Rituraj Mishra

Jean-Nicolas Dumez
email: jean-nicolas.dumez@univ-nantes.fr

Theoretical analysis of flow effects in spatially-encoded diffusion NMR

The measurement of translational diffusion coefficients by nuclear magnetic resonance (NMR) spectroscopy is essential in a broad range of fields including organic, inorganic, polymer and supramolecular chemistry. It is also a powerful method for mixture analysis. Spatially-encoded diffusion (SPEN-D) NMR is a time efficient technique to collect diffusion NMR data, which is particularly relevant for the analysis of samples that evolve in time. In many cases, motion other than diffusion is present in NMR samples. This is for example the case of flow NMR experiments for, e.g., online reaction monitoring, and in the presence of sample convection. Such motion is deleterious for the accuracy of DNMR experiments in general, and for SPEN DNMR in particular.

Limited theoretical understanding of flow effects in SPEN DNMR experiments is an obstacle to their broader experimental implementation. Here, we present a detailed theoretical analysis of flow effects in SPEN DNMR, and of their compensation, throughout the relevant pulse sequences. This analysis is validated by comparison with numerical simulation performed with the Fokker-Planck formalism. We then consider, through numerical simulation, the specific cases of constant, laminar and convection flow, and the accuracy of SPEN DNMR experiments in these contexts. This analysis will be useful for the design and implementation of fast diffusion NMR experiments, and for their applications.

INTRODUCTION

Nuclear magnetic resonance spectroscopy is a powerful approach to measure the translational diffusion coefficients of molecules in solution. [START_REF] Pagès | [END_REF] Diffusion NMR measurements are used to probe polymer sizes, [2][3][4][5] to characterise host-guest interactions, [6][7][8][9] and to measure the size of aggregates, [10][11][12][13] among other things. Diffusion NMR is also widely used as a way to separate the spectral information on components in a mixture, without physical separation of the components themselves. This approach is used for applications ranging from authentication 14,15 to reaction monitoring. 16,17 The measurement of diffusion coefficients by NMR is based on the application of a pair of magnetic field gradient pulses, separated by a delay. Diffusion during the delay results in an attenuation of the NMR signals. Conventional diffusion NMR experiments rely on the stepwise incrementation of the area of the gradient pulses across a series of consecutive scans. This results in experiment duration of a few minutes or more. Spatially Encoded Diffusion NMR (SPEN DNMR) makes it possible to collect a complete data set in a single scan of less than one second, by spatial parallelisation of the gradient pulse area. [18][19][20][21][22] In SPEN DNMR pulse sequence, the gradient pulses found in conventional DNMR are replaced by the combined application of a gradient pulse and a frequency swept pulse. This fast DNMR method has proven useful for the monitoring of chemical reactions, 22 and for the analysis of hyperpolarised samples. 23,24 Diffusion NMR experiments are sensitive to the displacements of molecules, even if they are not due to diffusion. In particular, DNMR experiments are sensitive to any mesoscopic displacements within the sample, and this can result in highly inaccurate estimates of the diffusion coefficients. For example, convection effects, if left uncompensated, are well-known to result in overestimated diffusion coefficients. [25][26][27][28] The accurate measurement of diffusion coefficients for a sample in continuous flow is also particularly challenging. 17,29 The effect of flow on conventional diffusion NMR and MRI is well studied theoretically and experimentally. [31][32][START_REF] Callaghan | Principles of Nuclear Magnetic Resonance Microscopy[END_REF][START_REF] Haacke | Magnetic Resonance Imaging Physical Principles and Sequence Design[END_REF][START_REF] Saib | [END_REF][36][37][38][39][40] Notably, it can be shown that a constant velocity flow results in an additional phase shift of the magnetization. For conventional experiments, an elegant convection compensation strategy was introduced by Jerschow and Mueller in 1998. 41 It consists of using two diffusion encoding steps instead of one, designed such that the effect of convection cancels out. This approach has become standard for DNMR experiments carried out in solvents that are prone to convection. [START_REF] Pagès | [END_REF]42 It has also been exploited for diffusion measurements in continuous flow. 17,43 Convection compensation has also been extended to the case of spatially-encoded diffusion NMR experiments. 22,24 Following the idea of flow-compensated conventional diffusion sequence, two diffusion encoding blocks are used instead of one. This has led to the possibility to collect accurate DNMR data for samples hyperpolarised with dissolution dynamic nuclear polarisation, 24 and also for the real-time monitoring of a chemical reaction in an organic solvent. 22 While simplistic numerical simulation and analytical calculations hinted at the validity of this approach, 24,44 flow effects in SPEN DNMR experiments remain poorly described an understood. This is also an obstacle in using these experiments for reaction monitoring by flow NMR.

In this article, we provide a detailed theoretical description of flow effects is SPEN DNMR experiments, supported by numerical spin simulation. We use the propagator model [START_REF] Callaghan | Principles of Nuclear Magnetic Resonance Microscopy[END_REF] to derive analytical expressions of the echo amplitude for the SPEN stimulated echo and double stimulated echo pulse sequence. These expressions work outside of the small displacement approximation that was used in earlier work, and are validated by exact numerical simulation using the SPINACH library. 19,[45][46][47] We also describe flow effects during the acquisition part of SPEN DNMR pulse sequences. This framework is then used to analyse three cases of practical importance, plug flow, laminar flow, and convection flow. In the three cases, the expected accuracy of SPEN DNMR experiments is discussed, and data processing strategies to improve it are described. Overall, this study provides both physical insights and practical tools for applications of SPEN DNMR in the presence of flow, be it for reaction monitoring or the analysis of hyperpolarised samples.

II. NUMERICAL METHODS

A. Numerical simulations for a single velocity

All the numerical simulations were performed with the SPINACH library, version 2.3.4934. 19,[45][46][47] An ensemble of uncoupled spins I = 1/2 was considered, with a translational diffusion coefficient of 8×10 -10 m 2 /s. The simulated pulse sequences are shown in Fig. 1. Simulations were performed with linearly swept chirp pulses with a duration of 1.5 ms and a bandwidth of 110 kHz. The encoding gradients had an amplitude of 0.2535 T/m, resulting in a size of 10 mm for the spatial region swept by the pulse. A sample length of 15 mm was equally divided in 3000 spatial grid points. The diffusion delay Δ was set to 150 ms. The effect of relaxation was not considered during the simulation. The unwanted coherences were removed by setting them equal to zero.

Without explicit acquisition

In order to characterise the encoding process only, the acquisition block was not simulated, and the transverse component of the magnetisation at the end of the encoding block was obtained as a function of position simply by retaining the corresponding element of the state vector.

The comparison with analytical expressions of the diffusion decay required a reference profile, that was obtained by running the simulation with the translational diffusion coefficient set to 0 m 2 /s. Experimentally, the reference profile can be obtained by using the minimum possible diffusion delay. While this introduces some additional error (because of diffusion during the spatial encoding block), this error is similar with and without flow effects.

With explicit acquisition

When simulated, the acquisition block of the pulse sequence consisted of a train of bipolar gradient pulses of strength ±0.52 T/m and of duration 2𝜏 for each pulse, preceded by a prephasing gradient pulse of strength -0.52 T/m and of duration 𝜏. Each gradient pulse of duration 𝜏 (2𝜏) is divided into 64 (128) points with the fixed dwell time 𝑑𝑤 of 1.5×10 -6 s. The EPSI block is shown in Fig. 1. In the following, the origin of the time axis for acquisition will be at the start of the prephasing gradient pulse, although the data points from 0 to 𝜏 are discarded. The segment from (4𝑞 + 1)𝜏 to (4𝑞 + 3)𝜏, with 𝑞 ∈ ℕ, will be called as odd echoes while the segment from (4𝑞 +

3)𝜏 to (4𝑞 + 5)𝜏 as even echoes throughout the manuscript. A combination of one odd and even echo gradient create a single loop and 256 such loops were used to acquire the data. The sign of prephasing and the bipolar gradient shown in Fig. 1c and 1d is for odd echo acquisition while for even echo acquisition, the reverse sign is used for both the gradients.

The resulting 1D data was rearranged into two 𝑀 × 𝑁 2D matrix, one for odd echoes and one for even echoes, where 𝑀 is the number of points per gradient pulses, and 𝑁 is the number of loops. The data was then 2D Fourier transformed to obtain space-frequency domain data. A slice (intensity as a function of z) was extracted at the location of the maximum in the spectral dimension.

A reference profile was obtained by running the simulation for the whole sequence with the translational diffusion coefficient set to 0 m 2 /s. The diffusion decay curve was divided by the reference profile to compensate for the effect of the spatial selectivity of the chirp + gradient block. The diffusion decay curve, after correction by the reference profile, was used to extract the diffusion coefficient via non-linear least square fitting.

When velocity-correction was applied for the detection period, the simulated signal was multiplied element-wise, before 2D FT, by the 𝑀 × 𝑁 matrix 𝑒 !"#$%& ! ' " ( * # +, $ -) , where 𝑡 / is varying from -𝜏 to 𝜏, 𝑛 0 varies from 1 to total number of loops, 𝐺 1 is the strength of acquisition gradient, and 𝑣 2 is the linear velocity (see section IV.C).

B. Numerical simulations with a velocity distribution

The effect of laminar and convection flow can be modelled by dividing the sample in elements of constant velocity, as illustrated in Fig. 2. For that purpose, a cross section of the NMR tube is divided in 𝑛 34 (cs in the subscript stands for cross-section) concentric rings of width 𝑑𝑟. In the case of convection flow, each ring is further divided into 𝑛 5 elements. The total simulated data is obtained with a weighted sum of independent 1D simulations, each performed with constant velocity.

Laminar flow

For laminar flow, the velocities corresponding to different rings were calculated according to: 34

𝑣(𝑟) = 𝑣 617 <1 -= 𝑟 𝑎 ? # @ ( 1
)
where 𝑟 is the radial distance, which varies from 0 to 𝑎, where 𝑎 is the radius of the cross-section of the sample, and 𝑣 617 is the maximum velocity at the center of the cross-section.

Simulations were performed for a grid of radial distance, 𝑟 " , from 0 to 2.5 mm in 281 equal steps. The SPEN DNMR simulations for flow compensated sequence were performed for all the velocities with the parameters, chosen in the starting of this section, except the velocity, dwell time (𝑑𝑤) and number the points in a gradient pulse (𝑚 8 ). The velocity was chosen to be 5 mm/s.

The 𝑑𝑤 was doubled, i.e., 3 × 10 !9 𝑠, and 𝑚 8 was halved, i.e., 64, to decrease the field of view (FOV) without changing the resolution.

