Cornel Oros
email: cornel.oros@univ-poitiers.fr

Blandine Zimmer
email: zimmer@unistra.fr

Budget uncertainty in a monetary union *

Keywords: budget uncertainty, robust control, monetary institutions. JEL classification: E 58, E 60, E 62

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

Introduction

Uncertainty about key macroeconomic aggregates and relationships governing the economy is an important challenge for policymakers and substantially influences their choices. 1 In recent years, uncertainty seems to have become particularly challenging for fiscal policy-makers, and this, especially in the European Monetary Union (EMU) member countries. Fiscal authorities may face uncertainty stemming from lots of factors, including bond markets pressures as well as factors due to economic, social or political instability. The analysis of the implications of the fiscal policy-makers' uncertainty on macroeconomic outcomes thus represents a crucial topic to be put into the agenda of academics and practitioners. As far as we know, only two theoretical studies have dealt with this issue. Di Bartolomeo et al. (2009) and Di Bartolomeo and Giuli (2011) develop a model where monetary and fiscal authorities face uncertainty about the parameters describing their policy effectiveness. They qualify Dixit and Lambertini (2003)'s result obtained under the symbiosis assumption by showing that, under multiplicative uncertainty, even if monetary and fiscal authorities share identical targets for output and inflation, the achievement of these targets is no longer guaranteed.

In this paper, we consider a monetary union (MU) where national governments face uncertainty about the exact amount of public spending to be financed. More precisely, when setting their fiscal policy, governments fear some spending disturbances they do not necessarily have under control and which may alter or invalidate their budget projections. In addition, we assume that their spending can only be financed by taxation. 2 To model their fiscal decision-making under this type of uncertainty, we use the robust control approach. 3 Through this approach, we assume that governments are unable to define any probability distribution to spending disturbances. To set an optimal tax rate under these circumstances, they seek to select a fiscal policy that is robust to the most pessimistic perspective, i.e. that remains optimal even under the worst possible outcome of spending disturbances.

We allow for some asymmetry among the MU governments in the sense that we consider that some of them have lower ability to hedge against spending shocks and are therefore more vulnerable to budget uncertainty than others. This vulnerability can be so high that they are obliged to attach priority attention to spending stabilisation. Their fiscal policy is then constrained as it mainly focused on short-term spending imperatives at the expense of the economy's output performance. We refer to this type of governments as "fiscal-constrained".

Obviously, each national government's spending uncertainty affects its fiscal decisions but not only. It is also likely to interfere in the common central bank's decisions and thereby affect the MU partner countries' situation. In this paper, our objective is twofold. First, we seek to outline the consequences of the governments' spending uncertainty for their fiscal decisions and, through it, for macroeconomic outcomes in the MU member countries. Second, we study the implications of this uncertainty for the macroeconomic effects of monetary institutions. In particular, we examine how the central bank's degree of inflation aversion as well as the number of MU member countries affect macroeconomic performances -in terms of inflation and output -in the presence of budget uncertainty.

It appears from our analysis that when the MU governments are vulnerable to spending disturbances, they set high tax rates. This exacerbated fiscal pressure translates into low output in the member countries, obliging the central bank to be accommodating by conducting an inflationary monetary policy. In an asymmetric MU, this result implies that countries where the government has high ability to hedge against spending disturbances will rapidly feel inconvenienced by the too inflationary monetary policy set by the central bank in reaction to the bad output situation in the partner countries whose government has lower ability to hedge against spending disturbances.

Our analysis also examines how changes in the monetary institutional environment can affect the governments' fear of spending disturbances. Results reveal that an increase in the central bank's concern about inflation exacerbates this fear, leading fiscal-constrained governments to set higher taxes at the expense of output. If these governments are in the majority in the MU, the central bank is induced to be more accommodating by conducting an inflationary monetary policy. Therefore, quite counter-intuitively, an increase in the central bank's concern about inflation can result into higher inflation. By studying the macroeconomic effects of a MU enlargement, we show that the entry of new countries aggravates the heterogeneity of the current members' output situation. Moreover, if the new entrants suffer from greater budget uncertainty than the current members, the latter may also experience an increase in the MU-inflation rate.

The rest of the paper is organized as follows. In the next section, we develop a MU-model with monetary-fiscal strategic interactions in which we integrate the issue of budget uncertainty. The implications of this uncertainty for the member countries' economic outcomes are discussed in section 3. Section 4 presents the macroeconomic effects of changes in the monetary institutional environment in the presence of governments' budget uncertainty. A final section concludes.

The model

We consider a monetary union (MU) composed of n countries (indexed by i, ∀i = 1, ..., n). Monetary policy is set by a common central bank (CB) whereas fiscal policies are decided at the national level by the member countries' governments.

Output x i in country i is given by:

x i = π -π e -τ i (1)
where π and π e are the actual and expected inflation rates respectively; τ i defines the tax rate in country i. Behind this relation lies the idea that unexpected inflation, by eroding real wages, induces firms to augment their demand for labour and thus their production. Greater taxation on the firms' revenues, on the contrary, discourages production. Hence, as is common in this literature (see Beetsma and Bovenberg, 1998, 1999 among others), fiscal policy has a negative impact on aggregate supply via taxation. We thus assume that taxation is used for consumption only and not investment, so that it has no productive effect on supply. 4 The common CB cares about deviations of both, inflation and output from their respective targets which, for convenience, we assume to be equal to zero. Its loss function is given by:

L CB = Iπ 2 + x 2
(2)

where π and x = x i /n respectively define the MU-wide inflation rate and the average output level in the monetary union. We here suppose that the central bank perfectly controls the MU-wide inflation rate so that its monetary policy instrument is π. Parameter I measures the CB's relative concern for inflation with respect to output. It can also be interpreted as the CB's degree of inflation aversion.5

National governments are concerned about both, the level of output and of public spending in their economy. The objectives of government in country i (henceforth, government i) are summarized as follows:

L G i = x 2 i + α (g i -gi ) 2 (3)
where g i and gi respectively define the country i's actual and targeted levels of public expenditures as shares of output. Parameter α measures the relative importance government i gives to its spending objective.6 When setting its fiscal decision, government i faces the following budget constraint:

g i = τ i (4)
This equation corresponds to a balanced budget requirement where taxation is the only source of financing public expenditures. Government i will thus have to tolerate some tax distortions in order to finance its positive target of public expenditures gi . The type of expenditures that we consider here corresponds to public consumption such as salaries of public employees and other current spending generated by the supply of public goods. It also encompasses social security spending and the payment of interest on public debt (which we do not explicitly model). We here abstract from the beneficial impact public spending may have on output as g i does not integrate public investment goods.

As it is noticeable, the spending target gi is specific to each country. For government i, it writes:

gi = g + i (5)
where g represents a fixed level of public spending and is expressed as a share of output. It can be interpreted as an average socially optimal level of spending in the MU.

According to this expression, government i has its own spending target that may deviate from the average socially optimal level in the MU g. Indeed, government i's spending can be affected by lots of specific disturbances such as bad business cycles developments, political and social instabilityobliging the government to increase social expenditures -or financial market frictions putting pressure on public debt interest rates. These disturbances are captured by i and render the exact amount of its spending highly uncertain for the government. To hedge against this uncertainty, government i may want to keep some leeway in its decision-making by taking account of i in its spending target.

A crucial assumption here is that government i is unable to assign any probability distribution over alternative outcomes of i . To determine its fiscal policy under this assumption, we use a robust control (non-Bayesian) approach which consists in setting its tax rate (and thus spending level) so that it is robust to the worst possible realization of i .

Following Hansen and Sargent (2005, 2008), this approach can be modeled as a game between government i and a fictitious "evil agent" whose aim is to set the disturbances i so as to maximize the government's welfare loss.

