Deformable Slice-to-Volume Registration for Motion Correction in Fetal Body MRI

IEEE TRANSACTIONS ON MEDICAL IMA GING, V OL. XX, NO. XX, XXXX 2020 1 Def or mab le Slice-to-V olume Registration f or Motion Correction of F etal Body and Placenta MRI Alena Uus, T ong Zhang, Laurence H. Jackson, Thomas A. Roberts, Mar y A. Rutherf ord, Joseph V . Hajnal and Maria Deprez Abstract — In in-utero MRI, motion correction f or fetal body and placenta poses a par ticular challenge due to the presence of local non-rigid transformations of or gans caused by bending and stretc hing. The existing slice- to-v olume registration (SVR) reconstruction methods are widely employ ed for motion correction of fetal brain that undergoes only rigid transformation. However , for recon- struction of fetal body and placenta, rigid registration can- not resolve the issue of misregistrations due to deformab le motion, resulting in degradation of features in the recon- structed volume. We propose a Deformable SVR (DSVR), a novel approach for non-rigid motion correction of fetal MRI based on a hierarc hical deformable SVR scheme to allow high resolution reconstruction of the fetal body and placenta. Additionally , a r obust sc heme for structure-based rejection of outliers minimises the impact of registration error s. The impro ved performance of DSVR in comparison to SVR and patch-to-volume registration (PVR) methods is quantitatively demonstrated in simulated experiments and 20 fetal MRI datasets from 28-31 weeks gestational age (GA) range with varying degree of motion corruption. In addition, we present qualitative ev aluation of 100 fetal body cases from 20-34 weeks GA range. Index T erms — MRI, Motion correction, Fetal motion, Slice-to-v olume registration, Deformab le registration. I . I N T R O D U C T I O N O VER the past two decades development of fast acqui- sition sequences along with advanced motion compen- sation techniques [1] has gradually allowed incorporation of MRI into clinical practice for imaging of fetal pathologies [2]. Single shot fast spin echo (ssFSE) sequences allow acquisi- tion of each slice in less than one second, which minimises the Copyright (c) 2020 IEEE. Personal use of this material is per- mitted. Howe ver , per mission to use this material for any other pur- poses must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. The final version of record is av ailable at http://dx.doi.org/10.1109/TMI.2020.2974844. This work was suppor ted by the NIH Human Placenta Project g rant [1U01HD087202-01], the Wellcome EPSRC Centre for Medical Engi- neering at King’ s College London (WT 203148/Z/16/Z), the Wellcome T rust and EPSRC IEH aw ard [102431] for the iFIND project and by the National Institute for Health Research (NIHR) Biomedical Research Centre based at Guy’ s and St Thomas’ NHS F oundation T rust and King’ s College London. All authors are with the School of Imaging Sciences & Biomed- ical Engineering, King’ s College London, King’ s Health P ar tners, St. Thomas’ Hospital, London SE1 7EH, United Kingdom (e-mail: alena.uus@kcl.ac.uk). impact of fetal motion artefacts on image quality . Howe ver , in 3D stacks, inter-slice motion still exists leading to either minor misalignments (Fig. 1.a) or complete loss of volumetric information (Fig. 1.b). Fig. 1. Fetal MRI: e xamples of stacks with minor (a) and sev ere (b) motion corruption acquired dur ing the same f etal exam and under the same orientation at different time points. Slice-to-volume re gistration in combination with super - resolution (SR) reconstruction is considered to be an efficient motion correction approach since it resolves out-of-plane motion [3]–[5]. The fact that the volumetric region of interest (R OI) is o versampled at different stack orientations ensures consistency of reconstructed volumes. Recent validation of SVR for fetal brain reconstruction sho wed strong correlation between 2D and 3D biometry values [6]. Since the SVR is based on rigid registration, its application has primarily focused on the brain as it undergoes only rigid motion. In general, fetal body and placenta are af fected by local non-rigid deformations [7], for example due to bending of fetal abdomen (Fig. 2.a) or maternal breathing, and the use of rigid registration leads to deteriorated reconstruction quality . Slices that are inconsistent with the most prev alent 2 IEEE TRANSACTIONS ON MEDICAL IMA GING, V OL. XX, NO. XX, XXXX 2020 body position are either rejected as outliers [5] or contribute as an error to the reconstructed volume, resulting in blurring of local features (e.g., spine) and loss of texture information (Fig. 2.b). Fig. 2. Example of a sequence of slices (a) acquired during the change of f etal trunk position and the corresponding SVR reconstructed volume (b). Note that bending deforms the shape of the spine and inter nal organs in both in-plane and through-plane directions. A. Related work The original concept of SVR for reconstruction of fetal brain from motion-corrupted MRI stacks was to interleave slice-to-volume registration with scattered data interpolation based on weighed sum of Gaussian kernels [8] or multilevel B- splines [9]. The SVR reconstruction frame work was gradually extended with SR reconstruction [3], [4], edge-preserving regularisation [4], outlier rejection [3], [5], intensity matching [5], total variation regularisation [10], sinc PSF model and GPU-parallelisation [11]. More recent works proposed to employ con volutional neural network (CNN) for fetal brain segmentation from MRI slices [12], [13] and prediction of transformations of slices to canonical atlas space [14], [15]. Though SVR has been developed primarily to reconstruct the