Volume and surface coil simultaneous reception (VSSR) method for intensity inhomogeneity correction in MRI

Abstract

BACKGROUND:

Addressing intensity inhomogeneity is critical in magnetic resonance imaging (MRI) because associated errors can adversely affect post-processing and quantitative analysis of images (i.e., segmentation, registration, etc.), as well as the accuracy of clinical diagnosis. Although several prior methods have been proposed to eliminate or correct intensity inhomogeneity, some significant disadvantages have remained, including alteration of tissue contrast, poor reliability and robustness of algorithms, and prolonged acquisition time.

OBJECTIVE:

In this study, we propose an intensity inhomogeneity correction method based on volume and surface coils simultaneous reception (VSSR).

METHODS:

The VSSR method comprises of two major steps: 1) simultaneous image acquisition from both volume and surface coils and 2) denoising of volume coil images and polynomial surface fitting of bias field. Extensive in vivo experiments were performed considering various anatomical structures, acquisition sequences, imaging resolutions, and orientations. In terms of correction performance, the proposed VSSR method was comparatively evaluated against several popular methods, including multiplicative intrinsic component optimization and improved nonparametric nonuniform intensity normalization bias correction methods.

RESULTS:

Experimental results show that VSSR is more robust and reliable and does not require prolonged acquisition time with the volume coil.

CONCLUSION:

The VSSR may be considered suitable for general implementation.

Keywords

Intensity inhomogeneity correction volume and surface coil simultaneously received magnetic resonance imaging

1. Introduction

In magnetic resonance (MR) images, the signal intensity of different portions of the same type of tissues should ideally be equivalent; however, in practice it tends to vary with the locations of tissues within an image. This adverse effect, referred to as intensity inhomogeneity, typically appears as a spurious smooth intensity variation across an image. Extensive studies indicate that MR image intensity inhomogeneity may be attributed to several factors, including 1) the inhomogeneous transmitted and received radiofrequency field (B1), 2) the bandwidth filtering of the received data, 3) uncompensated eddy currents from the gradient field, and the inherent properties of the imaged objects, that is, their shape, orientation, permeability, and dielectricity [1, 2, 3]. Intensity inhomogeneity is more severe in MR images acquired with surface coils because the surface coils suffer from serious received RF inhomogeneity with decreasing sensitivity as the distance from the coil increases [4]. Intensity inhomogeneity may significantly affect the post-processing and subsequent quantitative analysis of MR images, for example, when using a global threshold to segment a specific tissue or measuring proton concentration in proton density-weighted images [1, 2]. In addition, such issues may lead to the degradation of image quality, which then obstructs clinical diagnosis [3]. Therefore, procedures for the correction of intensity inhomogeneity are required in MR image analysis and post-processing.

Over the past several decades, many methods have been proposed to correct intensity inhomogeneity in MR images. Vovk provided a complete and detailed review of these methods and classified them as prospective and retrospective approaches [5]. The prospective approach is mainly performed through calibration and improvement of the image acquisition process or hardware [2, 6, 7, 8, 9, 10, 11, 12, 13], while the retrospective approach relies on the information of the acquired image and sometimes on prior knowledge [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]. The phantom-based approach estimates an intensity inhomogeneity field by acquiring an image of a uniform water or oil phantom with known properties, and then uses the obtained intensity inhomogeneity field to correct the surface coil image. One major limitation of this approach is that it cannot correct for patient-induced inhomogeneity. Additionally, phantom image profiles vary with the orientation and position of the phantom and coils. As a result, the residual intensity inhomogeneity of this approach can be as high as 30% [28], and it requires frequent phantom image acquisition. The multi-coil approach, first proposed by Lai [7], assumes that the intensity of the volume coil is inhomogeneous, so the intensity inhomogeneity field can be obtained by dividing the surface coil image by the volume coil image. One drawback of this method is the prolonged acquisition time, as both the surface coil and volume coil images are required for each acquisition. Moreover, the correction performance and robustness are limited by the accuracy of image registration between the surface and volume coils, which itself is a problem to be solved. The histogram-based method directly operates on the image intensity histogram without a priori knowledge of the intensity variation of the imaged objects; hence, it can be fully automated. Two well-known methods in this category include nonparametric nonuniform intensity normalization (N3), proposed in 1998, and N4 (an improved version of N3) proposed by Tustison in 2010. Experimental results show that these methods perform well in producing smooth intensity fields but often significantly alter the inherent inter-tissue contrast after correction. The filter-based method assumes that intensity inhomogeneity is a low-frequency artifact that can be separated from the spectrum of the image by the filter. The feasibility of the filter-based method is limited because this assumption is invalid when the anatomical structure spectrum and the intensity inhomogeneity spectrum overlap. In summary, all the existing intensity inhomogeneity correction methods present disadvantages to some extent, including alteration of tissue contrast, poor reliability and robustness, and prolonged acquisition time.