Concretely, this implies for government i to solve the following minmax program: min

τ i max i L G = x 2 i + α (g i -g) 2 -θ i 2 i (6)
where θ i defines the government's ability to hedge against spending disturbances. This parameter varies in the interval [θ; ∞[. 7 The certainty case corresponds to θ i → ∞. This is the common case in the literature where it is assumed that governments do not suffer from spending uncertainty and thus have a perfect control over their budget. Parameter θ i is indexed by i, implying that we allow for some asymmetry among MU-member countries.

An alternative method to model fiscal uncertainty would be to use a Bayesian approach where spending disturbances correspond to white noise stochastic shocks and where fiscal uncertainty is given by the variance of these shocks. This method suggests that governments can attach priors to budget disturbances, which seems difficult in reality. In particular, in a context of high political, social or financial instability it appears reasonable to assume that governments are unable to statistically measure their budget uncertainty.

The timing of the game is as follows. First, in each member country, the private sector rationally determines inflation expectations through the nominal wage setting process. Then, simultaneously, the MU governments determine their tax rate τ i using the robust control approach detailed above. Finally the common central bank selects π, the MU inflation rate. Since in practice monetary policy can be adjusted more quickly than fiscal policy, we assume that, when taking their decisions, governments anticipate the central bank's reaction to their decisions and thus act as Stackelberg leaders. 8 The game is solved by backward induction and we begin by considering the common central bank's program. 9 Minimizing loss function (2) with respect to π and taking the member countries' aggregate supply functions (1) as given, we have:

π = π e + τ 1 + I (7)
where τ = i τ i /n defines the average MU-wide tax rate.

With the rational expectations assumption (π e = π), we obtain:

π = τ I (8)
Solving government i's program with the robust control approach and taking rational expectations (so that, π e = π), we obtain the equilibrium level of tax rate in country i:

τ i = αgθ i (1 + I) n θ i [n (1 + I) (1 + α) -1] -α [n(1 + I) -1] (9)
Integrating this expression into the central bank's reaction (8), the output function (1) as well as the budget constraint (4) and considering rational expectations, we have the equilibrium values for output and public expenditures in country i, respectively: x i = -τ i and g i = τ i , and also obtain 8 An interesting alternative, could be to consider a reversed timing where the central bank is the Stackelberg leader and the national governments, the followers. This sequence of events could be relevant to describe particular cases such as the euro crisis where the European Central Bank often argued to "buy time" for national governments. We thank an anonymous referee for having raised this idea. Calculations for this timing are available on request.

9 Details on the derivation of the equilibrium outcomes are provided in the appendix.

the equilibrium expression for inflation in the MU: π = τ (with, as already specified, τ = i τ i /n). 10 We observe that macroeconomic performances in country i -i.e. τ i , x i and g i -only depend on θ i , the government i's ability to hedge against spending disturbances, and not on θ j (∀j = i), the other governments' uncertainty parameter. The MU-wide inflation rate π = is the only variable that depends on the θ parameter of all national governments.

Moreover, in our model, the distortion from the first best outcome is due to the presence of a positive (fixed) spending target g > 0, obliging the government to collect a positive amount of taxes (τ i > 0).11 This in turn reduces output (x i < 0) and forces the central bank to implement an expansionary and thus inflationary monetary policy (π > 0).

As for country i's equilibrium spending gap (g i -g), it can either be positive or negative, depending on the value of θ i and α. For instance, when α > θ i , government i pays high attention to its spending level (α high) whereas its ability to hedge against spending disturbances is relatively low (θ i low). α > θ i also implies that α/θ i > 1, which means that government i is more preoccupied by its spending disturbances (given the high importance it attaches to spending and its low ability to hedge against the disturbances) then by the economy's output level.12 In this case, government i does not hesitate to set strong fiscal pressure in order to finance excessive expenditures even though this discourages the private sector's productive investments. Here, country i's spending gap appears to be positive. In what follows, we qualify this type of government as fiscal-constrained, prioritizing expenditures imperatives at the expense of output. α/θ i > 1 can thus be interpreted as the degree of government i's fiscal-constraint ; the higher this ratio, the higher the government's constraint for short-term spending imperatives.

On the basis of these results, we can investigate the macroeconomic consequences of the governments' budget uncertainty.

Budget uncertainty is defined as the governments' incapacity to perfectly control their spending. Formally, budget uncertainty is inversely related to θ i : the lower θ i , the lower the government i's ability to hedge against spending disturbances.

From expression (9), we observe that budget uncertainty exacerbates the tax distortion due to the positive spending target. 13 We obtain the following result.

Result 1. A decrease in θ i , the government i's ability to hedge against spending disturbances translates into: i) higher levels of taxation and public spending and into a lower level of output in country i.

ii) an increase in the MU-wide inflation rate π -proportionally to 1/n corresponding to the country's weight in the CB's decision process.

Proof: See appendix. Indeed, when government i has low control over its spending (θ i low), it fears large disturbances and feels obliged to set high taxes in order to collect enough fiscal revenues to compensate for these disturbances. As a consequence to this strong fiscal pressure, output in country i is depressed. This in turn induces the central bank to implement a more expansionary and thus inflationary monetary policy, depending on the country i's weight in its decision process (1/n).

MU countries whose government has higher control over its spending (θ j high, ∀j = i) then suffer from the inflationary consequences of the CB's accommodating policy.

Macroeconomic effects of changes in monetary institutional parameters

After having clarified the implications of the governments' spending uncertainty, we can now proceed to examine the macroeconomic effects of a change in the CB's degree of inflation aversion as well as in the number of MU member countries.

Result 2. An increase in the central bank's degree of inflation aversion I translates into : i) higher taxes τ i and public spending g i as well as into lower output x i in the member countries where the government is fiscal-constrained (i.e. is characterized by α θ i > 1). ii) higher inflation in the MU if the majority of member countries are characterized by a relatively low θ i (i.e. θ i < θ 1 ).

Proof: See appendix. correspond to those observed in the standard case (see for instance Hefeker and Zimmer (2011) where a similar model is used with the assumption θ i → ∞).

This results states that when the member countries' governments are fiscal-constrained ( α θ i > 1), the CB's degree of inflation aversion exerts a detrimental impact on their macroeconomic performances.

Clearly, if the CB is highly inflation averse, it accommodates national tax hikes to a lesser extent, thereby rendering them more costly in terms of reduced output. Two opposite fiscal reactions to high CB inflation aversion are observable, depending on the governments' concern for spending disturbances relatively to their concern for output.

In the standard case where governments do not suffer from spending uncertainty (θ i → ∞), they adapt to high CB inflation aversion by setting low taxes. This improves their country's output performance but it also contributes to exacerbate their spending gap. Indeed, as has been observed earlier, in the case where α/θ i < 1 (and thus where θ i → ∞), the equilibrium spending level g i is lower than the target g, so that the deviation (g i -g) is negative. By reducing the tax level, and thereby the spending level g i , high CB inflation aversion finally aggravates this deviation.

However, in the case where governments are exposed to budget uncertainty (θ i has a finite value), high CB aversion to inflation makes them feel more vulnerable to spending disturbances.14 This in turn leads them to set higher taxes.

When governments are fiscal-constrained ( α θ i > 1), the fear of spending disturbances-effect prevails, explaining their high tax rate in response to high CB inflation aversion and consequently, their low output level and high spending gap (g i -g).

If these member countries are in the majority, the overall impact of CB inflation aversion on the MU-wide tax level is positive, translating into an expansionary monetary policy (see Eq. ( 8)). In the case where the MUgovernments' θ i is very low, this effect may be so strong that it compensates the direct inflation-reducing effect of CB inflation aversion highlighted in the standard literature on CB design. We then observe the counter-intuitive result where high CB inflation aversion is associated with high inflation.

If this is the case, the CB's concern for inflation eventually proves detrimental for real economic performances and this, not only in member countries where the government is fiscal-constrained but also in the others. Indeed, even though CB inflation aversion has a beneficial impact on production in these countries, it contributes to exacerbate spending deviations and inflation.

