Dr Roberto Stasi
email: roberto.stasi@stgeorges.nhs.uk

Professor Adrian Newland

Dr Patrick Thornton

Professor Ingrid Pabinger

Should Medical Treatment Options be Exhausted before Splenectomy is

Keywords: Immune Thrombocytopenia, Splenectomy, Thrombopoietin Agonists, Corticosteroids Immune Thrombocytopenia, Splenectomy, Thrombopoietin Agonists, Corticosteroids

Patients with primary immune thrombocytopenia (ITP) may require treatment to reduce the risk of serious bleeding if platelets remain consistently below 30 x 109/L. While approximately 70-80% of patients respond to an initial course of corticosteroids, relapse is common. For steroid-refractory patients, there is a choice between surgical splenectomy and further medical treatments, based on many factors including the patient's bleeding history, fitness for surgery, comorbidities, tolerance of adverse events, lifestyle and preferences. Treatments that have traditionally been used (corticosteroids, azathioprine, danazol) suppress the immune system, potentially predisposing patients to infection. Recent insights into the underlying pathophysiology of the disease have allowed the development of targeted therapies, including the thrombopoietin (TPO) receptor agonists, which enhance platelet production. Phase III trials have found romiplostim and eltrombopag to be well tolerated and effective in elevating platelet counts and reducing bleeding in both splenectomised and nonsplenectomised patients with chronic ITP. The B-cell targeted monoclonal antibody rituximab has also shown some potential in this setting, although data are currently limited and there are toxicity concerns. The decision whether to proceed to splenectomy or try other medical therapies in corticosteroidrefractory patients remains patient-specific. Splenectomy has its risks (including perioperative and long-term risks), and relapse/nonresponse are relatively common, but it offers the possibility of cure in the majority of patients. However, newer treatments may potentially allow splenectomy to be deferred for prolonged periods, as well as providing alternative treatment options for patients who fail splenectomy.

INTRODUCTION

Primary immune thrombocytopenia (ITP; previously referred to as idiopathic thrombocytopenic purpura), is defined as isolated thrombocytopenia (platelet counts (<100 x 10 9 /L) of unknown cause. Clinical manifestations vary and may be absent or range from petechiae or purpura and easy bruising to potentially life-threatening bleeding episodes. Whereas ITP in children is often characterised by abrupt onset of petechiae and purpura, associated with viral infection or immunisation, and shortlived (<6 months), ITP in adults typically has a more insidious onset and is more likely to follow a chronic course (≥12 months).

The severity of thrombocytopenia is the most important risk factor for major bleeding and management of chronic ITP is aimed at preventing bleeding, rather than normalising the platelet count. Treatment is usually indicated in patients with platelet counts <30 x 10 9 /L and those with counts between 30 and 50 x 10 9 /L with bleeding or at risk of bleeding (e.g planned surgery, dental extraction, parturition, active peptic ulcer) [START_REF] Pabinger | Guidelines for the investigation and management of idiopathic thrombocytopenic purpura in adults, children and in pregnancy[END_REF][START_REF] George | Idiopathic thrombocytopenic purpura: a practice guideline developed by explicit methods for the American Society of Hematology[END_REF]. Corticosteroids are the standard first-line treatment, while intravenous immune globulin (IVIg) and anti-D (with or without methylprednisolone and platelet transfusions) are used mainly for 'rescue' treatment of serious bleeding episodes.

Anti-D has also been an option for nonsplenectomised Rhesus-positive patients who are unable to receive corticosteroids, but is no longer available in the EU. Typically, a course of prednis(ol)one is given, at a dosage of 1 to 2 mg/kg/day, with dosage being tapered after a short time (usually within a few weeks), in order to avoid inducing corticosteroid-related adverse effects. Another regimen used in many countries is 1-4 courses of dexamethasone 40 mg/day for 4 consecutive days, at 14-day intervals [START_REF] Provan | International consensus report on the investigation and management of primary immune thrombocytopenia[END_REF].

Approximately 70-80% of patients respond to corticosteroids initially [START_REF] Provan | International consensus report on the investigation and management of primary immune thrombocytopenia[END_REF], but relapse is common with many patients requiring repeated or prolonged treatment. For secondline treatment, there is a choice between surgical splenectomy (in patients who are fit for surgery) and a wide range of medical treatments (Figure 1). While international guidelines for ITP have been published [START_REF] Pabinger | Guidelines for the investigation and management of idiopathic thrombocytopenic purpura in adults, children and in pregnancy[END_REF][START_REF] George | Idiopathic thrombocytopenic purpura: a practice guideline developed by explicit methods for the American Society of Hematology[END_REF][START_REF] Provan | International consensus report on the investigation and management of primary immune thrombocytopenia[END_REF], there is no consensus regarding the best sequence of treatments and treatment is individualised, based on such factors as the patient's bleeding history, comorbidities, tolerance of adverse events, degree of worry about disease burden, lifestyle, accessibility to care, and preferences. For reviews on the subject, see Bussell [START_REF] Bussel | Treatment of immune thrombocytopenic purpura in adults[END_REF], and Cines and McMillan [START_REF] Cines | Management of adult idiopathic thrombocytopenic purpura[END_REF].

As the choice of treatments has expanded in recent years with the introduction of several new agents, this article examines the question of whether medical treatment options should generally be exhausted before splenectomy is performed in adults with chronic severe ITP requiring treatment. Arguments for and against early splenectomy are presented.

ARGUMENTS AGAINST EARLY SPLENECTOMY

The natural history of adult ITP varies and spontaneous remissions can occur

Chronic ITP in adults has a variable and unpredictable course, with very wide interpatient heterogeneity. Spontaneous remissions (without splenectomy) occur in approximately 10% of patients, with and without medical treatment. There is increasing evidence that remissions can occur up to 1 or 2 years after onset [START_REF] Stasi | Long-term observation of 208 adults with chronic idiopathic thrombocytopenic purpura[END_REF][START_REF] Sailer | The course of severe autoimmune thrombocytopenia in patients not undergoing splenectomy[END_REF],

suggesting that surgery may be deferred for prolonged periods [START_REF] Provan | International consensus report on the investigation and management of primary immune thrombocytopenia[END_REF][START_REF] Sailer | The course of severe autoimmune thrombocytopenia in patients not undergoing splenectomy[END_REF][START_REF] Rodeghiero | Standardization of terminology, definitions and outcome criteria in immune thrombocytopenic purpura (ITP) of adults and children: Report from an International Working Group[END_REF]. For instance Sailer et al. found that in 114 patients with platelet count < 20 x 10 9 /L at diagnosis who were treated with first-line therapies (corticosteroids and/or IVIg), complete or partial remission was most likely to occur within the first 6 months (28 [30%] and 15

[13%] patients), but a further 17 complete and 8 partial responses occurred between 6 months and 3 years [START_REF] Sailer | The course of severe autoimmune thrombocytopenia in patients not undergoing splenectomy[END_REF]. Thus, approximately 60% of patients eventually achieved remission, supporting the argument for delaying definitive decisions in ITP.

Splenectomy results are unpredictable and it is associated with significant morbidity

Splenectomy has been utilised for treatment of 'idiopathic purpura' since the early 1900s [START_REF] Hitzrot | Splenectomy in Hemorrhagic Purpura: Idiopathic Purpura, Essential Thrombopenie (Frank). Purpura Hemorrhagic Protopathique (Hayem)[END_REF], when there was no rigorous testing of procedures. This procedure is associated with a number of risks, including complications of general anaesthesia and bleeding (the major immediate risk for an ITP patient), as well as perioperative complications such as pneumonia, wound/other infection, ileus, and thrombosis.

Complication rates vary considerably [START_REF] Kojouri | Splenectomy for adult patients with idiopathic thrombocytopenic purpura: a systematic review to assess long-term platelet count responses, prediction of response, and surgical complications[END_REF][START_REF] Portielje | Morbidity and mortality in adults with idiopathic thrombocytopenic purpura[END_REF][START_REF] Schwartz | Long term follow-up after splenectomy performed for immune thrombocytopenic purpura (ITP)[END_REF][START_REF] Naouri | Results of splenectomy for idiopathic thrombocytopenic purpura. Review of 72 cases[END_REF] and appear to be higher in those aged ≥60 years [START_REF] Cortelazzo | High risk of severe bleeding in aged patients with chronic idiopathic thrombocytopenic purpura[END_REF]. Laparoscopic splenectomy is associated with lower complication and mortality rates than open splenectomy [START_REF] Kojouri | Splenectomy for adult patients with idiopathic thrombocytopenic purpura: a systematic review to assess long-term platelet count responses, prediction of response, and surgical complications[END_REF][START_REF] Winslow | Perioperative outcomes of laparoscopic versus open splenectomy: a meta-analysis with an emphasis on complications[END_REF] (9.6 vs 12.9% and 0.2% vs 1%) [START_REF] Kojouri | Splenectomy for adult patients with idiopathic thrombocytopenic purpura: a systematic review to assess long-term platelet count responses, prediction of response, and surgical complications[END_REF], but is nevertheless associated with the risk of infectious complications. Moreover, follow-up times are much shorter and complications associated with surgery in general are still apparent. Overwhelming post-splenectomy infection (OPSI) is the major concern after splenectomy, although quantifying the risk is difficult because of the lack of consistent data. Other long-term complications include vascular events (Table 1), as recently reviewed by Crary and Buchanan [START_REF] Crary | Vascular complications after splenectomy for hematologic disorders[END_REF].

Approximately one-third of patients fail to achieve complete response to splenectomy and a substantial proportion of initial responders subsequently relapse [START_REF] Kojouri | Splenectomy for adult patients with idiopathic thrombocytopenic purpura: a systematic review to assess long-term platelet count responses, prediction of response, and surgical complications[END_REF][START_REF] Schwartz | Long term follow-up after splenectomy performed for immune thrombocytopenic purpura (ITP)[END_REF] (Figure 2). Although most relapses occur within the first 2 years after splenectomy, relapses continue to occur after that time point [START_REF] Schwartz | Long term follow-up after splenectomy performed for immune thrombocytopenic purpura (ITP)[END_REF][START_REF] Vianelli | Efficacy and safety of splenectomy in immune thrombocytopenic purpura: long-term results of 402 cases[END_REF] and it has been suggested that most patients eventually relapse [START_REF] Bell | Long-term outcome of splenectomy for idiopathic thrombocytopenic purpura[END_REF]. There is at present no widely accepted and reliable test to identify patients who will fail splenectomy. It is unclear whether indiumlabelled autologous platelet scanning [START_REF] Najean | The site of destruction of autologous 111 In-labelled platelets and the efficiency of splenectomy in children and adults with idiopathic thrombocytopenic purpura: a study of 578 patients with 268 splenectomies[END_REF] or response to high-dose IVIg [START_REF] Law | High-dose intravenous immune globulin and the response to splenectomy in patients with idiopathic thrombocytopenic purpura[END_REF][START_REF] Bussel | Do the acute platelet responses of patients with immune thrombocytopenic purpura (ITP) to IV anti-D and to IV gammaglobulin predict response to subsequent splenectomy?[END_REF] can accurately predict response. Moreover, platelet scanning is expensive and not yet widely available and results may be poor at very low platelet counts.

