Detecting default mode networks in utero by integrated 4D fMRI reconstruction and analysis

Abstract

Recently, there has been considerable interest, especially for in utero imaging, in the detection of functional connectivity in subjects whose motion cannot be controlled while in the MRI scanner. These cases require two advances over current studies: (1) multiecho acquisitions and (2) post processing and reconstruction that can deal with significant between slice motion during multislice protocols to allow for the ability to detect temporal correlations introduced by spatial scattering of slices into account. This article focuses on the estimation of a spatially and temporally regular time series from motion scattered slices of multiecho fMRI datasets using a full four‐dimensional (4D) iterative image reconstruction framework. The framework which includes quantitative MRI methods for artifact correction is evaluated using adult studies with and without motion to both refine parameter settings and evaluate the analysis pipeline. ICA analysis is then applied to the 4D image reconstruction of both adult and in utero fetal studies where resting state activity is perturbed by motion. Results indicate quantitative improvements in reconstruction quality when compared to the conventional 3D reconstruction approach (using simulated adult data) and demonstrate the ability to detect the default mode network in moving adults and fetuses with single‐subject and group analysis. Hum Brain Mapp 37:4158–4178, 2016. © 2016 Wiley Periodicals, Inc.

INTRODUCTION

In the last decade, there has been a growing interest in fMRI studies of young subjects whose motion cannot be controlled when in the scanner [Dijk et al., 2012; Satterthwaite et al., 2012]. These studies include task‐based experiments as well as resting state network analysis which lead to the understanding of functional connectivity in young children [Wilke et al., 2003] and fetuses [Gowland and Fulford, 2004; Schopf et al., 2011; Thomason et al., 2013]. Of particular interest, is the study of the default mode network (DMN) within resting state studies. Although the presence of this network in adults has been well established, specific details on how it develops during early brain maturation is still an open question. Recent studies [Doria et al., 2010] on premature neonates have shown that the DMN can be detected in late gestation (29–43 weeks). This provides the motivation for investigation of DMN development in utero.

Functional connectivity studies typically involve estimation of correlation between time series (at direct brain locations) or data‐driven time series analysis (such as ICA) to determine connectivity between regions of the brain. In the presence of large motion as exhibited in the datasets containing uncontrolled motion, this kind of analysis is challenging due to three reasons: (1) time series within each voxel need complex models for motion correction (gross volume alignment is not sufficient), (2) once these complex models have been estimated, the data needs to be reconstructed onto a regular grid for analysis, and (3) signal changes due to motion induces intensity artifacts (spin history artifacts) which affects the ability to perform accurate correlation analysis. The intensity change due to spin history is caused because a change in the fetal head's position after excitation will disrupt the tissue's steady state magnetization, which in turn affects the signal that is recorded. This effect then propagates to the next few volumes this creating a spin “history” effect.

Some of the early work in the area involves elimination of volumes containing large subject motion—scrubbing [Power et al., 2012; Thomason et al., 2013]. However, this method does not ensure that enough data is available for single subject spatiotemporal analysis. There is, therefore, a great need for developing accurate methods for motion estimation, reconstruction and intensity artifact correction to generate analysis‐ready reconstructions in the presence of large motion.

Methods commonly used within fMRI pipelines for motion correction and re‐ construction [Ashburner, 2012; Cox, 1996; Goebel, 2012; Smith et al., 2004; Strother, 2006] cannot accommodate such data since the subject may move even between slice acquisitions. Recently, several groups have begun addressing accurate motion estimation and reconstruction for structural MRI and DWI of moving subjects [Beall and Lowe, 2014; Bhagalia and Kim, 2008; Fogtmann et al., 2014; Gholipour et al., 2010; Kim et al., 2010; Rousseau et al., 2006; Studholme, 2011]. They propose methods for slice motion estimation and scattered data reconstruction within a three‐dimensional (3D) volume. These methods have been previously applied to fMRI data [Bhagalia and Kim, 2008; Seshamani et al., 2013a] with separate reconstruction of each 3D volume within the time sequence. However, it is well known that fMRI data is serially correlated [Chaari et al., 2011] and temporal smoothing is often applied as a post‐processing step. Hence, integrating information about the temporal structure of the data within the time series estimation from scattered data can improve the quality of the analysis‐ready reconstruction.

Integrated approaches for fMRI preprocessing have been of interest in recent literature. In the early part of the last decade, Ernst et al. [1999] proposed a method for simultaneous motion correction and distortion correction and Orchard et al. [2003] proposed a method for combined registration and activation detection. More recently, Roche [2011] proposed an algorithm that performs 4D registration and slice timing correction within one unified framework. All these methods, however, assume that the head moves slowly, and hence, they are able to integrate registration with these other preprocessing steps. Moreover, they use simple interpolation methods to reconstruct the brain. We however are interested in the case where head motion is much larger. For such cases, registration should be carried out separately (estimating volume and slice motion) and preprocessing can be fused with the reconstruction step. Therefore, we are interested in the problem of integrating spatial and temporal smoothing within a 4D reconstruction framework that uses previously estimated registration estimates and slice timing information. Four‐dimensional reconstruction of general medical image data has been a very active area of research. Hinkle et al. [2012] applied 4D reconstruction to respiratory correlated CT image reconstruction and Ritschl et al. [2012] proposed 4D reconstruction with adaptive weights for cardiac CT reconstruction. They performed adaptive weighting on temporal and spatial gradients for the iterative reconstruction, which depended on the amount of motion in the data. Van Reeth et al. [2014] performed 4D reconstruction of structural MRI of thoracic organs using only volume motion estimates. Within fMRI, 4D reconstruction has been applied to enhance parallel imaging reconstructions only for stationary or very slow moving subjects [Chaari et al., 2011].

