Cornelius Eichner
email: ceichner@cbs.mpg.de

Michael Paquette

Toralf Mildner

Torsten Schlumm

Kamilla Pléh

Lirian Samuni

Catherine Crockford

Roman M Wittig

Carsten Jäger

Harald E Möller

Angela D Friederici

Alfred Anwander

Increased Sensitivity and Signal-to-Noise Ratio in Diffusion-Weighted MRI using Multi-Echo Acquisitions

Keywords: Diffusion, dMRI, Multi-Echo, Segmented EPI, Post-Mortem, Relaxometry, Noise, SNR, Chimpanzee

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D R A F T Introduction

The vast potential of dMRI in neuroscience and clinical practice led to recent developments of highly specialized humansize MRI systems with very strong diffusion gradients of up to 300mT/m [START_REF] Setsompop | Pushing the limits of in vivo diffusion MRI for the human connectome project[END_REF][START_REF] Jones | Microstructural imaging of the human brain with a 'super-scanner': 10 key advantages of ultra-strong gradients for diffusion MRI[END_REF]. These novel systems allow advanced dMRI acquisitions with increased signal-to-noise ratio (SNR) and, thus, higher image resolution and stronger diffusionweightings. Diffusion-weighted MRI (dMRI) is capable of non-invasively probing microstructure and structural connectivity of brain tissue. As a purely structural measure, dMRI can also provide insights into the organization of post-mortem brain tissue. Such post-mortem dMRI acquisitions allow extremely high image resolutions at the cost of increased scan times [START_REF] Miller | Diffusion imaging of whole, post-mortem human brains on a clinical MRI scanner[END_REF][START_REF] Mcnab | The human connectome project and beyond: initial applications of 300 mt/m gradients[END_REF][START_REF] Dyrby | An ex vivo imaging pipeline for producing high-quality and high-resolution diffusion-weighted imaging datasets[END_REF]. Additionally, the fixation of the brain in paraformaldehyde solution produces a cross-linkage of proteins which re-duces the diffusivity of water molecules in the tissue and the directional contrast [START_REF] Roebroeck | Ex vivo diffusion MRI of the human brain: Technical challenges and recent advances[END_REF]. Hence, to achieve sufficient diffusion contrast, post-mortem diffusion-weightings need to be increased relative to in-vivo acquisitions. Despite its versatile applications in neuroscience and clinics, dMRI acquisitions and models suffer from various shortcomings. Since the diffusion contrast is realized by directionweighted signal attenuation, dMRI inevitably suffers from low SNR. This problem is systematically worsened for dMRI acquisitions with increased diffusion-weighting and higher image resolutions. In low SNR regimes, the typically employed magnitude dMRI signals become biased by non-Gaussian noise, thereby preventing accurate signal averaging and modeling [START_REF] Gudbjartsson | The rician distribution of noisy MRI data[END_REF][START_REF] Eichner | Real diffusion-weighted MRI enabling true signal averaging and increased diffusion contrast[END_REF][START_REF] Basu | Rician noise removal in diffusion tensor MRI[END_REF]. Due to the time-consuming diffusion contrast encoding, dMRI data are typically acquired using Echo-Planar-Imaging (EPI). However, EPI based acquisitions are especially prone to image distortions from eddy currents or magnetic field inhomogeneities [START_REF] Andersson | An integrated approach to correction for offresonance effects and subject movement in diffusion MR imaging[END_REF]. A further challenge of dMRI is its inefficient signal encoding strategy, in which a rather timeconsuming contrast encoding is followed by a short readout. Multiple strategies have been suggested to counteract typical issues associated with dMRI acquisitions. The signal bias of low SNR data can be overcome using phase-correction of the complex-valued dMRI dataset [START_REF] Eichner | Real diffusion-weighted MRI enabling true signal averaging and increased diffusion contrast[END_REF]. High in-plane acceleration using parallel imaging EPI can typically reduce geometrical distortions [START_REF] Heidemann | k-space and q-space: combining ultra-high spatial and angular resolution in diffusion imaging using ZOOPPA at 7 T[END_REF][START_REF] Eichner | Slice accelerated diffusion-weighted imaging at ultra-high field strength[END_REF][START_REF] Griswold | Generalized autocalibrating partially parallel acquisitions (GRAPPA)[END_REF][START_REF] Pruessmann | SENSE: sensitivity encoding for fast MRI[END_REF][START_REF] Hamilton | Recent advances in parallel imaging for MRI[END_REF]. For post-mortem dMRI acquisitions, these in-vivo strategies are not sufficient to achieve acceptable image quality. Captured air bubbles induce strong susceptibility differences within the post-mortem sample, making the background phase hard to estimate. In addition, post-mortem brain containers shift the tissue-air boundary from multiple centimeters to a distance of just a few millimeters. These problems aggravate EPI distortions, even when using parallel imaging acceleration. Segmented EPI (sEPI) acquisition strategies have been proposed to mitigate these problems and to achieve almost distortion-free EPI data -even under challenging post-D R A F T mortem conditions. Similar to other parallel imaging techniques, sEPI only captures small portions of the total k-space for each EPI shot. However, the missing k-space lines from segmented data undersampling are not reconstructed using additional receive coil information but rather acquired in separate shots. Hence, sEPI allows much higher acceleration factors than parallel imaging, resulting in considerably reduced image distortion. Segmented dMRI acquisitions can be achieved using interleaved segmentation along the phase encoding direction [START_REF] Butts | Interleaved echo planar imaging on a standard MRI system[END_REF][START_REF] Mckinnon | Ultrafast interleaved gradient-echo-planar imaging on a standard scanner[END_REF], or by segmentation of the readout direction [START_REF] Porter | High resolution diffusion-weighted imaging using readout-segmented echo-planar imaging, parallel imaging and a two-dimensional navigatorbased reacquisition[END_REF]. Due to gradient slew rate limitations, interleaved segmentation along the phase encoding direction can achieve higher acceleration than readout segmented acquisitions [START_REF] Wang | A comparison of readout segmented EPI and interleaved EPI in high-resolution diffusion weighted imaging[END_REF]. Similarly to dMRI, fMRI recordings may also suffer from low SNR conditions, which can result in artifacts and falsepositive results for BOLD activation patterns [START_REF] Poser | Investigating the benefits of multi-echo EPI for fMRI at 7 T[END_REF][START_REF] Speck | Functional imaging by I0-and t2*-parameter mapping using multiimage EPI[END_REF]. In this context, Multi-Echo (ME) imaging combined with acquisition acceleration strategies were shown to improve the functional sensitivity by weighted echo summation or the estimation of tissue parameters [START_REF] Kundu | Integrated strategy for improving functional connectivity mapping using multiecho fMRI[END_REF][START_REF] Poser | BOLD contrast sensitivity enhancement and artifact reduction with multiecho EPI: parallel-acquired inhomogeneitydesensitized fMRI[END_REF]. Despite their widespread use for functional imaging, ME acquisitions have not yet been evaluated for their applicability to diffusion-weighted MRI. In this context, short readout strategies such as sEPI can enable dense echo sampling of ME acquisitions. Hence the combination of segmented and ME acquisitions might be especially beneficial. In this work, we present a novel dMRI sequence for postmortem acquisitions. Multiple gradient echoes of highly segmented EPI trains are acquired to achieve acquisitions with low distortions and minimal echo time. The resulting ME-dMRI signals are combined in an SNR optimal way without noise bias, using a T * 2 decay model and statistical modeling incorporating the underlying noise distribution. The developed acquisition strategy was employed to acquire highresolution dMRI data of a post-mortem wild chimpanzee brain on a human-scale MRI system.