Splenectomy is an irreversible procedure that limits subsequent treatment options

As there is no current work on preservation of spleen tissue and later reimplantation, splenectomy is at present an irreversible procedure [START_REF] Bell | Role of splenectomy in immune (idiopathic) thrombocytopenic purpura[END_REF]. Patients who do not respond to splenectomy may not respond to many of the currently available immunosuppressive treatments [START_REF] George | Management of patients with refractory immune thrombocytopenic purpura[END_REF] and are ineligible for anti-D therapy [START_REF] Bell | Role of splenectomy in immune (idiopathic) thrombocytopenic purpura[END_REF], thus their subsequent treatment options are very limited. These patients have a poor prognosis: a 12-year follow-up of >100 patients who failed splenectomy found that almost 30% responded poorly to subsequent treatments. 30% of patients died: 16% from ITP-related causes (bleeding 10% or complications of treatment, including sepsis 6%) [Figure 3] [START_REF] Mcmillan | Long-term outcomes in adults with chronic ITP after splenectomy failure[END_REF]. A study by George et al. also indicated that patients who fail splenectomy have worse health-related quality of life (HRQoL) compared with non-splenectomised patients who have similar platelet counts [START_REF] George | Improved quality of life for romiplostim-treated patients with chronic immune thrombocytopenic purpura: results from two randomized, placebo-controlled trials[END_REF]. This was shown by lower scores for 7 of 10 scales of the disease-specific ITP-PAQ (ITP Patient Assessment Questionnaire) instrument: Symptoms, Bother, Activity, Social Activity, Fear, Psychological Health and overall quality of life.

Moreover, splenectomised patients are immunocompromised and therefore at risk of fatal bacterial infection, requiring lifelong continuing vigilance. Patients are generally immunised with pneumococcal, Haemophilus influenzae and meningococcal vaccinations at least 2 weeks before surgery, with revaccination according to local practices. Vaccinations may not be effective in patients who have received rituximab in the previous 6 months [START_REF] Provan | International consensus report on the investigation and management of primary immune thrombocytopenia[END_REF]. Vaccination against influenza is also recommended by some authorities [START_REF] Davies | Update of guidelines for the prevention and treatment of infection in patients with an absent or dysfunctional spleen[END_REF]. Antibiotic prophylaxis is required after surgery, with British authorities suggesting that this should be continued for several years [START_REF] Pabinger | Guidelines for the investigation and management of idiopathic thrombocytopenic purpura in adults, children and in pregnancy[END_REF], or lifelong [START_REF] Davies | Update of guidelines for the prevention and treatment of infection in patients with an absent or dysfunctional spleen[END_REF][START_REF] Makris | Long-term management after splenectomy. Lifelong penicillin unproved in trials[END_REF]. However, this practice is not based on strong evidence and is not actually incorporated in guidelines from other countries [START_REF] George | Idiopathic thrombocytopenic purpura: a practice guideline developed by explicit methods for the American Society of Hematology[END_REF]. Surveys have shown a need for better education of patients regarding the risk of post-splenectomy infection [START_REF] El-Alfy | Overwhelming postsplenectomy infection: is quality of patient knowledge enough for prevention?[END_REF].

Finally, splenectomy is increasingly seen as 'removal of a healthy organ' and many well-informed patients refuse splenectomy on this basis. This is reflected in the falling rates of splenectomy over recent years, as new treatments become available [START_REF] Rodeghiero | Is splenectomy still the gold standard for the treatment of chronic ITP?[END_REF].

New agents have changed the treatment paradigm.

Increased understanding of the pathophysiology underlying ITP has allowed the development of many new treatments. While conventional therapies such as corticosteroids and splenectomy primarily focus on reducing platelet destruction [START_REF] Dorner | New approaches of B-cell-directed therapy: beyond rituximab[END_REF][START_REF] George | Management of patients with chronic, refractory idiopathic thrombocytopenic purpura[END_REF], the finding that platelet production is suboptimal in a substantial proportion of patients with ITP [START_REF] Branehog | Platelet survival and platelet production in idiopathic thrombocytopenic purpura (ITP)[END_REF][START_REF] Branehog | Platelet survival and platelet production in idiopathic thrombocytopenic purpura (ITP) before and during treatment with corticosteroids[END_REF] has led to development of the TPO mimetics, which enhance platelet production and may therefore provide better outcomes [START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF].

Additionally, increased knowledge regarding the peripheral role of B-cells in autoimmune disease has led to evaluation of agents that target these cells [START_REF] Arkfeld | The potential utility of B cell-directed biologic therapy in autoimmune diseases[END_REF].

TPO mimetics

The identification of thrombopoietin (TPO) in the mid-1990s as the primary growth factor that regulates platelet production paved the way for development of a new class of agents, the TPO receptor agonists [START_REF] Kaushansky | Thrombopoietin: the primary regulator of platelet production[END_REF]. The 'peptibody' romiplostim [START_REF] Wang | Pharmacodynamics and pharmacokinetics of AMG 531, a novel thrombopoietin receptor ligand[END_REF][START_REF] Newland | An open-label, unit dose-finding study of AMG 531, a novel thrombopoiesis-stimulating peptibody, in patients with immune thrombocytopenic purpura[END_REF][START_REF] Bussel | AMG 531, a thrombopoiesis-stimulating protein, for chronic ITP[END_REF] was the first TPO mimetic to reach the clinic. Unlike the earlier recombinant TPOs [START_REF] Basser | Development of pancytopenia with neutralizing antibodies to thrombopoietin after multicycle chemotherapy supported by megakaryocyte growth and development factor[END_REF][START_REF] Li | Thrombocytopenia caused by the development of antibodies to thrombopoietin[END_REF], romiplostim does not cross-react with endogenous human TPO, since its active peptide domain does not share any sequence homology with native TPO [START_REF] Wang | Pharmacodynamics and pharmacokinetics of AMG 531, a novel thrombopoietin receptor ligand[END_REF][START_REF]Nplate® Summary of Product Characteristics[END_REF]. It is administered as a weekly subcutaneous injection, at a starting dose of 1 mcg/kg, which is individualised according to patient response. Data from two parallel Phase III trials in patients with severe and refractory chronic ITP indicated that treatment with romiplostim results in a platelet count of ≥50 x 10 9 /L in approximately 80% of patients. Eighty-eight percent of non-splenectomised and 79% of splenectomised patients achieved the target range of 50-200 x 10 9 /L for at least 4 weeks (Figure 4) [START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF]. Platelet increases are observed within 1-2 weeks of starting treatment, with approximately 50% of patients achieving platelet counts ≥50 x 10 9 /L within 2-3 weeks. Bleeding events are significantly reduced and the majority of patients are able to reduce or discontinue concurrent ITP therapy including steroids, azathioprine and danazol, as well as requiring less rescue medication (IVIG, and Anti-D) [Figure 4] [START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF]. An open-label extension study has demonstrated the long-term efficacy and tolerability of romiplostim in 142 patients treated for periods of up to 3 years [START_REF] Bussel | Safety and efficacy of long-term treatment with romiplostim in thrombocytopenic patients with chronic ITP[END_REF]. Platelet responses (≥50 x 10 9 /L and double the baseline value, in the absence of rescue medication within the preceding 8 weeks) were seen in 87% of patients. Many patients (~60%) were able to self-administer their romiplostim injections. A 5-year update was recently presented at the 2009 ASH Annual Meeting , in which it was shown that patients were able to maintain platelet counts within the target range with minimal dose adjustments and that adverse events did not increase over time [START_REF] Bussel | Long-Term Efficacy and Safety of Romiplostim for the Treatment of Patients with Chronic Immune Thrombocytopenia (ITP): 5-Year Update From An Open-Label Extension Study[END_REF]. Romiplostim has also been reported to improve HRQoL in chronic ITP patients [START_REF] George | Improved quality of life for romiplostim-treated patients with chronic immune thrombocytopenic purpura: results from two randomized, placebo-controlled trials[END_REF].

Adverse events were reported in almost all patients in the pivotal phase III romiplostim studies (romiplostim 100%, placebo 95%), but were generally mild to moderate and appeared to be related to the underlying disease [START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF]. Very few patients receiving long-term romiplostim treatment discontinue the drug because of adverse events [START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF][START_REF] Bussel | Safety and efficacy of long-term treatment with romiplostim in thrombocytopenic patients with chronic ITP[END_REF]. There was no evidence of increased risk of thromboembolic events [START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF][START_REF] Gernsheimer | Evaluation of bleeding and thrombotic events during long-term use of romiplostim in patients with Chronic Immune Thrombocytopenia (ITP)[END_REF] and no evidence of antibodies that cross-reacted with endogenous TPO or affected the platelet response [START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF][START_REF] Bussel | Safety and efficacy of long-term treatment with romiplostim in thrombocytopenic patients with chronic ITP[END_REF], except in one instance, where a patient transiently developed romiplostim-neutralizing antibodies. In two patients neutralizing antibodies to romiplostim were detected which did not cross-react with endogenous TPO. There is a risk of rebound thrombocytopenia after stopping treatment and patients who discontinue romiplostim should be carefully monitored.

Presence of/increased bone marrow reticulin has been found in a number of patients treated with various TPO mimetics [START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF][START_REF] Bussel | Safety and efficacy of long-term treatment with romiplostim in thrombocytopenic patients with chronic ITP[END_REF][START_REF] Kuter | Bone marrow fibrosis: pathophysiology and clinical significance of increased bone marrow stromal fibres[END_REF]. The clinical significance of these findings is yet to be clarified, although reticulin deposition is often present in the bone marrow of individuals with and without ITP and there has been no evidence of progression to collagen fibrosis, or clonal myeloproliferative disorder after romiplostim treatment (Table 1).