The FIDs acquired with even and odd echoes for each velocity are Fourier transformed (FT) along both dimensions separately to provide space-frequency (𝑧 -𝜔) domain data, 𝐼(𝑟).

Since the velocity 𝑣(𝑟) is independent of the angle 𝜙, the double weighted summation over variable radius 𝑟 and angle 𝜙 becomes a single sum as follows:

𝐼 016",1: = 2𝜋 K 𝑎 𝑛 34 , %& ";/ 𝑟 " 𝐼(𝑟 " ) (2)
The same procedure is used to obtain the reference laminar profile, 𝐼 016",1:

:<=

, except all the simulations were performed without diffusion. For analysis and display, the profiles are normalised by dividing the profiles by their maxima.

Convection flow

In the case of convection flow, the velocities vary as

where 𝐽 , and 𝐼 , are Bessel and modified Bessel functions, 𝑛 is the mode of flow, 𝑣 , is a system dependent scalar of velocity for each mode of flow and is non-zero only for odd 𝑛 and zero for even 𝑛, 𝜙 is varied from 0 to 2𝜋, 𝑘𝑟 and 𝑘𝑎 is defined respectively as 𝑅 1 //+ = : 1 ? and 𝑅 1 //+ . The Rayleigh number 𝑅 1 is given by 31

𝑅 1 = - 𝛽𝜌 # 𝑎 + 𝑐 8 𝑔 𝑑𝑇 𝑑𝑍 𝜂𝜅 (4)
where 𝛽 is the volumetric thermal expansion coefficient, 𝜌 is the fluid density, 𝑐 8 is the specific heat capacity, 𝑔 is the acceleration due to gravity, AB AC is temperature gradient, 𝜂 is the dynamic viscosity, and 𝜅 is the thermal conductivity. In the present article 𝑅 1 is taken to be 100.

The velocities were varied according Eq. 3 by incrementing the radial distance 𝑟 sequentially from 0 to 2.5 𝑚𝑚 (𝑎) in the steps of 𝑑𝑟 = 𝑎/𝑛 34 , where 𝑛 34 = 26. The angle 𝜙 was also sequentially varied from 0 to 2𝜋, in the steps of 𝑑𝜙 = 2𝜋/𝑛 5 , where 𝑛 5 = 25. Since for NMR experiments only vertical flow is observed therefore 𝑛 = 1 and 𝑣 / was chosen to be 1.5 mm/s. The 𝑣 / is not the maximum velocity unlike in the case of laminar flow. These values result into a 𝑛 5 × 𝑛 34 (25 × 26) velocity profile shown in Fig. 3. Since the profile was symmetrical with respect to 𝑥 -𝑧 plane, only 13 × 26 = 338 velocities were chosen to perform the simulation for the flow compensated SPEN DNMR sequence. Except for the value of 𝑣 / , all other parameters are the same as in laminar flow.

The 𝑘 -𝑡 domain fids obtained after the simulation are Fourier transformed in both dimensions to result into (64 × 256) space-frequency (𝑧 -𝜔) domain data, 𝐼(𝑟 " , 𝜙 D ) for each velocity. The final diffusion decay profile for the sample undergoing convection is obtained by weighted summation of 𝐼(𝑟, 𝜙) over the radius 𝑟, angle 𝜙.

𝐼 3E,*<3'"E, = K 2𝜋 𝑛 5 , ' D;/ K 𝑎 𝑛 34 , %& ";/ 𝑟 " 𝐼^𝑟 " , 𝜙 D _ (5)
By performing the simulation with zero diffusion coefficient, however following the same procedure described above, the reference profile 𝐼 3E,*<3'"E, :<= is obtained. The diffusion decay curve and reference profiles were extracted from 𝐼 3E,*<3'"E, and 𝐼 3E,*<3'"E, :<=

. For analysis and display, the profiles are normalised by dividing them by their maxima.

III. SPEN DNMR WITHOUT FLOW

Prior to introducing the effect of flow in spatially encoded diffusion NMR pulse sequences, in this section we will be introducing the SPEN STimulated Echo (STE) pulse sequence, used to acquire diffusion-NMR data, and the general analytical expression used for data analysis. [18][19][20][21] In this study, we rely on a description of diffusion NMR experiments in which magnetisation vectors are used to describe the spins of individual atoms in molecules, which undergo random Brownian motion.

This common representation gives correct results for mesoscopic quantities. Note, however, that the numerical simulation in SPINACH instead describes the magnetisation of mesoscopic volume elements. Molecular motion is not explicitly described, and its effect is accounted for by magnetisation passing between volume elements. The two descriptions are complementary.

A. Diffusion attenuation: qualitative description

Consider first a conventional spin echo sequence, shown in Fig. 1a. [START_REF] Pagès | [END_REF] The equilibrium magnetisation is first rotated to the transverse plane by the first 𝜋/2 pulse. The first gradient pulse then results in a linear variation of the spin's phase as a function of position, which corresponds to a magnetisation helix. Brownian motion during the diffusion delay then results in partial scrambling of the helix. The second magnetic field gradient pulse then refocuses the magnetisation helix. However, the refocusing is imperfect, because the molecules' positions have changed between the two gradient pulses. As a result, signal acquired after the gradient pair will be attenuated compared to the signal that would be acquired without gradients pulses, to an extent that depends on the pitch of the magnetisation helix, and thus on the area of the gradient pulses. Quantitatively, this attenuation is given by: 48

𝑆 = 𝑆 ? 𝑒 !% ( F ( G ( HI ) (6)
where 𝑆 ? is the amplitude in the absence of diffusion attenuation, 𝛾 is gyromagnetic ratio of the nuclei, 𝑔 is the gradient strength, 𝛿 is the gradient duration, 𝐷 is the diffusion coefficient, and Δ J is the diffusion delay, corrected to account for the finite width of the gradient pulse (for example,

Δ J = Δ -Δ -𝛿/3 in the classic stimulated echo pulse sequence).
This description applies similarly to the conventional stimulated echo pulse sequence, shown in Fig. 1b. The second and first 𝜋/2 pulses in that case serve to store magnetisation along the z axis, to mitigate the effects of relaxation and J modulation, but they have no effect on the diffusion encoding process (the information is temporarily transferred from the spin's phase to their amplitude).

Consider now the SPEN STE DNMR pulse sequence shown in Fig. 1c. [18][19][20][21] The hard 𝜋/2

pulses play the same role as in the conventional sequence. The gradient pulses are replaced by the combined application of a frequency-swept pulse and a gradient pulse. The result of this spatial encoding block is that the effective duration of the gradient pulse experienced by the spins depends on their position in the sample. Considering also the gradient pulse applied after the chirp pulse, the effective duration of the total gradient pulse varies from 0 at one end of the swept region to 2𝑇 < at the other end. This results in a quadratic dependence of the magnetisation's phase with respect to position. Pictorially, this corresponds to a magnetisation helix with a pitch that varies across the sample. Brownian motion during the diffusion delay does, as in the conventional experiment, scramble the helix. And, as in the conventional experiment, the perfect refocusing of the magnetisation, that would be achieved by the second chirp + gradient block in the absence of diffusion, is compromised by molecular motion. The key feature of the SPEN DNMR experiment is that the effect of diffusion is now position dependent. In the absence of flow, the signal acquired for a slice at position z (with a slice width such that the phase variation is approximately linear within the slice), is given by a generalised form of Eq. 6 :

49 𝑆 = 𝑆 ? 𝑒 !KL(2)M ( HI ) (7)
where 𝐷 is the diffusion coefficient, 𝛥′ is the effective diffusion delay, and 𝐾(𝑧) is the spatial derivative of the spin's phase 𝜙 NOPQ (𝑧) at the end of the first chirp + gradient block: 50

𝐾(𝑧) = 𝜕𝜙 NOPQ (𝑧) 𝜕𝑧 (8)
Equation 7 can be derived in several ways. Here we will use the propagator model, which provides a convenient way to then include flow effects.

B. Diffusion attenuation with the propagator model

Assuming that gradient pulses are sufficiently short for the effect of diffusion during the pulses to be negligible (the "narrow-pulse approximation"), the echo amplitude for a pair of identical gradient pulses separated by a delay Δ is given by 33

𝐸 = i 𝑃 4 k (𝑍, 𝛥)𝑒 "5(C) 𝑑𝑍 ( 9
)
where 𝑍 is the dynamic displacement in the gradient direction, 𝜙(𝑍) is the spin phase at the end of the second gradient pulse for a molecule displaced by 𝑍, and 𝑃 4 k (𝑍, 𝛥) is the average probability that molecules are displaced by 𝑍 in time 𝛥. If translational diffusion is the only motion, then this propagator is given by: 33

𝑃 4 k (𝑍, 𝛥) = (4𝜋𝐷𝛥 ) !/ # ⁄ 𝑒 !C ( + ⁄ HI (10)
In order to calculate the attenuation for a given pulse sequence, one needs to calculate the term 𝜙(𝑍). Since the pulse sequence is designed as an echo sequence, the contribution of chemical shift evolution to the phase will not be included during the phase calculation.

The spin phase after the first chirp + gradient block of the SPEN STE pulse sequence can be calculated by assuming that spins flip instantaneously when their resonance frequency matches that of the swept pulse. With this assumption, one has: 49

𝜙 NOPQ (𝑧) = - 𝛾 # 𝐺 < # 𝑅 𝑧 # -𝛾𝐺 < 𝑇 < 𝑧 (11)
For the SPEN STE pulse sequence, the phase 𝜙 NBP at the end of the second chirp + gradient block is thus

𝜙 NBP (𝑧, 𝑧 ? ) = - 𝛾 # 𝐺 < # 𝑅 𝑧 # -𝛾𝐺 < 𝑇 < 𝑧 + 𝛾 # 𝐺 < # 𝑅 𝑧 ? # + 𝛾𝐺 < 𝑇 < 𝑧 ? (12)
where 𝑧 ? and 𝑧 are the position of the molecule at the time of the first and second gradient pulse.

