Claire Rossignol

Florent Sureau

Emilie Chouzenoux

Claude Comtat

Jean-Christophe Pesquet

A BREGMAN MAJORIZATION-MINIMIZATION FRAMEWORK FOR PET IMAGE RECONSTRUCTION

Keywords: PET image reconstruction, Poisson noise, Majorization-Minimisation, Bregman divergence, GPU implementation

Positron emission tomography (PET) is a quantitative imaging modality widely used in oncology, neurology, and pharmacology. The data acquired by a PET scanner correspond to projections of the concentration activity, assumed to follow a Poisson distribution. The reconstruction of images from tomographic projections corrupted by Poisson noise is a challenging ill-posed large-scale inverse problem. Several available solvers use the majorization-minimization (MM) principle, though relying on various construction strategies with a lack of unifying framework. This work fills the gap by introducing the concept of Bregman majorization. This leads to a unified view of MM-based methods for image reconstruction in the presence of Poisson noise. From this general approach, we exhibit three algorithmic solutions and compare their computational efficiency on a problem of dynamic PET image reconstruction, either using GPU or CPU processing.

INTRODUCTION

Positron emission tomography (PET) is a quantitative medical imaging modality providing information on various physiological processes (e.g. tumor uptake in oncology, concentration of receptors, binding constant in pharmacology, etc). During PET acquisition, a radiotracer emits positrons that annihilate in the body of the patient with an electron, resulting in the emission of two back-to-back photons which can then be detected in coincidence by scintillation crystals located around the patient. The measured count data in PET is modeled as a Poisson random variable with mean related to the projection of the activity concentration [START_REF] Vardi | A statistical model for positron emission tomography[END_REF]. Reconstructing images of this activity concentration (or related physiological parameters) is therefore an ill-posed tomographic inverse problem.

Typical PET image reconstruction relies on the minimization of a penalized cost function, gathering a data fidelity term accounting for the Poisson nature of the noise and a regularization term incorporating priors on the sought image. Probably the most commonly used PET reconstruction algorithm in clinical routine is ML-EM (Maximum-Likelihood Expectation Maximization) [START_REF] Dempster | Maximum likelihood from incomplete data via the EM algorithm[END_REF][START_REF] De Pierro | On the relation between the ISRA and the EM algorithm for positron emission tomography[END_REF] and its accelerated version OSEM (Ordered Subset Expectation Maximization) [START_REF] Hudson | Accelerated image reconstruction using ordered subsets of projection data[END_REF], which simply minimize the Poisson fidelity under positivity constraints. Penalized versions are also available [START_REF] De Pierro | A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography[END_REF][START_REF] Erdogan | Monotonic algorithms for transmission tomography[END_REF], typically assuming a smoothness prior on the gradients of the image. The extension of these approaches to the case of dynamic PET image reconstruction is explored in [START_REF] Wang | Acceleration of the direct reconstruction of linear parametric images using nested algorithms[END_REF][START_REF] Matthews | Direct reconstruction of parametric images using any spatiotemporal 4D image based model and maximum likelihood expectation maximisation[END_REF][START_REF] Pustelnik | Parallel algorithm and hybrid regularization for dynamic PET reconstruction[END_REF]. More recently, deep learning techniques have also been investigated [START_REF] Mehranian | Model-based deep learning PET image reconstruction using Forward-Backward Splitting Expectation-Maximization[END_REF][START_REF] Gong | Iterative PET image reconstruction using Convolutional Neural Network representation[END_REF][START_REF] Gong | PET image reconstruction using Deep Image Prior[END_REF] with the advantage of a fast running time when using GPU devices. Remarkably, most aforementioned PET reconstruction algorithms rely on the same optimization methodology, namely they are instances of MM (Majorization-Minimization) approaches. The MM paradigm, introduced in [START_REF] Ortega | Iterative Solution of Nonlinear Equations in Several Variables[END_REF] relies upon the concept of majorant approximation. It has become very popular because of its ability to yield simple, efficient, and well sounded algorithms, and it is widely used in several fields of data science such as machine learning, image restoration, and signal processing [START_REF] Sun | Majorizationminimization algorithms in signal processing, communications, and machine learning[END_REF].

In this paper, our contribution is twofold. First, we propose a general framework relying on the concept of Bregman majorization, that encompasses famous image MM-based algorithms for reconstruction from Poisson data. This includes a large variety of existing works [START_REF] De Pierro | On the relation between the ISRA and the EM algorithm for positron emission tomography[END_REF][START_REF] De Pierro | A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography[END_REF][START_REF] Erdogan | Monotonic algorithms for transmission tomography[END_REF][START_REF] Mehranian | Model-based deep learning PET image reconstruction using Forward-Backward Splitting Expectation-Maximization[END_REF], and even yields new resolution schemes. Second, we select three possible choices for Bregman majorants and perform an extensive comparative analysis of the three associated algorithms in terms of computational efficiency. Namely, we present time execution comparisons on a problem of dynamic 2D PET image reconstruction. We evaluate both CPU and GPU implementations.

The paper is organized as follows. We present the PET image reconstruction inverse problem and the required mathematical background in Section 2. We then introduce in Section 3 our novel Bregman majorization framework and illustrate its applicability through three examples of interest. Section 4 evaluates these three solutions on the regularized reconstruction of a spatio-temporal PET sequence, and Section 5 provides some concluding remarks.

NOTATION AND BACKGROUND

Problem formulation

We consider the reconstruction of an image denoted by x ∈ [0, +∞) N , from an observed noisy sinogram y ∈ [0, +∞) M given by y = P(Hx + b),

where H ∈ [0, +∞) M ×N is the projection matrix modelling the geometry of the acquisition system [START_REF] Ortega | Iterative Solution of Nonlinear Equations in Several Variables[END_REF], b ∈ (0, +∞) M is a strictly positive background term (assumed to be known) [START_REF] Ortega | Iterative Solution of Nonlinear Equations in Several Variables[END_REF] and P(•) models a Poisson noise corruption process. An efficient strategy to tackle the inverse problem of reconstructing x given y, b, and H, resorts to performing a maximum a posteriori estimate of x [START_REF] Ortega | Iterative Solution of Nonlinear Equations in Several Variables[END_REF]. This amounts to solving the constrained optimization problem:

minimize x∈[0,+∞) N (f (x) = L(x) + R(x)). (2)
Herabove, L : R N → (-∞, +∞] is the neg-log-likelihood function expressed as

(∀x ∈ R N ) L(x) = KL(Hx + b, y), (3)
where KL is the Kullback-Leibler divergence defined, for every

(u, v) ∈ R 2 , as KL(u, v) =      -v log u + u if u > 0 and v > 0, u if u ≥ 0 and v = 0, +∞ otherwise. (4)
Moreover, R : R N → (-∞, +∞] is a regularization term that incorporates prior knowledge on the sought image.

Majorization-Minimization

Various methods have been proposed in the literature to solve Problem (2) [START_REF] Lange | EM reconstruction algorithms for emission and transmission tomography[END_REF][START_REF] Hudson | Accelerated image reconstruction using ordered subsets of projection data[END_REF][START_REF] Ortega | Iterative Solution of Nonlinear Equations in Several Variables[END_REF][START_REF] Mehranian | Model-based deep learning PET image reconstruction using Forward-Backward Splitting Expectation-Maximization[END_REF]. Most of them belongs to the class of majorization-minimization (MM) approaches [START_REF] Ortega | Iterative Solution of Nonlinear Equations in Several Variables[END_REF][START_REF] Hunter | A tutorial on MM algorithms[END_REF]. MM approaches are efficient iterative methods that minimize an objective function f through the minimization of a sequence of more tractable surrogates satisfying a majorizing condition. A function

qz is a tangent majorant of f at z ∈ R N if, for every x ∈ R N , f (x) ≤ qz(x) and f (z) = qz(z).
At each iteration k ∈ N of an MM algorithm, the new iterate x k+1 is the minimizer of the tangent majorant of f at the current iterate x k . The MM algorithm then reads

(∀k ∈ N) x k+1 ∈ argmin x∈R N q x k (x), (5)
with x 0 an initial vector belonging to the domain of the majorant function. Various algorithms can be built from this generic idea, depending on the structure of the majorant function [START_REF] Jacobson | An expanded theoretical treatment of iteration-dependent majorize-minimize algorithms[END_REF]. This work brings a novel perspective on MM methods for PET reconstruction, recasting them within a Bregmanian framework.

Bregman divergences

A key mathematical tool in our approach is the Bregman divergence.

Let us recall the definition of Bregman divergence, introduced in 1967 in [START_REF] Bregman | The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming[END_REF]. Let ϕ : R N → (-∞, +∞] be a strictly convex function, which is twice differentiable on the interior int dom ϕ of its domain. The Bregman divergence associated with ϕ is defined, for every (x, z) ∈ (int dom ϕ) 2 , as

D ϕ (x, z) = ϕ(x) -ϕ(z) -∇ϕ(z) ⊤ (x -z). (6)
In a nutshell, the quantity D ϕ (x, z) compares the gap between the function ϕ at x ∈ R N , and its linear approximation around x evaluated at z ∈ R N .