fetal brain MRI, it has also been applied to the re- construction of fetal thorax [16], [17] under the assumption of approximately rigid motion, due to the embedding in the rib cage. Gi ven the kno wn cardiac phases of each of the slices, SVR can also be employed for 4D fetal cardiac reconstruction from dynamic MRI [18]. Rigid SVR has also been applied to reconstruct MRI of placenta [19], which undergoes deformation due to the maternal breathing. Here the quality of the reconstructed image relies on the rob ust statistics to exclude the slices which have been deformed compared to the most common shape of the placenta present in the data. In [20], rigid SVR was further extended to patch-to- volume registration (PVR) which addresses the reconstruction of deformable organs by performing motion compensation in piecewise rigid fashion, thus allowing the reconstruction of the entire uterus. W ith respect to application of deformable SVR for motion correction, the existing solutions primarily focus on registra- tion of intra-operati ve slices with a pre-operativ e planning volume [21], [22] or multimodal registration (e.g., histology to MRI) [23], [24]. The majority of monomodal methods are based on rigid SVR for global alignment followed by Free Form Deformation (FFD) registration [25] for correction of non-rigid shape changes. Recently , [26] formalised deformable graph-based SVR approach validated on a 3D heart MRI dataset. Howe ver , the existing implementation is limited to in-plane deformations only . Model-based SVR methods inte- grating biomechanical models for physics-based regularisation were proposed in works of [27], [28]. B. Contr ib utions In this paper we present a novel approach for non-rigid motion correction in 3D volumes based on an extension of the rigid SVR reconstruction method [5] with hierarchical deformable registration scheme and structure-based outlier re- jection. The proposed DSVR method allows for both in-plane and out-of-plane correction of local non-rigid deformations of fetal body and placenta resulting in high quality volumetric reconstruction. The structure-based outlier rejection ensures that the residual registration errors are not propagated to the reconstructed volume. The performance of DSVR is ev aluated in simulated exper- iments, and using 20 fetal MRI datasets from 28-31 weeks GA range with varying degrees of motion corruption, by comparison to the rigid SVR and PVR. Furthermore, we present qualitative ev aluation of DSVR reconstruction quality on 100 iFIND 1 cases from 20-34 weeks GA range. I I . B A C K G R O U N D A typical fetal MRI dataset consists of multiple motion corrupted stacks S = { S l } l =1 ,...,L cov ering a specific R OI and acquired under different orientations. In the context of motion correction, SVR is used for iterativ e recov ery of a high resolution ’motion-free’ isotropic volume X from an array of K low resolution motion-corrupted slices Y = { Y k } k =1 ,...,K . It is formalised as follows [5]: Y ∗ k = M k X, y ∗ j k = s k e − b j k y j k , (1) where k is a slice index and j is a pixel index within each slice. The matrix M k describes spatial relationship between the acquired slices Y k = { y j k } j =1 ,...,N k and the reconstructed volume X = { x i } i =1 ,...,N , where each row { m k ij } i =1 ,...,N represents the acquisition PSF for vox el y j k , transformed according to the estimated motion parameters and sampled on the grid of the high resolution volume X . Intensity corrected slices are denoted by Y ∗ k = { y ∗ j k } j =1 ,...,N k , while B k = { b j k } j =1 ,...,N k and s k are the slice-dependent bias fields and scaling factors, correspondingly . The algorithm proceeds by interleaving slice-to-volume registration and super-resolution reconstructions for a fixed number of iterations ( q = 1 , ..., Q ). At each SVR iteration q , the current estimation of X is registered to slices { Y k } and the transformed PSFs { m k ( q ) ij } q =1 ,...,Q are updated according to the resulting spatial transformations. Next, as initialisa- tion of the SR reconstruction loop, the weighted Gaussian interpolation [8] is performed for estimation of X (0 ,q ) . Then, 1 iFIND Project: http://www .ifindproject.com A UTHOR et al. : DEFORMABLE SLICE-T O-VOLUME REGISTRA TION FOR MO TION CORRECTION OF FET AL BOD Y AND PLACENT A MRI 3 we perform super -resolution reconstruction [3] of the volume X by iterative gradient descent optimisation based on min- imisation of the sum of squared errors P j k e 2 j k + λR ( X ) , where λR ( X ) is an edge preserving regularisation term [5] and e j k are the errors between the original { y ∗ j k } and simulated ¯ Y k = { ¯ y j k } j =1 ,...,N k slices e j k = y ∗ j k − ¯ y j k , ¯ y j k = X i m k ( q ) ij x i (2) Each SR reconstruction iteration ( n = 1 , ..., N ( q ) S R ) includes expectation-maximization (EM) robust statistics scheme for rejection of outliers and estimation of { b j k } and s k x ( n +1 ,q ) i = x ( n,q ) i + α X kj p j k p slice k m k ( q ) ij e j k + αλ ∂ ∂ x i R ( X ) , (3) where p j k and p slice k are posterior probabilities of a v oxel or a slice not being an outlier . I I I . M E T H O D A. Overview of the algor ithm The proposed DSVR method is an extension of the rigid SVR SR reconstruction framew ork [5] described in Sec. II and it is summarised in Fig. 3 with the novel modules highlighted by red outline. Follo wing global rigid and FFD registration of all stacks, the template stack is used for initialisation of the registration target for the DSVR loop. At each DSVR iteration (Sec. III- C), the current estimation of X ( n,q ) is registered to each of the slices { Y k } . This is followed by the W eighted