Result 3 examines the implications of budget uncertainty for the macroeconomic effects of a MU enlargement.

Result 3. An increase in the number of monetary union member countries: i) leads to higher taxes τ i and public spending g i as well as to lower output x i in countries with a fiscal-constrained government ( α θ i > 1). ii) translates into an increase in inflation for countries whose government is less vulnerable to spending disturbances (θ i higher) than the government of the new entrants.

Proof: See appendix.

The process of MU enlargement triggers similar macroeconomic effects than an increase in CB inflation aversion. Indeed, as can be observed from expression (8), both institutional changes (increase in n and in I) contribute to moderate the CB's accommodating response to national tax decisions. This has two implications: first, it aggravates the output-reducing impact of tax hikes and second, it exacerbates the governments' fear of spending disturbances. 15 How governments adapt to this situation depends on whether they are more concerned by output or by their spending and spending disturbances (i.e whether α/θ i is higher or lower than 1).

Fiscal-contrained governments with α θ i > 1 will prefer to raise taxes and spending even though this implies a deterioration of output. MU enlargement finally results into poorer output performance in their countries.

As for member countries whose government is not fiscal-constrained (with α θ i < 1), even if they observe an improvement in their output performance with the MU enlargement -this effect has already been stressed by Beetsma and Bovenberg (1998) -they may experience an increase in inflation due to the more accommodating policy the CB adopts in response to their new partner countries' higher fiscal pressure.

Conclusion

In this paper, we extend a simple MU-model with strategic monetary-fiscal interactions by considering the case where national governments suffer from budget uncertainty due to spending disturbances. An important element in our analysis is the governments' ability to hedge against these disturbances. Our results reveal that governments whose ability is low feel obliged to set high taxes, thereby deteriorating output in their country. Their decisions however also have economic repercussions in countries whose government is less vulnerable to spending disturbances as the CB then conducts a more accommodating monetary policy resulting in higher inflation in the MU.

It also appears from our analysis that the governments' fear of spending disturbances depends on the monetary institutional environment. Indeed, we show that this fear is exacerbated when the central bank has strong concern for inflation. Fiscal-constrained governments, being focused on short-term spending imperatives, thus react to central bank inflation aversion by increasing taxes even though this implies lower output. As a result, the central bank is tempted to accommodate these decisions with an expansionary and thus inflationary monetary policy. If budget uncertainty in the MU is very high, this mechanism may be so strong that it challenges the traditional result that CB inflation aversion contributes to lower inflation.

Moreover, by allowing for asymmetric vulnerability of national governments to budget uncertainty, we observe that the MU enlargement is likely to aggravate the heterogeneity of the member countries' economic situation: the most-vulnerable countries may experiment a decrease in their already-low output level whereas the least-vulnerable countries may see their output level increase. Besides, it is quite possible that member countries whose government has high control over spending disturbances will have to accept higher inflation in the MU. This is the case if the government of the new entrants is extremely vulnerable to spending disturbances, obliging the common central bank to set a very accommodating and thus inflationary policy.

This paper takes into account the existence of some budget uncertainty that can weaken national governments in a MU and proposes a modelling of this uncertainty. Its results open the discussion to the broader debate on the economic governance in a MU. How should monetary and fiscal institutions be designed for the optimal functioning of a MU in the presence of heterogeneous budget uncertainty of national governments? This question may be of interest for future research.

In minimizing government i's loss function (6) with respect to τ i , we obtain the following condition:

[n (1 + I) (1 + α) -1] τ i -[αn (1 + I)] i = αn (1 + I) g+[n (1 + I) -1] (π-π e )
(11) In maximizing government i's loss function ( 6) with respect to i , we obtain the following condition:

ατ i + (θ i -α) i = αg (12)
Combining both conditions leads to the following expression for government i's tax rate:

τ i = αθ i (1 + I) ng + (θ i -α) [n(1 + I) -1] (π -π e ) θ i [n (1 + I) (1 + α) -1] -α [n(1 + I) -1] (13)
3. Taking rational expectations (π e = π), we finally obtain the equilibrium tax rate τ i as given in equation ( 9).

Proof of Result 1:

i) Differentiating τ i , the equilibrium tax rate in country i, with respect to θ i leads to:

δτ i δθ i = -gα 2 n(1 + I)[n(1 + I) -1] {θ i [n (1 + I) (1 + α) -1] -α[n(1 + I) -1]} 2 < 0 (14)
Consequently, we have: δg i δθ i = δτ i δθ i < 0 and δx i δθ i = -δτ i δθ i > 0.

ii) By differentiating π, the equilibrium inflation rate in the MU, with respect to θ i , we obtain: δπ δθ i = 1 n δτ i δθ i < 0.

Proof of Result 2:

i ) Differentiating τ i with respect to I leads to:

δτ i δI = αngθ i (α-θ i )
{θ i [n(1+I)(1+α)-1]-α[n(1+I)-1]} 2 . This derivative is positive when α > θ i . As a result: δg i δI = δτ i δI and δx i δI = -δτ i δI are respectively positive and negative when α > θ i .

ii ) According to expression (8), we have: . This derivative is positive

for θ i < α[n(1+I) 2 -1]
n(1+I) 2 (1+α)-1 ≡ θ 1 . 16

16 Note that θ 1 > θ ; θ being the minimum value of θ i defined in footnote 10.

Hence, if for the majority of member countries θ i < θ 1 , then i n ∂(τ i /I) ∂I is positive, implying that δπ δI > is positive too.

Proof of Result 3:

i ) The macroeconomic effects of the monetary unification process are captured by considering the transition from the case where n = 1 to the case n > 1. These effects can thus be determined by differentiating the equilibrium expression of τ i , g i and x i with respect to n. This leads to:

δτ i δn = αgθ i (1+I)(α-θ i )
{θ i [n(1+I)(1+α)-1]-α[n(1+I)-1]} 2 . This derivative becomes positive when: α > θ i ⇒ α θ i > 1. Consequently, δg i δn = δτ i δn and δx i δn = -δτ i δn become respectively positive and negative for α θ i > 1.

ii ) We know from result 1 that countries with a high θ i display a low level of taxation. If they join a MU with partner-countries where θ i is relatively lower and thus taxation relatively higher, they may have to accept a more inflationary monetary policy as this latter is then set by a common CB on the basis of the average tax rate in the MU (see Eq.( 8)).

  -θi[n(1+I) 2 (1+α)-1]+α[n(1+I) 2 -1]} {Iθ i [n(1+I)(1+α)-1]-αI[n(1+I)-1]} 2

This is consistent with the EMU situation where governments face a balanced-budget requirement in the medium term.

The robust control approach has been introduced into economic models by[START_REF] Hansen | Robust permanent income and pricing[END_REF] andHansen and Sargent (2005, 2008). A number of recent papers has used this approach to determine the optimal monetary policy in the case where some uncertainty is faced by central bankers (see for instance,[START_REF] Giannoni | Does model uncertainty justify caution? Robust optimal monetary policy in a forward-looking model[END_REF][START_REF] Giannoni | Robust optimal monetary policy in a forwardlooking model with parameter and shock uncertainty[END_REF] Tillmann, 2009a,b, 2014[START_REF] Tillmann | Robust monetary policy under uncertainty about the lower bound[END_REF], Woodford, 2010 among others).

Yet, the variable τ i could also be interpreted as the tax rate net of public investment so as to capture the productivity enhancing role of public expenditures. See for instance[START_REF] Ismihan | Does central bank independence lower inflation[END_REF] who explicitly consider the composition of public spending by distinguishing between public sector consumption and investment.

