Guillaume Holzer

Natacha Roux

Vincent Laudet
email: vincent.laudet@obs-banyuls.fr

Evolution of ligands, receptors and metabolizing enzymes of thyroid signaling

Keywords: Thyroid hormone receptor, Triiodothyronine, T3, Triiodothyroacetic acid, Triac, evolution

Thyroid hormones (THs) play important roles in vertebrates such as the control of the metabolism, development and seasonality. Given the pleiotropic effects of thyroid disorders (developmental delay, mood disorder, tachycardia, etc), THs signaling is highly investigated, specially using mammalian models. In addition, the critical role of TH in controlling frog metamorphosis has led to the use of Xenopus as another prominent model to study THs action. Nevertheless, animals regarded as non-model species can also improve our understanding of THs signaling. For instance, studies in amphioxus highlighted the role of Triac as a bona fide thyroid hormone receptor (TR) ligand. In this review, we discuss our current understanding of the THs signaling in the different taxa forming the metazoans (multicellular animals) group. We mainly focus on three actors of the THs signaling: the ligand, the receptor and the deiodinases, enzymes playing a critical role in THs metabolism. By doing so, we also pinpoint many key questions that remain unanswered. How can THs accelerate metamorphosis in tunicates and echinoderms while their TRs have not been yet demonstrated as functional THs receptors in these species? Do THs have a biological effect in insects and cnidarians even though they do not have any TR? What is the basic function of THs in invertebrate protostomia? These questions can appear disconnected from pharmacological issues and human applications, but the investigation of THs signaling at the metazoans scale can greatly improve our understanding of this major endocrinological pathway.

Introduction

Thyroid hormones (THs) are involved in many biological processes in vertebrates [START_REF] Holzer | Thyroid hormones: a triple-edged sword for life history transitions[END_REF], such as energy metabolism (reviewed in [START_REF] Mullur | Thyroid Hormone Regulation of Metabolism[END_REF], thermoregulation [START_REF] Lebon | Effect of triiodothyronine on mitochondrial energy coupling in human skeletal muscle[END_REF] but also development [START_REF] Delange | Iodine deficiency as a cause of brain damage[END_REF][START_REF] Flamant | Congenital hypothyroid Pax8(-/-) mutant mice can be rescued by inactivating the TRalpha gene[END_REF][START_REF] Göthe | Mice devoid of all known thyroid hormone receptors are viable but exhibit disorders of the pituitary-thyroid axis, growth and bone maturation[END_REF][START_REF] Morte | Deletion of the thyroid hormone receptor alpha 1 prevents the structural alterations of the cerebellum induced by hypothyroidism Proceeding of the[END_REF]. In addition, THs are a critical signal triggering metamorphosis in amphibians as well as in many fishes, and are therefore important hormones that control the life cycle in vertebrates [START_REF] Laudet | The origins and evolution of vertebrate metamorphosis[END_REF]. In humans, defects in THs signaling, either hyperthyroidism (too high THs concentration) or hypothyroidism (too low THs concentration), can lead to severe pathological conditions with a wide variety of symptoms such as tiredness, weight change, mood disorder, developmental delay, tachycardia. In addition, complete lack of THs is lethal. Thyroid cancers are the most common endocrine cancers with increasing incidence [START_REF] Pacini | Thyroid cancer: ESMO Clinical Practice Guidelines for diagnosis, treatment and follow-up[END_REF]. The primary treatment for such cancers is the complete or partial removal of the thyroid, leading to a massive disruption of the gland physiology [START_REF] Pacini | Thyroid cancer: ESMO Clinical Practice Guidelines for diagnosis, treatment and follow-up[END_REF]. Therefore, TH synthesis, its degradation and its signaling activity are the subject of many investigations.

Two molecules are collectively referred as THs: the native hormone thyroxine (3,3',5,5'-T4 or T4), which represents 80% of the hormone synthesized by the thyroid [START_REF] Sapin | Thyroxine (T4) and tri-iodothyronine (T3) determinations: techniques and value in the assessment of thyroid function[END_REF], and the active hormone triiodothyronine (3,3',5-T3 or T3) that has a 10-fold higher affinity for the receptor than T4 [START_REF] Chopra | Nature, source, and relative significance of circulating thyroid hormones[END_REF]. T4 is used as a precursor by three specific enzymes, the deiodinases that synthesize both active and inactive TH derivatives by catalyzing the removal of iodine atom from T4. More specifically, two reactions are distinguished. The outer ring deiodination, catalyzed by the deiodinase type II (Dio2, [START_REF] Kuiper | Biochemical mechanisms of thyroid hormone deiodination[END_REF], transforms T4 in target tissues into T3 (Figure 1). Dio2 is therefore considered as an activating deiodinase. It also turns T3 into 3,5-T2, a TH derivative long considered as inactive but for which accumulative evidences suggest a biological role [START_REF] Lietzow | 3,5-T2 alters murine genes relevant for xenobiotic, steroid, and thyroid hormone metabolism[END_REF][START_REF] Mendoza | 3,5-T2 Is an Alternative Ligand for the Thyroid Hormone Receptor β1[END_REF]. The inner ring deiodination is catalyzed by the deiodinase type III (Dio3) which is considered as an inactivating deiodinase as it turns T4 into reverse T3 (3-3'-5'-T3 or rT3) and T3 into 3-3'-T2 (Figure 1), compounds that have no biological activity [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript Chopra | Comparison of Inhibitory Effects of 3,5,3′-Triiodothyronine (T3), Thyroxine (T4), 3,3,′,5-Triiodothyronine (rT3), and 3,3′-Diiodothyronine (T2) on Thyrotropin-Releasing Hormone-Induced Release of Thyrotropin in the Rat in vitro[END_REF][START_REF] Moreno | Genetic basis of hypothyroidism: recent advances, gaps and strategies for future research[END_REF]. This process is also referred as an inner ring deiodination. The deiodinase type I (Dio1) has both outer ring and inner ring deiodination activity but with a lower activity than Dio2 and Dio3. Although it is required to regulate the normal level of TH, its biological role is less clear [START_REF] Maia | Deiodinases: the balance of thyroid hormone: type 1 iodothyronine deiodinase in human physiology and disease[END_REF].

THs act by binding to specific nuclear receptors: the thyroid hormone receptors (TRs), which belong to the nuclear receptor superfamily. TRs are ligand-dependent transcription factors that bind to DNA. TRs do not bind DNA alone but form a heterodimer with RXR, another nuclear receptor, and it is TR/RXR that forms the real functional unit of gene transcription control [START_REF] Kojetin | Structural mechanism for signal transduction in RXR nuclear receptor heterodimers[END_REF].In the classical view, TRs repress their target genes in absence of the ligand and activate them in presence of the ligand (reviewed in [START_REF] Gronemeyer | Principles for modulation of the nuclear receptor superfamily[END_REF]. Some genes undergo a negative regulation by THs and are actively repressed by liganded TRs [START_REF] Hollenberg | The human thyrotropin-releasing hormone gene is regulated by thyroid hormone through two distinct classes of negative thyroid hormone response elements[END_REF][START_REF] Matsunaga | Essential Role of GATA2 in the Negative Regulation of Type 2 Deiodinase Gene by Liganded Thyroid Hormone Receptor β2 in Thyrotroph[END_REF]. Additionally, ligand binding influences the receptor binding on DNA [START_REF] Ramadoss | Novel Mechanism of Positive versus Negative Regulation by Thyroid Hormone Receptor β1 (TRβ1) Identified by Genome-wide Profiling of Binding Sites in Mouse Liver[END_REF]. This suggests that the biological reality of TR transcription regulation is more complex than the classical model [START_REF] Flamant | Futures Challenges in Thyroid Hormone Signaling Research[END_REF]. There are two TRs in vertebrates, TRα and TRβ that emerged from the whole genome duplication events at the basis of this group [START_REF] Kuraku | Timing of genome duplications relative to the origin of the vertebrates: did cyclostomes diverge before or after?[END_REF][START_REF] Marchand | Molecular cloning and characterization of thyroid hormone receptors in teleost fish[END_REF][START_REF] Smith | Sequencing of the sea lamprey (Petromyzon marinus) genome provides insights into vertebrate evolution[END_REF]. Teleost fishes underwent an additional specific whole genome duplication which results in two TRα genes, TRα-A and TRα-B [START_REF] Escriva | The evolution of the nuclear receptor superfamily[END_REF][START_REF] Marchand | Molecular cloning and characterization of thyroid hormone receptors in teleost fish[END_REF].