Gaussian reconstruction and iterati ve SR reconstruction (Sec. III-B) with additional structure-based outlier rejection (Sec. III-D) step. The pipeline is performed for a predefined number of DSVR ( Q ) and SR ( N S R ) iterations. The rest of this section describes the nov el DSVR modules in detail. B. Incor porating def or mations into SR reconstruction In super-resolution SVR (Sec. II), the forward problem is modelled by applying the transformed PSFs { m k ij } i =1 ,...,N to high-resolution volume X to simulate (intensity-corrected) vox el ¯ y j k of the acquired slice k (2). The underlying PSF in the space of acquired data is a continuous function f j k ( u ) = f ( u − u j k ) where u is a location in the space of the acquired stack, u j k is the position of the voxel y j k and f is the shape of the acquisition PSF , which we model by a 3D Gaussian with zero mean and principal axis aligned with the axis of coordinate system of the acquired image. The transformation T k between locations u in space of acquired stack and the anatomical locations v is estimated by registration of the acquired slice Y k and the volume X , defining the transformed PSFs by m k ij = f j k ( T − 1 k ( v i )) , where v i is the location of the vox el x i in the anatomical space. In case of rigid SVR, the transformed PSFs are re-oriented Gaussians. T o correct for deformation of the fetal body and placenta the transformations T k ( u ) need to be deformable. Therefore in DSVR the PSFs are deformed using non-rigid transformations T k ( u ) and their shapes become non-Gaussian. The high resolution volume X Fig. 3. Proposed DSVR reconstruction algor ithm. The nov el elements are highlighted by red outline . is estimated iterati vely using (3) for both rigid and deformable cases. C . Hierarchical motion correction SVR of the fetal brain can be well constrained by acquir- ing sev eral stacks { S l } l =1 ,...,L in different orientations and assuming rigid motion of the region of interest, to recov er the ’true’ shape of the fetal brain. The fetal body and placenta, on the other hand, undergoes continuous deformation in time and DSVR is under-constrained in comparison to SVR. In order to overcome this limitation, a hierarchical scheme for gradual refinement of transformation during slice-to-volume registration is proposed. 1) V olumetric registration : At first, one of the stacks is selected as a template ( S template ) for initialisation of the global registration target. In order to eliminate the impact of global rotations and translations between stacks, the initial step includes 3D-to-3D rigid registration of the input stacks { S l } to a masked R OI in the template stack. The resulting transformations G R l are then used for initialisation of 3D-to- 3D global deformable registration of stacks to S template . The template stack cropped with a bounding box of the mask acts as the preliminary initialisation of the reconstructed volume X init . For the purpose of formalisation of DSVR registra- tion steps, we define a deformable registration operator as 4 IEEE TRANSACTIONS ON MEDICAL IMA GING, V OL. XX, NO. XX, XXXX 2020 D ( I targ et , I source , T init , d ) , where I targ et and I source are the source and target images, d represents the resolution of the de- formable transformation and T init is the input transformation. Then the global deformable stack registration is expressed as: G D l = D ( S l , X init , G R l , d init ) (4) In order to av oid ov er-fitting to the motion corrupted fea- tures of stacks, global transformation with low resolution d init is chosen and all stacks are smoothed using Gaussian blurring. Therefore, the output transformations G D l provide estimation of only large range (global) deformations between the trunk positions in the stacks and the template. The trunk mask is then transformed to all stacks and they are cropped to large bounding box R OIs. 2) Slice-to-volume registration : W e refine the motion param- eters by iterativ ely aligning the reconstructed volume to each individual slice. The v olume is re gistered to the slices (i.e., 3D- to-2D) rather than the slices to the volume to ensure that both in-plane and out-of-plane deformable motion is resolved. The first iteration of DSVR is performed by deformable re gistration of the smoothed template stack X init to each of the slices with low resolution transformations (5). T (0) k = D ( Y k , X init , G D k,l , d (0) ) (5) The B-spline control point spacing d ( q ) is decreased at e very DSVR iteration q , thus refining the resolution of the transfor- mation T ( q ) k . T ( q +1) k = D ( Y k , X ( n,q ) , T ( q ) k , d ( q +1) ) (6) This is coupled with decreasing SR regularisation parameter λ (3) to pre vent overfitting to the residual motion in the early stages and progressiv ely allowing more localised deformations as the features in X ( n,q ) become better defined. Fig. 4 illus- trates an example of the refinement of 3D transformation (in our case implemented by a B-spline control point grid) of T ( q ) k with respect to DSVR iteration q and reconstructed volume X ( n,q ) used as a template. It was identified experimentally that rigid registration should not be used during slice-to- volume registration steps since it disrupts the local deformation fields obtained during hierarchical refinement. The spatial relationship coefficients M ( q ) k are computed during each it- eration q after slice-to-volume registrations were completed, by transforming 3D Gaussian PSFs f j k using T ( q ) k . Fig. 4. An e xample of refinement of B-spline control point grid ( d ( q ) ) at each DSVR iteration (sagittal plane with respect to uterus). D . Structure-based outlier