PROPOSED APPROACH

In this section, we present the main methodological contribution of this paper. We show in Section 3.1 how Bregman divergences offer a both powerful and elegant framework for building tangent majorants for the objective function f involved in Problem (2), and then we derive in Section 3.2 a versatile MM algorithm to tackle this problem, so generalizing existing MM solvers from [START_REF] Mehranian | Model-based deep learning PET image reconstruction using Forward-Backward Splitting Expectation-Maximization[END_REF][START_REF] Erdogan | Monotonic algorithms for transmission tomography[END_REF].

A unifying Bregman majorization framework

Let us start by introducing the key notion of Bregman tangent majorant.

(∀x ∈ D) qz(x) = g(z) + ∇g(z) ⊤ (x -z) + DE z (x, z) g(x) ≤ qz(x). (7)
This definition generalizes previous concepts used for instance in [START_REF] Bauschke | Bregman monotone optimization algorithms[END_REF]. The main novelty here is that we allow the so-called Bregman metric DE z to vary with the reference point z. Up to the best of our knowledge, this has never been considered in the literature so far.

Starting from the above definition, we aim at building Bregman majorant functions of f in (2). Since f reads as the sum of two terms, we rely on the following useful additivity property.

Lemma 1. Let g1 and g2 be differentiable functions on an open set D ⊂ R N and let z ∈ D. Let E1,z (resp. E2,z) be strictly convex functions, which are differentiable on D, from which a Bregman tangent majorant of g1 (resp. g2) can be built. Let (α1, α2) ∈ [0, +∞) 2 , let θ ∈ R N , and let η ∈ R. Then a Bregman tangent majorant of x → α1g1(x) + α2g2(x) + θ ⊤ x + η is associated with α1E1,z + α2E2,z.

It is therefore possible to construct a Bregman tangent majorant of our cost function f , by simple affine combination of a Bregman majorant of the data fidelity term L and the regularization term R. In the following, we present three examples of strategies for building a Bregman majorant function for L.

Bregman majorant functions for Poisson data fidelity

Let us first focus on the majorization of function L defined in [START_REF] De Pierro | On the relation between the ISRA and the EM algorithm for positron emission tomography[END_REF]. For every m ∈ {1, . . . , M }, and x ∈ R N , let us define ℓm(x) = h ⊤ m x + bm > 0, with hm ∈ R N the m-th row of H. Then, on the positive orthant, Function (3) takes a finite value, namely it can be rewritten as

(∀x ∈ [0, +∞) N ) L(x) = M m=1 -ym log(ℓm(x)) + ℓm(x). (8)
We first show how judicious choices for the underlying Bregman divergence allows us to derive suitable majorants leading to simple MM updates.

Then, it can be shown that the Bregman tangent majorant of L for z ∈ (0, +∞) N , which is associated to E1,z is

(∀x = (xn) 1≤n≤N ∈ (0, +∞) N ) q1,z(x) =
We recover the separable majorant for L which was used to derive the recent FBSEM (Forward-Backward Splitting Expectation Maximisation) algorithm [START_REF] Mehranian | Model-based deep learning PET image reconstruction using Forward-Backward Splitting Expectation-Maximization[END_REF]. This algorithm is a regularised version of the MLEM algorithm from [START_REF] Lange | EM reconstruction algorithms for emission and transmission tomography[END_REF]. FBSEM is an MM algorithm whose majorant is built following a strategy initially introduced in [START_REF] De Pierro | On the relation between the ISRA and the EM algorithm for positron emission tomography[END_REF].

Example 2. For every z ∈ (0, +∞) N , let

(∀x ∈ [0, +∞) N ) E2,z(x) = N n=1 a2,n(z) x 2 n 2 , (12)
where, for every n ∈ {1, . . . , N },

a2,n(z) = M m=1 ym hm,n(zn + ζmbm) ℓm(z) c(zn, ρ). (13)
Hereabove, hm,n stands for the (m, n)-th entry of matrix H, and we set

c(zn, ρ) =      1 ρ 2 if zn = 0 - 2 zn
1 zn log ρ zn + ρ + 1 zn + ρ otherwise, (14)
The quantity N n=1 hm,n is assumed to be positive without loss of generality on H.

After some calculations, it can be proved that the Bregman tangent majorant of L at z associated to E2,z is

(∀x ∈ (0, +∞) N ) q2,z(x) = L(z) + ∇L(z) ⊤ (x -z) + N n=1 θn(z) 2 (xn -zn) 2 , (16)
where, for every n ∈ {1, . . . , N },

(∀z ∈ (0, +∞) N ) θn(z) = M m=1 c(zn, ρ) hm,n(zn + ζmbm) ℓm(z) , (17)
This quadratic separable majorant function can be obtained in a more classical manner by a clever combination of the majorant construction from [START_REF] Erdogan | Monotonic algorithms for transmission tomography[END_REF] and Jensen's inequality.

The two previous examples have illustrated that majorants used in popular MM algorithms for image reconstruction under Poisson noise are instances of the proposed Bregman framework. It is also possible to construct new majorants, as shown hereafter.

Example 3. Let us construct a variant of [START_REF] Gong | Iterative PET image reconstruction using Convolutional Neural Network representation[END_REF]. For every z ∈ (0, +∞) N , set

(∀x ∈ (0, +∞) N ) E3,z(x) = - N n=1 a3,n(z) log(xn + ρ) (18)
where, for every n ∈ {1, . . . , N },

a3,n(z) = M m=1 ym hm,n(zn + ζmbm) ℓm(z) , (19)
The same constants ρ and (ζm) 1≤m≤M as in the previous examples are used. The Bregman tangent majorant of L at z then reads

(∀x ∈ (0, +∞) N ) q3,z(x) = L(z) + ∇L(z) ⊤ (x -z) + DE 3,z (x, z). ( 20
)
Remark 1. The majorant in the first example involves log terms and is thus valid only on (0, +∞) N . In turn, in the second and third examples, it is possible to extend the majorizing property to every (x, z) ∈ [0, +∞) N by continuity arguments.

Bregman majorant of the complete loss function

We derived in the previous section three constructions of Bregman majorant functions for L. In general, we can now assume that L possesses a Bregman tangent majorant associated with some Ez and a domain of validity D. There remains to majorize the regularization term R. Let us assume that R is differentiable on R N with a β-Lipschitzian gradient, that is there exists β > 0 such that for every (x, z) ∈ (R N ) 2 , ∥∇R(x) -∇R(z)∥ ≤ β∥x -z∥. It follows from the descent lemma [START_REF] Bauschke | Convex Analysis and Monotone Operator Theory in Hilbert Spaces[END_REF] that a Bregman tangent majorant of R at every z ∈ R N is associated to β∥ • ∥ 2 /2. Therefore, by Lemma 1, a Bregman tangent majorant of the loss function f in Problem (2) at z ∈ D is associated with Ez = Ez + β∥ • ∥ 2 /2. In the following, we will denote qz such a majorant.

One MM algorithm to rule them all

We are now ready to state our general Bregman MM algorithm to solve Problem (2). First, let us point out that all the three constructions presented in Sec. 3.1 can be recast in a single framework. More precisely, for every (x, z) ∈ D 2 , f (x) ≤ qz(x). The k-th iteration of the MM algorithm reads as the minimizer of qz on D. In all our constructions, qz is a strictly convex separable function. Moreover, the components ( xn(z)) 1≤n≤N of its unique minimizer x(z) satisfy, for each n ∈ {1, . . . , N }, -a

n (z) xn(z) + ρ + (a (1) n (z) + β) xn(z) + dn(z) = 0, (0)
with dn(z) = a (0)

n (z) zn + ρ -(a (1) n (z) + β)zn + [∇R(z)]n + M m=1 hm,n 1 - ym h ⊤ m z + bm , (22)
where (a

(0) n (z), a (1)
n (z), ρ) are some non-negative values depending on the selected majorant. The N problems in [START_REF] Zubal | Computerized three-dimensional segmented human anatomy[END_REF] have closed form solutions, each of them being the root of second-order polynomial equation. The final algorithm then reads

x k+1 = max{ xn(x k ), 0} 1≤n≤N , (23)
initialized with x 0 ∈ (0, +∞) N . It is remarkable that, when R = 0 and the majorant from Example 1 is chosen, we retrieve the famous MLEM algorithm. If R ̸ = 0 and the same majorant is employed, the FBSEM method can be retrieved for a specific choice of its step-size.

EXPERIMENTAL RESULTS

In this section, we compare the three MM strategies derived previously, in a 2D+t simulation scenario of dynamic PET brain imaging.