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However, TH signaling is not a vertebrate innovation (Paris et al., 2008a) and it is established that TH-signaling was functional at the base of chordates (Paris et al., 2008a) and even possibly at the base of the bilaterians [START_REF] Bertrand | Evolutionary Genomics of Nuclear Receptors: From Twenty-Five Ancestral Genes to Derived Endocrine Systems[END_REF][START_REF] Wu | Thyroid hormone receptor orthologues from invertebrate species with emphasis on Schistosoma mansoni[END_REF]. Moreover, the investigation in the invertebrate chordate amphioxus (Branchiostoma sp) suggests that the 3,5,3'-triiodo-thyroacetic acid (Triac), a deaminated derivative of T3 (Figure 1), was a bona fide TRs ligand in the chordate common ancestor (Paris et al., 2008b). Thus, it is useful to describe what the studies of non-classical models bring to our understanding of TH signaling. In this review we will explore our current understanding of TH signaling in several metazoan groups starting from vertebrates toward more distant groups.

Even in vertebrates, the classical ligand can hide an astonishing diversity of active compounds

As introduced above, THs are involved in many biological processes. T3 is well acknowledged and recognized as the canonical ligand of TR in vertebrates. T4 is generally considered only as a precursor of T3 but several evidence, and in particular the recent detailed analysis of mouse strains in which the deiodinase genes have been inactivated, led to the suggestion that it may have a biological function in itself via TRs [START_REF] Galton | The Ups and Downs of the Thyroxine Pro-hormone Hypothesis[END_REF]. However we will not discuss much T4 and T3 here as the latest discoveries on their biological role are covered in other chapter of this issue. We will discuss here whether other molecules could be considered as ligand and the role of the deiodinases in the modulation of TH signaling.

As previously mentioned, there are two paralogs of vertebrate TRs, TRα and TRβ, which originate from the two rounds of whole genome duplication that happened at the base of all vertebrates [START_REF] Kuraku | Timing of genome duplications relative to the origin of the vertebrates: did cyclostomes diverge before or after?[END_REF]. This duplication allows the divergence of the two copies in terms of amino acid sequence and regulatory sequence. In the mouse, TRα and TRβ regulate different subsets of genes, when tested in the same chromatin context, indicating that they have different intrinsic properties [START_REF] Chatonnet | Genome-wide analysis of thyroid hormone receptors shared and specific functions in neural cells[END_REF]. This divergence between TRα and TRβ led to a slightly different pharmacology between the two receptors. Indeed, there are some TRβ selective compounds such as GC-1 that have been developed for clinical purpose [START_REF] Bleicher | Structural basis of GC-1 selectivity for thyroid hormone receptor isoforms[END_REF]. TRα is expressed in the early development whereas TRβ is expressed later [START_REF] Forrest | Distinct functions for thyroid hormone receptors alpha and beta in brain development indicated by differential expression of receptor genes[END_REF], indicating differences in regulation. In amphibians as well, the timing of TR expression is different between the two paralogs. TRβ is late expressed and self-induced by the surge of T3 at metamorphosis because of a thyroid response element in the promoter of the gene [START_REF] Machuca | Analysis of structure and expression of the Xenopus thyroid hormone receptor-beta gene to explain its autoinduction[END_REF]. This is not the case for TRα which is early expressed during Xenopus metamorphosis [START_REF] Eliceiri | Quantitation of endogenous thyroid hormone receptors alpha and beta during embryogenesis and metamorphosis in Xenopus laevis[END_REF][START_REF] Kawahara | Developmental and regional expression of thyroid hormone receptor genes during Xenopus metamorphosis[END_REF][START_REF] Yaoita | A correlation of thyroid hormone receptor gene expression with amphibian metamorphosis[END_REF]. In teleosts, TRα-A and TRα-B are also differentially expressed as exemplified in the flounder Paralichthys olivaceus, where TRα-A is express earlier at a higher level than TRα-B and TRβ [START_REF] Yamano | Differential Gene Expression of Thyroid Hormone Receptor α and β in Fish Development[END_REF]. This illustrates how TR duplication allows the divergence of biological roles between TRα and TRβ.

The sea lamprey Petromyzon marinus has two TRs, TR1 and TR2, whose evolution is not clearly understood yet. Indeed, in a phylogenetic reconstruction they do not group with the TRα and TRβ but together within an agnathan group at the base of the gnathostomes [START_REF] Manzon | Thyroid hormone and retinoid X receptor function and expression during sea lamprey (Petromyzon marinus) metamorphosis[END_REF]. The most singular feature of lamprey regarding TH pathway is its involvement in metamorphosis. Lamprey is the only vertebrate (to our knowledge) where a decrease of THs, instead of an increase, is observed at the onset of metamorphosis [START_REF] Youson | Concentrations of insulin and thyroid hormones in the serum of landlocked sea lampreys (Petromyzon marinus) of three larval year classes, in larvae exposed to two temperature regimes, and in individuals during and after metamorphosis[END_REF]. Consistently with this peculiarity, THs treatments delay lamprey metamorphosis [START_REF] Youson | Effects of exogenous thyroxine (T4) and triiodothyronine (T3) on spontaneous metamorphosis and serum T4 and T3 levels in immediately premetamorphic sea lampreys, Petromyzon marinus[END_REF] while goitrogen treatments (inhibitors of TH synthesis) induce a precocious metamorphosis [START_REF] Manzon | Variable effects of goitrogens in inducing precocious metamorphosis in sea lampreys (Petromyzon marinus)[END_REF]. This is even more curious since TR1 and TR2 behave as genuine TR and transactivate target genes in presence of [START_REF] Manzon | Thyroid hormone and retinoid X receptor function and expression during sea lamprey (Petromyzon marinus) metamorphosis[END_REF]. More curiously, the dynamic expression of lamprey TR1 during metamorphosis matches the remodeling of the tissues, suggesting that TR1 and therefore TH signaling is actively involved in metamorphosis [START_REF] Manzon | Thyroid hormone and retinoid X receptor function and expression during sea lamprey (Petromyzon marinus) metamorphosis[END_REF]. One explanation could be that lamprey TRs behave differently in vivo than in cellulo, where their activity has been tested, because of a specific co-factor that would repress instead of activate target genes. Alternatively, it is possible that the active compound in this species is not T3 and that the decrease in T3 level corresponds to its transformation into an unknown compound that will be the endogenous TR ligand and surge during metamorphosis.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT ligand (T4 or T3,
There is an increasing interest for the T3 derivative 3,5-T2 (Figure 1). Although it is classically considered as an inactive T3 derivative, 3,5-T2 actually exhibits biological activities (for review see: [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript | 3,5-Diiodothyronine (T2) is on a role. A new hormone in search of recognition[END_REF]. It can induce the mRNA synthesis of several genes such as TSH [START_REF] Moreno | Effect of 3,5-diiodo-Lthyronine on thyroid stimulating hormone and growth hormone serum levels in hypothyroid rats[END_REF], Dio1 [START_REF] Baur | 3,5-diiodo-L-thyronine stimulates type 1 5'deiodinase activity in rat anterior pituitaries in vivo and in reaggregate cultures and GH3 cells in vitro[END_REF] or TRβ (Ball et al., 1997). More generally, in mouse, 3,5-T2 has thyromimetic activity on the hypothalamus pituitary axis and lipid metabolism [START_REF] Jonas | 3,5-Diiodo-L-Thyronine (3,5-T2) Exerts Thyromimetic Effects on Hypothalamus-Pituitary-Thyroid Axis, Body Composition, and Energy Metabolism in Male Diet-Induced Obese Mice[END_REF] as well as on the liver transcriptome [START_REF] Lietzow | 3,5-T2 alters murine genes relevant for xenobiotic, steroid, and thyroid hormone metabolism[END_REF]. In the killifish Fundulus heteroclitus, 3,5-T2 has been shown to be a ligand for TRβ [START_REF] Mendoza | 3,5-T2 Is an Alternative Ligand for the Thyroid Hormone Receptor β1[END_REF], but this idea is still debated as 3,5-T2 has a very low binding potency on TR in rat and salmon [START_REF] Darling | Comparison of thyroid hormone binding to heptic nuclei of the rat and a teleost (Oncorhynchus kisutch)[END_REF]. Most of the studies on 3,5-T2 are now focused on its non-genomic effect, that is to say the effects that are not mediated by TRs but through cytoplasmic and membrane interactions with proteins (reviewed in [START_REF] Goglia | diiodothyronine[END_REF].