Theory

Description of the Sequence. The employed ME-dMRI sequence combines Stejskal-Tanner diffusion preparation [START_REF] Stejskal | Spin diffusion measurements: Spin echoes in the presence of a Time-Dependent field gradient[END_REF] with repetitions of N segmented EPI readouts at different echo times TE n (Fig. 1A). The spin-echo condition is realized at the first echo time TE 0 . Therefore, the signal in TE n sity of S 0 = S(TE 0 ) follows a T 2 decay whereas the subsequent multiple gradient-echoes decay with T * 2 (Fig. 1B). The signal envelope of ME-dMRI data as a function of TE n is then given by

S(TE n ) = S0 exp - TE 0 T 2 S 0 exp - TE n -TE 0 T * 2 (1)
Here, S 0 describes the diffusion-weighted signal without the T 2 decay component. Since this study mainly focuses on improving the SNR by acquiring multiple gradient echoes, the ME-dMRI signal decay will be considered with respect to the spin-echo signal S 0 :

S(TE n ) = S 0 exp - TE n -TE 0 T * 2 = S 0 exp - ∆TE n T * 2 (2)
Increasing Signal to Noise using Multi-Echo Acquisitions. ME-dMRI acquisitions provide additional data from multiple echoes which can be employed to increase the SNR.

Here, we estimate the SNR gain from a ME-dMRI signal combination using the Linear Least Squares (LLS) regression formulation. We will employ two assumptions: (i) The underlying T * 2 is known and will not be estimated from the ME-dMRI data. (ii) The measurement noise, , is assumed to follow a zero-mean Gaussian distribution with a standard deviation, σ. The measured signal, M , is described with Eq. 3:

M (TE n ) = S 0 exp - ∆TE n T * 2 + with ∼ N (0, σ 2 ) (3) Since T * 2 is known, exp -∆TE n T * 2
, is a constant for each TE n ). To estimate S 0 , we normalize each M (TE n ) with this constant. It becomes apparent that the relative error of S 0 estimations grows with TE. The error distribution is given by:

TEn = exp ∆TE n T * 2 ∼ N 0, σ exp ∆TE n T * 2 2
(4) Due to the increasing error, the overall benefit of using multiple gradient echoes will depend on the parameters ΔTE, T * 2 , and the number of acquired echoes. If late echoes with strong error contamination are employed, the accuracy of the S 0 estimation will decrease compared to early echoes. Under the assumption of Gaussian noise, S 0 can be estimated as S0 using LLS regression on multiple echoes.

S0 = argmin

S 0 1 N TE M (TE n ) exp ∆TE n T * 2 -S 0 2 (5)
The LLS estimation of S 0 is computed as the global minimum of Eq. 5.

S0 = 1 N TE M (TE) exp TE T * 2 ≡ S 0 + 1 N TE TE (6)
The S 0 estimate from the LLS regression of ME data with Gaussian noise follows a Gaussian distribution centered around S 0 .

S0 ∼ N        S 0 , σ N 2 TE exp TE T * 2 2 σ 2 ME        (7)
The

G SNR . G SNR = N TE exp TE T 2 2 (8)
For the limiting case of infinite T * 2 , this result corresponds to the square root of N which equals the error reduction obtained by N averages. This represents the theoretical maximum SNR gain for ME-dMRI acquisitions,

√

N . From Eq. 8 it is concluded that, for any given sampling scheme, the SNR gain is a function of tissue T * 2 . More advanced model fitting strategies such as non-linear and weighted optimization might further increase the SNR gain from using ME-dMRI data.

Sensitivity Gain using Statistical Data Modeling.

The assumption of zero-mean Gaussian noise generally does not hold for diffusion-weighted MRI, where low SNR values induce a signal bias. Therefore, for unbiased estimates of S 0 , it is beneficial to employ more advanced model fitting approaches, incorporating the nature of the underlying noise distribution. In contrast to LLS, the Maximum Likelihood Estimation (MLE) achieves parameter estimations of models given specific data distributions [START_REF] Rossi | Mathematical statistics[END_REF]. By maximizing the likelihood function, MLE finds the most probable parameters of a function S to describe a given set of measurement data. MLE proves especially useful for non-Gaussian data distributions, such as dMRI data. For optimal coil combinations in complex space, dMRI signals follow a Rician data distribution characterized by the standard deviation of the underlying complex-valued noise, σ C . Using MLE, model parameters of S, under a Rician data distribution are computed by maximizing the logarithm of the likelihood function, L (26):

log L ∼ TE log I 0 S i M i σ C 2 - TE S 2 i 2σ C 2 (9)
In this equation, I 0 refers to the modified Bessel function of the first kind of order zero. In contrast to LLS, MLE enables unbiased estimations of model parameters by including a noise distribution model into the parameter estimation [START_REF] Karlsen | Parameter estimation from rician-distributed data sets using a maximum likelihood estimator: application to T1 and perfusion measurements[END_REF][START_REF] Sijbers | Maximum likelihood estimation of signal amplitude and noise variance from MR data[END_REF]. MLE has been shown to provide highly efficient approximations of the data by approaching the Cramér-Rao lower bound for parameter estimations [START_REF] Karlsen | Parameter estimation from rician-distributed data sets using a maximum likelihood estimator: application to T1 and perfusion measurements[END_REF]. Due to the nonlinear weighted nature of MLE, an analytical SNR gain evaluation becomes nontrivial. We, therefore, employed numerical methods to assess the benefits of MLE parameter estimation.

Methods

To evaluate the benefit of using Multi-Echo dMRI acquisitions, we implemented a ME-dMRI sEPI sequence and acquired data from a post-mortem chimpanzee brain. We performed numerical simulations on synthetic ME-dMRI with matching acquisition parameters to compute the SNR gain as well as potential biases from reconstructions.

Numerical Simulations of Signal Reconstruction.

Monte Carlo simulations of ME reconstructions were employed to numerically assess reconstruction accuracy for low signals and the SNR benefit from ME-dMRI, using both LLS and MLE reconstructions. To ensure comparability with the acquired ME-dMRI chimpanzee data, simulations were performed on synthetic data with a similar ME sampling scheme (i.e., numbers of echoes, echo times).

Evaluation of the Reconstruction Bias. Diffusion-weighted MRI acquisitions typically suffer from low SNR -especially in the main direction of diffusion attenuation, where diffusion contrast is strongest. To preserve the diffusion contrast, it is crucial that ME reconstructions retain an unbiased estimation of S 0 , especially for small signals. Synthetic ME-dMRI data with T * 2 = 30ms were generated for three repetitions, at five equidistantly spaced echo times from TE = 0ms to TE = 23.6ms. Signal decay curves with S 0 = 1 were corrupted with complex noise. Both the real and magnitude part of the data were extracted to generate both Gaussian and Rician distributed data. Noise corrupted datasets were generated for 100 equidistantly spaced σ Noise , with σ Noise, max = 1 to σ Noise, min = 0.01, thereby creating decay curves at 100 different SNR levels (SNR min = 1, SNR max = 100). Please note that the SNR level is only valid for the first echo time,

D R A F T

as the signal intensity decays for later echoes. LLS and MLE reconstructions of both Gaussian and Rician distributed data were performed for 1000 repetitions of each SNR level.

Computation of SNR Gain. The analytical assessment of SNR gain from ME-dMRI data acquisitions shows a dependency of G SNR on the ME sampling scheme and the underlying T * 2 (Eq. 8). To numerically probe this relation for LLS and MLE reconstructions, we created synthetic ME data for 100 equidistantly spaced T * 2 values ranging from T * 2,min = 1 ms to T * 2,max = 100 ms. Synthetic data were generated at five equidistantly spaced echo times from TE = 0 ms to TE = 23.6 ms. Signal decay curves were corrupted with both Gaussian and Rician noise. The SNR of the noisy data was set to SNR = 5 at the first echo time. LLS and MLE reconstructions were performed for 1000 repetitions for each T * 2 value. Reconstructions using LLS regression were performed using Eq. 6. Reconstructions using MLE regression were performed by maximizing the log-likelihood of the signal (LLS for Gaussian noise and Eq. 9 for Rician data) using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm ( 29) as implemented in Python-SciPy [START_REF] Virtanen | SciPy 1.0 Contributors. SciPy 1.0: fundamental algorithms for scientific computing in python[END_REF]. For each T * 2 value, the SNR gain G SNR was computed as the ratio of the standard deviation of a single echo, σ Noise , to σ S 0 -the standard deviation obtainable from the fitting of multiple echoes.

