Jianping Huang
email: jianping829@gmail.com

Lihui Wang

Chunyu Chu

Wanyu Liu

Yuemin Zhu

Accelerating Cardiac Diffusion Tensor Imaging Combining Local Low-Rank and 3D TV Constraint

Keywords: :Cardiac Diffusion Tensor Imaging, Compressed sensing, Sparse sampling, Constrained reconstruction, Locally low-rank regularization

Object: Diffusion tensor magnetic resonance imaging (DT-MRI, or DTI) is a promising technique for invasively probing biological tissue structures. However, DTI is known to suffer from much longer acquisition time with respect to conventional MRI and the problem is worsened when dealing with in vivo acquisitions. Therefore, faster DTI for both ex vivo and in vivo scans is highly desired.

Materials and Methods:

This paper proposes a new compressed sensing (CS) reconstruction method that employs local low-rank (LLR) model and three-dimensional (3D) total variation (TV) constraint to reconstruct cardiac diffusion-weighted (DW) images from highly undersampled k-space data. The LLR model takes the set of DW images corresponding to different diffusion gradient directions as a 3D image volume and decomposes the latter into overlapping 3D blocks. Then, the 3D blocks are stacked as two-dimensional (2D) matrix. Finally, low-rank property is applied to each block matrix and the 3D TV constraint to the 3D image volume. The underlying constrained optimization problem is finally solved using the first-order fast method. The proposed method is evaluated on real ex vivo cardiac DTI data as a prerequisite to in vivo cardiac DTI applications.

Results:

The results on real human ex vivo cardiac DTI images demonstrate that the proposed method exhibits lower reconstruction errors for DTI indices, including fractional anisotropy (FA), mean diffusivities (MD), transverse angle (TA) and helix angle (HA), compared to existing CS-based DTI image reconstruction techniques.

Conclusion:

The proposed method provides better reconstruction quality and more accurate DTI indices in comparison with the state-of-the-art CS-based DW image reconstruction methods.

Introduction

Diffusion tensor magnetic resonance imaging (DT-MRI, or DTI) is an MRI technique that allows for investigating noninvasively the fiber architectures of the human heart [START_REF] Froeling | Diffusion Tensor MRI of the Heart -In Vivo Imaging of Myocardial Fiber Architecture[END_REF][START_REF] Naumova | Assessment of Heart Microstructure From Mouse to Man[END_REF][START_REF] Tournier | Diffusion Tensor Imaging and Beyond[END_REF][START_REF] Yang | Feature-based interpolation of diffusion tensor fields and application to human cardiac DT-MRI[END_REF][START_REF] Basser | a) MR diffusion tensor spectroscopy and imaging[END_REF][START_REF] Basser | Estimation of the Effective Self-Diffusion Tensor from the NMR Spin-Echo[END_REF][START_REF] Scollan | Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging[END_REF][START_REF] Holmes | Direct histological validation of diffusion tensor MRI in formaldehyde-fixed myocardium[END_REF][START_REF] Mekkaoui | Diffusion MRI in the heart[END_REF][START_REF] Pravdin | Mathematical model of the anatomy and fibre orientation field of the left ventricle of the heart[END_REF][START_REF] Lopez-Perez | Three-dimensional cardiac computational modelling: methods, features and applications[END_REF]. However, cardiac DTI is known to suffer from long acquisition time to obtain high quality images (in terms of temporal resolution, spatial resolution, and signal-to-noise-ratio-SNR) for both ex vivo [START_REF] Helm | Ex vivo 3D diffusion tensor imaging and quantification of cardiac laminar structure[END_REF][START_REF] Geerts | Characterization of the normal cardiac myofiber field in goat measured with MR-diffusion tensor imaging[END_REF][START_REF] Wu | MR diffusion tensor imaging study of postinfarct myocardium structural remodeling in a porcine model[END_REF][START_REF] Strijkers | Diffusion tensor imaging of left ventricular remodeling in response to myocardial infarction in the mouse[END_REF][START_REF] Yang | Interpolation of vector fields from human cardiac DT-MRI[END_REF] and in vivo [START_REF] Dou | Combined diffusion and strain MRI reveals structure and function of human myocardial laminar sheets in vivo[END_REF][START_REF] Wu | Diffusion tensor magnetic resonance imaging mapping the fiber architecture remodeling in human myocardium after infarction -Correlation with viability and wall motion[END_REF][START_REF] Nielles-Vallespin | In vivo diffusion tensor MRI of the human heart: Reproducibility of breath-hold and navigator-based approaches[END_REF] hearts. This is because DTI requires, with respect to conventional MRI, supplementary acquisitions at different (at least six) diffusion gradient directions. The problem is worsened when dealing with in vivo DTI acquisitions since patient movement and cardiac motion often cause image quality degradation and motion artifacts [START_REF] Nguyen | In Vivo Three-Dimensional High Resolution Cardiac Diffusion-Weighted MRI: A Motion Compensated Diffusion-Prepared Balanced Steady-State Free Precession Approach[END_REF][START_REF] Welsh | Higher-Order Motion-Compensation for In Vivo Cardiac Diffusion Tensor Imaging in Rats[END_REF][START_REF] Dou | Cardiac diffusion MRI without motion effects[END_REF][START_REF] Wei | Assessment of Cardiac Motion Effects on the Fiber Architecture of the Human Heart In Vivo[END_REF][START_REF] Wei | Free-Breathing Diffusion Tensor Imaging and Tractography of the Human Heart in Healthy Volunteers Using Wavelet-Based Image Fusion[END_REF]. Therefore, shortening acquisition time is highly desired for both ex vivo and in vivo DTI. It becomes indispensable in reducing motion artifacts and improving image quality for clinical cardiac DTI. Many attempts have been made to shorten the acquisition time by reducing the amount of acquisition data, such as parallel imaging [START_REF] Holdsworth | Robust GRAPPA-Accelerated Diffusion-Weighted Readout-Segmented (RS)-EPI[END_REF][START_REF] Bammer | Diffusion tensor imaging using single-shot SENSE-EPI[END_REF][START_REF] Bammer | Improved diffusion-weighted single-shot echo-planar imaging (EPI) in stroke using Sensitivity Encoding (SENSE)[END_REF][START_REF] Jaermann | SENSE-DTI at 3 T[END_REF][START_REF] Larkman | Parallel magnetic resonance imaging[END_REF], partial k-space imaging [START_REF] Hsu | Myocardial fiber orientation mapping using reduced encoding diffusion tensor imaging[END_REF][START_REF] Jiang | Accelerating MR diffusion tensor imaging via filtered reduced-encoding projection-reconstruction[END_REF], and simultaneous multi-slice (SMS) imaging [START_REF] Lau | Accelerated Human Cardiac Diffusion Tensor Imaging Using Simultaneous Multislice Imaging[END_REF][START_REF] Taron | Scan time minimization in hepatic diffusion-weighted imaging: evaluation of the simultaneous multislice acceleration technique with different acceleration factors and gradient preparation schemes[END_REF].

In recent years, compressed sensing (CS) has emerged as a new framework for reconstructing signals with high quality from less measurements than the traditional Shannon-Nyquist sampling theorem [START_REF] Candes | Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[END_REF][START_REF] Donoho | Compressed sensing[END_REF][START_REF] Candes | Near optimal signal recovery from random projections: Universal encoding strategies[END_REF]. CS exploits sparsity or compressibility of signals in certain domain (pixel or transform domain) and combines sampling and compression into a unified framework. To date, CS has been successfully applied to biomedical imaging [START_REF] Graff | Compressive sensing in medical imaging[END_REF][START_REF] Wang | Compressive Sensing for Biomedical Imaging[END_REF], and has shown great potential for MRI [START_REF] Lustig | Compressed sensing MRI[END_REF][START_REF] Hollingsworth | Reducing acquisition time in clinical MRI by data undersampling and compressed sensing reconstruction[END_REF][START_REF] Chen | Compressed sensing MRI via fast linearized preconditioned alternating direction method of multipliers[END_REF] and computed tomography (CT) [START_REF] Ritschl | Iterative 4D cardiac micro-CT image reconstruction using an adaptive spatio-temporal sparsity prior[END_REF][START_REF] Hu | Improved total variation minimization method for few-view computed tomography image reconstruction[END_REF][START_REF] Rigie | Joint reconstruction of multi-channel, spectral CT data via constrained total nuclear variation minimization[END_REF].

In light of the time-reducing potential of CS and considering that the diffusion-weighted (DW) images obtained along different diffusion gradient directions of DTI are often correlated, a constrained image reconstruction technique for cardiac DTI based on a regularization framework was proposed [START_REF] Adluru | Constrained reconstruction of sparse cardiac MR DTI data[END_REF], in which the total variation (TV) constraint was chosen in both spatial domain and diffusion direction to accelerate DTI acquisitions. Both sparsity prior and intra-and inter-correlation of DW images were also embedded in a single constraint term in the CS extensions (distributed CS) to further reduce DTI acquisition time [START_REF] Wu | Accelerated MR Diffusion Tensor Imaging Using Distributed Compressed Sensing[END_REF]. Utilizing the inter-image correlation of DW images, the combination of CS and parallel imaging further improved acquisition efficiency [START_REF] Shi | Parallel imaging and compressed sensing combined framework for accelerating high-resolution diffusion tensor imaging using inter-image correlation[END_REF]. By stacking the DW images as column vectors of a matrix, the resulting matrix is then rank-deficient, which allowed the authors of [48,49] to formulate the CS-based DTI image reconstruction from undersampled k-space as a low-rank matrix approximation problem. Observing that phase changes drastically across diffusion gradient directions, a phase-constrained low-rank (PCLR) approach was developed [START_REF] Gao | PCLR: Phase-Constrained Low-Rank Model for Compressive Diffusion-Weighted MRI[END_REF]. In [START_REF] Welsh | Model-based reconstruction of undersampled diffusion tensor k-space data[END_REF][START_REF] Zhu | A model-based method with joint sparsity constraint for direct diffusion tensor estimation[END_REF][START_REF] Dong | Model-based reconstruction for simultaneous multislice and parallel imaging accelerated multishot diffusion tensor imaging[END_REF], model-based CS methods for DTI were proposed, which use the signal intensity model to directly estimate diffusion tensor fields from undersampled k-space data.

Meanwhile, local low-rank (LLR) model has been recently proposed in various medical imaging applications such as quantitative water-fat MRI [START_REF] Lugauer | Accelerating multi-echo water-fat MRI with a joint locally low-rank and spatial sparsity-promoting reconstruction[END_REF], dynamic MRI image reconstruction [START_REF] Trzasko | Local versus global low-rank promotion in dynamic MRI series reconstruction[END_REF] and MRI parameter mapping [56]. Compared to global low-rank (GLR) methods that capture global correlation among whole images, the LLR model is more suitable for accounting for local information. The present study proposes a new CS reconstruction method that employs both LLR model and three-dimensional (3D) TV constraint to reconstruct cardiac DTI images. The LLR model takes the set of DW images corresponding to different diffusion gradient directions as a 3D volume and decomposes the latter into overlapping 3D blocks. Then, the 3D blocks are stacked as two-dimensional (2D) matrix. Finally, low-rank property is applied to each block matrix and the 3D TV constraint to the 3D image volume. The underlying constrained optimization problem is finally solved using the first-order fast method. The proposed method is evaluated on real ex vivo cardiac DTI data as a prerequisite to in vivo cardiac DTI applications.