Eq. 12 may be rearranged as:

𝜙 NBP (𝑧, 𝑧 ? ) = -𝛾𝐺 < 𝑇 < (𝑧 -𝑧 ? ) l1 + 𝛾𝐺 < 𝑅𝑇 < (𝑧 ? + 𝑧)m (13)
Introducing the dynamic displacement, 𝑍 = 𝑧 -𝑧 ? , one has:

𝜙 NBP (𝑍) = -𝛾𝐺 < 𝑇 < 𝑍 l1 + 𝛾𝐺 < 𝑅𝑇 < (2𝑧 -𝑍)m (14)
𝜙 NBP (𝑍) = -𝛾𝐺 < 𝑇 < 𝑍 <1 + 2 𝛾𝐺 < 𝑅𝑇 < 𝑧@ + 𝛾 # 𝐺 < # 𝑅 𝑍 # (15)
For translational diffusion alone, the mean squared displacement is given by 2𝐷Δ, and the last term on the right-hand side of Eq. 15 is negligible provided that

2𝐷𝛥 ≪ 𝜋𝑅 𝛾 # 𝐺 < # (16)
This condition means that the diffusion length is much smaller than the length of the spatial region over which the phase variation can be considered to be linear. 50 This quantity will be referred to as the encoding slice width. This condition is usually verified, giving:

𝜙 NBP (𝑍) ≈ -𝛾𝐺 < 𝑇 < 𝑍 <1 + 2 𝛾𝐺 < 𝑧 𝑅𝑇 < @ (17)
The approximation of neglecting the squared dynamic displacement in the phase calculation will be referred to as the small-displacement approximation. Equation 17 can be rewritten by identifying the spatial derivative of the spin's phase at the end of the chirp + gradient block:

𝜙 NBP (𝑍) ≈ 𝐾(𝑧)𝑍 (18)
The echo amplitude calculated from Eqs. 9, 10 and 18 provides, after some algebra, the required diffusion-decay equation:

𝐸 NBP H (𝑧) = 𝑒 !KL(2)M ( H∆ (19)

C. Echo planar spectroscopic imaging

The spatial-spectral information embedded in the diffusion decay curve obtained after the SPEN STE sequence is unravelled by a train of bipolar gradient pulses, preceded by a prephasing gradient pulse. This acquisition block is known as echo planar spectroscopic imaging (EPSI). In Fig. 1c and Fig. 1d, EPSI blocks are shown as the final step of the pulse sequences. The phase acquired by the magnetization during the EPSI block is given by

𝜙 13T (𝑡) = -𝛾 Mi 𝑑𝑡 J 𝐺(𝑡 J ) ' ? P 𝑧 (20)
where 𝐺(𝑡′) is the variable acquisition gradient strength (which is +Ga for positive pulses and -Ga for negative pulses). Fig. 4a shows the result of a numerical simulation of an EPSI block, together with the analytical expression given by Eq. 20. The phase during acquisition varies linearly with positive and negative slopes respectively for positive and negative gradients. Further, the phase refocuses at the middle of the odd echo (positive gradient), and even echo (negative gradient).

Data processing and acquisition in MRI is conveniently described by introducing the variable

𝑘(𝑡) = -𝛾 ∫ 𝑑𝑡 J 𝐺(𝑡 J ) ' ?
. The EPSI block results in a zig-zag trajectory in a 2D 𝑘 -𝑡 space. The data from the prephasing gradient is discarded (or simply not acquired). The data from the odd echoes forms a 2D matrix that can be Fourier transformed to give a spectroscopic image. The data from even echoes is processed similarly. The two can be co-added when they give comparable results, which is the case in the absence of flow. The spectroscopic data is then used to extract the diffusion coefficient via least square fitting method with the model Eq. 19 or more precisely Eq. 7.

IV. VELOCITY EFFECTS IN SPEN DNMR

Conventional diffusion NMR pulse sequences are sensitive to flow effects. When molecules move with constant velocity 𝑣 2 during a stimulated echo pulse sequence, spins acquire an additional phase variation that is proportional to 𝑣 2 and to the diffusion delay. Similarly, flow also imparts an additional phase to the spins, and to the signal, in SPEN STE pulse sequences. It has been shown, as in the case of conventional diffusion NMR pulse sequences, that the use of two diffusion-encoding steps instead of one makes it possible to refocus the velocity-induced phase 51,52 . For example, the SPEN double stimulated echo pulse (DSTE) pulse sequence, shown in Fig. 1d, was used for experiments in low-viscosity organic solvents. 22,24 It consists of two consecutive SPEN STE blocks separated by a 𝜋 pulse. In this section we will be calculating analytically velocity effects in SPEN DNMR pulse sequence, using the propagator model.

A. Simplified calculation of velocity effects

The effect of a molecular displacement with constant velocity 𝑣 2 during the diffusion delay of a STE pulse sequence can be taken into account in the propagator model by modifying the propagator as:

𝑃 4 k (𝑍, 𝛥) = (4𝜋𝐷𝛥 ) !/ # ⁄ 𝑒 !(C!* # I) ( + ⁄ HI (21)
The distribution of dynamic displacements is now centred on 𝑣 2 Δ. The echo amplitude for the SPEN STE block can then still be calculated according to Eq. 9. Let us assume first that the small displacement approximation is fully valid. This gives:

𝐸 NBP,1 H,* (𝑧) = 𝑒 !KL(2)M ( HI 𝑒 "L(2)* # I (22)
The superscript refers to the fact that both diffusion and velocity effects are taken into account, while the subscript a refers to the fact that an approximate expression of the spin's phase was used.

Consider now the SPEN DSTE pulse sequence. The spin's phase at the end of the final chirp + gradient block is:

𝜙 HNBP (𝑧, 𝑧 ? , 𝑧 / ) = -𝛾𝐺 < 𝑇 < (𝑧 / -𝑧) M1 + %& * VB * (𝑧 + 𝑧 / )P + 𝛾𝐺 < 𝑇 < (𝑧 -𝑧 ? ) M1 + %& * VB * (𝑧 ? + 𝑧)P (23)
where 𝑧 ? , 𝑧, and 𝑧 / are the position at the time of the first, second, and fourth chirp + gradient block (the spin's position is assumed to be unchanged between the second and third blocks).

Equation 23 may be rewritten by introducing the dynamic displacements 𝑍 = 𝑧 -𝑧 ? , and 𝑍 J = 𝑧 / -𝑧 during the first and second diffusion encoding blocks:

𝜙 HNBP (𝑍, 𝑍′) = -𝛾𝐺 < 𝑇 < 𝑍′ <1 + 𝛾𝐺 < 𝑅𝑇 < 2𝑧@ + 𝛾 # 𝐺 < # 𝑅 𝑍′ # + 𝛾𝐺 < 𝑇 < 𝑍 <1 + 𝛾𝐺 < 𝑅𝑇 < 2𝑧@ - 𝛾 # 𝐺 < # 𝑅 𝑍 # (24)
Assuming that the small-displacement approximation is valid:

𝜙 HNBP (𝑍, 𝑍′) ≈ -𝛾𝐺 < 𝑇 < 𝑍′ <1 + 𝛾𝐺 < 𝑅𝑇 < 2𝑧@ + 𝛾𝐺 < 𝑇 < 𝑍 <1 + 𝛾𝐺 < 𝑅𝑇 < 2𝑧@ (25)
Identifying 𝐾(𝑧), Eq. 25 can be written:

𝜙 HNBP (𝑍, 𝑍′) ≈ 𝐾(𝑧)𝑍 J -𝐾(𝑧)𝑍 (26)
Substituting the value of phase from Eq. 26 and the average probability factor 𝑃 4 k (𝑍, 𝛥) from Eq. 21 in Eq. 9 results into the echo amplitude after the final chirp + gradient block of the SPEN DSTE pulse sequence:

𝐸 HNBP,1 H,* (𝑧) = 𝑒 !#KL(2)M ( HI (27)
The above analytical expression shows that the phase factor, 𝑒 "L(2)* # W , appeared during the first stimulated echo due to flow is compensated after a 𝜋 pulse and second stimulated echo.

Numerical simulations provide a powerful mean to test the validity of analytical expressions and of the underlying approximations. Fig. 5 and Fig. 6 show a comparison between the calculated echo amplitude and phase for the SPEN STE and DSTE pulse sequences, given by Eqs 22 and 27, and the result of a numerical simulation of these pulse sequence. Both the magnitude and the phase of the transverse magnetisation are shown. Note that the result of Eq.

22 and 27 is multiplied for that comparison by the reference profile obtained by numerical simulation in the absence of diffusion (see section II), since the analytical calculation does not account for the spatial selectivity of the chirp pulse.

It can be seen that the linear phase observed for the STE sequence in the presence of flow is suppressed for the DSTE sequence. However, while there is good agreement between analytical calculation and numerical simulation of the magnitude in the absence of flow, there is a clear difference between the calculated and the simulated results in the presence of flow. In fact, when the simulated data is fitted according to Eq. 27, a value of 5.06(±0.06)×10 -10 m 2 /s is obtained in the presence of flow, against 7.95(±0.00)×10 -10 m 2 /s in the absence of flow.

The discrepancy between numerical simulations and analytical calculation can be traced back to the validity of the small-displacement approximation. While it is always valid in the case of diffusion alone, it is not necessarily the case when flow is present as well. For example, with a velocity of 0.01 m/s and a diffusion delay of 150 ms, molecules move by 1.5 mm between two gradient pulses.

B. Diffusion attenuation and convection compensation, full calculation

In order to separate the effect of diffusion and flow in the calculation of the echo amplitude, it is helpful to make the change of variables

𝑍 ⟵ 𝑍 + 𝑣 2 𝛥 (28)
in Eq. 9. With this replacement, the propagator, Eq. 21, accounts for diffusion only and becomes equivalent to the propagator shown in Eq. 9, while the phase shift becomes, in the STE case:

𝜙 NBP = 𝑘(𝑧)(𝑍 + 𝑣 2 𝛥) + (𝑍 + 𝑣 2 𝛥) # 𝛾 # 𝐺 < # 𝑇 < 2𝜋𝐵𝑊 (29)
The small-displacement approximation remains valid for diffusion, meaning that terms including 𝑍 # can be neglected. This gives:

𝜙 NBP = M𝑘(𝑧) + 2𝑣 2 𝛥 𝛾 # 𝐺 < # 𝑇 < 2𝜋𝐵𝑊 P 𝑍 + 𝑘(𝑧)𝑣 2 𝛥 + 𝑣 2 # 𝛥 # 𝛾 # 𝐺 < # 𝑇 < 2𝜋𝐵𝑊 (30)
Combining Eq. 9, 10, and 30 gives, after some algebra:

𝐸 NBP H,* (𝑧) ≃ 𝑒 !XKY(2)M ( HIZ +* # ( I ( % + & * + B * ( (#$[\) ( HIZ+Y(2)* # I % ( & * ( B * #$[\ HI] 𝑒 "Y(2)* # I 𝑒 "X* # ( I ( % ( & * ( B * #$[\ ] (31)
For typical values of the linear velocity, the argument of the complex exponential in Eq. 31 is

negligibly small, such that:

𝐸 NBP H,* (𝑧) ≈ 𝑒 !XKY(2)M ( HIZ +* # ( I ( % + & * + B * ( (#$[\) ( HIZ+Y(2)* # I % ( & * ( B * #$[\ HI] 𝑒 "Y(2)* # I (32)
Defining the encoding slice width as

𝑙 < = #$V % ( & * ( , where 𝑅 = [\ B *
, and root mean square displacement (diffusion length) as 𝜆 = √2𝐷Δ, this equation becomes

𝐸 NBP H,* (𝑧) ≈ 𝑒 !Y(2) ( H∆ 𝑒 "Y(2)* # ∆ 𝑒 !#Y(2)* # I ^( 0 * 𝑒 !#* # ( I ( X 0* ] ( (33)
Fig. 5a shows a comparison between the simulated diffusion decay, and the analytical calculation according to Eq. 33. In this case, the simulated and calculated curves are in very good agreement. The small-displacement approximation can be invalid for the flow contribution, in which case the full expression given by Eq. 33 should be used. The small-displacement approximation remains valid for the diffusion contribution. This is consistent with the fact the displacement due to velocity is larger than the encoding slice width, while that due to diffusion is not.