G SNR = σ Noise σ S 0 (10)
In order to employ the numerically obtained MLE SNR gains (Eq. 10) to experimental T * 2 data, they were globally smoothed using a Savitzky-Golay filter and subsequently interpolated using cubic polynomials, as implemented in Python-SciPy. The SNR gain map was calculated by applying this interpolation function on the pre-calculated T * 2 map.

Data Acquisition.

Specimen. MRI data were acquired from the brain of a 6year-old juvenile wild female chimpanzee from Taï National Park, Côte d'Ivoire [START_REF] Wittig | Taï Chimpanzees[END_REF]. The animal died from natural causes without human interference. The brain was extracted on-site by a veterinarian and immersion-fixed with 4% paraformaldehyde with a very short post-mortem interval of only 4 h. The performing veterinarian was specifically trained in field primate brain extractions, wearing full Personal Protective Equipment, and adhering to the necropsy protocols of the field site. The procedures followed the ethical guidelines of primatological research at the Max Planck Institute for Evolutionary Anthropology, which were approved by the ethics committee of the Max Planck Society. The specimen was transferred to Gerstrictly following CITES protocol regulations. After fixation for 6 months, the superficial blood vessels were removed, the paraformaldehyde was washed out in phosphatebuffered saline and the brain was placed for scanning in an egg-shaped acrylic container filled with perfluoropolyether (PFPE). To prevent potential leakage of PFPE during the acquisition, the container was vacuum sealed using commer-cially available synthetic foil packaging (Caso Design, Arnsberg, Germany).

MR Data Acquisition.

A Stejskal-Tanner diffusion-weighted MRI sequence [START_REF] Stejskal | Spin diffusion measurements: Spin echoes in the presence of a Time-Dependent field gradient[END_REF] was implemented to enable segmented EPI acquisitions of multiple echoes on a human clinical MRI system (see Fig. 1A). Diffusion-weighted MRI data of the post-mortem specimen were acquired at 3T on a MAGNE-TOM Skyra Connectom MRI system (Siemens Healthineers, Germany) using a maximum gradient strength of GMax = 300 mT/m with a slew rate of 200T/m/s and a 32 channel phased-array coil (Siemens Healthineers, Erlangen) with the following imaging parameters: 0.8mm nominal isotropic resolution, FoV = 128 × 96 mm 2 , TR = 6105ms, TE = [45.0, 50.9, 56.8, 62.7, 68.6]ms, 40 segments, Adaptive-Combine coil-combination [START_REF] Walsh | Adaptive reconstruction of phased array MR imagery[END_REF], no partial Fourier, no parallel acceleration, whole-brain coverage with 80 slices. The ME-dMRI acquisition time was extended by approximately 30% compared to a Single-Echo (SE) acquisition with otherwise identical parameters. Segmented EPI echo time-shifting was employed to minimize phase-discrepancies between segments [START_REF] Feinberg | Phase errors in multi-shot echo planar imaging[END_REF]. Three repetitions of 60 diffusion-weighted volumes (b = 5000s/mm 2 ) alongside with 7 interspersed b0 images per repetition were acquired. Due to fixation artifacts, the strong diffusion-weighting of b = 5000s/mm 2 generated an average signal attenuation of 70%. To reduce potential impacts of magnetic field drift resulting from lengthy post-dMRI acquisitions, the acquisition was split into multiple 1h scans with prior frequency adjustment. To minimize impacts from short term instabilities such as vibration and tissue movement, 90 minutes of dummy scans were run prior to the actual data acquisition [START_REF] Dyrby | An ex vivo imaging pipeline for producing high-quality and high-resolution diffusion-weighted imaging datasets[END_REF]. Data from these dummy scans were discarded from all further analyses. For a statistical characterization of Rician noise of the dMRI aca noise map was recorded with identical parameters as the ME-dMRI sequence but without signal excitation (0.8 mm nominal isotropic resolution, FoV = 128 × 96mm 2 ×80sl, TR = 6105ms, TE = 45.0ms, 40 segments, Adaptive-Combine coil-combination, no partial Fourier, no parallel acceleration). A 3D ME-FLASH sequence with 21 echoes was acquired for an accurate calculation of quantitative T * 2 with high SNR: 0.7mm nominal isotropic resolution, FoV = 112 × 100.1 × 98mm 3 , TR = 50ms, TE = 2.2 -42.5 ms, θ = 32°. ME-dMRI Reconstruction. ME-dMRI S 0 was reconstructed voxel-wise, using both LLS (Eq. 6) and MLE regression (Eq. 9). Here, all three repetitions of ME-dMRI data were jointly employed for the estimation of S 0 . The quantitative FLASH T * 2 map was registered to the ME-dMRI data and included as a ground truth estimation for both LLS and MLE reconstructions. This enabled voxel-wise S 0 calculation for ME-dMRI using the T * 2 map. MLE reconstruction of Rician data requires a standard deviation estimate of the underlying complex noise, σC. The whole-brain noise distribution was characterized using the acquired noise map, using a recently published method to describe multi-coil data [START_REF] St-Jean | Automated characterization of noise distributions in diffusion MRI data[END_REF]. Due to employed Adaptive-Combine coil-combination in complex space, the magnitude dMRI data approximate a Rician D R A F T data distribution [START_REF] Sakaie | Retrospective correction of bias in diffusion tensor imaging arising from coil combination mode[END_REF]. Hence, Eq. 9 is applicable for computations of S 0 . MLE reconstruction was performed similarly to the preceding simulations, using BFGS optimization.

Results

Numerical Simulations of Signal Reconstructions.