In the domain of fetal fMRI imaging, only a few groups have addressed motion correction and spin history correction. Some of the early work in spin history correction in adult fMRI was done by Friston et al. [1996] and Bhagalia and Kim [2008]. Seshamani et al. [2012] first showed that slice motion correction affects single subject ICA analysis and that quantitative MRI methods can be used to further improve analysis [Seshamani et al., 2013b]. However, they only used 3D linear reconstructions for scattered data interpolation. More recently, Ferrazzi et al. [2014] proposed a fetal fMRI processing framework that uses noniterative linear 3D and 4D reconstruction and perform group analysis on 16 fetal subjects in the age range of 30.37 ± 4.35 weeks. Ferrazzi et al. [2014] also address spin history artifacts. In their work, they compute slice motion estimates explicitly and use these estimates to correct for intensity changes. More recently, Seshamani et al, 2014, Seshamani et al, 2015 have used a quantitative MRI technique that uses dual echo information to estimate R2* maps for addressing spin history artifacts. The R2* value expresses the signal relaxation that occurs during readout due to intra‐voxel dephasing of magnetization. It can be estimated by linear fitting of values from two or more T2*‐weighted echo planar imaging (EPI) images. R2* maps are less prone to spin history artifacts since they are created by a differential relationship of T2*‐weighted images acquired at two or more echo times. Since the same spin history is present in all T2*‐weighted images used to create the R2* map, the effect cancels out.

This work differs from Ferazzi's work in the following ways: (1) We use iterative 4D reconstruction with the point spread function whereas they only use single step interpolation, (2) we present quantitative experiments on adult subjects which has not been performed in their work, (3) we validate the presence of the default mode in single subjects at late gestational ages where DMN have previously been established (and not simply perform group analysis on a large age range), and 4) we use a quantitative MRI approach that generates an R2* map from dual echo data to provide robustness to the spin history effect, whereas they correct for spin history using motion estimation.

In summary, this article proposes a method that integrates 4D density adapted iterative reconstruction with preprocessing steps of slice timing correction, spatial smoothing, and temporal smoothing. This ensures that data interpolation before analysis takes place only once, and hence, the data does not suffer from intermediate interpolation artifacts. We present ICA analysis on moving adults as well as on fetuses and compare networks obtained from existing 3D reconstruction methods and the proposed method and show the enhancement in DMN with the proposed method. These results can have a significant impact on the neuroscience community allowing fcMRI studies that were previously considered difficult or impossible to analyze.

MATERIALS AND METHODS

fMRI data is conventionally acquired as a series of T2* weighted multislice echo planar acquisitions collected sequentially over time [Bandettini et al., 1993]. Let the true (underlying) signal in the brain be denoted as X and the acquired slice data S consisting of N slices be denoted as: $\widehat{S}=\{s_1\dots s_N\}$. Each slice consists of a set of K voxels $s_i=\left\{{\stackrel{\sim }{s}}_{i}1\dots {\stackrel{\sim }{s}}_{iK}\right\}$. Here, we assume the voxels within each EPI slice to be spatially consistent (i.e., due to MRI acquisition occurring in terms of spatial frequencies, motion does not act separately on voxel values to cause simple within‐slice geometric distortions but may result in blurring or other global artifacts). Between the acquisition of each slice, the head is free to exhibit full 3D rigid motion described by a set of parameters {M1 … MN}. Given a slice to volume alignment estimate of these motion parameters [Fogtmann et al., 2014—Fig. 1], the objective of the fMRI reconstruction problem is to compute an estimate $\widehat{X}$ of the true image. We begin by considering a slice acquisition model of the form:

$$s_i=D_i{B}_i{M}_{i}X+ n_i$$ (1)

where Di is the subsampling matrix, Bi is the blur matrix representing the point spread function, and ni is the observation noise. We acquire one EPI slice over a period of approximately 30 ms and two echoes within 60 ms. The model, therefore, is used to compute an average transformation of all voxels within a slice. With visual confirmation, we have observed that there is no significant signal degradation caused by intra‐slice motion artifacts. [Ferrazzi et al., 2014]. This is because the acquisition is fast enough that within‐ slice motion artifacts are minimal for most slices even in the case of significant motion. If we use a slice alignment algorithm to estimate the rigid motion mapping of each slice into a common anatomical coordinate frame [Seshamani et al., 2013a] and the subject is undergoing large motion, they may in general be distributed in an uneven pattern over this common anatomical space. As signal change over time is critical in fMRI analysis, and each slice is acquired at a distinct temporal point, both the time and location of the slices must be considered. Furthermore, as each 3D stack of slices occurs within a continuous sequence of frames, we should in general also consider the possible contributions of slices in neighboring frames when estimating the signal at a given anatomical location and time point. Thus, estimating the signal at voxels on a regular 4D grid from these points is a scattered data reconstruction problem. We, therefore, consider a general 4D point spread function that allows us to incorporate the influence of both spatial and temporal neighbors for scattered data reconstruction.

Figure 1.

Examples of between‐slice motion correction of fMRI of moving fetal brain. The slice is being aligned to the reference volume. Left: Before slice alignment. Green arrows point to the area on the intersection where there is a visible misalignment. Middle: Alignment after slice registration. Right: Orientation of all slices in one stack after registration. All three columns of this figure are showing the same same slice. [Color figure can be viewed at http://wileyonlinelibrary.com.]

Four‐Dimensional Iterative Reconstruction

We define a set of N regularly sampled slice intensities (with K voxels) as: $\widehat{X}=\left\{{\widehat{x}}_i\mathrm{..}\widehat{x}N\right\}$which is our final reconstruction. We compute this reconstruction with a deconvolution technique (Previous work in 4D fMRI reconstruction uses simple interpolation only—Ferrazzi et al., 2014). The first step of the deconvolution involves a backward projection of the measured values onto the 4D grid that distributes the intensities of the scattered data spatially and temporally into the estimated time series using a full 4D Gaussian point spread function. Forward projection is the procedure of recomputing an estimate of the observed scattered slices $\widehat{S}=\{{\widehat{s}}_1\dots {\widehat{s}}_N\}$ from the model using Eq. (1). Figure 2 shows a pictorial example of these procedures. The reconstruction estimate is then refined by maximizing the conditional probability density function of the observed slice intensities given the current estimate of the reconstruction:

$${\max }_{X}P\left(\widehat{X}|S\right)= \frac{P\left(S|\widehat{X}\right)P\left(\widehat{X}\right)}{P\left(S\right)}$$ (2)

where

$$P\left(S|\widehat{X}\right)= {\Pi }_{k=1}^K\frac{e-\mathcal{E}({\widehat{s}}_i,s_i)/2{\sigma }_k^2}{{\sigma }_k\sqrt{2\pi }}$$

Figure 2.