It is interesting to compare the expression of the echo amplitude obtained with (Eq. 22)

and without (Eq. 33) making the small-displacement approximation for the flow contribution. Out of the two extra exponential term, the second one is close to one, while the first one has a noticeable role. In fact, if a simulated decay is fitted with Eq. 33, then a diffusion coefficient of 7.77(±0.00)×10 -10 m 2 /s is obtained (against 5.39(±0.01)×10 -10 m 2 /s using Eq. 22).

A similar calculation can be performed in the DSTE case. Here we simply report the result that is obtained by making the small-displacement approximation for diffusion only:

𝐸 HNBP H,* (𝑧) ≈ 𝑒 !#H∆Y(2) ( 𝑒 !+Y(2)* # ∆ ^( 0 * 𝑒 !_* # ( I ( X 0* ] ( (34)
Fig. 5b shows a comparison between simulated diffusion decay and analytical expression for DSTE, and the two are in excellent agreement.

Several points can be noted from a comparison of Eqs 27, 33 and 34. First, one can see that, in analogy with the conventional case, double diffusion encoding for SPEN DNMR makes it possible to refocus velocity induced phase variations. However, double diffusion encoding does not compensate for the fact that the position of the encoded region changes between the beginning and the end of each diffusion delay. The use of Eq. 34 for data analysis still makes it possible to retrieve the correct value of the diffusion coefficient, provided that the velocity is known. This will be further discussed below.

C. EPSI: velocity compensation and motion correction

In order to analyse the effect of flow during EPSI, the effect of a constant velocity term on the gradient phase was calculated by replacing 𝑧 by 𝑧 ? + 𝑣 2 𝑡′, where 𝑧 ? is the initial position at the time 𝑡 = 0, in Eq. 20. [START_REF] Haacke | Magnetic Resonance Imaging Physical Principles and Sequence Design[END_REF] The resulting phase during acquisition will hence be given by

𝜙 13T * (𝑡) = -𝛾 i 𝑑𝑡 J 𝐺(𝑡 J )(𝑧 ? + 𝑣 2 𝑡′) ' ? (35)
where 𝐺(𝑡′) is variable acquisition gradient strength and is +Ga for positive pulse and -Ga for negative pulses. While the phase gets refocused at the middle of odd and even echo in absence of flow, (Fig. 4a) the phase in presence of flow only refocuses at the middle of even echoes. It can be shown if we calculate the total phase accumulated at 4𝜏, [START_REF] Haacke | Magnetic Resonance Imaging Physical Principles and Sequence Design[END_REF]40 𝜙 13T `= (𝑡 = 4𝜏) = -𝛾 ∫ 𝑑𝑡 J (-𝐺 1 )(𝑧 ? + 𝑣 2 𝑡′)

- ? -𝛾 ∫ 𝑑𝑡 J (𝐺 1 )(𝑧 ? + 𝑣 2 𝑡′) #- - -𝛾 ∫ 𝑑𝑡 J (𝐺 1 )(𝑧 ? + a- #- 𝑣 2 𝑡′) -𝛾 ∫ 𝑑𝑡 J (-𝐺 1 )(𝑧 ? + 𝑣 2 𝑡′) +- a- = +𝛾𝐺 1 =𝑧 ? 𝜏 + 𝑣 2 -( # ? -𝛾𝐺 1 =𝑧 ? (2𝜏 -𝜏) + 𝑣 2 +-( !-( # ? -𝛾𝐺 1 =𝑧 ? (3𝜏 -2𝜏) + 𝑣 2 b-( !+-( # ? + 𝛾𝐺 1 =𝑧 ? (4𝜏 -3𝜏) + 𝑣 2 /9-( !b-( # ? = 0 (36)
This means that under flow condition, the data from even echoes should be more reliable.

The expression obtained from Eq. 35 can be validated with the result of numerical simulations. The phase of a magnetisation vector at a given position can be obtained from the density matrix as a function of time. Since the velocity induced dephasing is position independent, the comparison can be made for any position in the sample. Fig. 4b shows a comparison between analytical and simulated phases during EPSI for a slice at z = 4.5 mm, for the first loop. The two are in perfect agreement.

Using data from even echoes ensures that the magnetisation is suitably refocused at the middle of the gradient pulse even with non-zero velocity. This does not, however, address the fact that the position of the encoded region changes during acquisition. With the parameters used for the simulation (dwell time = 1.5×10 -6 s, number of loops = 256, number of points in odd/even echo = 128, velocity (vz) = 0.01 m/s ), the position varies in the range of few 𝜇𝑚 to 1 𝑚𝑚, it results in shifting of magnetisation along the spatial axis. This effect is most easily observed by comparing the Fourier transform of the first and last acquired echoes, for a SPEN DNMR pulse sequence, shown in Fig. 7. If uncorrected, this displacement will introduce an error for the estimated diffusion coefficient. This effect can also be described by considering the phase of the magnetisation throughout the echo train. The phase during the nl th even echo can be written as:

𝜙 13T * (𝑡) = 𝛾𝐺 1 𝑡 / M𝑧 ? + 𝑣 2 (𝑡 / + 8𝑛 0 𝜏) 2 P ( 37
)
where 𝑡 / is varying from -𝜏 to 𝜏. Correction by this additional phase in 𝑘-dimension will result into linear shift in density matrices along the 𝑧-dimension. The overall density matrix in 𝑘 -𝑡 dimension can be obtained by

𝜌 = ∫ 𝜌(𝑧)𝑒 "#$5 !%, -(') 𝑑𝑧 𝜌 = ∫ 𝜌(𝑧)𝑒 Z"#$%& ! ' " 2 . 𝑒 Z"#$%& ! ' " c * # ' " # d 𝑒 Z"#$%& ! ' " ( * # +, $ -) 𝑑𝑧 (38)
Since the factor 𝑒 Z"#$%& ! ' " c * # / " ( d ≈ 1 with the chosen parameters, i.e., 𝑣 2 = 0.01 𝑚/𝑠, 𝑡 / = -64 × 1.5 × 10 !9 to 64 × 1.5 × 10 !9 , therefore

𝜌 = ∫ 𝜌(𝑧)𝑒 "#$%& ! ' " 2 . 𝑒 "#$%& ! ' " ( * # +, $ -) 𝑑𝑧 (39)
On multiplying the 𝑘 -𝑡 space data by 𝑒 !"#$%& ! ' " ( * # +, $ -) to remove the effect of additional phase results into a non-sheared 𝑧 -𝜔 space data, as shown in Fig. 6b.

V. FLOW SIMULATIONS

Having clear understanding of flow effects during the encoding and acquisition part, the effect of different kinds of flow distributions on SPEN DNMR sequences can be studied. The constant/plug flow corresponds to the simplest situation, the other two most often encountered flow in NMR are laminar flow 34 and convection flow. 32 In the further section we will discuss these three kinds of flows in the context of SPEN D-NMR.

A. Plug flow

The first case of interest is that of plug flow, that is, motion with a single and uniform velocity.

This case was also studied with simulation in Ref. 24 Fig. 8 shows the result of the complete simulation of a SPEN DSTE pulse sequence. In panel 8a and 8b, the simulated data was processed without velocity correction, and fitted with Eq. 34 (which accounts for velocity effects). It can be seen that the resulting diffusion coefficient, 6.27 (±0.14) × 10 -10 m 2 /s, is under-estimated by 14 %.

In contrast, when the data is processed with velocity correction, the estimated diffusion coefficient is 7.90(±0.01) ×10 -10 m 2 /s , which is much closer to the correct value, as shown in panels 8c and 8d. Overall, in order to obtain the correct value of the diffusion coefficients, the effects of flow have to be accounted for during both encoding and detection, and this requires knowledge of the value of the linear velocity. The SPEN DSTE sequence, using even echoes, makes it possible to avoid velocity induced dephasing, but not distortions of the spatial profile. Note that, even if it is not a priori known, the velocity may be measured by NMR, using, for example, a spin-echo based sequence. In principle it may even be possible to obtain the velocity from the phase difference between the centre points of even and odd echoes in the EPSI data. This can be achieved for the present simulated data, but in practice it would be susceptible to errors due to, e.g. chemical shift evolution.

These results may be compared with those of Ref. 24 , which also considered a double-diffusion encoding pulse sequence. In that work, however, flow was only included during the diffusion delays, and not during detection, for the simulations. The observed error, of about 12 %, was then due to the fact that Eq. 19 was used for the fit, which does not account for velocity effects.

Interestingly, as shown in Fig. 9, when velocity effects are not accounted for in the analysis, the fitted diffusion coefficient varies linearly with the input coefficient. The separation power of the experiments would thus still be preserved to some extent. It can be noted, however, that the associated error bar is larger when velocity is not accounted for, because the data is not suitably described by the model. The agreement between fitted and input values is conserved in the presence of noise. By introducing varying levels of noise in the data, it was observed that the estimated uncertainty remains lower than 0.01 m 2 /s as long as signal-to-noise ratio (S/N) remain ≥ 100.

B. Laminar flow

Laminar flow is the side-by-side movement of layers of liquid along the direction of flow. The layer near to the surface moves with the minimum velocity mostly due to friction with the surface, however, the layers away from the surface move with higher velocity and reaches a maximum velocity at the centre of the cylinder. The velocity varies from 0 at the edge to 𝑣 617 in the centre, and has mean value ∫ 𝑟𝑑𝑟 𝑣 2 1 ?

/ ∫ 𝑟𝑑𝑟 = 𝑣 617 /2 1 ?

. Since the velocity in each layer is assumed to be constant, the profile obtained with SPEN DNMR in the case of laminar flow can be modelled as a weightage average of the various constant velocity profiles, as discussed in section II.A.