ME Reconstruction Accuracy. The Monte Carlo simulation results on reconstruction accuracy are summarized in Fig. 2 (top). For Gaussian distributed data, both LLS and MLE reconstruction achieve an accurate and unbiased reconstruction of the signal S 0 = 1 over the full range of simulated SNR values. For Rician distributed data the LLS reconstructions of data with SNR≤10 resulted in an overestimation of S 0 . The simulations show that the overestimation of S 0 for Rician data increases steadily with decreasing SNR values. This fact is particularly problematic for the reconstruction of dMRI data, where diffusion contrast is provided through signal attenuation. MLE reconstructions did not show overestimations of S 0 at low(er) values and allowed an unbiased ME reconstruction of S 0 values down to SNR = 1. Monte Carlo simulations suggest that employing MLE in ME-dMRI reconstructions is favorable due to its ability to deal with low SNR values of S 0 . SNR Figure 2 (bottom) summarizes the SNR gain, depending on the underlying T * 2 decay. Under the assumption of Gaussian noise, the results precisely follow the analytical prediction of SNR gain from Eq. 8. For growing T * 2 values, the SNR gain of ME-dMRI asymptotically the theoretical maximum SNR gain by using 5 acquisitions (i.e., echoes), √ 5. When more echoes are recorded, the theoretical maximum SNR gain will also increase. For the LLS reconstruction of ME data, the employed sampling scheme did not automatically result in an increase in SNR. Both the simulations and the analytical prediction reveal an SNR gain with LLS only for T * 2 values above 20ms. This shortcoming of LLS reconstruction can be explained by the increasing error term with TEn (Eq. 4) -for very short T * 2 values the error of later echoes ( TE ) is too high to achieve an SNR gain. This can be mitigated by minimizing the echo dependent error term by means of fast and dense sampling of early echoes. MLE shows a different behavior of SNR gain across the simulated T * 2 range for both the Gaussian and Rician data distributions. In both cases, SNR loss was not observed -even for short T * 2 values. Instead, the SNR gain converges to G SNR = 1 for small T * 2 values, where neither SNR gain nor loss will occur. Furthermore, MLE reconstruction achieves a greater SNR gain than LLS over the entire range of simulated T * 2 values. MLE on Gaussian data reduces to a least-squares problem, which is similar to the LLS algorithm. Therefore, the SNR gain compared to the LLS computation from Equation 6 might be attributed to the employed nonlinear BFGS optimization algorithm. The key advantage of MLE optimization is the ability to achieve SNR gains > 1 over the whole T * 2 range, especially for Rician distributed data. In summary, MLE reconstruction enables accurate and unbiased reconstructions of S 0 with high SNR. Monte Carlo simulations suggest that MLE is an optimal reconstruction method for reconstructing ME-dMRI data. 3A compares reconstruction results from Single-Echo and Multi-Echo dMRI acquisitions. The raw data quality of the first echo is shown in the top row. The SNR gain of the acquired ME-dMRI data (three repetitions, five echoes) becomes visible in comparison with the SE-dMRI data (three repetitions, single echo). When comparing ME-dMRI reconstructions, it is apparent that the diffusion attenuation contrast is considerably more pronounced for MLE reconstructions. Therefore, the ME-dMRI reconstruction results support the previous simulation results by demonstrating that MLE regression prevents signal bias for small S 0 values. This becomes especially visible in the diffusion-weighted data, where the diffusion induced signal attenuation is much more pronounced. Figure 3B shows the signal intensity distribution for MLE and LLS ME-dMRI reconstructions. Noise-induced bias becomes visible when comparing the signal distributions across the wholebrain volume for both diffusion-weighted and non-diffusionweighted volumes. Here, LLS reconstructions show a tendency towards increased image intensities -i.e., a weakening of the diffusion contrast compared to MLE.

ME-dMRI Reconstruction. Figure

SNR Gain Map. Figure 4 displays the whole-brain T *

2 map as well the associated SNR gain from using ME-dMRI alongside with MLE reconstruction. Given a specific ME sampling scheme the voxel-specific SNR is defined by the underlying T * 2 map (Fig. 4A). The quantitative T * 2 measurements show a distribution, ranging from 20ms to 80ms across the brain (Fig. 4B). The numerically generated SNR gain for this T * 2 distribution using MLE is summarized in Fig. 4C. The SNR gain from a single repetition of ME-dMRI shows a tissuespecific SNR gain of 1.6 (WM, equivalent to 2.6 averages) and 1.9 (GM, equivalent to 3.6 averages). From the G SNR histogram in Fig. 4D, it is apparent that different tissue types generate distinct SNR gains. Inclusions of air bubbles can reduce T * 2 within a small radius as a result of susceptibility differences. In such areas, the Multi-Echo combination does not allow significant SNR gain, as T * 2 is too short. Please note that these results are shown for a single Multi-Echo combination. Experimentally, a total of three repetitions were recorded, increasing the final SNR by an additional factor of √ 3.

Discussion

In dMRI acquisitions, accurate and unbiased measurements of signal attenuation are key to reconstruct fiber orientations or diffusion models with sufficient accuracy. Diffusionweighted MRI measurements are based on selective signal attenuation and consequently suffer from intrinsically low SNR. In advanced dMRI, spatial resolution and diffusionweighting are continuously increased [START_REF] Setsompop | High-resolution in vivo diffusion imaging of the human brain with generalized slice dithered enhanced resolution: Simultaneous multislice (gSlider-SMS)[END_REF][START_REF] Haldar | Whole-brain quantitative diffusion MRI at 660 µm resolution in 25 minutes using gSlider-SMS and SNR-enhancing joint reconstruction[END_REF][START_REF] Veraart | On the scaling behavior of water diffusion in human brain white matter[END_REF]. Such measurements more accurately capture the structure of the brain and allow better characterizations of underlying tissue mi- crostructure. However, low SNR regimes are a limiting factor in such advanced dMRI acquisitions, thereby dampening the diffusion contrast and accurate model estimations from such measurements.

D R A F T

Here we present a novel strategy to increase SNR and reduce the signal bias from non-Gaussian noise for advanced dMRI acquisitions with low SNR. In this context, we developed a diffusion-weighted sEPI sequence capable of recording Multi-Echo signals following each diffusion preparation period. The Multi-Echo data are reconstructed using a signal relaxation model and a quantitative T * 2 map. The additionally required T * 2 map can be recorded within a few minutes -a time effort disproportionate to typically time-consuming post-mortem dMRI measurements. To ensure accurate and optimal reconstructions of ME-dMRI data, we performed numerical Monte-Carlo simulations of different reconstruction algorithms and data types across various signal parameters. The simulations demonstrated optimal SNR gain and minimal signal bias using Maximum Likelihood Estimation reconstruction incorporating the Rician distribution of the data. Both simulations and analytical evaluation of the optimization problem showed an SNR gain dependency on both underlying T * 2 and the Multi-Echo sampling density. In our case, the SNR gain of white matter was 1.6 -which is equivalent to 2.6 averages. For grey matter, the SNR gain was 1.9 -equivalent to 3.6 averages. The SNR gain of up to 3.6 averages comes at the cost of an only slightly extended measurement time of approximately 30%. The second advantage of ME reconstructions using MLE is the low signal bias. Since MLE can incorporate the underlying noise distribution into the S0 computation, the recon-structed signal remains unbiased, even for very low SNR levels of SNR 1. An LLS reconstruction of the same data led to signal bias already present at SNR = 10. Therefore, MLE allows an unbiased reconstruction of the ME-dMRI data of signals with attenuations of almost an additional order of magnitude. This is particularly important in diffusion imaging, where low signals must be calculated with maximum precision. To put our proposed method to direct use, we recorded postmortem dMRI data of a wild chimpanzee brain with high resolution and strong diffusion-weighting. The reconstruction of the acquired ME-dMRI data resulted in high-quality results with a noticeable SNR gain. In addition, the ME-dMRI reconstructions are in agreement with the simulations such that the desired diffusion contrast strongly increased when MLE reconstruction was used. The implementation of this sequence on a human-scale MRI system capable of a maximum gradient strength of 300mT/m allowed the acquisition of dMRI data with high diffusionweightings to study the connectivity of whole brains up to human size. Thereby, sufficient directional diffusion contrast was achieved -also in post-mortem tissue, which requires stronger b-values to achieve similar contrast compared to invivo tissue. The high spatial resolution of the acquired dMRI data provides the basis for a more accurate reconstruction of the white matter tracts compared to typical in-vivo scans. This reduces the potential pitfalls of diffusion MRI tractography [START_REF] Jones | White matter integrity, fiber count, and other fallacies: the do's and don'ts of diffusion MRI[END_REF] and allows reconstructing the endpoints of the fiber pathways with greater precision. This is of particular relevance in the evolutionary context of the current study. The strong in-plane acceleration of the sEPI acquisition allows minimizing image distortions which are caused by susceptibility differences. This enables more precise measurements of anatomical structures and is most relevant for postmortem acquisitions, which may include captured air bubbles and strong susceptibility contrasts at the edges of the brain container.

