Yannick Fargier
email: yannick.fargier@developpement-durable.gouv.fr

Sérgio Palma Lopes

Cyrille Fauchard

Daniel François

Philippe Côte

DC-Electrical Resistivity Imaging for embankment dike investigation: A 3D extended normalisation approach

Keywords: Embankment hydraulic structures, Electrical Resistivity Imaging, Apparent resistivity concept, Normalisation

Levee, dike and earth embankment dam structures are difficult to assess because of their length and complexity. Managers often include geophysical investigations in the overall dike condition assessment and the DC-Electrical Resistivity Imaging (ERI) method is particularly applicable owing to its costeffectiveness and its potential sensitivity to internal erosion. However, due to the truly 3D nature of embankment dikes, implementing inline longitudinal tomographies along with conventional 2D inversion is likely to yield image artifacts. 3D effects from external causes (geometry, water reservoir) can be predicted and therefore we present a new approach based on redefining the normalisation principle to derive apparent resistivities from the measured data. The aim is to provide a set of pre-processed apparent resistivities that are not contaminated by external 3D effects and that yield more reliable results when processed within a 2D conventional inversion scheme. The presented approach is successfully applied to synthetic and real data sets, proving superior to the conventional 2D approach, although data acquisition

Introduction

Hydraulic earthfill structures such as the embankment dams, dikes and levees are essential infrastructures. A variety of functions are performed by hydraulic embankments in interest of populations such as energy production, waterway freight transport, water retention and storage and protection against flood events [START_REF] Fauchard | Geophysical and geotechnical methods for diagnosing flood protection dikes. Guide for implementation and interpretation[END_REF]Royet, 2006). However, embankment dikes and dams are subject to several phenomena such as water infiltration and internal erosion, which may lead to mechanical weakness and even breaching (Foster et al., 2000a;[START_REF] Fell | The state of the art of assessing the likelihood of internal erosion of embankment dams, water retaining structures and their foundations[END_REF].

Stability assessment methodologies more often include geophysical investigations for the identification of weak segments and for the optimization of geotechnical testing [START_REF] Carlsten | Radar techniques for indicating internal erosion in embankment dams[END_REF][START_REF] Mériaux | Diagnosis and management of plant growth on embankment dams and dykes[END_REF]. More precisely, the common geophysical practice includes high output investigation methods for fast zoning purposes, and DC-electrical resistivity imaging (ERI) for a higher resolution locating and characterizing of defaults [START_REF] Fauchard | Geophysical and geotechnical methods for diagnosing flood protection dikes. Guide for implementation and interpretation[END_REF]Royet et al., 2012). Thanks to recent improvements in data acquisition, ERI is now widely used for dike survey and monitoring [START_REF] Hennig | The effect of dike geometry on different resistivity configurations[END_REF]Sjödahl et al., 2006Sjödahl et al., , 2008;;Tsourlos et al., 1999). Advantages of ERI based techniques are numerous. They are moderately fast to implement, cost-effective and highly sensitive to DC-electrical conductivity contrasts commonly found in dikes due to state and variability of encountered materials (clay content, moisture content in vadose zone, temperature, porosity or compaction level) [START_REF] Johansson | Seepage monitoring in an earth embankment dam by repeated resistivity measurements[END_REF]. For cost-effectiveness reasons (dikes being long linear structures), ERI is usually applied in a conventional way, based on a line of equidistant electrodes parallel to the longitudinal direction (e.g. on the crest axis). When the layout includes two or more parallel lines, these are usually obtained or processed separately and inverted within two-dimensional (2D) type inversion schemes (except in few cases e.g. [START_REF] Cho | Crossline resistivity tomography for the delineation of anomalous seepage pathways in an embankment dam[END_REF], but still with a 2D type of inversion).

However, dike geometry and internal property distribution clearly violates such a simple 2D assumption leading to potential artifacts in resulting 2D images [START_REF] Hennig | The effect of dike geometry on different resistivity configurations[END_REF]Tsourlos et al., 1999). The development of data processing techniques for improving ERI relevance for dike investigation is clearly essential. Although fully 3D approaches would address the problem in a more rigorous manner, they do not benefit from the cost-effectiveness of 2D data acquisition procedures for dike assessment.

In this context, we propose to still carry out a classical 2D ERI acquisition technique and then to insert external 3D information in the data before performing the conventional 2D data inversion, similarly to previously published work for other applications [START_REF] Fox | Topographic effects in resistivity and induced polarization surveys[END_REF]Vickery and Hobbs, 2002). This information is included through a new data normalisation scheme that leads to apparent resistivities corrected for external 3D effects. In this paper, the common 2D ERI practice and related potential pitfalls are presented. Then, the conventional normalisation technique is i) redefined and ii) developed to address the specific limitations of dike longitudinal survey. The new normalisation approach takes into account the known neighbouring media (external causes of 3D effects). Finally, this new development is applied to both synthetic and real case data sets and results are compared with conventional 2D inversion results.

Application of 2D ERI investigation to embankment dikes: background and limitations

Common methodology

DC-ERI method is usually used to image rapidly and efficiently variations along the longitudinal or transverse directions of the surveyed dike (Sjödahl et al., 2006(Sjödahl et al., , 2008)). A 2D longitudinal survey implies the positioning of a line of electrodes along the structure whether it is on the crest, the slopes or at the toe of the dike (Figure 1(a)). But, in this case, the 2D assumption implies that the resistivity does not vary in the transverse direction perpendicular to the electrode line. From this point of view, a simple scheme representing a cross section of a hydraulic structure (Figure 1(b)) clearly shows that 2D inversion schemes cannot be used theoretically to process geo-electrical data from a longitudinal ERI survey. Obviously, the stronger the 3D in-situ features, the less rigourous the use of 2D inversion. Thus, it is important in a first approach to identify and quantify the effects related to the 3D behaviour of the surveyed structure and surroundings.

Potential pitfalls

Dikes and earth embankment dams are structures of which the 3D geometry and resistivity distribution have a disturbing effect on 2D inversion results. However, it is important to determine what 3D effects can be considered as disturbing or not. This study leads us to separate media having an effect on the measurements in two categories: i) the media that we need to be assessed (usually the dike body and foundation) ii) neighbouring media that are not to be assessed (e.g. the water reservoir).

Consequently, the effects of the dike topography and water reservoir can be considered as disturbing. The dike topography, the geometry of the reservoir and its resistivity distribution are all information that can be measured directly. Some national regulations regarding the safety of hydraulic structures require a monitoring of the topography of the structure and the water level in the reservoir (ex: by LiDAR techniques [START_REF] Mallet | Full-waveform topographic lidar : state-of-theart[END_REF]). This information can be directly supplied by the asset manager. Moreover, the electrical resistivity distribution in the water reservoir can also be measured with adequate equipment during the geophysical campaign without adding a significant cost.

We performed a parametric study to quantify the effects on the measurements caused by the dike geometry and the water reservoir. A Finite Element Method (Comsol Multiphysics software (COMSOL Multiphysics, 2009)) was used to solve the forward problem and simulate geo-electrical survey data.

Main principle and results are shown Figures 2 and3. The principle of this study was to simulate 4-electrodes (quadrupole) Wenner measurements on a dike surface, as shown in the Figure 2(a), in varying the inter-electrode spacing a and the distance d between the quadrupole and the water reservoir. The resistivity of the dike is 1000 Ohm-m whereas water resistivity is 100 Ohm-m. Then, the simulated transfer resistance (R t ) is obtained by numerically computing the potential difference between two potential electrodes divided by the injected current intensity (I). Then, the simulated R t is multiplied by the Geometrical Factor (GF) computed analytically (Wenner protocol for a flat homogenous half space) to obtain the apparent resistivity (ρ a ). The result of this numerical modelling is illustrated in the form of a matrix (Figure 2(b)). For this particular case (geometry, resistivity contrast), the effects of the water volume and the topography are clearly visible because the simulated apparent resistivities do not equal the resistivity of the dike body (1000 Ohm-m). A maximum negative effect (about -35 % relative to the dike resistivity) is found for an inter-electrode spacing of about 20 m and when the distance between the quadrupole and the reservoir is the lowest.