In this study, we propose a new volume and surface coil simultaneous reception (VSSR)-based approach for intensity inhomogeneity correction for MR images. The magnetic resonance imaging (MRI) device hardware was modified such that the receiving chain was able to simultaneously acquire signals from both the volume and surface coils. This method was could reduce the prolonged scan time due to separate acquisition of the volume coil image and eliminate the registration process, improving the robustness of the algorithm. Because the volume coil image must be acquired simultaneously with the surface coil image high spatial resolution, it has a low signal-to-noise ratio (SNR). To overcome this disadvantage, different methods have been used to properly denoise the volume coil image, from which the bias field can be calculated and used to correct the intensity inhomogeneity of the surface coil image. The performance of the proposed VSSR method was extensively evaluated on MR images with different anatomies, acquisition sequences, imaging resolutions, and orientations. The results indicate that, compared with the most popular multiplicative intrinsic component optimization (MICO) [18] and N4ITK methods [29], VSSR is more robust and reliable, and it does not require prolonged acquisition time; therefore, it is more suitable for clinical implementation as compared to MICO.

2. Materials and methods

The acquired intensity-inhomogeneous surface coil image $v(x,y)$ can be generally modeled as

$\displaystyle v(x,y)=u(x,y)\times b(x,y)+n(x,y),$ (1)

where $u(x,y)$ represents the inhomogeneity-free image, $b(x,y)$ is the bias field that can be assumed to be a smooth and slowly changing multiplicative field, and $n(x,y)$ is the background noise. Because the surface coil image has a high SNR, the noise background $n(x,y)$ can be ignored, and the model may be further simplified as

$\displaystyle v(x,y)=u(x,y)\times b(x,y)$ (2)

The key to intensity inhomogeneity correction is to calculate the bias field $b(x,y)$ so that an inhomogeneity-free image $u(x,y)$ can be recovered from $v(x,y)$ . For MR images, the volume-coil image in general is much more homogenous and can be taken as a bias-free image that represent the actual inter-tissue contrast. Therefore, the values of the bias field can be calculated at selected locations by directly dividing the surface coil image by the volume coil image acquired at the same position and with the same imaging parameters. For any continuous bounded two-dimensional inhomogeneous intensity field $b(x,y)$ , a curved surface can be fitted with a finite polynomial function, as defined by Eq. (3).

$\displaystyle b(x,y)=\sum_{i=0}^{m}\sum_{j=0}^{n}a_{i}b_{j}x^{i}y^{j}=\omega^{% T}G(x,y),$ (3)

Figure 1.

Denoising of volume coil image to improve SNR. The first, second and third image respectively represent volume coil image, NL-means denoised, and BM4D denoised.

Figure 2.

Process of the proposed VSSR method.

where $G(x,y)$ and $\omega^{T}$ represent the basis functions and the coefficients of the basis function, respectively, for fitting the bias field. A fourth-order polynomial fitting was chosen to approximate $b(x,y)$ , i.e., $m=$ 4, $n=$ 4, after substituting the fitting precision and calculation time. Equation (4)–(6) show the forms of $X$ , $Y$ , and $\omega^{T}$ , respectively.

$\displaystyle X=(x^{0}\ \ x^{1}\ \ x^{2}\ \ x^{3}\ \ x^{4}),$ (4)

$\displaystyle\omega^{T}=\left(\begin{array}[]{ccccc}a_{0}b_{0}&a_{1}b_{0}&a_{2% }b_{0}&a_{3}b_{0}&a_{4}b_{0}\\ a_{0}b_{0}&a_{1}b_{1}&a_{2}b_{1}&a_{3}b_{1}&0\\ a_{0}b_{2}&a_{1}b_{2}&a_{2}b_{2}&0&0\\ a_{0}b_{3}&a_{1}b_{3}&0&0&0\\ a_{0}b_{4}&0&0&0&0\\ \end{array}\right)$ (5)

$\displaystyle Y=(y^{0}\ \ y^{1}\ \ y^{2}\ \ y^{3}\ \ y^{4}).$ (6)

The proposed VSSR method requires simultaneous image acquisition from the volume and surface coils. This can guarantee that both images are obtained exactly at the same position and with the same imaging parameters; therefore, no image registration and fusion is required. However, this may be expected to result in a very lowSNR volume coil image because this image must be acquired at the same spatial resolution as the surface coil. The low-SNR volume coil image cannot be used directly to fit the bias field because the noise would severely affect the fitting accuracy. Instead, the volume coil image must be denoised first to improve the SNR. We compared several denoising algorithms, including BM4D [30] and NL-means [31]. As shown in Fig. 1, BM4D was selected as having a better SNR improvement. Because background noise also tends to have some additional effects on the fitting accuracy of the bias field, a mask is used so that only the bias field in the target area is fitted. Figure 2 schematically illustrates the process of the proposed VSSR method.

Figure 3 shows the flow diagram of our VSSR algorithm, and the key steps can be sequentially summarized as follows:

•

Acquire the volume coil and surface coil images simultaneously in a single scan.