rejection 1) Global structure-based outlier rejection : During each iter- ation q , after the registration and prior to the Gaussian recon- struction step (see Fig. 3), misregistered slices are removed to ensure that global registration errors are not propagated into the initial estimation and further SR reconstruction loop. The quality of registration is assessed as global normalised cross correlation (NCC) between the original slice Y ∗ k and the current estimation of the output volume X ( n,q ) transformed with T ( q ) k within the masked slice R OI. The slices with transformations resulting in correlation lower than a threshold value T N C C are excluded. The corresponding slice outlier criteria are computed as: w G k = ( 1 , if 1 N k P N k j =1 ( y ∗ j k − µ y ∗ )( x T j k − µ x n ) σ y ∗ σ x > T N C C 0 , otherwise , (7) where { x T j k = X ( n,q ) ( T ( q ) k ( u j k )) } j =1 ,...,N k is the trans- formed high resolution volume resampled on the grid of the slice Y k . The v alues µ y ∗ , µ x , σ y ∗ and σ x are the corresponding intensity means and standard deviation of { x T j k } and Y ∗ k . 2) Local str ucture-based outlier rejection : DSVR of de- formable objects can be prone to regional misregistrations and ov erfitting. Therefore, an additional step for regional outlier rejection is introduced. At each SR iteration n (see Fig. 3), the regions of simulated slices with low structural similarity are excluded from contribution to the reconstructed volume. It is based on local structural similarity (SSIM) maps { sm j k } between the simulated and original slices: sm j k = (2 µ r ∗ µ ¯ r + c 1 )(2 σ r ∗ ¯ r + c 2 ) ( µ 2 r ∗ + µ 2 ¯ r + c 1 )( σ 2 r ∗ + σ 2 ¯ r + c 2 ) , (8) where r ∗ and ¯ r are the regions in the original Y ∗ k and simulated ¯ Y k ( n ) slices centered around vox el j with circular window and µ r ∗ , µ ¯ r , σ 2 r ∗ and σ 2 ¯ r are the corresponding average and variance intensity values and σ r ∗ ¯ r is the cov ariance of r ∗ and ¯ r . As defined in [29], values c 1 and c 2 used in order to balance the division with weak denominator are computed as ( k 1 L ) 2 and ( k 2 L ) 2 , where L is the dynamic range of intensities in r ∗ and k 1 and k 2 are equal to 0.001 and 0.003, correspondingly . The outlier criteria of slice voxels with similarity < T S S I M are set to zero: w L j k = ( 1 , if sm j k > T S S I M 0 , otherwise (9) 3) Incor porating structure-based outlier rejection into SR re- construction : Outlier rejection is incorporated into SR recon- struction (3) by scaling the contribution of the reconstruction error e j k by a weight w j k : x ( n +1 ,q ) i = x ( n,q ) i + α X kj w j k m k ( q ) ij e j k + αλ ∂ ∂ x i R ( X ) (10) In our previous work [5] this weight was set based on EM robust statistics on vox el and slice intensities to p j k p slice k . The proposed total structural outlier criteria for a vox el defining its contribution to the reconstructed volume is computed as: w S j k = w G k w L j k (11) A UTHOR et al. : DEFORMABLE SLICE-T O-VOLUME REGISTRA TION FOR MO TION CORRECTION OF FET AL BOD Y AND PLACENT A MRI 5 In Section V -D we will show that the combination of the two schemes by setting w j k = p j k p slice k w S j k outperforms the individual outlier rejection schemes. I V . I M P L E M E N T A T I O N A. Input data requirements The input dataset includes stacks of different orientations, an approximate mask covering the R OI (i.e., fetal body or placenta) and a selected template, which can be either one of the stacks or a scout scan. The global structure of the target object needs to be preserved in the template stacks, as it is used for initialisation of the registration target. Minor to av erage degree of motion corruption of the template is acceptable and is resolved by Gaussian blurring. The sev erity of motion is visually assessed with respect to the degree of loss of volumetric structural information (see Fig. 1). Rigid SVR requires masking of the ROI in the template stack in order to eliminate the impact of the independent motion of the mother and the fetus. On the other hand, FFD registration does not require precise masking and in our experience preforms better for lar ger ROIs. V ariable orientations of input stacks help to prevent over - fitting to a particular motion-corrupted stack. The minimal requirement for SR reconstruction of an isotropic volume from multiple stacks is two sufficiently different orientations. It was identified experimentally that using 5 to 8 stacks is sufficient for good quality reconstruction depending on the amount of motion corruption, resolution and SNR lev el of the original volumes. Similarly to the capture range limitation of SVR [11], gradient-descent based deformable registration methods are not capable of resolving motion in volving large degree rotations or excessi ve bending, which should be taken into account with respect to selection of input stacks. B. Deformable registr ation The B-spline FFD registration [25] with NMI similarity measure was chosen for both deformable SVR and global registration steps due to the lower computational requirements compared to the diffeomorphic registration such as FFD pa- rameterised by stationary velocity (SV) fields [30]. Although SV FFD ensures in vertibility of transformations, it did not lead to an indicativ e improvement of reconstruction results while significantly increasing processing time, which made it not feasible for our application. T ypically , the reconstruction pipeline requires 3 SVR itera- tions ( Q = 3) each of which is follo wed by 10 to 30 SR ( N ( q ) S R ) iterations with gradually refined re gularisation parameters. The resolution of B-spline FFD transformation is controlled by changing the resolution of the B-spline control point (CP) spacing d . W e choose resolution scheme with B-spline control point spacings d (0) = d init , d (1) = 2 / 3 · d init , d (2) = 1 / 3 · d init . As we show in Sec. V -C, it was identified experimentally that 15 mm → 10 mm → 5 mm CP refinement ( d init = 15 mm ) produces the optimal reconstruction quality for our fetal test cases and 0 . 