Two maximum positive effects (about +20 % relative to the dike resistivity) are observed for a minimum inter electrode spacing (a=1 m) and for measurements performed on topography edges. It can be noted that when the inter-electrode spacing is greater than 40 m the apparent resistivities increase again due to the limited width of the water reservoir in the model. It is confirmed that topography artificially increases conventionnaly calculated apparent resistivities (near the convex areas) whereas it can be seen that the water has an opposite effect. However, such results cannot cover all situations and serve as master curves on the field although they give useful and qualitative information and show that 3D effects are significant.

Principle, contribution and limitation of the normalisation technique

According to [START_REF] Kunetz | Principle of direct current resistivity prospecting[END_REF] the normalisation is an operation transforming the measure of R t into an observable that does not depend on the position of the electrodes and on the geometry of the investigated medium.

This method is widely used to compare measurements and qualitatively detect anomalies [START_REF] Loke | Lectures notes on 2-D and 3-D electrical imaging surveys[END_REF]. This operation is performed by means of the following expression:

ρ a = R meas t × GF = R meas t × ρ h R modρ h t (1)
Where ρ a represents the generalized apparent resistivity, R meas t the measured transfer resistance, GF the generalized Geometrical Factor and R modρ h t the simulated transfer resistance on a homogeneous medium of resistivity ρ h (the electrode positions and the medium geometry being identical in both real and synthetic models).

In consequence, Equation 1 defines the apparent resistivity as the resistivity that would be observed after the inversion of one measure alone, and assuming that the auscultated medium is homogeneous.

This principle is applied to the previous parametric study to normalize the effect of the topography. This implies to set all resistivities of the model to 1

Ohm-m by considering the reservoir and the dike as part of this homogeneous block [START_REF] Marescot | A general approach for dc apparent resistivity evaluation on arbitrarily shaped 3d structures[END_REF] and then apply Equation 1. Figure 3 or for the electrode positions and the medium topography (numerical GF based on a homogeneous medium of given geometry). This normalisation assumes that i) the dike body and foundation bloc is homogeneous, ii) the resistivity contrast between the disturbing medium (the water reservoir) and the investigated medium (the dike) is known and iii) the geometries of both media are known.

Normalisation of the effect of the water reservoir

However, even if it exists theoretical limitations, we admit here that the inversion of (even approximately) normalised apparent resistivities always leads to more reliable results than the inversion of raw data not accounting for geometry and water volume effects.

Impact of 3D effects and normalisation on inversion results

We think that is interesting to study the impact of the 3D effects on the imaging result. For this purpose, we present a numerical test of the gradually more complete normalisations (1: with a conventional GF, 2: with a generalized GF, 3: with the EN technique). The test is based on a model presenting a more complex geometry (varying cross-section) and six cylindrical heterogeneities crossing the dike body in the transverse direction (Figure 6). This normalisation technique supposes that a single resistivity ratio (contrast) is selected to compute all measured apparent resistivities over the whole dike surface. However, a real embankment dike is never homogeneous and its resistivity distribution remains unknown. Consequently, in real cases, the resistivity ratio between the dike and the water reservoir cannot be consid-ered as unique for a whole set of DC-resistivity measurements. Thus, the natural variability in embankment dikes and dams restricts the applicability of the suggested "EN" technique.

In order to demonstrate this limitation an additional synthetic test was performed. This study is similar to that used in the previous test (figure 6) except that the dike body is now composed of two contrasting stretches (Figure 8 3. An Enhanced Extended Normalisation approach

Concept

The previous section discusses two main limitations restricting the use of the EN technique : i) the resistivity contrast between the water reservoir and the dike has to be known to a certain accuracy level ii) The resistivity distribution of the dike body has to be sufficiently constant (homogeneous medium). In order to overcome these restrictions, we present a new approach that Enhances the Extended Normalisation (EEN) technique and better matches the original apparent resistivity definition [START_REF] Kunetz | Principle of direct current resistivity prospecting[END_REF].

As a consequence of [START_REF] Kunetz | Principle of direct current resistivity prospecting[END_REF] apparent resistivity definition (as derived in Equation 1), one can say that in the trivial case of a homogeneous medium (of arbitrary geometry) the apparent resistivity equals the true resistivity, irrespective of the medium geometry. Conversely, one can postulate that the inversion of a single measurement to adjust a single model parameter (the "true" resistivity of the investigated medium assumed to be homogeneous) would lead this true resistivity to tend to the measured apparent resistivity. Therefore, we suggest in this paper that an apparent resistivity can be considered as the result of a basic inversion process for which the particular electrode positions are considered and the model is assumed to be homogeneous. Although in real cases the medium can rarely be considered homogeneous, one can still carry out such a straightforward inversion for each individual measured apparent resistivity. This concept is the basis of the procedure presented in the following sections.

Methodology

The method presented within the framework of this article takes the form of a pre-processing function. This method modifies the measured data into apparent resistivities corrected for the effects of the topography and the water reservoir and partly accounting for the inhomogeneity of the dike body.

This methodology, schematized Figure 9, introduces three kinds of input parameters:

DEM = [X topo , Y topo , Z topo ]; (2)
ρ mes water ;

(3)

d mes = ρ mes a 1 ρ mes a 2 . . . ρ mes a N T ; (4)
DEM is a matrix containing elevation data used for building the numerical model (dike and reservoir). ρ mes water is the DC-electrical resistivity of the water reservoir. d mes represents the vector of the measured data (apparent resistivities), N is the number of quadrupole measurements. The procedure consists in two steps as follows.

Step 1

The objective of Step1 is to provide the "mean" resistivity of the dike needed as an input to Step2. A basic inverse problem is used for which the inverse model is only composed of two inversion "cells" (dike body and water reservoir). Within these cells of known geometry, the model is considered to be homogeneous. Therefore, only two model parameters are needed.

m step1 = ρ dike ρ water T ; (5)
Where ρ water is the resistivity of the water reservoir medium and ρ dike that of the dike body medium. In order to perform the inversion, the matrix of Fréchet derivatives is built by calculating the pole-pole sensitivities by means of the adjoint state method (Park and Van, 1991) and then by recombining the pole-pole to get the sensitivities associated to the electrode arrays (quadrupoles) in the acquisition protocol. The finite element method (see section 2.2) is used, with mesh deformation to simulate the topography, to solve the forward problem and compute the sensitivity matrix G step1 :

G step1 =           δρ mes
          ; (6)
As shown in Equation 6, the dimension of this sensitivity matrix is only [N,2] (which is quite different from most sensitivity matrices usually appearing in discrete geophysical inversion). The "effective" mean model m step2 is then adjusted by solving the basic inverse problem as follows ( 7) :

(G T step1 W T d W d G step1 + λ step1 I step1 )m step2 = G T step1 W T d W d (d mes ) (7)
where the diagonal of the matrix W d contains estimated measurements uncertainties and I step1 is the [2x2] identity matrix and λ step1 = [λ dike , λ water ] T is the damping factor which can be different for the water and the dike terms. Depending on the reliability of the a priori information on the water resistivity, a more or less high damping factor is selected for adjusting the resistivity of the water part of the model. However, the inverse problem is well-determined. so, the choice of these parameters does not modify the result radically. Finally, this step supplies resistivities for both the dike body and the water reservoir considered as homogeneous and that best explains the measured data in the sense of a least squares criterion.

m step2 = ρ step2 dike , ρ step2 water T ; (8)
However, this could have been performed, more simply but less accuratly, by selecting the mean of the shallowest apparent resistivity measurements (lowest inter electrode spacing) to limit the topography and reservoir effects (Figure 4).

Step 2

The only objective of the previous step is to provide an initial model for the main step presented here. The role of this main step is to yield apparent resistivities corrected for the effect of the water reservoir and the topography and accounting for the medium inhomogeneities.

Following the concept introduced in section 3.1, the idea is to estimate a resistivity for the dike body seen as homogeneous that best fits each measurement considered alone. Thus, by inverting individually each measurement gets one dike resistivity per measured datum and ends up with N resistivities. As previoulsly stated, it can be inferred from the apparent resistivity definition [START_REF] Kunetz | Principle of direct current resistivity prospecting[END_REF] that each resistivity estimated alone should then be regarded as an apparent resistivity that accounts for the medium geometry. In addition here, we propose that this apparent resistivity correction accounts for the presence of a water reservoir and supports dike body inhomogeneity. Therefore, we extend the concept saying that each apparent resistivity corrected for topography and water reservoir effects should be seen as a corresponding resistivity for the dike body considered as homogeneous.