Other TPO mimetics recently developed include the synthetic small molecule agent eltrombopag [START_REF] Bussel | Eltrombopag for the treatment of chronic idiopathic thrombocytopenic purpura[END_REF][START_REF] Jenkins | Phase 1 clinical study of eltrombopag, an oral, nonpeptide thrombopoietin receptor agonist[END_REF]. It is given as an oral once-daily dose, on an empty stomach (separated from divalent cation-containing foods and supplements by at least 4 hours) [START_REF]Revolade Summary[END_REF]. Phase III data (n=114 patients) have been published [START_REF] Bussel | Effect of eltrombopag on platelet counts and bleeding during treatment of chronic idiopathic thrombocytopenic purpura: a randomised, double-blind, placebo-controlled trial[END_REF]. Eltrombopag (initial dose 50 mg/day) achieved platelet counts of ≥50x10 9 /L on day 43 in 59% of patients, while decreasing bleeding symptoms. Adverse events were reported in 59% of eltrombopag and 37% of placebo recipients. Hepatobiliary laboratory abnormalities were more common with eltrombopag than with placebo and cataracts were reported with similar frequency in both treatment groups [START_REF] Bussel | Effect of eltrombopag on platelet counts and bleeding during treatment of chronic idiopathic thrombocytopenic purpura: a randomised, double-blind, placebo-controlled trial[END_REF]. Longer-term data from a phase III extension study [START_REF] Bussel | Long-term safety and efficacy of oral eltrombopag for the treatment of idiopathic thrombocytopenic purpura (ITP)[END_REF] and a 6-month phase III study [START_REF] Cheng | Oral Eltrombopag for the Long-Term Treatment of Patients with Chronic Idiopathic Thrombocytopenic Purpura: Results of a Phase III, Double-Blind, Placebo-Controlled Study (RAISE)[END_REF] appear to support these findings but are yet to be fully published in the literature.

Rituximab

The anti-CD20 antibody rituximab, which selectively depletes B-cell lymphocytes, is licensed for the treatment of non-Hodgkin's lymphoma (NHL), chronic lymphocytic leukaemia (CLL) and rheumatoid arthritis [START_REF]Mabthera Summary of Product Characteristics[END_REF] and has been used extensively offlabel for treating a range of autoimmune diseases, including ITP [START_REF] Arnold | Systematic review: efficacy and safety of rituximab for adults with idiopathic thrombocytopenic purpura[END_REF]. The optimal dose and timing of rituximab in chronic ITP are yet to be defined and dosage schedules in most studies have been based on those used in the lymphoma setting, i.e weekly doses of 375mg/m 2 for 4 weeks.

An analysis of data from descriptive and comparative studies suggests that rituximab produces a 63% overall response rate (46% complete response rate; >150 x10 9 /L) in patients with chronic ITP, although the definition of response varied widely in the reported trials [START_REF] Arnold | Systematic review: efficacy and safety of rituximab for adults with idiopathic thrombocytopenic purpura[END_REF]. The median time to response was 5.5 weeks from the first dose and median duration of response 10.5 (range 3.0-20.0) months. Retreatment with rituximab was successful in inducing repeat responses in relapsed complete responders [START_REF] Hasan | Repeated courses of rituximab in chronic ITP: Three different regimens[END_REF]. Phase III data from the first-line setting (n=103 patients) have recently been reported: a combination of rituximab and dexamethasone achieved a response rate of 63%, versus 36% for dexamethasone alone (P = 0.004). This combination provided an effective salvage therapy for 56% of patients who were refractory to dexamethasone [START_REF] Zaja | Dexamethasone plus rituximab yields higher sustained response rates than dexamethasone monotherapy in adults with primary immune thrombocytopenia[END_REF].

Toxicities of rituximab include infusion reactions (headache, fever, chills, hypotension, bronchospasm), particularly with the first dose, severe mucocutaneous reactions, risk of hepatitis B reactivation and Progressive Multifocal Leukoencephalopathy (PML) [START_REF]Mabthera Summary of Product Characteristics[END_REF] (Table 1). The overall risk of fatal adverse events is estimated at 2.9% [START_REF] Arnold | Systematic review: efficacy and safety of rituximab for adults with idiopathic thrombocytopenic purpura[END_REF]. PML, while rare, has an extremely high mortality rate of 90% [START_REF] Carson | Progressive multifocal leukoencephalopathy after rituximab therapy in HIV-negative patients: a report of 57 cases from the Research on Adverse Drug Events and Reports project[END_REF]. Concern regarding such events has led to warnings on the FDA [START_REF]Information for Healthcare Professionals: Rituximab (marketed as Rituxan)[END_REF] and EMEA [START_REF]Mabthera Summary of Product Characteristics[END_REF] labelling. However, it is important to note that many of these events have occurred in heavily immunosuppressed lymphoma patients who were receiving other treatments.

A low-dose rituximab regimen (100mg weekly for 4 consecutive weeks) has been explored in ITP patients, with encouraging results [START_REF] Provan | Activity and safety profile of low-dose rituximab for the treatment of autoimmune cytopenias in adults[END_REF][START_REF] Zaja | Lower dose rituximab is active in adults patients with idiopathic thrombocytopenic purpura[END_REF]. In one small series sustained complete response was achieved in four of 7 patients (57%) and no infusion reactions were seen [START_REF] Provan | Activity and safety profile of low-dose rituximab for the treatment of autoimmune cytopenias in adults[END_REF]. In a slightly larger series overall and complete responses were achieved in 21/28 (75%) and 12/28 (43%) patients respectively [START_REF] Zaja | Lower dose rituximab is active in adults patients with idiopathic thrombocytopenic purpura[END_REF]. Further studies are warranted to confirm these preliminary data, as a lower dose may be associated with a lower risk of toxicities.

Other targeted agents under development

Other targeted agents are being developed for ITP and these may expand the list of treatment options in the future. As well as additional TPO receptor agonists and Bcell-depleting agents, other approaches that are being studied include Syk kinase inhibitors [START_REF] Podolanczuk | Of mice and men: an open-label pilot study for treatment of immune thrombocytopenic purpura by an inhibitor of Syk[END_REF], targeting of co-stimulatory signal (e.g the CD80/CD86 inhibitor CTLA-4-Ig [Abatacept]), B-cell survival signal, regulatory T-cells and macrophage FcγR function (reviewed by Li and Hou [START_REF] Li | Emerging drugs for idiopathic thrombocytopenic purpura in adults[END_REF]).

ARGUMENTS FOR EARLY SPLENECTOMY

We have a century of history and experience with splenectomy

Splenectomy has been utilised to treat 'idiopathic purpura' since the early 1900s [START_REF] Hitzrot | Splenectomy in Hemorrhagic Purpura: Idiopathic Purpura, Essential Thrombopenie (Frank). Purpura Hemorrhagic Protopathique (Hayem)[END_REF] and remained the 'first-line, gold standard procedure' until the 1950s, when steroids were introduced [START_REF] Watson-Williams | The treatment of idiopathic thrombocytopenic purpura; a review of ninety-three cases[END_REF]. While many additional medical therapies have since emerged, splenectomy remains the second-line treatment of choice for many physicians treating ITP.

Splenectomy provides durable long-term responses for most patients and responses can be predicted

No other treatment has the overall success rate of splenectomy, with approximately two-thirds of patients achieving durable complete response [START_REF] Kojouri | Splenectomy for adult patients with idiopathic thrombocytopenic purpura: a systematic review to assess long-term platelet count responses, prediction of response, and surgical complications[END_REF][START_REF] Vianelli | Efficacy and safety of splenectomy in immune thrombocytopenic purpura: long-term results of 402 cases[END_REF]. Vianelli et al. estimated a >70% probability of maintaining response for 5 years after surgery, based on their follow-up of 402 splenectomised patients [START_REF] Vianelli | Efficacy and safety of splenectomy in immune thrombocytopenic purpura: long-term results of 402 cases[END_REF].

111 Indium-labelled autologous platelet scanning may provide a sensitive predictor of response [START_REF] Najean | The site of destruction of autologous 111 In-labelled platelets and the efficiency of splenectomy in children and adults with idiopathic thrombocytopenic purpura: a study of 578 patients with 268 splenectomies[END_REF][START_REF] Todorovic-Tirnanic | Prediction of the splenectomy efficacy in chronic immune thrombocytopenic purpura[END_REF]. Among patients shown to have splenic platelet destruction, approximately 90% will respond to splenectomy, while a similar proportion of those with hepatic or diffuse platelet destruction fail splenectomy [START_REF] Najean | The site of destruction of autologous 111 In-labelled platelets and the efficiency of splenectomy in children and adults with idiopathic thrombocytopenic purpura: a study of 578 patients with 268 splenectomies[END_REF]. A good response to IVIg may predict a favourable response to splenectomy [START_REF] Law | High-dose intravenous immune globulin and the response to splenectomy in patients with idiopathic thrombocytopenic purpura[END_REF], as may younger age; higher peak platelet count at splenectomy and having received ≤1 previous therapy (all P<0.0001 by univariate analysis) [START_REF] Vianelli | Efficacy and safety of splenectomy in immune thrombocytopenic purpura: long-term results of 402 cases[END_REF].

The safety profile of splenectomy is acceptable: immediate risks are known and can be minimised

Several advances in surgical practice over the years have led to a significant decrease in mortality and complication rates associated with splenectomy [START_REF] Kojouri | Splenectomy for adult patients with idiopathic thrombocytopenic purpura: a systematic review to assess long-term platelet count responses, prediction of response, and surgical complications[END_REF]. Predniso(lo)ne or IVIg can be given to raise the platelet count prior to surgery and thus reduce the risk of bleeding [START_REF] George | Idiopathic thrombocytopenic purpura: a practice guideline developed by explicit methods for the American Society of Hematology[END_REF]. Laparoscopic splenectomy, introduced in 1991, has been associated with less blood loss, more rapid recovery and lower complication and mortality rate than open splenectomy [START_REF] Kojouri | Splenectomy for adult patients with idiopathic thrombocytopenic purpura: a systematic review to assess long-term platelet count responses, prediction of response, and surgical complications[END_REF][START_REF] Winslow | Perioperative outcomes of laparoscopic versus open splenectomy: a meta-analysis with an emphasis on complications[END_REF]. Preoperative vaccination and postoperative antibiotics have led to declining rates of fatal sepsis. Indeed, cases that have been reported occurred prior to the introduction of pneumococcal vaccination [START_REF] George | Idiopathic thrombocytopenic purpura: a practice guideline developed by explicit methods for the American Society of Hematology[END_REF]. Results of two analyses (n = 402 and 208 patients, respectively) found that no cases of fatal sepsis have occurred in Italy [START_REF] Stasi | Long-term observation of 208 adults with chronic idiopathic thrombocytopenic purpura[END_REF][START_REF] Vianelli | Efficacy and safety of splenectomy in immune thrombocytopenic purpura: long-term results of 402 cases[END_REF]. Overall, the risk of septicaemia following splenectomy may be less than the risk of intracranial haemorrhage in a nonsplenectomised ITP patient.

Currently available medical treatments have limitations

In general, treatments used for ITP have considerable adverse effects, as summarised in Table 1. Elderly patients and those with comorbid conditions may be at greater risk.