The literature also refers to I as the CB's degree of independence. For a distinction between CB inflation aversion (or conservatism) and independence, see for instanceEijffinger and Hoeberichts (1998, 2008), Hughes Hallett and[START_REF] Hughes Hallett | Independence before conservatism: transparency, politics, and central bank design[END_REF],[START_REF] Weymark | Inflation, government transfers, and optimal central bank independence[END_REF] and[START_REF] Hefeker | Uncertainty and fiscal policy in an asymmetric monetary union[END_REF].

 6 For convenience, we assume that national governments share the same weight α as well as the same output target, which is normalized at zero.

The lower bound θ will be defined below in footnote 10.

We assume that, for each government, θ i is sufficiently high for the denominator of expression 9 to be positive. This implies:θ i > α[n(1+I)-1]n(1+I)(1+α)-1 = θ ; θ being the minimum value of θ in our model.

The first best outcome corresponds to a situation where: τ i = x i = π = 0 and g i = g.

Indeed, according to the government's loss function (Eq. 6), the relative weight attached to output is equal to 1.

 13 Note that budget uncertainty disappears when θ i → ∞, which means that government i has a perfect control over its spending. By setting θ i → ∞, equilibrium outcomes

This latter effect hinges on the observation that a higher degree of CB inflation aversion triggers an increase in i , the government i's anticipation of spending disturbances. Mathematically, this writes as follows: ∂ i ∂I . Calculations are available upon request.

This latter effect hinges on the observation that a higher number of member countries triggers an increase in i , the government i's anticipation of spending disturbances. Mathematically, this writes as follows: ∂ i ∂n . Calculations are available upon request.

Appendix

Derivation of the equilibrium tax rate τ i : Equilibrium outcomes are derived from a three-step procedure. Solving the game backwards:

1. We begin by minimizing the central bank's loss function (2) with respect to π and taking the member countries' aggregate supply functions (1) as given. We obtain:

where τ = i=L,H τ i /n.

2. We then solve government i's (i = L, H) minmax program.


Jules Gregory

Anita Paisant

Luisa Paulatto

Lucas Raynaud

Caroline Bertin

Anne Kerbaol

Marie-Pierre Vullierme

Valérie Paradis

Valérie Vilgrain

Maxime Ronot
email: maxime.ronot@aphp.fr

Prof Maxime Ronot

Limited added value of contrast-enhanced ultrasound over B-mode for the subtyping of hepatocellular adenomas

Keywords: "adenoma, liver cell", "liver neoplasms", "contrast media", "ultrasonography" -Specificity US -Ultrasound

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

INTRODUCTION

HCAs are monoclonal tumors that are now considered to be a heterogeneous entity with several subtypes [START_REF] Zucman-Rossi | Genotype-phenotype correlation in hepatocellular adenoma: new classification and relationship with HCC[END_REF]. They differ in their histopathological features, pathomolecular expression pattern, clinical behavior and have highly variable imaging features [START_REF] Laumonier | Hepatocellular adenomas: magnetic resonance imaging features as a function of molecular pathological classification[END_REF]. A molecular classification has divided HCA in several subgroups [START_REF] Bioulac-Sage | Hepatocellular adenoma subtype classification using molecular markers and immunohistochemistry[END_REF][START_REF] Nault | Molecular Classification of Hepatocellular Adenoma Associates With Risk Factors, Bleeding, and Malignant Transformation[END_REF][START_REF] Nault | Molecular classification of hepatocellular adenoma in clinical practice[END_REF]: HNF1-α inactivated adenomas (H-HCA), inflammatory adenomas (I-HCA), ß-catenin exon 3 mutated HCA (b ex3 HCA), ß-catenin exon 7/8 mutated HCA (b ex7,8 HCA) , Sonic Hedgehog adenomas (sh-HCA), and a fifth group with no particular morphological or molecular features [START_REF] Nault | Molecular Classification of Hepatocellular Adenoma Associates With Risk Factors, Bleeding, and Malignant Transformation[END_REF]. Each HCA subtype is potentially associated with different developmental risk factors [START_REF] Farges | Changing trends in malignant transformation of hepatocellular adenoma[END_REF][START_REF] Laurent | European experience of 573 liver resections for hepatocellular adenoma: a crosssectional study by the AFC-HCA-2013 study group[END_REF]. In the last update of the HCA classification, Nault et al. [START_REF] Nault | Molecular Classification of Hepatocellular Adenoma Associates With Risk Factors, Bleeding, and Malignant Transformation[END_REF] reported that b ex3 HCAs were associated with a higher risk of malignant transformation (47% transformed or borderline tumors vs 8% in other subgroups), recently described sh-HCAs appear to be associated with a higher risk of bleeding (71% of symptomatic bleeding in sh-HCA vs 14% in other subgroups), I-HCAs have both a risk of symptomatic bleeding (10%) and malignant transformation (10%), while H-HCAs are known to be more indolent. Thus, although patient management and treatment decisions are based on several features including patient gender and tumor size, accurate subtyping appears to be equally important to guide management, which can range from a conservative approach to surgical resection [START_REF]EASL Clinical Practice Guidelines on the management of benign liver tumours[END_REF].

Although liver lesions are often discovered incidentally on ultrasound, tumor characterization is limited on B-mode images and further imaging studies are usually needed. Thus far, most studies on HCA subtyping have relied on MR imaging [START_REF] Ronot | Hepatocellular adenomas: accuracy of magnetic resonance imaging and liver biopsy in subtype classification[END_REF] which is currently considered to be the most effective modality for the characterization of liver lesions [START_REF]EASL Clinical Practice Guidelines on the management of benign liver tumours[END_REF]. Nevertheless, contrast-enhanced ultrasound (CEUS) has significantly improved the detection and characterization of focal liver lesions by grayscale sonography [START_REF] Claudon | World Federation for Ultrasound in, U. European Federation of Societies for, Guidelines and good clinical practice recommendations for Contrast Enhanced Ultrasound (CEUS) in the liverupdate 2012: A WFUMB-EFSUMB initiative in cooperation with representatives of AFSUMB, AIUM, ASUM, FLAUS and ICUS[END_REF][START_REF] Quaia | Comparison of diagnostic performance of unenhanced vs SonoVue -enhanced ultrasonography in focal liver lesions characterization. The experience of three Italian centers[END_REF][START_REF] Bernatik | Unclear focal liver lesions in contrast-enhanced ultrasonography--lessons to be learned from the DEGUM multicenter study for the characterization of liver tumors[END_REF].

Because it is easy to perform, affordable and safe with no risk of nephrotoxicity, this technique has become increasingly popular in liver imaging and has become part of the routine work-up in some centers [START_REF] Tranquart | Role of contrast-enhanced ultrasound in the blinded assessment of focal liver lesions in comparison with MDCT and CEMRI: Results from a multicentre clinical trial[END_REF][START_REF] Strobel | Contrast-enhanced ultrasound for the characterization of focal liver lesions--diagnostic accuracy in clinical practice (DEGUM multicenter trial)[END_REF]. The development of second-generation intravascular microbubble contrast agents and the use of a very low mechanical index has significantly improved the continuous real-time assessment of microvascular flow and dynamic enhancement patterns by CEUS. It is now well known that CEUS is more effective than color and power Doppler ultrasound for the detection of tumor vascularity [START_REF] Strobel | Clinical evaluation of contrastenhanced color Doppler sonography in the differential diagnosis of liver tumors[END_REF][START_REF] Strobel | Tumor-specific vascularization pattern of liver metastasis, hepatocellular carcinoma, hemangioma and focal nodular hyperplasia in the differential diagnosis of 1,349 liver lesions in contrast-enhanced ultrasound (CEUS)[END_REF]. This is important because tumor vascularity is a key pattern for tumor characterization. HCAs contain sinusoids that are perfused solely by arteries and that lack portal veins, and HCAs subtypes harbor different microvascular characteristics. For instance I-HCAs contain clusters of small arteries surrounded by inflammatory infiltrates with foci of sinusoidal dilatation whereas H-HCAs do not present marked vascular abnormalities [START_REF] Bioulac-Sage | Hepatocellular adenoma subtype classification using molecular markers and immunohistochemistry[END_REF][START_REF] Grazioli | Hepatic adenomas: imaging and pathologic findings[END_REF]. Therefore, one may hypothesize that CEUS may be able to capture those microvascular differences. To date, most studies on CEUS have focused on the differentiation between HCAs and focal nodular hyperplasia (FNH), and data on the value of CEUS in HCA subtyping are limited [START_REF] Roche | Differentiation of focal nodular hyperplasia from hepatocellular adenomas with low-mechanical-index contrastenhanced sonography (CEUS): effect of size on diagnostic confidence[END_REF][START_REF] Taimr | A Model-Based Prediction of the Probability of Hepatocellular Adenoma and Focal Nodular Hyperplasia Based on Characteristics on Contrast-Enhanced Ultrasound[END_REF][START_REF] Kong | Contrast-enhanced ultrasound in combination with color Doppler ultrasound can improve the diagnostic performance of focal nodular hyperplasia and hepatocellular adenoma[END_REF].

