12
		•	CI only	•	CI only
		Matrix quiet	APHAB
		•	CI only	•	CI only
		•	CI + CROS
		Matrix noise
		•	CI only
		•	CI + CROS
			chronic experience CI + CROS
	1 month	Matrix quiet	SSQ12
		•	CI only	•	CI + CROS
		•	CI + CROS	APHAB
		Matrix noise	•	CI + CROS
		•	CI only	APS-SSD
		•	CI + CROS	•	CI + CROS
			chronic experience CI + CROS
	3 months	Matrix quiet	SSQ12
		•	CI only	•	CI + CROS
		•	CI + CROS	APHAB
		Matrix noise	•	CI + CROS
		•	CI only	APS-SSD
		•	CI + CROS	CI + CROS
			chronic experience CI only
	3.5 months			SSQ12
				•	CI only
				APHAB
				•	CI only
				APS-SSD (subset)
				•	CI only
	chronic experience CI + CROS/CI only (depending on subject's choice)
	1 year			APS-SSD (subset)
				•	CI + CROS

Table 3

 3 Results of Wilcoxon signed rank statistic for APHAB, SSQ12 and APS-SSD questionnaires. Grey shading indicates statistical significance.

Table 4

 4 Results of Wilcoxon signed rank statistic for speech intelligibility measurements in quiet and in noise. Grey shading indicates statistical significance.

					Z	p
	AP	Ease of Communication 0.296	0.767
	HA B	Background Noise	0.764	0.445
		Reverberation		0.140	0.889
		Aversiveness		0.153	0.878
		Global			0.357	0.721
	SS	Speech			0.357	0.721
	Q1
	2	Spatial			1.070	0.285
		Quality			0.357	0.721
		Overall			1.125	0.260
	AP	Home			1.529	0.126
	S-
	SS	Work/School		0.770	0.441
	D	Social			2.090	0.037
		General			2.666	0.008
		Overall			1.886	0.059
		quiet (N = 8)	SCROS NCI (N = 7)	S0 NCI (N = 7)
		Z	p	Z	p	Z	p
	baseline	2.380 0.017 2.366 0.018 2.197 0.028
	1 month	2.380 0.017 2.366 0.018 2.028 0.043
	3 months	2.521 0.011 2.366 0.018 2.366 0.018