Only a minority of patients with ITP achieve lasting remission with corticosteroids [START_REF] Dem Borne | High dose intravenous methylprednisolone or high dose intravenous gammaglobulin for autoimmune thrombocytopenia[END_REF][START_REF] Kuku | The early and long-term results of oral high-dose methylprednisolone treatment in adult patients with idiopathic thrombocytopenic purpura[END_REF][START_REF] Cheng | Initial treatment of immune thrombocytopenic purpura with high-dose dexamethasone[END_REF][START_REF] Stasi | Pulsed intravenous high-dose dexamethasone in adults with chronic idiopathic thrombocytopenic purpura[END_REF] and long-term treatment is associated with multiple well-documented, doserelated adverse effects, as well as an increased risk of infection [START_REF] Talar-Williams | Complications of corticosteroid therapy[END_REF][START_REF] Saag | Low dose long-term corticosteroid therapy in rheumatoid arthritis: an analysis of serious adverse events[END_REF] (Table 1).

Over time, these detrimental effects may outweigh their benefits. IVIg and Anti-D also produce only short-lasting responses and are associated with significant toxicities, as well as risks inherent to pooled blood products such as transmission of infections (Table 1).

Immunosuppressive agents (azathioprine, cyclosporine, cyclophosphamide) are not curative and often not well tolerated (Table 1). Suppressing the immune system may predispose patients to infection. Indeed, infections account for approximately half of all deaths in patients with ITP [START_REF] Stasi | Long-term observation of 208 adults with chronic idiopathic thrombocytopenic purpura[END_REF][START_REF] Portielje | Morbidity and mortality in adults with idiopathic thrombocytopenic purpura[END_REF]. Alkylating agents should be avoided in those who plan to have children and immunosuppressants should not be given to pregnant women. Cyclosporin A should be used very carefully in the elderly and avoided in those with renal insufficiency.

While the TPO mimetics look to be a promising treatment option, long-term data are limited, especially for eltrombopag, although 5-year safety and efficacy data have recently been reported for romiplostim [START_REF] Bussel | Long-Term Efficacy and Safety of Romiplostim for the Treatment of Patients with Chronic Immune Thrombocytopenia (ITP): 5-Year Update From An Open-Label Extension Study[END_REF]. In general, continued treatment is required to maintain the treatment response and rebound thrombocytopenia has been seen after stopping treatment. The clinical significance of increased bone marrow reticulin in patients treated with TPO mimetics [START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF][START_REF] Bussel | Safety and efficacy of long-term treatment with romiplostim in thrombocytopenic patients with chronic ITP[END_REF][START_REF] Kuter | Bone marrow fibrosis: pathophysiology and clinical significance of increased bone marrow stromal fibres[END_REF]] is yet to be clarified.

Hepatotoxicity has been seen with eltrombopag [START_REF] Bussel | Effect of eltrombopag on platelet counts and bleeding during treatment of chronic idiopathic thrombocytopenic purpura: a randomised, double-blind, placebo-controlled trial[END_REF] and monitoring of liver function is recommended during treatment [START_REF]Revolade Summary[END_REF]. Possible risks of TPO mimetics include thrombotic/thromboembolic complications if platelet counts exceed the normal range, although ITP itself may be associated with increased thromboembolic risk [START_REF] Aledort | Prospective screening of 205 patients with ITP, including diagnosis, serological markers, and the relationship between platelet counts, endogenous thrombopoietin, and circulating antithrombopoietin antibodies[END_REF]. As these agents stimulate the TPO receptor there is also the theoretical possibility that they might stimulate progression of existing haematopoietic malignancies or Myelodysplastic Syndromes (MDS) [START_REF]Nplate® Summary of Product Characteristics[END_REF][START_REF]Revolade Summary[END_REF].

In Europe, romiplostim is indicated for adult chronic immune (idiopathic) thrombocytopenic purpura (ITP) splenectomised patients who are refractory to other treatments (e.g. corticosteroids, immunoglobulins). Nplate may be considered as second-line treatment for adult non-splenectomised patients where surgery is contraindicated [START_REF]Nplate® Summary of Product Characteristics[END_REF][START_REF]Revolade Summary[END_REF]. However, this is not the case in the USA, where both romiplostim and eltrombopag are available for use in patients with chronic ITP, regardless of splenectomy status [START_REF]Nplate Prescribing information[END_REF][START_REF]Promacta Prescribing Information[END_REF].

Data supporting the use of rituximab in chronic ITP are limited, being derived mainly from case series. Randomised controlled trials are required to establish the efficacy of the drug. Available data show long-term efficacy and safety concerns, with only a minority of patients maintaining a long-term response. Patel et al. found that almost half of patients with a response duration >1 year relapsed over a 5-year follow-up [START_REF] Patel | Long Term Follow-Up of Patients with Immune Thrombocytopenic Purpura (ITP) Whose Initial Response to Rituximab Lasted a Minimum of 1 Year[END_REF]. While reported toxicities (Table 1) have occurred mainly in patients being treated for lymphoma and the risk may be lower in ITP patients, the risk: benefit is likely to differ considerably between these two settings.

Quality of life and cost issues.

For patients who achieve an adequate platelet response to splenectomy, the disease burden is minimised, with less bleeding symptoms, fatigue, and concerns over everyday life. They may be free from ITP medication for years if the platelet response is maintained.

Clearly, financial considerations may impact the choice of treatment modality.

Successful splenectomy is a once-only cost, provided that accessory spleen exploration is not required, and may be similar to that of a single course of IVIg [START_REF] Adams | Pharmacoeconomics of therapy for ITP: steroids, i.v.Ig, anti-D, and splenectomy[END_REF].

In contrast, immunosuppressive treatments usually need to be continued long-term, although dose reduction may be possible and some patients can even maintain longterm remissions off-therapy. With the TPO mimetics continued treatment is generally required to sustain the response [START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF].

Reimbursement will differ between countries and not all would reimburse for costly new medical treatments in a patient who refuses splenectomy. Additionally, in some developing countries, the range of available treatments may be restricted.

Conclusions

Generally accepted criteria for splenectomy in patients with chronic ITP include severe thrombocytopenia (platelet count <10 x 10 9 /L) or platelet counts <30 x 10 9 /L with high risk of bleeding; and the requirement for continuous corticosteroid therapy to maintain 'safe' platelet counts [START_REF] Stasi | Idiopathic thrombocytopenic purpura: current concepts in pathophysiology and management[END_REF]. In 1996, George et al. [START_REF] George | Idiopathic thrombocytopenic purpura: a practice guideline developed by explicit methods for the American Society of Hematology[END_REF] noted that there were 'inadequate data to make evidence-based recommendations on the appropriate indications and timing for splenectomy, on when the benefits of splenectomy might outweigh its potential harms, and on appropriate preoperative management.' Since that time, increasing clinical knowledge has allowed development of effective targeted therapies including the TPO mimetics. With these agents, it may be possible to 'buy time' for patients who are unable or unwilling to undergo splenectomy, maintaining a safe platelet count while allowing for a chance of spontaneous remission, and thereby deferring splenectomy for prolonged periods. Thus, some physicians argue that in general, this irreversible and immunocompromising procedure should not be performed before exhausting available medical treatment options. There are some exceptions, such as patients who wish to become pregnant, those who are 'sick of' or cannot receive medical treatments. With the emergence of new treatment options, it is likely that many well-informed patients will refuse splenectomy.

On the other hand, splenectomy does offer a very good chance of cure, with the possibility of being free from ITP medication for many years if the platelet response is maintained. With advances in surgical practice and management, the risks are well identified and acceptable. Progress has been made towards predicting which patients will respond, although testing is not widely available and predictors of response have not been fully validated. Moreover, new medical treatment options such as the TPO mimetics are now available for patients in whom splenectomy fails, as well as those in whom splenectomy is contraindicated.

Thus, the decision whether to proceed to splenectomy or try other medical therapies in corticosteroid-refractory patients remains patient-specific. There are no data to demonstrate better outcomes if this procedure is performed early on in the disease course and it is hoped that the treatment algorithm will become clearer in the near future as more information on newer treatments becomes available. Ultimately, identifying the 'right patient at the right time' requires careful weighing of the risks of splenectomy with the expected benefits for the individual, as well as full discussion with the patient.

Figure 1 .Figure 2 .Figure 3 .Figure 4 .

 1234 Figure 1. Treatment options for chronic ITP. * indicates treatments with minimal data and considered to have potential for considerable toxicity [3]. § The IV anti-D product Winrho SDF was withdrawn from the European market in 2009.

Table 1 . Summary of response rates and adverse effects associated with first and second-line treatments used for ITP. *The IV anti-D product Winrho SDF was withdrawn from the market in 2009 because of safety concerns.

 1 Romiplostim: arthralgia, dizziness, insomnia, myalgia, pain in extremity, abdominal pain, shoulder pain, dyspepsia, paraesthesia[START_REF]Nplate Prescribing information[END_REF]. Eltrombopag: nausea, vomiting, menorrhagia, myalgia, paraesthesia. cataract, dyspepsia, hepatotoxicity[START_REF]Promacta Prescribing Information[END_REF]. Both: rebound thrombocytopenia after stopping treatment, increased bone marrow reticulin, immunogenicity, Hypothetical risks: thrombotic/thromboembolic complications, progression of existing haematopoietic malignancies or Myelodysplastic Syndromes (MDS), alterations in blood cell parameters[START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF][START_REF] Newland | An open-label, unit dose-finding study of AMG 531, a novel thrombopoiesis-stimulating peptibody, in patients with immune thrombocytopenic purpura[END_REF][START_REF] Bussel | AMG 531, a thrombopoiesis-stimulating protein, for chronic ITP[END_REF][START_REF]Nplate® Summary of Product Characteristics[END_REF][START_REF] Bussel | Safety and efficacy of long-term treatment with romiplostim in thrombocytopenic patients with chronic ITP[END_REF][START_REF] Bussel | Eltrombopag for the treatment of chronic idiopathic thrombocytopenic purpura[END_REF][START_REF] Bussel | Effect of eltrombopag on platelet counts and bleeding during treatment of chronic idiopathic thrombocytopenic purpura: a randomised, double-blind, placebo-controlled trial[END_REF][START_REF] Kumagai | Pharmacodynamics and pharmacokinetics of AMG 531, a thrombopoiesis-stimulating peptibody, in healthy Japanese subjects: a randomized, placebo-controlled study[END_REF][START_REF]Promacta FDA ODAC briefing document[END_REF].

