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The authors have declared that no competing interests exist.

Conceived and designed the experiments: LY XZ. Performed the experiments: QY. Analyzed the data: XL. Wrote the paper: XL XZ.

Real-time functional magnetic resonance imaging (rtfMRI) is a recently emerged technique that demands fast data processing within a single repetition time (TR), such as a TR of 2 seconds. Data preprocessing in rtfMRI has rarely involved spatial normalization, which can not be accomplished in a short time period. However, spatial normalization may be critical for accurate functional localization in a stereotactic space and is an essential procedure for some emerging applications of rtfMRI. In this study, we introduced an online spatial normalization method that adopts a novel affine registration (AFR) procedure based on principal axes registration (PA) and Gauss-Newton optimization (GN) using the self-adaptive β parameter, termed PA-GN(β) AFR and nonlinear registration (NLR) based on discrete cosine transform (DCT). In AFR, PA provides an appropriate initial estimate of GN to induce the rapid convergence of GN. In addition, the β parameter, which relies on the change rate of cost function, is employed to self-adaptively adjust the iteration step of GN. The accuracy and performance of PA-GN(β) AFR were confirmed using both simulation and real data and compared with the traditional AFR. The appropriate cutoff frequency of the DCT basis function in NLR was determined to balance the accuracy and calculation load of the online spatial normalization. Finally, the validity of the online spatial normalization method was further demonstrated by brain activation in the rtfMRI data.

Real-time functional magnetic resonance imaging (rtfMRI) is a recently emerged technique that permits the online observation of brain activity during recording. This technique is essential for a variety of applications, such as neurofeedback, in which subjects are trained to self-regulate the local blood oxygen level dependent (BOLD) response in specific brain areas to improve their behavioral performance

In offline fMRI applications, spatial normalization is usually used as a standard procedure when an accurate identification of specific functional regions is needed. In many rtfMRI applications, such as the clinical brain operation

Some commomly used offline spatial normalization methods generally cannot be accomplished in a single TR on a current typical personal computer. One such method

To take advantage of regional localization in stereotactic space, a few studies have attempted to apply spatial normalization in rtfMRI

Based on these findings, we advanced the offline spatial normalization method in SPM8 and implemented an online spatial normalization method that can be accomplished in a time interval shorter than a TR (such as 2 s). This method consists of procedures of affine registration (AFR) and nonlinear registration (NLR)

Real data were acquired from a finger tapping run in an rtfMRI experiment, which consisted of eight on-going runs

Brain scans was performed at the MRI Center of Beijing Normal University using a 3.0-T Siemens MRI scanner. A single-shot T2*-weighted gradient-echo, echo-planar imaging (EPI) sequence (TR/TE/flip angle = 2000 ms/40 ms/90°, matrix size = 64×64, voxel size = 3.1×3.1×4.8 mm^{3}, slice thickness = 4 mm, slice gap = 0.8 mm) was used to acquire each image with 32 axial slices in the interleaved order. The subjects’ heads were cushioned to reduce their head movements.

Affine registration (AFR) is normally the first step of spatial normalization (^{(0)}; at the ^{(n)} is updated according to the following rule

The image registration includes affine registration (AFR) and nonlinear registration (NLR), which are used to estimate the optimal normalization parameters. The image transformation is then used to transform the source images to a stereotactic space using the estimated parameters; tri-linear interpolation is used in this study. The PA-GN(β) AFR method is advanced based on traditional AFR, in which the PA provides a better initial estimate for GN with the self-adaptive β parameter for the iteration step adjustment.

In spatial normalization, the AFR from a random individual image space to a standard stereotactic space is relatively complex; this makes GN a tedious iterative process, particularly when meeting an inappropriate initial estimate

At first, images _{i}_{i}_{i}_{i}_{i}_{f} = (_{c}_{c}_{c}_{f} is calculated using Equation (3a)

where

Three eigenvectors of _{f} are the principal axes: _{x}_{11} _{21} _{31}]^{T}, _{y}_{12} _{22} _{32}]^{T}, _{z}_{13} _{23} _{33}]^{T}; these axes lie closest to the _{f} = [_{x}_{y}_{z}_{g} and eigenvector matrix _{g} of image _{i}

The parameter vector derived from the matrix _{PA} is the optimized initial estimate, ^{(0)}, for GN.