The rest of the paper is organized as follows. In Section 2, the mathematical formulation of the proposed method and experimental settings are given. Then, in Section 3, the proposed method is evaluated on human ex vivo heart DW images and compared to the state-of-the-art methods. Finally, the discussion and conclusion are given in Sections 4 and 5, respectively.

Materials and methods

Proposed method

Assuming that x l is a vectorised DW image and u l F is a partial Fourier transform for th l diffusion direction. The undersampled k-space data y l of the DW image for each direction in k-space can then be formulated as:

yx u l l l l F   , (1)
where l  is the observed noise and l = 1, 2,…, L the diffusion direction, and

u l F P F  with F
denoting Fourier transform and P the undersampling pattern (mask). Note that in practical acquisitions, raw k-space data are always complex and non-Hermitian symmetric. As a result, the corresponding spatial DW image x l is always complex and contains a spatial phase.

All the undersampled k-space data Y of the DW images in all the diffusion gradient directions can be written as: F is a partial Fourier transform for all the diffusion directions and is defined as:

u Y F X     , (2) where 
1 0 0 u u u L F F F        . ( 3
)
The DW images are sparse/compressible in certain domain such as wavelet domain. In addition, since the DW images acquired in different diffusion gradient directions have similar anatomical structures, they are somewhat correlated. Consequently, by stacking these images as column vectors of a matrix X , the latter will be low rank. Then, the reconstruction of DW images from undersampled k-space data is performed by solving the following optimization problem (i.e. GLR model, as illustrated in figure 1(a)): Using the above-described LLR method, the reconstruction then becomes the following optimization problem:

2 1 2 1 arg min 2 u X X F X Y X T X            (4)
  2 * 2 1 arg min 3 2 u b X b X F X Y R X TV D X            , ( 5
)
where u F is the partial Fourier transform for all diffusion directions as defined in

        2 2 2 , , , , 1, , , , , 1, , , , , 1 2 , , , , 3
i j k i j k i j k i j k i j k i j k i j k i j k i j k TV D X D X X X X X X X          



, where ,, i j k D means the forward finite-difference operators along the horizontal, vertical, and diffusion gradient directions of DW images, respectively. This problem can be effectively solved using the Fast Composite Splitting Algorithm (FCSA) introduced in [START_REF] Huang | Efficient MR image reconstruction for compressed MR imaging[END_REF]. This method is based on the combination of both variable and operator splitting techniques, which decompose the regularization problem (5) into two simpler regularization subproblems. The main steps of this method is as follows: (a) splitting variable x into two variables

  1,2 i i
x  ; (b) performing operator splitting to minimize total variation regularization and nuclear norm regularization subproblems over   1,2 i i

x  respectively, and (c) obtaining the solution x by linear

combination of   1,2 i i x  . Let   2 2 1 2 u f X F X Y 
that is a convex and smooth function with the

Lipschitz constant L f ,   1 * b b g X R X    
that is a convex but non-smooth function and

    2 3 g X TV D X   . Then, the       12 g X g X g X 
problem can be divided into two subproblems: nuclear norm regularization and TV-norm regularization. Each subproblem is actually a convex function that can be solved by a proximal mapping operation [START_REF] Beck | A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems[END_REF]:

     12 3 * and 2 kk b g g TV D b X prox R X x X prox X x         .
According to [START_REF] Beck | A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems[END_REF], given a continuous convex function g(x) and any scalar q > 0, the proximal map associated with function g is defined as: tol : the tolerance parameter.

     2 2 1 arg min 2 u prox x u u x          , where  is the inverse of the Lipschitz constant L f having     ' 2 2 1 2 T u u u f F X Y F F X Y         with  
INIT:

1 0 1 1 , 1, 0, 0; t X r k L       REPEAT: 1; kk    ; kk g x r f r          1 * 2 3 12 ; 2; ; 2 k bg b k g TV D kk k X prox R X x X prox X x XX X                ; kk X abs X    2 1 1 1 4 ; 2 k k t t      1 11 1 ; k k k k k k t r X X X t       UNTIL kK  OR 1 2 2 kk k XX tol X    . OUTPUT:   k X

abs X 

: the reconstructed DW images.

Experimental data

The real DW data correspond to ex vivo samples of the human hearts [START_REF] Helm | Evidence of structural remodeling in the dyssynchronous failing heart[END_REF][START_REF] Helm | Ex vivo 3D diffusion tensor imaging and quantification of cardiac laminar structure[END_REF][START_REF] Helm | Measuring and Mapping Cardiac Fiber and Laminar Architecture Using Diffusion Tensor MR Imaging[END_REF] from the website http://cvrgrid.org/data/ex-vivo. The corresponding acquisition parameters are the following: image size=256×256×134, image spatial resolution=0.43×0.43×1.0 mm 3 , and number of diffusion gradient directions 21. In the present study, seven slices of the image volume have been used to evaluate the proposed method (the b 0 image of the 5 th slice was shown in figure 2(a)). We used the same k-space sampling patterns as those used in [START_REF] Lustig | Sparse MRI: The application of compressed sensing for rapid MR imaging[END_REF][START_REF] Tsai | Reduced aliasing artifacts using variable-density k-space sampling trajectories[END_REF], which concern Cartesian undersampling patterns with one-dimensional (1D) variable density phase-encode random undersampling (i.e. in k y direction) and 2D variable density random undersampling pattern. An example of the 1D and 2D random k-space undersampling patterns is shown in figure 2(b) and figure 2(c), in which the sampling ratio (R) was set to 15%.

The above initial DW data are in fact spatial magnitude data (so, their corresponding k-space data are complex but Hermitian symmetric) while in practice DW data are always spatial complex because the acquired raw k-space data are always complex and non-Hermitian symmetric. To mimic actual acquisitions, we have rendered the magnitude DW data complex in the following manner: a) take the Fourier transform of spatial magnitude DW data, providing complex but Hermitian-symmetric k-space data; b) undersample the complex k-space data, thus making the k-space data asymmetric; c) add complex Gaussian white noise to the asymmetric k-space data, rendering them even more asymmetric; d) take the inverse Fourier transform of the undersampled noisy k-space data, leading to complex spatial DW data containing phase information.

Evaluation

To evaluate the performance of the proposed method (LLR+TV3D), comparison was performed with zero-filling (replace the non-acquired k-space data by zeros and then inverse Fourier transform the zero-filled k-space data), joint sparsity (JS) [START_REF] Wu | Accelerated MR Diffusion Tensor Imaging Using Distributed Compressed Sensing[END_REF], JS with TV3D (JS+TV3D), global low-rank (GLR) [48], GLR with TV3D (GLR+TV3D) and, local low-rank without TV3D (LLR) methods.

In addition to qualitative assessment consisting of visually comparing reconstruction results, several quantitative indices were calculated for the DW images reconstructed with different methods.

They are the fractional anisotropy (FA), mean diffusivity (MD), helix angle (HA) and transverse angle (TA) [START_REF] Streeter | Fiber orientation in the canine left ventricle during diastole and systole[END_REF][START_REF] Scollan | Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging[END_REF].

The MD characterizes the mean diffusivity of the tissue:

1 2 3 MD 3      . ( 6
)
The FA is used to describe the diffusion anisotropy of the tissue:

        2 2 2 1 2 3 222 1 2 3 3 MD MD MD FA 2                 . ( 7
)
The HA is defined as the angle between the projection of the primary eigenvector onto the tangent plane and the imaging plane, and the TA is defined as the angle between the projection of the primary eigenvector onto the imaging plane and the tangent plane [START_REF] Streeter | Fiber orientation in the canine left ventricle during diastole and systole[END_REF][START_REF] Scollan | Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging[END_REF]. The pair (HA, TA)

describes completely fiber orientation.

To quantitatively compare different reconstruction methods, the root mean square errors (RMSE)

was first calculated for each slice according to:

    2 2 - RMSE rec ref vec x vec x N  , (8)

Parameter setting

In the following experiments, 1D variable density phase-encode random undersampling was used.

The ISNR was set to 20 dB. The Daubechies wavelets with four decomposition levels were used.

The threshold parameter  in soft-thresholding operator for each 3D block was set in an adaptive manner using Stein's unbiased risk estimate (SURE) thresholding [START_REF] Lagae | A comparison of methods for generating Poisson disk distributions[END_REF]. The regularization parameter  was set to 0.1 and the 3D block size Reconstructions from undersampled k-space (sampling ratio 25%) using (a) zero-filling method (RMSE=15.0506), (b) JS method (RMSE =14.1850), (c) JS+TV3D method (RMSE=12.9166), (d) GLR method (RMSE=12.9376), (e) GLR+TV3D method (RMSE=12.5925), (f) LLR method (RMSE=13.0880) and (g) the proposed method (RMSE=11.9483).

Results

Visual comparison

Sampling ratios

Robustness to noise

The performance of reconstruction from undersampled DTI data using the proposed method for

Sampling patterns

Figure 9 shows the reconstruction performance of the proposed method on two different sampling patterns, namely the 1D variable density random undersampling in phase-encoding direction and 2D variable density random undersampling pattern [START_REF] Lustig | Sparse MRI: The application of compressed sensing for rapid MR imaging[END_REF][START_REF] Marseille | Nonuniform phase-encode distributions for MRI scan time reduction[END_REF], in terms of FA, MD, TA and HA (with sampling ratios from 10% to 50% and without noise). As observed, for the same sampling ratio, the

Choice of patch size

The choice of patch size [ , , ]

Discussion

Combination of local low-rank and 3D TV constraints

The comparison of the reconstructions with and without 3D TV constraints shows that the proposed method (with 3D TV) always generated the smallest mRMSE regardless of sampling ratios (figure 7), which means that the reconstruction using the combination of local low-rank penalty and 3D TV penalties clearly reduces reconstruction artifacts and preserves image edges and fine structures. This can be explained as follows. Since the proposed method operates on image blocks, the matrix is more rank-deficient from local image blocks than from 3D image volume. As a result, the use of the LLR allows better reconstructing local image structure information, but may produce excessive edge blurring in the case of high undersampling ratios (e.g. undersamplng ratio of 0.1).

Meanwhile, the 3D TV constraint is particularly suitable for reconstructing edges, but tends to over-smooth image details at high undersampling ratios. Hence, the combination of the two constraints has enabled us to achieve better reconstruction quality.