Settings and dataset

We simulated a 2D 1 hour 18 F-FDG dynamical PET exam on a Biograph 6 TruePoint TrueV PET system (Siemens Healthcare, Erlangen, Germany), using a slice of the Zubal phantom [START_REF] Zubal | Computerized three-dimensional segmented human anatomy[END_REF]. We followed the set up of [START_REF] Chalampalakis | Use of dynamic reconstruction for parametric Patlak imaging in dynamic whole body PET[END_REF] to generate dynamic realistic projection data with an analytical simulator [START_REF] Stute | Analytical simulations of dynamic PET scans with realistic count rates properties[END_REF]. Generic projector and backprojector based on Joseph's method [START_REF] Joseph | An improved algorithm for reprojecting rays through pixel images[END_REF] were defined as operators for PyTorch and Tensorflow, using C++ and Cuda for the GPU version / C++ with OpenMP parallelization for multithreaded CPU. Each projection was only defined by the position of the two crystals involved, without assumption on a specific geometry (e.g. cylindrical system).

For reconstruction, we used a mixed regularization term consisting of smoothed spatial TV and temporal Tikhonov regularisation, as in [START_REF] Cadoni | A block parallel majorize-minimize memory gradient algorithm[END_REF], which has indeed a Lipschitzian gradient. The dynamic exam was subdivided into 24 time frames reconstructed simultaneously with a voxel size of 2.2 mm × 2.2 mm, and took into account all corrections as in [START_REF] Chalampalakis | Use of dynamic reconstruction for parametric Patlak imaging in dynamic whole body PET[END_REF].

The GPU solution was run on a 32 GB NVIDIA Tesla V100-SXM2, with block size optimized to reduce computation time. A comparison was made with a multi-threaded CPU implementation using OpenMP and 52 threads run on 52 distinct 2.10GHz Intel(R) Xeon(R) Gold 6230R cores.

Numerical results

Algorithms 1-3 correspond to MM algorithm [START_REF] Stute | Analytical simulations of dynamic PET scans with realistic count rates properties[END_REF] based on the majorants (11), ( 16), [START_REF] Bauschke | Convex Analysis and Monotone Operator Theory in Hilbert Spaces[END_REF], respectively. We show, in Fig. 1, the convergence speed of the algorithms in terms of the relative distance between the outer iterate (corresponding to x k ) and the limit point x∞, approximated for each method by performing 10,000 iterations. One can observe that Algorithm 1 outperforms the two others in terms of convergence speed. Fig. 2 provides a visual translation of these differences in convergence speeds. These results can be explained by considering the number of projections or backprojections needed to minimize each surrogate. It turns out that the computational cost of each iteration is dominated by the time needed to perform a backprojection (0.98s for a GPU-based implementation versus only 0.0016s for a projection). One iteration of Algorithm 1 requires only one backprojection against two for Algorithm 3 and three for Algorithm 2. This is also reflected by Tab. 1 where Algorithm 2 appears to be more than 2.5 times slower than Algorithm 1. This table also shows that our GPU implementation leads to a reduction of computation time by a factor larger than 10 compared to the use of the multithreaded CPU with 52 cores. We have focused on the PyTorch implementation, but similar results have also been obtained with Tensorflow.

CONCLUSION

In this paper, we have proposed a new Bregman majorization framework which unifies MM approaches used for PET image reconstruction. In our PET simulations, three MM algorithms derived from specific choices of Bregman majorants have been compared in terms of convergence speed. We have also evaluated the gain in computation time resulting from a GPU implementation instead of a multithreaded CPU implementation. It is worthy to note that the proposed framework is quite general and also applies to many other inverse problems involving Poisson data. This work also opens perspectives in terms of optimization of the algorithm parameters through differential programming techniques on GPUs [START_REF] Mehranian | Model-based deep learning PET image reconstruction using Forward-Backward Splitting Expectation-Maximization[END_REF].

Implementation

Example 1 .

 1 Let us define, for every z ∈ (0, +∞) N , the function(∀x ∈ (0, +∞) N ) E1,z(x) = -N n=1 a1,n(z) log xn, (9) where (∀n ∈ {1, . . . , N }) a1,n(z) = M m=1 ym hm,nzn ℓm(z) .

  with ρ = min 1≤m≤M ζmbm, (∀m = {1, . . . , M }) ζm = 1/ N n=1 hm,n.

Fig. 1 .

 1 Fig.1. Relative distance between the outer iterate and the limit point as a function of computational time, for GPU-based implementations.

Fig. 2 .

 2 Fig. 2. Reference image (first column) ; Reconstructed images after 100 s (first row) and 1000 s (second row) of GPU computation time, for Algorithm 1 (second column), Algorithm 2 (third column) and Algorithm 3 (fourth column).

  Definition 1. Let g be a differentiable function on an open set D ⊂ R N and let z ∈ D. Let Ez be a strictly convex function which is differentiable on D. Let DE z be the Bregman divergence associated with Ez. qz : D → R is the Bregman tangent majorant of g at z associated with Ez if

Table 1 .

 1 Algorithm 1 Algorithm 2 Algorithm 3 Comparisons of execution time for CPU-based and GPUbased implementations, for 100 iterations, in seconds.

	PyTorch CPU	1351	3536	2246
	PyTorch GPU	87	255	162


Laura Locatelli
email: laura.locatelli@unimi.it

Mehdi Inglebert

Priti Roberta Scrimieri

Kumari Sinha

Gian Vincenzo Zuccotti

Paolo Milani

Lionel Bureau

Chaouqi Misbah

Jeanette A M Maier

Inglebert Mehdi

Priti Kumari Sinha

Human endothelial cells in high glucose: New clues from culture in 3D microfluidic chips

Keywords: Endothelium, microfluidics, microvasculature on a chip, diabetes, glucose, cytoskeleton

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

INTRODUCTION

Vascular endothelial cells (EC), which are located at the innermost layer of the blood vessel wall, preserve vascular integrity, guarantee the adequate perfusion of all the tissues and regulate metabolic homeostasis (Circ Res (2018)123:477). Beyond their role as a barrier between the blood and the surrounding tissues, EC serve fundamental functions in maintaining blood fluidity, regulating vascular tone, and contributing to immunity and inflammation. EC display a high degree of plasticity and modulate their activities in response to various mechanical and biochemical stimuli to maintain tissues homeostasis [START_REF] Dejana | The molecular basis of endothelial cell plasticity[END_REF]. Indeed, being at the interface with the blood, they sense and respond to any variation of blood composition. In addition, EC are constantly subjected to shear stress, generated by blood flow and tangential to the endothelial surface [START_REF] Song | Fluid forces control endothelial sprouting[END_REF], and hydrostatic pressure, due to blood pressure which originates a circumferential stretch [START_REF] Gordon | The Importance of Mechanical Forces for in vitro Endothelial Cell Biology[END_REF]. These mechanical forces model endothelial shape, cytoskeleton and function [START_REF] Carmeliet | Mechanisms of angiogenesis and arteriogenesis[END_REF][START_REF] Tzima | A mechanosensory complex that mediates the endothelial cell response to fluid shear stress[END_REF][START_REF] Dufort | Balancing forces: Architectural control of mechanotransduction[END_REF][START_REF] Blackman | A new in vitro model to evaluate differential responses of endothelial cells to simulated arterial shear stress waveforms[END_REF].

Among others, high concentrations of glucose impair endothelial function. Accordingly, diabetes, a complex metabolic disease characterized by hyperglycemia, is associated with endothelial dysfunction leading to macro-and micro-vascular complications that are responsible for high morbidity and mortality [START_REF] Thomas | Update on diabetes classification[END_REF][START_REF] El-Asrar | Soluble CD40L in children and adolescents with type 1 diabetes: Relation to microvascular complications and glycemic control[END_REF][START_REF] Sena | Endothelial dysfunction -a major mediator of diabetic vascular disease[END_REF][START_REF] Shi | Macro-and microvascular endothelial dysfunction in diabetes[END_REF]. Diabetes affects more than 300 million people worldwide and causes the death of about 1.6 million people per year [START_REF] Stepan | Blood glucose levels in diabetic patients following corticosteroid injections into the hand and wrist[END_REF]. Experiments performed on human EC in culture have demonstrated that high glucose induces oxidative stress and glycation-driven modifications of proteins, thus promoting a pro-inflammatory and pro-thrombotic phenotype [START_REF] Domingueti | Diabetes mellitus: The linkage between oxidative stress, inflammation, hypercoagulability and vascular complications[END_REF][START_REF] Flammer | The assessment of endothelial function: From research into clinical practice[END_REF][START_REF] Davignon | Role of endothelial dysfunction in atherosclerosis[END_REF][START_REF] Barakat | Blood flow and arterial endothelial dysfunction: Mechanisms and implications[END_REF]. These results were obtained in monolayers of EC in two-dimensional (2D) culture systems, in which the cells are grown on a flat substrate in the absence of flow. Undoubtedly, this experimental approach has yielded important hints in cell biology, biochemistry and drug discovery. However, 2D cell culture systems present a number of limitations, since they do not replicate the dynamic and complex structural organization of the endothelium. Consequently, alternative experimental models have been developed to better mimic the complexity of the vascular system and provide new insights in various fields, from basic research to the clinics, including the screening of new drugs and the development of new tools for regenerative medicine [START_REF] Rimann | Synthetic 3D multicellular systems for drug development[END_REF]. Thanks to the merge of microfluidic technology and cell biology, it is now possible to culture EC in perfusable networks of microchannels and follow their behavior upon exposure to various stimuli.