To achieve this step a new inverse problem is developed (Equation 9) :

(G T step2 W T d W d G step2 + λI step2 )δm pert = G T step2 W T d W d (d mes -d calc ) (9)
Two new variables must be computed to solve this equation:

1. The modeled apparent resistivities (d calc );

d calc = ρ calc a 1 ρ calc a 2 . . . ρ calc a N T ; (10)
2. The matrix of the Fréchet derivatives (G step 2 ).

G step2 =            δd calc 1 δρ dike 0 • • • 0 δd calc 1 δρ water 0 δd calc 2 δρ dike • • • 0 δd calc 2 δρ water . . . . . . . . . . . . . . . 0 0 • • • δd calc N δρ dike δd calc N δρ water            ; ( 11
)
These two parameters are obtained by solving a complete forward problem with the determined resistivities of water reservoir and dike body from Step1.

In the sensitivity matrix (Equation 11), the left-hand side [N × N] diagonal block expresses the concept of each measurement being inverted individually. This is obviously different from usual sensitivity matrices where all data may be sensitive to all model parameters. Even though all N inversion parameters m 1 to m N represent the same physical parameter (the resistivity of the dike body when assumed homogeneous), they have different values for each measurement and have to be considered separately. Thus, they are N distinct parameters. In cases where the water resistivity and the reservoir geometry are well known (reliable a priori information), this diagonal block can be considered alone. This leads to a trivial scheme (equivalent to N independent processes individually applied to each measured datum). In the sensitivity matrix (Equation 11), we propose to add the right-hand side column to simultaneously estimate the water resistivity.

In the framework of this study, we prefer keeping the resistivity of the water reservoir as a free parameter of which range can be controlled by adjusting a damping factor (for example : λ reservoir = 1000 × λ dike ). This leads to the more general case where the water resistivity may be known inaccurately or may slightly vary in space and time.

The solution of Equation 9 is a perturbation vector δm pert that allows to update the inversion "model" containing the corrected apparent resistivities ρ corr a following Equation 12:

ρ corr a = [ρ step2 dike + δm pert (1 : N), ρ step2 water + δm pert (N + 1)] (12)
Thus, the corrected ρ corr a are the output of the presented pre-processing method, supplying the apparent resistivities that can be processed with 2D type of inversion software.

Synthetic results

The EEN technique is applied to the numerical study presented Figure Figure 12 presents the imaging results obtained with the Res2Dinv software for various normalisation levels applied to the same measured data set.

Concerning the inversion parameter λ, we imposed the same parameters as for the synthetic case (ratio=1000) and an equivalent noise measurement.

The mean resistivities resulting from Step1 are 1429 ohm-m and 79.9 ohm-m for the dike and reservoir respectively. The first global conclusion that would arise from the upper resistivity sections 12(a) with no normalisation of the reservoir or topography is that the dike is composed of two layers horizontal layers of varying thicknesses. The upper layer (5 to 8 m thick) appears to be more resistive (about 1000 to 2000 ohm-m) and shows some resistivity variations. The lower layer seems significantly less resistive (100 to 500 ohm-m)

and could be interpreted as the alluvial substratum of varying upper limit (between 8 and 12 m deep below the crest). These results show that the normalisation of the topography effect alone (Figure 12 shows some new heterogeneities between the dike body and the foundation (x=200 m) which may be critical for the safety assessment of the structure (internal erosion below the foundation). The last inversion result (Figure 12(d)) shows a very similar result to the previous one (12(c)) although it tends to limit significantly more the presence of the lower conductive layer, which will be discussed in the following section.

Concerning the four inversion results (figure 12) we do not prefer to say that a result is better than another, each one bringing of additional details.

We think that the better interpretation consists in comparing the results between them in order to see the possible 3D pitfalls. In this manner a more robust interpretation can be performed.

Discussion

In the previous result (Figure 12(d)) presenting a 2D-inversion of real data corrected for the combined topography and water reservoir effects, the bottom conductive layer was not fully removed. Consequently, two interpretations can be proposed.

From an optimistic point of view, one can say that this layer actually exists and that the correction procedure performed well providing a reliable image of the resistivity section.

From an opposite point of view, one could conclude that the subsisting conductive layer is an artefact due to an incomplete correction of the combined topography and water reservoir effects. This incomplete normalisation can come from resistivity variations in the water reservoir not taken into account. Those variations can have an effect on the measurements, especially for high resistivity contrast between the dike body and the water reservoir.

A solution would be to accuratly measure the resistivity variations in the water reservoir and to impose this distribution during the inversion process.

Finally, a more realistic point of view is to conclude that the presented correction approach has proved some efficiency although some 3D combined effects (due to the water reservoir and other external media, the topography and the internal resistivity distribution of the dike body) still remain.

It can be noted that such combined 3D effects cannot be supported by a data normalisation or correction procedure and can only be delineated by means of a fully 3D acquisition and inversion process. It could be noted that the study focuse on quite homogenous structures. Structures such as earth embankment dams often have strong heterogeneities (concrete or clay core) that could reinforce this phenomenon.

Moreover, this study presents a successful outcome for the new normalisation because the dike body present a strong contrast between the dike body and the water reservoir. In less contrasting cases, one can anticipate that the added value of the EEN technique would be lower.

The EEN procedure does not add a cost to the survey except for the water resistivity measurement. Concerning the computational cost, as we can see in Figure 9, in addition to the stage of inversion, this technique requires the calculation of 1 to 2 additional 3D forward problems as well as the calculation of two matrices of Fréchet derivatives of size Nx4. In general, for a common longitudinal DC-ERI survey based on 96 inline electrodes, this correction approach needs 10 minutes for the processing of 1500 quadrupole measurements with an E5405 Intel Xeon @2 GHz CPU and requires less than 4 Gb of RAM.

Conclusion

Nowadays, 2D-ERI is a commonly employed method within the overall condition assessment methodology hydraulic embankment structures. However, the use of a 2D inversion scheme leads to artifacts due to combined 3D effects. Those artifacts are often interpreted as real layers (alluvial foundation for the water reservoir effect) or anomalies and limit the robustness of the interpretation and the assessment of real anomalies. Numerical studies are used to demonstrate and quantify some 3D effects specific to dike investigations and their impact on the reconstructed models for 2D longitudinal surveys. Then a classical technique, the normalisation, is redefined and used to suppress the topography effects on the data. This technique is extended to the normalisation of the effect of the water reservoir in the case of dike in load condition. First, we simply assume that the embankment dike is homogeneous and second, we enhance this concept to arbitrary resistivity distributions. Results show that the EEN technique is able to support the non-homogeneity of the dike body and to satisfactorily suppress the effect of the water reservoir. When applied to real data, this new approach leads to an improved interpretation of the survey. Consequently, the technique proves usefull when data are contaminated by "external" 3D effects of which causes (topography, external neighbouring media such as a water reservoir) are well documented or directly identifiable on site without adding a real cost to the survey campaign. In this context, this technique could also be employed to normalise the effect of sheet piles, concrete facing and internal networks on measurements. It can be noted, that the effect of an internal core (rockfill dams for example) on the EEN procedure has not been studied in this paper.

Authors think that these hydraulic structures deserve specific attention (due to internal erosion) and further research. Our approach cannot account for all 3D effects, particularly those due to the actual dike resistivity distribution ("internal" causes). In conclusion, further studies are needed to build cost-effective inversion strategies well-adapted to long dike investigation at reasonable speed.