Thus, the aim of this study was to compare the features of hepatocellular adenoma (HCA) subtypes in B-mode and contrast-enhanced ultrasound (CEUS) to estimate the possible value of CEUS for the subtyping of hepatocellular adenomas.

MATERIALS AND METHODS

Patient selection

This was a single center retrospective study. Institutional Review Board approval was obtained, and informed consent was waived.

All patients who had undergone contrast-enhanced ultrasound of the liver from January 2009 to October 2016 were searched for in the local Picture Archiving and Communication System (Carestream, Rochester, NY, USA). Only patients with pathologically proven HCAs and a complete CEUS cineloop were included in the study. In case of multiple HCAs, only tumors that were identified on CEUS were included. Clinical and biological information, including gender, age, body mass index, the use of oral contraceptives and/or anabolic steroids and liver function test results were retrieved from medical charts. The location, number and size of HCAs were collected from surgical notes and pathology reports or if these were not available, from MR imaging reports.

Figure 1 summarizes the flow chart of the study. A total of 1785 patients were identified. Six hundred and sixty-eight (37%) patients were excluded because there was no related pathology report. One thousand and fifty-four (59%) were excluded because there was no mention of HCA on the pathology report. Sixty-three patients had pathologically proven HCAs.

Twenty-nine of these (46 %) were excluded because CEUS data were not complete (25 women [96%] and one man, median age [Q1, Q3] 44.5 years old [36, 55], 14 I-HCAs and 12 H-HCAs). Included HCAs were either H-HCAs or I-HCAs, except for one HCA that was unclassified. This lesion was excluded from the analysis. The final population included 31 women [94%] and two men [6%], median age [Q1-Q3] 43.5 years old [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]).

Pathological Analysis

All cases were reviewed by a pathologist (_) with 25 years of experience in hepatocellular pathology. Tumors were classified according to morphological and immunohistochemical (IHC) criteria in the most recent version of the HCA classification [START_REF] Zucman-Rossi | Genotype-phenotype correlation in hepatocellular adenoma: new classification and relationship with HCC[END_REF][START_REF] Bioulac-Sage | Hepatocellular adenoma subtype classification using molecular markers and immunohistochemistry[END_REF][START_REF] Nault | Molecular Classification of Hepatocellular Adenoma Associates With Risk Factors, Bleeding, and Malignant Transformation[END_REF]. Details of the pathological analysis are reported in the Appendix.

In the presence of multiple lesions, we only included nodules that were identified by CEUS and could be correlated with pathologically-proven lesions.

Ultrasound and contrast-enhanced ultrasound examinations

All ultrasound studies were performed by senior radiologists (each with more than 10 years of experience in abdominal radiology) using Aixplorer (Supersonic Imagine, France) or Aplio 500 (Canon, Japan) ultrasound machines. First, a baseline investigation of the liver was performed in B-mode using gray scales with a 3.5 MHz curvilinear-array transducer. Dynamic real-time contrast-enhanced ultrasound was then performed using contrast-enhanced imaging, with the same 3.5 MHz curvilinear-array transducer, with a focus on the area of interest. A low mechanical index (<0.2) was selected to avoid microbubble disruption.

Contrast-enhanced ultrasound studies were performed immediately after the administration of 1,2-1,8 mL of sulfur hexafluoride-filled microbubbles according to the location and depth of the lesion (SonoVue, Bracco, Italy). A bolus was administered with a 20-Gauge peripheral IV cannula followed by 10 mL of saline and the timer was started. A second injection of Sonovue was performed when necessary or to explore a second lesion. The entire examination was recorded to allow for later review.

Imaging review

All images were retrospectively and separately reviewed by two abdominal radiologists (_ and _, with 3 and 15 years of experience in abdominal imaging, respectively). Reviewers were aware of the diagnosis of HCA but blinded to the pathological subtype. Interreader agreement was evaluated. In case of disagreement, a consensus reading was performed, which was considered to be the final reading for statistical analysis.

Readers were asked to evaluate in B-mode and for each lesion the degree of liver steatosis (none/mild, moderate/marked), echogenicity (classified as hypoechoic, isoechoic, or hyperechoic to the adjacent liver parenchyma), homogeneity (homogeneous or heteregeneous), shape (regular, lobulated) and the presence of calcifications inside the lesion.

Arterial (0-30s), portal-venous (31-120s), and delayed phase (121-360s) enhancement patterns were documented following Sonovue injection as hypoenhancing, isoenhancing and hyperenhancing. Other documented characteristics were enhancement homogeneity (homogeneous or not), filling direction (centripetal, centrifugal or mixed), the presence of central stellate arteries, non-enhancing zones and a peripheral rim of persistent enhancement or washout.

The degree of enhancement described the intensity of the signal in relation to the adjacent parenchyma [START_REF] Claudon | World Federation for Ultrasound in, U. European Federation of Societies for, Guidelines and good clinical practice recommendations for Contrast Enhanced Ultrasound (CEUS) in the liverupdate 2012: A WFUMB-EFSUMB initiative in cooperation with representatives of AFSUMB, AIUM, ASUM, FLAUS and ICUS[END_REF]. Centrifugal filling was defined as initial central enhancement that progressed to the periphery of the lesion over time. Centripetal filling was defined as initial peripheral enhancement that progressed to the center of the lesion over time. The arterial phase filling pattern was considered mixed if enhancement occurred throughout the lesion with no centrifugal or a centripetal filling. Central stellate arteries were defined as the presence of enhancing central arteries with a spoke-wheel or star-like morphology. A nonenhancing zone was defined as a non-enhancing area on all phases. A rim of persistent enhancement was described in the portal-venous or delayed phase when thicker or more conspicuous than the rim surrounding background lesions.

Washout was described as a reduction in enhancement in all or part of the liver lesion, resulting in hypoenhancement, and could apply to any enhancement even without arterial phase hyperenhancement. Washout was characterized as early (before 60 seconds) or late (at or after 60 seconds) depending on its onset after contrast administration [START_REF] Wilson | CEUS LI-RADS: algorithm, implementation, and key differences from CT/MRI[END_REF].

Statistical Analysis.

Qualitative variables and hepatocellular adenoma subtypes were compared in contingency tables using the Chi-square or Fisher's exact test. Data were expressed as medians with interquartile ranges for quantitative variables. All tests were 2-tailed; a p value <0.05 was considered to be statistically significant. We selected variables with a p value of <0.01 as discriminant features to test the performance of the different combinations. Kappa statistics were calculated to assess inter-reader agreement in each finding. Agreement was graded as κ <0.20, poor; 0.20-0.39, fair; 0.40-0.59, moderate; 0.60-0.79, substantial; or 0.80-1.00, almost perfect. All confidence intervals were calculated with 1000 bootstrap iterations.