There is another class of TH derivatives of pharmacological interest: the acid acetic analog of TH: Tetrac and Triac (Figure 1). These compounds are synthesized in peripheral tissues such as liver [START_REF] Ruters | Metabolism of Triiodothyroacetic Acid (TA3) in Rat Liver. II. Deiodination and Conjugation of TA3by Rat Hepatocytes and in Rats in Vivo[END_REF]), kidneys, (Flock et al., 1965) and brain [START_REF] Rall | Metabolism of L-thyroxine and L-3:5:3'triiodothyronine by brain tissue preparations[END_REF] by deamination of the TH backbone. Although little is known about their metabolism, the TH aminotransferase and the L-amino acid oxydase are likely involved in their synthesis (for reviews see [START_REF] Engler | The deiodination of the iodothyronines and of their derivatives in man[END_REF][START_REF] Wu | Alternate pathways of thyroid hormone metabolism[END_REF]. Because of its short half-life [START_REF] Goslings | Comparison of the Metabolism and Distribution of L-Triiodothyronine and Triiodothyroaeetic Acid in the Rat: A Possible Explanation of Differential Hormonal Potency[END_REF][START_REF] Wu | Alternate pathways of thyroid hormone metabolism[END_REF], Triac is considered to have an overall low biological activity [START_REF] Wu | Alternate pathways of thyroid hormone metabolism[END_REF] and is not considered as a true endogenous TR ligand. Nonetheless, Triac has the same affinity for TRα than T3, and a two times higher affinity for TRβ than T3 [START_REF] Messier | In vitro effect of Triac on resistance to thyroid hormone receptor mutants: potential basis for therapy[END_REF][START_REF] Schueler | Binding of 3,5,3'triiodothyronine (T3) and its analogs to the in vitro translational products of c-erbA protooncogenes: differences in the affinity of the alpha-and beta-forms for the acetic acid analog and failure of the human testis and kidney alpha-2 products to bind T3[END_REF][START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript Takeda | Triiodothyroacetic Acid Has Unique Potential for Therapy of Resistance to Thyroid Hormone[END_REF], which results in a higher transcription activity [START_REF] Messier | In vitro effect of Triac on resistance to thyroid hormone receptor mutants: potential basis for therapy[END_REF][START_REF] Schueler | Binding of 3,5,3'triiodothyronine (T3) and its analogs to the in vitro translational products of c-erbA protooncogenes: differences in the affinity of the alpha-and beta-forms for the acetic acid analog and failure of the human testis and kidney alpha-2 products to bind T3[END_REF][START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript Takeda | Triiodothyroacetic Acid Has Unique Potential for Therapy of Resistance to Thyroid Hormone[END_REF]. As a consequence, clinical use of Triac in hormone replacement therapy is considered to have a better outcome than T4 or T3 treatments [START_REF] Guran | 9 years follow-up of a patient with pituitary form of resistance to thyroid hormones (PRTH): comparison of two treatment periods of D-thyroxine and triiodothyroacetic acid (TRIAC)[END_REF][START_REF] Kunitake | 3,5,3′-Triiodothyroacetic Acid Therapy for Thyroid Hormone Resistance[END_REF]. Another interesting feature of Triac is that it does not require the monocarboxylate transporter 8 (MCT8) for its cellular uptake contrary to T3 [START_REF] Kersseboom | In Vitro and Mouse Studies Supporting Therapeutic Utility of Triiodothyroacetic Acid in MCT8 Deficiency[END_REF]. Therefore, Triac is a very interesting therapeutic molecule for pathologies with mutation of the MTC8 transporter. For instance, this is the case in the Allan-Herndon-Dudley syndrome where T3 uptake to the brain is impaired and T3 treatment is not effective [START_REF] Kersseboom | In Vitro and Mouse Studies Supporting Therapeutic Utility of Triiodothyroacetic Acid in MCT8 Deficiency[END_REF]. This is also true for Tetrac, the acidic derivative of T4 (Figure 1), which has a very low affinity for TR but still has a biological activity in MCT8 deficient mice [START_REF] Horn | Tetrac Can Replace Thyroid Hormone During Brain Development in Mouse Mutants Deficient in the Thyroid Hormone Transporter Mct8[END_REF]. Unfortunately, the question of the cellular uptake of Triac and Tetrac through specific transporters remains poorly investigated. Competition assay with the transporter Oatp14 shows that Triac can inhibit the uptake of T4, suggesting that Oatp14 can also transport Triac [START_REF] Tohyama | Involvement of Multispecific Organic Anion Transporter, Oatp14 (Slc21a14), in the Transport of Thyroxine across the Blood-Brain Barrier[END_REF]. Nevertheless, the question of the transport of Triac was not addressed directly and the affinity of the transporter for T4 is much higher than for Triac [START_REF] Tohyama | Involvement of Multispecific Organic Anion Transporter, Oatp14 (Slc21a14), in the Transport of Thyroxine across the Blood-Brain Barrier[END_REF]). To our knowledge, it is therefore not known how Triac and Tetrac are transported through cell membrane. Thus, although Tetrac and Triac are considered to have a low biological activity and are not viewed as canonical TR ligands, they are endogenous TH derivatives and can exert, in some

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extend, a THs signaling (reviewed in [START_REF] Senese | Thyroid: biological actions of "nonclassical" thyroid hormones[END_REF]. Another compound, the 3-Iodothyronamine (T1AM), can be produced through the decarboxylation of the T4 backbone (Figure 1, for review see [START_REF] Scanlan | Endogenous 3-Iodothyronamine (T1AM): More Than We Bargained For[END_REF]. Although its synthesis and biological role remain obscure, some evidence show that they have a biological role [START_REF] Braulke | 3-Iodothyronamine: a novel hormone controlling the balance between glucose and lipid utilisation[END_REF]. This calls for a deeper investigation of T1AM and more generally, the decarboxylated analogs of THs.

Ligands are not the only actors capable of modulating TH signaling. As T4 is produced centrally in the thyroid gland, the deiodinases, expressed in target tissues, are key controllers of THs signaling. The importance of deiodinase is highlighted by the study of amphibian models. One striking feature of amphibian metamorphosis is the late regression of the tadpole tail. How is the tail protected from the remodeling action of thyroid hormones (which at the same time induce limb growth) during a large part of the metamorphosis? The local expression of the deiodinase provides an explanation for this phenomenon since it controls the local amount of available T3 [START_REF] Becker | The type 2 and type 3 iodothyronine deiodinases play important roles in coordinating development in Rana catesbeiana tadpoles[END_REF][START_REF] Kawahara | Role of type III iodothyronine 5 deiodinase gene expression in temporal regulation of Xenopus metamorphosis[END_REF]. First, during early metamorphosis (stage 49, [START_REF] Cai | Expression of type II iodothyronine deiodinase marks the time that a tissue responds to thyroid hormone-induced metamorphosis in Xenopus laevis[END_REF] Dio2 is expressed in the limb buds, which locally turns T4 into T3, enhancing TH signaling and ultimately resulting in limbs growth and development [START_REF] Brown | Thyroid hormone controls multiple independent programs required for limb development in Xenopus laevis metamorphosis[END_REF]. At the same time, Dio3 is highly expressed in the tail resulting in its preservation as Dio3 transforms T4 and T3 in inactive derivatives [START_REF] Becker | The type 2 and type 3 iodothyronine deiodinases play important roles in coordinating development in Rana catesbeiana tadpoles[END_REF]. As a consequence, there is no or little T3 signaling in the tail at this early period, which means limbs and tail can coexist at the same time. Later in metamorphosis (stage 62), Dio3 expression turns off in the tail, and concomitantly there is a surge of Dio2 expression. As a consequence, the local level of T3 rises and this induces the regression of the tail cells [START_REF] Cai | Expression of type II iodothyronine deiodinase marks the time that a tissue responds to thyroid hormone-induced metamorphosis in Xenopus laevis[END_REF]. The local expression of the deiodinases controls the local availability of THs, which explains how a systemic signaling can be delayed in a specific organ. Interestingly, this regulation at the local level of TH also happens in other species such as teleost fishes, since Dio2 and Dio3 are also differentially expressed during their metamorphosis [START_REF] Campinho | Molecular and cellular changes in skin and muscle during metamorphosis of Atlantic halibut (Hippoglossus hippoglossus) are accompanied by changes in deiodinases expression[END_REF][START_REF] Isorna | Iodothyronine deiodinases and thyroid hormone receptors regulation during flatfish (Solea senegalensis) metamorphosis[END_REF]. Such a local regulation is also critical in the TH effect on seasonality, which will however not be discussed here (for review see [START_REF] Dardente | Thyroid Hormone and Seasonal Rhythmicity[END_REF]. The deiodinase expression seems overall conserved in vertebrates. For instance, Dio2 is expressed in the skin of amphibians and fish during their metamorphosis as well as in their brains [START_REF] Becker | The type 2 and type 3 iodothyronine deiodinases play important roles in coordinating development in Rana catesbeiana tadpoles[END_REF][START_REF] Campinho | Molecular and cellular changes in skin and muscle during metamorphosis of Atlantic halibut (Hippoglossus hippoglossus) are accompanied by changes in deiodinases expression[END_REF][START_REF] Lorgen | Functional Divergence of Type 2 Deiodinase Paralogs in the Atlantic Salmon[END_REF][START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript Manzon | Regulation of pituitary thyrotropin gene expression during Xenopus metamorphosis: negative feedback is functional throughout metamorphosis[END_REF]. Nevertheless, some species specificities exist, as for instance Dio1 that has been lost in the amphibian Rana catesbeiana [START_REF] Becker | The type 2 and type 3 iodothyronine deiodinases play important roles in coordinating development in Rana catesbeiana tadpoles[END_REF].