D R A F T

The discussed ME approach is not limited to post-mortem dMRI sEPI acquisitions. The concept of ME-dMRI could also be used to increase the SNR and reduce signal bias in other settings. Segmented EPI dMRI acquisitions might also be acquired in-vivo, utilizing phase-navigators [START_REF] Porter | High resolution diffusion-weighted imaging using readout-segmented echo-planar imaging, parallel imaging and a two-dimensional navigatorbased reacquisition[END_REF][START_REF] Holdsworth | Readout-segmented EPI for rapid high resolution diffusion imaging at 3 T[END_REF] or advanced reconstruction mechanisms [START_REF] Chen | A robust multi-shot scan strategy for high-resolution diffusion weighted MRI enabled by multiplexed sensitivity-encoding (MUSE)[END_REF][START_REF] Mani | Comprehensive reconstruction of multi-shot multi-channel diffusion data using mussels[END_REF]. ME-dMRI is particularly advantageous for accelerated sequences with a very short EPI readout time, where the signal of the multiples echos is still sufficient considering the T * 2 decay. Therefore, with strong in-plane acceleration, in-vivo applications of ME-dMRI data might also be feasible. ME-dMRI acquisition schemes are not exclusively applicable by using sEPI. Instead, they can also be extended to other dMRI acquisition strategies such as steady-state free precession (SSFP) dMRI (3) to increase the SNR and reduce noise bias of the data. Due to the non-EPI single line readout of SSFP dMRI sequences, the SNR increase could be even larger due to a denser sampling of early echoes. is applicable to all MRI modalities where non-Gaussian noise can induce signal biases. Noise informed MLE fitting can be beneficial for the quantitative mapping of magnetic tissue properties. For example, noise informed MLE reconstruction could be advantageous for other quantitative MRI strategies using Multi-Echo acquisitions such as ME-FLASH [START_REF] Helms | Quantitative FLASH MRI at 3T using a rational approximation of the ernst equation[END_REF] or ME-MP2RAGE [START_REF] Metere | Simultaneous quantitative MRI mapping of t1, t2* and magnetic susceptibility with Multi-Echo MP2RAGE[END_REF]. Multi-Echo reconstructions are commonly performed using LLS [START_REF] Weiskopf | Estimating the apparent transverse relaxation time (r2(*)) from images with different contrasts (ESTATICS) reduces motion artifacts[END_REF][START_REF] Tabelow | hMRI -a toolbox for quantitative MRI in neuroscience and clinical research[END_REF]. Especially at high resolutions or for post-mortem acquisitions, signal bias effects may be circumvented using advanced regression strategies such as MLE. We expect advanced fitting strategies to also be beneficial to diffusion relaxometry, where signal attenuation is generated not only from diffusion-weighting but also from additional mechanisms such as T 1 relaxation and T 2 relaxation [START_REF] Hutter | Integrated and efficient diffusion-relaxometry using ZEBRA[END_REF][START_REF] Slator | Combined diffusion-relaxometry MRI to identify dysfunction in the human placenta[END_REF][START_REF] Tax | Characterizing diffusion of myelin water in the living human brain using ultra-strong gradients and spiral readout[END_REF].

Conclusion

Here we present Multi-Echo dMRI -a new concept to both increase image SNR and simultaneously reduce signal-biases of noise-corrupted dMRI data for post-mortem acquisitions. Diffusion MRI acquisitions typically suffer from a low temporal encoding efficiency, where a time-consuming contrast encoding is followed by a rather rapid acquisition of only one signal. Through the rapid sequential recording of multiple echoes, this new acquisition and reconstruction strategy makes better use of the diffusion-weighted signal and results in a more time-efficient contrast encoding. The presented ME-dMRI technique might also be beneficial to invivo dMRI acquisitions as well as quantitative relaxometry.

D R A F T

Fig. 1 .

 1 Fig. 1. Multi-Echo dMRI Acquisitions. (A) ME-dMRI acquisition employs a Stejskal-Tanner dMRI sequence, followed by N GREs after the first echo. ME-dMRI signals are described using a mixed decay model, where the first echo follows T2 decay and the latter echoes follow T * 2 decay. (B) ME-dMRI data are multi-dimensional with N echo times and multiple diffusion directions.

Fig. 2 .

 2 Fig. 2. Monte Carlo Simulation Results for ME Reconstructions using MLE and LLS Regression. Top Left: Reconstructed S0 = 1 for 1000 repetitions for multiple Gaussian SNR levels (Log Scale). Error bars of curve show standard deviations across the simulation population. No signal bias is induced, even for very low SNR levels. Bottom Left: SNR Gain for LLS and MLE ME-dMRI reconstructions for Gaussian data at various T * 2 decays. Monte Carlo simulations of the LLS reconstruction display high agreement with the analytical derivation of SNR gain. MLE reconstruction achieves higher SNR gain, especially at lower T * 2 values. Top Right: Reconstructed S0 = 1 for 1000 repetitions for multiple Rician SNR levels. LLS reconstruction bias occurs for SNR≤10 and increases with decreasing SNR values. MLE performs an accurate estimation of S0 up to SNR = 1. Bottom Right: SNR Gain MLE ME-dMRI reconstructions on Rician data. MLE reconstruction achieves comparable SNR gain as for Gaussian data MLE across the entire range of T * 2 .

Fig. 3 .

 3 Fig. 3. Exemplary Single-Echo and Multi Echo Reconstructions for B0 and Exemplary Diffusion Directions. (A) Single-Echo: The non-averaged Single-Echo diffusion-weighted data display very poor SNR (top row). Threefold averaging of dMRI data introduces improvements of image SNR scaled by √ 3 (second row). Multi Echo: Multi Echo dMRI acquisitions displays clearly visible SNR benefits. When comparing LLS (row three) and MLE reconstructions (row four), the benefits of noise informed MLE reconstructions become evident. MLE reconstructions display a much stronger diffusion contrast due to a better reconstruction of diffusion signal attenuation. (B) Distributions of reconstructed ME-dMRI data show differences, only for low signal intensities in both dMRI data without (left) and with diffusion-weighting (right).

Furthermore 2 -

 2 Fig. 4. T * 2 -dependent SNR Gain of ME-dMRI Acquisitions. (A) Whole-brain T * 2 map in orthographic view. (B) The T * 2 histogram displays a bimodal T * 2 distribution across the brain with WM T * 2 30ms and GM T * 2 60ms. Voxels with very low T * 2 values (< 25ms) are likely caused by residual air bubbles. (C) Whole-brain map of T * 2

  standard deviation, σ ME , of this S 0 distribution leads to an analytical expression of SNR gain from LLS ME signal estimation compared to employing only single echo data,

	A	Pulse Sequence -Multi Echo Di¡usion Sequence	B	Multi Echo Di¡usion Data
		Di¡usion Weighting	Multi Echo Readout	Diffusion Weighting Directions
			Echo 1	Echo 2	...	Echo n
						t
		T 2 Decay	S 0 =S(TE 0 )	T 2 * Decay	S n =S(TE n )	Echo
		Signal at First Echo		. . .
				ME dMRI Signal Model
		Radiofrequency Pulse
		Diffusion Weighting Gradient
		Signal Readout (e.g., Segmented EPI)
			R A F T
		D

ACKNOWLEDGEMENTS

CE and MP are supported by the SPP 2041 'Computational Connectomics' of the German Research Foundation, DFG. MP is supported by a scholarship (PDF-502732-2017) from the Natural Sciences and Engineering Research Council of Canada (NSERC). The Max Planck Society provides core funding for the Taï Chimpanzee Project since 1997. We are grateful to the Ministère de l'Enseignement Supérieur et de la Recherche Scientifique and the Ministère de Eaux et Forêts of Côte d'Ivoire and the Office Ivorien des Parcs et Réserves for permissions to conduct the research; also to the Centre Suisse de Recherches Scientifiques for their long-term support and the staff members of the Taï Chimpanzee Project for their continuous work in the field.