Top: Process of back projection and forward projection of a point on a slice to and from a 4D Image. Backward projection: distributing the intensities of the scattered data onto a regular grid. Forward projection: recomputing an estimate of the point on the slice from the regular grid estimates using Eq. (1). Bottom: two‐dimensional pictorial example of projection of one point on slice. The green points show the kernel used to model the through plane slice profile of the imaging estimate. When using a kernel for back projection, the scattered data point intensity is first weighted with the kernel which is then distributed. When using the kernel for forward projection, the inverse procedure is applied. [Color figure can be viewed at http://wileyonlinelibrary.com.]

P ( $\widehat{X}$) is a prior on $\widehat{X}$ and P (S) is a constant with respect to $\widehat{X}$ Thus, this problem is equivalent to obtaining the MAP estimate by minimizing the log likelihood function:

$${\min }_X f\left(X,S\right)= {\sum }_{k=1}^K \mathcal{E}\left(\widehat{s_k},s_k\right)+R\left(\widehat{X}\right), \widehat{X}>0$$ (3)

where ε is a distance function and R is the regularization (prior) term. The optimum solution can be obtained by iteratively minimizing f with respect to $\widehat{X}$.

By‐products of reconstruction

Reconstruction in this manner enables us to obtain two types of information about the data. The first is what we refer to as a density map:

$$D=\{d_1\dots d_N\}$$

where di represents the density value at voxel i. A density map is constructed by back projection of a uniform unit intensity image (an image where all voxel intensities are 1), using the volume and slice motion estimates. Voxel intensities in the density map represent the scattering of the measured voxel data. A higher density value implies that the neighborhood of that point contains more contributing measurements. Figure 3 shows examples of density maps when there is very little motion (left) and large motion (right).

Figure 3.

Sagittal views of density maps. Left: Very little motion and scattering. Right: Large motion. Brighter areas indicate higher density values and darker areas indicate lower density values.

The second type of information we can obtain about the reconstruction is the residual reconstruction error. We define this as:

$$R= \{r_1\dots r_N\}$$

where ri represents the residual error value at voxel i. This residual error is computed as the difference between the backprojected and forward projected points. To deal with outliers [Gholipour et al., 2010], we follow the work of Fogtmann et al. [2014] and use the Huber Norm [Huber, 1964] which is a robust norm that is less sensitive to outliers compared to the Euclidean norm. In the next few sections, we describe how we use this information to enhance the reconstruction and analysis.

Point Spread Function for Iterative Reconstruction

Techniques for structural imaging from motion scattered slices have recently begun to use iterative deconvolution techniques [Fogtmann et al., 2012; Rousseau et al., 2006; Scherrer et al., 2012], rather than direct interpolation, to provide an optimal estimate of the 3D volume image, given the observed slice data. Such methods seek to iteratively deconvolve the measurement point spread function from the multislice and multiplane datasets with differently orientated anisotropic resolutions, to create an optimal 3D image with isotropic resolution. The point spread function used in that case is derived directly from the imaging process. In fMRI analysis, post‐processing however also depends on post‐filtering the data to trade spatial or temporal [Friston et al., 2000] resolution for increased signal to noise. This may involve both spatial and temporal filters. Here, rather than use a separate post processing filter set, we propose to directly incorporate the post processing filter within the reconstruction framework. This has the advantage of providing further stability to missing data and forces iterations to estimate a temporally and spatially smooth time series at a specified resolution that best explains the acquired measured slices. The exact choice of parameters for the kernels is described in the experiments section. Additionally, we apply slice timing correction to adjust for the change in slice time acquisition across each volume. The next few subsections describe how we incorporate these and the adaptations we make to deal with scattered data.

Space time weighting

The 4D point spread function can be written as:

$$G\left(x,y,z,t\right)= \frac{1}{2\pi {\sigma }^2}{e}^{\frac{x^2}{2{\sigma }_x^2}+\frac{y^2}{2{\sigma }_y^2}+\frac{z^2}{2{\sigma }_z^2}+\frac{t^2}{2{\sigma }_t^2}}$$ (4)

where the σ values represent the point spread in x, y, z, and t. Multislice fMRI acquisitions that are acquired on a slice by slice basis contain a time lag between the acquisition of the first slice in the volume and the last slice in the volume [Sladky et al., 2011]. To compare the time series of voxels across slices, intensities can simply be interpolated to estimate the appearance of slices occurring at identical times, when no slice to slice motion occurs. Here, however, we integrate this temporal accounting explicitly into the scattered slice reconstruction process. This also secondarily eliminates a source of interpolation error arising from an additional interpolation step. To further simplify fMRI analysis, the timings of all the slices in each target reconstruction volume frame are specified to be identical. Slice time and space weighting is applied as described below.

To account for differences in timing, we include a general slice timing weight in the interpolation process. Let v1 be the time of the acquired point and let v2 be the timing of the point to be reconstructed. We incorporate an explicit space time weighting factor τ that relates temporal and spatial dimensions (seconds to mm) in the point spread function to account for the difference in slice timing within and between volumes as:

$$G\left(x,y,z,t,v1,v2\right)= \frac{1}{2\pi {\sigma }^2}{e}^{\frac{x^2}{2{\sigma }_x^2}+\frac{y^2}{2{\sigma }_y^2}+\frac{z^2}{2{\sigma }_z^2}+\frac{t^2}{2{\sigma }_t^2}+\frac{{(v1-v2)}^2}{\tau }}$$ (5)

where 1/τ is the parameter that relates space and time. We select this parameter empirically. This is implemented as a set of separable Gaussian filters in the input slice coordinate system.