	Treatment	Initial response rates/time to	Risks/adverse events
		response/duration of response
		[3]
	First-line
	Corticosteroids	70-80%/several days -several	Weight gain, cushingoidism, mood swings, insomnia,hypertension, osteoporosis,
		weeks/? a	immunosuppression, increased risk of infection, peptic ulcer, hyperglycaemia, psychosis,
			glaucoma, cataract, impaired wound healing, skin changes, adrenal insufficiency [69]
	IVIg	≤80%/2-4 days/2-4 weeks	Headache, fever, nausea/vomiting, allergic reactions/anaphylactic shock, hypotension;
			reversible haemolytic anaemia [77]
			Risks associated with pooled blood product e.g. transmission of infections
	IVAnti-D	≤80%/4-5 days/3-4 weeks	Malaise, fever, chills, nausea/vomiting, anaphylaxis, cutaneous reactions, hypotension,
			tachycardia, life-threatening intravascular haemolysis [78, 79]*
			Risks associated with pooled blood product e.g. transmission of infections
			Restricted to Rhesus-positive, nonsplenectomised patients
	Second-line
	Splenectomy	80%/1-24 days/5-10 years in 67%	General risks of surgery (complications of general anaesthesia, bleeding, wound infection,
		of patients	thrombosis); perioperative complications: pneumonia, transient/prolonged ileus, need for
			transfusion, overwhelming post-splenectomy infection [10-13, 15, 80, 81]
			Long-term vascular complications: thromboembolism/atherosclerosis, pulmonary arterial
			hypertension [16, 24, 71, 82-84]

Acknowledgements

This article is based on a debate between the authors, which took place in Berlin,

Germany on June 4th 2009 during the 14th European Haematology Association

Congress and was supported by Amgen Europe GmbH, Zug, Switzerland. The authors thank Julia Balfour, Medical Writer, Kilconquhar, Scotland for assistance with the preparation of the manuscript, with financial support from Amgen.

Conflicts of interest disclosures

Authors conflict of interest declarations are as follows: Prof. Newland -Research funding from Amgen, Baxter, GSK and Genentech; consultant and speaker for Amgen and GSK; advisory board for GSK and Pangenetics; Dr. Stasi -advisory boards and/or speaker for GSK and Amgen. Dr Pabingerspeaker and advisory boards for Amgen and GSK. Dr Thornton has no conflicts of interest to declare.


MD Rita Mencucci
email: rita.mencucci@unifi.it

MD Iacopo Paladini

MD Ugo Menchini

Jean Jacques Gicquel

MD Jean Jacques Gicquel

PhD Rosanna Dei

Inhibition of viral replication in vitro by antiviral-treated amniotic membrane. Possible use of amniotic membrane as drugdelivering tool

Keywords: amniotic membrane transplantation, antiviral-treated amniotic membrane Word Count (excluding, title

come

Inhibition of viral replication in vitro by antiviral-treated amniotic membrane.Possible use of amniotic membrane as drug-delivering tool.

The use of amniotic membrane (AM) in the treatment of epithelial defects dates around the first quarter of 20 th century; its use in the treatment of epithelial defect ophthalmology was first reported in 1946. [START_REF] Sorsby | AMNIOTIC MEMBRANE GRAFTS IN CAUSTIC BURNS OF THE EYE: (Burns of the second degree)[END_REF] Later only a few reports only were published. [START_REF] Dua | The amniotic membrane in ophthalmology[END_REF][START_REF] Azuara-Blanco | Amniotic membrane transplantation for ocular surface reconstruction[END_REF] The breakthrough came with the development of modern preservation technology. [START_REF] Solomon | Amniotic membrane grafts for nontraumatic corneal perforations, descemetoceles, and deep ulcers[END_REF][START_REF] Sridhar | Amniotic membrane transplantation in acute chemical and thermal injury[END_REF] The use of fresh AM is hindered by the risk of transmission of blood-borne infections; this made necessary to improve cryopreservation, although differences between fresh and cryopreserved AM have been reported. [START_REF] Tekin | Preserved human amniotic membrane transplantation in the treatment of primary pterygium[END_REF] AM, consisting of thick basement membrane and an avascular stromal matrix, is able to express multiple anti-angiogenic factors, anti-inflammatory proteins, growth factors, and protease inhibitors. The recent surge of interest in the ophthalmic uses of AM has led to its application in a large number of conditions for a variety of indications like, among others, conjunctival and corneal reconstruction, inflammatory disorders, and ocular infections. [START_REF] Solomon | Amniotic membrane grafts for nontraumatic corneal perforations, descemetoceles, and deep ulcers[END_REF][START_REF] Sridhar | Amniotic membrane transplantation in acute chemical and thermal injury[END_REF][START_REF] Ainsworth | A novel use of amniotic membrane in the management of tube exposure following glaucoma tube shunt surgery[END_REF] Many mechanisms have been invoked in relation to its clinical application, such as reduction of inflammation, inhibition of vascularization, anti-infective properties, promotion of epithelialization, and limitation or prevention of scarring. [START_REF] Espana | Amniotic membrane transplantation for reconstruction after excision of large ocular surface neoplasias[END_REF][START_REF] Kee | Amniotic membrane graft for late-onset glaucoma filtering leaks[END_REF][START_REF] Ti | Amniotic membrane transplantation in entropion surgery[END_REF] Amniotic membrane transplantation (AMT) has become somehow a routine intervention in a variety of ocular pathologic conditions, infective or not. [START_REF] Solomon | Amniotic membrane transplantation for reconstruction of the conjunctival fornices[END_REF] When used as a graft (epithelial side up), AM is expected to become incorporated in the recipient tissue. If it is used as a patch (epithelial side down), it works as a biological bandage affording cover for a limited duration or a combination of these. The use of AM has been also suggested in the treatment of infectious keratitis, because of its intrinsic anti-infective properties probably mediated by its anti-inflammatory effects, and because AM may act as a long term drug delivery system. [START_REF] Nubile | Multilayer amniotic membrane transplantation for bacterial keratitis with corneal perforation after hyperopic photorefractive keratectomy: case report and literature review[END_REF][START_REF] Gicquel | Amniotic membrane transplantation in severe bacterial keratitis[END_REF][START_REF] Kim | Amniotic membrane transplantation in infectious corneal ulcer[END_REF] In this respect, the utilization of AM also in wound healing, skin lesions, and burns has to be mentioned. [START_REF] Singh | Development and evaluation of silverimpregnated amniotic membrane as an antimicrobial burn dressing[END_REF][START_REF] King | Expression of natural antimicrobials by human placenta and fetal membranes[END_REF][START_REF] Mermet | Use of amniotic membrane transplantation in the treatment of venous leg ulcers[END_REF][START_REF] Hasegawa | Amnia for intractable skin ulcers with recessive dystrophic epidermolysis bullosa: report of three cases[END_REF] Addressing the use of AM to deliver drugs, we had previously reported the antibacterial activity of antibiotic (Netilmicin)-treated AM in an in vitro model. Antibiotic uptake was dose-dependent, and occurred rapidly; our observations seemed promising in view of the possible clinical applications. [START_REF] Mencucci | Antimicrobial activity of antibiotic-treated amniotic membrane: An in vitro study[END_REF] AMT has been recently proposed for the management of ulcerative and necrotizing herpetic stromal keratitis in conjunction with antivirals and corticosteroids. [START_REF] Knickelbein | Management of herpes simplex virus stromal keratitis: an evidence-based review[END_REF] In Europe, nucleotide analogues such as Acyclovir® and Trifluridine® are often used topically for the treatment of stromal herpes keratitis. Acyclovir® is a synthetic purine nucleoside analogue with in vitro and in vivo inhibitory activity against herpes simplex virus types 1 (HSV-1), 2 (HSV-2), and varicella-zoster virus (VZV). The inhibitory activity of Acyclovir is highly selective due to its Its range of activity includes HSV1, HSV2, CMV, vaccinia virus, and possibly adenovirus.

Because of its toxicity, topical preparations only are available. [START_REF] Grady | Antibiotic and chemotherapy[END_REF] The aim of our study was therefore to evaluate AM as a delivering system for antiviral drugs. We report an in vitro study assessing the inhibition of viral replication by AM treated with ACV and TFU.

Materials and Methods

AM: The Tuscan regional cornea bank, Lucca, Italy kindly donated the human material. One preserved AM was threphined into 10 AM samples, diameter 2,5 cm. Each sample was weighted.

Virus: A clinical isolate of HSV 1 from an oro-facial lesion was used throughout the study. A stock suspension of the virus grown in cell cultures was aliquoted and stored frozen.

Antivirals: Acyclovir® (ACV), for IV use, 250 mg, and Trifluridine® (TFU) 1%, eyedrops were used in the study. ACV was dissolved in Balanced Salt Solution (BSS, ICN Biomedicals Inc. Aurora, OH, USA) to 50 mg/ml; ACV solution and TFU eyedrops were further diluted in BSS, down to 10mg/ml the first and 0.08mg/ml the latter.

AM preparation:

The AMs were trephined into 7 mm diameter samples, with a corneal trephine (Operaid, OPHTEC Groningen, The Nederlands). The samples were washed 5 min in BSS, laid onto a sterile gauze to remove the excess of liquid, and then placed in individual wells of 24-well microplates containing 0.5 ml of the antiviral solution or BSS (control).

After 60 minutes incubation at 37 o C on a benchtop shaker, the fluid was aspirated. The AM samples were washed 3 times x 5 min in BSS to remove the non adsorbed drug, and the excess of liquid removed by draining.

Cell cultures: Vero cells, a continuous cell line from monkey kidney were purchased from Istituto Zooprofilattico Sperimentale della Lombardia e dell'Emilia-Romagna, Brescia, Italy.

Results

The weight of the ten AM samples averaged 0.23 g ± 0,06, range: 0.16-0.30 g, indicating a certain variation among the samples. A preliminary experiment showed that AM soaked in 50 mg/ml ACV was capable to inhibit significantly the development of HSV1 in cell cultures, as judged by the CPE extent compared to controls (25% ± 7.1 of the monolayer vs 75% ± 7.1, P< 0.02).

The microscopic examination of various microscopic fields allows a comprehensive evaluation of each monolayer, thus making possible to quantitate the extension of the typical morphologic alterations in each experimental point. The preliminary observation could not rule out a possible intrinsic antiviral effect of the AM, therefore antiviral-soaked AM was compared to BSS-soaked AM and control infected cells, Table 1.

Whereas ACV-AM did significantly inhibit viral replication, the addition of non-treated AM had no significant effect on viral replication. By considering the viral genomes on pooled cell cultures, the figures were consistent with the results shown in Table 1: 6.2x10 5 HSV DNA copies for ACV-AM treated cultures compared to 20.0x10 6 and 25.2x10 6 for AM treated cultures and controls respectively.

Discussion

Herpes Simplex and Varicella-Zoster viruses are potentially sight threatening. The tissue damage is sometimes directly dependent on the infectious agent replication, but is also due the inflammatory response, originally aimed to limit the infective process (harmful to the conjunctival and corneal epithelium).

AMT has been reported to be an effective surgical procedure for the reconstruction of the ocular surface and to reduce corneal inflammation. [START_REF] Kim | Amniotic membrane transplantation in infectious corneal ulcer[END_REF][START_REF] Tseng | Amniotic membrane transplantation with or without limbal allografts for corneal surface reconstruction in patients with limbal stem cell deficiency[END_REF][START_REF] Lee | Amniotic membrane transplantation for persistent epithelial defects with ulceration[END_REF][START_REF] Kruse | Multilayer amniotic membrane transplantation for reconstruction of deep corneal ulcers[END_REF] It has been recently suggested the use of AMT both in the early treatment of infectious corneal ulcers as well as in the management of acute ulcerative and necrotizing stromal herpes keratitis. [START_REF] Kim | Amniotic membrane transplantation in infectious corneal ulcer[END_REF] Anti-infective properties of AM are probably related to its anti-inflammatory effects, thus counteracting the strong inflammatory response elicited by microorganisms, and not against the agent itself; therefore, an effective and adequate antimicrobial therapy is mandatory to ensure control of infection.