Ittai Bar-Siman-Tov

Olivier Rozenberg

Cyril Benoît

Israel Waismel-Manor

Asaf Levanon

Ben Tair

Itay Zeev

Ori Cohen

Itamar Harari

Eyal Hashash-Daniel

Chani Kanfi

Yuval Kot

Evgeny Maor

Nina Saburov

Stepanets

Measuring Legislative Activity during the Covid-19 Pandemic: Introducing the ParlAct and ParlTech Indexes

Keywords: Covid-19, coronavirus, legislatures, parliaments, legislative activity, crisis, index I

This research note introduces two novel indexes designed to measure legislative activity (ParlAct) and use of digital devices to maintain legislative functions (ParlTech) during the first wave of the Covid-19 pandemic. We also introduce a novel comprehensive dataset on the functioning of legislatures during a critical period of the pandemic, providing scores of 152 domestic legislatures on both ParlAct and ParlTech indexes. Finally, we argue that both indexes could also serve as templates for future research on legislative activity during other pandemics, crises and contingencies.

INTRODUCTION

During Spring 2020, the Covid-109 pandemic brought an unprecedented challenge for parliaments and legislatures all around the world (Bar-Siman-Tov 2020; Norton 2020). Considering the gravity of the health crisis, and the need for prompt action, granting special emergency powers to the executive was the typical, and certainly not unprecedented, response [START_REF] Bjørnskov | This Time Is Different? -On the Use of Emergency Measures During the Corona Pandemic[END_REF][START_REF] Grogan | COVID 19 and States of Emergency: Introduction & List of Country Reports[END_REF]. At the same time, however, questions about the role of the other governmental branches become of prime importance [START_REF] Ginsburg | Binding the Unbound Executive: Checks and Balances in Times of Pandemic[END_REF][START_REF] Petrov | The COVID-19 Emergency in the Age of Executive Aggrandizement: What Role for Legislative and Judicial Checks?[END_REF]. Among them, legislatures are especially important given their role within political systems -whether these systems are pluralistic or not. Parliaments constitute indeed a universal political institution that was, crucially, largely threatened from various standpoints during the pandemic. Three distinct (though interrelated) series of threats posed by the current context are worth mentioning.

First, parliaments do have a material dimension: they are places where human beings sit together and engage iteratively in verbal exchanges. Social distancing measures, such as lockdowns and limitations on assembling, pose obvious threats in that respect. In countries such as Canada, Fiji, Ireland, Mexico, New Zealand and Oman, business was limited. 1 In others, like Haiti, India, Malaysia, Serbia, Switzerland, the UK or Zambia, legislatures were even adjourned or dissolved for several weeks, and in some cases, months.2 It has been estimated that, as of April 8 th 2020, two billion people in the world had their legislatures shut or limited due to these policies [START_REF] Provost | Alarm as 2 billion people have parliaments shut or limited by Covid-19[END_REF]. Despite the measures taken, a few assemblies turned into clusters of the pandemic with the infection -and sometimes death -of MPs, clerks and assistants. This was notably the case in France and Iran (Bar-Siman-Tov 2020).

Second, legislatures also constitute the main institution in which opposition to government has an influential say and possesses a range of symbolic and material resources. This, of course, implies that the expression of dissenting or diverging views can be guaranteed from the benches of the parliament. The Covid-19 pandemic was again a challenge from that perspective given the difficulty of expressing alternative views and criticisms in times of national unity. Challenging the responses offered by governmental (often legitimized by medical authorities) was indeed delicate when questions of life and death were at stake. Last but not least, legislatures are not only law-making authorities but are also expected to engage in a range of oversight activities [START_REF] Griglio | Parliamentary Oversight under the Covid-19 Emergency: Striving against Executive Dominance[END_REF]. Questioning ministers, tabling topical debates or conducting in-depth investigations, sometimes through a special committee, is indeed a crucial feature of the 'democratic kit' and are essential to ensure public accountability of elected officials, particularly when it comes to policies. Granted, the context of the Covid-19 have not made these tasks impossible to perform but has certainly rendered it more difficult. Some of them, as parliamentary questions, require that the parliament be open. Moreover, and as mentioned above, it soon appeared that some governments took the opportunity of the situation to get rid of major parts of parliamentary scrutiny. A comparative survey thus reports that the risk of 'pandemic backsliding' was particularly severe in countries such as El Savador, Hungary, India, Philippines, Serbia, Sri Lanka and Uganda [START_REF] Edgell | An Update on Pandemic Backsliding: Democracy Four Months After the Beginning of the Covid-19 Pandemic[END_REF][START_REF] Lührmann | Pandemic Backslading: Does Covid-19 Put Democracy at Risk?[END_REF].

Measuring legislative activity under a pandemic (and particularly a pandemic of this specific kind) is thus a crucial issue -not only for political scientists and legal scholars interested in how legislatures responded or were affected by the spread of Covid-19, but also for the public at large. This brief research note provides the foundation for such measurement. It introduces two novel indexes measuring legislative operation under Covid-19. The first (ParlAct) captures legislative activity on an ordinal scale. The second index (ParlTech), also on an ordinal scale, focuses on the use of digital devices that have served to maintain some legislative functions in spite of lockdowns or similar measures. In addition to discussing their properties, we provide scores for both indexes in 152 countries (i.e. nearly all countries in the world with a population of over 1,000,000), based on an original and novel dataset -one of the most comprehensive datasets collected on the operation of parliaments during the first stage of Covid-19. The remainder of this paper is organized as follows. Section II briefly reviews existing research on governmental activity under Covid-19. Section III presents our method and data collection strategies. Sections IV and V introduce ParlAct and ParlTech indexes, respectively. Section VI introduces our dataset. Section VII discuss our findings, and Section VIII concludes by drawing their implications for future research on legislative activity during critical events. II.

EXISTING RESEARCH ON GOVERNMENTAL ACTIVITY UNDER COVID-19

Significant efforts have been paid by a number of academic institutions, NGOs, and civic organizations to track and report governments' responses and activities since the spread of Covid-19. Many of these initiatives gather various data, documents and visualization on the policies that have been adopted by different governments around the world (e.g., the Covid-19 Law Lab jointly established by the World Health Organization, the United Nations and others3 ; the Worldwide Non-pharmaceutical Interventions Tracker for COVID-19 by IBM4 ; the Coronavirus Government Response Tracker by University of Oxford [START_REF] Hale | Coronavirus Government Response Tracker[END_REF]), or their impact on democracy and freedoms (e.g., the Global Monitor of COVID-19´s Impact on Democracy and Human Rights by International IDEA and others5 ; the COVID-19 Civic Freedom Tracker by the ICNL, ECNL and others6 ; V-Dem's Pandemic Backsliding Project [START_REF] Lührmann | Pandemic Backslading: Does Covid-19 Put Democracy at Risk?[END_REF]). Others, focus on gathering substantive qualitative reports and scholarly analysis on legislative and governmental responses from around the world (e.g., the Lex-Atlas: Covid-19 project7 ; Comparative Covid Law8 ; as well as many special issues in journals and blogs9 ). Many additional initiatives are listed in COVID-DEM, an info hub for tracking, compiling, and sharing information on how state responses to Covid-19 are impacting democratic governance [START_REF] Daly | Databases -COVID-DEM[END_REF].