Adaptive kernel selection

For a 1D separable Gaussian kernel centered at point qi, the value at location

q, is computed as:

$$K\left(q,q_i\right)= e^{-\frac{{\left(q-q_i\right)}^2}{{\sigma }^2}}$$

When there is variation in the measured voxel data density due to scattering, the number of points within the neighborhood of points in the kernel (the support for the kernel) will not be comparable. What this means is that fewer points would support the estimation of a point with the same kernel size when the points start spreading out. To account for this problem, we incorporate adaptive kernel regression to extend the support for the kernel to contain adequate samples [Pham and Vliet, 2003; Takeda et al., 2007]. The support for the kernel around a point can be determined from its density value d_i. We adapt the above kernel using the density estimate as:

$$K\left(q,q_i\right)= e^{-\frac{d_i^2{(q-q_i)}^2}{{\sigma }^2}}$$

In practice, we maintain the kernel size and adapt the values in the kernel vector by exponentiating each one by a factor of d ² and then normalizing the resulting kernel to sum up to 1.

Algorithm Summary and Details

The reconstruction algorithm depends on steps involving backward projection, forward projection, and gradient computation described below:

1. Backward projection with a 4D point spread function: Given 4 1D kernels gx, gy, gz, and gt (for each of the four directions) and a slice S, back projection involves distributing the intensity values in the slice onto the regular grid (4D volume). We first convolve each 1D in‐plane kernel (gx and gy) with the slice. For the kernel in the out of plane direction z, we process each point on a voxel by voxel basis. We create a vector that distributes the intensity value of the point using gz. To include point spread in the time direction, we further spread each point in the vector in the timing direction using gt, to create a plane. Each point in the plane is then distributed around its neighbors using linear weighting and the slice timing weight. To adjust for differences in densities, the density value is divided out of the final intensity.

2. Forward projection with a point spread function: this involves estimation of slice intensity values given the regular grid (4D volume). For estimating the intensity value of a point in a slice, we first evaluate the plane around a point (spread in z and t). Each point in this plane is evaluated using 4D linear interpolation. The weights used for back projection are then divided out to and summed up to generate a slice intensity. Once all the values in the slice are computed, the gx and gy filters are applied to obtain the estimate of the intensity of a point in the slice.

3. Gradient Computation: Given an estimate of the underlying 4D volume $\widehat{X}$, we first forward project this to estimate slices $\widehat{S}$. The residual error between input S and $\widehat{S}$ is computed. This residual error is backprojected and added to the regularization term which is computed using a Huber neighborhood function on $\widehat{X}$ . We use the Huber norm ε [Huber, 1964] for robust estimation of the intensity mismatch to obtain this solution. Convergence of the Limited Broyden–Fletcher–Goldfarb–Shanno (LBFGS) in our data typically requires around five iterations using a gradient tolerance of less than 1e−6.

The algorithm incorporates these three steps in the following manner:

Input: Raw Data (S), Slice Motion Estimates

• Perform backward project of input data S onto a regular grid to generate X

• Minimize Eq. (3) using X and S with an iterative algorithm

  • Since this is an unconstrained optimization problem, we use the LBFGS algorithm [Byrd et al., 1995; Morales and Nocedal, 2011; Zhu et al., 1997] which is a well‐known algorithm for solving such problems. The “limited” term refers to the fact that the algorithm is adapted to perform on a limited amount of memory. We use zero lower bounds since intensity values in the magnitude images we are reconstructing and analyzing cannot be negative.

  • Each iteration requires an estimate of the forward projection and gradient given the current estimate.

DATA ACQUISITION

Adult Data

Dual‐echo fMRI studies were acquired on two adult subjects: Subjects 1 and 2. Subject 1's study was acquired on a Philips 3T Achieva Scanner: TR = 3 s, TE = 15 ms and 45 ms, 40 slices, axial 3‐mm slices. Three resting state acquisitions were collected. In the first acquisition, the subject was stationary and in the second acquisition, the subject nodded her head slowly. In the third, the subject nodded her head with a larger range of motion. The first three rows of Table 1 show the range of motion for these three acquisitions. Subject 2's study was acquired on a Philips 1.5T Achieva Scanner again with TR = 3 s, TE = 15 ms and 45 ms, 40 slices, axial 3‐mm slices. Two resting state acquisitions were collected. In the first one, the subject was stationary and in the second one, the subject performed a large nodding motion. The last two rows of Table 1 show the rotation and translation parameters for these datasets.

Table 1.

Head motion during acquisition of moving subjects. [Color figure can be viewed at http://wileyonlinelibrary.com.]

Dataset	Field strength	Subject	Translation motion	Rotation motion
1	3T	1
2	3T	1
3	3T	1
4	1.5T	2
5	1.5T	2

Column 4: Estimated translation parameters (X, Y, and Z). Column 5: Estimated rotation parameters (X, Y, and Z). First three rows show motion trajectories of acquisitions on Subject 1 and last two show trajectories of acquisitions on Subject 2.

Fetal Data

We selected eight singleton subjects all in the late stage of development: 32 weeks and older (Table 2) from the University of Washington Fetal Brain Database for our experiments. This age group is comparable to the ages of premature neonatal subjects where the presence of DMN have previously been established [Doria et al., 2010]. Hence, this is suitable for analysis‐based validation of the proposed methods on in utero data.

Table 2.

Demographic Information of all eight fetal subjects

Fetal subject number	Mother's age	Baby's gestational age	Baby's gender
1	34 years	35.1 weeks	Male
2	30 years	35.6 weeks	Female
3	36 years	34.4 weeks	Male
4	32 years	32.7 weeks	Female
5	30 years	34.2 weeks	Male
6	34 years	34.4 weeks	Female
7	32 years	37.0 weeks	Unknown
8	33 years	33.0 weeks	Male

Scanning was performed on a Philips 1.5T Achieva scanner, using a 16‐channel Torso XL coil and dual echo data (magnitude and phase) was saved. The scan parameters were: TR = 3 s, TE1 = 15.6 ms, TE2 = 45 ms, 40 axial 3‐mm slices, 92 dynamics, SENSE factor = 2. During each scan, the coil was placed in the closest possible position to the fetal head to maximize SNR and the scan was planned to avoid any wrapping of the parts of maternal anatomy into the field of view. We also acquired 3–4 stacks of T2‐weighted HASTE scans in 3 orthogonal planes each with spatial resolution 1.0 × 1.0 × 3.0 mm, TE/TR = 150–250/1,000–3,000, acquisition time 5 min. We estimated slice motion using the SIMC algorithm [Kim et al., 2010]. A high resolution reconstruction was created from the different stacks of HASTE data using the method described in Fogtmann et al. [2012]. This reconstruction was used for viewing functional connectivity results. Figures 4 and 5 show the head motion trajectories of all fetal datasets.