  Figure 3(a)(as compared to Figure 2(b)), the procedure nearly completely cancels the effect of the topography.Indeed, apparent resistivities do not show a dependency on the geometry as they do not exceed the true dike resistivity anymore and no effects are observed near edges (convex or concave areas). The apparent resistivity decrease zone in the graph only relates to the presence of the water reservoir. Consequently, this normalisation reveals the effect of the water reservoir alone on the measurements (conductive zone, figure3(a)). To reveal the topography effect alone, the relative variations ((ρ a 1 -ρ a 2 )/ρ a 2 ) between the

Figures 2 ,

 2 Figures 2, 3 and 4 have shown that the effect of the water reservoir can be predominant. This study also shows that it is possible to compute the theoretical effect of the water reservoir on the measurement and to normalise the topography effect. The objective of this section is to present an approach that allows to additionally normalise the water reservoir effect on the

  Figures 7(b) and 7(c) show respectively the inversion results after removing the effect of the dike topography and after removing the combined effects of the topography and water reservoir. This result clearly shows that the more conductive layer (Figure 7(a) and 7(b)) is in fact an artifact due to the effect of the water reservoir on the simulated measurements and that the highly resistive zone on the right hand side of the upper layer Figure 7(a) is partly influenced by the dike topography. Figure 7(c) shows that the locating of the six anomalies (due to the modeled heterogeneities) is clearly improved by applying the EN technique.

  (a)): A resistive stretch on the left hand side (2000 Ohm-m) and a more conductive stretch on the right hand side (1000 Ohm-m).

  Figures 8(b) to 8(d) present the results at the 4 th iteration of the 2Dinversion process (also based on the Res2dinv software). Figure 8(b) shows the resistivity section obtained when inverting data without normalisation approach. Figure 8(c) presents the case where the resistivity ratio is selected at its maximum value (2000/80=25) and shows a resistive layer artifact on the right hand side of the model due to the over-estimation for the resistivity contrast for this area. Figure 8(d) presents the opposite case with a conductive layer artifact on the left hand side due to an under-estimated resistivity contrast (1000/80=12.5). This result clearly shows that neglecting the spatial variability of the dike body when normalising the data inevitably underestimates (or inversely, overestimates) the resistivity contrast between the water reservoir and the investigated embankment. This leads to an unsuitable normalisation level (too strong or too weak) of the 3D external effects which in turn causes artifacts in the resulting image.

8

  and presented in the section 2.5 (same model, same acquisition protocol) with 6 anomalies buried in a double-compartment dike. The objective is to demonstrate the added value of the new normalisation procedure. Figure 10 shows the inversion result obtained with data normalized with the new method (EEN) and using the Res2Dinv commercial software. in order to obtain the corrected apparent resistivities we impose λ dike = 0.01 and λ water = 10 during Step1 and Step2 and a measurement noise of 0.5%. The mean resistivities resulting from Step1 are 1324 ohm-m and 80.1 ohm-m for the dike and reservoir respectively. The presented imaging result corresponds to the 4 th iteration with a RMS value lower than 1 %. This result shows the superiority of the new technique in this case as very few artifacts are present in the inversion result compared to Figures 8(a) to 8(c) where false layers could be denoted. Moreover, a better assessment of the anomalies is performed allowing a more robust interpretation of the imaging result.4. Case studyA survey in high output conditions ("roll-along" longitudinal survey) was performed in situ on a dike owned and managed by EDF (Electricité De France) in the Southern France (Figure11) in the framework of a more general assessment campaign. For this purpose, 96 electrodes were aligned with a 5 m electrode spacing on the central axis of the crest. The investigated dike is a water retaining structure leading water to a very close hydro-electricity production plant and was in full load condition at the time of the DC-ERI survey. The dike is 6 to 7 m high. The sealing is ensured by a concrete facing on the upstream side. We measured the resistivity of water on the surface of the reservoir with various locations and found a constant value of 80.2 ohm-m ±0.5 ohm-m. A Wenner-Schlumberger acquisition procedure including 1502 quadrupole measurements was performed. Figure11shows the electrode cable layout near the location of the water reservoir. Available information on the construction phase and the geological context of the area indicate that the dike body is composed of recent coarse alluvial deposits exploited in the vicinity and corresponding to the foundation of the structure.

  (b)) lowers the overall resistivity of the dike body and leaves room for what could be seen as an intermediate layer (upper limit between 3 and 6 m deep below the crest). The third result (Figure 12(c)) indicates that adding the normalisation of the water reservoir effect tends to push away the presumed conductive layer that could be seen at the bottom of the resistivity section (12(a) and (b)) and therefore increases the interpreted thickness of the dike body up to 13 m. Consequently, it can be concluded that this previous conductive layer in sections 12(a) and (b) is partly an artifact due to the effect of the water reservoir on the measured data. Moreover, the inversion result presented on Figure 12(c) (based on the normalisation extended to the water reservoir effect)

Figure 1 Figure 2 :Figure 3 :Figure 4 : 30 Figure 5 :

 1234305 Figure 1: 1(a) Perspective view of a schematic dike with various electrode cable layouts 1(b) schematic section of a dike in load condition presenting some barriers to infiltrations and three longitudinal cable layouts.

Figure 6 :Figure 7 :

 67 Figure 6: Bloc figure presenting (a) a perspective view of the dike model used for the numerical test exhibiting a varying topography and containing six heterogeneities and (b) a schematic longitudinal section of this model showing the location of the 6 conductive cross-sectional "pipes".

Figure 8 :

 8 Figure 8: Numerical test demonstrating the limitations due to dike inhomogeneity: (a) a longitudinal section of the dike model composed of two contrasting stretches and the six conductive anomalies and the 2D-inversion results based on (b) raw data (no normalisation applied), (c) with an underestimated and (d) an overestimated resistivity contrast when normalising the data for the combined effect of the water reservoir and the topography.

Figure 9 :

 9 Figure 9: Scheme illustrating the steps of the EEN technique.

Figure 10 :

 10 Figure 10: Figure shows the inversion result obtained with apparent resistivity data set normalized with the EEN technique. The true location of the six anomalies and the limit between the stretches are also illustrated.

Acknowledgment

The authors wish to thank EDF-CIH as well as the research projects ERINOH and DOFEAS for the funding and access to the site, and more particularly Jean Robert Courivaud and Julien Cintract for the assistance on site. We also thank Dr Mathieu Le Feuvre and the reviewers for the discussions and their impact on the article. Park, S.K., Van, G.P., 1991. Inversion of pole-pole data for 3-d resistivity structure beneath arrays of electrodes. Geophysics 56, 951-960. Royet, P., 2006. La surveillance et l'entretien des petits barrages. Ed. Cemagref, 78 p. Royet, P., Palma Lopes, S., Fauchard, C., Mériaux, P., Auriau, L., 2012. Rapid and cost-effective dike condition assessment methods: geophysics and remote sensing. Technical Report. Deliverable 32, FP7-ENV-2009 FloodProBE project. Sjödahl, P., Dahlin, T., Johansson, S., Loke, M.H., 2008. Resistivity monitoring for leakage and internal erosion detection at hällby embankment dam. Journal of Applied Geophysics 65, 155-164. Sjödahl, P., Dahlin, T., Zhou, B., 2006. 2.5d resistivity modeling of embankment dams to assess influence from geometry and material properties. Geophysics 71, G107-G114. Tsourlos, P.I., Szymanski, J.E., Tsokas, G.N., 1999. The effect of terrain topography on commonly used resistivity arrays. Geophysics 64, 1357-1363. Vickery, A.C., Hobbs, B.A., 2002. The effect of subsurface pipes on apparentresistivity measurements. Geophysical Prospecting 50, 1-13. Geophys. Prospect.