The profile in the case of laminar flow, 𝐼 016",1: and the corresponding reference profile 𝐼 016",1:

:<= (obtained with zero diffusion coefficient), are used as input for analysis. In this case, the correction for velocity effects during EPSI, described in section IV.C, cannot be performed.

Attempts to perform this correction using the mean velocity were unsuccessful. This is unsurprising, since the average of profiles that are shifted by different amounts is not expected to be the same as a single profile shifted by the mean displacement. This means that motion during detection can limit the accuracy of SPEN DNMR experiments carried out on a sample that experience laminar flow.

The simulated data in the case of even echoes is shown in Fig. 10a. When this data is fitted with Eq. 34, using the mean velocity, to extract the diffusion coefficient, a value of 6.45(±0.04)×10 - 10 m 2 /s is obtained for the diffusion coefficient. This result is consistent with the plug flow case where the additional velocity correction was not performed and the diffusion coefficient was found to be 6.27(±0.14)×10 -10 m 2 /s. Note that a value of 5.87(±0.06)×10 -10 m 2 /s is obtained with Eq. 27 is used for the fit, illustrating the fact that the error is reduced when velocity-effects during encoding are accounted for.

The data acquired for the odd echoes was also processed through the same procedure discussed above and had resulted into 5.97(±0.07)×10 -10 m 2 /s diffusion coefficient which is further from the simulated value. The diffusion decay curve with reference profile and the fitted curve have been shown in Fig. 10. The less accurate diffusion coefficient while processing with odd echoes further testifies the processing of even echo acquired data for the extraction of diffusion coefficient.

Overall, this means that convection compensated SPEN DNMR sequences should be able to achieve 20 % accuracy when applied to a sample that flows with a laminar flow. These results will be compared against experimental measurement, that will require the use of a low-pulsation pump. Indeed, any time dependence of the velocity would severely compromise the possibility to retrieve accurate diffusion information with spatially encoded diffusion NMR.

C. Convection flow

Convection is a heat transfer process in a fluid through the motion of matter, and happens due to temperature differences between two parts of the sample. In many PFG NMR experiments, the effect of convections translates into inaccurate estimates of the diffusion coefficients, 53 and this is also true for spatially encoded diffusion NMR. A typical convection velocity profile for an NMR tube is shown in . The difference between the density of heated and colder particles results into a complicated velocity distribution in the NMR tube. The possibility to compensate for this effect in SPEN DNMR experiments is illustrated in Fig. 11, which shows the result of numerical simulation performed with a convection-compensated SPEN DSTE pulse (Fig. 1d).

The estimated diffusion coefficient, using Eq. 27 (which is equivalent to Eq. 34 with using 𝑣 2 = 0), and no velocity correction during processing, is found to be to be 7.90(±0.00)×10 -10 m 2 /s, when the data acquired during even echoes were processed. In contrast, with odd echo data the diffusion coefficient was found to be 8.94(±0.05)×0 -10 m 2 /s. As in the case of constant and laminar flow, the even echo data provides more reliable results than the odd echo data. Further the diffusion coefficient is more accurate than the one obtained for the laminar flow. It is due to the fact that in convection, the effect of velocities throughout the sample gets compensated due to its anti-symmetrical distribution with respect to centre of the tube. In the case of laminar flow that the inability of performing the velocity effect correction results into the deviation from the accurate value of diffusion coefficient. In contrast, in the case of convection, although the same correction is not performed, compensation of error occurs between the effect of positive velocities in one half of the sample, and that of negative velocities in the other half.

Overall, these results explain why the convection compensated SPEN DNMR pulse sequence should have high accuracy in the case of convection flow, as was observed experimentally.

VI. CONCLUSIONS

In summary, we have provided a detailed description of flow effects in SPEN DNMR pulse sequences, through theoretical analyses and numerical simulations. These results explain the possibility to measure accurate diffusion coefficients with convection-compensated SPEN DNMR pulse sequences. They also give methods that should be applicable to systems in continuous flow, based on the processing of even-echo data only, and, in the case of plug flow, on a correction for sample motion effect. Overall, this works provides both physical insight and practical tools for applications of spatially encoded diffusion NMR methods in the presence of sample flow.

Author's contributions FIGURES

Fig. 1 .

 1 Fig. 1. Diffusion NMR pulses sequences. Hard RF pulses are shown as filled rectangles, swept RF pulses are shown as rectangles with an arrow, gradients pulses are represented as empty rectangles. The roman numbers (I, II, III, IV) in the bottom of (b) and (c) are used to show the helices at the corresponding positions of the pulse sequence. (a) Pulsed field gradient spin echo sequence. (b) Pulsed field gradient stimulated echo sequence. (c) Stimulated echo pulse sequence for spatially encoded diffusion-ordered NMR spectroscopy (SPEN DOSY STE). (d) Flow compensated double stimulated echo pulse sequence for spatially encoded diffusion-ordered NMR spectroscopy (SPEN DOSY DSTE). For sequence (b) and (c), the transverse magnetization as a function of axis-z is shown at specific stages of the sequence.

Fig. 2 .Fig. 3 . 54 Fig. 4 .

 23544 Fig.2. Cross-section of an NMR tube representing the grids used for integration when simulating laminar and convection flow.

Fig. 5 .

 5 Fig. 5. Comparison between simulated and analytical echo amplitudes for the (a) SPEN STE and (b) SPEN DSTE pulse sequence, with constant velocity. Simulated echo amplitudes are shown in green. Analytical echo amplitudes obtained with the small displacement approximation for both diffusion and flow are shown in pink (Eq. 22 and 27. Analytical echo amplitudes obtained without the small displacement approximation for diffusion (Eq. 33 and Eq. 34) are shown in blue.

  After stimulated echo (STE) (b) After double stimulated echo (DSTE)

Fig. 6 .

 6 Fig. 6. Comparison between simulated and analytical phases for the (a) SPEN STE and (b) SPEN DSTE pulse sequence, with constant velocity. Simulated phases are shown in green. Analytical phases are shown in pink (Eq. 22 and 27).

Fig. 7 .Fig. 8 .

 78 Fig. 7. Diffusion decay profiles (a) without and (b)with velocity correction after first (𝑛 $ = 1) and last EPSI loop (𝑛 $ = 256).

34 zFig. 9 .

 349 Fig. 9. Comparison between input and fitted values of the diffusion coefficient, for a series of values of the input diffusion coefficient. The analysis of the simulated data is carried out with (blue) and without (red) taking into accoung velocity effects.

Fig. 10 .

 10 Fig.10. Laminar flow simulation. Diffusion decay profile (red) and reference profile (green) obtained by processing and analysis of (a) even or (b) odd echoes of the EPSI train. Diffusion decay data (red circle), obtained after dividing the diffusion decay profile by reference profile and fitted curve (blue line) after processing and analysis of (a) even or (b) odd echoes of the EPSI train. Without correction the diffusion coefficient is found to be 6.45(±0.04)×10 -10 m 2 /s, while after correction the value of diffusion coefficient is 5.97(±0.07)×10 -10 m 2 /s.

34 AmplitudeFig. 11 .

 3411 Fig.11. Convection flow. Diffusion decay profile (red) and reference profile (green) obtained by processing and analysis of (a) even or (b) odd echoes of the EPSI train. Diffusion decay data (red circle), obtained after dividing the diffusion decay profile by reference profile and fitted curve (blue line) after processing and analysis of (a) even or (b) odd echoes of the EPSI train. Without correction the diffusion coefficient is found to be 7.90(±0.00)×10 -10 m 2 /s, while after correction the value of diffusion coefficient is 8.94(±0.05)×10 -10 m 2 /s.

34 Amplitude

 34 Diffusion decay curve and reference profile Even echo processing (b) Reference profile corrected diffusion data and fitted curve with Eq.34 Amplitude (a.u.) z (mm) z (mm) Odd echo processing (c) Diffusion decay curve and reference profile (d) Reference profile corrected diusion data and fitted curve with Eq.

ACKNOWLEDEGEMENT

This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement no 801774), the Region Pays de la Loire (Connect Talent HPNMR). The authors also acknowledge the French National Infrastructure for Metabolomics and Fluxomics MetaboHUB-ANR-11-INBS-0010 (www. metabohub.fr) and the Corsaire metabolomics core facility (Biogenouest).

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.


Aurélie Jourdes

Margaux Lafaurie
email: margaux.lafaurie@univ-tlse3.fr

Guillaume Martin-Blondel

Pierre Delobel

Marie Faruch

Sandrine Charpentier

Vincent Minville

Stein Silva

Claire Thalamas

Agnès Sommet

Guillaume Moulis

Muriel Alvarez

Jacques Amar

Michel Attal

Laurent Balardy

Frédéric Balen

Odile Beyne-Rauzy

Ourdia Bouali

Fanny Bounes

Christophe Bureau

Louis Buscail

Lionel Calviere

François Chollet

Isabelle Claudet

Arnaud Constantin

Alexa Debard

Del Arnaud

Karen Bello

Julien Delavigne

Alain Delrieu

Stanislas Didier

Olivier Faguer

Bernard Fourcade

Etienne Georges

Sophie Grunenwald

Hélène Guyonnet

Christophe Hanaire

Nassim Hein

Olivier Kamar

Pierre Lairez

Jérémie Mansat

Carle Pariente

Pierre Paul

Grégory Payoux

Agnès Pugnet

Christian Ribes

Yves Recher

Adeline Rolland

Jean Ruyssen-Witrand

Laurent Sabatier

Jean-Pierre Sailler

Nicolas Salles

Marion Sans

Annick Secher

Olivier Toulza Sevely

Clinical characteristics and outcome of hospitalized patients with SARS-CoV-2 infection at Toulouse University hospital (France). Results from the Covid-clinic-Toul cohort

Keywords: COVID-2019, SARS-CoV-2, epidemiology. Résumé COVID-19, SARS-CoV-2, épidémiologie acute respiratory distress syndrome, COPD: chronic obstructive pulmonary disease, ICU: intensive care unit, NA: Not available

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

Introduction

The Coronavirus disease 2019 (COVID- [START_REF] Plaçais | COVID-19: Clinical, biological and radiological characteristics in adults, infants and pregnant women. An up-to-date review at the heart of the pandemic[END_REF], caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has been first reported in Wuhan, China, in December 2019 [START_REF] Zhu | A Novel Coronavirus from Patients with Pneumonia in China[END_REF][START_REF]Report of clustering pneumonia of unknown etiology in Wuhan City[END_REF]. It has subsequently spread to other provinces of China and then worldwide. The World Health Organization declared COVID-19 outbreak a pandemic on March 11, 2020. SARS-CoV-2 causes viral pneumonia that can lead to severe acute respiratory distress syndrome (ARDS) and even death. Previous studies have reported the clinical, biological and radiological characteristics of the first infected patients in Wuhan area [START_REF] Huang | Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China[END_REF][START_REF] Chen | Epidemiological and clinical characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan, China: a descriptive study[END_REF][START_REF] Wang | Clinical Characteristics of 138 Hospitalized Patients With 2019 Novel Coronavirus-Infected Pneumonia in Wuhan, China[END_REF], and other authors have compared the epidemiological and clinical features of patients with COVID-19 in Wuhan and other regions in China [START_REF] Xu | Clinical findings in a group of patients infected with the 2019 novel coronavirus (SARS-CoV-2) outside of Wuhan, China:retrospective case series[END_REF][START_REF] Lei | A cross-sectional comparison of epidemiological and clinical features of patients with coronavirus disease (COVID-19) in Wuhan and outside Wuhan, China[END_REF][START_REF] Guan | Clinical characteristics of coronavirus disease 2019 in China[END_REF]. Especially, disease evolution and risk factors of complications, essentially ARDS, have been described in this population [START_REF] Wu | Risk factors associated with acute respiratory distress syndrome and death in patients with coronavirus disease 2019 pneumonia in Wuhan, China[END_REF][START_REF] Zhou | Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China:a retrospective cohort study[END_REF]. Due to a lack of consensual hospitalization criteria, data about hospitalized patients are heterogeneous.