We compared the effects of high concentrations of glucose on ECs in the classical 2D static culture vs a microfluidic 3D-flow culture system. We utilized the previously described "microvasculature on a chip" [START_REF] Tsvirkun | Microvasculature on a chip: Study of the Endothelial Surface Layer and the flow structure of Red Blood Cells[END_REF]. Since EC display a significant heterogeneity at the structural and functional levels according to their position in the vascular tree, we compared human EC isolated from the umbilical vein (HUVEC), a consolidated model of macrovasculature, and human dermal microvascular EC (HDMEC). To this purpose, it is noteworthy that microvascular EC represent the majority of the endothelium since they line a surface about 50 times larger than macrovascular EC [START_REF] Danese | Immune regulation by microvascular endothelial cells: directing innate and adaptive immunity, coagulation, and inflammation[END_REF].

We focused on the cytoskeleton and the glycocalyx, both targets of mechanical and biochemical signals arising from the microenvironment and both involved in mechanosensing and mechanotransduction [START_REF] Ingber | Cellular mechanotransduction: putting all the pieces together again[END_REF][START_REF] Locatelli | Mitophagy contributes to endothelial adaptation to simulated microgravity[END_REF]. The cytoskeleton is a dynamic structure which maintains the shape and the organization of the cell, and contributes to governing micro and macro-vascular EC response [Frontiers 2021]. The glycocalyx is a glycoproteic complex which coats the luminal surface of vascular endothelium and controls permeability as well as blood cell adhesion to the endothelium (Butler, JM, Am J Pathol 2020). In 3D cultures exposed to 0.4 Pa shear stress high glucose induced alterations of cytoskeletal organization in HUVEC without exerting any effect on the glycocalyx.

Under the same experimental conditions, pronounced cytoskeletal rearrangements occurred in HDMEC and this was associated with increased apoptosis. However, because shear stress levels are higher in capillaries than in arteries or veins (Front. Physiol. 11:861.doi: 10.3389/fphys.2020.00861), we also cultured HDMEC in 3D with a shear stress of 4 Pa and found that high glucose induces marked alterations of the cytoskeleton but no apoptosis, suggesting that the rate of flow is fundamental for a correct interpretation of microvascular cell behavior in 3D microfluidic systems.

Interestingly, in HUVEC and HMEC cultured in the microfluidic devices high glucose does not alter glycocalix thickness.

MATERIALS AND METHODS

2D Static Cell culture

HUVEC and HDMEC from Lonza (Basel, Switzerland) were cultured on 2% fibronectin coated dishes using EBM-2 and EGM-2 MV, respectively, and used up to passage 4 according to manufacturer's instructions. HUVEC were used as a model for macrovascular EC, while HDMEC for microvascular EC. In some experiments, D-Glucose (Sigma Aldrich, St. Louis, Missouri, USA) was added to normal medium, in which the concentration of glucose is 1 mg/mL (5.5 mM, CTR), to obtain a final concentration of 5.4 mg/mL (30 mM, D-glu). L-glucose (30 mM, L-glu) was used as a control of osmolarity. The experiments were repeated four times.

3D-Flow Cell culture

In 3D experiments, HUVEC and HDMEC were cultured in microfluidic devices fabricated using a standard soft-lithography technique [START_REF] Tsvirkun | Microvasculature on a chip: Study of the Endothelial Surface Layer and the flow structure of Red Blood Cells[END_REF]. After coating with fibronectin (2%), the cells were seeded and subjected to a constant flow of 1 μL/min of their growth medium so that the cells in the innermost channels of the microfluidic network (section 30 × 30 μm) experience a wall shear stress close to the physiological post capillary vein condition (about 0.4 Pa). HDMEC were also exposed to a constant flow of 10 μL/min to generate a ~ 4 Pa shear stress, a value reflecting the one occurring in the microvasculature. Cells were cultured in the microfluidic devices for 7 days before beginning the experiment and then they were fixed for immunofluorescence. The experiments were repeated three times.

Western blot

Cells in 2D static conditions were lysed in 10 mM Tris-HCl (pH 7.4) containing 3 mM MgCl2, 10 mM NaCl, 0.1% SDS, 0.1% Triton X-100, 0.5 mM EDTA and protein inhibitors. Equal amounts of proteins were separated by SDS-PAGE on 4-20% Mini-PROTEANTGX Stain-free Gels (Bio-Rad,Hercules, CA,USA) and transferred to nitrocellulose membranes by using Trans-Blot® TurboTM Transfer Pack (Bio-Rad, Hercules, CA, USA). Western blot was performed using antibodies against Actin (Tebu Bio-Santa Cruz, Magenta, Italy) and nitrocellulose sheets of these Stain-free Gels were used as control loading. Secondary antibodies labelled with horseradish peroxidase (Amersham Pharmacia Biotech Italia, Cologno Monzese, Italy) were used and immunoreactive proteins were detected with the ClarityTM Western ECL substrate (Bio-Rad, Hercules, CA, USA). Images were captured with a ChemiDocMP Imaging System (Bio-Rad, Hercules, CA, USA). The experiment was repeated at least three times. A representative blot is shown.

Confocal imaging

Cells were fixed in phosphate-buffered saline containing 4% paraformaldehyde and 2% sucrose pH 7.6, permeabilized with Triton 0.3%, and incubated with phalloidin-TRITC (Thermo Fisher Scientific, Waltham, Massachusetts, USA) for 1 h at 4°C [START_REF] Locatelli | Mitophagy contributes to endothelial adaptation to simulated microgravity[END_REF]. Nuclei were stained using Hoechst 33342 (Molecular Probes). Wheat Germ Agglutinin (WGA) Alexa Fluor 488 Conjugate (5 µg/ml, Molecular Probes) was utilized to stain the glycocalyx. Cells were then mounted with ProLong™ Gold Antifade Mountant (Invitrogen, Carlsbad, California, USA) and images were acquired using a 40X objective in oil by a ZEISS 710 confocal microscope. Images were analyzed using ImageJ.

Actin alignment quantification

Images derived from fluorescence microscopy for F-actin on HDMEC and HUVEC in control medium and in the presence of 5.4 mg/mL of D-or L-glucose were analyzed using the OrientationJ plugin of ImageJ, as described in detail in [START_REF] Inglebert | The effect of shear stress reduction on endothelial cells: A microfluidic study of the actin cytoskeleton[END_REF] to obtain orientation maps in which an angle theta is attributed to every pixels involved in oriented actin structures. For 2D images, an ideal horizontal axis was assumed as theta=0; in 3D the direction of flow within the 30 × 30 μm channel was assumed as theta=0. Angular distributions of actin fibers were calculated over 30 angular bins of width 3°, spanning the range from 0 to 90°. Pixels displaying an angle theta or -theta were counted in the same angular bin centered on theta. Distributions were plotted as the fraction of image pixels (called "frequency" in the following figures) whose angle falls within a given bin.

Apoptosis quantification

The Click-iT® TUNEL Alexa Fluor® 488 Imaging Assay (Thermofisher Scientific) was performed on HDMEC culture in 2D or 3D according to manufacturer's instruction.

Statistical analysis

Data are reported as means ± SD. The data were normally distributed, and they were analyzed using one-way repeated-measures ANOVA. The p-values deriving from multiple pairwise comparisons were corrected by the Bonferroni method. Statistical significance was defined for a p-value ≤ 0.05.

Regarding the figures, * p ≤ 0.05; ** p ≤ 0.01; *** p ≤ 0.001; **** p ≤ 0.0001.

RESULTS

The effect of glucose on the actin cytoskeleton in HUVEC and HDMEC in 2D culture

We investigated the effect of high D-glucose containing medium on the actin cytoskeleton in HUVEC and HDMEC cultured in 2D in a petri dish under static conditions. The cells were exposed to high (30 mM) concentration of extracellular D-glucose for 24 h. Culture medium (CTR) and L-glucose 30 mM (L-glu) were used as controls. We then analyzed the total amounts of actin by western blot as well as its organization after staining with fluorescent phalloidin (Figure 1). In HUVEC we found that D-glucose has no significant effect on total actin content (Figure 1A) and its organization in fibers (Figure 1B) as evaluated by western blot and confocal microscopy, respectively. In addition, we quantified the orientation of actin fibers in several images of HUVEC cultured for 24 h with normal and high glucose-containing medium. HUVEC display many actin fibers both in CTR and Dand L-glucose conditions and no differences in the total orientation of the fibers was found (Figure 1C). Also in HDMEC western blot shows no differences of actin content upon exposure to high glucose vs their controls (Figure 1D). Confocal microscopy after staining with fluorescent phalloidin shows that in basal condition (CTR) HDMEC display less fibers than HUVEC together with an enrichment of cortical actin. After culture in D-glu for 24h, F-actin resulted disorganized, with a lower amount of stress fibers and the presence of short or globular structures. No modulation of the orientation was found (Figure 1F). Nuclear staining highlights the presence of condensed and fragmented nuclei, hallmark of apoptosis, in D-glu treated HDMEC (Figure 1E). L-glucose has no effects.