85 mm output resolution. The corresponding optimal regularisation λ ( q ) values were chosen as 0 . 1 → 0 . 05 → 0 . 02 similarly to the SVR settings in [5]. C . Str ucture based outlier rejection par ameters Analysis of the choice of the structural similarity thresh- olds showed that the optimal values corresponding to ade- quate registration quality are T N C C = 0 . 75 for global and T S S I M = 0 . 6 for local regions. Using lower values might lead to inclusion of regions that were erroneously overfitted. The 20 mm diameter for SSIM kernel was experimentally identified as optimal for the feature sizes in 28-31 weeks GA range subjects, e.g., the transverse diameter of fetal kidneys for this GA range varies within 15 − 25 mm [31]. D . Software pac kages and hardware requirements DSVR framework was implemented based on MIR TK 2 library with multi-CPU parallelisation of registration and re- construction steps. The structure and functionality of the core reconstruction steps follow the IR TK-based 3 implementation of the original SVR reconstruction method [5]. The code is av ailable online as a part of SVR TK 4 package. The major advantage of MIR TK registration library is the use of conjugate gradient descent optimisation [32] that significantly increases computational efficienc y of FFD reg- istration that constitutes the most time-consuming part of DSVR pipeline. Depending on the ROI size (related to GA of the subjects), number of stacks, output resolution and the system configuration, the reconstruction time can typically vary between 15 to 60 minutes. V . E X P E R I M E N T S A N D R E S U L T S W e ev aluate DSVR based on the comparison to the rigid SVR method [5] that was recently reported to produce the best results for placenta reconstruction [19] and its GPU version [11] was employed for 3D fetal cardiac reconstruction in [17]. Furthermore, DSVR is compared to the recently introduced PVR method designed for motion correction in large FoV regions [20]. The reconstruction quality is ev aluated using intensity and structural similarity metrics. A. Fetal MRI data The fetal MRI data used for ev aluation contains 20 iFIND T2-weighted datasets of fetuses from 28-31 weeks GA range. This particular GA range was selected due to the lower amplitude of mov ement and higher pre valence of bending and stretching [7], since this study focuses on correction of local non-rigid deformations of organs rather than global change of fetal body position. The iFIND acquisitions were performed on a 1.5T MRI using ssFSE sequence with TR = 15000 ms, TE = 80 ms, v oxel size = 1.25 x 1.25 x 2.5 mm, slice thickness 2.5 mm and slice spacing 1.25 mm. The stacks were acquired under different orientations, with 100-160 slices per stack, depending on GA and orientation. Each of the datasets contains 6 stacks with minimum 3 different orientations without major SNR loss. 2 MIR TK: https://github.com/BioMedIA/MIR TK 3 IR TK: https://github.com/BioMedIA/IR TK 4 SVR TK: https://github.com/SVR TK/SVR TK 6 IEEE TRANSACTIONS ON MEDICAL IMA GING, V OL. XX, NO. XX, XXXX 2020 The datasets were divided into 2 groups with respect to sev erity of motion. The minor motion group contains 10 cases that include stacks only with minimal loss of structural infor- mation. In 10 cases from the sev ere motion group, the majority of stacks hav e se vere misalignment of slices. The severity of motion corruption was visually estimated by an operator with respect to the consistency of volumetric information in all three planes (Fig. 1) as well as the changes of the global fetal body position between the stacks. T emplate stack selection was performed manually based on the degree of motion corruption and the position of the fetal body similar to the other stacks. T ABLE I S T A C K MO T I O N CO R RU P T I O N AS S E S S M E N T : S E Q U E N T I A L S L I C E NC C. Minor motion datasets Sever e motion datasets 0.688 ± 0.071 0.475 ± 0.130 The amount of motion in each stack was also assessed as the average NCC between sequential slices for a masked ROI. T ab. I demonstrates that the severe motion datasets have lower av erage NCC range than the minor motion datasets. B. Simulated e xperiment In order to assess the general capability of DSVR to recover consistent volumetric information and local anatomy features, we perform a phantom experiment with simulated non-rigid motion. At first, a high quality volume reconstructed from a minimal motion dataset is selected as a reference. Next, fi ve sets of slice transformations (incorporating both local non- rigid and global rigid and non-rigid components) extracted from other existing reconstruction cases are used to generate motion-corrupted stacks from the reference volume. In this experiment, each of the fiv e simulated datasets con- tains six generated stacks that ha ve different orientations and a mask defining trunk R OI in the template stack. The default DSVR reconstruction pipeline is ex ecuted for all datasets. In addition, rigid SVR [5] and PVR [20] reconstructions are performed for comparison to the state-of-the-art methods. Fig. 5 shows coronal plane view of the original reference volume ( X ), one of the stacks with simulated deformable motion ( S 0 ), DSVR reconstructed volume ( X DS V R ) along