These contributions are useful to get a broad picture of policies adopted across the globe. Subtler cross-national indexes are nonetheless still needed to capture how specific institutions have been affected or managed to continue their operation under the pandemic. This particularly applies to legislatures. Recent accounts suggest that the three core functions they fulfill (representation, scrutiny and legislation) require fine-grained analysis, as these activities are inherently multi-dimensional [START_REF] Rayment | Pandemic Parliaments: Canadian legislatures in a Time of Crisis[END_REF]). Yet, to our knowledge, existing efforts in that respect essentially consist of single-country or small-n studies (see e.g. the studies discussed in Cormacain and Bar-Siman-Tov, 2020b; and see also [START_REF] Chaplin | Fashioning a Pandemic Parliament: Getting On with Getting On[END_REF][START_REF] Malloy | The Adaptation of Parliament's Multiple Roles to Covid-19[END_REF][START_REF] Thomas | Westminster Parliaments: Comparing Four Approaches to Emergency Lawmaking and Scrutiny[END_REF] or essentially descriptive reports (e.g., Inter-Parliamentary Union, 2020; Crego and Mańko 2020; Murphy, 2020; Law Library of Congress 2020; Smith et al. 2020). 10 To fill this gap, we developed a novel, quantitative index specifically focused on legislative activity during the Covid-19 pandemic. Moreover, as technological and digital devices were crucial for many legislatures' continued operation across the globe (e.g., Del [START_REF] Monte | Remote Voting in the European Parliament and National Parliaments[END_REF][START_REF] Rozenberg | Post Pandemic Legislatures. Is real democracy possible with virtual parliaments?[END_REF][START_REF] Williamson | Virtual Members: Parliaments During the Pandemic[END_REF], we also developed a separate index to capture the extent to which these devices were used. Introducing a second index also enables us to draw a subtler picture of the legislatures' functioning: some legislatures have been active but mainly though virtual meetings whereas other kept working as usual.

It should be acknowledge that our main focus with both indexes is to offer a comparative and quantitative tool on the ability of legislatures to continue to operate during the pandemic. This in itself is a crucial measure, as the continued operation of the legislature is important not only for symbolic reasons, but is also a necessary prerequisite for it to perform its various functions, such legislating, oversight etc. Yet, it should be noted that our indexes provide only the basic (even if prerequisite and indispensable) level of examination on the functioning of legislatures. Our indexes could provide the basis for follow-up in-depth case-studies that will add the substantive qualitative examination of how well legislatures actually carried out their functions after being able to maintain or resume operation (e.g., quality of legislative oversight, extent, quality and constitutionality of legislation enacted, etc.). They could also provide the basis for follow-up qualitative studies on how the use of digital tools influenced to operation of parliament (such as the quality of deliberation, participation and rights of the opposition parties, of back benchers, changes in obstruction, etc.). The data produced by our indexes could give direction on which countries constitute appropriate cases for such case studies.

III.

METHODS AND DATA COLLECTION

We first undertaken a comprehensive analysis of how the Covid-19 pandemic and the measures taken to mitigate its effects can affect the operation of legislatures. This notably included an analysis of how the unique characteristics of this crisis interact with the institutional features of legislatures and the way they function (for an elaborate discussion, see Bar-Siman-Tov 2020).

Both indexes were developed by an international multidisciplinary team made of specialists of law (and especially legisprudence), legislative studies, comparative political science, political methodology and medicine. We used these two indexes to respectively assess legislative functioning and use of digital tools in legislatures during their response to the initial shock of Covid-19 as a new, threatening and unknown global risk (we focused on legislatures' operation during March 23 rd until April 6 th , 2020, which is shortly after Covid-19 was officially proclaimed a global pandemic by the World Health Organization on March 11). To document country scores for ParlAct and ParlTech in all countries beyond 1,000,000 inhabitants, data collection relied on a threefold approach. The first was to mobilize an extensive network of numerous academic experts on legislatures. 11 Each expert was asked to complete a substantive report about the current operation of the legislature in her country (which facilitated the development of the index and ensure its validity), and at the next stage, to answer a short survey, assessing the legislative activity and technological solutions' usage based on the indexes in their country of expertise. One hundred and seventy-two experts kindly shared with us information on their country of expertise. 12 11 The methodology for creating this network of academic experts was as follows: we reached out to our extensive network of leading academic experts on parliaments (emailing over 200 academics). The network was then extended through a snowball method (asking the colleagues in our original network to suggest additional experts), and by asking for recommendations on additional experts through several relevant academic networks: The International Association of Legislation, COVID-DEM (directed by Tom Daly), the Constitutional Democracy Listserv (edited by Mark Graber), Researchgate, and Academia.edu.

12 The full list of the experts is available at this address: XXX [REMOVE FOR ANONIMACY]

Expert surveys inevitably result in some bias (see [START_REF] Hooghe | Reliability and validity of measuring party positions: The Chapel Hill expert surveys of 2002 and 2006[END_REF] for a review). We thus complemented our first approach by collecting a range of comparative reports from international and national parliamentary research centers focusing on parliamentary activity in various countries during the same period. 13 Finally, we collected reports from hundreds of daily newspaper articles and entries in legislatures' websites with information pertaining to the legislatures' functioning in each of our countries' sample. Publications in English, French, Hebrew and Spanish were directly retrieved. Publications in other languages were translated using Google Translate.

We then controlled for the reliability of both indexes. We independently asked two coders to determine ParlAct and ParlTech scores for each country, based on the information in our datasets without seeing the scores from the experts' survey. Intercoder reliability calculated using Krippendorff's alpha was at α = 0.81.

IV.

MEASURING LEGISLATIVE ACTIVITY: THE PARLACT INDEX

The ParlAct Index is an ordinal scale ranging from 1 (legislature is completely closed) to 10 (legislature is fully functioning). Scores 1 to 4 deal with closed legislatures, differentiating those who shut down due to Covid-19 from the ones shut down due to a usual break unrelated to the crisis (such as Easter break or elections recess), whose duration was possibly changed due to Covid-19. Scores 5 to 9 deal with partially operating legislatures, while differentiating types and levels of partial operation: scores 5-7 focus on partial operation in the sense of which legislative institutions (committees or plenum) operate; scores 8-9 focus on partial operation in the sense of meetings' frequency. A 10 score indicates a fully operating legislature (Table 1). Of course, in-between cases are possible, and therefore optimal use of the indexes allows for in-between scores (e.g., 9.5).

It should be noted that one of our early insights was that the behavior of legislatures in various countries changed (sometimes multiple times) throughout this ongoing crisis. Moreover, various legislatures around the world have normal recesses (due to holidays etc.) in different times during the year. Therefore, when using our indexes, it is important to instruct respondents from all countries to focus on the same clearly defined period. Our index asks respondents to report whether their legislature was supposed to be in session, and whether (and how) its operation changed due to covid-19, during this defined period. For example, we asked all our respondents to report only on legislative operation from March 23rd until April 6th 2020 (as we focused on legislatures' response to the initial shock of a new global health risk). To measure long term effects or changes over time, the data collection based on the index should be repeated, each time focusing on a different carefully defined period throughout this prolonged pandemic.

MEASURING LEGISLATIVE USE OF TECHNOLOGICAL AND DIGITAL SOLUTIONS: THE PARLTECH INDEX

In several countries, the use of digital devices helped maintain legislative operations, even if considerable variations are observable from one country to another. Thus, we adopted a similar approach to the ParlAct Index, focusing not only on whether or not digital devices were used (1), but also differentiating among various uses -ranging from mere communication with other governmental bodies and hearing experts (2) to remote voting (4) (Table 2). Both plenum and committees use digital devices such as videoconferencing and remote voting in lieu of physical presence 14 To avoid too much complexity, we did not add sub-categories for the various interactions between 6-7 and 8-9. Hence, generally, for 8-9, it is possible to count one meeting by day whatever the type of meeting (plenary or committee). However, respondents should be encouraged to provide an in-between number when appropriate and to add verbal explanations in such cases. We originally examined all 159 countries in the world with a population of over 1,000,000. Eventually seven countries (Benin, Dominican Republic, Malawi, Oman, Qatar, Republic of Yemen, and Trinidad and Tobago) were excluded from the current report, because we were not able to triangulate our data and be confident enough about its reliability. We were still left with a very extensive dataset of 152 countries, making this one of the most comprehensive dataset in the world to explore the operation of legislatures during the initial stage of covid-19. For Cuba, Pakistan, and Panama, we were able to report ParlAct, but not ParlTech (indicated by *). For two countries (Palestine and Sudan) we indicate a 0, because we found that they lacked an operating legislature long before covid-19.