Figure 4.

Rotation Parameters of the head motion during acquisition of Subject 1–8. Motion is estimated on a slice by slice basis. RX, RY, and RZ show rotational motion around the X, Y, and Z axes, respectively. [Color figure can be viewed at http://wileyonlinelibrary.com.]

Figure 5.

Translation Parameters of the head motion during acquisition of Subject 1–8. Motion is estimated on a slice by slice basis. TX, TY, and TZ show translational motion along the X, Y, and Z axes, respectively. [Color figure can be viewed at http://wileyonlinelibrary.com.]

To deal with spin history artifacts, we computed an R2* map (S. Seshamani [2014]) from these reconstructions on a voxel‐by‐voxel basis. The R2* map was generated as follows:

$$R2*\left(x\right)= \frac{\mathrm{l}\mathrm{n}\left(I_1\left(x\right)\right)-\mathrm{l}\mathrm{n}\left(I_2\left(x\right)\right)}{{\mathrm{T}\mathrm{E}}_2-{\mathrm{T}\mathrm{E}}_1}$$

where x is a voxel, I ₁ and I ₂ are the intensities in the reconstructions of the early and later echoes respectively, with echo times TE1 and TE2.

PREPROCESSING

Distortion Correction

Geometric distortion due to susceptibility [Hutton et al. [2002]) of the magnetic field is a common problem in EPI data. Several methods have been proposed for distortion correction. In this work, we applied a dynamic correction algorithm [Blazejewska et al., 2014] which is adapted from Lamberton et al. [2007]. This method uses two image echoes only for the initial step, after which it estimates the distortion field only by updating this with the phase map of the second echo. We adapted this method for moving datasets by applying distortion correction on each slice separately and by not performing temporal unwrapping of the phase image.

Volume and Slice Motion Correction

Following distortion correction, volume motion estimation was performed by registering all the volumes in the time series to the fourth volume [Studholme et al., 1999]. (The first three volumes were discarded to allow for signal stabilization.) Once the volumes had been aligned, a cascaded slice to volume approach [Seshamani et al., 2013a] was used to register slices to account for motion between slice acquisitions. For this, a target volume was generated by averaging a sequence of 10 volumes where the subject moved minimally. The slices in the entire fMRI sequence were then registered to this target volume by minimizing the sum of squared intensities. Slice motion estimates were updated with these values and then further refined by alternating between reconstruction with the current estimate, generation of a target volume from all volumes and then registration to the target volume.

EXPERIMENTAL RESULTS

Simulated Motion Data

Data generation

Ten frames from a stationary adult dataset (Dataset 2 described in the next section) were selected and averaged. These were replicated to generate a time series of 100 time points. A region of interest (ROI) was then manually selected as shown in Figure 6 and artificial block activation with effect size 1% was injected into this region (Fig. 6). This block activation would be in accordance with the typical signal change observed in a task‐based fMRI experiment. For each volume, Gaussian noise (stddev 2% of the signal), volume motion (stdev of 0.5d eg of rotation around the x axis [nodding]) and slice motion (stdev of 0.1 mm translation and 0.1 degrees rotation) were applied. We generated four datasets (Table 3), each using a different projection model. Figure 7 shows the motion parameters generated for each of these datasets. Note that the standard deviations listed above are for between slice motion, which therefore generates a realistic range of volume motion when it accumulates, as shown in the Figure 7. In addition, we also generated a ground truth dataset (G) with linear slice projection, Gaussian noise, and no motion.

Figure 6.

Top: Manually selected ROI where artificial block activation was injected in simulated adult datasets. Bottom: Average Time Series of injected activation. [Color figure can be viewed at http://wileyonlinelibrary.com.]

Table 3.

Description of four different simulated datasets used in experiments

Dataset	Simulation model
A	3D Linear slice projection
B	3D Gaussian slice projection
C	4D Linear slice projection
D	4D Gaussian slice projection

Figure 7.

From left to right: Simulated volume motion trajectories for datasets of datasets A, B, C, and D. Top row shows rotation parameters and bottom row shows translation parameters. The dominant motion is rotation around the x axis. [Color figure can be viewed at http://wileyonlinelibrary.com.]

Validation of reconstruction

We reconstructed each of four datasets using the motion parameters applied in the generation step, resulting in 16 different reconstructions. Spatial smoothing parameters in all Gaussian reconstructions used 7‐mm FWHM and the temporal smoothing parameter for the 4D Gaussian reconstruction was 3s FWHM. Preprocessing was applied to the ground truth and all reconstructions with the same parameters, except the ones generated with 4D Gaussian reconstruction.

Spatial smoothing was applied to the ground truth and reconstructions with linear slice projections. Temporal smoothing was applied to the reconstructions with 3D slice projections and the linear 4D projection as well. This then brought all four types of reconstruction to a form which could be analyzed and compared. A correlation map was created for the preprocessed ground truth and each reconstruction by computing the correlation between every pair of voxels within the ROI. The Euclidean distances between the correlation map of each reconstruction and that of the ground truth are reported in Table 4.

Table 4.

Distance between ground truth and estimated correlation maps

Dataset	Linear 3D Rec	Gaussian 3D Rec	Linear 4D Rec	Gaussian 4D Rec
A	0.002496	1.2744	11.424	1.275
B	0.26502	0.033344	19.924	0.033325
C	0.0011828	2.973	22.026	2.9743
D	2.025	0.059177	2.0251	0.058653

Bold values indicate the method the with the smallest distance measure.

For linear projections, the linear 3D reconstruction outperforms all the others

We also note that the 4D linear reconstructions are the worst in all cases by a large amount. This is due to the fact that the reconstruction carries out a linear interpolation in time and an additional temporal smoothing had to be applied to it be able to compare it with the other results. These results verify that using the appropriate model is crucial for reconstruction. However, it is important to note that the Gaussian model more closely matches the slice profile of real fMRI data. Experiments in the next section confirm this and further demonstrate the strength of the proposed method.