To date, clinical characteristics and outcomes of patients outside China have been reported mostly in Asia, Italy and in the Unites States of America, and mostly for patients admitted to intensive care units (ICU) [START_REF] Young | Epidemiological features and clinical course of patients infected with SARS-CoV-2 in Singapore[END_REF][START_REF] Grasseli | Baseline characteristics and outcomes of 1591 patients infected with SARS-CoV-2 admitted to ICUs of the Lombardy region, Italy[END_REF][START_REF] Popescu | COVID-19 in a tertiary hospital from Romania: epidemiology, preparedness and clinical challenges[END_REF][START_REF] Garg | Hospitalization rates and characteristics of patients hospitalized with laboratory-confirmed coronavirus disease 2019 -COVID-NET, 14 states, March 1-30, 2020[END_REF][START_REF] Richardson | Presenting characteristics, comorbidities, and outcomes among 5700 patients hospitalized with COVID-19 in the New York City area[END_REF][START_REF] Myers | Characteristics of hospitalized adults with COVID-19 in an integrated health care system in California[END_REF][START_REF] Lescure | Clinical and virological data of the first cases of COVID-19 in Europe: a case series[END_REF][START_REF] Cummings | Epidemiology, clinical course, and outcomes of critically ill adults with COVID-19 in New York City: a prospective cohort study[END_REF]. Descriptive data about clinical presentation, comorbidities, treatment, and outcomes of hospitalized patients in France are lacking [START_REF] Plaçais | COVID-19: Clinical, biological and radiological characteristics in adults, infants and pregnant women. An up-to-date review at the heart of the pandemic[END_REF]. Moreover, prognosis factors specific to European hospitalized patients must be identified. Therefore, we developed the Covid-clinic-Toul cohort, recording data about all patients hospitalized for a SARS-CoV-2 infection at the Toulouse University hospital, South of France (2800 beds, unique tertiary hospital covering an area of about 3 million inhabitants).

The aim of this study was to describe demographics, clinical, biological and radiological features, as well as outcome at Day 14 after admission (admission in an intensive care unit, mechanical ventilation, death) in patients included in the Covid-clinic-Toul cohort until April 20, 2020.

Methods

1. Study design and participants

The Covid-clinic-Toul cohort records data about all patients hospitalized for SARS-CoV-2 at the Toulouse University hospital. First patients (from March 7 to April 1) were included retrospectively and data from subsequent patients hospitalized after April 1 were collected prospectively. All the patients primarily admitted at the Toulouse University hospital (not transferred from another hospital) were included. Exclusion criteria was the opposition to data collection. All patients, or their representatives for those not able to understand the purpose of the study, were informed by a letter given at admission to hospital and/or sent to their place of residency. This cohort has been approved by institutional review board (n°RnIPH 2020-31), in accordance with the French data protection authority (MR004, Commission Nationale de l'Informatique et des Libertés, CNIL).

In the present study, we selected the patients included in the Covid-Clinic-Toul up to April 20, 2020 and with a SARS-CoV-2 infection proven by reverse transcriptase polymerase chain reaction (RT-PCR). All patients enrolled in this cohort were diagnosed according to interim guidance of theWorld Health Organization [START_REF] Who | ) infection is suspected: interim guidance[END_REF].

Data collection

We collected demographics, clinical, laboratory, radiological (description of chest computed tomography -CT-scans), and treatment data within the first 24 hours after admission, as well as outcome at Day 14 after admission (see below). Data were extracted from electronic medical records and recorded in an electronic data collection form.

The date of disease onset was defined by the day on which the first symptom was noticed.

Duration of symptoms was defined by the time between first symptoms and admission at the hospital. Chest-CT scans were classified as mild, moderate, severe, or critical by the extent of lung lesions, according to the severity score of the French Society of Radiology that assesses the extent of lesions [START_REF]Chest CT severity score of the French Society of Radiology[END_REF].

Outcome on Day 14 after admission

The primary outcome was composite, including admission to ICU, need of mechanical ventilation and death occurring during the 14 days after admission to the hospital.

Statistical analysis

We described the characteristics of the whole population, and then by two categories of subgroups: first, the patients admitted to ICU at Day 1 of admission to the hospital versus others; then, among the patients not admitted to ICU at Day 1, those with occurrence of the composite outcome versus others. Continuous variables were expressed as mean and standard deviation (SD) or median and interquartile range (IQR) depending on their distribution. Categorical variables were presented as numbers of patients and percentages. We described, using Kaplan-Meier curves, the occurrence of the composite outcome and of death within the 14 days after admission in the subgroup of patients not admitted to ICU at Day 1, as well as the occurrence of death within the 14 days after admission in the whole population.

Results

Patient characteristics (whole population)

A total of 263 patients were included in this study. Data are summarized in Table 1. The median age was 65 years (IQR: 54-76), and 155 patients (58.9%) were male. Among these, 227 (86.3%) had one or more chronic medical illness. Overweight (36.1%), obesity (28.3%), hypertension (39.5%), chronic pulmonary disease (21.6%) and diabetes (19.8%) were the most common coexisting medical conditions. Immunosuppression was found in 9.1% of the patients. Only one patient had infection by the human immunodeficiency virus (HIV), with normal lymphocyte count. Thirty-one (11.8%) patients were exposed to angiotensin converting enzyme inhibitors (ACEis), 45 (17.1%) to angiotensin receptor blockers (ARBs), 19 (7.2%) to corticosteroids and 6 (2.3%) to non-steroidal anti-inflammatory drugs (NSAIDs).

The median duration of symptoms at admission was 7.0 days (IQR: 4.0-10.0). On admission, most patients had experienced cough (74.3%) and presented with fine crackles at pulmonary auscultation (62.9%). Less frequent symptoms were diarrhea (35.5%), anosmia (31.0%), dysgeusia (39.8%) and confusion (8.2%).

On admission, patients had moderate lymphopenia (median: 0.9 x 10 9 /L, IQR: 0.7-1.3) and moderate elevation of C-reactive protein (median: 52.4 mg/L, IQR: 27.0-107.6). Platelet count was normal in most patients.

Most patients (96.2%) had a chest CT-scan at admission, with a « moderate » and « severe » score in 139 (54.9%) and 64 (25.3%) patients, respectively. Thirty-three patients (12.5%) had received hydroxychloroquine, 9 (3.4%) lopinavir/ritonavir and only one patient (1.9%) remdesivir within the first 24 hours after admission. Most patients (62.7%) were given antibiotic treatment, mostly cephalosporins, amoxicillin/clavulanic acid and macrolides.

Outcome

Of the 263 patients, 111 (42.2%) were admitted to ICU because of the development of organ dysfunction, ARDS or need of oxygen therapy ≥ 5 L/minute during the 14 first days of hospitalization. The median time from onset of symptoms to ICU admission was 8.0 days (IQR: 5.0-11.0). Mechanical ventilation was required in 61 patients (23.2%).

Nineteen patients (7.2%) had died within the 14 days after admission, including 7 in ICU.

Characteristics of these 19 patients are presented in Table 2. All of them were aged >65 years and had one or more chronic medical illness, except one patient who was 49 year-old with no other comorbidity than obesity and died of thrombo-embolic complication, sepsis and ARDS.

Limitation of life-sustaining treatment was made in 14 patients (73.7%). Causes of death was ARDS for all the patients, plus pulmonary embolism (n=3), acute heart failure (n=4) and sepsis (n=3).

Occurrence over time of death in the whole population, as well as occurrence of death and of the composite outcome in patients not admitted to ICU at Day 1 are presented in Fig. 123.

Patient characteristics in the subgroup of patients admitted to the ICU at Day 1 versus others

On admission, 213 patients (81.0%) were admitted to general wards and 50 patients (19.0%) were admitted to the ICU at Day 1. In the subgroup of those admitted to the ICU, patients were more frequently men (66.0% vs 57.3%) and smokers (25.0% vs 7.1%). Except for obesity (42.0% vs 24.7%), there was no other predominance in comorbidities. They were not more frequently exposed to ACEis, corticosteroids or NSAIDs but were more frequently exposed to ARBs (24.0% vs 15.5%). Clinical features and time from first symptoms to admission were similar. Laboratory results showed higher serum concentrations of ferritin (median: 1570 µg/L vs 863 µg/L), C-reactive protein (median: 110.9 mg/L vs 46.2 mg/L) and higher levels of troponin (51.7% with troponin > 14 ng/L vs 33.3%) in patients hospitalized in the ICU at Day 1. Chest CT-scan results werecorrelated with clinical severity in these patients (49.0% and 10.2% of "severe" and "critical" CT-scans in ICU patients vs 19.6% and 0.5%, respectively). Most of these patients (96.0%) received an antibacterial therapy during the first day of hospitalization and 38.0% received hydroxychloroquine.