In invertebrate chordates, TRIAC is an endogenous active compound.... Because of its prominent role in frog and flatfish metamorphosis and since this process is widespread in metazoans, outside vertebrates, most of the studies on TH are focused on its role in post-embryonic development [START_REF] Laudet | The origins and evolution of vertebrate metamorphosis[END_REF].

The study of the cephalochordate Branchiostoma floridae (Figure 2) shed light on the origin of TH signaling in chordates. Indeed, its metamorphosis (the spectacular transformation of an asymmetric pelagic larva into a symmetrical benthic juvenile) is controlled by TH (Paris et al., 2008a(Paris et al., , 2008b)). The main difference though, is that the ligand of the amphioxus TR is neither T4 nor T3 which are unable to bind to the receptor, but their derivative Triac [START_REF] Paris | Active Metabolism of Thyroid Hormone During Metamorphosis of Amphioxus[END_REF](Paris et al., , 2008b)). It has been shown that in amphioxus, the TR ligand binding pocket is smaller due to some specific mutations and is unable to accommodate T4 or T3. In contrast, Triac being smaller due to the lack of an amino group can enter into the pocket and regulate the conformational change of the receptor. As a consequence, the Amphioxus TR behaves as a bona fide TR: it binds DNA, forms a heterodimer with RXR, binds Triac as a ligand and induces the transactivation of target genes. Triac treatment of amphioxus larvae

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effectively leads to a precocious metamorphosis, and treatment with a TR antagonist such as NH3 delays it. TR expression peaks at metamorphosis and there is a thyroid response element in the promoter of the TR, as for TRβ in vertebrates (Paris et al., 2008b). Moreover, one of the 5 known deiodinases in B. floridae has been biochemically characterized and proven to be specialized in Triac deiodination [START_REF] Klootwijk | A Nonselenoprotein from Amphioxus Deiodinates Triac But Not T3: Is Triac the Primordial Bioactive Thyroid Hormone?[END_REF], indicating that Triac specialized metabolism effectively exists in this species. Studies of the amphioxus Branchiostoma blecheri have shown that Triac signaling regulates C/EBP, a vertebrate TH target gene, suggesting again a conserved TH signaling pathway in cephalochordates [START_REF] Wang | Up-regulation of C/EBP by thyroid hormones: A case demonstrating the vertebrate-like thyroid hormone signaling pathway in amphioxus[END_REF]. Together, these data build the hypothesis that the TH pathway and its biological roles appear at the basis of chordates (Paris and Laudet, 2008).

... but not in all known cases since the tunicate TR appears as an orphan receptor.

In tunicates (Figure 2), another invertebrate chordate and sister group of vertebrates, TH also appears to have a role in metamorphosis. However the current situation in this group is unclear. Indeed, the role of TH is quite clear but how this role is mediated remains unknown. Some experiments suggest that TH treatments on larvae accelerate the (already very rapid) metamorphosis and settlement of the larvae, although this is less spectacular than in the case of amphibians or amphioxus [START_REF] Patricolo | The effect of L-thyroxine on the metamorphosis of Ascidia malaca[END_REF][START_REF] Patricolo | Presence of thyroid hormones in ascidian larvae and their involvement in metamorphosis[END_REF]. The presence of T4 in Ciona intestinalis has been suggested by immunodetection methods (D' Agati and Cammarata, 2006). This is however not entirely convincing since the specificity of the antibody used is unclear, as it has been assessed only in the context of compounds known in human. Therefore, these data indicate that there probably exists a TH-like compound, but do not formally prove that it is T4. An ortholog of vertebrate deiodinase has been identified in the tunicate Halocynthia roretzi with both T4 and rT3 as substrates (D' Agati and Cammarata, 2006;[START_REF] Sheperdley | An Ascidian Homolog of Vertebrate Iodothyronine Deiodinases[END_REF]. A clear TR ortholog has been cloned, but this receptor is very divergent, in particular in the ligand binding domain (25% sequence identity with human TRs, whereas the amphioxus LBD display 38% [START_REF] Carosa | Ciona intestinalis nuclear receptor 1: a member of steroid/thyroid hormone receptor family[END_REF]. Almost 20 years after its cloning, this receptor remains enigmatic as it behaves as an orphan receptor. None of the known TH derivatives are able to regulate its transcriptional activity. The original authors, as well as ourselves, have tried many different compounds but none of them are able to bind or activate the receptor [START_REF] Carosa | Ciona intestinalis nuclear receptor 1: a member of steroid/thyroid hormone receptor family[END_REF]. Therefore, it seems clear that there is a secretion of TH-like compounds in tunicates [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript | Comparative expression analysis of transcription factor genes in the endostyle of invertebrate chordates[END_REF][START_REF] Ogasawara | Ascidian homologs of mammalian thyroid peroxidase genes are expressed in the thyroid-equivalent region of the endostyle[END_REF], but so far there is no evidence that the effects of TH on tunicates are mediated by the known TR ortholog.

Echinoderms provide another mysterious case...

Echinoderms comprise species such as sea stars, sea urchins, sea cucumbers and sand dollars (Figure 2). Our knowledge of the role of THs in the metamorphosis in echinoderms is reminiscent of the situation observed in tunicates. TH-like compounds are detected in echinoderms tissues and accelerate the complex metamorphosis of the Eiffel-tower-shaped larvae into the benthic juvenile in various sea urchins [START_REF] Chino | Formation of the adult rudiment of sea urchins is influenced by thyroid hormones[END_REF][START_REF] Heyland | Thyroid hormone metabolism and peroxidase function in two non-chordate animals[END_REF] and sand dollars species [START_REF] Heyland | Thyroid hormones determine developmental mode in sand dollars (Echinodermata: Echinoidea)[END_REF][START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript | Induction of metamorphosis in the sand dollar Peronella japonica by thyroid hormones[END_REF]. T4 can also accelerate sea stars development in a dose-dependent manner [START_REF] Johnson | Thyroxine-Accelerated Larval Development in the Crown-of-Thorns Starfish, Acanthaster planci[END_REF]. Interestingly, nuclear extract of the sea urchin Hemicentrotus pulcherrimus can bind T4 [START_REF] Saito | Binding Properties of Thyroxine to Nuclear Extract from Sea Urchin Larvae[END_REF], indicating that a factor within the nucleus, and not the cytoplasm, can bind the hormone. This may therefore be considered as an indication in favor of the presence of a nuclear receptor acting as a TR. And indeed there is a TR ortholog present in echinoderm genomes [START_REF] Tu | Gene structure in the sea urchin Strongylocentrotus purpuratus based on transcriptome analysis[END_REF]. Nevertheless, as in tunicates, the formal demonstration of THs binding to the isolated TR is still lacking in echinoderms. We have tested all the compounds we

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could think of in the Paracentrotus lividus TR that we have isolated in our lab, without detecting any positive hit (M. Paris, G.H. and V.L. unpublished results). Therefore, as for tunicates, it is impossible to conclude that TH signaling, through TR and transcriptional activation of target genes, is involved in echinoderm metamorphosis as in cephalochordates and vertebrates. In the sea urchin, Strongylocentrotus purpuratus, it has been shown that iodine uptake in the larvae is dependent of a peroxidase activity and not the sodium/iodine symporter found in vertebrates [START_REF] Miller | Iodine accumulation in sea urchin larvae is dependent on peroxide[END_REF]. This may be reminiscent of an active thyroid function and leads to the conclusion that there is a specific iodine metabolism in echinoderms [START_REF] Miller | Iodine accumulation in sea urchin larvae is dependent on peroxide[END_REF]. In any case, it indicates that the vertebrate model of iodine uptake cannot be generalized in all chordates. But if and how such a metabolism is translated to a hormonal control of life-history transition, is still an open question in these species. One explanation could be an exogenous origin of iodinated compounds, supplied by algae, which are used as hormones [START_REF] Chino | Formation of the adult rudiment of sea urchins is influenced by thyroid hormones[END_REF][START_REF] Heyland | Cross-kingdom hormonal signaling: an insight from thyroid hormone functions in marine larvae[END_REF].