Determination of regularization parameter

The regularization parameter  was empirically determined. It also impacts on reconstruction quality. Figure 11

Effect of sampling patterns

As observed (figure 9), the 2D variable density random undersampling pattern gives better performance than the 1D variable density random undersampling pattern. This can be explained as follows. It is well known that when k-space is undersampled, the zero-filled inverse Fourier reconstruction exhibits aliasing artifacts since the Nyquist criterion is violated. The appearance of the aliasing artifacts depends on the undersampling pattern. Equispaced sampling results in coherent folding effects; as a result, image structure overlapping is very visible. In contrast, random or pseudo-random undersampling leads to incoherent interferences [START_REF] Lustig | Compressed sensing MRI[END_REF][START_REF] Marseille | Nonuniform phase-encode distributions for MRI scan time reduction[END_REF]; the final effect of the interferences appears much like additive random noise and consequently, the reconstructed image preserves more initial information. Figure 12 shows an example where the sampling patterns and the corresponding images reconstructed using zero-filling method are given.

Note however that, although ideal, the 2D variable density random undersampling pattern cannot be implemented on current MRI systems whereas the implementation of 1D variable density random undersampling (in phase-encoding direction) scheme is simpler and requires only minor modifications to existing pulse sequences [START_REF] Lustig | Sparse MRI: The application of compressed sensing for rapid MR imaging[END_REF][START_REF] Marseille | Nonuniform phase-encode distributions for MRI scan time reduction[END_REF].

Influence of phase information

In the present study, image reconstruction is formulated as an optimization problem (Eq. 5), in which there are three terms. In each of the three terms, complex images (i.e. phase information) were used. However, we have not used the complex images all the time during the reconstruction process.

Indeed, after calculating the above three terms, we used the magnitude of complex image when computing

  2 1 1 1 4 2 k k t t    and   1 11 1 k k k k k k t r X X X t       , in which   kk X abs X 
. That aimed to simplify the calculation while focusing on the energy of images by taking the magnitude of complex image. It is however possible to use only the magnitude of complex image (by taking   gg x abs x 

) or simply take as such the complex image all the time during the reconstruction, which will then lead to respectively the so-called "Abs" method (no phase information is used) and "Complex" method (phase information is used). Of course, no matter what method we used, the last step is always to take the magnitude of complex image as the final desired image.

The results for ISNR=0 dB (noise-free) and ISNR=20 dB are respectively illustrated in Figure 13 and Figure 14.

These results show that, for highly undersampled k-space data (sampling ratio smaller than 15%), the proposed method gives rise to smaller errors with respect to the cases of using the magnitude of complex image or using purely complex image. After certain sampling ratio (saying greater than 20%), using the magnitude of complex image leads to the best results while using complex image during the whole reconstruction process yields the worst results. The difference in performance between the three methods can be explained as follows. The "Abs" method always works on the energy (magnitude) of complex image. Since in MRI, images are always produced in such a way that the imaginary part of the complex image is small with respect to the real part, the magnitude image always preserves such importance proportionality during all the calculations. In contrast, with the "Complex" method, the imaginary part has been left to freely and "arbitrarily" vary, which may amplify its weight and thus generate bigger errors. Our proposed method is situated between them with the imaginary part more or less confined. On the other hand, for a given acquisition, k-space data can be altered and highly asymmetric, or equivalently the formation of the phase can be very complicated. A number of factors, such as k-space sampling (random, irregular, etc.), noise, cardiac pulsations, respiratory motion, and multi-shot induced phase incoherence, can contribute to the formation of phase. Although the present study was also dealt with phase information, as shown in the above, but this phase stems from k-space undersampling and noise. In the future, it would be interesting to investigate multi-shot DWI reconstruction using explicit phase (by estimating for example low-resolution phase map from the fully sampled k-space data of each shot) or implicit phase (by using a structured low-rank matrix completion scheme [START_REF] Froeling | Diffusion Tensor MRI of the Heart -In Vivo Imaging of Myocardial Fiber Architecture[END_REF]) to recover artifact-free images. Also, it is possible to undersample multi shot acquisitions using compressed sensing, the estimation of phase from the data would however be more complex and effective correction of motion-induced ghosting artifacts would be more difficult.

More specifically for phase problems in cardiac DTI, there are phase changes not only in a given diffusion gradient direction (low variation) but also across diffusion gradient directions (drastic variation). It would then be interesting to study undersampled reconstruction based on phase correction [START_REF] Naumova | Assessment of Heart Microstructure From Mouse to Man[END_REF], phase-constrained [START_REF] Tournier | Diffusion Tensor Imaging and Beyond[END_REF] or phase regularized reconstruction [START_REF] Yang | Feature-based interpolation of diffusion tensor fields and application to human cardiac DT-MRI[END_REF].

Application to in vivo cardiac DTI

The successful use of the proposed sampling-reconstruction method on in vivo cardiac DTI data would be conditioned by other two factors: motion correction and registration. Motion artifact may be due to cardiac and/or respiratory motion or any other phenomena such as arrhythmia. It is reflected by the presence of MRI signal loss. In in vivo DTI acquisitions, due to physical and technical limitations of MRI machines, all the images cannot be acquired at the same time point. Therefore, image registration is mandatory to correct for geometrical inconsistency among different scans. However, for a given in vivo DTI dataset, we are not able to determine the origin of errors in the calculated DTI indices if we do not separately consider sampling-reconstruction, motion and registration. In any case, if the sampling-reconstruction does not work, that will not make sense to investigate motion correction or image registration. However, motion correction and image registration in cardiac DTI still remain very challenging problems. Designing new imaging sequences less sensitive to motion artifacts, such as MUSE [START_REF] Chen N-K, Guidon | A robust multi-shot scan strategy for high-resolution diffusion weighted MRI enabled by multiplexed sensitivity-encoding (MUSE)[END_REF] and 3D-DISPENSE [START_REF] Zhang | Three-dimensional diffusion imaging with spiral encoded navigators from stimulated echoes (3D-DISPENSE)[END_REF] techniques, could be an interesting way to explore. Once the problems are resolved, in vivo data would be rather close to the situation of ex vivo data.

Another particularity of in vivo cardiac DTI is the mixture of noise and artifacts due for example to motions. Noise designates electronics noise and thermal noise from subject while artifacts represent degradations due to motions. Therefore, once appropriate motion correction (and image registration to some extent) is achieved, in vivo data would be rather close to the situation of ex vivo data.

Conclusion

This work has proposed an efficient method for reconstructing DW images in DTI from highly undersampled k-space data using the LLR model and 3D TV constraints. The LLR model exploits the fact that the block matrices constructed from the set of DW images corresponding to different diffusion gradient directions are more strongly rank-deficient than the global matrix formed of entire DW images. The reconstruction using the combination of local low-rank penalty and 3D TV penalties thus enables us to improve reconstruction performance. The results on real human ex vivo cardiac DW images showed that, for a large range of sampling ratios from 10% to 50%, the proposed method provides better reconstruction quality and more accurate DTI indices such as mean diffusivity, fractional anisotropy, helix angle and transverse angle, in comparison with the state-of-the-art CS-based DW image reconstruction methods. In the future work, we will apply the proposed method to in vivo cardiac DTI. To this end, phase correction, motion correction and image registration would have to be performed to obtain correct DTI indices.

  where

  term, X  is the nuclear norm or sum of singular values of the matrix X, 1 TX  is the l1-norm of X with sparsity transform T, and 0   and 0   are the regularization parameters. However, as mentioned before, GLR models involving entire images capture only globally correlated information in the image. We are then led to use the LLR model to account for local image information. As illustrated in figure 1(b), the LLR model-based method includes the following main steps: a) consider the set of DW images corresponding to different diffusion gradient directions as a 3D image volume; b) divide the 3D image volume into overlapping 3D image blocks of size size in the diffusion gradient direction; c) stack each 2D DW image block of size xy nn  as a column vector of a 2D matrix, thus forming a block matrix of size x y d n n n  ( i b matrix in figure 1(b)); d) apply low-rank property (singular values shrinkage operator) to the block matrix; e) reconstruct the DW images X by concatenating all the block matrices.

Fig. 1

 1 Fig.1Illustration of the principle of global low-rank (GLR) and local low-rank (LLR) methods. In the GLR matrix X, each column corresponds to an entire DW image and the number of its columns is equal to the number of diffusion gradient directions L.

  (3), b R is the operator that extracts the th b block,  designates the set of blocks,   3 TV D  is the TV regularization term, which can either be the anisotropic or the isotropic TV norm. In this paper,

  reconstruction problem[START_REF] Basser | a) MR diffusion tensor spectroscopy and imaging[END_REF] is outlined in the following algorithm. INPUT: K : the maximum number of iterations; , : the regularization parameters; ,, x y d n n n : the block sizes;

Fig. 2

 2 Fig. 2 Example of (a) the b 0 image of the 5 th slice, (b) 1D random k-space undersampling mask and (c) 2D variable density random k-space undersampling pattern with a sampling ratio of 15% (i.e. keeping 15% of the full k-space data).



  the calculated quantity and the reference quantity, and N the total number of signals. Then, the mean RMSE (mRMSE) values of FA, MD, TA and HA were calculated to evaluate and compare the reconstruction performance.The observation measurement Y is corrupted by complex Gaussian white noise  with standard deviation n  . The associated input SNR (ISNR)[START_REF] Carrillo | Sparsity Averaging Reweighted Analysis (SARA): a novel algorithm for radio-interferometric imaging[END_REF] is defined as denoting the standard deviation of the reference image.

Figures 3 to 6

 6 Figures 3 to 6 show the T-DWI, FA, MD, TA and HA maps of 5 th slice with the sampling ratio of 25%. In the calculations, the diffusion tensors corresponding to the complete k-space were taken as the references. As observed, the FA, MD, TA and HA maps generated by the proposed method are visually better than those obtained with the other methods.

Fig. 3 Fig. 4

 34 Fig. 3 FA maps of 5 th slice. Top row: FA reconstruction maps. Middle row: FA error maps. Bottom row: the ROIs marked by the red boxes in the error maps. The reference FA is shown in the first column of the top row. Reconstructions

Fig. 5

 5 Fig. 5 TA maps of 5 th slice. Top row: TA reconstruction maps. Middle row: TA error maps. Bottom row: the ROIs marked by the red boxes the in error maps. The reference TA is shown in the first column of the top row. Reconstructions from undersampled k-space (sampling ratio 25%) using (a) zero-filling method (RMSE=15.2867), (b) JS method (RMSE =14.7117), (c) JS+TV3D method (RMSE=13.4796), (d) GLR method (RMSE=13.3053), (e) GLR+TV3D method (RMSE=13.1900), (f) LLR method (RMSE=13.7366) and (g) the proposed method (RMSE=12.6375).

Fig. 6

 6 Fig. 6 HA maps of 5 th slice. Top row: HA reconstruction maps. Middle row: HA error maps. Bottom row: the ROIs marked by the red boxes in the error maps. The reference HA is shown in the first column of the top row.