Julien Dubreuil

Gilles Salles

Juliette Bozzetto

Jeremie Tordo

Loïc Djaïleb

Alina Berriolo-Riedinger

Julien Leenhardt

Francesco Giammarile

Michel Meignan

Andrea Skanjeti

of 18F-FDG-PET/CT in lymphoma after treatment: a pictorial review

Keywords: evaluation, false positive, lymphoma, PET, pitfalls Usual and unusual pitfalls

come

Introduction

Fluorine-18-fluorodeoxyglucose ( 18 F-FDG) PET/computed tomography (CT) is now a standard of care for initial staging in Hodgkin lymphoma (HL), diffuse large B cell lymphoma (DLBCL), and follicular lymphoma (FL) [START_REF] Barrington | Role of imaging in the staging and response assessment of lymphoma: consensus of the International Conference on Malignant Lymphomas Imaging Working Group[END_REF][START_REF] Cheson | Recommendations for initial evaluation, staging, and response assessment of Hodgkin and non-Hodgkin lymphoma: the Lugano classification[END_REF]. Its high diagnostic performance leads to an up-staging in about 20% of cases. Furthermore, 18 F-FDG-PET/CT is recommended for both end-of-treatment and interim evaluation (after two or four cycles of chemotherapy in case of HL and DLBCL). For HL, 18 F-FDG-PET/CT shows very high negative and positive predictive values at the end-oftreatment and in the interim evaluation [START_REF] Gallamini | Early interim 2-[ 18 F]fluoro-2-deoxy-D-glucose positron emission tomography is prognostically superior to international prognostic score in advanced-stage Hodgkin's lymphoma: a report from a joint Italian-Danish study[END_REF], but lower negative and positive predictive values in DLBCL [START_REF] Mamot | Final results of a prospective evaluation of the predictive value of interim positron emission tomography in patients with diffuse large B-cell lymphoma treated with R-CHOP-14 (SAKK 38/07)[END_REF]. In FL, 18 F-FDG-PET/CT evaluation is recommended only at the end-of-treatment [START_REF] Barrington | Role of imaging in the staging and response assessment of lymphoma: consensus of the International Conference on Malignant Lymphomas Imaging Working Group[END_REF][START_REF] Cheson | Recommendations for initial evaluation, staging, and response assessment of Hodgkin and non-Hodgkin lymphoma: the Lugano classification[END_REF], with low negative and positive predictive values for relapse [START_REF] Dupuis | Impact of [( 18 )F]fluorodeoxyglucose positron emission tomography response evaluation in patients with high-tumor burden follicular lymphoma treated with immunochemotherapy: a prospective study from the Groupe d'Etudes des Lymphomes de l'Adulte and GOELAMS[END_REF].

The interpretation criterion commonly used and recommended is the Deauville five-point scale [START_REF] Barrington | Role of imaging in the staging and response assessment of lymphoma: consensus of the International Conference on Malignant Lymphomas Imaging Working Group[END_REF][START_REF] Cheson | Recommendations for initial evaluation, staging, and response assessment of Hodgkin and non-Hodgkin lymphoma: the Lugano classification[END_REF]. According to international recommendations, Deauville 4 (uptake moderately increased compared with the liver at any site) and 5 (uptake markedly increased compared with the liver at any site) are considered positive, whereas Deauville 1 (no uptake above the background) and 2 (uptake ≤ mediastinum) are considered a complete metabolic response, and Deauville 3 (uptake > mediastinum but ≤ liver) as a probable complete metabolic response. Few studies [START_REF] Itti | An international confirmatory study of the prognostic value of early PET/CT in diffuse large B-cell lymphoma: comparison between Deauville criteria and DeltaSUVmax[END_REF] have used semiquantification with delta-standardized uptake value (SUV) with good results, but this method should be more reproducible before being used in clinical practice [START_REF] Barrington | Role of imaging in the staging and response assessment of lymphoma: consensus of the International Conference on Malignant Lymphomas Imaging Working Group[END_REF][START_REF] Cheson | Recommendations for initial evaluation, staging, and response assessment of Hodgkin and non-Hodgkin lymphoma: the Lugano classification[END_REF].

Although 18 F-FDG-PET/CT is of great value in lymphoma evaluation, its specificity is limited, and many diseases can mimic a progression or a refractory disease [START_REF] Castellucci | 18 F-FDG PET in malignant lymphoma: significance of positive findings[END_REF], leading to a major impact on patient management. Recent studies have shown an excellent reproducibility between nuclear physicians, although lower between local and expert readers [START_REF] Barrington | PET-CT for staging and early response: results from the response-adapted therapy in advanced Hodgkin lymphoma study[END_REF][START_REF] Kluge | Inter-reader reliability of early FDG-PET/CT response assessment using the Deauville scale after 2 cycles of intensive chemotherapy (OEPA) in Hodgkin's lymphoma[END_REF], highlighting the necessity to recognize pitfalls in 18 F-FDG-PET/CT lymphoma evaluation. The aim of this pictorial review is to describe the most frequent pitfalls usually found in PET evaluation lymphoma, which can be responsible for falsepositive results and diagnostic errors with important consequences on patient management [START_REF] Groheux | Cryptorchidism as a potential source of misinterpretation in ( 18 )FDG-PET imaging in restaging lymphoma patients[END_REF].

Current infection/inflammation

The most frequent pitfall at interim and the end of treatment is related to infectious disease, in particular, lung infection. These are easy to recognize, especially if no lung disease was described before treatment. On PET images, the 18 F-FDG pattern is mild and diffuse, and CT images usually show small peribronchic opacities with a tree-in-bud sign [START_REF] Walker | Imaging pulmonary infection: classic signs and patterns[END_REF]. These results should not be related to a progressive disease and a CT control should be performed a few weeks after the end of antibiotic treatment. Conversely, in case of complete disease response with only one pulmonar nodule left, a second cancer should be suspected, especially in case of tobacco smoking (Fig. 1). Interstitial lung disease secondary to rituximab or bleomycine should also be well recognized, although CT scan is the method of choice for diagnosis [START_REF] Wagner | Rituximab-induced interstitial lung disease[END_REF].

A previous mediastinum bulky mass, according to our experience, can induce local infection with positive uptake in lung sub pleural parenchyma (Fig. 2). This type of false positive has already been reported and it is hypothesized that bulky mass leads to inflammatory changes in pleura and pulmonary parenchyma because of its anatomical contiguity [START_REF] Han | High incidence of falsepositive PET scans in patients with aggressive non-Hodgkin's lymphoma treated with rituximab-containing regimens[END_REF]. In the same way, splenic involvement with a mass observed on CT at baseline could induce the inflammatory process observed on 18 F-FDG-PET/CT after treatment (Fig. 3). A biopsy should be performed in case of doubt before considering partial response.

Thymus hyperplasia

Another well-known pitfall in thoracic evaluation is thymus hyperplasia, also called rebound hyperplasia. The thymus gland is the largest during childhood and gradually disappears in young adults [START_REF] Bogot | Imaging of thymic disorders[END_REF]. Thymus hyperplasia is frequently observed on follow-up until 6 months, and less frequently during the following 2 years [START_REF] Jerushalmi | Physiologic thymic uptake of 18 F-FDG in children and young adults: a PET/CT evaluation of incidence, patterns, and relationship to treatment[END_REF]. This phenomenon is secondary to chemotherapy treatment that induces suppression of thymus activity [START_REF] Choyke | Thymic atrophy and regrowth in response to chemotherapy: CT evaluation[END_REF][START_REF] Kissin | Benign thymic enlargement in adults after chemotherapy: CT demonstration[END_REF], followed by regrowth and hyperplasia in about 5% of adults [START_REF] Brink | Increased metabolic activity in the thymus gland studied with 18 F-FDG PET: age dependency and frequency after chemotherapy[END_REF]. 18 F-FDG uptake is usually described in young adults after systemic therapy [START_REF] Pagliai | PET scan evaluation of thymic mass after autologous peripheral blood stem-cell transplantation in an adult with non-Hodgkin's lymphoma[END_REF], but can persist after 40 years [START_REF] Langer | Thymic hyperplasia with hemorrhage simulating recurrent Hodgkin disease after chemotherapy-induced complete remission[END_REF] or occur before therapy in case of hyperthyroidism or corticotherapy [START_REF] Jerushalmi | Physiologic thymic uptake of 18 F-FDG in children and young adults: a PET/CT evaluation of incidence, patterns, and relationship to treatment[END_REF][START_REF] Moul | Thymic hyperplasia in newly diagnosed testicular germ cell tumors[END_REF]. Most patients (60%) showed an inverted V pattern of thymic uptake, (Fig. 4) with additional unilateral mediastinal extension A 66-year-old man with T lymphoma. Initial 18 F-FDG-PET/CT (a) showed an intense uptake of supradiaphragmatic and infradiaphragmatic lesions with increased 18 F-FDG uptake of a subsolid lung nodule depicted on CT (define as pure ground-glass nodule or part-solid ground-glass nodule). After four cycles of chemotherapy, a new evaluation 18 F-FDG-PET/CT was performed (b), showing complete response of all lesions except the lung subsolid nodule uptake (c, d) with a SUV max of 5.2 (arrows). A lung fibroscopy was performed and indicated infection, without neoplastic process certainly on an emphysematous bulla (another emphysematous bulla without infection is visible on the posterior chest wall). CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; SUV max , maximum standardized uptake value. A 60-year-old man with DLBCL with infradiaphragmatic lymph nodes and massive spleen involvement (mass on 18 F-FDG-PET/CT) (a). After four cycles of chemotherapy, 18 F-FDG-PET/CT was considered positive, showing one persistent spleen uptake on the initial site, with a SUV max of 6.07 and a Deauville score at 4 (b-d). A splenectomy was performed, showing on pathologic analysis a necrotic and inflammatory lesion without lymphoma infiltration. CT, computed tomography; DLBCL, diffuse large B cell lymphoma; 18 F-FDG, fluorine-18-fluorodeoxyglucose; SUV max , maximum standardized uptake value.