A loss of TH signaling in ecdysozoa

Genomics data indicate that there is no TR in ecdysozoans, group including insects [START_REF] Bertrand | Evolutionary Genomics of Nuclear Receptors: From Twenty-Five Ancestral Genes to Derived Endocrine Systems[END_REF]; Figure 2) or nematodes [START_REF] Kostrouchova | Nuclear receptors in nematode development: Natural experiments made by a phylum[END_REF]. Although some authors suggest a TR ortholog in the crustacean Daphnia pulex [START_REF] Wu | Thyroid hormone receptor orthologues from invertebrate species with emphasis on Schistosoma mansoni[END_REF], this sequence appears divergent from the other identified TRs and is therefore not a good candidate for a TR ortholog. In addition, no experimental data confirm that the encoded protein behaves as a genuine TR.

This question is of course particularly interesting in the context of the well-known metamorphosis of arthropods and in particular in insects. However, in arthropods, metamorphosis and growth are not controlled by THs but by two other hormones: the juvenile hormone that promotes growth and prevents metamorphosis [START_REF] Riddford | Cellular and Molecular Actions of Juvenile Hormone 1. General Considerations and Premetamorphic Actions[END_REF] and the steroid derivative hormone ecdysone (reviewed in [START_REF] Thummel | Flies on steroids--Drosophila metamorphosis and the mechanisms of steroid hormone action[END_REF]. Ecdysone binds the Ecdysone receptor, a nuclear receptor that forms a heterodimer with USP, the ortholog of RXR [START_REF] Yao | Functional ecdysone receptor is the product of EcR and Ultraspiracle genes[END_REF]. This similarity in the biological function (post-embryonic developmental control) between THs and ecdysone and their mechanisms (nuclear receptor mediated signal) allowed some authors to draw interesting comparisons between the two signaling systems (reviewed in [START_REF] Flatt | Comparing thyroid and insect hormone signaling[END_REF]. As an illustration, TH derivatives T4, T3, rT3 and 3,5-T2 (Figure 1) have been suggested to decrease the oocyte length in the insect Locusta migratoria [START_REF] Davey | Fenoxycarb and thyroid hormones have JH like effects on the follicle cells of Locusta migratoria in vitro[END_REF][START_REF] Davey | Do thyroid hormones function in insects?[END_REF]. However, such an observation of the effect of an exogenously provided compound is not a proof that an endogenous pathway is regulating the process. The presence of TH derivative T2 or mono iodinated thyronine in the locust has been suggested but still lacks a clear confirmation [START_REF] Flatt | Comparing thyroid and insect hormone signaling[END_REF]. More surprisingly, T3 seems to be able to enter insect cells and T3 treatments with a deiodinase inhibitor are less effective to reduce oocyte size than T3 alone, suggesting the existence of a deiodinase-dependent activity [START_REF] Davey | Do thyroid hormones function in insects?[END_REF]. Nevertheless, these data are still difficult to interpret. Since there is no TR ortholog in insects, how is this signal integrated? In addition, to our knowledge, no deiodinase has been identified in insect despite the fact that the molecular signature of those enzymes is well known. Moreover, THs bind cell membrane in insects and competes with the juvenile hormone, suggesting that the two compounds may act on the same membrane receptor [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript | Functional binding of a vertebrate hormone, L-3,5,3'-triiodothyronine (T3), on insect follicle cell membranes[END_REF]. Thus, the TH effect observed in insects might be caused by the displacement of juvenile hormone. Furthermore, as there are no TRs, the TH binding on membrane is reminiscent of the non-genomic pathway mentioned above (reviewed in [START_REF] Goglia | diiodothyronine[END_REF]. As a conclusion, TH derivatives have some marginal effects on insects but their mechanism of action remains largely elusive, casting some doubt on the

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importance of this pathway in ecdysozoa. Given the absence of TH related genes in insects (i.e. TR, deiodinase), the presence of a chordate-like TH signaling remains dubious, and we remain on the opinion that this pathway is not endogenously present in ecdysozoa and has therefore been lost in the common ancestor of this group (see below). Nevertheless, it could be interesting to reinvestigate the influence of TH in insects under the light of the non-genomic pathway or the influence of iodinated compounds found in insect food (i.e. plant, [START_REF] Eales | Iodine metabolism and thyroid-related functions in organisms lacking thyroid follicles: are thyroid hormones also vitamins? Proceedings of the Society for Experimental Biology and Medicine[END_REF][START_REF] Heyland | Cross-kingdom hormonal signaling: an insight from thyroid hormone functions in marine larvae[END_REF].

Contrasting evidence about TH signaling in lophotrochozoans

Lophotrochozoans (Figure 2) are the sister taxa of ecdysozoa and cluster animals such as molluscs, annelids and flatworms. The situation regarding TH signaling is very different than for ecdysozoans since their genomes contain clear TR orthologs [START_REF] Bertrand | Evolutionary Genomics of Nuclear Receptors: From Twenty-Five Ancestral Genes to Derived Endocrine Systems[END_REF]. Moreover experimental data indicate that TH signaling is possible in this group. The suggestion of a TH metabolism in annelids and molluscs has been proposed in the 50's with experiments showing an incorporation of the iodine isotope I 131 in their foreguts [START_REF] Gorbman | Utilization of radioiodine by invertebrates, with special study of several annelida and mollusca[END_REF]. For instance, the sea hare Aplysia californica harbors a peroxidase gene that is ortholog to the vertebrate thyroid peroxydase (TPO) that is able to incorporate I 125 into T4, indicating a possible endogenous synthesis of TH [START_REF] Heyland | Thyroid hormone metabolism and peroxidase function in two non-chordate animals[END_REF]. Another example comes from the Pacific oyster Crassostrea gigas. HPLC experiments have shown that this mollusk contains T4 and T3. In addition its genome contains a TR that can bind DNA on a thyroid response element. However no convincing evidence of activation of this TR by THs has been reported by these authors. Their data indicate a possible weak activation at very high concentration of T4, T3 and Triac (1µM, Huang et al., 2015). Therefore, the biological function of this TR ortholog remains unknown although these finding suggest that TH signaling may be functional in lophotrochozoans. At last, this allows to conclude that TR signaling must have been present in the ancestor of all bilaterian animals and that therefore, when it is not present, this means that it has been secondarily lost.

TH at the base of the metazoan tree

Genomic data from the cnidarians Acropora millepora [START_REF] Grasso | The evolution of nuclear receptors: evidence from the coral Acropora[END_REF] and Nematostella vectensis [START_REF] Putnam | Sea Anemone Genome Reveals Ancestral Eumetazoan Gene Repertoire and Genomic Organization[END_REF] or the porifera Amphimedon queenslandica [START_REF] Srivastava | The Amphimedon queenslandica genome and the evolution of animal complexity[END_REF] display no clear TR ortholog, suggesting that the diversification of TR from ancestral nuclear receptor did occur only in bilaterians [START_REF] Bertrand | Evolutionary Genomics of Nuclear Receptors: From Twenty-Five Ancestral Genes to Derived Endocrine Systems[END_REF][START_REF] Tarrant | Endocrine-like Signaling in Cnidarians: Current Understanding and Implications for Ecophysiology[END_REF]. Therefore, TR should be considered as a bilaterian-specific gene (Figure2). However, some studies suggested that T4 and iodinated compounds can induce the strobilation (polyp to medusa transition) of the cnidaria Aurelia aurita [START_REF] Spangenberg | Thyroxine induced metamorphosis in Aurelia[END_REF][START_REF] Spangenberg | Development studies of Aurelia (jellyfish) ephyrae which developed during the SLS-1 mission[END_REF], despite the absence of identified TR ortholog. This raises the following questions: How is this signaling integrated? Is there a T4-specific metabolism in cnidarians? Is this effect specific or not? The finding that the RXR ortholog of A.aurita and its ligand, 9-cis retinoic acid, are clearly involved in strobilation in the very same species is therefore puzzling [START_REF] Fuchs | Regulation of Polyp-to-Jellyfish Transition in Aurelia aurita[END_REF]. If RXR was already involved in metamorphosis control at the base of metazoans, what was the role of TR, once it appears it bilaterians, on the TR/RXR heterodimer? What is the partner, if any, of RXR in cnidarian in controlling the strobilation and other similar metamorphosis-reminiscent processes? Why is RXR always implicated in metamorphosis control in chordates (with TR) in ecdysozoan (with EcR) and in cnidarian (with still an elusive partner, if any, [START_REF] Holstein | Life-history evolution: at the origins of metamorphosis[END_REF]? All these questions remain open and are very interesting path to explore in the future.