Statistical analyses were performed using R software, version 3.1.3 (R Foundation for Statistical Computing, Vienna, Austria).

RESULTS

Clinical and pathology findings.

Clinical and laboratory results are summarized in Table 1, pathology results in Table 2. Twenty-two patients (65%) had I-HCAs while the other 12 had H-HCAs (33 %). One patient had both an I-HCA and an H-HCA, five had two I-HCAs, one had three I-HCAs, one had two H-HCAs and one had three H-HCAs.

The total number of

Pathological analysis was performed on resected specimens in 21 cases, and on biopsies in the remaining 13 cases.

Indications for liver CEUS were indeterminate lesions on MR imaging or on CT in one patient who could not undergo MR imaging (20/22, 91% of I-HCAs; and 3/12, 25% of H-HCAs), prebiopsy ultrasound (5/12, 42% of H-HCAs) and lesion follow-up (2/22, 9% of I-HCAs; and 4/12, 33% of H-HCAs).

B-mode ultrasound features.

Details of the features of B-mode ultrasound are provided in Table 3.

Briefly, all of the H-HCAs except one were homogeneously hyperechoic with well-defined borders (14/15, 93%). Most I-HCAs were either hypoechoic (23/29, 79%) or isoechoic (4/29, 14%) and 12 (41%) were heterogeneous whereas 17 (59%) were homogeneous. One of the two hyperechoic I-HCAs presented with grade 2 steatosis on pathological analysis while the other was a heterogeneous patchwork of hyperechoic and hypoechoic areas.

A statistically significant difference was found between the two subtypes of HCAs on B-mode ultrasound for echogenicity and homogeneity (p = 0.001 and 0.001), as well as for background liver steatosis (12/29 for I-HCAs vs. 0/15 for H-HCAs, p = 0.001). There was no difference in lesion size between homogeneous and heterogeneous HCAs (respectively, median size [Q1-Q3]: 3.9 cm [2.2-5.5] and 5.5 cm [3.3-6.5], p=0.17).

Contrast-enhanced ultrasound features.

The imaging findings on contrast-enhanced sonography are summarized in Table 4 and The most common H-HCAs enhancement patterns were hyperenhancement on arterial (14/15, 93%) images, followed by isoenhancement on portal phase (11/15, 73%), and isoenhancement on delayed phase (14/15, 93%) acquisitions. The most common enhancement combinations were "hyper-iso-iso" (10/15, 67%) (Figure 4), and "hyper-hyperiso" (3/15, 20%). One H-HCA was "iso-iso-iso", and another showed moderate late washout.

All of the 15 HCAs demonstrated homogeneous enhancement on all phases, without central stellate arteries, non-enhancing zones or peripheral rims with persistent enhancement.

Most HCAs demonstrated mixed filling (12/15, 87%).

The most common enhancement patterns of I-HCAs were marked hyperenhancement on arterial phase (27/29, 93%) images, isoenhancement on portal venous phase (15/29,52%), and isoenhancement on delayed phase (21/29, 72%) images. The most common enhancement combinations were "hyper-iso-iso" (13/29, 45%) (Figure 5), "hyper-hyper-iso" (7/29, 24%), "hyper-hypo-hypo" (4/29, 14%) (Figure 6), and "hyper-hyper-hyper" (2/29, 7%).

There was one "iso-iso-iso" one "hyper-iso-hypo", and another "iso-hypo-hypo" I-HCA.

Washout was detected in six I-HCAs (21%).

Heterogeneous enhancement on the portal-venous and delayed phase acquisitions was observed in six out of 29 I-HCAs (21%), and a non-enhancing zone was identified in three of them (10%). Central stellate arteries were identified in one hepatocellular adenoma (3%) which was the lesion with the "hyper-hyper-hyper" enhancing pattern. None of the 29 I-HCAs showed a rim of persistent enhancement. Most of them demonstrated mixed filling (21/29, 72%).The only statistically significant difference between the two subtypes of HCAs found on contrast-enhanced ultrasound was for enhancement homogeneity on portal and delayed phase (for both phases, 23/29 for I-HCAs vs. 15/15 for H-HCAs, p = 0.04) acquisitions. Heterogeneous HCAs tended to be larger than homogeneous HCAs on portal and delayed phase acquisitions (median size [Q1-Q3] for both phases, respectively: 6.3 cm [4-7] and 3.7 cm [2.1-5.3], p=0.06).

Washout was mainly observed in I-HCAs, but this was not significantly different (p = 0.27).

Two of the lesions with washout presented with liver steatosis. Early washout was detected in 2/6 (33%) I-HCAs. No difference in lesion size was observed between HCAs with washout and those with sustained enhancement (median size [Q1-Q3]: 5 cm [3.2-6.4] and 4.5 cm [2.9-6], respectively, p=0.58).

Combination of discriminant features

Discriminant features (p < 0.01) were all found in B mode images (tumor echogenicity, tumor homogeneity and the presence or absence of moderate or marked liver steatosis). The performances of the different combinations are presented in Table 5. When at least one out of three signs were present (absence of tumor hyperechogenicity, tumor heterogeneity, moderate or marked liver steatosis), the sensibility for the identification of H-HCA was 100%.

When tumor hyperechogenicity was combined with tumor homogeneity, the specificity for an H-HCA was 100%.

Inter-reader agreement

The inter-reader agreement and confidence intervals are shown in Table 3 for pre-contrast ultrasound and Table 4 for contrast-enhanced ultrasound. Almost perfect inter-reader agreement was only observed for the interpretation of liver and lesion echogenicity on B-mode ultrasound, arterial phase hyperenhancement on contrast-enhanced sonography, as well as rare features such as calcifications, central stellate arteries, non-enhancing zones and a peripheral rim of persistent enhancement. Conversely, agreement was poor for lesion contours on B-mode ultrasound. A fair to moderate level of inter-reader agreement was observed for other ultrasound features.

DISCUSSION

The results of this study show that there are some differences in the features of HCA subtypes on B-mode ultrasound and CEUS, especially H-HCA and I-HCA. Nevertheless, and despite these differences, the value of CEUS appears to be limited for the differentiation of subtypes because most CEUS features, and especially enhancement patterns, overlap between subtypes.

CEUS now plays a significant role in diagnostic algorithms of the liver [START_REF]EASL Clinical Practice Guidelines on the management of benign liver tumours[END_REF]. The World and European Federations for Ultrasound in Medicine and Biology 2012 Guidelines recommend CEUS for the characterization of focal liver lesions either incidentally discovered on routine ultrasound, or detected on ultrasound in patients with a known history of malignancy [START_REF] Claudon | World Federation for Ultrasound in, U. European Federation of Societies for, Guidelines and good clinical practice recommendations for Contrast Enhanced Ultrasound (CEUS) in the liverupdate 2012: A WFUMB-EFSUMB initiative in cooperation with representatives of AFSUMB, AIUM, ASUM, FLAUS and ICUS[END_REF].