Figure 7 Fig. 7

 77 Figure 7 compares the reconstruction performance (mRMSE of FA, MD, TA and HA) of different methods as a function of sampling ratios ranging from 10% to 50%. As observed, the proposed method resulted in clearly smaller errors than the other methods for all the quantitative indices.

Fig. 8

 8 Fig. 8 Reconstruction performance of the proposed method with various ISNRs and sampling ratios (Rs) on human heart data. (a) mRMSE of FA. (b) mRMSE of MD. (c) mRMSE of TA. (d) mRMSE of HA.

Fig. 9

 9 Fig. 9 Effect of sampling patterns on (a) mRMSE of FA, (b) mRMSE of MD, (c) mRMSE of TA, and (d) mRMSE of HA.

Fig. 10

 10 Fig. 10 Effect of block sizes on reconstruction quality. (a) mRMSE of FA. (b) mRMSE of MD. (c) mRMSE of TA. (d) mRMSE of HA.

Fig. 11

 11 Fig. 11 Effect of regularization parameters (DW image of 5 th slice, ISNR 20 dB). (a) RMSE of FA. (b) RMSE of MD.

Fig. 12 k

 12 Fig. 12 k-space undersampling patterns and the corresponding images reconstructed using zero-filling method. (a) DW image of 5 th slice in a given diffusion gradient direction; (b) Equispaced k-space undersampling; (c) 1D variable density random k-space undersampling in phase-encoding direction; (d) 2D variable density random undersampling.

  Comparison of reconstructions using or without using phase information for ISNR=0 dB (noise-free). (a) mRMSE of FA, (b) mRMSE of MD, (c) mRMSE of TA, and (d) mRMSE of HA. "Abs" no phase information is used. "Complex": phase information is used. Comparison of reconstructions using or without using phase information for ISNR=20 dB. (a) mRMSE of FA, (b) mRMSE of MD, (c) mRMSE of TA, and (d) mRMSE of HA. "Abs" no phase information is used. "Complex": phase information is used.

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (no. 61701105, 61661010, 61601057), the Natural Science Foundation of Heilongjiang Province of China (no. QC2017066), the Nature Science Foundation of Guizhou province (Qiankehe J No.20152044), the Project funded by China Postdoctoral Science Foundation (no. 2017M610199), and the Program PHC-Cai Yuanpei 2018 (N° 41400TC).

Author contribution statement

Informed consent This manuscript does not contain clinical studies or patient data. The DW data of the human hearts in this study from the website http://cvrgrid.org/data/ex-vivo.

Conflict of interest

The authors declare that they have no competing interests.


Pietro Mesirca

Vadim V Fedorov

Thomas J Hund

Angelo G Torrente

Isabelle Bidaud

Peter J Mohler

PhD Matteo E Mangoni
email: matteo.mangoni@igf.cnrs.fr

Pharmacologic Approach to Sinoatrial Node Dysfunction

Keywords: Sinus Node Dysfunction, SAN, G protein-activated K + channels, Cav1.3, Ankyrin-B, Tertiapine-Q

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

Introduction

The cardiac impulse is generated in the sinus node (SAN) by a highly-integrated mechanism involving ion channels, intracellular Ca 2+ dynamics, membrane receptors and connexins (1; 2). Despite the intrinsic robustness of the pacemaker mechanism, SAN dysfunction (SND) constitutes a relatively common clinical condition, especially among the population over 65 (1/600, (3)). SND generally manifests as an insufficiency of the heart rate to meet the needs of the organism. SND may be differentiated into reversible (acute), or chronic symptomatic forms [START_REF] Kusumoto | ACC/AHA/HRS Guideline on the Evaluation and Management of Patients With Bradycardia and Cardiac Conduction Delay: Executive Summary: A Report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines, and the Heart Rhythm Society[END_REF].

Acute SND is generally handled pharmacologically or by temporary transvenous or transaesophageal pacing (4; 5). In contrast, only a few options are currently available to treat chronic symptomatic SND, and to date permanent electronic pacing (PPM) by an implanted electronic pacemaker remains the primary and definitive therapy (4; 5). In this regard, symptomatic SND and heart block account for about half of the total pacemaker implantations in the U.S [START_REF] Rodriguez | Update on sick sinus syndrome, a cardiac disorder of aging[END_REF] and this is predicted to double over the next half century [START_REF] Jensen | Incidence of and risk factors for sick sinus syndrome in the general population[END_REF]. In addition, clinical studies indicate an increasing necessity for implantation of complex electronic pacemakers (8).

In this review, we will discuss some of the most documented forms of primary and secondary SND, especially in relation to current pharmacologic management. Research over the last 20 years has considerably advanced our knowledge of SND aetiology. Several genes coding for ion channels [START_REF] Schulze-Bahr | Pacemaker channel dysfunction in a patient with sinus node disease[END_REF][START_REF] Milanesi | Familial sinus bradycardia associated with a mutation in the cardiac pacemaker channel[END_REF][START_REF] Milano | HCN4 mutations in multiple families with bradycardia and left ventricular noncompaction cardiomyopathy[END_REF][START_REF] Schweizer | The symptom complex of familial sinus node dysfunction and myocardial noncompaction is associated with mutations in the HCN4 channel[END_REF][START_REF] Schweizer | cAMP sensitivity of HCN pacemaker channels determines basal heart rate but is not critical for autonomic rate control[END_REF][START_REF] Baig | Loss of Ca(v)1.3 (CACNA1D) function in a human channelopathy with bradycardia and congenital deafness[END_REF][START_REF] Liaqat | Identification of CACNA1D variants associated with sinoatrial node dysfunction and deafness in additional Pakistani families reveals a clinical significance[END_REF][START_REF] Kuss | Familial Sinus Node Disease Caused by a Gain of GIRK (G-Protein Activated Inwardly Rectifying K(+) Channel) Channel Function[END_REF][START_REF] Stallmeyer | A Mutation in the G-Protein Gene GNB2 Causes Familial Sinus Node and Atrioventricular Conduction Dysfunction[END_REF][START_REF] Lodder | GNB5 Mutations Cause an Autosomal-Recessive Multisystem Syndrome with Sinus Bradycardia and Cognitive Disability[END_REF][START_REF] Veldkamp | Contribution of sodium channel mutations to bradycardia and sinus node dysfunction in LQT3 families[END_REF][START_REF] Smits | A mutation in the human cardiac sodium channel (E161K) contributes to sick sinus syndrome, conduction disease and Brugada syndrome in two families[END_REF][START_REF] Ackerman | HRS/EHRA expert consensus statement on the state of genetic testing for the channelopathies and cardiomyopathies: this document was developed as a partnership between the Heart Rhythm Society (HRS) and the European Heart Rhythm Association (EHRA)[END_REF], scaffolding proteins [START_REF] Scouarnec | Dysfunction in ankyrin-Bdependent ion channel and transporter targeting causes human sinus node disease[END_REF], cytoskeleton proteins [START_REF] Holm | Several common variants modulate heart rate, PR interval and QRS duration[END_REF], as well as connexins and proteins involved in cardiac development have been linked to previously unexplained forms of primary familial SND [START_REF] Ishikawa | Inherited bradyarrhythmia: A diverse genetic background[END_REF]. Furthermore, development of animal models of primary and secondary SND, as well as ex vivo exploration of SANs from human hearts with history of SND have shed new light in the mechanisms of secondary forms of SND. These approaches have identified a host of novel targets for managing SND, including cardiac G protein-activated IKACh/IAdo (GIRK1/GIRK4) [START_REF] Mesirca | Cardiac arrhythmia induced by genetic silencing of 'funny' (f) channels is rescued by GIRK4 inactivation[END_REF][START_REF] Mesirca | G protein-gated IKACh channels as therapeutic targets for treatment of sick sinus syndrome and heart block[END_REF][START_REF] Lou | Upregulation of adenosine A1 receptors facilitates sinoatrial node dysfunction in chronic canine heart failure by exacerbating nodal conduction abnormalities revealed by novel dual-sided intramural optical mapping[END_REF][START_REF] Long | Chronic heart failure increases negative chronotropic effects of adenosine in canine sinoatrial cells via A1R stimulation and GIRK-mediated IKado[END_REF][START_REF] Li | Redundant and diverse intranodal pacemakers and conduction pathways protect the human sinoatrial node from failure[END_REF] and Ca 2+ -activated small conductance K + (SK) channels [START_REF] Weisbrod | SK4 Ca2+ activated K+ channel is a critical player in cardiac pacemaker derived from human embryonic stem cells[END_REF][START_REF] Haron-Khun | SK4 K(+) channels are therapeutic targets for the treatment of cardiac arrhythmias[END_REF](32). The identification of GIRK channels as potential molecular targets for SND may extend the indication of pharmacologic approaches to chronic forms of SND. More generally, it is possible that innovative molecules targeting specific SND mechanism will help manage chronic SND, which is now handled only by PPM.

Clinical Definition of SAN Dysfunction

The diagnosis of SND is based on the correlation between the patient's symptoms and ECG hallmarks (see also Supplementary Appendix 1), which provide important criteria for PPM (4; 5; 33). Historically, SND patients have been identified as having one or more of the following ECG findings [START_REF] Ferrer | The sick sinus syndrome in atrial disease[END_REF]: (i) persistent, unexpected sinus bradycardia (Figure 1), (ii) short periods of sinus arrest during which atrial or junctional rhythms replace normal sinus rhythm, (iii) long periods of sinus arrest in the absence of junctional rhythms, resulting in cardiac standstill, and finally (iv) episodes of sinus exit block not related to drug therapy (34; 35). This early definition of SND remains in use in current clinical guidelines (4; 5; 36). Sinus bradycardia is generally defined as a heart rate below 50 bpm [START_REF] Kusumoto | ACC/AHA/HRS Guideline on the Evaluation and Management of Patients With Bradycardia and Cardiac Conduction Delay: Executive Summary: A Report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines, and the Heart Rhythm Society[END_REF]. Sinus pauses or sinus arrest are included in the current definition of SND, particularly when manifest as 'tachycardia-bradycardia syndromes', in which sinus bradycardia, pauses or arrest follow periods of abnormal atrial tachycardia, atrial fibrillation or flutter [START_REF] Page | ACC/AHA/HRS Guideline for the Management of Adult Patients With Supraventricular Tachycardia: A Report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines and the Heart Rhythm Society[END_REF]. In tachycardia-bradycardia syndromes, SND can manifest as poor or sluggish return of sinus rhythm following cardioversion [START_REF] Lown | Electrical reversion of cardiac arrhythmias[END_REF] (Supplementary Figure 1). Another hallmark of SND is chronotropic incompetence, defined as the inability of heart rate to attain 80% of the expected heart rate during exercise [START_REF] Brubaker | Chronotropic incompetence: causes, consequences, and management[END_REF]. Symptomatic SND carries invalidating symptoms that can impact quality of life (36). One of the most common symptoms of SND is syncope, which is present in about half of SND patients (5; 40). While asymptomatic bradycardia is not associated with adverse outcomes, patients with untreated symptomatic SND have high risk of deterioration to cardiovascular events including atrial fibrillation [START_REF] John | Sinus Node and Atrial Arrhythmias[END_REF], heart failure [START_REF] Alonso | Association of sick sinus syndrome with incident cardiovascular disease and mortality: the Atherosclerosis Risk in Communities study and Cardiovascular Health Study[END_REF] and systemic thromboembolism (5; 40). Age-dependent SND and chronotropic incompetence are associated with an increased risk of cardiovascular death and overall mortality (4).