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Iodinated molecules in algae: what link with TH signaling?

The synthesis of TH by the thyroid gland, with the contribution of an enormous precursor, thyroglobulin, appears clearly to be vertebrate specific [START_REF] Holzer | Thyroglobulin Represents a Novel Molecular Architecture of Vertebrates[END_REF]. This observation raises the question of how TH derivatives are formed in non vertebrate species such as amphioxus or sea urchin, which are devoid of thyroid gland. In some invertebrate chordates such as amphioxus and tunicates, the existence of an evolutionary precursor of the thyroid gland called the endostyle may provide a possible solution, but in these species there is no gene reminiscent of thyroglobulin [START_REF] Holzer | Thyroglobulin Represents a Novel Molecular Architecture of Vertebrates[END_REF]. In addition, outside chordates there is no sign of endostyle or of thyroglobulin, and the way THs are formed remains a complete mystery. However, the identification of iodine bound to organic molecules in algae, particularly cyclic ones [START_REF] Barre | The halogenated metabolism of brown algae (Phaeophyta), its biological importance and its environmental significance[END_REF][START_REF] Miller | Endocrine interactions between plants and animals: Implications of exogenous hormone sources for the evolution of hormone signaling[END_REF] could provide an explanation, and the supply of TH by algae (that is through feeding) have been suggested in sea urchin [START_REF] Heyland | Cross-kingdom hormonal signaling: an insight from thyroid hormone functions in marine larvae[END_REF]. Under this hypothesis, TR should be considered as a sensor, indicating the food availability and controlling development and life-history transitions depending on food availability. This would make sense as life-history transitional steps are always demanding and energy-consuming processes [START_REF] Heyland | Thyroid hormones determine developmental mode in sand dollars (Echinodermata: Echinoidea)[END_REF][START_REF] Wright | The fat body of bullfrog (Lithobates catesbeianus) tadpoles during metamorphosis: Changes in mass, histology, and melatonin content and effect of food deprivation[END_REF].Furthermore, the physiological function of TR and TH in most animals in which it has been explored, mammals but also fish, is connected to energy regulation and the control of large physiological equilibria [START_REF] Habibi | New insights into thyroid hormone function and modulation of reproduction in goldfish[END_REF][START_REF] Little | Thyroid hormone actions are temperature-specific and regulate thermal acclimation in zebrafish (Danio rerio)[END_REF].

Conclusion

In this review, we have discussed about the main actors of TH signaling: the ligands, the receptors and the main metabolizing enzymes. We started on vertebrates, for which THs action is best understood, and discussed about related taxa for which evidence is more scarce until we reached the base of the metazoan tree, and even outside in algae (Figure 2). By doing so, we have highlighted the strong bias existing in our knowledge of the pathway (and more generally all hormones): considering the vertebrate situation as the classical situation and using it as the reference to investigate the non-vertebrate situation. This may not be (and even more: this is most probably not) what happened during evolution. Indeed, the roles of TH signaling, and what we consider as a canonical endogenous ligand (i.e. T3) might actually be a vertebrate specificity [START_REF] Klootwijk | A Nonselenoprotein from Amphioxus Deiodinates Triac But Not T3: Is Triac the Primordial Bioactive Thyroid Hormone?[END_REF]Paris et al., 2008a).

TH signaling is a striking example of what non classical models can bring to our understanding of an endocrinological pathway. Indeed, these models are used to address different kinds of questions that shed a new light on the biological role of THs. In particular these models allow pleading for a complete unbiased chemical and biochemical characterization of the TH-like compounds present. Several key questions on that matter remain unanswered even in mammals, in particular how deaminated derivatives such as Triac and Tetrac are formed. In addition, there are some indications that TH-like compounds may be more diverse outside vertebrates than in vertebrates. For example in amphioxus there are eight iodine symporter related genes that may participate to the transport of TH-like compounds, as well as five genes related to thyroid peroxidase and five deiodinase genes (Paris et al., 2008a), therefore suggesting an exquisite degree of sophistication in the metabolism and transport of these active compounds. Nevertheless, actual biological functions of these genes have not been investigated yet. Another interesting question would be the role of alternative ligands such as 3,5-T2 and Triac even in mammals. These have been

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dismissed as minor players but, as non-genomic action 20 years ago, should perhaps no longer be neglected. Additionally, the non-genomic effects of THs remain to be investigated outside vertebrates, which could shed a new light on the evolution of THs signaling.

Another important avenue is of course the question of the peculiar mode of formation of THs from a huge precursor protein, thyroglobulin, which exhibits a very complex trafficking in a specialized organ, the thyroid gland. This is clearly a specificity of vertebrates, which has hidden how other metazoans produce THs (or extract them from their food). This should be put in a wider perspective, namely the question of iodine supply and storage, and remains to be analyzed in an unbiased manner. We anticipate that this may provide drastic paradigm changes in the way we consider TH formation in vertebrates. The question of whether thyroglobulin is always the only precursor of TH in vertebrate may appear as heterodox but may benefit from a reappraisal.

Lastly, the connection between the three main aspects of TH in vivo function, the control of metabolism, the regulation of seasonality and the control of post-embryonic stages transitions (that is metamorphosis) remains a very important question [START_REF] Holzer | Thyroid hormones: a triple-edged sword for life history transitions[END_REF]. The fact that food availability is central in all these aspects is important to notice, and the role of TH in basic aspects of nutrition biology (from appetite regulation to digestion and growth) may provide a unifying theme for the biological role of these still enigmatic hormones. Diversity is the hallmark of biology: on thyroid hormone studies as in other aspects of our science, we should take advantage of this diversity and use it as an inspiration to explore new avenues.

Holzer et al., Highlights

The biological role of non-canonical ligands remains to be explored in vertebrates.

Comparative endocrinology shows that T4 and T3 might not be the original TR ligands.

The role of non-canonical ligands remains to be understood outside vertebrates.

Figure 1 :

 1 Figure 1: The classical TH derivatives. Inner and outer rings are indicated above T4. Red arrows indicate outer ring deiodination performed by Dio2. Blue arrows indicate inner ring deiodination performed by Dio3. Grey arrows indicate deiodination performed by Dio1. Green arrows indicate deaminations. The orange arrow indicates a decarboxylation. The interrogation mark under the T1AM indicates that although possible from TH, the synthesis of this compound remains unknown.

Figure 2 :

 2 Figure 2: Schematic metazoan phylogeny. The phylogenetic relationships between the main taxonomic groups discussed in this review are represented. Each group is indicated by a bracket. The vertebrate specific TR duplication is indicated.


IADI Alexia Missoffe
email: alexia.missoffe@univ-lorraine.fr.

Finite Difference Transmission Line model for the design of safe multi-sections cables in MRI

Keywords: Finite Difference Transmission Line model radiofrequency, transfer function, cables, MRI safety, phase effects, pacemaker leads radiofrequency, transfer function, cables, MRI safety, phase effects, pacemaker

Purpose: To show the relevance of a simple finite difference transmission line model for help in the design of safe cables in 1.5 T MRI's using the multi-section cable approach.

Methods: A two section wire will be studied as a function of the length of the two different sections. The result concerning the heating of the electrodes for a constant electrical field excitation along the wire as well as the estimation of the correction phase factor will be compared to full-wave simulation results. Such information allows estimation of the worst case heating of the cable in MRI taking into account the phase effects.

Results:

The transmission line predicts correctly the full-wave simulation results. The optimum length of the second section reduces by 37% the worst case heating at the electrode compared to the best case unique section wire.

Conclusion:

The multi-section cable design can reduce the heating of cables in MRI taking into account the phase effects. The finite difference transmission line model presented is a simple valuable tool to estimate the worst case heating of multi-section cables thus helping to optimize the design of such cables.