In addition to the initial estimate, the iteration step has a large effect on the convergence speed of GN. In a previous GN(α) method ^{(n)} is β at the ^{(n)} of the cost function CF^{(n)} reaches the following condition:

^{(n)}. If the cost function changes rapidly (e.g., at the beginning of the iteration), ^{(n)} is defined as follows:^{(n)} might be undesirable for the Wolfe conditions. To ensure that β^{(n)} adaptively adjusts

Following AFR, the nonlinear registration (NLR) procedure is often used to reduce the gross shape differences that are not accounted for by linear deformation (^{−2} same as the condition of

The number _{x}_{y}_{z}_{c}_{c}_{c}

Using the bisection method, the value of _{c}_{c}_{c}

The assessment consisted of two steps and was performed on a personal computer with an Intel Core CPU (Intel(R) Core(TM) i7-3770 CPU @ 3.4 GHz). First, compared with traditional AFR, the accuracy and runtime of the proposed PA-GN(β) AFR were validated in both simulation and real data. As described in _{max(1,2)}, the matrix correlation coefficient between two transformation matrices _{1} and _{2}, and MSE were used to compare the difference between the traditional AFR and PA-GN(β) AFR. The D_{max(1,2)} was defined as follows:_{i,}_{1}, _{i,}_{2} were the resampled positions of voxel _{1} and _{2}, respectively. In addition, the convergence rate and iteration number were used to further assess the performance of PA-GN(β) AFR.

The source image (

Given Parameters | Traditional AFR | PA-GN(β) AFR | ||

x | 10 | 10.0223107±0.0179137 | 10.0223111±0.0179141 | |

y | −12 | −12.0034754±0.0124250 | −12.0034757±0.0124249 | |

z | −15 | −15.0874369±0.0374636 | −15.0874362±0.0374632 | |

x | 10 | 10.0064315±0.0184493 | 10.0064331±0.0184481 | |

y | −20 | −20.0298397±0.0251481 | −20.0298423±0.0251474 | |

z | 30 | 29.9833938±0.0308602 | 29.9833950±0.0308604 | |

x | 1.1 | 1.0995272±0.0001853 | 1.0995272±0.0001853 | |

y | 1.2 | 1.1985918±0.0003134 | 1.1985918±0.0003134 | |

z | 0.9 | 0.9039135±0.0005948 | 0.9039135±0.0005948 | |

x | −0.01 | −0.0097952±0.0003445 | −0.0097952±0.0003445 | |

y | −0.02 | −0.0188380±0.0005639 | −0.0188380±0.0005639 | |

z | 0.03 | 0.0293605±0.0003499 | 0.0293604±0.0003499 | |

_{max(r,e)}/mm |
0.1547590±0.0204909 | 0.1547565±0.0204910 | ||

0.9999961±0.0000026 | 0.9999961±0.0000026 | |||

0.0090348±0.0013417 | 0.0090348±0.0013418 | |||

0.4337496±0.0381319 | 0.3318283±0.0153614 |

Second, after integrating PA-GN(β) AFR and NLR with an appropriate _{c}_{0} was the number of activation voxels using offline spatial normalization and _{1} was the number of co-activation voxels by online and offline spatial normalization. The activation center _{i}_{i}

The AFR parameters estimated using traditional AFR and PA-GN(β) AFR, which fitted the image ^{−5} (_{max(r,e)}) between the referenced matrix _{r}), which consisted of the given parameters, and the matrix (_{e}), which consisted of the parameters estimated using traditional AFR or PA-GN(β) AFR, was much less than a voxel size (3.1×3.1×4.8 mm^{3}) for both AFR methods. In addition, the correlation coefficients of _{r} with _{e} derived from the two AFR methods were both almost 1 (

The mean cost function change with the number of iterations across subjects showed the convergence rate of the optimization process using GN with or without different modifications (

(A) AFR without improvements; (B) AFR with β parameter only; (C) AFR with PA only; (D) PA-GN(β) AFR. The mean iteration number using the traditional AFR was 14.05±1.24, while that using the PA-GN(β) AFR was 9.50±0.50¸ which is approximately two-thirds of the traditional AFR requirement. Each dot represented a subject in the right figure, and there were fourteen dots overlapping with the six dots, as shown.