SAN Pacemaking: general overview

The SAN is a highly-complex, heterogeneous tissue [START_REF] Boyett | The sinoatrial node, a heterogeneous pacemaker structure[END_REF]. Surprisingly, pacemaker cells do not constitute the predominant cell type in the SAN. Early studies of SAN tissue indicated that atrial myocytes [START_REF] Verheijck | Distribution of atrial and nodal cells within the rabbit sinoatrial node: models of sinoatrial transition[END_REF] and fibroblasts [START_REF] De Maziere | Spatial and functional relationship between myocytes and fibroblasts in the rabbit sinoatrial node[END_REF] are important constituents of SAN structure and integrative properties. More recently, RNA sequencing indicates that the SAN is composed of atrial myocytes, adipocytes, epithelial cells, fibroblasts, vascular endothelial cells, macrophages and neurons [START_REF] Linscheid | Quantitative proteomics and single-nucleus transcriptomics of the sinus node elucidates the foundation of cardiac pacemaking[END_REF]. In addition to heterogeneous cellular composition, pacemaker cells within the SAN are poorly-coupled electrically [START_REF] Ten Velde | Spatial distribution of connexin43, the major cardiac gap junction protein, visualizes the cellular network for impulse propagation from sinoatrial node to atrium[END_REF]. This low inter-cellular conductance is due to high expression of Cx45 and low or absent expression of Cx43 in pacemaker cells [START_REF] Ten Velde | Spatial distribution of connexin43, the major cardiac gap junction protein, visualizes the cellular network for impulse propagation from sinoatrial node to atrium[END_REF][START_REF] Verheijck | Electrophysiological features of the mouse sinoatrial node in relation to connexin distribution[END_REF](48). Finally, the SAN region includes specific non-conductive structures and redundant impulse propagation pathways (29; 49) that help ensure proper intra-sinus and sinus-to-atria conduction (50; 51).

Normal pacemaking depends on a unique action potential (AP) profile of SAN pacemaker cells. Importantly, the SAN AP undergoes a spontaneous diastolic depolarization phase driving the membrane voltage from the end of the repolarization to the threshold of the following action potential (Figure 2). Catecholamines positively regulate the slope of the diastolic depolarization via activation of ß-adrenergic receptors (ßARs). The adrenergic activation stimulates the synthesis of cAMP, that positively regulates the activity of several ion channels of the plasma membrane, and the intracellular ryanodine receptors/Ca 2+ -release channels (RyR2) embedded in the sarcoplasmic reticulum (SR) (2; 52) (Figure 2). In antagonism with ßARs, muscarinic type 2 receptors (M2Rs) and adenosine type 1 (A1Rs) receptors decrease pacemaking by promoting down-regulation of intracellular cAMP and by inducing opening of G protein activated K + channels (GIRK1/GIRK4) underlying the IKACh / IKAdo current [START_REF] Wickman | Abnormal heart rate regulation in GIRK4 knockout mice[END_REF]. Current understanding of the generation of the heartbeat is best summarized by the "coupled-clock" model of pacemaking [START_REF] Lakatta | A coupled SYSTEM of intracellular Ca2+ clocks and surface membrane voltage clocks controls the timekeeping mechanism of the heart's pacemaker[END_REF], stating that generation of diastolic depolarization is the result of a functional interplay between activity of ion channels at the plasma membrane and local diastolic RyR2-dependent Ca 2+ release, which is coupled to the diastolic depolarization via activation of the Na + /Ca 2+ exchanger (NCX1) (2; 52; 54). Different ion channels of the plasma membrane contribute to the generation and the regulation of the diastolic depolarization and will be discussed here briefly.

The hyperpolarization-activated "funny" current If, is activated at the end of the repolarization phase of the action potential and supplies inward current throughout the range of the diastolic depolarization (55). Catecholamines shift If activation curve to more positive voltages, while acetylcholine induces a negative shift. These opposing effects are explained by the direct sensitivity of f-channels to cAMP (56), which increases the probability of channel opening at a given voltage [START_REF] Difrancesco | Modulation of single hyperpolarization-activated channels (i(f)) by cAMP in the rabbit sino-atrial node[END_REF]. F-channels are encoded by the hyperpolarization activated cyclic nucleotide gated channel (HCN) family, which comprises four distinct isoforms HCN1-HCN4. However, in the SAN, the predominant isoform is HCN4, accounting for 80% of the total HCN mRNAs [START_REF] Shi | Distribution and prevalence of hyperpolarization-activated cation channel (HCN) mRNA expression in cardiac tissues[END_REF]. Moreover, HCN1 protein is almost exclusively expressed in the human SAN rather than in atrial myocardium (59). Both T-and L-type Ca 2+ channels are expressed in SAN pacemaker cells. Cav3.1 and Cav3.2 mRNAs are expressed in the SAN however, the predominant functional T-type isoform in the adult SAN is Cav3.1 [START_REF] Mangoni | Bradycardia and slowing of the atrioventricular conduction in mice lacking CaV3.1/alpha1G T-type calcium channels[END_REF]. In spite of this low availability, Cav3.1 knockout mice (Cav3.1 -/-) present with moderate SAN rate reduction (-10%) and prolonged atrioventricular (PR) conduction interval [START_REF] Mangoni | Bradycardia and slowing of the atrioventricular conduction in mice lacking CaV3.1/alpha1G T-type calcium channels[END_REF]. SAN pacemaker cells concomitantly express two distinct L-type Ca 2+ channel isoforms, Cav1.3 and Cav1.2 [START_REF] Mangoni | Functional role of L-type Cav1.3 Ca2+ channels in cardiac pacemaker activity[END_REF]. Cav1.3-mediated ICaL is characterized by a more negative threshold for activation than Cav1.2-mediated ICaL (-45 mV for Cav1.3-vs -25 mV for Cav1.2mediated ICaL, respectively) [START_REF] Mangoni | Functional role of L-type Cav1.3 Ca2+ channels in cardiac pacemaker activity[END_REF]. Under basal conditions, Cav1.3 -/-pacemaker cells show erratic generation of automaticity, a lack of the linear phase of the diastolic depolarization [START_REF] Torrente | L-type Cav1.3 channels regulate ryanodine receptor-dependent Ca2+ release during sino-atrial node pacemaker activity[END_REF] and a strong reduction of the total inward diastolic current compared to control littermates (26; 62).

Voltage-gated "neuronal" (n)Nav Na + channels underling the sino-atrial TTX-sensitive Na + current (INaTTX) have been shown to contribute to pacemaking and intra-nodal conduction in the mouse, rabbit and human SAN [START_REF] Maier | An unexpected requirement for brain-type sodium channels for control of heart rate in the mouse sinoatrial node[END_REF][START_REF] Baruscotti | A TTX-sensitive inward sodium current contributes to spontaneous activity in newborn rabbit sino-atrial node cells[END_REF](65)[START_REF] Li | Impaired neuronal sodium channels cause intranodal conduction failure and reentrant arrhythmias in human sinoatrial node[END_REF]. Several nNav1 isoforms have been proposed to contribute to sino-atrial INaTTX.. While nNav1.1 and nNav1.3 have been proposed to contribute to INaTTX in mouse and rabbit [START_REF] Maier | An unexpected requirement for brain-type sodium channels for control of heart rate in the mouse sinoatrial node[END_REF], nNav1.6 appears to play a dominant role in human intra-nodal conduction and SND [START_REF] Li | Impaired neuronal sodium channels cause intranodal conduction failure and reentrant arrhythmias in human sinoatrial node[END_REF]. The "cardiac" (c)Nav1.5 isoform underlies the TTX-resistant INa. in the mouse SAN, but its contribution to excitability may be limited to intra-nodal or nodal-atrial impulse conduction. Consistent with this hypothesis, mice haplo-insufficient for Nav1.5 present with atrio-ventricular and intra-ventricular conduction defects, rather than with SND.

Ion channels of the transient receptor potential channels family (TRP) contribute to SAN activity [START_REF] Demion | TRPM4, a Ca(2+)-activated nonselective cation channel in mouse sino-atrial node cells[END_REF][START_REF] Sah | Ion channel-kinase TRPM7 is required for maintaining cardiac automaticity[END_REF][START_REF] Ju | Store-operated Ca2+ influx and expression of TRPC genes in mouse sinoatrial node[END_REF]. TRPC channels contribute to store-operated Ca 2+ entry in pacemaker cells [START_REF] Ju | Store-operated Ca2+ influx and expression of TRPC genes in mouse sinoatrial node[END_REF]. TRPM7 channels contribute to pacemaking by regulating HCN4 channels in the sinus and atrioventricular node [START_REF] Sah | Timing of myocardial trpm7 deletion during cardiogenesis variably disrupts adult ventricular function, conduction, and repolarization[END_REF]. TRPM4 channels contribute to the basal beating rate of SAN pacemaker cells [START_REF] Demion | TRPM4, a Ca(2+)-activated nonselective cation channel in mouse sino-atrial node cells[END_REF].

More recently, members of Ca 2+ activated K + channel family (KCa) have been linked to pacemaking in mouse and rabbit SAN. KCa have been subdivided into Big [START_REF] Lai | BK channels regulate sinoatrial node firing rate and cardiac pacing in vivo[END_REF], Intermediate [START_REF] Haron-Khun | SK4 K(+) channels are therapeutic targets for the treatment of cardiac arrhythmias[END_REF] and Small (32; 72) conductance K + channels. These channels have differential sensitivity to Ca 2+ . Big KCa (BK) are primarily voltage-dependent with positive regulation by Ca 2+ [START_REF] Gueguinou | KCa and Ca(2+) channels: the complex thought[END_REF]. In contrast, Intermediate and Small KCa (IK and SK, respectively) are voltage-independent and highly sensitive to Ca 2+ [START_REF] Haron-Khun | SK4 K(+) channels are therapeutic targets for the treatment of cardiac arrhythmias[END_REF]. Such sensitivity to Ca 2+ is mediated by the association with calmodulin (CaM) [START_REF] Gueguinou | KCa and Ca(2+) channels: the complex thought[END_REF] and at least for SK channels coupling with L-type Ca 2+ channels has been demonstrated (74; 75). SK isoforms have been identified with different sensitivity to the specific inhibitor apamin (SK1, SK2 and SK3) [START_REF] Gueguinou | KCa and Ca(2+) channels: the complex thought[END_REF]. All three SK isoforms are expressed in the SAN (32).