INTRODUCTION

MRI has become an essential imaging modality for soft tissue. At the same time, patients implanted with devices such as pacemakers, defibrillators or neurostimulators are more and more common as the population in developed country ages. These implanted medical devices use a lead to transfer the energy from the implanted active case to the desired organ in the body such as the heart or the brain. Currents are induced on the conducting leads by the MRI radiofrequency field and can result in consequent heating of the tissue at the interface with the implanted stimulation electrode and to induced voltages at the input impedance of the active case. These input voltages can lead to dysfunction of the implanted device presenting further risk for the patient. Serano et al. [START_REF] Serano | A Novel Brain Stimulation Technology Provides Compatibility with MRI[END_REF] proposed to use the "resistive tapered stripline" (RTS) technology introduced by Bonmassar (2) for electroencephalogram (EEG) cables for deep brain stimulators leads. This technology introduces discontinuities in the conductivity of the line such that the radiofrequency energy is reflected at the interfaces therefore modifying the response of the lead compared to a continuous conductivity line. To model a two section wire, Serano et al. [START_REF] Serano | A Novel Brain Stimulation Technology Provides Compatibility with MRI[END_REF] considers that the implanted wire acts as an antenna and a transmission line. The analytical model they use was introduced for a discontinuous transmission line with multiple reflections (3) but with a feeding port at the end of the line. This model was adapted to an EEG cable submitted to a distributed excitation field by an external antenna such as a radiofrequency MRI coil by Bonmassar (2). This model considers that the signal delivered to the electrode is a term corresponding to the total signal received by both monopoles corresponding to the two sections that constitute the cable minus the different components of the signal reflected back to the opposite end to the electrode. In (2), Bonmassar says that the expression of the signal received by the two monopoles is valid for the short monopole approximation. The model was established for EEG cables for which the surrounding medium is air. Therefore the wavelength of the radiofrequency field which is about 4.7m for a 1.5T MRI is indeed large in front of the length of the EEG cables. Nevertheless, it seems contradictory to consider that the wavelength is short enough to use the transmission line model to model the possible reflections at the discontinuities and to apply at the same time the short monopole approximation. Moreover, for implanted cables in a tissue imitating material the wavelength is divided by approximately 10 compared to air. Therefore as, for example, the length of deep brain stimulator leads is at least tens of cm, the short monopole approximation is no longer valid.

In [START_REF] Serano | A Novel Brain Stimulation Technology Provides Compatibility with MRI[END_REF], Serano et al. present this analytical model but finally analyze the possibilities offered by the RTS model with full-wave numerical simulations. And they do not confront the potential results of this analytical model with the full-wave simulation results. In (4) I presented a modified transmission line model for a cable embedded in tissue imitating gel at 64 MHz. It was inspired by previous work by Acikel et al. [START_REF] Acikel | Modeling of Radio-Frequency Induced Currents on Lead Wires during MR Imaging Using a Modified Transmission Line Method[END_REF] but with a simple passive model for the electrode in contrast with the Thevenin equivalent model presented in [START_REF] Acikel | Modeling of Electrodes and Implantable Pulse Generator Cases for the Analysis of Implant Tip Heating under MR Imaging[END_REF] by the same group. It models the excitation from the MRI radiofrequency antenna as a distributed excitation all along the cable. It was shown that there is an equivalence between our transmission line model and the function transfer model introduced by Yeung et al. [START_REF] Yeung | RF Heating due to Conductive Wires during MRI Depends on the Phase Distribution of the Transmit Field[END_REF], its full potential for complex cables later brought to light by Park et al.(8). This transfer function model allows to take into account the effect of the phase distribution of the incident field on the potential heating at the lead electrode [START_REF] Yeung | RF Heating due to Conductive Wires during MRI Depends on the Phase Distribution of the Transmit Field[END_REF]. Indeed Serano et al. [START_REF] Serano | A Novel Brain Stimulation Technology Provides Compatibility with MRI[END_REF] show that their two section design can reduce the heating at the electrode compared to conventional leads but for a given configuration in the American Society for Testing Materials (ASTM) phantom [START_REF] Astm F | Standard Test Method for Measurement of Radio Frequency Induced Heating On or Near Passive Implants During Magnetic Resonance Imaging[END_REF]. This configuration corresponds approximately to a constant phase and constant amplitude incident field. The incident field in the human body varies significantly and phase effects need to be taken into account to ensure patient safety. If one follows Park et al. [START_REF] Park | Calculation of MRI-Induced Heating of an Implanted Medical Lead Wire with an Electric Field Transfer Function[END_REF] formalism, the worst case heating at the electrode of a cable taking into account the phase effects can be estimated by the following information. First the heating at the electrode for a constant amplitude and constant phase incident field and second by the amplitude and phase distribution of the normalized transfer function. Such information allows the estimation of the heating at the electrode for a given constant amplitude of the incident field that can be considered to be the maximum possible electrical field in the human body and the worst phase distribution that is given by the transfer function distribution [START_REF] Yeung | RF Heating due to Conductive Wires during MRI Depends on the Phase Distribution of the Transmit Field[END_REF][START_REF] Park | Calculation of MRI-Induced Heating of an Implanted Medical Lead Wire with an Electric Field Transfer Function[END_REF].

The transmission line model presented in (4) was built for insulated wires of simple cylindrical geometry, the conductor being a full cylinder in contrast to the fine layers of metal deposited on a substrate of the RTS technology. For this simple cylindrical insulated wire, analytical expressions of the transmission line parameters exist [START_REF] Hertel | The Insulated Linear Antenna-Revisited[END_REF]. The RTS technology uses conductivity discontinuities of the layers of the different sections to create the reflections of the wave. In this work the discontinuities were created by changes in the insulation thickness and relative permittivity ε r . The transmission line model is solved by the finite difference method with the incident field along the cable as an input. The result is the current and voltage distribution along the cable. The active power at the load impedance gives an evaluation of the heating at the electrode. It can be solved with varying parameters along the cable with no further effort compared to a uniform cable. The finite difference model also allows to get the transfer function model. Therefore, it allows to study multi-section cables heating taking into account the phase effects in a very straight forward way.

This work aims at demonstrating that this finite difference transmission line model is indeed a reliable tool to study the possible heating of a simple two-section cable taking into account the phase effects. Results will be compared to full-wave simulation results of the losses at the electrodes of the cable under a constant phase and constant amplitude incident field and of the transfer functions that allows to get the correction phase factor to estimate the worst case heating. The commercial software CST MICROWAVE STUDIO® (CST® MWS®, Darmstadt, Germany) was used for the full-wave simulations.

THEORY Evaluation of the worst case heating taking into account the phase effects.

Park et al. [START_REF] Park | Calculation of MRI-Induced Heating of an Implanted Medical Lead Wire with an Electric Field Transfer Function[END_REF] uses the following formalism for the estimation of the scattered electrical field at the electrode as a function of the incident field.

where E1(P) is defined as the scattered field at the electrode for a constant amplitude and phase incident field of 1V/m. TF N (z) is defined as the normalized transfer function such as which results directly from the definition of E1(P). The heating at the electrode is proportional to the square of the scattered electrical field. The worst case heating appears when all the terms under the integral are in phase meaning that the phase of the incident field is minus the phase of the transfer function to a constant close. If one fixes the amplitude of the incident field to be constant and equal to the maximum along the path in the human body E inc_max , the worst case heating can be estimated by the following equation.

Therefore knowing E1(P) and the value of that is the correction phase factor, one can estimate the worst case heating of the two section cable for different lengths of the different sections.

Finite difference transmission line model.

In the finite difference transmission line model, the cable is described by two vectors Z and Y that represent the impedance per unit length Z(z) and admittance per unit length Y(z) at each of the N nodes of the one dimension model. It is also described by two load impedances Z LOAD1 and Z LOAD2 that represent the termination conditions. The input to the model is the complex incident field E inc (z) at each node. The finite difference model takes the following matrix form:

where V and I are the voltage and current distribution along the cable. Dz1 and Dz2 are NxN matrixes that operate a first order derivation and MZ and MY are NxN diagonal matrixes containing the parameters vectors Z and Y. The boundary conditions are implemented at the N th and last line of the whole matrix.

The heating is actually proportional to the square of the current or voltage at the load. The calibration factor can be determined from a temperature measurement for a known incident field. E1(P) is proportional to the current or voltage at the load for a incident field E inc constant in amplitude and phase. In this study there is no need to evaluate the calibration factor as the aim is to compare E1(P) between the different multi-section cables.

As mentioned in (4) the transfer function and therefore the correction phase factor can be determined simply from the finite difference model. Inversing the square matrix expresses the current and voltage distribution as a function of the incident field and more particularly the current and voltage at the loads as a function of the incident field. The formalism is then exactly the one of the transfer function. The transfer function for the left load is the N-1 first values of the first line of the inverse matrix. For the right load it is the N-1 first values of the N th line of the inverse matrix. Normalizing this transfer function allows to estimate the correction phase factor.

The square of the product of E1(P) times the correction phase factor estimation of the worst case heating of the two-section cables and compare them to study the added value of this multi-section design compared to a one section design taking into account the phase effects.

METHODS

Transmission line model of the two-section cable.