Real Data Experiments

Parameter selection with adult data

The slice time adjustment parameter—τ—is experimentally determined. For this, we use two different measures: DMN Correlation Distance and white matter (WM) Correlation. The DMN Correlation distance is a metric that measures the discrepancy between the DMN extracted on a ground truth reconstruction and the reconstruction in question. A smaller value indicates that the correlations in the reconstruction are closer to the pattern in the ground truth. The WM correlation gives a measure of how different the time series in the WM regions are from that extracted on the DMN. A good reconstruction would allow us to distinguish between the WM signal and the default mode signal and therefore a higher discrepancy value of WM correlation would indicate a better reconstruction. The computation of the two metrics are explained below:

• The DMN Correlation Distance is computed by first generating a 3D linear reconstruction on a stationary dataset and performing ICA analysis to automatically extract the default mode component. This component is then thresholded to generate an ROI. A correlation map that contains correlation values between every pair of voxels in the ROI using the 3D linear reconstruction is then computed. This gives the ground truth map (the currently accepted procedure for obtaining default mode on stationary adult data). For a 4D reconstruction, the same ROI is used to compute a correlation map and the Euclidean distance between this map and the ground truth map is the DMN Correlation distance. This metric gives a measure of how different the correlation values within the DMN are with a different type of reconstruction.

• For WM Correlation, WM ROIs are manually selected. The correlation of each of the time series of each of the voxels in the WM ROIs to the average time series within the default mode ROI (calculated above) is computed. The average value of all these correlations is reported as the WM Correlation. This metric gives a measure of how correlated WM voxels are to the DMN. A smaller value indicates less correlation of WM with the DMN, and a better reconstruction.

Given the volume and slice motion estimates, we carried out 4D Gaussian reconstructions on all adult datasets by varying the parameter τ from 10 to 90 in steps of 20. The 4D Gaussian reconstructions were carried out with FWHM of 7 mm for the spatial filter and FWHM of 3 s for the temporal filter (these are typical values used for fMRI preprocessing). We then extracted ICA components with fast ICA [Hyvarinen, 1999] directly from this data (since no further processing is required) and compared the components across the parameter range. Tables 5 and 6 show the measures computed.

Table 5.

Experiment for selection of τ

τ	Dataset 1	Dataset 2	Dataset 3	Dataset 4	Dataset 5
10	9.17	66.99	60.08	9.82	179.83
30	8.12	69.83	60.08	12.73	164.14
50	9.54	69.39	61.22	12.13	168.26
70	7.54	69.25	61.42	11.91	172.38
90	5.89	69.25	61.53	11.81	175.19

This parameter is used to weight the relationship of space and time in the 4D reconstruction. The table shows DMN correlation distance with varying τ parameter for adult datasets.

Table 6.

Experiment for τ parameter selection

τ	Dataset 1	Dataset 2	Dataset 3	Dataset 4	Dataset 5
10	0.41	0.46	0.44	0.18	0.17
30	0.38	0.50	0.48	0.20	0.20
50	0.47	0.51	0.49	0.20	0.20
70	0.43	0.52	0.50	0.20	0.21
90	0.36	0.52	0.50	0.20	0.21

This parameter is used to weight the relationship between space and time in the 4D reconstruction. This table shows WM correlation with varying τ parameter for adult datasets.

Summary of parameter selection

In general, we observed that WM Correlation increases with an increase in τ for most datasets. Hence, it is better to select a smaller τ value. However, no particular trend was observed with the DMN correlation distance. When comparing the DMN distance of τ = 10 and τ = 30, we observe that the DMN distance is greater for τ = 10 in two datasets, greater for τ = 30 on two datasets and the same for one dataset. However, we observed that the automatically extracted ICA components appear less noisy with τ = 30 compared to when τ = 10 on the moving data (Fig. 8). Hence, overall, we choose τ = 30 as the parameter for all the rest of our experiments.

Figure 8.

Comparing default mode and motor components in stationary and moving adults with varying tau. Top to bottom: adult dataset 1–5. Left: τ = 10, Right: τ = 30; Row 1 and Row 4 are stationary datasets. Rows 2, 3, and 5 are moving datasets. Components appear less noisy with τ = 30 compared to when τ = 10 on the moving data. [Color figure can be viewed at http://wileyonlinelibrary.com.]

DMN analysis

Adult data experiment.

We performed experiments to compare the results of 3D and 4D reconstructions on real adult data. For this, we used τ = 30 in all our experiments. Three types of reconstructions were carried out: 3D Linear, 3D Gaussian, and 4D Gaussian. In all three, we incorporated slice time weighting. The Gaussian reconstructions included a density adapted kernel selection. The 3D linear reconstruction was further smoothed spatially and temporally with FWHM of 7 mm for spatial filtering and FWHM of 3 s for temporal filtering. The 3D Gaussian reconstruction was smoothed temporally with FWHM of 3 s. The three were then ready for comparison.

ICA components were extracted from all three types of reconstructions for Datasets 1–5 as shown in Figure 9. For stationary datasets (Rows 1 and 4, Fig. 9), we did not observe much of a visual difference in the components across the reconstructions. For dataset 2 (second row, Fig. 9), we observed that the 3D linear reconstruction does not yield any default mode component and the 3D Gaussian reconstruction's result is also noisy compared to the 4D reconstruction's result. For dataset 3 (third row, Fig. 9), we observed that the 3D linear reconstruction yields a noisy component (observe the red area in the sagittal image) in comparison to the 4D reconstruction. The 4D component also covers a larger volume than the 3D Gaussian component, although those two are a little harder to distinguish. For Dataset 5 (fifth row, Fig. 9), the 3D linear reconstruction did not generate a very strong component. The 3D Gaussian and 4D Gaussian however both have a strong frontal component similar to that of the stationary dataset.

Figure 9.

Comparing ICA components extracted on real adult data using 3D simple, 3D Gaussian, and 4D Gaussian reconstructions for Datasets 1–5 (top to bottom). The components from the moving data were then compared to those of the stationary data resulting in DICE coefficients reported in Table VII. [Color figure can be viewed at http://wileyonlinelibrary.com.]