CEUS has been mainly studied and evaluated for the differentiation between FNH (associated with specific features) and hepatocellular adenomas [START_REF] Roche | Differentiation of focal nodular hyperplasia from hepatocellular adenomas with low-mechanical-index contrastenhanced sonography (CEUS): effect of size on diagnostic confidence[END_REF][START_REF] Taimr | A Model-Based Prediction of the Probability of Hepatocellular Adenoma and Focal Nodular Hyperplasia Based on Characteristics on Contrast-Enhanced Ultrasound[END_REF][START_REF] Kong | Contrast-enhanced ultrasound in combination with color Doppler ultrasound can improve the diagnostic performance of focal nodular hyperplasia and hepatocellular adenoma[END_REF] in the liver. However, since the HCA subtypes differ in microvascular structure, with I-HCAs characterized by inflammation, congestion and sinusoidal dilatation, we hypothesized that they would show stronger and earlier enhancement than H-HCAs. Our results do not support this hypothesis, since most lesions of both subtypes showed arterial phase hyperenhancement. This does not support the results of the retrospective study published by Laumonier et al. that included H-HCAs and I-HCAs [START_REF] Laumonier | Role of contrast-enhanced sonography in differentiation of subtypes of hepatocellular adenoma: correlation with MRI findings[END_REF]. The authors have reported a significant difference in CEUS arterial phase enhancement patterns with 100% and 62% of I-HCAs and H-HCAs, respectively showing hyperenhancement [START_REF] Laumonier | Role of contrast-enhanced sonography in differentiation of subtypes of hepatocellular adenoma: correlation with MRI findings[END_REF]. In contrast, and in line with our results, Manichon et al. did not report any difference, with all lesions showing arterial phase hyperenhancement [START_REF] Manichon | Hepatocellular Adenoma: Evaluation with Contrast-Enhanced Ultrasound and MRI and Correlation with Pathologic and Phenotypic Classification in 26 Lesions[END_REF]. The present results could be due to the extreme sensitivity of low mechanical index CEUS to small amounts of circulating microbubbles in these heavily arterially supplied lesions. This would make it very difficult to grade the enhancement pattern even at very early contrast periods (8-12s post-injection), and thus decrease the discriminative value of this phase. Most HCAs showed indifferent filling (33/44, 75%), while centripetal enhancement, initially described on angiography and first reported by Kim et al. [START_REF] Kim | Focal nodular hyperplasia and hepatic adenoma: differentiation with low-mechanical-index contrastenhanced sonography[END_REF], and which is described as a common pattern in adenomas (ranging from 20 to 94%) [START_REF] Kong | Contrast-enhanced ultrasound in combination with color Doppler ultrasound can improve the diagnostic performance of focal nodular hyperplasia and hepatocellular adenoma[END_REF][START_REF] Laumonier | Role of contrast-enhanced sonography in differentiation of subtypes of hepatocellular adenoma: correlation with MRI findings[END_REF][START_REF] Manichon | Hepatocellular Adenoma: Evaluation with Contrast-Enhanced Ultrasound and MRI and Correlation with Pathologic and Phenotypic Classification in 26 Lesions[END_REF][START_REF] Wang | Hepatocellular adenoma: comparison between real-time contrast-enhanced ultrasound and dynamic computed tomography[END_REF], was not frequent in the current study (7/44, 16%).

One interesting finding was the heterogeneous appearance on both portal and delayed phase acquisitions that was only found in one fifth of I-HCAs, especially in large lesions. This pattern was not assessed by Laumonier et al. [START_REF] Laumonier | Role of contrast-enhanced sonography in differentiation of subtypes of hepatocellular adenoma: correlation with MRI findings[END_REF] or Wang et al. [START_REF] Wang | Hepatocellular adenoma: comparison between real-time contrast-enhanced ultrasound and dynamic computed tomography[END_REF]. In addition, the presence of non-enhancing areas, which probably represents the presence of necrosis, even if this was not significant, was also only found in 10% of I-HCA subtype lesions.

Another important finding was washout, and in particular its early onset, detected in two I-HCAs. Indeed, the distribution and retention of contrast micro-bubbles in the sinusoidal network that do not pass into the interstitial space explains why delayed phase CEUS is essential to distinguish benign lesions from malignancies [START_REF] Bhayana | Hypervascular liver masses on contrast-enhanced ultrasound: the importance of washout[END_REF][START_REF] Onofrio | Hypoechoic focal liver lesions: Characterization with contrast enhanced ultrasonography[END_REF]. During the delayed phase, the retention of microbubbles in most benign lesions is similar or greater than that in the adjacent parenchyma, while it is lower in malignancies. However, not all lesions with washout are malignant and it has been shown that HCAs can exhibit washout, perhaps due to the lack of portal venous tracts and terminal hepatic veins [START_REF] Zucman-Rossi | Genotype-phenotype correlation in hepatocellular adenoma: new classification and relationship with HCC[END_REF], resulting in gradual hypoechogenicity compared to the adjacent parenchyma [START_REF] Kong | Contrast-enhanced ultrasound in combination with color Doppler ultrasound can improve the diagnostic performance of focal nodular hyperplasia and hepatocellular adenoma[END_REF]. In the current study, washout was identified in one fifth of I-HCAs and in only one H-HCA. The washout rate in HCAs in two previous studies ranged from 37 to 53% in the study by Kim et al. [START_REF] Kim | Focal nodular hyperplasia and hepatic adenoma: differentiation with low-mechanical-index contrastenhanced sonography[END_REF] and up to 60% in that by Kong et al. [START_REF] Kong | Contrast-enhanced ultrasound in combination with color Doppler ultrasound can improve the diagnostic performance of focal nodular hyperplasia and hepatocellular adenoma[END_REF], whatever the subtype. In a recent study that mainly involved I-HCAs, seven of the 14 I-HCAs showed washout [START_REF] Garcovich | Contrast-enhanced ultrasound patterns of hepatocellular adenoma: an Italian multicenter experience[END_REF], while in the CEUS study by Laumonier et al.,[START_REF] Quaia | Comparison of diagnostic performance of unenhanced vs SonoVue -enhanced ultrasonography in focal liver lesions characterization. The experience of three Italian centers[END_REF] of the 17 I-HCAs showed washout [START_REF] Laumonier | Role of contrast-enhanced sonography in differentiation of subtypes of hepatocellular adenoma: correlation with MRI findings[END_REF]. These discrepancies are probably due to inter-reader variability. As shown by the overall moderate inter-reader agreement in the present study, CEUS is not an easy technique to assess subtle vascular features. Furthermore, inter-reader variability is known to be significant for washout, even when it is a major feature such as in hepatocellular carcinoma on MR imaging [START_REF] Davenport | Repeatability of diagnostic features and scoring systems for hepatocellular carcinoma by using MR imaging[END_REF]. In addition, we feel that the moderate and slow washout of HCAs [START_REF] Kong | Contrast-enhanced ultrasound in combination with color Doppler ultrasound can improve the diagnostic performance of focal nodular hyperplasia and hepatocellular adenoma[END_REF][START_REF] Dietrich | Differentiation of focal nodular hyperplasia and hepatocellular adenoma by contrast-enhanced ultrasound[END_REF] makes this agreement even weaker. We found no relationship between the presence of washout and HCA size or the underlying steatosis of the surrounding liver. We also did not find that lesion echogenicity on B-mode ultrasound significantly interfered with washout assessment.

In the current study the added value of CEUS over B-mode ultrasound was limited. Tumor echogenicity and heterogeneity on B-mode appeared to provide valuable and reproducible information on HCAs subtypes. Most H-HCAs were homogeneously hyperechoic due to the marked fat content of these tumors. A specificity of 100% was obtained when these two features were present. In other words, in the setting of suspicion of HCA, a hyperechoic and homogenous lesion on B-mode was necessarily an H-HCA. The sensibility to rule out an H-HCA reached 100% when these two features were combined with the absence of obvious liver steatosis on ultrasound. That is, a lesion that did not present with at least one of these features was not an H-HCA. Nevertheless, these results should be interpreted with caution because our population was limited to a preselected HCA sample. Thus, in our opinion, MR imaging remains the first line tool for tumor characterization and HCA subtyping [START_REF]EASL Clinical Practice Guidelines on the management of benign liver tumours[END_REF][START_REF] Ronot | Hepatocellular adenomas: accuracy of magnetic resonance imaging and liver biopsy in subtype classification[END_REF][START_REF] Tse | Qualitative and Quantitative Gadoxetic Acidenhanced MR Imaging Helps Subtype Hepatocellular Adenomas[END_REF] and the role of CEUS for the subtyping of HCAs remains unchanged from that of the EASL 2016 guidelines [START_REF] Liver | EASL Clinical Practice Guidelines on the management of benign liver tumours[END_REF]. Further studies are needed to assess whether CEUS has added or complementary value to MR imaging in distinguishing HCAs subtypes.