in 24% and focal midline uptake in 16% of studies (Fig. 5) [START_REF] Jerushalmi | Physiologic thymic uptake of 18 F-FDG in children and young adults: a PET/CT evaluation of incidence, patterns, and relationship to treatment[END_REF]. The SUV max is usually moderately intense (about 3,7), but can be above 4 in 44% of patients [START_REF] Jerushalmi | Physiologic thymic uptake of 18 F-FDG in children and young adults: a PET/CT evaluation of incidence, patterns, and relationship to treatment[END_REF]. In case of mediastinal mass at initial staging, it is always challenging to distinguish residual disease from thymus hyperplasia. MRI with diffusion weight-imaging and biopsy should be performed in doubtful cases.

Granulomatosis

A frequent pitfall is the persistent hilar and mediastinal lymph nodes uptake, which can be related to various diseases. Sarcoidosis should be systematically evoked because of its frequency [START_REF] Ungprasert | Epidemiology of sarcoidosis 1946-2013: a population-based study[END_REF] and its well-known association with lymphoma [START_REF] Brincker | The sarcoidosis-lymphoma syndrome[END_REF]. Granulomatosis can also be induced by new treatment including immunotherapy (pembrolizumab, nivolumab; see below) [START_REF] Montaudie | Pulmonary sarcoidlike granulomatosis induced by nivolumab[END_REF][START_REF] Paydas | Pulmonary sarcoidosis induced by the anti-PD-1 monoclonal antibody pembrolizumab or post-immunotherapy granulomatous reaction: which is more appropriate terminology?[END_REF]. The persistence of mediastinal lymph nodes on 18 F-FDG-PET/CT is not sufficient to affirm the relapse of lymphoma or refractory disease as Zinzani et al. [START_REF] Zinzani | Histological verification of positive positron emission tomography findings in the follow-up of patients with mediastinal lymphoma[END_REF] have shown that only 57% of positive lymph nodes found during the follow-up were true positive. In case of symmetric mediastinal-hilar lymph node uptake, a control of non-progression should be performed after a few months (Fig. 6). Conversely, in case of atypical uptake, a biopsy should be considered (with mediastinoscopy or endobronchial ultrasonography) before proposing another line of treatment.

Other nonspecific lymph nodes

Similarly, cervical lymph nodes are often persistent at the end of treatment on 18 F-FDG-PET/CT imaging. A recent study [START_REF] An | Clinical significance of posttreatment F-fluorodeoxyglucose uptake in cervical lymph nodes in patients with diffuse large B-cell lymphoma[END_REF] has shown the lack of specificity of F-FDG-PET/CT 6 months after the end of treatment showed a characteristic pattern of V inverted on MIP because of thymus hyperplasia, with a SUV max of 4.4 (arrows) (b-f). One-year follow-up confirmed this diagnosis. CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; HL, Hodgkin lymphoma; SUV max , maximum standardized uptake value. A 33-year-old man with HL. Initial 18 F-FDG-PET/CT (a) showed an intense uptake of a bulky mass and supradiaphragmatic lymph nodes. At the end of treatment, 18 F-FDG-PET/CT showed a moderate uptake of anterior mediastinum, which increased after 2 months (SUV max = 12.2) (b-d), leading to surgical resection. No lymphoma was found. CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; HL, Hodgkin lymphoma; SUV max , maximum standardized uptake value. A 36-year-old man with a supradiaphragmatic HL (a). After three cycles of chemotherapy, 18 F-FDG-PET/CT showed an intense 18 F-FDG uptake of inguinal lymph nodes (SUV max = 9.9) (b-d), which was not involved on initial staging (arrows). A biopsy was performed, showing the inflammatory process. CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; HL, Hodgkin lymphoma; SUV max , maximum standardized uptake value. positive cervical lymph nodes in the follow-up as only 9% of them were positive for lymphoma at the end of treatment. Furthermore, cervical lymph node hyperplasia are frequent in teenagers and children [START_REF] Hu | Cervical lymph node hyperplasia on [( 18 )F]-fluorodeoxyglucose positron emission tomography/computed tomography scan after treatment of children and adolescents with malignant lymphoma[END_REF].

In the same way, axillary lymph nodes can be a source of false-positive results. A usual case is tracer extravasation [START_REF] Wagner | A false-positive finding in therapeutic evaluation: hypermetabolic axillary lymph node in a lymphoma patient following FDG extravasation[END_REF][START_REF] Chiang | Potential false-positive FDG PET imaging caused by subcutaneous radiotracer infiltration[END_REF]: the lymph node is usually not enlarged and shows an adipose tissue component. In clinical practice, axillary lymph node uptake after treatment should be considered as pathologic only if associated with another abnormal uptake, increasing the rate of true positivity from 20.8 to 79.6%, [START_REF] Tsamita | Clinical significance of axillary findings in patients with lymphoma during follow-up with 18F-fluorodeoxyglucose-PET[END_REF]. In case of bilateral 18 F-FDG uptake, axillary hyperplasia should also be considered [START_REF] Muthukrishnan | Follicular hyperplasia: a potential falsepositive finding on PET/CT imaging in the evaluation of lymphoma[END_REF]. Finally, a second cancer can occur, in particular, breast cancer for women [START_REF] Tsamita | Clinical significance of axillary findings in patients with lymphoma during follow-up with 18F-fluorodeoxyglucose-PET[END_REF].

According to our experience, inguinal lymph nodes uptake is also responsible for a high rate of false positives [START_REF] Castellucci | Potential pitfalls of 18 F-FDG PET in a large series of patients treated for malignant lymphoma: prevalence and scan interpretation[END_REF]. A single inguinal lymph node uptake should not be subjected to biopsy, especially if there was no initial involvement in the same location (Fig. 7), and a followup after a few months can be performed. In doubtful cases, an ultrasonography with cytologic analysis should be performed.

Nonspecific digestive uptake

There is physiological 18 F-FDG uptake in the stomach, duodenum, small, and large intestine because of peristalsis, mucosal structures, or lymphocytic cell concentration. Thus, 18 F-FDG-PET/CT assessment of digestive involvement could be less specific at initial staging. At interim or end-of-treatment evaluation, reduced specificity is often related to ulcerative or mucosal lesions (Fig. 8) [START_REF] Yi | 18 F-FDG uptake and its clinical relevance in primary gastric lymphoma[END_REF][START_REF] Phongkitkarun | Lymphomatous involvement of gastrointestinal tract: evaluation by positron emission tomography with ( 18 )F-fluorodeoxyglucose[END_REF].