To further quantify these results, we compared the components of the moving subjects to the components of the stationary data. We created a binary image with the component from the stationary data for each subject and analogous component images for all the moving acquisitions, and then calculated the DICE coefficients [Dice, 1945] to determine the overlap of the components from stationary and moving acquisitions. Table 7 shows the DICE coefficients that have been calculated. We note that in all cases, the 4D reconstruction provides a better component than that extracted from the 3D linear reconstruction. In addition, the 4D reconstruction further improves or performs on par with the 3D Gaussian reconstruction depending on the dataset. Hence, we can clearly conclude that on real moving data, 4D Gaussian reconstruction is the best choice in these cases. One of the limitations of the current work is that a group analysis could not be performed in the adult subjects. This is due to the availability of limited amount of moving (through plane nodding) data that we could acquire.

Table 7.

Table showing DICE coefficients of ICA components extracted from moving data compared to ICA components extracted on stationary data

Acquisition	3D simple DICE coeff	3D Gaussian DICE coeff	4D DICE coeff
3T, Small Motion, Resting State	No Component	0.27	0.35
3T, Large Motion, Resting State	0.37	0.47	0.47
1.5T, Large Motion, Resting State	0.21	0.29	0.31

Fetal data experiments.

For the fetal subjects, we acquired dual echo data and generated R2* maps. For each subject, we generated 4D reconstructions of the early and later echo data. For the sake of comparison, we also generated 3D reconstructions [Ferrazzi et al., 2014; Seshamani et al., 2012] of the early and later echo data. For the space‐time weighting parameter, we used τ = 30 in all our experiments.

This gave us one R2* map corresponding to the 4D reconstruction and one R2* map corresponding to the 3D reconstruction. These R2* maps were preprocessed with spatial smoothing (FWHM = 9 mm) and temporal smoothing (5 s). To show the strength of R2* mapping, we first performed seed analysis on the subjects undergoing large motion (Subjects 7 and 8). We picked a seed in the PCC region of the fetal brain. Figure 10 shows the results on the two different subjects. The first column shows seed placement, the second column shows the seed correlation on the T2* weighted time series of the second echo (43 ms), the third column shows the seed correlation in the 3D reconstruction and the fourth column shows seed correlation in the 4D reconstruction. The artifacts appearing in the second column (T2*) do not appear in the R2* reconstructions in the third and fourth column which clearly shows that spin history artifacts have been addressed. The 4D reconstruction also has a larger region of correlation compared to the 3D reconstruction. In Subject 7, the prefrontal cortex area also shows higher correlation in the 4D reconstruction, compared to the 3D reconstruction.

Figure 10.

Seed analysis of Subjects 7 and 8. Columns left to right: seed placement, correlation analysis on T2* weighted image (echo at 43 ms), correlation analysis on 3D reconstruction, correlation analysis on 4D reconstruction\r\n. [Color figure can be viewed at http://wileyonlinelibrary.com.]

Single‐subject ICA analysis was then carried out on the 3D and 4D R2* maps and 11–20 components were extracted on all subjects. To ensure repeatability, ICA analysis was carried out multiple times by varying the number of components extracted. Components resembling the DMN were identified (manually) only if they appeared consistently 2 or more times (while varying the number of components). Figures 11 and 12 show the default mode components extracted on all fetal subjects. For each subject, the row on top shows the component extracted with the 3D reconstruction and the row in the middle shows the component extracted with the 4D reconstruction. In particular, we observe the DMN of most of the fetuses is more pronounced in the 4D result than the 3D case. In Subject 1, the prefrontal cortex appears in the 4D result whereas it does not appear at all in the 3D component. In Subject 2, the 4D component has a larger connectivity in the PCC and frontal area, and also presents some connectivity in the inferior parietal cortex. In Subjects 3 and 4, the 4D component has a larger connectivity in the PCC. In Subject 5, there is a small visibility of connectivity in the inferior parietal cortex in the 4D result, which is absent in the 3D component. In Subject 6, there is less noise in the 4D component (motor cortex) compared with the 3D component. However, both components show good connectivity of the PCC and parietal lobules. In Subject 7, there is better connectivity of the PCC and the 4D component appears less noisy as well. Finally in Subject 8, the PCC and parietal cortex show significantly better connectivity in the 4D component compared to the 3D component. In summary, all the 4D components are a significant visual improvement compared the 3D component for single subject analysis.

Figure 11.

Default mode components extracted on fetal subjects 1–4. For each subject, Top: ICA result on 3D reconstruction. Bottom: ICA result on 4D reconstruction. [Color figure can be viewed at http://wileyonlinelibrary.com.]

Figure 12.

Default mode components extracted on fetal subjects 5–8. For each subject, Top Row: ICA result on 3D reconstruction. Bottom: ICA result on 4D reconstruction. [Color figure can be viewed at http://wileyonlinelibrary.com.]

Following this, we carried out a group analysis using all eight subjects. To bring all subject anatomies to the same coordinate frame, we performed a deformable registration of the high resolution HASTE images between each subject and a reference subject (Fetal Subject 4). The 3D and 4D fMRI reconstructions of the individual subjects were then registered to the HASTE reconstructions of the respective subjects and then warped to the coordinate system of the reference subject using the deformations computed in the previous step. Group ICA analysis (no weighting) was then performed separately on the 3D and 4D datasets by applying spatial smoothing (9‐mm FWHM) and temporal smoothing (5 s FWHM) and voxels containing very high R2* values in the cortex (greater than 20) were thresholded out. Figure 13 shows the default mode component obtained after extracting 16 components on 3D (top row) and 4D (bottom row) reconstructions. We also visualize the component extracted on the 4D data on a raw fetal MRI slice of the reference subject by rendering the surface and superimposing the component and MRI slice at the midline in Figure 14.

Figure 13.

Default mode components extracted on group analysis of eight fetal subjects. Comparing 3D (upper row) and 4D (lower row) components. [Color figure can be viewed at http://wileyonlinelibrary.com.]

Figure 14.

Four‐dimensional group analysis component super imposed on a raw MR slice. [Color figure can be viewed at http://wileyonlinelibrary.com.]

Observe that the default mode component of the 3D reconstruction is not as pronounced as on the 4D reconstruction. Although there is activation in the pre‐frontal cortex, the component does not contain much of the posterior cingulate cortex or the medial lateral parietal lobes, which are present in the 4D component. This shows the strength of the proposed method even in the case of group analysis.