with its difference with the reference ( X DS V R − X ) and SVR ( X S V R ) and PVR ( X P V R ) results. Prior to the analysis of the results, in order to avoid possible impact of the global change of the body position, the reconstructed volumes were aligned to the reference using FFD registration with large CP spacing (15 mm). All three methods successfully reconstructed the major anatomy structures including topology of kidneys and spine. Ho wever , in SVR and PVR outputs, misregistrations due to non-rigid deformations led to blurring of texture of local features and higher errors. The corresponding quantitative comparison of the motion- free reference volume and fiv e DSVR, SVR and PVR re- constructions in terms of normalised root mean square er- ror (NRMSE), peak signal-to-noise ratio (PSNR) and NCC computed for the same masked ROI covering fetal trunk is giv en in T ab . II. All results are statistically significant with Fig. 5. Simulated experiment: original ref erence volume ( X ), one of the generated motion-corrupted stac ks ( S 0 ), SVR ( X S V R ), PVR ( X P V R ) and DSVR ( X DS V R ) reconstruction results and their difference with the reference (coronal plane). T ABLE II S I M U L A T E D EX P E R I M E N T : S V R , P V R A N D DS V R VS . R E F E R E N C E . Method NRMSE PSNR NCC SVR 0.119 ± 0.002 28.916 ± 0.479 0.938 ± 0.003 PVR 0.182 ± 0.009 25.602 ± 0.383 0.882 ± 0.009 DSVR 0.078 ± 0.008 32.560 ± 0.859 0.973 ± 0.006 p < 0 . 001 . There is a strong correlation between the original and DSVR volumes. The worse results for the SVR outputs indicate that the impact of non-rigid deformations on texture cannot be resolved by rigid registration even with rejection of outliers. The reconstructed PVR volumes also hav e lo wer similarity to the reference volumes. T ABLE III S I M U L A T E D EX P E R I M E N T : S V R VS . D S V R T R E [ M M ] . SVR TRE [mm] DSVR TRE [mm] 2.279 ± 0.509 0.797 ± 0.158 W e also calculated target registration error (TRE) to ev al- uate av erage displacement error of the estimated non-rigid transformations compared to the the original ones used for generation of motion-corrupted stacks. Comparison of TRE for DSVR and SVR reconstruction is presented in T ab . III. DSVR TRE values are significantly lower in comparison to SVR and statistically significant with p < 0 . 001 . C . Reconstr uction of f etal body In fetal body reconstruction, due to the absence of the ground truth as well as the constantly changing shape of A UTHOR et al. : DEFORMABLE SLICE-T O-VOLUME REGISTRA TION FOR MO TION CORRECTION OF FET AL BOD Y AND PLACENT A MRI 7 the trunk organs, assessment of the quality of reconstructed volumes is challenging. In [5], leave-one-out analysis was proposed for ev aluation of SVR results. It is based on the comparison of the original { Y ∗ k } to simulated { ¯ Y k } slices for a stack that was registered in SVR step but excluded from SR reconstruction thus not contributing to the output v olume. T ab. IV presents quantitative comparison of SVR, PVR, DSVR and DSVR with structural outlier rejection (DSVR+S) results for the same masked ROI of the excluded stack for 20 datasets. The v alues for PVR results are given primarily for a reference, since, due to the dif ferences in implementation, comparison is performed for simulated and original patches with overlapping regions rather than for slices. Furthermore, PVR employs different SR reconstruction pipeline and does not provide an option for stack exclusion. T ABLE IV F E TAL B O DY R E C O N S T R U C T I O N . L E AV E - O N E - O U T A N A L Y S I S : SV R , P V R , D S V R A N D D S V R + S . Method NRMSE PSNR NCC Minor motion group (10 datasets): SVR 0.229 ± 0.023 24.328 ± 0.920 0.780 ± 0.084 PVR* 0.264 ± 0.050 22.438 ± 1.371 0.712 ± 0.120 DSVR 0.177 ± 0.021 26.764 ± 1.139 0.863 ± 0.038 DSVR+S 0.174 ± 0.025 26.764 ± 1.249 0.867 ± 0.043 Sev ere motion group (10 datasets): SVR 0.275 ± 0.025 23.219 ± 0.861 0.646 ± 0.068 PVR* 0.280 ± 0.046 21.873 ± 1.436 0.633 ± 0.107 DSVR 0.222 ± 0.032 25.422 ± 0.619 0.831 ± 0.043 DSVR+S 0.214 ± 0.033 25.746 ± 0.597 0.844 ± 0.040 (*) PVR comparison was performed on the patch level. The results for both minor and sev ere motion datasets show that DSVR surpasses SVR and PVR for both intensity and structural characteristics. Additional structural outlier rejection (DSVR+S) produces a significant improvement only for the sev ere motion datasets. This is expected since minor motion assumes high NCC v alues of registration output and DSVR+S should produce only minimal impact. All results apart for comparison of DSVR and DSVR+S for minor motion cases are statistically significant with p < 0 . 005 . For one of the minor motion cases shown in Fig. 6 (sagittal plane view) when the trunk positions in all stacks are approximately aligned and there are no sev ere non-rigid deformations, SVR successfully reconstructs the global trunk topology . Howe ver , due to bending motion, there is a notice- able loss of structure in the spine region as well as the general degradation of texture. PVR allows reconstruction of the large R OI and partially resolves these artefacts improving definition of the spine. Ho wev er, the introduced smoothing lowers image quality in terms of interpretation and resolution of small features. On the other hand, DSVR results are characterised by high definition of the local anatomy structures. It also has to be noted that there is a noticeable change in the position of the trunk between different reconstruction methods caused by the different approaches for initialisation of the registration target ( X init ). SVR and PVR use the av erage of all stacks after global rigid stack registration