In HUVEC and HDMEC glycocalix was hard to detect and discontinuous, and no differences were observed in treated or untreated cells (data not shown). These results are in keeping with data from the literature indicating that shear stress is important for the development and maintenance of the glycocalix [START_REF] Yilmaz | The role of endothelial glycocalyx in health and disease[END_REF].

After seeding, HUVEC were grown to confluence in the presence of a steady flow of culture medium. Channels of nominal section 30 × 30 μm were subjected for 7 days to a wall shear stress of about 0.4 Pa, which represents the conditions occurring in veins, and then perfused with medium containing either physiological or high concentrations of glucose (5.5 or 30 mM, respectively). 24 h later the cells were stained with phalloidin. As shown in figure 2A

The effect of glucose on actin cytoskeleton in HDMEC cultured in 3D-microfluidic devices

We then turned our attention to HDMEC, which have never been cultured in 3D microfluidic systems.

Initially, our aim was to compare HUVEC and HDMEC and, therefore, HDMEC were exposed to a shear stress of 0.4 Pa in medium containing normal or high glucose. After 24 h in the chip in the presence of high D-glucose, HDMEC presented many apoptotic/fragmented nuclei and most of the channels in the microfluidic device were blocked by cells detached from the wall of the channel (data not shown), making the analysis of actin cytoskeleton impossible. Therefore, we reduced the time of exposure to high glucose to 16 h. In HDMEC cultured in CTR and L-glucose medium, actin fibers aligned with the direction of the flow, although they were less orderly organized than in HUVEC, and the nuclei appeared intact. In HUVEC treated with high D-glucose, stress fibers were disassembled and fragmented and tended to accumulate in the periphery of the cell (Figure 3A).

We then exposed HDMEC to 4 Pa shear stress for 16 and 24 and performed the same analysis (Figure 3A, right panels). Since comparable results were obtained after culture in the presence of high Dglucose for16 or 24 h, we only show the data captured at XX h. Increased shear stress impacts on the structure of the cytoskeleton. Stress fibers are less organized and their orientation is more chaotic than in cells exposed to low shear stress. High D-glucose massively disassembles and fragments actin fibers, while L-glucose has no effect. Nuclei appear intact.

We also stained the glycocalyx and analyze its thickness in both the experimental conditions. Also in HDMEC, glycocalyx staining (upper panels) and thickness (lower panels) were not affected in all the conditions tested (Figure 3B).

The induction of apoptosis in D-glucose treated HDMEC cultured in 2D static condition and in 3Dmicrofluidic device

As previously shown, HDMEC treated with high D-glucose display many fragmented nuclei, suggesting that D-glucose induces apoptosis in these cells. To asses this we used the TUNEL assay, a method for detecting DNA fragmentation by labeling the 3′-OH end in the doublestrand DNA breaks generated by internucleosomal cleavage during apoptosis. Figure 4 shows that high D-glucose induces DNA damage in HDMEC grown in 2D (Figure 4A) or in 3D only under low shear stress (Figure 4B), while 4Pa shear stress prevents D-glucose induced apoptosis (Figure 4C). These results were confirmed by the analysis of nuclear parameters, i.e. nuclear area, nuclear perimeter and the brightness of each nuclear staining, which, as described in [START_REF] Mandelkow | Detection and Quantification of Nuclear Morphology Changes in Apoptotic Cells by Fluorescence Microscopy and Subsequent Analysis of Visualized Fluorescent Signals[END_REF], represent a direct correlation with the induction of apoptosis (Supplementary figure).

DISCUSSION

Hyperglycemia is responsible for macro-and micro-vascular complications that account for most of the morbidity and mortality of diabetic patients [START_REF] Beckman | Vascular complications of diabetes[END_REF]. As the endothelium is fundamental for vascular integrity [START_REF] Cahill | Vascular endothelium -Gatekeeper of vessel health[END_REF], it is relevant that in vitro studies have demonstrated the detrimental effects of high extracellular glucose on endothelial function [START_REF] Scrimieri | Reactive oxygen species are implicated in altering magnesium homeostasis in endothelial cells exposed to high glucose[END_REF]. These studies have been performed in the absence of shear stress in 2D conditions. It is becoming clear that 2D culture, while significantly advanced our knowledge on endothelial cells, can generate results which deviate the in vivo behavior. To overcome these restraints, bio-inspired microfluidic devices have been developed to emulate the 3D structure of the vessel and to include fluid perfusion so that also mechanobiological cues are taken into account (Duval 2017). In this study we utilized the "vasculature on a chip", which has previously been exploited for studying HUVEC (), because it mimics the geometrical features of the vasculature with sequential bifurcations and microvessels of different caliber [START_REF] Tsvirkun | Microvasculature on a chip: Study of the Endothelial Surface Layer and the flow structure of Red Blood Cells[END_REF]. Here we compare the response to high glucose of primary human EC cultured in 2D static conditions or in 3D perfused channels. Moreover, since significant differences are reported in EC from different districts in terms of phenotype, gene expression and function [START_REF] Aird | Endothelial cell heterogeneity[END_REF], we used both macro-and micro-vascular human EC.

In 2D culture conditions, high glucose for 24 h did not alter HUVEC cytoskeletal organization and actin content. Moreover, there is no evidence of nuclear fragmentation, a hallmark of apoptosis. This result is in agreement with previous reports, showing the occurrence of apoptosis only after long times of exposure to high glucose [START_REF] Zhang | High glucose induces apoptosis of HUVECs in a mitochondria-dependent manner by suppressing hexokinase 2 expression[END_REF][START_REF] Sheu | High glucose induces human endothelial cell apoptosis through a phosphoinositide 3-kinase-regulated cyclooxygenase-2 pathway[END_REF][START_REF] Ido | Hyperglycemia-induced apoptosis in human umbilical vein endothelial cells: Inhibition by the AMP-activated protein kinase activation[END_REF]. In particular, Ido et al [START_REF] Ido | Hyperglycemia-induced apoptosis in human umbilical vein endothelial cells: Inhibition by the AMP-activated protein kinase activation[END_REF] detected no differences in morphology and a similar percentage of apoptotic cells (3-4%) in HUVEC incubated for 24 h in media containing 5 or 30 mmol/l glucose, while by 72 h about 18% of cells exposed to high glucose are apoptotic [START_REF] Ido | Hyperglycemia-induced apoptosis in human umbilical vein endothelial cells: Inhibition by the AMP-activated protein kinase activation[END_REF]. When cultured in 3D microfluidic chips, no signs of apoptosis were detected, but differences in the alignment of actin fibers emerged in HUVEC exposed to high glucose. The glycocalyx, is the primary structure exposed to blood flow and acts as a sensor that transmits the mechanical stimulus to the actin cytoskeleton of the cells.13,18. Since shedding of the glycocalyx contributes to diabetes-induced vascular dysfunction [START_REF] Yilmaz | The role of endothelial glycocalyx in health and disease[END_REF], we hypothesized that cytoskeletal alterations could be due to alterations of the glycocalyx [START_REF] Brower | High glucose-mediated loss of cell surface heparan sulfate proteoglycan impairs the endothelial shear stress response[END_REF]. Alterations of glycocalyx, composition and/or structure, as observed for example in db/db transgenic diabetic mice [START_REF] Targosz-Korecka | AFM-based detection of glycocalyx degradation and endothelial stiffening in the db/db mouse model of diabetes[END_REF], render the cells less sensitive to flow and, consequently, impair the shear stress response, because less force is transmitted to the cell interior. However, we did not detect alteration in the thickness of the glycocalix.

It is believed that stress fiber alignment in response to shear stress is feature of all endothelial cells. However, it has been reported that brain microvascular EC respond differently to physical stimuli when compared to macrovascular EC and do not align with flow [START_REF] Reinitz | Human brain microvascular endothelial cells resist elongation due to shear stress[END_REF]. We obtained similar results with HDMEC, since the cells show randomly oriented actin fibers, which are not completely aligned with the flow. These results underscore significant differences in the morphology and flow-driven alignment between HUVEC and HDMEC.

Our experiments also demonstrate that HDMEC are more sensitive than HUVEC to high glucose. Indeed, in 2D culture conditions, we found cytoskeletal disorganization and clear evidence of apoptosis in HDMEC after exposure to 30 mM of D-glucose for 24 h. These events are even more pronounced when the cells are cultured in 3D microfluidic chips. Cytoskeletal disassembly is clear after 16 h of culture in 30 mM D-glucose. Stress fibers are fragmented and tend to accumulate at the periphery of the cells. After 24 h of culture in high glucose in 3D, nuclear fragmentation is conspicuous and most of the cells detach from the vessel wall. As mentioned above for HUVEC, we hypothesize that high glucose might jeopardize the integrity of the glycocalyx. In addition, excessive accumulation of reactive oxygen species might impair cell viability and lead to the onset of apoptosis [START_REF] Peng | High glucose induced oxidative stress and apoptosis in cardiac microvascular endothelial cells are regulated by FoxO3a[END_REF].