Familial Primary SAN Disease and Associated Conduction Defects

While SAN disease and SND are often associated with aging or with different cardiovascular pathologies such as heart failure (76; 77), work over the past two decades has identified familial forms of SND (24; 78). In fact, congenital forms of SAN disease have been instrumental in providing molecular insights into the critical and non-redundant molecular pathways underlying SAN automaticity and signaling. Multiple ion channels and ion channel subunits are now associated with SAN disease.

HCN4 gene (HCN4) variants are linked with human asymptomatic bradycardia or SAN disease [START_REF] Schulze-Bahr | Pacemaker channel dysfunction in a patient with sinus node disease[END_REF][START_REF] Milanesi | Familial sinus bradycardia associated with a mutation in the cardiac pacemaker channel[END_REF][START_REF] Milano | HCN4 mutations in multiple families with bradycardia and left ventricular noncompaction cardiomyopathy[END_REF][START_REF] Schweizer | The symptom complex of familial sinus node dysfunction and myocardial noncompaction is associated with mutations in the HCN4 channel[END_REF]. Mechanistically, variants have been associated with altered channel membrane targeting, aberrant ion channel activation [START_REF] Milanesi | Familial sinus bradycardia associated with a mutation in the cardiac pacemaker channel[END_REF] or conductance [START_REF] Schweizer | The symptom complex of familial sinus node dysfunction and myocardial noncompaction is associated with mutations in the HCN4 channel[END_REF], as well as dysfunction in channel regulation by cyclic nucleotides (9; 13). Of note, human HCN4 variants are linked with other forms of cardiovascular disease beyond the SAN demonstrating the key role of this ion channel [START_REF] Milano | HCN4 mutations in multiple families with bradycardia and left ventricular noncompaction cardiomyopathy[END_REF]. Beyond HCN4, human variants in SCN5A are linked with SND [START_REF] Benson | Congenital sick sinus syndrome caused by recessive mutations in the cardiac sodium channel gene (SCN5A)[END_REF]. Loss-offunction of the SCN5A gene encoding for Nav1.5 accounts for 5% of total incidence of primary conduction system dysfunction including SND in humans (21; 80). SCN5A variants are linked with familial SND, bradycardia, conduction disorders, as well as atrioventricular block (24; 78). However, similar to variants in other key cardiac ion channels, SCN5A variants are linked with other forms of atrial and ventricular arrhythmia.

While not as robustly expressed in the working myocardium as Cav1.2, Cav1.3 channels (CACNA1D) are highly expressed in the SAN (61; 81-83) (see also preceding section). While rare, human CACNA1D variants that alter channel activity are linked with human SND (14; 15). Cav1.3 channels have been linked also to neonatal complete heart block related to lupus [START_REF] Boutjdir | Molecular and ionic basis of congenital complete heart block[END_REF]. Mechanistically, heart block has been explained by the presence of maternal auto-antibodies against Cav1.3 channels (85; 86). In addition to Cav1.3, T-type Cav3.1 channels (encoded by CACNA1G) have also been linked with human bradycardia and heart block related to neonatal lupus (84; 87). TRPM4 (encoded by TRPM4), also called transient receptor potential cation channel subfamily M member 4, is a nonselective calcium-regulated channel expressed in the SAN and atria. TRPM4 variants have been widely linked with a number of human cardiac phenotypes including sinus bradycardia likely through modulation of the SAN cell membrane potential (88; 89).

Alterations in a number of SAN and atrial accessory and calcium regulatory proteins have been associated with human SND. Ankyrin-B, encoded by ANK2, is a cytoskeletal adaptor protein that associates with a host of cardiac ion channels, transporters, signaling molecules, and structural proteins. Consistent with animal models lacking ankyrin-B, humans harboring specific variants in ANK2 may display bradycardia and conduction defects [START_REF] Scouarnec | Dysfunction in ankyrin-Bdependent ion channel and transporter targeting causes human sinus node disease[END_REF]. Mechanistically, ankyrin-B dysfunction alters multiple critical SAN proteins, including Cav1.3 and NCX1, resulting in aberrant diastolic depolarization. It is likely that specific genetic and environmental factors influence SND penetrance and severity in the human population based on the degree of ankyrin-B loss-of-function and potential secondary variants or environmental factors. Similar to ankyrin-B, cardiac caveolin-3 (CAV3) variants, while linked with ventricular arrhythmia, have also shown to be associated with bradycardia [START_REF] Vatta | Mutant caveolin-3 induces persistent late sodium current and is associated with long-QT syndrome[END_REF]. Mechanistically, caveolin-3 variants may impact multiple ionic currents to influence SAN node automaticity.

More recently, an exciting set of papers have linked human variants in proteins that regulate heterotrimeric G proteins to SND. To date, both GNB5 and GBN2 variants are linked with sinus bradycardia/SND (17; 18). Similar to other genes outlined in this review, individuals harboring variants may display additional non-cardiac phenotypes including cognitive disorders. Mechanistically, these variants may impact the activity of IKACh, inducing current gain-of-function and consequent sinus bradycardia and atrioventricular block. Consistent with this hypothesis, mutation in KCNJ3 and KCNJ5 inducing gain-of-function of GIRK1 and GIRK4 were shown to be linked with familial SAN disease (KCNJ3 encodes GIRK1; KCNJ5 encodes GIRK4) (16; 91).

Dysfunction in cardiac calcium regulatory proteins are linked with familial SND. Calsequestrin 2 (CASQ2) is a calcium-binding protein that also serves a critical role in regulating local calcium release and automaticity. The cardiac ryanodine receptor (RYR2) is a central regulatory node responsible for excitation-contraction coupling. Variants in either RYR2 or CASQ2 are associated with bradycardia and potentially fatal arrhythmias in response to catecholamines [START_REF] Bhuiyan | Expanding spectrum of human RYR2-related disease: new electrocardiographic, structural, and genetic features[END_REF][START_REF] Postma | Absence of calsequestrin 2 causes severe forms of catecholaminergic polymorphic ventricular tachycardia[END_REF][START_REF] Postma | Catecholaminergic polymorphic ventricular tachycardia: RYR2 mutations, bradycardia, and follow up of the patients[END_REF]. In particular, catecholaminergic polymorphic ventricular tachycardia (CPVT) is a life threatening familial ventricular arrhythmia associated with mutations in CASQ2 or RYR2 [START_REF] Bezzina | Genetics of sudden cardiac death[END_REF]. RYR2-associated CPVT is characterized by increased Ca 2+ release from the SR at rest and under adrenergic activation [START_REF] Bezzina | Genetics of sudden cardiac death[END_REF]. However, some CPVT patients carrying mutations in RYR2 present also with moderate sinus bradycardia (96; 97). Bradycardia has been explained by tonic Ca 2+ -dependent inactivation of ICaL and reduction of basal SR Ca 2+ load in SAN pacemaker cells (96; 97).

Additional forms of inherited SND involve a host of cardiac proteins with a range of functions in the myocyte. For example, human variants in MYH6 that encodes cardiac muscle myosin are linked with SND (as well as other non-SAN electrical and structural phenotypes) [START_REF] Holm | A rare variant in MYH6 is associated with high risk of sick sinus syndrome[END_REF]. Like myosin, lamins A and C have multiple roles for cardiac function. Encoded by LMNA, lamin A variants are associated with sinus bradycardia and conduction system disorders [START_REF] Van Berlo | Metaanalysis of clinical characteristics of 299 carriers of LMNA gene mutations: do lamin A/C mutations portend a high risk of sudden death?[END_REF]. Finally, variants in a number of other genes including SHOX2 (100), a transcription factor involved in differentiation of the SAN, have been linked with cardiac SAN and/or atrioventricular block phenotypes.

It is important to note that like other forms of familial human disease, penetrance and disease severity will depend on both secondary genetic, environment, and social factors. Thus, caution should always be utilized when interpreting genetic information from individual variant carriers.

Genetic mouse models of primary SND

A wide variety of genetically modified mouse models have been generated to study SAN disease. Among the first mouse models of SND were those involving knockout of ion channels important for SAN membrane excitability. Early studies found that Cav1.3 -/-mice showed congenital deafness, bradycardia and irregular heart rate (101). Further work has shown that Cav1.3 - /-mice constitute a model of the SAN Dysfunction and Deafness (SANDD) syndrome, which is characterized by sinus bradycardia and atrioventricular conduction dysfunction [START_REF] Baig | Loss of Ca(v)1.3 (CACNA1D) function in a human channelopathy with bradycardia and congenital deafness[END_REF]. Indeed, Cav1.3 -/-mice have pronounced sinus bradycardia, associated with sinus pauses, atrial fibrillation and flutter, and 2 nd -degree atrioventricular block (26; 61; 102). Global knockout of Hcn4 prevents proper development of the SAN and conduction system resulting in embryonic lethality (103). Inducible Hcn4 knockout mice have also been generated and found to have either mild SND with sinus pauses (104) or severe bradycardia and conduction system defects incompatible with life (105). Knockout of Hcn1 induces bradycardia and SND in the mouse (106). Mice carrying genetically silenced If conductance show sinus bradycardia and SND associated with 2 nd -degree atrioventricular block and ventricular arrhythmia [START_REF] Mesirca | Cardiac arrhythmia induced by genetic silencing of 'funny' (f) channels is rescued by GIRK4 inactivation[END_REF]. On the other hand, mice lacking cAMPdependent regulation of HCN4 show moderate sinus bradycardia, consistently to what observed in individuals carrying cAMP regulation defective HCN4 (9; 13).

Consistent with the clinical findings, mice heterozygous for Nav1.5 display bradycardia, sinus exit block, and reduced excitability of pacemaker cells (107). Proteins important for intracellular ion homeostasis have also been explored using genetic mouse models. Atrial-specific knockout of the NCX1 (sarcolipin-Cre crossbred with NCX1 floxed mouse) display sinus arrest, burst pacemaking and junctional escape rhythm (108). In a similar vein, knockout of the SR Ca 2+ buffer calsequestrin disrupted SAN Ca 2+ handling leading to irregular pacemaking and SND, consistent with observations in patients (109).