Characteristics in the subgroup of patients not admitted to the ICU at Day 1, according to the outcome at Day 14

On Day 14, among the 213 patients who were initially hospitalized in regular medical wards, 72 patients (33.8%) had an unfavorable outcome, and 15 died. These patients, being compared with those who were still alive without ICU admission on day 14, were more frequently men (68.1% vs 51.8%) with a history of hypertension (51.4% vs 34.0%) or diabetes (26.4% vs 15.6%). They were more frequently exposed to ARBs (20.8% vs 12.8%). Anosmia and dysgeusia were less frequently reported in patients with unfavorable outcome (18.2% and 19.0% vs 35.3% and 50.0% respectively). These patients were given more frequently antibiotic and hydroxychloroquine treatments during the first 24 hours after admission (76.4% and 12.5% vs 44.0% and 3.5%, respectively).

Discussion

We report here a case series of 263 hospitalized patients with laboratory-confirmed SARS-CoV-2 infection. One hundred and eleven patients (42.2%) needed ICU and nineteen patients died (7.2%) within 2 weeks after their admission.

The median age of this cohort (65 years, IQR 54-76) is higher than in the three largest cohorts from China (median ages between 47 and 56 years). We also observed a higher prevalence of comorbidities [START_REF] Guan | Clinical characteristics of coronavirus disease 2019 in China[END_REF][START_REF] Wu | Risk factors associated with acute respiratory distress syndrome and death in patients with coronavirus disease 2019 pneumonia in Wuhan, China[END_REF][START_REF] Zhou | Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China:a retrospective cohort study[END_REF]. Among hospitalized patients with COVID-19 in China, the percentage of patients who required ICU care ranged from 5% to 32% [START_REF] Guan | Clinical characteristics of coronavirus disease 2019 in China[END_REF], less than in our cohort which included both "critical care unit" and "intensive care unit" patients. Compared to national epidemiological data, median age of the patients included in the Covid-Clinic-Toul cohort was slightly higher (65 versus 61.5 years). However, characteristics of the ICU-hospitalized patients were consistent with national data with a male predominance and high prevalence of chronic medical illnesses [START_REF]COVID-19 point épidémiologique[END_REF]. Mortality rate among hospitalized patients ranged from 0% to 11% in the first reports [START_REF] Chen | Epidemiological and clinical characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan, China: a descriptive study[END_REF][START_REF] Wang | Clinical Characteristics of 138 Hospitalized Patients With 2019 Novel Coronavirus-Infected Pneumonia in Wuhan, China[END_REF][START_REF] Young | Epidemiological features and clinical course of patients infected with SARS-CoV-2 in Singapore[END_REF]. Mortality rate in our study may have been underestimated due to an initially broad hospitalization criteria. Moreover, we censored the follow-up at Day 14 after admission. All patients who died had comorbidities and most of them were aged over 65 years. Causes of death were ARDS for all the patients. We also observed pulmonary embolism in 15.8% of the deceased patients, in accordance with previous reports [START_REF] Helms | High risk of thrombosis in patients with severe SARSCoV-2 infection: a multicenter prospective cohort study[END_REF].

We observed more smokers and overweight patients among those admitted to the ICU at Day 1, which is concordant with previous studies [START_REF] Arentz | Characteristics outcomes of 21 critically ill patients with COVID-19 in Washington State[END_REF][START_REF] Vardavas | COVID-19 and smoking: A systematic review of the evidence[END_REF][START_REF] Simonnet | High Prevalence of Obesity in Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) Requiring Invasive Mechanical Ventilation[END_REF]. In our cohort, we observed a predominance of male gender, hypertension, and diabetes in patients with poor outcome within the 14 days after their admission. Grasseli et al. also reported a high prevalence of men and patients with chronic hypertension in their cohort of ICU patients [START_REF] Grasseli | Baseline characteristics and outcomes of 1591 patients infected with SARS-CoV-2 admitted to ICUs of the Lombardy region, Italy[END_REF]. Zhou et al. and Whu et al. also identified hypertension as a risk factor of ARDS [START_REF] Wu | Risk factors associated with acute respiratory distress syndrome and death in patients with coronavirus disease 2019 pneumonia in Wuhan, China[END_REF][START_REF] Zhou | Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China:a retrospective cohort study[END_REF]. This may explain the higher proportion of patients exposed to ARBs among those with unfavorable outcome [START_REF] Jarcho | Inhibitors of the Renin-Angiotensin-Aldosterone System and Covid-19[END_REF][START_REF] Fosbol | Association of AngiotensinConverting enzyme inhibitor or angiotensin receptor blocker use with COVID-19 diagnosis and mortality[END_REF]. However, we found no difference in proportion of older and other chronic medical illnesses between ICU patients and non-ICU patients. Severe patients had also higher biological inflammatory parameters and troponin levels at admission. Myocardial injury has been described and associated with severity [START_REF] Wang | Clinical Characteristics of 138 Hospitalized Patients With 2019 Novel Coronavirus-Infected Pneumonia in Wuhan, China[END_REF][START_REF] Zhou | Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China:a retrospective cohort study[END_REF][START_REF] Arentz | Characteristics outcomes of 21 critically ill patients with COVID-19 in Washington State[END_REF][START_REF] Mo | Clinical characteristics of refractory COVID-19 pneumonia in Wuhan, China[END_REF].

We did not observe a more frequent outcome occurrence in patients who had taken NSAIDs or corticosteroids before admission, but few patients were exposed. This may be explained by public information before the onset of the epidemic in France.

Anosmia and dysgeusia were less frequently reported in critically ill patients, which is consistent with previous studies reporting these symptoms as associated with mild cases [START_REF] Spinato | Alterations in smell or taste in mildly symptomatic outpatients with SARS-CoV-2 infection[END_REF].

However, this finding must be taken with caution due to missing data regarding these symptoms.

This study has several limitations. First, only patients with laboratory-confirmed COVID-19 were included; suspected but undiagnosed cases were ruled out, especially those with typical clinical and radiological presentation but with negative RT-PCR (10% of the COVID-19 patients admitted to the emergency department at the Toulouse University hospital; unpublished data). However, chest-CT has higher sensitivity than RT-PCR assay [START_REF] Ai | Correlation of chest CT and RT-PCR testing in coronavirus disease 2019 (COVID-19) in China: a report of 1014 cases[END_REF][START_REF] Long | Diagnosis of the Coronavirus disease (COVID-19): rRT-PCR or CT ?[END_REF].

The characteristics of patients with compatible CT-scan and negative RT-PCR need to be further described. Second, some data were missing. In particular, smoking status, anosmia and dysgeusia were not systematically searched in the beginning of the pandemics. Third, the first patients were retrospectively included. Fourth, criteria for admission to ICU may have varied over time during the study period with improved knowledge of the disease by physicians.

Lastly, we presented patient characteristics at admission and outcome at Day 14. This is useful for predictive models, but we did not assess in detail what happened between Day 1 and Day 14 (including treatments administered after the first 24 hours following admission [START_REF] Long | Diagnosis of the Coronavirus disease (COVID-19): rRT-PCR or CT ?[END_REF][START_REF] Fadel | Early Short Course Corticosteroids in Hospitalized Patients with COVID-19[END_REF][START_REF] Liu | Successful use of methylprednisolone for treating severe COVID-19[END_REF][START_REF] Geleris | Observational Study of Hydroxychloroquine in Hospitalized Patients with Covid-19[END_REF][START_REF] Mahevas | Clinical efficacy of hydroxychloroquine in patients with covid-19 pneumonia who require oxygen: observational comparative study using routine care data[END_REF][START_REF] Tang | Hydroxychloroquine in patients with mainly mild to moderate coronavirus disease 2019: open label, randomised controlled trial[END_REF][START_REF] Huang | Preliminary evidence from a multicenter prospective observational study of the safety and efficacy of chloroquine for the treatment of COVID-19[END_REF][START_REF] Wang | Remdesivir in adults with severe COVID-19: a randomised, double-blind, placebo-controlled, multicentre trial[END_REF][START_REF] Grein | Compassionate Use of Remdesivir for Patients with Severe Covid-19[END_REF][START_REF] Mcmahon | Remdesivir for the Treatment of Covid-19 -Preliminary Report[END_REF]) .

Conclusion.

This cohort provides data on patients hospitalized for COVID-19 in a University hospital in the south of France, the Toulouse University hospital, and confirms some epidemiological findings: a high frequency of comorbidities in hospitalized patients, a high frequency of male gender and obesity for initial severity; and important rates of admission to ICU, mechanical ventilation, and death.

Legends of figures

Figure 1 .

 1 Figure 1. Occurrence over time of death in the whole population of patients admitted to

Figure 2 .

 2 Figure 2. Occurrence of death in patients not admitted to ICU at Day 1 of admission (n=213).

Figure 3 .

 3 Figure 3. Occurrence of admission to ICU, need for mechanical ventilation or death in

Table 1 .

 1 Characteristics of the 263 patients hospitalized for a SARS-CoV-2 infection proven by RT-PCR included in the Covid-Clinic-Toul cohort until April 20, 2020.

	Variables	All patients
		(n=263)

Patients admitted to the ICU at Day 1 of hospitalization Among the patients not admitted to the ICU at D1 of

  Missing values: current smoker, n=148; time from first symptoms to admission, n=2; temperature, n=7 ; heart rate, n=7 ; respiratory rate, n=12 ; arterial pressure, systolic/diastolic, n=6; oxygen saturation, n=2 ; lymphocyte count, n=35; platelet count, n=10; C-reactive protein, n=9; creatinine level, n=6; serum ferritin, n=200; D-dimers, n=227; troponin, n=150, lactate dehydrogenase, n=213.