In summary, our results demonstrate that i) the detrimental effect of high glucose is more pronounced in HDMEC than in HUVEC and this might have important clinical implications; and ii) the presence of flow sensitizes the cells to high glucose, thus reinforcing the concept that EC integrate biochemical and mechanical signals through complex circuitries to evoke comprehensive functional response.

LEGENDS TO THE FIGURES

  (left panel), HUVEC CTR and L-glucose treated cells show spindle-like morphology in response to flow, whereas HUVEC in D-glucose are less elongated. Stress fibers are clearly visible, but they tend to be shorter in HUVEC exposed to high D-glucose. While actin fibers in CTR and L-glucose HUVEC align to the direction of flow, they tend to be less flow-aligned in D-glucose treated cells. The orientation of F-actin was studied and the angle formed by actin fibers in relation to flow direction was plotted as described above. No alterations were detected (Figure 2A, right panels). The nuclei were conserved. We then stained the glycocalyx using fluorescent WGA and analyzed the thickness. CTR, D-and Lglucose samples reveal comparable glycocalyx staining (Figure 2B left panel) and thickness (Figure 2B right panel).

Figure 1 .

 1 Figure 1. The effect of high glucose on HUVEC cytoskeleton in 2D culture conditions.

Figure 2 .

 2 Figure 2. The effect of high glucose on HDMEC cytoskeleton and apoptosis in 2D culture conditions.

Figure 3 .

 3 Figure 3. The effect of high glucose on actin cytoskeleton and nuclei in HUVEC and HDMEC cultured

ACKNOWLEDGEMENTS C.M. and L.B. thank CNES (Centre National d'Etudes Spatiales) and C.M. thanks the French-German University Programme ``Living Fluids'' (Grant CFDA-Q1-14) for the financial support. P.M., G.V.Z., J.A.M. thank Regione Lombardia, Project PRINTMED.

No potential conflict of interest was reported by the authors.

The effect of glucose on actin cytoskeleton in HUVEC cultured in 3D-microfluidic devices HUVEC were cultured in microfluidic channels that mimic a vascular network. Specifically, we utilized the device described in [START_REF] Tsvirkun | Microvasculature on a chip: Study of the Endothelial Surface Layer and the flow structure of Red Blood Cells[END_REF], which has previously been used for HUVEC.

All these in vitro studies, EC are either (i) cultured under "no flow" conditions until confluence, and then placed under hydrodynamic shear, or (ii) cultured under flow from the moment they are plated into the flow device, but experiencing the same level (high or low) or pattern (laminar, recirculating, graded, or pulsating) of shear stress from the start of the culture. Most studies, therefore, investigated the response of EC when the flow is "switched on" or of EC submitted to specific shear conditions applied steadily from "time zero."

Strikingly enough, only a very limited number of works have addressed the question of the response of already shear-adapted EC to a loss of shear stress stimulation, 26,27,39-42 as would occur, for instance, in occlusive microvascular events, or as a result of altered hemodynamics such as encountered in space flights 43,44 or in ground simulations of microgravity conditions. 45 The quantification of green fluorescence of different images was performed using imageJ and the mean of each sample was plotted. Statistical analysis was performed using ANOVA.

Supplemental data

Supplementary figure: The effect of high glucose on nuclear morphology in HDMEC cultured in 2D culture condition or in 3D-microfluidic channels.

HDMEC were cultured in medium containing normal or high D-or L-glucose for 16h in 2D and in 3D condition. HDMEC were observed by confocal microscopy for nuclear staining using Hoechst 33342 and the quantification of Area, Perimeter and Brightness of each nucleus of different images was performed using ImageJ and plotted. Statistical analysis was performed using ANOVA.


Claire Ballot
email: claire.ballot@u-bordeaux.fr

Stephanie Mathey

Christelle Robert

Stéphanie Mathey

WORD IMAGEABILITY AND NEIGHBOURHOOD IN MEMORY

Keywords: Free recall, recognition memory, word imageability, orthographic neighbourhood size

come

Introduction

In recent decades, researchers have provided evidence suggesting that the semantic features of words influence word memory (e.g., [START_REF] Acheson | The effect of concurrent semantic categorization on delayed serial recall[END_REF]. Other studies have addressed the effects of non-semantic word features, especially orthographic characteristics, and have also reported a critical influence on word memory performance (e.g., [START_REF] Glanc | Orthographic distinctiveness and memory for order[END_REF]. Interestingly, the effect of semantic and orthographic properties could be dependent on the type of memory task [START_REF] Cox | Information and processes underlying semantic and episodic memory across tasks, items, and individuals[END_REF][START_REF] Lau | An item-level analysis of lexical-semantic effects in free recall and recognition memory using the megastudy approach[END_REF]; see also [START_REF] Balota | Attentional control and flexible lexical processing: Explorations of the magic moment of word recognition[END_REF] for similar arguments in the field of word recognition). Using a megastudy approach, [START_REF] Lau | An item-level analysis of lexical-semantic effects in free recall and recognition memory using the megastudy approach[END_REF] showed that the structural features of words, namely their orthographical features, accounted for more variance in tasks driven by familiarity processes (i.e., recognition tasks), while semantic features accounted for more unique variance in tasks requiring more resources (i.e., recall tasks). Further to these findings, it is important to get a better understanding of how the effects of orthographic and semantic features combine to influence memory performance in both types of tasks. This was the aim of the present study.

Word imageability, defined as the ease with which a word evokes a mental image (e.g., [START_REF] Desrochers | Subjective frequency and imageability ratings for 3,600 French nouns[END_REF], is usually used as a measure of the semantic richness of words (e.g., [START_REF] Yap | An abundance of riches: cross-task comparisons of semantic richness effects in visual word recognition[END_REF]. Word imageability has been found to be a strong predictor of memory performance [START_REF] Cortese | Recognition memory for 2,578 monosyllabic words[END_REF]. The advantage of high-imageability words in memory performance can be explained in the dual-coding theory (e.g., [START_REF] Paivio | Imagery and verbal processes[END_REF][START_REF] Paivio | Dual coding theory: Retrospect and current status[END_REF] by assuming a dual representation of these words within two independent systems: a verbal (linguistic) and a non-verbal (imagistic) system (e.g., Strain et al., 1995 in a naming task). As regards the type of memory task, it has been observed that the influence of word imageability is more evident in recall [START_REF] Rubin | Predicting which words get recalled: Measures of free recall, availability, goodness, emotionality, and pronunciability for 925 nouns[END_REF] than in recognition tasks [START_REF] Lau | An item-level analysis of lexical-semantic effects in free recall and recognition memory using the megastudy approach[END_REF].

As argued by [START_REF] Lau | An item-level analysis of lexical-semantic effects in free recall and recognition memory using the megastudy approach[END_REF], this differential effect across memory tasks is due to the demands of the tasks. In particular, the semantic properties of words would have a greater influence in more "demanding" memory tasks such as in recall because semantic richness is particularly useful for the processes of reconstruction of the degraded word trace after encoding or for the search processes in memory during retrieval (see also [START_REF] Poirier | Memory for related and unrelated words: Further evidence on the influence of semantic factors in immediate serial recall[END_REF]. Retrieval being facilitated in recognition memory by the presence of a clue, the semantic features of words, such as word imageability, would play a weaker role in this memory task (Hunt & Eliott, 1980).