In real data, the first image was affine registered to the EPI template of SPM8, in which the AFR parameters were also estimated using both PA-GN(β) AFR and the traditional AFR. The maximum distance (D_{max}) between the matrices estimated using traditional AFR and PA-GN(β) AFR was 0.1317±0.2293 mm, which was much less than one voxel size, while the matrix correlation coefficient of the two matrices was 0.99995±0.00014. Before AFR, the MSE between the first image of real data and the EPI template was 0.7301±0.0701. After traditional AFR, the MSE was reduced to 0.2851±0.0148, and after PA-GN(β) AFR, the MSE was reduced to 0.2854±0.0152. A paired

(A) AFR without improvements; (B) AFR with the β parameter only; (C) AFR with PA only; (D) PA-GN(β) AFR. The mean iteration number using the traditional AFR was 15.75±1.58, while that using the PA-GN(β) AFR was 8.60±1.07, which is approximately 50% of the traditional AFR requirement. Each dot represented a subject in the right figure, and there were six dots overlapping with the fourteen dots, as shown.

After PA-GN(β) AFR, NLR with different _{c}_{c}_{c}_{c}_{c}_{c}_{c}_{c}_{c}

L_{c}/mm |
Accurary | Runtime (sec.) | ||

MSE |
Image registration | Image transformation | Total | |

0.2626±0.0135 | 2.0520±0.2475 | 0.0827±0.0083 | 2.1347±0.2453 | |

0.2641±0.0135 | 1.2733±0.1126 | 0.0801±0.0066 | 1.3534±0.1149 | |

0.2656±0.0136 | 1.0376±0.0860 | 0.0794±0.0064 | 1.1171±0.0850 | |

0.2667±0.0138 | 1.0046±0.1038 | 0.0803±0.0067 | 1.0849±0.1040 | |

0.2716±0.0143 | 0.8598±0.0705 | 0.0789±0.0054 | 0.9387±0.0734 |

Comparison of the individual activation maps using online and offline spatial normalization showed no significant differences across subjects (paired ^{3}) and were predominantly less than 2 mm.

There were slight differences, such as the areas indicated in the blue circles, but no significant differences were observed between the activation patterns.

ROI | AAL Atlas | Activation Coverage Rate | Activation Center Distance | ||

Rate (%) | Subject Number | Distance/mm | Subject Number | ||

94.56±4.51 | 18/20 | 0.6986±0.6425 | 18/20 | ||

95.94±4.05 | 18/20 | 0.4884±0.2586 | 20/20 | ||

96.85±3.04 | 18/20 | 0.4554±0.3155 | 20/20 | ||

91.95±9.22 | 16/20 | 0.7167±0.3644 | 20/20 | ||

97.67±1.36 | 20/20 | 0.3660±0.3238 | 20/20 | ||

95.88±4.84 | 18/20 | 0.6867±0.5081 | 20/20 | ||

96.86±3.79 | 19/20 | 0.1821±0.1705 | 20/20 |

The proposed online spatial normalization significantly improved the performance of traditional AFR using PA and the self-adaptive β parameter, while the accuracy was maintained the same as with the traditional AFR. In addition, the proposed method provided a reasonable way to determine the appropriate cutoff frequency of the DCT basis function in NLR. Overall, the proposed method completed within one TR and reached the runtime requirement of rtfMRI on the current typical personal computer, while its accuracy was relatively close to the offline spatial normalization method.

The PA, which has coarse but global properties, is a rigid registration method based on the shape and intensity of the entire brain image. Without a suitable initial estimate, the GN method would require a large number of iterations and might not reach the global optimum

The self-adaptive β parameter can improve the performance of GN while maintaining stability and accuracy. The β parameter, which is dependent on the change rate of cost function, could achieve the same effect as the α parameter

As a real-time algorithm in rtfMRI, the proposed method can also avoid the negative effect of inter-run motion on the accuracy of the normalized images and ROI position. During the rtfMRI experiment, which commonly consists of a series of runs and may last a long time, it is impossible for the subject to keep his head immobile; the inter-run motion thus accumulates and sometimes cannot be ignored in the continuous runs (

The images were obtained from one subject’s first image in each of eight on-going runs of an rtfMRI experiment, which lasted approximately 90 mins.

Online spatial normalization can be valuable for investigations and applications of rtfMRI, but some details need to be specified and improved when applying it in rtfMRI. In each run, the images are normally aligned to the first image by head motion correction before the normalization, which makes the rigid differences between these realigned images relatively small. Thus, both AFR and NLR can be only performed for the first image in each run. Then using the estimated parameters, the image transformation is performed to normalize the subsequent images in the same run, which have been realigned to the first image prior to spatial normalization. In addition, considering the DCT basis functions are lack of physical meaning with respect to inter-subject anatomical variability, other alternative NLR method with lower computational loads could be used for online spatial normalization. The improvement on NLR methods needs further investigations.