There is a growing number of mouse models with SND and defects in unconventional ion channels and accessory proteins not typically invoked when discussing SAN pacemaking. For example, the background K + channel TREK-1 has recently emerged as a novel determinant of SAN excitability and pacemaking. Specifically, mice with cardiac specific ablation of TREK-1 show bradycardia with frequent sinus pause (110). At the cell level, TREK-1-deficient SAN pacemaker cells show a depolarized maximum diastolic potential and altered firing rate. Similarly, several TREK-1 interacting partners have been linked to SND in mice, including the cytoskeletal protein βIV-spectrin (111) and members of the Popeye-domain containing (POPDC) family (112). Mouse models of TRPM4 related SND have been generated. Although the TRPM4 knockout (TRPM4 -/-) mouse shows no difference in heart rhythm compared to wild-type counterparts, pharmacological inhibition of TRPM4 slows spontaneous beating in wild-type but not TRPM4 -/-atria (113). Furthermore, TRPM4 mice show more frequent episodes of sinus pauses and prominent conduction block compared to wild-type counterparts (114). TRPM7 is a divalent channel-kinase abundantly expressed in mouse and human heart. Global as well as sinus/atrioventricular noderestricted knockout of TRPM7 slows the diastolic depolarization in pacemaker cells and induces bouts of sinus pause and conduction block [START_REF] Sah | Timing of myocardial trpm7 deletion during cardiogenesis variably disrupts adult ventricular function, conduction, and repolarization[END_REF]. As discussed above, Ankyrin-B is an adapter protein important for proper membrane localization of multiple ion channels and transporters important for normal SAN excitability and pacemaking. Human variants in ANK2 have been linked to a complex arrhythmia syndrome including severe SND requiring pacemaker implantation [START_REF] Scouarnec | Dysfunction in ankyrin-Bdependent ion channel and transporter targeting causes human sinus node disease[END_REF]. Consistent with the human phenotype, mice heterozygous for ankyrin-B display severe bradycardia and enhanced resting heart rate variability compared to wild-type littermates [START_REF] Scouarnec | Dysfunction in ankyrin-Bdependent ion channel and transporter targeting causes human sinus node disease[END_REF].

Mouse models have been instrumental in studying the link between dysregulation of gene expression and SND. Notably, mice deficient for the transcription factor Tbx3 show defects in development of the SAN and of the conduction system. They show also SND characterized by bradycardia and sinus pause presenting in the embryonic stage (115). The cardiac homeobox transcription factor Nkx2-5 has been studied using an atrial-specific knockout model, which shows hyperplasia of the working myocardium and conduction system, resulting in a broad spectrum of arrhythmias including bradycardia and conduction block and perinatal lethality (116). Mechanistically, Nkx2-5 deficiency was shown to activate Notch signaling and enhance myocyte proliferation early in development. Interestingly, Notch signaling is also activated with injury and a genetic mouse model has been used to study effects of transient Notch activation in the atria with observations of reduced SCN5A expression and structural remodeling of the SAN, resulting in sinus bradycardia and sinus pause (117). Genetic mouse models have also elucidated a role for signaling through the multifunctional Ca 2+ /calmodulin-dependent kinase II in SND in the setting of neurohumoral dysregulation. Specifically, transgenic mice overexpressing a CaMKII inhibitory peptide (AC3-I) were found to be resistant to development of fibrosis and sinus pause following chronic angiotensin II infusion (118). As new experimental models have been developed and applied to study SAN function and disease, so too have a host of computational models of pacemaker activity (See Supplementary Appendix 2). These models will prove important for understanding SND as the discovery of new mechanisms progresses.

Secondary forms of SND in humans and animal models

Secondary forms of SND account for the majority of patients. Indeed, the incidence of SND correlates with age, co-morbidities such as hypertension, diabetes, presence of cardiovascular disease and elevated plasma concentrations of cystatin-c and natriuretic peptide [START_REF] Jensen | Incidence of and risk factors for sick sinus syndrome in the general population[END_REF]. However, current guidelines generally make distinction between secondary forms of SND associated with systemic disease, cardiovascular disease and drug intoxication [START_REF] Kusumoto | ACC/AHA/HRS Guideline on the Evaluation and Management of Patients With Bradycardia and Cardiac Conduction Delay: Executive Summary: A Report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines, and the Heart Rhythm Society[END_REF]. In relation to systemic conditions, SND can be a secondary manifestation of endocrine disease such as hypothyroidism and diabetes, inflammatory or rheumatologic disorders, plasma ionic imbalance and infectious disorders (4; 76).

Abnormal input of the autonomic nervous system is a potential cause underlying SND. In some patients, intrinsic SND can be worsened by autonomic nervous system imbalance (119). In addition, increased vagal input (hypervagotonia) has been proposed to constitute the direct cause of SND manifestations (119). Clinical studies have established a correlation between endurance athletic training and an increased risk of bradyarrhythmia, atrioventricular block (120) and atrial fibrillation (121), requiring PPM (122). Both hypervagotonia and intrinsic remodelling of SAN ion channels expression have been proposed as mechanisms of SND in endurance athletes. If current and HCN4 are downregulated in animal models of athletic training (123; 124). In addition, the heart rate of endurance athletes shows reduced sensitivity to the If blocker ivabradine, suggesting reduced HCN expression (123). It is thus possible that both changes in the sympathovagal balance and intrinsic remodeling of ion channels in SAN pacemaker cells contribute to bradyarrhythmia induced by athletic training.

Often SND secondary to cardiovascular disease is associated with atrial tachyarrhythmia and atrial fibrillation. In early studies, SND was present in 5% of patients affected by atrial fibrillation for less than one year. However, SND incidence increased up to 45% in patients suffering from atrial fibrillation for 10 years or more [START_REF] Lown | Electrical reversion of cardiac arrhythmias[END_REF]. Interestingly, in a canine model of atrial fibrillation induced by atrial tachypacing, SND was explained by a reduction in the expression of If -channels (125). This mechanism can account for SND associated with chronic or persistent atrial fibrillation. However, since a significant number of patients present with progressively worsening SND, in which association with atrial fibrillation and conduction dysfunction constitute late comorbidities, it is an attractive hypothesis that early pharmacologic handling of SND may prevent associated arrhythmias. Ischemic disease can also lead to SND. Typical examples of ischemic conditions favoring SND are acute stenosis or thrombosis of the SAN artery (126) and myocardial infarction (127). As discussed above, heart failure is a major provider of secondary SND. Several mechanistic aspects of how myocardial heart failure leads to SND are still to be identified. However, in rabbit (128), canine (129) and mouse (130) models of heart failure, reduction of pacemaker activity has been attributed to down-regulation of If current and its predominant SAN isoform HCN4, with consequent SND.

Myocardial infarction can often degenerate into heart failure and consequently, bring secondary SND forms. A study combining myocardial infarction with diabetic condition showed an increase in oxidized CaMKII, apoptosis of pacemaker cells, SND and mortality in wild-type mice. These effects were prevented in knockin mice expressing oxidation-resistant CaMKII, in which paired methionines in the CaMKII regulatory domain mutated to valines (131). Oxydation of CaMKII could thus constitute an important mechanism in SND secondary to myocardial infarction and neurohumoral dysregulation potentially leading to heart failure (118).

To date, several mechanisms have been proposed to account for age-related SND. The reader can find a detailed discussion about age related SND in a recent review by Peters et al. (132). Interestingly, similar to other secondary forms of SND, decline of pacemaker activity with ageing is attributed to intrinsic remodeling of the SAN structure and expression of ion channels involved in automaticity. Decrease in the intrinsic electrical coupling due to progressive tissue fibrosis has been proposed as a primary factor in age-related SND (see Csepe et al. for review (133)). However, some individuals having high degree of SAN fibrosis can be under normal sinus rhythm (134). In addition, recent work demonstrated slowed intrinsic pacemaker activity and reduced densities in If, ICaL and ICaT in SAN pacemaker cells of bradycardic aged mice (135). It is thus possible that both structural and ionic factors contribute to age-related SND in a patient's dependent way.

Pharmacological approaches to SND in the current clinical practice

There is a wide panel of potentially usable drugs for acute bradycardia and SND however, the most widely used are catecholaminergic agonists like isoproterenol, atropine, aminophylline and theophylline. Isoproterenol is a β-selective agonist devoid of vasoconstrictional effects. Isoproterenol has shown some positive effects in ameliorating heart rate in patients with bradycardia. However, because isoproterenol administration can induce also supraventricular tachycardia (136), its use is recommended only for intra-hospital management of acute SND or electrophysiological evaluation of SND (4). Since β-adrenergic activation augments the myocardial oxygen demand accompanied by coronary vasoconstriction, its use is not indicated in SND associated with cardiac ischemic disease (4). Other catecholaminergic agonists such as epinephrine or dopamine present more complex effects because of their mixed αand βreceptor activation (137). Use of catecholamines is thus indicated only under intra-hospital and haemodynamic monitoring conditions (4). Atropine is a well-known inhibitor of muscarinic receptors. Clinical studies have showed heart rate improvement in patients with acute bradycardia and SND, including secondary to myocardial infarction (138; 139). Atropine is also used for diagnostic evaluation of SND (140; 141). However, some adverse effects have been reported with atropine, including tachycardia and psychotic states (138; 141). Theophylline and aminophylline belong to the pharmaceutical class of methylxanthines. Theophylline in particular, is probably the most widely used drug to handle SND under out of hospital settings. The beneficial effect of methylxanthines in improving heart rate is attributed to their blocking action on adenosine receptors (142), which could make these drugs suitable in handling bradycardia in post-transplantation hearts (143; 144) and following spinal cord injury (145). In a limited clinical study, theophylline has also showed improvement of heart rate, without significant adverse effects, which prevented PPM (146).

Drug intoxication constitutes an additional challenge for pharmacologic handling of bradycardia attributable to SND (4). Frontline treatment of SND following intoxication with βblockers, Ca 2+ channels blockers and digitalis (digoxin) exist. Intoxication with β-blockers can be handled by administration of glucagon, which stimulates hepatic adenylate cyclase leading to increased glycolysis. No systematic clinical studies including cohorts of patients is available to validate the use of glucagon for SND secondary to intoxication with β-blockers (147). However, available data support the concept of antagonizing the effect of β-blockers and Ca 2+ channels blockers using glucagon or insulin to improve heart rate in patients' SND symptoms (148). Finally, intravenous bolus of calcium-gluconate can be used to oppose to the effects of Ca 2+ channels blockers such as verapamil or amlodipine (4; 148). Digoxin intoxication induces complex arrhythmia pattern and bradyarhythmia (149). Digoxin is a poorly dialyzable drug consequently, treatment of SND secondary to glycoside intoxication is applied using specific anti-digoxin antibodies (150). Immunotherapy against digoxin intoxication is effective in improving heart rate, with relative low associated mortality (151).