The orthographic features of words have also been found to influence memory performance, in particular through the study of orthographic distinctiveness (e.g., [START_REF] Cortese | Relating distinctive orthographic and phonological processes to episodic memory performance[END_REF][START_REF] Glanc | Orthographic neighborhood size effects in recognition memory[END_REF], 2012). The concept of orthographic distinctiveness refers to the structural features of a word that make it physically unusual or interesting [START_REF] Zechmeister | Orthographic distinctiveness[END_REF]. In other words, a word is distinct if it shares few or no characteristics with the other words in memory (Hunt & Eliott, 1980). Over the last few decades, orthographic distinctiveness has been operationalized by taking into account the lexical similarity of words, and in particular by considering orthographic neighbourhood size which corresponds to the number of words that can be formed by changing a single letter in the stimulus word (N index, Coltheart et al., 1977; see also [START_REF] Justi | Orthographic neighborhood effects in recognition and recall tasks in a transparent orthography[END_REF]. For example, the orthographic neighbours of the word sleet are sleep, fleet, sheet, skeet, sweet, slept, sleek (N=7). In recognition memory, Glanc andGreene (2007, 2012) found a mirror effect of N with a decrease in hit rates and an increase in false alarm rates for high-N words compared to low-N words (see also [START_REF] Cortese | Relating distinctive orthographic and phonological processes to episodic memory performance[END_REF][START_REF] Freeman | Item effects in recognition memory for words[END_REF][START_REF] Heathcote | Word frequency and word likeness mirror effects in episodic recognition memory[END_REF]Justi & Jeager, 2017;[START_REF] Kang | Pathway control in visual word processing: Converging evidence from recognition memory[END_REF]. Because high-N words share many sublexical components with other words in memory, they are less distinctive than low-N words, and so they are more difficult to retrieve in memory [START_REF] Cortese | Relating distinctive orthographic and phonological processes to episodic memory performance[END_REF][START_REF] Glanc | Orthographic neighborhood size effects in recognition memory[END_REF]. Orthographic distinctiveness, and in particular the number of orthographic neighbours, is an important factor to consider when conducting research in the field of word memory, especially in recognition memory tasks where word retrieval involves familiarity processes that are highly sensitive to the structural properties of words [START_REF] Lau | An item-level analysis of lexical-semantic effects in free recall and recognition memory using the megastudy approach[END_REF]. Memory tasks that require more effortful retrieval processes would be less sensitive to the orthographical features of words (Hunt & Eliott, 1980). Interestingly, in their work on orthographic neighbourhood effects in a recognition task, [START_REF] Glanc | Orthographic neighborhood size effects in recognition memory[END_REF] found that the N effect was no longer observed when encoding instructions were driven by the semantic aspects of words (i.e., when questions were asked about the meanings of words). This was taken as evidence that the semantic processing of words could overcome the effects of orthographic distinctiveness in memory. The question of whether and to what extent the orthographic and semantic properties of words exert a mutual influence on free recall and recognition is therefore important to address. Also, since N effects in memory are now well-established in English, it is important to clarify such effects in French, a language whose N effects reputedly have greater difficulty appearing in visual recognition (Andrews, 1997).

The aim of present study was to examine the effects of word imageability and orthographic neighbourhood on free recall and recognition and to specify how and to what extent these effects might combine in both memory tasks. As suggested by [START_REF] Lau | An item-level analysis of lexical-semantic effects in free recall and recognition memory using the megastudy approach[END_REF], human memory is flexible enough to adapt to the word features as well as to the constraints of the task in order to optimise performance. In that sense, word properties play an important role in memory performance, but this role depends on the type of properties and on the type of memory task. Semantic features improve the effortful search and reconstruction processes underlying the recall task to a greater extent, whereas orthographic features further impact the familiarity processes that underlie recognition memory performance. An important issue that remains to be addressed here is the mutual influence of semantic and orthographic characteristics on memory with regard to the two types of memory tasks in order to specify common and task-specific processes related to word properties in word memory. We hypothesised that word imageability enhances memory performance, especially in the free recall task which involves more demanding search and reconstruction processes during retrieval (Hunt & Eliott, 1980;[START_REF] Lau | An item-level analysis of lexical-semantic effects in free recall and recognition memory using the megastudy approach[END_REF]. In line with previous studies [START_REF] Glanc | Orthographic neighborhood size effects in recognition memory[END_REF], 2012), we expected words with a high N to exhibit a lower memory performance than words with a low N, especially in the recognition memory task where the structural properties of words are more prominent [START_REF] Lau | An item-level analysis of lexical-semantic effects in free recall and recognition memory using the megastudy approach[END_REF]. Moreover, the effect of orthographic neighbourhood might also be sensitive to word imageability, such that the N effect could be reduced for highly imageable words whose semantic aspects are more prominent. To test these hypotheses, we orthogonally manipulated word imageability and the number of orthographic neighbours in two long-term memory tasks that are widely used in the literature (i.e., free recall and recognition). As already stated, these two tasks can help to disentangle common and task-specific effects of word features in order to provide a better understanding of the cognitive processes underlying word memory performance.

Method Participants

A total of 45 undergraduate students (M age = 23.01 years, SD age = 3.19) took part in the experiment. They were all native French speakers and reported having normal or corrected-tonormal vision. All participants provided voluntary informed consent prior to participation.

Materials

The stimuli were 80 words of 4 to 7 letters selected from the lexical database of [START_REF] Desrochers | Subjective frequency and imageability ratings for 3,600 French nouns[END_REF], which provides imageability and subjective word frequency ratings for a corpus of French words. Other characteristics were taken from the French lexical database Lexique 3.8 [START_REF] New | The use of film subtitles to estimate word frequencies[END_REF]. Half of the words had a high N (N > 6) while the other half had a low N (N < 3, for a similar procedure see [START_REF] Glanc | Orthographic neighborhood size effects in recognition memory[END_REF], p <.001. In each of these two orthographic neighbourhood conditions, half of the words were highly imageable (scores above 3.5 on the 7-point scale proposed by [START_REF] Desrochers | Subjective frequency and imageability ratings for 3,600 French nouns[END_REF] and the other half were low-imageability words (scores below 3.5 on the 7-point scale), p <.001. In summary, the materials consisted of 20 low-imageability words with a high N (e.g., saveur [flavor]), 20 low-imageability words with a low N (e.g., total

[total]), 20 high-imageability words with a high N (e.g., carré [square]) and 20 highimageability words with a low N (e.g., nuage [cloud]).

The four word conditions were matched on subjective word frequency, objective word frequency (in occurrences per million), number of syllables and number of letters (ps > .10).

The main statistical characteristics of the materials are presented in Table 1.

-------------------- Insert Table 1 --------------------
Four mixed lists of 20 stimuli were drawn up so that each list contained 5 words per experimental condition. For the purpose of the recognition task, 80 French words that had lexical characteristics similar to those of the experimental words were selected as distractors.

Procedure

Participants were tested individually in a quiet room and performed a free-recall task after providing written consent. The task was controlled by a personal computer using the E.Prime 2.0 software. During the study phase, participants were instructed to memorise the words presented one by one. Each word appeared in lowercase in the centre of a computer screen for 3,000 ms and was preceded by a 1000-ms fixation cross. At the end of the list, a screen instruction required each participant to count down for 30 seconds. Next, participants had to write the words they remembered on a sheet of paper. No time limit or recall order constraints were imposed for recall. Immediately afterward, another list appeared and the procedure was replicated. The presentation of the words was randomised within each list and the list appearance order was counterbalanced across participants to control for list order effects. Following the four study and recall phases, participants performed a recognition task (for a similar procedure see [START_REF] Lohnas | Parametric effects of word frequency in memory for mixed frequency lists[END_REF]. In the recognition task, 160 words were presented on the computer screen, in a different random order for each participant. The 80 words from the previous recall task were mixed with 80 new words used as distractors.

Participants were asked to decide whether each word appearing on the screen was "new" or "old" by pressing one of the two buttons on the computer keyboard. The buttons were tailored to the participant's laterality so that they would respond "old" with the dominant hand and "new" with the other hand. The words were preceded by a 1000-ms fixation cross and remained on the screen until the participant responded.

Results

Separate analyses of variance (ANOVAs) were performed on hits for recall, hits for recognition memory, false alarms, and on an index of sensitivity (d') based on the hits and false alarms in order to assess recognition memory performance, with N and word imageability as within-subject factors. Two words identified as outliers (|SDR| > 4) were excluded. The results are shown in Table 2.

Free Recall

The analysis of hits showed a significant effect of word imageability, F(1, 44) = 37.87, p <.001, η²p = .46. High-imageability words were recalled better (M =.44) than low-imageability words (M =.35). No significant effect of N was found, F < 1. Importantly, the interaction between word imageability and N was significant, F(1, 44) = 7.91, p = .007, η²p = .15. More precisely, the effect of N was significant for low-imageability words, F(1, 44) = 4.49, p = .04, η²p = .09, showing that high-N words were recalled less (M = .33) than low-N words (M = .38). No significant effect of N was found for high-imageability words, F(1, 44) = 3.01, p = .09, η²p = .06.

Recognition

The analysis of hit rates showed a significant effect of word imageability, F(1, 44) = 17.07, p <.001, η²p = .28. High-imageability words were recognised better (M =.79) than lowimageability words (M =.74). A significant effect of N was also found, F(1, 44) = 15.17, p <.001, η²p = .26. High-N words were recognised less (M = .74) than low-N words (M = .79).

Finally, the interaction between word imageability and N was significant, F(1, 44) = 4.48, p =.04, η²p = .09. More precisely, a significant N effect was found for low-imageability words, F(1, 44) = 15.10, p <.001, η²p = .26, showing that low-imageability words with high N were recognised less (M = .70) than low-imageability words with low N (M = .78). The N effect was not significant for high-imageability words, F(1, 44) = 1.85, p =.18. Concerning false alarm rates, a significant effect of word imageability was found, F(1,43) = 10.73, p =.002, η²p = .19. Low-imageability words exhibited fewer false alarms (M = .08) than high-imageability words (M = .11). The N effect was not significant F < 1. We found a significant interaction between word imageability and N, F(1, 44) = 9.18, p = .004, η²p = .17. The N effect was significant for low-imageability words, F(1, 44) = 4.08, p = .049, η²p = .09, showing that low-imageability words with high N exhibited more false alarms (M = .09) than low-imageability words with low N (M = .07). The N effect was also reliable for high-imageability words, F(1, 44) = 4.16, p =.047, η²p = .09, showing that high-imageability words with high N produced fewer false alarms (M = .09) than words with low N (M = .12).