Brown adipose tissue activation

Brown fat tissue is a well-known potential source of misinterpretation. Its involvement in cold-induced and diet-induced thermogenesis [START_REF] Mar Gonzalez-Barroso | The human uncoupling protein-1 gene (UCP1): present status and perspectives in obesity research[END_REF] leads to tissue activation, which can induce intense 18 F-FDG uptake in the supraclavicular area, mediastinum (anterior and posterior), and in the perirenal area [START_REF] Truong | Focal FDG uptake in mediastinal brown fat mimicking malignancy: a potential pitfall resolved on PET/CT[END_REF]. These uptakes should not be considered an incomplete response on 18 F-FDG-PET/CT evaluation. Conversely, an intense and diffuse uptake of brown adipose tissue should not mask an incomplete response (Fig. 9). In doubtful cases, repeating 18 F-FDG-PET/CT after appropriate premedication by propranolol or diazepam is necessary [START_REF] Soderlund | Reduction of FDG uptake in brown adipose tissue in clinical patients by a single dose of propranolol[END_REF][START_REF] Rakheja | Intravenous administration of diazepam significantly reduces brown fat activity on 18 F-FDG PET/CT[END_REF][START_REF] Boellaard | FDG PET/CT: EANM procedure guidelines for tumour imaging: version 2.0[END_REF].

Fat necrosis

Another source of false-positive results is fat mesentery necrosis, described in few case reports [START_REF] Akiyama | False positive ( 18 )F-FDG PET/CT uptake by fat necrosis during chemotherapy for malignant lymphoma[END_REF][START_REF] Dubreuil | FDG PET/CT findings in abdominal fat necrosis after treatment for lymphoma[END_REF][START_REF] Belakhlef | Fat necrosis mimicking B-cell lymphoma: a PET/CT and FDG study[END_REF], and only one study [START_REF] Kashyap | High FDG activity in focal fat necrosis: a pitfall in interpretation of posttreatment PET/ CT in patients with non-Hodgkin lymphoma[END_REF] is available on this topic. According to our experience, fat necrosis should be considered in case of 18 F-FDG uptake corresponding to low-density tissue on CT images and is usually described in fat mesenteric folds. Furthermore, mesenteric lymph nodes are frequently described on the PET/CT baseline evaluation,

which can be related to panniculitis, especially if the other sites of initial disease completely responded (Fig. 10). However, confirmation by biopsy is required as 18 F-FDG-PET/CT cannot distinguish fat necrosis from lymphoma.

Bone response 18 F-FDG-PET/CT can be sufficient in baseline evaluation to assess bone marrow involvement in DBLCL and HL only in case of focal uptake [START_REF] Barrington | Role of imaging in the staging and response assessment of lymphoma: consensus of the International Conference on Malignant Lymphomas Imaging Working Group[END_REF][START_REF] Cheson | Recommendations for initial evaluation, staging, and response assessment of Hodgkin and non-Hodgkin lymphoma: the Lugano classification[END_REF]. However, focal bone uptake can be related to small fractures during bone regeneration after chemotherapy. These fractures are usually 18 F-FDG avid if recent [START_REF] Joshi | Honda sign on 18-FDG PET/CT in a case of lymphoma leading to incidental detection of sacral insufficiency fracture[END_REF] and can be difficult to distinguish from residual disease, especially in case of initial bone involvement in the same area (Fig. 11). In case of doubt, a control by 18 F-FDG-PET/CT should be proposed.

Lymphoma transformation

18 F-FDG-PET/CT can be used for the end-treatment evaluation of indolent lymphoma including FL. In case of incomplete response and increased lesion uptake (SUV max ), lymphoma transformation should be systematically evoked. Indeed, histological transformation can occur up to 20% of patients at the end of treatment [START_REF] Sarkozy | Risk factors and outcomes for patients with follicular lymphoma who had histologic transformation after response to first-line immunochemotherapy in the PRIMA trial[END_REF]. According to Bodet-Milin et al. [START_REF] Bodet-Milin | Investigation of FDG-PET/CT imaging to guide biopsies in the detection of histological transformation of indolent lymphoma[END_REF], transformation of indolent lymphoma should be considered if SUV max is above 14, with a positive predictive value and a negative predictive value of 93.9 and 95.3%, respectively. In this case, a new biopsy should be performed focused on the suspicious lesion (Fig. 12).

This transformation usually occurs on the initial pathologic site. However, discordant evolution with new site involvement and a complete response on initial sites have been described [START_REF] Alinari | Discordant response to chemotherapy: an unusual pattern of fluoro-deoxy-Dglucose uptake in heavily pre-treated lymphoma patients[END_REF]. According to our experience, lymphoma transformation is the main situation of discordant evolution. To our knowledge, discordant evolution with a complete response on initial sites and a proved progression on a new site are almost non-existent for HL and rare for DLBCL and FL, except in the central nervous system (Fig. 13) [START_REF] Burrows | Central nervous system Hodgkin lymphoma developing during systemic chemotherapy[END_REF], but because of the high risk of false positivity and the impact on treatment management, a biopsy should always be performed.

Second malignancy

18 F-FDG-PET/CT has excellent diagnosis performance for lymphoma, but is also used in others malignancies that can be detected at initial staging [START_REF] Papajik | Synchronous second primary neoplasms detected by initial staging F-18 FDG PET/CT examination in patients with non-Hodgkin lymphoma[END_REF] and at the end of treatment (Fig. 14). In particular, lung cancer [START_REF] Zhang | Unsuspected synchronous lung cancer unveiled on FDG PET after chemotherapy for non-Hodgkin lymphoma[END_REF] and colon cancer [START_REF] Zhuang | Incidental detection of colon cancer by FDG positron emission tomography in patients examined for pulmonary nodules[END_REF] should be considered especially after 50 years of age.

Postsurgical uptake

Increased 18 F-FDG uptake is systematically observed after surgical intervention, especially in the next 3 months after surgery. Thus 18 F-FDG-PET/CT is not

A 48-year-old man with FL. Initial 18 F-FDG-PET/CT (a) showed an intense uptake of supradiaphragmatic and infradiaphragmatic lesions with bulky mesenteric and a diffuse medullar uptake with positive bone marrow biopsy. At the end of treatment, an 18 F-FDG-PET/CT was performed (b) and showed a complete metabolic response. However, a focal and intense uptake of cauda equina appeared (SUV max = 12.75) without correspondence on CT (arrows) (c, d). A complementary MRI (e) was performed and showed a nodule contrast-enhanced of cauda equina, with bone adjacent edema of S1. The biopsy performed 3 months later on contiguous bone lysis confirmed the relapse of lymphoma, probably related to initial dural involvement. CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; FL, follicular lymphoma; SUV max , maximum standardized uptake value. recommended in lymphoma evaluation during the 6 weeks following surgery [START_REF] Boellaard | FDG PET/CT: EANM procedure guidelines for tumour imaging: version 2.0[END_REF]. Furthermore, 18 F-FDG uptake can last for months (Fig. 15), especially if a surgical device has been implanted. For example, inguinal hernia repair with implantation of a mesh prosthesis leads to persistent uptake during many years because of foreign body reaction (Fig. 16) [START_REF] Bahceci | Intense FDG uptake around the inguinal surgical mesh 5 years after operation: case report and review of the literature[END_REF][START_REF] Aide | Persistent foreign body reaction around inguinal mesh prostheses: a potential pitfall of FDG PET[END_REF].

Immunotherapy

During the last few years, immunotherapy (rituximab, brentuximab, ibrutinib, pembrolizumab, etc.) has shown efficacy, especially for HL [START_REF] Younes | Results of a pivotal phase II study of brentuximab vedotin for patients with relapsed or refractory Hodgkin's lymphoma[END_REF][START_REF] Moskowitz | Brentuximab vedotin as consolidation therapy after autologous stemcell transplantation in patients with Hodgkin's lymphoma at risk of relapse or progression (AETHERA): a randomised, double-blind, placebo-controlled, phase 3 trial[END_REF] and DLBCL [START_REF] Younes | Combination of ibrutinib with rituximab, cyclophosphamide, doxorubicin, vincristine, and prednisone (R-CHOP) for treatment-naive patients with CD20-positive B-cell non-Hodgkin lymphoma: a non-randomised, phase 1b study[END_REF]. However, this new therapy is responsible for false-positive results because of lymphocyte infiltration [START_REF] Skoura | False-positive 18 F-FDG PET/CT imaging: dramatic 'flare response' after rituximab administration[END_REF]. Thus, new criteria are available (Lyrics criteria) [START_REF] Cheson | Refinement of the Lugano classification response criteria for lymphoma in the era of immunomodulatory therapy[END_REF], which define three distinct types of indeterminate response: type 1, defined as increase of initial lesion of at least 50% in the first 12 weeks of treatment, for which a control in the next 12 weeks or a biopsy is strongly recommended; type 2, defined as increase of initial lesions or apparition of new lesions at any time during treatment for which a biopsy is strongly recommended; and type 3, defined as increase in 18 F-FDG uptake without a concomitant increase in lesion size fulfilling the criteria for progression disease. In some cases, patients can fulfill criteria for different types of indeterminate response (Fig. 17).

