1 Introduction
Arterial spin labeling (ASL) is a noninvasive MRI technique which uses magnetically labeled blood water as an endogenous tracer for assessing cerebral blood flow (CBF) [5]. Hadamard timeencoded(te)ASL is a timeefficient approach which provides the possibility to combine the superior SNR of ASL to acquire data at different inflow times to obtain dynamic ASLdata [15]. When Hadamard teASL is done with and without flowcrushing, 4D magnetic resonance angiography (MRA) and arterial input function (AIF) measurements can be obtained next to the perfusion scans. While this approach improves quantification and enhances information content, it is a factor two slower, since both crushed and noncrushed data need to be acquired. Accelerating teASL quantification can be done either by acquiring subsampled data in kspace or by reducing the rank of the Hadamard matrix. However, these methods can end up reducing image quality and/or signaltonoise (SNR) ratio.
In this work, we propose an endtoend 3D convolutional neural network (CNN) for the reconstruction of multitimepoint 4D MRA and perfusion scans by using halfsampled crushed as well as halfsampled noncrushed Hadamard teASL scans, to maintain image quality and provide accurate CBF quantification. Recently, CNNs have shown outstanding performance in medical imaging [16, 4, 7]. However, very few CNN reconstruction techniques have been proposed in the context of MRA and perfusion reconstruction. In [6] a Unet shape CNN for boosting SNR and resolution of ASL scans has been proposed. Guo et al. proposed a CNN based method for improving 3D perfusion image quality by the combined use of single and multidelay pseudocontinuous arterial spin labeling (PCASL) and an anatomical scan [8]. In Guo’s study, ground truth perfusion maps were obtained by positron emission tomography scans. In [10]
a temporal CNN approach was proposed for perfusion parameter estimation in stroke. The proposed CNN takes in the signals of interest (i.e., concentrationtime curves and the AIF) to produce estimated perfusion parameter maps including cerebral blood volume (CBV), CBF, timetomaximum, and mean transit time.
In this work, different from the previous works, we employ CNNs in order to accelerate the simultaneous acquisition of 4D MRA and perfusion measurements. One of the challenging issues is the different properties of the outputs of the proposed CNN since MRA is intrinsically sparse and has much more elongated structures than the smooth perfusion map. We tackle this issue by employing different weighting of the loss functions of these two outputtypes and by balancing extracted samples during training. The proposed CNN leverages the idea of dense blocks [11], arranging them in a typical Ushape [12]. Loop connectivity patterns in dense blocks improve the flow of gradients throughout the network and strengthen feature propagation and feature reusability [16]. In this investigation, we compare the performance of several loss functions: mean square error (MSE), VGG16 perceptual loss, structural similarity index (SSIM) and multilevel SSIM (MLSSIM). The main contributions of our work are:

To the best of our knowledge, we are the first to propose acceleration of the reconstruction of 4D MRA and perfusion images using interleaved subsampled crushed and noncrushed Hadamard teASL scans. To allow subsampling, we employed an endtoend 3D CNN for decoding.

We employed a framework for generating training and validation 4D MRA and perfusion scans by generalizing the Buxton kinetic model for a Hadamard teASL signal. Different from [17], we consider the kinetic arterial model to take into account the arterial compartment.