The cable studied was a 53 cm long insulated cable with 1 cm of insulation removed at both ends. It had a 0.75 mm radius. The first section of the cable of length L2 was insulated by a 0.25 mm thick insulation with a relative permittivity of 3. The second section of the cable of length L1 will be insulated by a 1.1 mm thick insulation with a relative permittivity of 1.6. It was considered to be embedded in tissue imitating gel with a relative permittivity of 80 and a conductivity of 0.47 S/m at 64 MHz. The transmission line parameters Z and Y are calculated from the analytical expressions given in [START_REF] Hertel | The Insulated Linear Antenna-Revisited[END_REF]. The value of the load impedance is estimated from solving the inverse problem on the simulated transfer function in (4). Nyenhuis et al. [START_REF] Nyenhuis | 2015 Comput. Cardiol. Conf. CinC[END_REF] raised the issue that the measured transfer function depends on the boundaries of the phantom. We realized that the simulated transfer function using the reciprocity approach is also sensitive to the phantom boundaries. The transmission line model of the finite difference model was determined by solving the inverse problem on the full-wave simulation of the transfer function with the cable placed in an ASTM phantom such as represented in Figure 1. The inverse problem was solved by fixing Z and Y to the analytical values given in (10) so the only variable parameters are the end load impedances. As the simulated transfer function depends on the phantom boundaries, the extracted load impedances for the finite difference transmission line model also depend on the boundaries of the phantom.

All the transmission line parameters at 64 MHz for this placement in the ASTM phantom are summarized up in Table 1.

Z (ohm/m) Y(S/m) Z LOAD L2
85.1+j 361.7 0.0319+j0.1875 66.1-j39.9 L1 85.1+j 361.7 0.0010+j 0.0384 66.1-j39.9

Table 1 Transmission line model parameters for the two section cable.

The length L1 will be varied from 0 cm to 53 cm every cm the extreme cases corresponding to a one section cable or insulation material 2 and insulation material 1. L1 and L2 take into account the 1 cm length of the bare electrodes at both ends.

Validation of the estimation of E1(P) by the Finite Difference Transmission Line model

We placed the model of the 53 cm long two-section cable along the length of an ASTM phantom as represented in Figure 1. We excited with a plane wave excitation with a propagation direction x and a linear polarization of the electrical field along z as in Figure 1. Because of the boundaries of the ASTM phantom, the incident field at the position of the cable was not exactly constant in amplitude and phase.

For each value of L1, the mean losses on a 2 mm side cube at both electrodes were calculated. As the cable is dissymmetric due to the two different sections, the losses at the left and right end will not be the same. Both were studied and the behavior of the predicted losses at the electrodes as a function of L1 from the transmission line model were compared to the full-wave results. An arbitrary scaling factor has to be applied between both sets of data.

The entry to the transmission line model was the incident field that was extracted from the full-wave CST simulation of the empty phantom excited by the plane-wave excitation. In the full-wave simulation, it was not possible to have simultaneously a constant amplitude and phase incident field and take into account the boundaries of the ASTM phantom. But if the transmission line model predicts correctly the losses at both electrodes as a function of L1 for a given approximately constant incident field it is likely it will predict correctly the losses for a constant amplitude and phase incident field E1(P).

Validation of the estimation of transfer function by the Finite Difference Transmission Line model

The full-wave simulation of the transfer function is made following the reciprocity approach proposed in [START_REF] Feng | A Technique to Evaluate MRI-Induced Electric Fields at the Ends of Practical Implanted Lead[END_REF]. The electrode studied is excited locally by a short monopole and the current density along the cable is then the transfer function that can be normalized. The position of the cable in the ASTM phantom for these simulations is the same as the one presented in Figure 1 for the plane wave simulations.

To evaluate if the correction phase factor is correctly estimated by the transmission line model, we compared the transmission line transfer function to the full-wave simulated transfer function for the two section cable described above with L2=10 cm for both electrodes. Indeed as the cable is asymmetric the transfer function of electrode 1 is different from the transfer function of electrode 2. If the amplitude and phase of the normalized transfer functions are accuratly estimated, the correction phase factor is correctly estimated too. The comparison was also made for a three section cable of the same length and geometry with a first section of length 20 cm with insulation material 2, a second section of 21 cm with insulation material 1 and a third section of 12 cm with insulation material 2. This assesses the ability of the finite difference transmission line model for even more complex cables for which the determination of an analytical model becomes even more complex.

Worst case heating as a function of length of section 1

The transmission line model was used to predict the worst case heating variations at the two electrodes of the two-section cable as a function of L1. This was estimated from the square of E1(P) times the correction phase factor for each value of L1. The potential benefit of the two section cable was compared to the one section cable with the insulation material which gives the least worst case heating.

RESULTS

Validation of the estimation of E1(P) by the Finite Difference Transmission Line model

Figure 2 shows the results of the losses at both electrodes of the two section cable as a function of the length of the cable insulated by insulation material 1 L1. The results given by the Finite Difference Transmission Line model coincide very well with the full-wave simulation results. There is abrupt change for electrode 1 which is on the side of insulation material 1 when the cable is entirely insulated by material 1 for the full-wave simulations. The same phenomenon is observed for electrode 2 when the cable is entirely insulated by material 2. No explanation was found. Nevertheless, on the whole, although the incident field was not exactly constant in amplitude and phase, we can conclude that the Finite Difference Transmission Line model is a good tool to evaluate the relative heating of a two section cable under a constant phase and constant amplitude incident field E1(P). Figure 3 shows the amplitude and phase of the normalized transfer functions of the two electrodes of a two section cable. The origin of z-axis is at the electrode meaning that the direction along the cable is different depending on which electrode we look at. There is a very good agreement between the predicted transfer functions by the full-wave simulations and the Finite Difference Transmission Line model. One can notice that the transfer functions are different as the cable is indeed asymmetric. A discontinuity in the first derivative is observed at the junction of the two different materials for the amplitude and for the phase.

Figure 4 shows the results of the comparison for an even more complex three section cable for which the determination of an analytical solution becomes too cumbersome. The results are in very good agreement showing the potential of the Finite Difference Transmission Line model to be a good design tool.

Worst case heating as a function of length of section 1

The finite difference model having been validated against full-wave simulations, it is used to predict E1(P) and the correction phase factor of the two section cable as a function of the length of the cable insulated by material 1 L1. Figure 5 presents the relative worst case heating of the two section cable as a function of L1 for both electrodes deduced from E1(P) and the correction phase factor as explained in the theory section. It happens that the worst case heating curves as a function of L1 for both electrodes are exactly the same although E1(P) and the transfer functions were not the same. A theoretical explanation can probably be found. The best case for the one section cable is the cable entirely insulated by material 1. The results are therefore normalized to this case to evaluate the benefit of the two section design. For L1=41 cm (taking into account the bare electrode this means 40 cm of cable really insulated by material 1) and L2=12 cm (11 cm of cable insulated by material 2), there is a reduction of 37% of the worst case potential heating compared to the one section case.

DISCUSSION AND CONCLUSIONS

The aim was to show the relevance of a Finite Difference Transmission Line model to help in the design of safe multi-section cables in MRI. The reliability of the model was shown by comparison to full-wave simulation results. The agreement was very good. The Finite Difference Transmission Line model can therefore be used to estimate the worst case heating taking into account the phase effects therefore helping in the design of cables that are really MRI compatible.

Fig. 1

 1 Fig. 1 Full-wave simulation setup for the plane-wave simulations and the transfer function simulations.

Fig. 2

 2 Fig. 2 Comparison of the losses at the electrodes of a two section cable predicted by a full-wave plane wave simulation and the Finite Difference Transmission Line model as a function of the length of the section insulated by material 1 L1. a) Electrode 1 on insulation material 1 side. b) Electrode 2 on insulation material 2 side.

Fig. 3

 3 Fig. 3 Comparison of the transfer function predicted by full-wave simulations based on the reciprocity approach and the Finite Difference Transmission Line for a two section cable with L2=10 cm and L1=43 cm. a) Transfer functions amplitude. b) Transfer functions phase.

Fig. 4

 4 Fig. 4 Comparison of the transfer function predicted by full-wave simulations based on the reciprocity approach and the Finite Difference Transmission Line for a three section cable with a first 20 cm section of insulation material 2, a second 21 cm section of insulation material 1 and a third 12 cm section of material 2. 2 a) Transfer functions amplitude. b) Transfer functions phase.

Fig. 5

 5 Fig. 5 Worst case heating of a two section cable as a function of L1 normalized to the one section case of the cable entirely insulated by material 1.

ACKNOWLEDGMENTS

The author thanks Thérèse Barbier from the IADI laboratory (Nancy, France) for useful discussions about the RTS design. The author thanks her Aunt Colette Thomson for correcting the English. And finally the author thanks Cédric Pasquier for funding through Région Lorraine and FEDER.