These therapies are also responsible for false-positive results related to treatment, such as granulomatosis, arthritis, hepatitis, pancreatitis, hypophisitis, and colitis [START_REF] Kwak | Cancer immunotherapy: imaging assessment of novel treatment response patterns and immune-related adverse events[END_REF]. All these side effects can be detected on 18 F-FDG-PET/CT and should not be confused with lymphoma (Fig. 18).

Conclusion

As we know, 18 F-FDG-PET/CT is now a standard of care to assess response to treatment. Most of the time, it is easy to identify complete response. However, we should bear in mind potential pitfalls that can lead to wrong response evaluation, in particular, lymph nodes uptake and thymus hyperplasia. Secondary malignancy is, according to our experience, a frequent source of pitfalls and should be considered systematically in case of unusual positive 18 F-FDG-PET on follow-up evaluation. A complementary CT or MRI scan should also be performed in case of doubt. Furthermore, it is crucial to keep in mind that a complete response on the initial site with the appearance of a new lesion in a new location is rare for HL and DLBCL, but more frequently in FL, especially in case of lymphoma transformation. Finally, a biopsy should be performed to prove residual disease, especially in the case of treatment by immunotherapy.

Fig. 1

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Fig. 2 (

 2 Fig. 2

Fig. 3

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18

 18

Fig. 5

 5 Fig. 5

Fig. 6

 6 Fig. 6

  A 68-year-old woman with FL. Initial PET/CT (a) showed pathologic uptake of supradiaphragmatic and infradiaphragmatic lymph nodes (arrows on a).18 F-FDG-PET/CT at the end of treatment (b) showed a complete response in the infradiaphragmatic area, but persistent and increased uptake of mediastinal lymph nodes (arrows on b) (d, e). Patient refused biopsy, but the 1-year18 F-FDG-PET/CT follow-up did not show any progression of mediastinal uptake and no relapse of lymphoma disease (c). A mediastinal granulomatosis was evoked. CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; FL, follicular lymphoma.

  Fig. 7

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Fig. 9 (

 9 Fig. 9

Fig. 10

 10 Fig. 10

  year-old man with a relapse of FL. The pretherapeutic18 F-FDG-PET/CT (a) showed a supradiaphragmatic disease associated with panniculitis (c), without clear 18 F-FDG uptake. After three cycles of chemotherapy (b), all initial pathologic sites showed complete response. Conversely, an intense18 F-FDG uptake appeared in mesenteric folds (arrows), without a mass clearly visible on CT (d, e). A biopsy was performed, in favor of fat necrosis. The 18 F-FDG-PET/CT performed one month later was considered negative. CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; FL, follicular lymphoma.

Fig. 11

 11 Fig. 11

  year-old man with DLBCL. Initial PET/CT showed a large sacral lesion (SUV max = 26.9) with supradiaphragmatic lymph nodes (a). After three cycles of chemotherapy, interim18 F-FDG-PET/CT showed a clear response (b), except a persistent focus of the right sacrum (SUV max = 7) (arrows on d) (c, d). On CT images, there was a fracture line corresponding to the focal uptake (arrows on d). Treatment was continued and no relapse has been reported after 6 months. CT, computed tomography; DLBCL, diffuse large B cell lymphoma; 18 F-FDG, fluorine-18-fluorodeoxyglucose; FL, follicular lymphoma; SUV max , maximum standardized uptake value.

Fig. 12

 12 Fig. 12

  year-old man with lung MALT lymphoma. Initial18 F-FDG-PET/CT (a) showed a moderate uptake of a pathologic lesion located in the left lung (SUV max = 6.4) (c, d) associated with a subcarenar lymph node (SUV max = 8.4). After six cycles of chemotherapy, a new evaluation18 F-FDG-PET/CT was performed (b) and showed a decrease in the size of the lung lesion on CT (f), whereas an increase of uptake was observed on18 F-FDG-PET (arrow on b) (e). SUV max reached 29.4. A new biopsy confirmed a transformation in B cell lymphoma. CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; MALT, mucosa-associated lymphoid tissue; SUV max , maximum standardized uptake value.

Fig. 13

 13 Fig. 13

Fig. 14

 14 Fig. 14

  year-old woman with HL. Initial 18 F-FDG-PET/CT (a) showed intense and suspicious uptake of supradiaphragmatic and infradiaphragmatic lymph nodes. At the end of treatment, few peripancreatic lymph nodes persisted. After 1 and 5 years of follow-up, and because of the significant evolution on18 F-FDG-PET/CT (b-d), a diagnosis of neuroendocrine tumor was suggested (arrows on b-d), confirmed by angio-CT (arrow on e) (e) and cephalic duodenopancreatectomy. CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; HL, Hodgkin lymphoma; SUV max , maximum standardized uptake value.

Fig. 15

 15 Fig. 15

  year-old man with nodular lymphocyte predominant HL. Initial 18 F-FDG-PET/CT (a) showed an intense uptake of supradiaphragmatic and infradiaphragmatic lesions with splenic, liver, and renal involvement. At the end of treatment, an18 F-FDG-PET/CT was performed (b), showing a lung infection and persistent uptake in the axillary area (SUV max = 5), without the corresponding nodule on CT (arrows) (c, d). Because of the initial biopsy performed in the same site, a postsurgery uptake was considered. A control 6 months after the end of treatment showed no lymphoma cells, but inflammatory scarring tissue, and confirmed the diagnosis. CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; HL, Hodgkin lymphoma; SUV max , maximum standardized uptake value.

Fig. 16

 16 Fig. 16

  year-old man with DLBCL. Initial 18 F-FDG-PET/CT (a) showed an intense uptake of a supradiaphragmatic and infradiaphragmatic lymph nodes. An interim 18 F-FDG-PET/CT after four cycles (b) of chemotherapy showed a complete response, except in the right inguinal area (SUV max = 12) (arrows) (c, d). CT images findings evoked a previous inguinal hernia surgery. Patient had a history of right inguinal hernia repair that was performed 4 years ago. CT, computed tomography; DLBCL, diffuse large B cell lymphoma; 18 F-FDG, fluorine-18-fluorodeoxyglucose; SUV max , maximum standardized uptake value.

Fig. 17

 17 Fig. 17

  year-old patient with a relapse of HL after allogeneic stem cell transplantation.18 F-FDG-PET/CT before treatment with nivolumab (a) showed an intense uptake of supradiaphragmatic lesions. After seven cycles of chemotherapy with nivolumab (b), few lesions (arrow) increased of18 F-FDG uptake in right cervical nodes and right axillary lymph nodes (for right cervical nodes: SUV max 13.4 vs. 7.4 before treatment) without an increase in lesion size (immune response type 3).18 F-FDG-PET/CT performed 3 months later (c) showed an excellent partial response of these lesions, without significant metabolic or morphologic changes, and confirmed treatment efficacy. CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; HL, Hodgkin lymphoma; SUV max , maximum standardized uptake value.

Fig. 18

 18 Fig. 18

  year-old woman with HL. Initial 18 F-FDG-PET/CT (a) showed an intense focus uptake into the lung because of a relapse, proven by biopsy. After eight cycles of chemotherapy with pembrolizumab (b), few new lesions were observed in the mediastinohilar area (arrows) (b). A granulomatosis induced by immunotherapy was suspected, especially because of the fact that the initial lung lesion disappeared.18 F-FDG-PET/CT performed 6 months later (c) showed global stability and confirmed a false-positive result because of immunotherapy. CT, computed tomography; 18 F-FDG, fluorine-18-fluorodeoxyglucose; HL, Hodgkin lymphoma; SUV max , maximum standardized uptake value.

Acknowledgements

Conflicts of interest

There are no conflicts of interest.