WORD IMAGEABILITY AND NEIGHBOURHOOD IN MEMORY 10

Concerning d' values, no significant effect of word imageability was found, F(1, 44) = 1.29, p =.26. The N effect was significant, F(1,44) = 7.59, p =.009, η²p = .15. High-N words were discriminated less well (M = 2.24) than low-N words (M = 2.41). Finally, the interaction effect between word imageability and N was significant, F(1,44) = 9.89, p =.003, η²p = .18.

The N effect was significant for low-imageability words, F(1, 44) = 22.18, p <.001, η²p = .33, showing that low-imageability words with a high N were discriminated less well (M = 2.09) than low-imageability words with a low N (M = 2.49). No N effect was found for highimageability words, F < 1.

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Discussion

The aim of the present study was to investigate the main and combined effects of word imageability and orthographic neighbourhood in free recall and recognition tasks. The main findings can be summarised as follow. An effect of word imageability was found on both free recall and recognition memory while the effect of orthographic neighbourhood was evident in the recognition task and not in free recall. Moreover, the effect of orthographic neighbourhood was found to depend on word imageability in both free recall and recognition.

These results are discussed in terms of the common and task-specific processes involved in word memory performance.

Effects of word imageability and orthographic neighbourhood on free recall and recognition

Overall, the results clearly showed that high-imageability words were recalled better and recognised better than low-imageability words. These findings are in line with previous ones from studies that used free recall [START_REF] Rubin | Predicting which words get recalled: Measures of free recall, availability, goodness, emotionality, and pronunciability for 925 nouns[END_REF] or recognition [START_REF] Cortese | Recognition memory for 2,578 monosyllabic words[END_REF] tasks. The memory advantage of high-imageability words can be ascribed to their semantic richness that would enhance their retrieval in memory, whatever the task is. It is important to note here that semantic richness also makes words less distinctive in memory because they share multiple semantic features with other words [START_REF] Lau | An item-level analysis of lexical-semantic effects in free recall and recognition memory using the megastudy approach[END_REF]. In the present study, the increase in false alarms observed for high-imageability words compared to low-imageability words supports the idea of a difficulty in discriminating high-imageability words because of their semantic richness. The effects of word imageability could also be accounted for by the dual-coding theory [START_REF] Paivio | Imagery and verbal processes[END_REF][START_REF] Paivio | Dual coding theory: Retrospect and current status[END_REF] which posits that highimageability words benefit from a dual coding in a verbal and a non-verbal system in comparison with low-imageability words, which benefit from a coding in a single verbal system. Although the effect of word imageability was observed in both tasks, it explains more variance for the hit rates in recall than in recognition (respectively 46% vs. 28%), which is fully consistent with findings from previous megastudies that have suggested a higher influence of the semantic features of words in effortful and resource-demanding memory tasks (Hunt & Eliott, 1980;[START_REF] Lau | An item-level analysis of lexical-semantic effects in free recall and recognition memory using the megastudy approach[END_REF]. Therefore, common memory processes might underlie imageability effects in both recall and recognition tasks but to various extents, with a stronger role of semantics in recall than in recognition. Note that, in agreement with the procedure used by [START_REF] Lohnas | Parametric effects of word frequency in memory for mixed frequency lists[END_REF], the recognition task always followed the free recall task in the present study. The interest here was that the recall performance was comparable to that of previous studies in which the participants recalling the words did not perform any recognition previously (e.g., [START_REF] Cortese | Relating distinctive orthographic and phonological processes to episodic memory performance[END_REF][START_REF] Rubin | Predicting which words get recalled: Measures of free recall, availability, goodness, emotionality, and pronunciability for 925 nouns[END_REF]. As a consequence of this constant task order, we cannot however reject the hypothesis that word recall might have enhanced encoding, therefore facilitating subsequent word recognition.

Future studies should be designed to investigate this issue further.

In contrast to the imageability effect that clearly occurred in both memory tasks, we found that the influence of orthographic similarity on memory depended on the task.

Although the orthographic neighbourhood effect failed to emerge in free recall, the N effect was evident in recognition. More precisely, low-N words were recognised better and discriminated better than high-N words. In line with results from previous studies [START_REF] Cortese | Relating distinctive orthographic and phonological processes to episodic memory performance[END_REF][START_REF] Glanc | Orthographic neighborhood size effects in recognition memory[END_REF], 2012 in English;[START_REF] Justi | Orthographic neighborhood effects in recognition and recall tasks in a transparent orthography[END_REF] in Portuguese), these latter findings confirm that orthographic distinctiveness plays an important role in recognition memory and extend this conclusion to the French language. Our result showing that the N effect was confined to the recognition task suggests that the influence of orthographic properties is favored by recognition-specific processes. As suggested in previous studies (e.g., [START_REF] Goh | Testing the myth of the encoding-retrieval match[END_REF], the cue provided in the recognition task is less diagnostic if it shares components with multiple traces. By extending this assumption to neighbourhood effects, words with few orthographic neighbours would be more easily recognised when they present a clue during the memory recognition task, since they share no or few orthographic characteristics with other words stored in memory. Conversely, clues relating to words with a high N would be more difficult to associate with a trace in episodic memory because of their orthographic resemblance to many other words stored in memory.

Combined effect of word imageability and orthographic neighbourhood on free recall and recognition

Another important purpose of this study was to determine whether word imageability and orthographic neighbourhood exert a combined influence in memory tasks. The results showed that the effect of orthographic neighbourhood was sensitive to imageability in both free recall and recognition. Concerning low-imageability words, high-N words were both recalled less and recognised less than low-N words. When false alarms were considered in the recognition task, a mirror effect of N was observed for low-imageability words. High-N words were discriminated less well than low-N words when their imageability was low. For high-imageability words, the effect of orthographic neighbourhood was no longer observed on recall and recognition memory. This pattern of results in both free recall and recognition suggests that semantic and orthographic factors are interdependent in different memory tasks (Hunt & Eliott, 1980;[START_REF] Nishiyama | Usage of semantic representations in recognition memory[END_REF] and that their mutual intervention relies on shared memory processes. More precisely, when access to the semantic information in the word is high (as is the case for high-imageability words), the semantic rather than the orthographic features are preferentially used during the processes of recollection. Conversely, when few semantic characteristics are available (as is the case for low-imageability words), the orthographic properties of words could be used during the processes of recollection. These findings can also be accommodated by the dual-coding theory [START_REF] Paivio | Imagery and verbal processes[END_REF][START_REF] Paivio | Dual coding theory: Retrospect and current status[END_REF]. In this framework, low-imageability words would be coded in a verbal system only, which would allow for the orthographic neighbourhood to influence the processing of the word. For highimageability words, the dual coding within a linguistic and an imagistic system would privilege the coding of semantic and imagistic information in the words, in this case word imageability. As already mentioned, the general increase in false alarms for these words might be due to their semantic richness which makes them less distinctive in memory. Also note that for high-imageability words, the rate of false alarms was lower for high-N words than for low-N words. For these high-imageability words, it is therefore possible that access to semantic information depends to some degree on orthographic neighbourhood. Interference from neighbours could delay access to semantic information for high-N words whereas access to semantic information would be easier for low-N words. This phenomenon would be restricted to false alarms because the processes underlying the production of false alarms would be different from those underlying the hits (e.g., see [START_REF] Yonelinas | The nature of recollection and familiarity: A review of 30 years of research[END_REF].

Conclusion

In summary, this study provides additional arguments that should help to shed more light on the issue on the semantic and orthographic characteristics that underlie common and specific processes involved in memory tasks. First, the imageability effect suggests that the semantic features of words are used in both recall and recognition tasks but to a greater extent in the recall task, which implies more effortful and resource-demanding processes of recollection. Second, the effect of orthographic neighbourhood size, which only emerged in the recognition task, rather suggests that orthographic features are mainly useful in tasks driven by familiarity processes. Furthermore, the semantic and orthographic properties of words produced a combined influence on both free recall and recognition, highlighting their interdependent role in memory. In particular, word retrieval processes would be influenced by the orthographic features of words only when semantic information is not or is barely available. Such common and specific effects of semantic and orthographic properties across memory tasks suggest that human memory is flexible and is able to adapt to the features of words as well as to the constraints of the task in order to optimise memory performance (see also [START_REF] Cox | Information and processes underlying semantic and episodic memory across tasks, items, and individuals[END_REF][START_REF] Lau | An item-level analysis of lexical-semantic effects in free recall and recognition memory using the megastudy approach[END_REF]. Further studies should be designed to clarify the specific and common influence of word properties on memory by using several other memory tasks and by manipulating the context of encoding.

Disclosure statement

No potential conflict of interest was reported by the authors.