We propose a CNN with a multilevel loss function and compare the proposed method with several loss functions, i.e. MSE, VGG16 perceptual loss, and SSIM.
2 Proposed approach
2.1 Proposed Network
Fig. 1 illustrates the proposed network, which takes subsampled crushed and subsampled noncrushed interleaved ASL data as input and outputs dynamic MRA and perfusion scans. For managing GPU memory, the network was implemented patchbased. The input patches (of size ) are extracted from subsampled Hadamard tecrushed and tenoncrushed scans. The outputs of the network are 14 patches of size containing perfusion and angiography patches, each at seven different timepoints. In this study, we considered a Hadamard matrix of rank 8, so the inputs are 8 patches in total (4 crushed, 4 noncrushed). In each dense block two (
)convBNleaky ReLu and one (
)convBNleaky ReLu, as a bottleneck layer, are stacked. Loop connectivity patterns in dense blocks are employed to improve the flow of gradients [11]. The bottleneck layers are used to increase the number of feature maps in a tractable fashion, which make the training process easier while leading to a more compact model. A downsampling unit is followed by one maxpooling layer with a stride of . In order to solve the wellknown checkerboard issue of the convtranspose layer, for the upsampling layer the feature maps are resized by a constant trilinear resize convolution kernel, similar to [3]. In this work we investigate the impact of several loss functions for the defined problem: MSE, which is the norm, VGG16 perceptual loss [13], SSIM which is composed of luminance, contrast and structural error, and MLSSIM, which is calculated based on weighting the SSIM loss function for different levels of the network, see Fig. 1.2.2 Dataset generation
In pCASL the arterial spins are magnetically labeled with a radiofrequency inversion pulse applied below the imaging slices in the neck vessels. The labeled blood then travels via the arteries towards the brain tissue, where they pass from the capillary compartment into the extravascular compartment. After a certain delay time after labeling which is known as the postlabeling delay (PLD) a socalled labeled image is acquired. A control image is acquired without prior labeling and by subtraction of these two images, the perfusion image can be generated. For the Hadamard tepCASL technique, the labeling module (the typical duration of 34 seconds) is divided into several blocks (subboli) and a Hadamard matrix is used to determine whether a block will be playedout in label or control condition. For each voxel the Hadamard tepCASL signal can contain both perfusion signal as well as label still residing in the arteries, i.e. angiography signals.
Since it is difficult to acquire substantial amounts of real data, we propose to model the input data, allowing to generate a sufficient amount of training data. The ground truth output data is created by decoding fully sampled Hadamard teASL crushed and noncrushed data [15]. For this purpose, we create datasets based upon a tracer kinetic model for the Hadamard timeencoded pCASL signal that describes the signal a function of arterial arrival time (AAT), bolus arrival time (BAT) and CBF. In this study, for calculating the signal, the AAT and BAT information are obtained from in vivo data. The CBF maps are taken from the BrainWeb dataset by assigning CBFvalues to white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF).
Fig. 2 shows the proposed framework for synthetically generating training and validation datasets. For this goal, we leverage the wellknown Buxton kinetic model [1], which has been defined for normal ASL, and defined a tracer delivery function (for tissue voxels and arteries) and a tracer accumulation (perfusion) function for each bolus of Hadamard encoded labeling scheme. The final kinetic model is then generated by performing the convolution of the AIF and the residue function. Equations (1) and (2) define the obtained model for large arteries and tissue signals for a Hadamard scheme of 8 encoding steps respectively. These equations can be generalized for Hadamard matrices of higher rank.
(1) 
(2) 
in which is label duration for the subbolus, is the number of subboluses, is the magnetization of arterial blood, is AAT which represents the arrival time of the labeled blood in the artery, is BAT which represents the arrival time of labeled blood in the tissue, is the arterial blood relaxation time, is CBF (millimeter per gram per second), is static tissue signal, aCBV is arterial cerebral blood volume,
(3) 
(4) 
and
(5) 
is if the bolus in the row is control, and it is if the bolus in the row is label. For voxels containing large arteries, the pCASL signal can be computed by . The calculated tracer kinetic model is a function of AAT, BAT and CBF. In this study, the anatomic structures are obtained from the BrainWeb database [2]. In order to obtain the tracer signal, the AAT and BAT and blood maps are extracted from in vivo data, then registered with a subject from the BrainWeb dataset by Elastix [14]. The ground truth, i.e. 4D MRA and perfusion scans, are obtained by normal Hadamard decoding of the pCASL images [9]. To evaluate the generated data, the signal evolution pattern was validated by the Buxton curve model [1].
In this study, the dataset was generated for a Hadamard8 matrix with seven blocks of respectively 1300, 600, 400, 400, 400, 300 and 300 ms with an additional 265 ms delay before the start of readout. Using the permuted in vivo information (include 6 BAT, 4 AAT) and registering those with the anatomical information from the BrainWeb dataset (consisting of 20 normal subjects and CBF) and calculating the Hadamard tepCASL (equations (1) and (2)), this study contains 1564 distinct simulated datasets each including crushed and noncrushed input data for 8 Hadamardencodings. By decoding each of the generated crushed and noncrushed tepCASL data, the corresponding angiographic and perfusion output data at 7time points, as the ground truth, are obtained. The scans were divided into 1096 subjects for training, 155 for validation and 313 for testing.
3 Experimental Results
We implemented the proposed networks in Google’s Tensorflow. The patch extraction was done parallel and randomly using a multithreaded daemon process on the CPU and then patches were fed to the network on the GPU during the training process. To tackle the sparsity of MRA with respect to the perfusion scans, 75 percent of the patches were extracted from the region containing arteries. The input patches were augmented by white noise extracted from a Gaussian distribution with zero mean and random standard deviation between 0 and 5, lefttoright flipping, and random rotation (up to
).Evaluation of the proposed networks has been performed by calculating SSIM, MSE, signal to noise ratio, and peak signal to noise ratio (pSNR), comparing the ground truth reconstruction using full sampling with that of the neural network using subsampling. Table 1 tabulates a quantitative comparison between the mentioned loss functions. Fig. 3 depicts the boxplots of the metrics on the test set. The network with SSIM loss function with a value of has the highest value for SSIM metric, and the network with MLSSIM loss function with has the second rank for perfusion reconstruction. While the network with MLSSIM loss function with the values of , and for MSE, SNR and pSNR respectively, has a better performance than its competitors. Also, this network with the values of , and for respectively SSIM, MSE and SNR, exceeded the other mentioned networks for angiography reconstruction. Fig. 4 exemplifies the qualification compassion for 4D MRA and perfusion reconstruction between the different CNNs. It takes an average of 205232 ms from the MLSSIM network to reconstruct all perfusion and angiography scans from the interleaved sparselysampled crushed and noncrushed data of size .
Loss function  SSIM  MSE  SNR  pSNR  of param  
MSE  
91.60  0.17  1.15  32.24  169,152  
69.34  2.28  0.09  5.95  
SSIM  
91.59  0.17  1.30  32.19  169,152  
96.34  2.60  5.38  0.09  
PL  
91.66  0.92  1.29  33.15  169,152  
96.15  2.64  0.06  5.33  
MLSSIM  
91.96  0.18  1.33  21.07  181,692  
96.38  2.40  0.14  5.74  
4 Conclusion
We proposed a 3D endtoend fully convolutional CNN for accelerating 4D MRA and perfusion reconstruction from halfsampled crushed and noncrushed pCASL data. We leveraged loop connectivity patterns in the network architecture to improve the flow of information during the gradient updates. For training and validation purposes we developed a data generator framework based on the generalized kinetic model for the pCASL signal. The generated dataset included 1096 scans for training, 155 scans for validation and 313 for testing. The proposed network with MLSSIM loss function achieved a SSIM of , MSE of , SNR of , and pSNR of for perfusion/angiography reconstruction.
In conclusion, the proposed network obtained promising results for the challenging problem of 4D MRA and perfusion reconstruction. The method, therefore, may assist an accelerated MRI scanning workflow. A further step of this study is enriching the training and validation datasets with in vivo data.
Acknowledgements. This work is financed by the Netherlands Organization for Scientific Research (NWO), VICI project 016.160.351.
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