Heilingenhaus demonstrated how AMT significantly modifies the course of necrotizing stromal keratitis induced by HSV-1. The effect was associated with suppression of inflammation, rapid epithelialization, and reduction of stromal necrosis. [START_REF] Heiligenhaus | Improvement of HSV-1 necrotizing keratitis with amniotic membrane transplantation[END_REF][START_REF] Heiligenhaus | Management of acute ulcerative and necrotising herpes simplex and zoster keratitis with amniotic membrane transplantation[END_REF] In addition, in a mouse model of HSV stromal keratitis, AMT was effective in promoting corneal wound healing and in reducing inflammation, probably related to the reduced expression and activity of matrix and metallo proteinases and increased expression of tissue inhibitors of metalloproteinases. [START_REF] Heiligenhaus | Improvement of HSV-1 necrotizing keratitis with amniotic membrane transplantation[END_REF][START_REF] Heiligenhaus | Transplantation of amniotic membrane in murine herpes stromal keratitis modulates matrix metalloproteinases in the cornea[END_REF] In a murine experimental model, the improvement of herpetic ulcerative keratitis after AMT is suggested to be due to a reduced expression and activity of Matrix Metallo-proteases MMP-8 and MMP-9, increased or sustained expression of Tissue Inhibitors of metallo-proteases TIMP-1 and TIMP-2. [START_REF] Heiligenhaus | Transplantation of amniotic membrane in murine herpes stromal keratitis modulates matrix metalloproteinases in the cornea[END_REF] Concerns have been raised on the possibility that AMT in the management of infectious keratitis could be a risk factor for superinfections or viral reactivations, thus leading to a severe corneal damage and a disturbance of the normal healing process. However, besides this well known anti-inflammatory effect of AM, an intrinsic antiviral property should be taken in consideration.

Paradowska reported that human placenta contains endogenous tumor necrosis factors and interferons, possible mediators of the non specific antiviral immunity. [START_REF] Paradowska | Antiviral nonspecific immunity of human placenta at term: possible role of endogenous tumor necrosis factors and interferons[END_REF] Moreover, AM may express cistatin E, a novel human cystein proteinase effective in inhibition of viral replication. [START_REF] Bjorck | Cystatin C, a human proteinase inhibitor, blocks replication of herpes simplex virus[END_REF][START_REF] Korant | Cystatin, a protein inhibitor of cysteine proteases alters viral protein cleavages in infected human cells[END_REF][START_REF] Ni | Cystatin E is a novel human cysteine proteinase inhibitor with structural resemblance to family 2 cystatins[END_REF] Chronic infection of the cornea by Herpes simplex virus (HSV) remains an important cause of unilateral blindness. The development of nontoxic topical antiviral agents has been an important step forward in management of herpes keratitis.

AMT could be taken into consideration as adjunctive therapy for the anti-inflammatory and supposed direct antiviral properties of AM. [START_REF] Heiligenhaus | Management of acute ulcerative and necrotising herpes simplex and zoster keratitis with amniotic membrane transplantation[END_REF] The possibility to use AM to deliver drugs has been first suggested by Kim [START_REF] Kim | Amniotic membrane transplantation in infectious corneal ulcer[END_REF] and Heilinghaus [START_REF] Heiligenhaus | Management of acute ulcerative and necrotising herpes simplex and zoster keratitis with amniotic membrane transplantation[END_REF] and then by Mencucci et al. [START_REF] Mencucci | Antimicrobial activity of antibiotic-treated amniotic membrane: An in vitro study[END_REF] and Gicquel et al. [START_REF] Gicquel | Amniotic membrane transplantation in severe bacterial keratitis[END_REF] As expected, AM can absorb ACV or TFU; antiviral uptake occurs quite rapidly. The antiviral effect of treated-AM was evidenced by the development of the typical cytopathic effect as well as quantitation of viral genomes in tissue culture cells compared to control infected cells.

The reduction compared to control cultures was significant with both antivirals, and it was dose-dependent, as it was with antibiotic-treated AM. The incorporation of TFU into cellular DNA explains the aspecific toxic effect on tissue culture cells by AM treated with higher concentrations (10mg/ml and 2mg/ml) of the drug. Its lack of selectivity is well known; on the other hand, AM treated with higher concentrations might be used in vivo: 10mg/ml correspond to the concentration in the eye drop preparation. The difference could be explained by the fact that in vivo dilution and dispersion of the instilled drug occur, and also that AM could achieve drug concentration. These observations confirm and extend our previous work on antibiotic-treated AM. As in the previous study, we could not find a significant effect by non-treated AM: the viral yield was only slightly reduced compared to controls. Our in vitro model might not be suitable to detect the intrinsic antiviral effect. On the other hand, the lack of intrinsic anti-infective activity in our in vitro model does not rule out such an activity in vivo, where the anti-inflammatory and the healing properties of AM might be implemented.

The aim of our study was not to prove the superiority of AM treated with antivirals to the antiviral alone, but the possibility to combine the anti-inflammatory properties of AM with the capability of delivering drugs. Moreover, the question about the patient's compliance: the intensive topical treatment to ensure adequate drug concentrations could be not so strictly necessary, thus improving the patient's comfort and also reducing the burden on the nursing staff; moreover, drug-soaked AM should prove superior when there are difficulties in frequent instillations such as with children, elderly, or handicapped people.

In conclusion our study, confirming and extending our previous observations on antibiotictreated AM, suggests the potential application of antiviral-treated AM in the management of herpetic ocular infections as adjunctive therapy for its anti-inflammatory, supposed direct antiviral properties and as a drug delivery system.

  affinity for the enzyme thymidine kinase (TK) encoded by HSV and VZV. This viral enzyme converts Acyclovir® into Acyclovir® monophosphate, a nucleotide analogue. The monophosphate is further converted into diphosphate by cellular guanylate kinase and into triphosphate by a number of cellular enzymes. The block of viral DNA is accomplished in three ways: 1) competitive inhibition of viral DNA polymerase, 2) incorporation into and termination of the growing viral DNA chain, and 3) inactivation of the viral DNA polymerase. Trifluridine is a synthetic pyrimidine nucleoside analogue which inhibits enzymes of the DNA pathway and is incorporated into progeny viral DNA (but also cellular) causing imperfect transcription of late mRNA, hence the production of useless viral proteins.

  Vero cells monolayers appear by direct inspection of the culture plates through an inverted tissue culture microscope (LEICA DMIL, LEICA Wetzlar, Germany) as polygonal-shaped cells firmly attached to the bottom of the culture vessel. Cells were grown in Minimal Essential Medium (MEM)-10% Fetal Calf Serum (FCS) (ICN Biomedicals Inc. Aurora, OH, USA).Cell cultures infection and assessment of viral replication:Vero cells were used 24 hr after seeding in 24-well plates, when they reached semi-confluence as assessed by inverted microscope examination. The growth medium was removed, and the cell monolayers washed.Cells were inoculated with 200μl viral suspension. After a 90 minutes incubation at 37 o C in 5% CO 2 , the inoculum was removed, and 1ml of the maintenance medium (MEM-2% FCS) was added. One AM sample (either antiviral-treated or BSS-treated) was placed, epithelial side up, over the cell culture in each well. Plates were incubated at 37 o C in 5% CO 2 up to 5 days. Cell monolayers were inspected daily to evaluate, in comparison to monolayers of noninfected cells and infected cells without addition of AM, the development of the typical cytopathic effect (CPE): rounding up (large round cells starting in cluster or small foci, which then extend to the entire monolayer) and detachment of cultured cells.Antiviral activity CPE extent:Each monolayer was observed at low magnification, 40X, with the inverted microscope; 10 diameters per well, that is experimental point, were considered for the presence of clusters of enlarged round refractile cells in individual wells. The presence and extension of CPE was recorded as percentage of each monolayer showing the morphologic changes. Viral DNA assessment. It was carried out by Quantitative-PCR by means of HSV2 Q-PCR Alert (Nanogen Advanced Diagnostics, Buttigliera Alta (TO), Italy)following the manufacturer's instructions. Briefly, at the end of the incubation period, the cultures were harvested, pooled according to treatment, washed and resuspended in equal volumes of lysing solution. The oligonucleotide mixture was added to the reaction mixture, together with the specific fluorescent probe; and 20 μl/well were transferred to the amplification microplate. Five μl of lysed samples were added, the plate sealed and transferred to the real time thermal cycler. Positive (10 5 to 10 2 HSV DNA copies) and negative (sterile distilled water) controls were carried out in parallel. Viral DNA copies were evaluated in comparison to the positive controls.Results were expressed as means ± SD, and evaluated by one-way ANOVA and the Bonferroni multiple comparison test.

Table 1 :

 1 Antiviral activity of AM treated 60min with 50mg/ml ACV

	Treatment CPE extent
		mean±SD	n*
	Control	71.7±14.0 12
	AM	68.3±16.4 12
	ACV-AM 28.3±17.0 a 12
	CPE extent: percentage of cells showing the typical cytopathic effect
	* number of experimental points

a The CPE extent was significantly lower compared to controls or non-treated AM (P< 0.001)

Table 2

 2 shows the antiviral activity of AM treated with different concentrations of either ACV or TFU. Antiviral activity decreased by lowering the concentration of both antivirals. The inhibition of viral growth was significant in comparison to control or non-treated AM, with the exception of AM treated with 0.08mg/ml TFU. It has to be added that AM soaked in 10mg and 2mg/ml TFU produced an aspecific toxic effect, evidenced microscopically by the rapid degeneration, within 1 d, of the entire monolayer.

Table 2 :

 2 Antiviral activity of AM treated 60min with different concentrations of ACV or

	TFU
	Treatment	CPE extent
		mean±SD	n*
	Control	60.0±8.9	6
	AM	56.7±10.3	6
	ACV-AM 10mg/ml 31.7±7.5 a 1	6
	ACV-AM 25mg/ml 20.0±11.0 a 2 6
	ACV-AM 50mg/ml 13.3±5.2 a 3	6
	TFU-AM 0.08mg/ml 40.0±0	2
	TFU-AM 0.4mg/ml 20.0±14.1 a 4 2
	CPE extent: percentage of cells showing the typical cytopathic effect
	* number of experimental points
	a The CPE extent was significantly lower compared to controls or non-treated AM ( a 1 P=0.02,
	a2 and a 4 P = 0.001, a 3 P< 0.001


Gyromap for a two-dimensional Hamiltonian fluid model derived from Braginskii We consider a plasma described by means of a two-dimensional fluid model across a constant but non-uniform magnetic field B = B(x, y)ẑ. The dynamical evolution of the density and the vorticity takes into account the interchange instability and magnetic field inhomogeneities. First, in order to described the Finite Larmor Radius effects we apply the gyromap to build a Hamiltonian model with ion temperature from a cold-ion model. Second, we show that the gyromap is justified using Braginskii's closure for the stress tensor as well as an apt ordering on the fluctuating quantities.