and DSVR uses the selected template stack. Therefore, the SVR and PVR Fig. 6. Example of motion correction for a minor motion dataset: motion corrupted stack, SVR, PVR and DSVR reconstructions (sagittal plane). solutions conv erge to an intermediate av eraged state, whereas DSVR con ver ges to the trunk shape in the template stack. Fig. 7. Compar ison of SVR and DSVR in presence of non-r igid motion: original acquired slice ( Y k ) vs. slices simulated from SVR and DSVR ( ¯ Y k ). The yellow isolines delineate the structure in the or iginal slice, and show misalignment with SVR reconstr uction due to limitation of rigid motion correction. The problem is resolved by non-r igid motion correction in DSVR. A typical example of failed rigid SVR due to non-rigid motion is gi ven in Fig. 7 where one of the original slices Y k is compared to the corresponding simulated slices ¯ Y k from SVR and DSVR reconstructions. The kidney and bladder regions are segmented in order to assess the registration accuracy . In this case, SVR could not correct the impact of spine bending thus con verging to an av erage position with displaced kidney and resulting in large errors { e j k } . On the other hand, FFD registration improv es the mapping ( T k ) between Y k and X ( n,q ) . The deformation of ROI boundaries in DSVR output indicates the high degree of non-rigid deformation. For one of the se vere motion dataset results shown in Fig. 8 (coronal plane view), large slice misregistration errors lead to a se vere degradation of local features in SVR. PVR resolves this producing a clear trunk structure, howe ver , similarly to the previous example, the smoothed te xture lowers the quality of definition of abdominal org ans. Although there is an improv ement in DSVR vs. SVR output, a significant amount of artefacts due to misregistrations still remains. As mentioned 8 IEEE TRANSACTIONS ON MEDICAL IMA GING, V OL. XX, NO. XX, XXXX 2020 in Sec. III, the employed gradient-descent FFD method is not capable of resolving large bending and rotations therefore leading to misregistrations. Structural outlier remov al (DSVR+S) improves the output by minimising the contribution of registration errors to recon- struction. It also increases the proportion of rejected slices, which, for severe motion datasets, can v ary between 20 - 50 % of the total slice number . In comparison, the original EM robust statistics [5] results in only 10 - 15 % slices being rejected, which seems to be insufficient in major motion cases. Fig. 8. Example of motion correction for a se vere motion dataset: motion corr upted stack, SVR, PVR and DSVR reconstructions (coronal plane). D . Par ametric study Regularisation parameters that control the smoothness of the transformations in DSVR hav e significant impact on the quality of reconstruction. Transformations with large CP spacings allow for correction of the global body shape, but are not efficient for recovery of local features. On the other had, too small CP spacing will lead to overfitting and unre- alistic deformations. W e experimentally determined that the optimal multi-resolution scheme for fetal body dimensions is 15 mm → 10 mm → 5 mm for 3 iterations. W e ev aluated the regularisation schemes with the CP spac- ings d (0) , d (1) = 2 / 3 · d (0) and d (2) = 1 / 3 · d (0) for the subsequent DSVR iterations. The d (0) value was varied from 30 mm to 5 mm for fiv e se vere motion datasets. W e calculated NCC between simulated { ¯ Y k } and original { Y ∗ k } slices for the masked fetal body ROI in all stacks. Fig. 9 shows the av erage NCC values ov er the fiv e subjects for different initial transformation resolutions d (0) . The average SVR output value is provided for the reference. W e can observe that d (0) =15mm Fig. 9. CP spacing analysis: NCC between the or iginal ( Y ∗ k ) vs. simulated ( ¯ Y k ) slices. results in optimal performance and further refinement does not improv e the results due to overfitting to the motion artifacts. T ABLE V O U T L I E R R E J E C T I O N S C H E M E A S S E S S M E N T : N C C B E T W E E N ( Y k ) AN D ( ¯ Y k ) AN D PR O P O RT I O N O F EX C L U D E D S L I C E S . Method NCC % of excluded slices EM 0.828 ± 0.028 13.41 ± 2.88 % EM + G-STR 0.839 ± 0.037 38.51 ± 15.28 % EM + L-STR 0.834 ± 0.031 18.85 ± 5.17 % EM + L-STR + G-STR 0.841 ± 0.036 35.59 ± 12.29 % L-STR + G-STR 0.837 ± 0.039 30.19 ± 11.06 % In addition, we performed quantitativ e assessment of the impact of the structural outlier rejection steps on the re- construction quality and number of excluded slices. T ab. V presents the results for 5 sev ere motion datasets with the de- fault processing pipeline and different combinations of outlier rejection methods: EM-based method proposed in [5], global structural slice-lev el rejection based on global NCC (G-STR), and local region rejection method based on SSIM maps (L- STR). W e report NCC between original Y k and simulated slices ¯ Y k of the excluded stack within the masked fetal body R OI, and the average proportion of the excluded slices. It can be observed that combination of all three outlier rejection steps results in best performance in sev ere motion cases. E. Reconstruction of placenta Furthermore, the performance of SVR, PVR and DSVR for reconstruction of placenta was compared for 10 iFIND fetal MRI cases. Each of the datasets contains 5 orthogonal stacks cov ering the entire uterus and reconstructions are performed for the masked uterus R OI similarly to [19]. The corresponding results of the leave-one-out analysis are presented in T ab . VI in terms of NCC between the original Y k and simulated ¯ Y k slices of the same masked R OI of an excluded stack. The proposed DSVR method outperforms both other methods. All results are statistically significant with p < 0 . 