This study has several limitations. First its retrospective design makes post-hoc interpretations difficult. However, all CEUS were performed by highly experienced radiologists and only high-quality frame quality images, including complete cineloops and timers to ensure reliable phase identification, were included. Secondly, there was a possible recruitment bias because not all cases of HCAs are assessed by CEUS in our institution. Some of the selected patients may have undergone CEUS because of inconclusive MR images, resulting in assessment of atypical hepatocellular adenomas. To evaluate this bias, we recorded the indication for CEUS, and found that previous inconclusive MR images were mainly found in I-HCAs. Moreover, we only selected patients with pathologically proven HCAs, classified by morphological and immunohistochemical criteria. Also, even if this study is the largest cohort of HCAs evaluated by CEUS imaging, it only included the two major HCAs subtypes. Finally, we did not precisely correlate imaging patterns to pathological findings, because samples available for some of the lesions were obtained by core biopsy, and not all lesions were surgically resected.

In conclusion, the value of CEUS features appears to be limited for HCA subtyping since most of them, especially enhancement patterns, did not significantly differ between tumor subtypes. When the diagnosis of HCA is suspected on CEUS, B-mode features should be considered for tumor subtyping. Indeed, the combination of B-mode lesion hyperechogenicity, lesion homogeneity and the absence of obvious liver steatosis may be useful to distinguish inactivated HNF1-α from inflammatory HCAs. A, B-mode ultrasound demonstrates a 2 cm moderately hypoechoic and heterogeneous lesion located in segment VIII. B -D, Contrast-enhanced ultrasound (CEUS) images obtained 9 and 10 seconds after injection show arterial phase hyperenhancement with peripheral and intralesional vessels and mixed filling. E, At the end of the arterial phase, the lesion is homogeneously hyperenhanced. F, In the delayed phase, the lesion is isoechoic with no washout. 25) 0.12 H-HCA, HNF1-α inactivated hepatocellular adenoma; I-HCA, inflammatory hepatocellular adenoma; OP, oestroprogestative; BMI, body mass index; N, upper limit of normal values; ALT, Alanine aminotransferase; CRP, C-reactive protein. Unless otherwise noted, data are numbers of patients, with the percentage in parentheses. ♦ One patient had both an I-HCA and an H-HCA, five had two I-HCAs, one had three I-HCAs, one had two H-HCAs and one had three H-HCAs. * Median (Q1-Q3)

  HCAs was 44, including 29 (66%) I-HCAs, 15 (34%) H-HCAs. Median tumor size (Q1-Q3) was 4.5 cm (2.8-5.8). No significant difference was found between I-HCAs and H-HCAs for lesion size (median size [Q1-Q3]: 4.8 cm [3.2-6.3] vs. 3.7cm [2.1-5.3], p=0.18).

the enhancement patterns are shown in Figure 2 .

 2 The distribution of HCAs B-mode enhancement patterns in relation to lesion echogenicity are described in Figure3.

Table 3 -Table 4 -Table 5 -

 345 Comparison of ultrasound B-mode features of inflammatory (I-HCA) and HNF1-α inactivated HCA (H-HCA) subtypes. Comparison of contrast-enhanced ultrasonographic (CEUS) features of inflammatory (I-HCA) and HNF1-α inactivated HCA (H-HCA) subtypes. Performances of the different combinations of discriminant features (lesion echogenicity, lesion homogeneity, liver steatosis on B-mode) to identify H-HCA (n = 15) from I-HCA (n = 29).

Figure 1 -

 1 Figure 1 -Flowchart of the study population.

Figure 2 -

 2 Figure 2 -Frequency of the enhancement patterns in H-HCAs (a) and I-HCAs (b). The first column represents the HCA enhancement on arterial phase, and the second one on delayed phase. White corresponds to hyperenhancement, light grey to isoenhancement and dark grey to hypoenhancement.

Figure 3 -

 3 Figure 3 -Bar graph of the distribution of H-HCAs (a) and I-HCAs (b) enhancement patterns according to tumor B-mode echogenicity. White corresponds to hyperenhancement, light grey to isoenhancement and dark grey to hypoenhancement.

Figure 4 -

 4 Figure 4 -36-year-old female patient with an inactivated HNF1-α hepatocellular adenoma (H-HCA). A, B-mode ultrasound shows a 7 cm hyperechoic and homogeneous lesion located in segment VII. B -D, Contrast-enhanced ultrasound (CEUS) images obtained 10, 11 and 12 seconds after injection show arterial phase hyperenhancement with centripetal arterial filling. E, By the end of the arterial phase, CEUS shows a completely and homogeneously filled tumor.F and G, On portal and delayed phases, the lesion is isoechoic to the surrounding liver, without washout.

Figure 5 -

 5 Figure 5 -25-year-old female patient with an inflammatory hepatocellular adenoma (I-HCA).

Figure 6 -

 6 Figure 6 -37-year-old female patient with an inflammatory hepatocellular adenoma (I-HCA). A, B-mode ultrasound demonstrates a 6 cm slightly heterogeneous hypoechoic lesion located at the tip of segment VI. B -D, Contrast-enhanced ultrasound (CEUS) images obtained 10, 11 and 14 seconds after injection show arterial phase hyperenhancement with mixed filling. E -G, On portal and delayed phases, the lesion demonstrates progressive washout (arrowheads).

Table legends Table 1 -

 legends1 Clinical and biological characteristics of patients according to the HCA subtype

Table 2 -

 2 Pathological characteristics of HCA subtype.

Table 1 : Clinical and biological characteristics of patients according to the HCA subtype.

 1

		I-HCA	H-HCA	p
		patients (n=22)	patients (n=12)
		lesions (n=29 ♦ )	lesions (n=15 ♦ )
	Gender (%)			0.67
	-Female	21 (95)	11 (92)
	-Male	1 (5)	1 (8)
	Median age (Q1-Q3)	43.5 (35-52) *	43 (35-51) *	0.36
	BMI (kg/m 2 )	28 (22-32) *	24.2 (20-30) *	0.11
	BMI > 25 kg/m 2	15 (68)	3 (25)	0.07
	OP (or anabolic) use (years)	10 (0-14) *	0 (0-15) *	0.04
	OP (or anabolic) use > 2 years 18 (82)	2 (17)	0.02
	Diagnostic modality:			0.03
	Surgery	19 (86)	3 (25)
	Biopsy	3 (14)	9 (75)
	Laboratory tests (times N):
	γ-GT	2.7 (1-4) *	1.4 (1-2.9) *	0.10
	Transaminases (ALT)	1.6 (1-2.3) *	2.0 (1-3.4) *	0.26
	Alkaline phosphatases	1.6 (1-4.2) *	1.3 (1-2.5) *	0.19
	Inflammatory syndrome (CRP	8 (36)	0 (-)	0.01
	or fibrinogen)
	Solitary HCA	13 (59)	4 (33)	0.14
	Multiple HCA < 10	9 (41)	5 (42)	0.68
	Multiple HCA ≥ 10	0 (-)	3 (

 9) 0 (-) 2 0 (-) 0 (-) 3 0(-) 0 (-) H-HCA, HNF1-α inactivated hepatocellular adenoma; I-HCA, inflammatory hepatocellular adenoma. Unless otherwise noted, data are numbers of HCAs, with the percentage in parentheses. ♦ One patient had both an I-HCA and an H-HCA, five had two I-HCAs, one had three I-HCAs, one had two H-HCAs and one had three H-HCAs.

) 0 H-HCA, HNF1-α inactivated hepatocellular adenoma; I-HCA, inflammatory hepatocellular adenoma; CI, confidence interval. Data are numbers of HCAs, with the percentage in parentheses.