I. INTRODUCTION

In laboratory plasma devices like tokamaks or in astrophysical plasmas, two-dimensional reduced fluid models have been used to investigate various instabilities and their impact on turbulent transport. These reduced models are very useful in practice since their theoretical and numerical analyses are simpler than for complete models. At the same time they display important features of the underlying turbulent phenomena with more clarity than the complete models. The standard procedure used for the derivation of these reduced models is to start from the equations of motion of a parent model (e.g., that given by the continuity and the momentum equations) and to perform an ordering with respect to one or several small parameters on the variables of the system (e.g., density and potential fluctuations) and on the electromagnetic field. This ordering is suggested by the physics and the geometry of the phenomenon under consideration (e.g., one might want to filter out irrelevant time or length scales). It is desirable that the reduced model preserves the main ingredients of the parent model under this reduction procedure, as for instance the Hamiltonian symmetry. Typical parent models have indeed this Hamiltonian symmetry, e.g., the collisionless Maxwell-Vlasov equations [1,2] or ideal magnetohydrodynamics [3]. However, in such a derivation procedure obtained by working at the level of the equations of motion, neglecting terms can produce "mutilations" [4] of the original fluid equations by breaking this symmetry. These mutilations, which introduce incorrect dissipative terms, have a drastic impact on the properties of the physical system. The loss of the Hamiltonian structure indeed generates a more intricate interpretation of the numerical results, and in general clouds the relation with the parent model and its properties. In fact, as shown for example in models describing magnetic reconnection [5,6], the Hamiltonian structure helps the interpretation and explanation of complex physical processes observed in numerical simulations. Among the other advantages of the Hamiltonian structure, there is the possibility of identifying systematically invariants of motion (e.g., Casimir invariants or conserved quantities linked to continuous symmetries), and applying tools of Hamiltonian perturbation theory and methods to investigate the stability of equilibria. However, for some reduced models, the important property of possessing a Hamiltonian structure has not been shown. For instance, this is the case of the two-dimensional fluid model taken from Ref. [7]. This four-field model includes Finite Larmor Radius (FLR) effects as in Refs. [8,9], the drift velocity ordering as in Ref. [10] and the gyroviscous terms as in Refs. [11,12]. Moreover, magnetic inhomogeneities are kept in the continuity equation as in Refs. [7,[13][14][15]. For this particular model, the Hamiltonian structure has not been found even though the model has been shown to be energy conserving. In this paper, we consider the main obstacle associated with the search for the Hamiltonian structure of this four-field model which is already encapsulated in a two-field model for the density and the vorticity fields. This two-field model is obtained from the four-field model by suppressing the parallel dynamics (along the magnetic field), and the poloidal magnetic and parallel flow fluctuations, and reads

∂n ∂t = -[φ, n] -φ, 1 B + n, 1 B , (1)
∂∆φ ∂t = -[φ, ∆φ] + (1 + T ) n, 1 B -T ∇ • [n, ∇φ] , (2)
where n = n(x, y, t) is the logarithm of the normalized density fluctuations, φ = φ(x, y, t) is the normalized electrostatic potential, B = B(x, y) is the normalized magnetic field, T is the constant ion temperature normalized by the electron temperature and [f, g] = ẑ • ∇f × ∇g is the canonical bracket in the plane across the magnetic field B = Bẑ. All the derivatives are defined on the perpendicular plane. The bracket [φ, n] corresponds to the dynamics due to the E × B drift, and the bracket [n, 1/B] corresponds to the term driving the interchange instability. When addressing the question of the Hamiltonian structure of the model ( 1)-( 2), it is easy to show that, provided that boundary terms vanish, a conserved quantity for the model is

I = 1 2 d 2 x (1 + T )n 2 + |∇φ| 2 , (3)
where the first part corresponds to the potential energy for ions and electrons and the second part is the kinetic energy. This conserved quantity I is interpreted as the total energy of the system and is a natural candidate for the Hamiltonian. Nevertheless, in spite of having a conserved quantity, the model ( 1)-( 2) does not seem to possess a Hamiltonian formulation, at least of the Lie-Poisson type, which is the most common form for reduced fluid models. More precisely, Poisson brackets between functionals F and G of the form

{F, G} = 2 i,j,k=1 d 2 x V k ij ξ i + α k j B δF δξ j , δG δξ k + W k ij ξ i + α k j B ∇ δF δξ j ; ∇ δG δξ k ,
where the vector bracket is defined by

[A; B] = i [A i , B i ], the terms α k j , V k ij and W k ij are constant, ξ 1 = n , ξ 2 =
∆φ and δF/δξ is the functional derivative of the functional F with respect to ξ, fail to give the desired equations of motion ( 1)-( 2) when applied to I. Even if a bracket giving Eqs. ( 1)-( 2) with the invariant I defined by Eq. ( 3) has been found, it does not satisfy Jacobi identity and thus is not a Poisson bracket. The reason for the difficulty to find a Hamiltonian structure resides in the co-existence of compressibility terms (those containing 1/B in the continuity equation of the electrons) with the ion-gyroviscous term (in the vorticity equation). The compressibility terms are often retained in the continuity equation (see, e.g., Refs. [7,[13][14][15]) in order to account for the fact that the velocity field is not incompressible in the presence of an inhomogeneous magnetic field. If these compressibility terms are neglected in the two-field model, the resulting system is Hamiltonian [13,16]. On the other hand, it has been shown that the system obtained by keeping these terms and eliminating the ion-gyroviscous terms is also Hamiltonian [13]. It is thus the simultaneous presence of the two contributions which seems to complicate the search for a Hamiltonian structure. This leads to the problem of finding a Hamiltonian model accounting for both compressibility terms and FLR corrections. An elegant and effective way to introduce FLR corrections to a cold-ion model, while preserving the Hamiltonian structure, was introduced in Refs. [13,17] and was referred to as the gyromap. The gyromap procedure was rigorously found from the Braginskii's closure for the stress tensor [18] only for the three-field model described in Refs. [8,13] which does not contain the compressibility terms in the continuity equation. In this paper, we apply the gyromap procedure to the cold-ion limit of the two-field model with the compressibility terms. We show that all the FLR correction terms produced by this method are obtained from the Braginskii's closure for the stress tensor, by means of an expansion based on a physically sound ordering. The paper is organized as follows: In Sec. 2, we apply the gyromap procedure to the cold-ion version of the two-field model ( 1)-( 2). In Sec. 3, we show that the resulting model is directly obtained from a systematic expansion.

II. THE GYROMAP

The gyromap algorithm was introduced in Ref. [13] in order to introduce FLR corrections to a cold-ion model, while preserving the Hamiltonian structure. The model with FLR corrections obtained through this procedure possesses the same bracket of the original cold-ion model, but different dynamical variables and Hamiltonian. The fact that the Poisson bracket is inherited from the cold-ion Hamiltonian model ensures that the resulting model is Hamiltonian. As a by-product, the Casimir invariants of the resulting model with FLR corrections become easily available. We also recall that, as mentioned in Ref. [13], the gyromap procedure possesses the desirable features that the cold-ion limit (T = 0) of the post-gyromap model gives the initial cold-ion model, and that the diamagnetic effects predicted by the kinetic theory are conserved at the first order. In what follows we use dimensionless quantities, i.e. we rescale space variables by the sonic Larmor radius ρ s , the density by the equilibrium density n 0 , the charge by the electric charge e, the electron and ion temperatures by the electron temperature T e , the magnetic field B by the spatial mean value B 0 and time by the inverse of the ion cyclotron frequency ω c,i = eB 0 /m i where m i is the ion mass. We start with the cold-ion version of Eqs. (1)-(2) which describes the dynamical evolution of the plasma density n and the vorticity ∆φ

∂n ∂t = -[φ, n] -φ, 1 B + n, 1 B , ∂∆φ ∂t = -[φ, ∆φ] + n, 1 B .
We consider the system whose field variables are n(x, y) and φ(x, y). Here we do not specify the time dependence of the variables which is implicitly assumed. In the algebra of observables which are functionals of n and φ, the Hamiltonian structure is defined by the Hamiltonian This bracket verifies all the required properties for a Poisson bracket like bilinearity, antisymmetry, Jacobi identity and Leibniz identity. The gyromap procedure is initiated from the Hamiltonian defined by

H(n, φ) = 1 2 d 2 x n 2 +
H(n, Φ) = 1 2 d 2 x (1 + T )n 2 + |∇Φ| 2 , ( 4
)
where Φ is the stream function for the FLR model. The choice of Eq. ( 4) as Hamiltonian is motivated by the requirement of adding the ion internal energy to the cold-ion Hamiltonian and having a kinetic energy term whose relation with the cold-ion kinetic energy is retrieved a posteriori. We introduce an auxiliary variable ξ defined by ∆Φ = ξ + T ∆n/2. The shift of T ∆n/2 corresponds to a shift of half the magnetization velocity. This is the required transformation in order to yield the proper FLR corrections [13].

The change of variables, N = n and ξ = ∆Φ -T ∆n/2, includes a change of functional derivatives,

δ δN = δ δn + T 2 ∆ δ δ∆Φ , δ δξ = δ δ∆Φ .
Hence the bracket expressed in the variables (n, Φ), which is still a Poisson bracket, is the following,

{F, G} = d 2 x n + 1 B δF δn + T 2 ∆
With the Hamiltonian defined by Eq. ( 4), the equation of motion for the density is

∂n ∂t = {n, H} = -Φ + T 2 ∆Φ, n + 1 B + (1 + T ) n, 1 B . (7)
We assume that the continuity equation for electrons is unaffected by FLR corrections. Therefore comparing Eq. ( 1) with Eq. (7) gives the following relation between Φ and φ:

1 + T 2 ∆ Φ = φ + T n. (8)
On the other hand, the equation for the generalized vorticity ∆Φ is given by

∂∆Φ ∂t = {∆Φ, H} = -[Φ, ∆Φ] + (1 + T ) 1 + T 2 ∆ n, 1 B + T ∇ • n + 1 B , ∇Φ - T 2 4 ∆ ∆Φ, n + 1 B . (9)
Equations ( 7)-( 9) are the final result of the gyromap procedure. They include FLR corrections and the resulting system has a Hamiltonian structure since the bracket ( 6) is obtained from the Poisson bracket ( 5) by a change of variables.