005 . Fig. 10 shows an example of motion-corrected outputs of SVR, PVR and DSVR of placenta. Placenta is primarily af fected by respiratory motion, and is subject to stretching and bending. A UTHOR et al. : DEFORMABLE SLICE-T O-VOLUME REGISTRA TION FOR MO TION CORRECTION OF FET AL BOD Y AND PLACENT A MRI 9 As a result, DSVR provides better reconstruction quality compared to the alternativ e methods. T ABLE VI P L A C E N TA R E C O N S T RU C T I O N . L E AV E - O N E - O U T A N A L Y S I S : SV R , PV R A N D D S V R ( N C C ) . SVR PVR* DSVR+S 0.639 ± 0.085 0.726 ± 0.045 0.792 ± 0.072 (*) PVR comparison was performed on the patch level. Fig. 10. Example of motion correction for placenta: motion-corrupted stack, SVR, PVR and DSVR+S reconstructed volumes (coronal plane). F . Qualitative analysis T o assess the applicability of DSVR across gestational ages, we performed qualitati ve e valuation for 100 iFIND fetal body cases randomly selected from 20-34 weeks GA range. The reconstructed v olumes were graded by trained clinicians with respect to the image quality in [0; 4] range (4 corresponding to high quality). V olumes with grades ≥ 2 were considered to hav e sufficient quality for further analysis and interpretation. The distribution of grades for each week of GA is presented in Fig. 11. A verage grades per week of GA varied within 2.5 - 3.5 range ( 3 . 09 ± 0 . 78 ). The primary causes of lower grades were motion for younger subjects and low SNR for older subjects. Only 6% of all cases failed (grades < 2 ) due to sev ere motion which could not be resolved by gradient descent based FFD registration. Further details of the analysis are presented in Supplementary material. V I . D I S C U S S I O N A N D C O N C L U S I O N S W e proposed and implemented a novel DSVR method for compensation of non-rigid motion in fetal MRI. It allows Fig. 11. Quality of DSVR reconstr uctions of fetal body region for 100 reconstr ucted iFIND cases vs . GA. Squares represent the average grade per week of GA, and bars represent the r ange of values. reconstruction of high resolution 3D volumes from multiple stacks of slices af fected by non-rigid motion. Therefore, DSVR extends application of slice-to-volume reconstruction to fetal body and placenta. Unlike the con ventional rigid SVR methods, DSVR is capable of correction of local deformations of organs caused by bending and stretching. Correction of both in- and out-of- plane non-rigid motion is ensured by registration of the volume to slices rather than slices to volume. The challenge of the absence of a ’ stable’ shape is addressed by hierarchical FFD SVR scheme initialised by one of the stacks that gradually con ver ges to a stable state. The fact that the stacks ha ve different orientations helps to prev ent overfitting to motion artefacts. In addition, structure-based outlier rejection step is introduced to minimise the impact of misregistration errors on the reconstructed volume. The method was quantitativ ely ev aluated on 20 fetal MRI datasets from 28-31 weeks GA range. This age range was chosen due to high incidence of stretching and bending, whereas large rotation and translation motion is less prev alent compared to younger subjects [7]. Comparison to the state-of- the-art solutions showed that DSVR surpasses both SVR and PVR methods for minor and se vere motion datasets. This was further confirmed by an additional experiment with simulated non-rigid motion. DSVR reconstructed 3D fetal body volumes are characterised by well defined features and texture of the spine, heart and abdominal organs. The current implementation of DSVR is not designed for correction of large amplitude motion, including, large rotations and bending, due to the limited capture range of the employed gradient descent based optimisation methods, and therefore relies on outlier rejection in such cases. The qualitati ve study of DSVR reconstruction of fetal body for 100 iFIND cases from 20-34 weeks GA range showed that large amplitude motion primarily affects datasets of subjects under 25 weeks GA. In future, this limitation can be addressed by application of CNN-based methods, as already proposed for rigid SVR fetal brain reconstruction [14], [15]. W e further demonstrated that DSVR outperforms both SVR and PVR for 3D placenta reconstruction. In future, introducing 10 IEEE TRANSACTIONS ON MEDICAL IMA GING, V OL. XX, NO. XX, XXXX 2020 additional decoupling of maternal motion would potentially improv e correction of large amplitude motion. Although DSVR reconstructed volumes can be used for qualitativ e analysis, the question of volume-preserv ation for DSVR reconstruction still remains open. Quantitative mea- surements performed on DSVR reconstructed volumes can be influenced by various factors such as the position and shape of the fetal body in the template, number of stacks or CP spacing. This limitation should be addressed in future by introducing further model-based constrains on deformation fields along with automation of template selection and masking steps. A P P E N D I X I S U P P L E M E N T A RY D A T A Supplementary material presents the details of qualitative analysis of DSVR reconstruction quality for 100 iFIND cases, the full versions of Fig. 5, 6, 8, DSVR reconstruction of the whole uterus for twin pregnanc y case, and visual representa- tion of the DSVR algorithm. A C K N O W L E D G M E N T Thank you to Matthew Fox, Joanna Allsop, Ana Gomes and Elaine Green for their ov ersight during the scanning of volunteers and patients. 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