Finally, we quantify the quality of our reconstructions and extracted components from single subject analysis using our group analysis result. First, we compute DICE coefficients between each of the single subject components and the group component. This shows the discrepancy between each of the single subject components and the group result. Table 8 shows the values computed on components extracted from 3D and 4D reconstructions. We observe that in most cases, the DICE coeffeicient is greater in the 4D component case. This shows that there is greater overlap between the 4D single subject result and the group analysis. Next, we quantify our reconstructions using Temporal SNR (TSNR). The TSNR is commonly used in fMRI analysis for comparing the quality of datasets. A higher TSNR value implies a better reconstruction. The TSNR can be calculated within a certain region of the brain using masks. We first calculated TSNR values within DMN regions extracted using single subject analysis. These values are shown in Table 9 (Columns 2 and 5). Since these regions are not the same, we then generated masks using the whole brain and the group analysis result and evaluated the TSNR values in the 3D and 4D reconstructions. In all cases, we observe that the 4D reconstruction has higher TSNR values.

Table 8.

Table showing DICE coefficients of single subject ICA components of fetal subjects, compared with the group analysis ICA component obtained with 4D reconstruction (the 3D reconstruction group analysis did not produce an ICA component)

Fetal subject number	3D dice coefficient	4D dice coefficient
1	0.16	0.06
2	0.10	0.13
3	0.03	0.19
4	0.12	0.18
5	0.17	0.20
6	0.07	0.07
7	0.12	0.13
8	0.06	0.11

In most cases, there is a higher DICE coefficient (overlap) between the 4D component and the group result when compared to the 3D component.

Table 9.

Table showing TSNR values using different masks

Subject	3D single subject	3D full head	3D group	4D single subject	4D full head	4D group
1	4.55	4.82	4.28	5.40	6.44	5.94
2	5.33	7.00	7.40	19.01	19.02	18.04
3	5.06	4.84	4.68	16.61	15.43	14.23
4	4.19	4.25	3.94	6.41	6.76	7.33
5	4.81	5.01	4.71	21.30	21.99	21.42
6	5.57	6.49	5.87	22.42	30.90	27.76
7	4.47	4.55	3.91	14.46	15.19	13.51
8	3.88	4.06	3.88	11.13	11.60	10.37

The first three columns show the TSNR values computed on the 3D reconstruction. The last three columns show TSNR values computed on the 4D reconstruction. For single subject values, the mask used was the single subject component calculated using that reconstruction. For the full head values, the full head mask was used and for group values, the group analysis DMN extracted was used. For this computation, all subject heads were warped to the template subject's head. Note that the 4D reconstructions consistently have higher TSNR values.

DISCUSSION AND CONCLUSION

In this article, we have described an fMRI processing and analysis framework specifically designed for multiecho fetal brain studies where head motion cannot be controlled. The approach uniquely integrates full 4D iterative time series reconstruction with connectivity analysis, for motion scattered multislice fMRI acquisitions. The proposed method performs adaptive kernel selection, slice timing accommodation, and estimates a spatially and temporally smooth time series directly from the observed EPI slices. Quantitative MRI techniques are used to deal with spin history artifacts.

In terms of basic processing, this contributes advances in a number of areas. First, previous work on fMRI motion correction has used a direct 3D or 4D (noniterative) interpolation. The iterative optimization we use forms a robust and optimal estimate of MRI intensity changes from spatially and temporally neighboring EPI voxels. Second, this process also incorporates slice time correction and Gaussian smoothing into the reconstruction framework. Although slice time correction and smoothing have been incorporated into several existing packages, we for the first time incorporate it within a single 4D time series estimation, which also avoids the need for repeated interpolations. Third, within the time series estimation, we have specifically addressed the issue of weighting of measurements separated in time or space. Unlike Ferrazzi et al. [2014], who select a weighting factor arbitrarily, we make use of a parameter selection experiment with ICA analysis for choosing a suitable weighting for the type of data we are processing. And finally, within this framework we also develop a density‐adapted kernel selection scheme within the 4D iterative reconstruction to specifically handle motion induced changes in sample density.

As a basis for evaluation of the approach, we have presented quantitative results of reconstruction and analysis with these methods on moving adult data where activations are better understood. Our experimental analysis using synthetic motion trajectories and actual motion time series illustrates the effect of the approach on the final analysis. Note that these experiments were performed only on limited datasets due to the lack of publicly available datasets of adult resting state fMRI undergoing large through plane motion. Investigation of the effect of these methods on larger adult databases is an area for future work.

Finally, we have also shown functional connectivity results with default mode extraction for the first time from single subject fetal studies and group analysis on fetuses in an age range of 32–37 weeks. Our experiments demonstrate the strength of the methods and make a very strong case for their potential impact on resting state fetal studies.

One of the limitations of the work currently is that the R2* maps are first estimated at each acquired slice and used to reconstruct the 4D time series (with deconvolution) after between‐slice motion estimation. However, deconvolution of R2* maps can generate some instability since the R2* is a nonlinear function of the T2*‐weighted values and hence may have a much more complex point spread model. This problem can potentially be addressed by extension of methods as described in Seshamani et al. [2015], to the 4D problem. Another limitation of the current work is with the determination of the space time parameter τ. Since obtaining ground truth (knowledge of networks) on fetal datasets is challenging, we use a value for the parameter estimated on adult datasets directly on fetal datasets as well. However, this may not be the optimal choice and indeed the parameter selection might vary from dataset to dataset. This opens up some open questions as to what would be an ideal way to estimate this parameter and what information should be used to compute it. Experiments on late gestation fetuses with comparison after birth or with premature neonate data where DMN have been detected could be useful for this estimation. Another avenue for open problems is in uncertainty adapted analysis.

Future work entails incorporating distortion correction within the 4D reconstruction framework and incorporating the 4D reconstruction within the slice registration framework. From an experimental point of view, we are interested in algorithm testing on a large database of fetuses and exploring new methods for analysis of multislice scattered data using by‐products of the reconstruction framework. More experimental work to directly compare the R2* mapping method with direct intensity correction [Ferrazzi et al., 2014] can also provide more insight into the strengths and weaknesses of both approaches which have currently not been compared.