By expanding the operator (1 + T ∆/2) -1 for small T and making use of Eq. ( 7), it is possible to obtain an expression for Eq. ( 9) valid for small ion temperature T (in terms of n and φ),

∂∆φ ∂t = -[φ, ∆φ] + n, 1 B + T n, 1 B -∇ • [n, ∇φ] -[∇φ;∇∆φ] +T 2 [∇∆n;∇φ] -[∇n;∇∆φ] -2 [n, ∆n] + 2∆ 1 + ∆ 2 n, 1 B - ∆ 4 ∆φ, n + 1 B + 1 2 [∇φ;∇∆φ] + 1 4 ∆φ, ∆ 2 φ + O(T 3 ). ( 10
)
This expression is useful, because it allows one to directly compare the leading order terms of the vorticity equation (10), with the vorticity equation as given in Ref. [16] [see also Eq. ( 2)] which refers to a model where the only FLR term is -T ∇•[n, ∇φ]. We notice that already at the order O(T ), the two equations differ from an FLR correction term given by -T [∇φ; ∇∆φ]. From Eq. ( 10), it is also straightforward to see that, in the limit T → 0, the FLR model is correctly reduces to the original cold-ion model, as expected. In summary, in order to obtain a Hamiltonian structure with the ion temperature, the gyromap procedure starts from the Hamiltonian structure without ion temperature and then considers FLR effects using a change of variables.

In what follows, we consider Braginskii's closure for the stress tensor in order to derive a model with FLR terms and compare it with the above model given by Eqs. ( 7)- (9).

III. DERIVATION FROM BRAGINSKII'S CLOSURE

We first consider the dynamics of a plasma composed of two species, ions and electrons. In a simplified magnetic geometry where the magnetic field is constant (but non-uniform) and its direction is fixed, we restrict the plasma dynamics to the plane transverse to the magnetic field lines, i.e. all dynamical variables only depend on the two coordinates x and y. The dynamical variables are the ion and electron densities, n i (x, y) and n e (x, y), and the ion and electron velocity fields v i (x, y) and v e (x, y). We assume a quasi-neutrality hypothesis which allows us to reduce the number of variables, i.e. we consider that n i (x, y) = n e (x, y) which is denoted n(x, y) in what follows. The dynamical equation for the density is given by the continuity equation for the electrons,

∂n ∂t + ∇ • (nv e ) = 0.
Due to the quasi-neutrality assumption, the same equation holds for ions, which translates into

∇ • (n(v e -v i )) = 0. ( 11
)
The dynamical equation for the velocity field v s (x, y) of the species s, where s refers to ions or electrons, is given by

µ s n ∂ ∂t + v s • ∇ v s = n (E + v s × B) -e s T s ∇n -e s ∇ • π s , (12)
where E is the electric field, T s is the dimensionless temperature of the species s (i.e. T i = T and T e = 1), µ s its dimensionless mass (i.e. µ i = 1 and µ e = m e /m i ≪ µ i because the mass of the electron m e is negligible compared to the one of the ions m i ) and e s its dimensionless charge (i.e. e i = 1 and e e = -1). The stress tensor associated with the species s, denoted π s , is taken from Ref. [18]. For each species, it is composed of viscosity terms identified by viscosity coefficients of various orders. Within a strong magnetic field approximation, we only consider the two higher order viscosity terms labeled by η 0 and η 3 with η 0 ≫ η 3 . The viscosity coefficients for ions are η i 0 = 0.96nT τ i ≫ η i 3 = nT /2 where τ s is the normalized collisional time for the species s.

In what follows, we only use the part of the stress tensor perpendicular to the magnetic field lines. Given these approximations, the divergence of the stress tensor for ions becomes

∇ • π i = -α i τ i T ∇ (n∇ • v i ) + T 2 [nẑ × ∆v i -(ẑ × ∇n • ∇)v i + (∇n • ∇)(ẑ × v i )] ,
where α i = 0.32. The viscosity coefficients for electrons are η e 0 = 0.73nτ e ≫ η e 3 = -nµ e /2 where τ e is the collisional time for the electrons. We consider the following approximation for the divergence of the stress tensor for the electrons

∇ • π e = -α e τ e ∇ (n∇ • v e ) ,
where α e = 0.24. The dimensionless equation for the velocity field of each species becomes

µ s n ∂ ∂t + v s • ∇ v s = -n∇φ + nBv s × ẑ -e s T s ∇n + α s τ s e s T s ∇ (n∇ • v s ) -µ s e s T s 2 [nẑ × ∆v s -(ẑ × ∇n • ∇)v s + (∇n • ∇)(ẑ × v s )] . (13)
We apply the cross product with ẑ/nB to Eq. ( 13) in order to obtain the velocity as the sum of the E × B, the diamagnetic, the polarization drifts and some gyroviscous contributions from the stress tensor,

v s = ẑ × ∇ (φ + e s T s log n) B + µ s 1 B ∂ ∂t + v s • ∇ ẑ × v s - α s τ s e s T s nB ẑ × ∇(n∇ • v s ) -µ s e s T s 2B [∆v s + (ẑ × ∇ log n • ∇)(ẑ × v s ) + (∇ log n • ∇)v s ] . (14)
We expand all dimensionless quantities in the following way

1/B = 1 + ε/ B, φ = ε φ, n = 1 + εñ, v s = εv (1) s + ε 2 v (2)
s . The small parameter ε ≪ 1 denotes the amplitude of the fluctuations of the electromagnetic field as well as that of the dynamical variables n and v s . Moreover, the temporal variations of these quantities are small so that the temporal variation is denoted ε∂/∂t. In what follows, we omit the tildas over the fluctuating quantities for simplicity. Here we consider the model for weak collisionality (i.e. µ s /τ s ≪ 1) such that τ i is of order 1/ε and τ e ≪ 1/ε. In addition T is of order one, and the parameters α s are of order ε (i.e. α i τ i T is of order 1 and α e τ e ≪ 1). The leading order of Eq. ( 14) (terms proportional to ε) gives

1 + µ s e s T s 2 ∆ v (1) s = ẑ × ∇ (φ + e s T s n) -α s τ s e s T s ẑ × ∇(∇ • v (1) s ).
From the previous equation, we directly obtain that ∇ • v

e = 0. From the expansion of Eq. ( 11), we also conclude that ∇

• v (1) i = 0. Therefore the equation for v (1) s becomes 1 + µ s e s T s 2 ∆ v (1) s = ẑ × ∇ (φ + e s T s n) , (15)
so that the first order velocity is the sum of the E × B velocity and the diamagnetic velocity with FLR corrections on the left hand side. The second order of the velocity v s is given by

1 + µ s e s T s 2 ∆ v (2) s = 1 B v (1) s + µ s ∂ ∂t + v (1) s • ∇ ẑ × v (1) s -eT s nẑ × ∇n -α s τ s e s T s ẑ × ∇ ∇ • v (2) s - µ s e s T s 2 (ẑ × ∇n • ∇)(ẑ × v (1) s ) + (∇n • ∇)v (1) s , (16)
where we have used Eq. ( 15) for v

s . We notice that we have also used the expansion ∇ log(1+εn) = ε∇n-ε 2 n∇n+ O(ε 3 ). As a first step, for the electrons, we see that from Eq. ( 15), the first order of the electron velocity is the sum of the E × B velocity and the electron diamagnetic velocity v (1) e = ẑ × ∇ (φn) ,

and the second order of the electron velocity is

v (2) e = 1 B v (1) e + nẑ × ∇n + α e τ e ẑ × ∇ ∇ • v (2) e .
From this equation, we get that the divergence of v

(2) e is equal to the divergence of v

e /B, and using Eq. ( 17), it becomes

∇ • v (2) e = φ -n, 1 B . (18)
The continuity equation of the electron density at the second order in ε becomes 1) e • ∇n = 0, or equivalently, using Eqs. ( 17)-( 18),

∂n ∂t + ∇ • v (2) e + v (
∂n ∂t = -φ, n + 1 B + n, 1 B .
In fact, the first order of the ion velocity given by Eq. ( 15) suggests a change of variables (1 + T 2 ∆)Φ = φ + T n with which we can write the first order of the ion velocity into We notice that this change of variables is also the one suggested by the gyromap [see Eq. ( 8)]. Using this variable Φ, the continuity equation becomes

∂n ∂t = -1 + T 2 ∆ Φ, n + 1 B + (1 + T ) n, 1 B . ( 19
)
As a second step, we work with the continuity equation for ions which is

∂n ∂t + ∇ • v (2) i + v (1) i
• ∇n = 0.

(20)

First we obtain the following formula for the divergence of v

(2) i from Eq. ( 16),

1 + T 2 ∆ ∇ • v (2) i = - ∂∆Φ ∂t -[Φ, ∆Φ] + Φ, 1 B - T 2 [∆Φ, n] -T [∇Φ; ∇n] . (21)
Next we multiply Eq. ( 20) by (1 + T ∆/2) in order to use the Eq. ( 21) and we insert Eq. ( 19) so as to obtain

∂∆Φ ∂t = -[Φ, ∆Φ] + (1 + T ) 1 + T 2 ∆ n, 1 B + T ∇ • n + 1 B , ∇Φ - T 2 4 ∆ ∆Φ, n + 1 B . (22)
We notice that Eqs. ( 19)-( 22) coincide with Eqs. ( 7)-( 9), which were obtained by applying the gyromap. Therefore, we have shown that the terms generated from the gyromap are obtained consistently from Braginskii's closure for the stress tensor by making use of an appropriate ordering.

In summary, it is possible to construct a model with FLR corrections and its Hamiltonian structure from a cold-ion model which possesses a Hamiltonian structure by applying a gyromap procedure which generates all the relevant FLR terms at the leading order. The change of variables introduced by the gyromap is directly given by the definition of the stream function at the first order of the ion velocity. We have shown that the two-field reduced model ( 7)-( 9) is obtained using the Braginskii's closure for the stress tensor by considering an apt ordering on the dynamical variables.

  v

  's closure for magnetized plasmas O. Izacard, 1 C. Chandre, 1 E. Tassi, 1 and G. Ciraolo 2 1 Centre de Physique Théorique -UMR 6207, Campus de Luminy -case 907, 13288 Marseille cedex 09, France 2 Laboratoire de Mécanique, Modélisation & Procédés Propres -UMR 6181, Technopôle de Château-Gombert, 13451 Marseille cedex 20, France (Dated: March 15, 2011)

  |∇φ| 2 ,

	and by the Poisson bracket
	{F, G} = d 2 x	n +	1 B	δF δn	,	δG δn	+	δF δn	,	δG δ∆φ	+	δF δ∆φ	,	δG δn	+ ∆φ	δF δ∆φ	,	δG δ∆φ	.

Acknowledgements

We acknowledge financial support from the Agence Nationale de la Recherche. This work was supported by the European Community under the contract of Association between EURATOM, CEA and the French Research Federation for fusion studies. The views and opinions expressed herein do not necessarily reflect those of the European Commission.