New pharmacologic targets to SND in animal models

Recently, it has also been possible to test new potential pharmacologic approaches to SND by targeting GIRK channels. Our group has tested this hypothesis by crossing Girk4 -/-mice with mice in which If conductance has been genetically silenced [START_REF] Mesirca | Cardiac arrhythmia induced by genetic silencing of 'funny' (f) channels is rescued by GIRK4 inactivation[END_REF]. Genetic ablation of IKACh effectively rescued SND and atrioventricular dysfunction in these double-mutant mice and prevented also SND-associated ventricular arrhythmia [START_REF] Mesirca | Cardiac arrhythmia induced by genetic silencing of 'funny' (f) channels is rescued by GIRK4 inactivation[END_REF]. Interestingly, isoproterenol was effective in elevating the heart rate of these mice, but failed to correct SND hallmarks such as sinus pauses and atrioventricular dysfunction [START_REF] Mesirca | Cardiac arrhythmia induced by genetic silencing of 'funny' (f) channels is rescued by GIRK4 inactivation[END_REF], suggesting that direct inhibition of IKACh could be a more effective strategy than catecholaminergic stimulation. Furthermore, genetic ablation of IKACh was effective in rescuing SND and atrioventricular dysfunction also in SANDD Cav1.3 -/-mice [START_REF] Mesirca | G protein-gated IKACh channels as therapeutic targets for treatment of sick sinus syndrome and heart block[END_REF]. Rescuing of SND is observed also by direct inhibition of IKACh by tertiapine-Q (Figure 3). This phenomenon of "compensatory" genetic or pharmacologic targeting of IKACh can provide new therapeutic option for SND in the future (26; 152) (see also Supplementary Appendix 3).

While no primary forms of SND linked to KCa channels have been described to date, evidence indicating that the activity of these channels can contribute to arrhythmia, atrioventricular dysfunction and SND exists. Global deletion of SK2 channels in mice is pro-arrhythmic and induces atrioventricular block (74; 153), thus suggesting that the alteration of SK current could lead to SND. Consistent with this hypothesis, it was shown that pharmacological inhibition of SK current recovers tachycardia-bradycardia syndrome in a model of Ca 2+ overload caused by NCX1 deletion (32). Similarly, selective inhibition of the IK isoform SK4 was sufficient to reduce delayed afterdepolarizations and arrhythmic Ca 2+ transients in a CPVT model [START_REF] Haron-Khun | SK4 K(+) channels are therapeutic targets for the treatment of cardiac arrhythmias[END_REF]. Mechanistically, hyperactivation of SK or IK channels in these models could lead to the hyperpolarization of SAN cells, as it has been shown in a model of neurons (154). Consistent with this hypothesis, selective inhibition of SK4 channels rescued SAN arrhythmia and SND, suggesting that the family of KCa channels could be an additional pharmacologic target to treat SND.

Human SAN as model of SND

The human SAN complex is a specialized and heterogeneous intramural 3D structure with multiple intranodal pacemakers and several specialized sinoatrial conduction pathways (SACPs), which are responsible for the transmission of electrical impulses to the right atrium (155; 156). The human SAN pacemaker-conduction complex relies heavily on a sophisticated machinery of multiple molecular pathways that communicate within the 3D structure in order to efficiently maintain physiologically relevant heart rate (Figure 4)(49; 66). However, there is a paucity of studies addressing mechanisms that contribute to automaticity and intranodal conduction directly in the human SAN complex at the molecular, cellular, and tissue levels [START_REF] Li | Redundant and diverse intranodal pacemakers and conduction pathways protect the human sinoatrial node from failure[END_REF].

Disease-induced remodeling of many of the molecular components critical to SAN function can lead to SND in humans (27; 156; 157). However, the majority of these molecular components critical to SAN function have been studied only in animal models, which may have significantly different functional and anatomical features compared to the human SAN, especially when studying aged and/or diseased human SAN with SND. The development of optimal treatments for SND will require in-depth knowledge of the mechanisms involved in robust human SAN rhythm regulation. However, substantial gaps exist in data on SAN functions obtained directly from the human SAN (157; 158), and considerable understanding is inferred from animal models, which may not reproduce the human clinical SND phenomena (156), or from clinical electrogram recordings that are restricted only to the atrial surface (155; 159).

Recent studies of the ex vivo human heart (49; 66; 160) directly address these limitations (Figure 4 and Supplementary Figure 4). To establish the efficient use of explanted human hearts with intact SANs, a rigorous and robust state-of-the-art approach has been developed to investigate e human hearts (with and without arrhythmia including SND) with 3D integrative approaches under ex vivo physiological conditions. Explanted human chronic failing hearts are acquired alive from the OSU cardiac transplantation program. Donor hearts with and without cardiac diseases and comorbidities (e.g. hypertension, diabetes and history of chronic smoke and alcohol consumption/abuse) are collected from LifeLine of Ohio, local organ donation organization (161). These multidisciplinary integrated approaches have identified that SND may be orchestrated by (i) heterogeneous fibrotic structural remodeling in SACPs (49; 133; 160), (ii) compartment specific molecular remodeling in If pacemaker channels (HCN1/HCN2/HCN4)(59) and/or (iii) adenosine A1 receptor and IKAdo (GIRK1/GIRK4) (Supplementary Figure 4) (27; 29; 161) and/or (iv) neuronal (n)Nav (nNav1.6) and cNav1.5 isoforms in human SAN [START_REF] Li | Impaired neuronal sodium channels cause intranodal conduction failure and reentrant arrhythmias in human sinoatrial node[END_REF]. Recent, optical mapping studies revealed that unlike cNav, nNav may predominantly contribute to SAN intranodal conduction, rather than atrial conduction. On the other hand, cNav play important roles in both SAN pacemaking and conduction, especially during adenosine or atrial pacing challenges to prevent intranodal conduction failure. Impairment of Nav can lead to SAN exit block, disorganized intranodal pacemakers, and SAN micro-and macro-reentry. Furthermore, these functional observations are supported by higher expression of nNav (Nav1.1 and Nav1.6) and lower expression of cNav1.5 in human SAN pacemaker cells versus the surrounding atrial myocardium. Importantly, several nNav transcripts were vulnerable to cardiac remodeling associated with heart failure, cardiac hypertrophy and modifying risk factors including history of chronic alcohol consumption, which could promote a substrate for SAN arrhythmias [START_REF] Li | Impaired neuronal sodium channels cause intranodal conduction failure and reentrant arrhythmias in human sinoatrial node[END_REF].

From a clinical perspective, ex-vivo human SAN studies (66) highlight limiting the use of drugs that may block nNav channels especially when vagal tone is high, or in heart failure (162) and atrial fibrillation (163) patients with high plasma levels of adenosine. Furthermore, the ex-vivo human studies also suggest that region-specific SAN disease remodeling, such as fibrotic infiltration (133), significantly contribute to the intrinsic region-specific SAN conduction abnormalities, and arrhythmias (Figure 4). Disease-induced structural remodeling may exacerbate region-specific conduction abnormalities induced by both Nav blockers (66) and adenosine through GIRK channels and predispose to SND (Supplementary Figure 4). As such specific GIRK4 channel blockers (e.g. Tertiapin-Q) can prevent SAN pacemaker arrest and exit block induced by adenosine and parasympathetic hyperactivity and eventually be used in patients with atrial fibrillation and SND [START_REF] Li | Redundant and diverse intranodal pacemakers and conduction pathways protect the human sinoatrial node from failure[END_REF].

In summary, integrative ex-vivo human SAN studies revealed that the availability of multiple redundant structural compartments (intranodal pacemakers and SACPs) and molecular components in the human SAN are important backup mechanisms to robustly protect SAN conduction and pacemaking, and prevent rhythm failure and SND, in the context of multiple disease-induced conduction impairments (29; 133; 160).

Conclusions and perspectives

The development of new pharmacologic and molecular strategies to handle chronic primary and secondary forms of SND has been complicated by a lack of knowledge about the mechanisms underlying this complex pathology. However, new and unexpected mechanisms of SND have been described during the last years using human genetics, animal models of SND, as well as ex vivo SAN from human hearts with history of secondary SND. These investigations have indicated potentially innovative pharmacologic targets to manage SND such as GIRK and SK channels. Furthermore, exploring animal models of SND and human SAN may help redirect the application of antiarrhythmic drugs and create innovative therapies for concomitant control of SND and associated arrhythmias. We expect that additional new SND mechanisms will be unraveled in the coming years with extensive functional genomics exploration of primary familial SND and development of new cellular and animal models of secondary forms of SND. Progress in biophysics and molecular biology 120 [START_REF] Boyett | The sinoatrial node, a heterogeneous pacemaker structure[END_REF][START_REF] Mangoni | Genesis and regulation of the heart automaticity[END_REF][START_REF] Lamas | The mode selection trial (MOST) in sinus node dysfunction: design, rationale, and baseline characteristics of the first 1000 patients[END_REF], 164-178. [START_REF] Csepe | Human sinoatrial node structure: 3D microanatomy of sinoatrial conduction pathways[END_REF]

Figure 1 .

 1 Figure 1. 12 lead ECG showing severe sinus bradycardia and rhythm strip showing sinus pauses as a manifestation of SND. Baseline heart rate was 45 bpm. Courtesy of Dr. Francis Marchlinski, University of Pennsylvania.

Figure 2 .

 2 Figure 2. (A) Schematic of a sinoatrial node (SAN) pacemaker cell showing the main membrane bound receptors and ion channels together with RyR2, the SR calcium pump SERCA and the Na + /Ca 2+ exchanger (NCX1). (B) Simulated transmembrane potential (Vm) during a spontaneous action potential (AP) generated by a computational model of the mouse SAN myocyte (164), with color-code corresponding to the major AP phases [colors also indicate corresponding underlying currents in (A)]: Diastolic depolarization (red), AP upstroke (green), repolarization (blue). See also the extended version of this Figure in the online Appendix (Supplementary Figure 2).

Figure 3 .Figure 4 .

 34 Figure 3. Rescuing of SND and atrioventricular dysfunction by IKACh targeting. Tertiapine-Q rescues SND in Cav1.3 -/-mice. Administration of the GIRK pore blocker tertiapin-Q (tertiapin, central panel) normalizes heart rate (right panel). The central panel shows a close up view of a structural model of tertiapin bound to the GIRK pore. K17 and D164 indicate residues important for peptide activity. Adapted from reference (35), with permission by Whiley and Son.

Acknowledgments

The IGF group is a member of the Laboratory of Excellence "Ion Channel Science and Therapeutics" supported by a grant from ANR (ANR-11-LABX-0015). Research supported by the Fondation pour la Recherche Medicale "Physiopathologie Cardiovasculaire" (DPC20171138970, M.E.M.), by the Agence Nationale de la Recherche (ANR-15-CE14-0004-01, M.E.M.). Work in Ohio State was supported by NIH HL115580 and HL135109 (VVF), HL135096 (TJH), HL134824 (TJH and PJM), HL135754 (PJM) and by funding from the Bob and Corrine Frick Center for Heart Failure and Arrhythmia Research. We thank the Lifeline of Ohio Organ Procurement Organization and the Division of Cardiac Surgery at The OSU Wexner Medical Center for providing the explanted hearts. We also thank the Fondation Leducq (TNE 19CVD03 to M.E.M and P.J.M.) for supporting the "Fighting Against Sinus Node Dysfunction and Associated Arrhythmias" (FANTASY) network.