	(%)
	Mild, n (%)	34 (13.4)	1 (2.0)	33 (16.2)	12 (16.9)		21 (15.8)
	Moderate, n (%)	139 (54.9)	17 (34.7)	122 (59.8)	29 (40.8)	hospitalization (n=213) 93 (69.9)
	Severe, n (%)	64 (25.3)	Yes (n=50; 19.0%) 24 (49.0)	No (n=213; 40 (19.6)	Admission to ICU, 27 (38.0)	No admission to ICU, 13 (9.8)
	Critical, n (%)	6 (2.4)	5 (10.2)	81.0%) 1 (0.5)	mechanical ventilation or 1 (1.4)	mechanical ventilation or 0 (0)
	Treatment administered during the Age, median (IQR), years first 24 hours after admission Men, n (%) Oxygen therapy, n (%) Antibiotics, n (%)	65 (54-76) 155 (58.9) 212 (80.6) 165 (62.7)	67 (56-73) 33 (66.0) 50 (100) 48 (96.0)	64 (53-76) 122 (57.3) 162 (76.1) 117 (54.9)	death at Day 14 (n=72; 33.8%) 69 (60-79) 49 (68.1) 66 (91.7) 55 (76.4)	death at Day 14 (n=141; 66.2%) 63 (50-74) 96 (68.1) 73 (51.8) 62 (44.0)
	Comorbidities Hydroxychloroquine, n (%)	33 (12.5)	19 (38.0)	14 (6.6)	9 (12.5)		5 (3.5)
	≥ 1 comorbidity, n (%) Lopinavir/ritonavir, n (%)	227 (86.3) 9 (3.4)	42 (84.0) 5 (10.0)	185 (86.9) 4 (1.9)	67 (93.1) 4 (5.6)		118 (83.7) 0 (0)
	Overweight (BMI: 25-30 kg/m²), n Remdesivir	88/244 (36.1) 1 (1.9)	14/50 (28) 1 (2.0)	74/194 (38.1) 0 (0)	29/68 (42.7) 0 (0)	45/126 (35.7) 0 (0)
	(%) Detailed outcomes at Day 14 after
	Obesity (BMI > 30 kg/m²), n (%) admission Admission to ICU, n (%)	69/244 (28.3) 111 (42.2)	21/50 (42.0) 50 (100)	48/194 (24.7) 61 (28.6)	19/68 (27.9) 61 (84.7)	29/126 (23.0) -
	Hypertension, n (%) Mechanical ventilation, n (%)	104 (39.5) 61 (23.2)	19 (38.0) 29 (58.0)	85 (39.9) 32 (15.0)	37 (51.4) 32 (45.7)		48 (34.0) -
	Diabetes, n (%) Death, n (%)	52 (19.8) 19 (7.2)	11 (22.0) 4 (8.0)	41 (19.2) 15 (7.0)	19 (26.4) 15 (20.8)		22 (15.6) -
	Cardiovascular disease, n (%) Discharged, n (%)	35 (13.3) 173 (65.8)	6 (12.0) 21 (42.0)	29 (13.6) 152 (71.4)	13 (18.1) 32 (44.4)		16 (11.3) 120 (85.1)
	Cerebrovascular disease, n (%)	17 (6.5)	2 (4.0)	15 (7.0)	6 (8.3)		9 (6.4)
	Chronic lung disease, n (%)	57 (21.6)	11 (22.0)	46 (21.6)	19 (26.4)		27 (19.1)
	Chronic kidney disease, n (%)	24 (9.1)	3 (6.0)	21 (9.8)	9 (12.5)		12 (8.5)
	Chronic liver disease, n (%)	2 (0.8)	0 (0)	2 (0.9)	2 (2.7)		0 (0)
	Malignancy <5 years, n (%)	27 (10.3)	5 (10.0)	22 (10.3)	10 (13.9)		12 (8.5)
	Immunosuppression, n (%)	24 (9.1)	4 (8.0)	20 (9.4)	10 (13.9)		10 (7.1)
	Current smokers, n (%)*	11/115 (9.3)	4/16 (25.0)	7/99 (7.1)	3/35 (8.6)		4/64 (6.3)
	Exposure to selected drugs
	NSAIDs, n (%)	6 (2.3)	1 (2.0)	5 (2.3)	1 (1.4)		4 (2.8)
	Corticosteroids, n (%)	19 (7.2)	3 (6.0)	16 (7.5)	8 (11.1)		8 (5.7)
	ACE inhibitors, n (%)	31 (11.8)	4 (8.0)	27 (12.7)	11 (15.3)		16 (11.3)
	ARBs, n (%)	45 (17.1)	12 (24.0)	33 (15.5)	15 (20.8)		18 (12.8)
	Signs and symptoms
	Cough, n (%) Chest CT scan at admission	253 (96.2)	49 (98.0)	204 (95.8)	71 (98.6)		133 (94.3)
	Chest CT scan severity score
	No typical sign of COVID-19, n	10 (4.0)	2 (4.1)	8 (3.9)	2 (2.8)		6 (4.5)

*Abbreviations: ACE: angiotensin converting enzyme; ARBs: angiotensin receptor blockers; BMI: body mass index; CT: computed tomography; ICU: intensive care unit; IQR: interquartile range; NSAIDs: non-steroidal anti-inflammatory drugs; RT-PCR: reverse transcriptase polymerase chain reaction.

Acknowledgments

The authors deeply thank Christophe Morin, Gaëlle Barencourt, Caroline Hurault-Delarue, Charlotte Vert and Julien Jacquot for their help in data acquisition and Isabelle Olivier for reglementary aspects.

Disclosure of interest

The authors declare that they have no competing interest related to this study. The Covidclinic-Toul cohort is funded by the Toulouse University hospital.


Benjamin Fernandez

MD Chetana Lim

PhD Claire Goumard

MD Fabiano Perdigao

MD Geraldine Rousseau

MD Eric Savier

MD Alessandra Mazzola

MD Filomena Conti

PhD ; Olivier Scatton

Prof Olivier Scatton

Liver Transplantation from Donors with Down Syndrome

2

To the Editors:

The current organ shortage has resulted in extended criteria for donor selection. The use of risky cadaveric liver donors, most of which are older, obese or donation after circulatory death donors has been developed to face the growing organ demand. As improvements in medical care for patients with Down Syndrome (DS) have led to an increase in their life expectancy, the question of potential liver donors with DS should be considered. Because congenital vascular malformations of the liver have been described in patients with DS, LT using a graft from a donor with DS may be challenging. We report here, for the first time, two cases of successful cadaveric liver transplantation (LT) from donors with DS.

Case series

The first recipient was a 38-year-old man with alcoholic and metabolic syndrome cirrhosis who underwent orthotopic LT. The donor was a 28-year-old man with a history of DS who died from a post-traumatic intracerebral bleeding. Previous medical history included thyroidectomy and cholecystectomy. Laboratory explorations showed: total bilirubin = 7 μmol/l, aspartate-aminotransferase = 24 IU/l, alanine aminotransferase = 20 IU/l, γglutamyltransférase = 89 IU/l, alkaline phosphatase = 136 IU/l, prothrombin time = 72%.

Computed tomography revealed a complete stenosis of the left branch of the portal vein and an atrophy of the left lobe (Figure 1A). The right branch of the portal and the portal vein remained patent. No other cardiac and vascular abnormalities were found. Caval reconstruction was performed using the Piggyback technique. Portal reconstruction was performed using portoportal anastomosis. Arterial and biliary reconstructions were performed as usual. The cold ischemia time was 480 minutes. Anticoagulation including low-molecularweight heparin as a prophylaxis again the extension of portal vein thrombosis and aspirin as a prophylaxis against arterial thrombosis was started in intensive care unit. The patient underwent relaparotomy for intra-abdominal bleeding on postoperative day 12, but no bleeding spot was identified. Two months after LT, the patient is alive with normal liver function and persisting left portal vein stenosis (Figure 1B).

The second recipient was a 33-year-old woman with a history of Kasai procedure for biliary atresia. She developed secondary biliary cirrhosis. The donor was a 47-year-old man with a history of DS who died from an acute obstruction of his permanent tracheostomy. Previous medical history included permanent tracheostomy for severe laryngeal papillomatosis.

Laboratory explorations showed: total bilirubin = 9 μmol/l, aspartate-aminotransferase = 31 IU/l, alanine aminotransferase = 24 IU/l, γ-glutamyltransférase = 24 IU/l, alkaline phosphatase = 72 IU/l, prothrombin time = 69%. Computed tomography did not reveal any cardiac, venous, portal or arterial anomalies. The cold ischemia time was 446 minutes. Caval, portal, arterial and biliary reconstructions were performed as usual. Anticoagulation included aspirin as a prophylaxis against arterial thrombosis. Two months after LT, the patient is alive with patent vascular reconstructions and normal liver function.

Discussion

To our knowledge this is the first series of successful LTs from donors with DS, suggesting that such graft from DS should not be excluded from liver donation. While congenital cardiac anomalies and intra-abdominal malformations are common, congenital vascular malformations of the liver have been described in children with DS [START_REF] Burdall | Congenital Vascular Malformations of the Liver: An Association With Trisomy 21[END_REF] . The latter are defined by the vascular connection between the hepatic artery, portal and hepatic veins and inferior vena cava. They may be divided into two categories according to the nature of the vascular connections (Figure 2): i) veno-venous connections (i.e, shunt between portal venous and systemic venous system) including portocaval shunts (shunt between the portal vein and 4 inferior vena cava, the so-called Abernathy malformation) and patent ductus venosus (i.e, shunt from left portal vein to the hepatic vein confluence), and ii) arterio-venous (shunt between hepatic artery and hepatic veins or inferior vena cava) and arterio-portal (shunt between hepatic artery and portal vein with subsequent risk of portal vein aneurysm) shunts.

Interestingly, a novel portal vein malformation not previously described is the left portal vein stenosis, as seen in one of our two cases. In this case of congenital left portal vein stenosis, we only use additional anticoagulation as this stenosis cannot be re-vascularized with the retrograde approach through the portal vein using vascular angioplasty using balloon catheter or stenting. Moreover, performing an in situ or ex vivo left hepatectomy was judged as an excessive option with specific risks brought by the liver parenchymal surface potentially leading to bleeding or bile leak.

As for other genetic abnormalities, one case of LT using a donor with Turner syndrome (45 XO chromosomal status) has been reported in 1994 [START_REF] Pulvirenti | Successful liver transplantation from a donor with chromosomal abnormality (45,XO)[END_REF] . In this case, the donor had a replaced hepatic artery arising from the superior mesenteric artery.

Because no particular vascular malformation predominated in patients with DS, decision to use liver graft from a donor with a DS should be taken on a case-by-case basis. In the case of complex congenital connection between the arterial and portal venous system with potential subsequent arterioportal hypertension and portal vein aneurysm, liver transplant surgeons should be cautious before using this king of graft. Indeed, these arterioportal malformations would probably need secondary embolization of arterioportal shunts, surgery with ligation of the feeding arterial vessels, segmentectomy or lobectomy [START_REF] Bogert | An unusual presentation of a congenital intrahepatic arterioportal fistula in an infant with Down syndrome[END_REF][START_REF] Golewale | Portal vascular anomalies in Down syndrome: spectrum of clinical presentation and management approach[END_REF] . In a modern era of graft assessment by computed tomography, the decision to use or not this kind of graft can be made easily. If ultrasound is used to assess the liver graft, then liver transplant teams should ask for computed tomography scan evaluation in order to seek for potential anatomical variations and shunts.

In summary, the use of a liver graft from a donor with DS for LT is safe and feasible. A meticulous assessment for vascular anomalies of the liver by computed tomography scan at least should be performed before accepting the graft. 6

Figure 1 .

 1 Figure 1. Liver transplantation using a liver graft from a donor with Down Syndrome

Figure 2 .

 2 Figure 2. Classification of congenital vascular malformations of the liver in patients with