VI.

THE DATASET: PARLACT AND PARLTECH SCORES FOR WORLD LEGISLATURES

VII. DISCUSSION

Scores for ParlAct indicate that the situation substantially differs from one country to another. The same proportion of countries -one out of five -are working as usual (10 score) or are closed due to Covid-19 (scores 1 and 2). If we put aside legislatures that were on usual break during the period under consideration, half of the legislatures of the world has been working partially -which confirms the scientific interest of this issue. The average grade for the whole countries is of 6.6 and varies between continents: 7.8 in Americas and Europe, 6.7 in Asia, 6 in Oceania and 5.3 in Africa.

Further analysis is required to investigate these results. Still, it can be observed that mortality due to Covid-19 seemingly played on a limited role as, at the time of the fieldwork, the pandemic was mostly developed in Asia and Europe and nearly not in Africa. The state of democracy is also to be considered as established democracies may have secured more efficiently the usual functioning of their legislatures. Yet, again, a complex picture emerges from Table 3 as we find established democracies at the bottom of the ParlAct ranking (for instance India, Switzerland and the UK) as well as authoritarian regimes among the countries where the parliament maintained their operations (for instance Bahrain, Belarus or Burundi). This observation questions the very category of legislatures and parliaments beyond their obvious commonalities: the constraining power of the parliament vis-à-vis the executive is not similar from one country to another which may explain why some (democratic or undemocratic) leaders may try to silence it or not.

Finally, the functioning of legislatures is moderately correlated with their capacity to use digital devices (Pearson's r of 0.34 for the whole sample and 0.15 for the countries situated between 5 and 9 of the ParlAct scale). Figure 1 offers a visualization on how the 152 legislatures are located on both axes. Note: the size of the circle accounts for the number of legislatures corresponding to a given dot. Countries populated with more than 100 million inhabitants are located and specified by name.

Source: the authors Online conferences certainly helped many legislatures to keep their committees (and more rarely the plenary) working but cannot be considered as a universal rescuer for parliamentary politics. Again, this observation should be considered in the light of the unequal access to digital technologies between countries. The choice for a partial or total online functioning of legislatures also raises delicate legal and political issues. In many cases, laws and regulations have not foreseen this largely unprecedented situation. Chile, for instance, had to change its constitution to permit virtual parliamentary decision-making. In Colombia, the Constitutional Court held that Congress cannot hold virtual sessions based on an authorization provided by a governmental emergency decree that allowed all branches of government to hold virtual sessions (Bar-Siman-Tov, 2020). In other countries, such as Canada and the UK, the choice for hybrid meetings was a matter of intense political controversies between the government and the opposition [START_REF] Bar-Siman-Tov | Covid-19 Meets Politics: The Novel Coronavirus as a Novel Challenge for Legislatures[END_REF][START_REF] Malloy | The Adaptation of Parliament's Multiple Roles to Covid-19[END_REF]. From a more theoretical standpoint, the capacity of parliamentary politics to fully perform is questioned by the remote functioning of legislatures [START_REF] Rozenberg | Post Pandemic Legislatures. Is real democracy possible with virtual parliaments?[END_REF]. As a result, the dominant political culture(s) and legal tradition(s) also influence the choice for adopting technology which may account for part of the variation of the ParlTech scale.

VIII. CONCLUSION

In this brief research note, we offered two novel indexes for the assessment of the functioning of legislatures during pandemics. Our new indexes constitute a unique universal resource for evaluating and comparing legislatures worldwide. They could allow researchers and civic society to continuously monitor, measure and compare the operation of parliaments during the current pandemic, as well as during future pandemics and other emergencies and crises, such as wars, major terrorist attacks, or environmental catastrophes.

Based on these indexes, we also offered a novel dataset on the functioning of legislatures worldwide during the initial crucial period of the global Covid-19 pandemic. The scores in our dataset indicate that the situation substantially differs across countries; and that, while some parliaments are fully functioning or are completely closed due to Covid-19, the greatest proportion of world legislatures are partially working to varying degrees. This demonstrates that a binary report of whether parliament is operating or not is too crude and paints an inaccurate picture of the real world. This confirms the scientific interest and practical importance of the ordinal index we created. Further analyses are required to investigate our dataset.

This contribution can serve as a basis for future research that would investigate the complex institutional effects of this and future similar crises, and help assess more accurately whether the Covid-19 actually constitutes a potential threat for parliamentary democracy and its most vital organ. We hope that our ParlAct and ParlTech indexes, as well as our dataset, would become helpful tools for academic researchers, parliamentary research institutions, and civic society, worldwide.

Figure 1 .

 1 Figure 1. The location of 152 legislatures on both axes

Table 1 -

 1 Legislative Activity (ParlAct) Index Legislature was supposed to be in session this time of the year, but shut down due to Covid-19

	SCORE DESCRIPTION
	1
	2	Legislature is closed due to a usual break (e.g. holiday break, election recess), which has
		started earlier or was extended due to Covid-19
	3	Legislature is closed due to a usual break (e.g. holiday break, election recess), whose
		duration was not changed due to Covid-19
	4	Legislature is on a usual break (e.g. holiday break, election recess), whose duration was not
		prolonged due to Covid-19, but held 1-2 emergency meetings due Covid-19
	5	Legislature is operating in skeletal form: plenum and committees are closed, while
		leadership of the legislature (e.g., some very small forum of speakers, party leaders)
		continue to meet
	6	Legislature is partly operating: committees are operating whereas plenum is closed
	7	Legislature is partly operating: plenum is operating whereas committees are closed
	8	Legislature is officially fully operating, but meetings are sparse and are significantly less
		frequent than during ordinary times (e.g., 0-2 meetings in the last 2 weeks) 14
	9	Legislature is officially fully operating, but meetings were reduced and are somewhat less
		frequent than during ordinary times (e.g., 3-4 meetings in the last 2 weeks)
	10	Legislature is fully operating as usual
	V.

Table 2 -

 2 Legislative use of Technology (ParlTech) Index Physical presence still used in debate and vote, but digital devices such as videoconferencing are used to communicate with other governmental bodies, hearings, etc.

	SCORE DESCRIPTION
	1	Physical presence still used in debate and vote (or legislature is closed). No special digital
		devices adopted
	2
	3	Plenum still requires physical presence, but committees use digital devices such as
		videoconferencing and remote voting in lieu of physical presence
	4

  Table 3 shares our dataset, displaying ParlAct and ParlTech scores of legislatures in 152 countries from March 23 rd until April 6 th 2020. 15

Table 3 -

 3 Country-scores for ParlAct and ParlTech

	COUNTRY

Ibid.

https://covidlawlab.org

https://ibm.github.io/wntrac/

https://www.idea.int/gsod-indices/#/indices/world-map?covid19=1

https://www.icnl.org/covid19tracker/

www.lexatlas-c19.org

https://www.comparativecovidlaw.it/

See, e.g.,(Cormacain and Bar-Siman-Tov, 2020a; https://www.theregreview.org/2020/04/20/comparingnations-responses-covid-19/; https://verfassungsblog.de/category/debates/fighting-covid-19-debates/; https://www.cambridge.org/core/blog/tag/country-responses-to-the-covid19-pandemic/

 10 We should note two recent important initiatives from after this article was submitted: the InterPares Parliamentary Data-tracker; and the Parliaments in the Pandemic project organized by the Research Committee of Legislative Specialists of the International Political Science Association.

The full list of reports from international and national parliamentary research centers is available at this address: XXX[REMOVE FOR ANONIMACY]

This research was supported by a research grant from the Israel National Institute for Health Policy Research (#2020/553).