•

Use the BM4D algorithm to denoise the volume coil image for SNR improvement.

•

Make a mask based on the volume coil image and retain the target image area only.

•

Divide the surface coil image $v(x,y)$ by the denoised volume coil image $u(x,y)$ to obtain the values of the bias field at discrete locations.

Figure 3.

Flowchart of the proposed VSSR intensity inhomogeneity correction algorithm.

•

Apply the polynomial fitting method to approximate the bias field function $b(x,y)$ .

•

Finally, correct the acquired surface coil image by dividing by the bias field function.

3. Results

A commercial 1.5T MR scanner with 16 parallel receiving channels, made by Alltech Medical Systems LLC (Chengdu, China), was slightly modified in terms of coil selection and coil bias control to enable simultaneous image acquisition from the volume and surface coils. For the head images, eight channels from the head-only coil and two channels from the volume coil were selected. For abdominal images, eight channels from the abdominal coil, six channels from the spinal coil, and two channels from the volume coil were selected for simultaneous reception. Image reconstruction and data processing for the proposed VSSR method were performed using MATLAB 2015b on a Mac computer (2.2 GHz 6-Core Intel Core i7 processor with 16 GB 2400 MHz DDR4 RAM).

We first compared the required acquisition time between the proposed VSSR method and the traditional MICO algorithm, which requires two separate scans for one high-resolution surface coil image and one low-resolution volume coil image as a reference. According to Table 1, The time saved by the VSSR method is more than one-third of the total scan time of the MICO algorithm.

Table 1
Scan time for a typical high-resolution surface coil image and low-resolution volume coil image required for MICO algorithms

	TR (ms)	TE (ms)	Slice	Resolution (mm ${}^{2}$ )	Scan time (ms)
T1 GRE (gradient echo sequence)	273	5.2	20	1 $\times$ 1	72
Ref	–			2 $\times$ 2	37
T2 FSE	5716	95	20	1 $\times$ 1	108
Ref	–			2 $\times$ 2	62

${}^{1}$ FSE: Fast spin echo.

Figure 4 shows a typical result of T2 fast spin echo (FSE) images corrected successfully by the proposed VSSR method. It is clearly observed that the corrected images appear much more homogenous, especially near the center of the brain, and the inter-tissue contrast was well maintained among the gray matter, white matter, cerebrospinal fluid, fat, etc. The correction performance was consistently satisfactory at different slice locations. We also compared our method with the MICO algorithm. As shown in Fig. 5, the MICO algorithm introduced some undesirable artifacts, while the VSSR approach was able to make good corrections.

Figure 4.

Correction of T2 FSE images using the proposed VSSR method. Row a: volume coil image; row b: surface coil image; row c: images corrected by VSSR method. Each column represents images at different slice locations.

Figure 5.

Comparison of the VSSR and MICO algorithm. Rows a and b show the results of the VSSR and MICO algorithms, respectively, for head and abdomen images.

Figure 6.

Intensity inhomogeneity correction of the head MR image with different contrast and orientations at a resolution of 1 mm $\times$ 1 mm. Row a: volume coil images; row b: Surface coil images; row c: VSSR corrected images; row d: MICO corrected images; row e: N4ITK corrected images; column I: T1 GRE Sagittal; column II: T1 GRE Axial; column III: T1 GRE Coronal; column IV: T2 FSE Sagittal; column V: T2 FSE Axial; VI: T2 FSE Coronal.

Figure 7.

Intensity inhomogeneity correction of head MR images with different contrasts and orientations at a resolution of 2 mm $\times$ 2 mm.

Figure 8.

Intensity inhomogeneity correction of the abdomen images with different contrast, orientation, and resolutions. Row a: volume coil image; row b: Surface coil image; row c: VSSR corrected images; row d: MICO corrected images; row e: N4ITK corrected. Column I: T1 GRE In-Phase, Axial, 1.5 mm $\times$ 1.8 mm resolution; Column II: T1 GRE Out-Phase, Axial, 1.5 mm $\times$ 1.8 mm resolution; Column III: T1 GRE, Axial, resolution: 1.8 mm $\times$ 1.5 mm; IV Column: T2 Balanced SSFP, Coronal, 1.2 mm $\times$ 1.2 mm resolution; Column V: T2 Double Shot FSE, Axial, 1.2 mm $\times$ 1.2 mm resolution; VI: T2 FSE with fat saturation, 1.2 mm $\times$ 1.2 mm resolution.

The intensity inhomogeneity bias field changes with different imaging orientations, resolutions, and acquisition sequences. To verify the reliability and limitations of the proposed algorithm, extensive in vivo experiments were performed, and the correction performance was evaluated thoroughly against the wisely used MICO and N4TIK algorithms. As shown in Figs 6–9, the experimental results indicate that the VSSR method was more efficient and robust. For example, the MICO algorithm was effective in the correction of high-resolution MR images of the head but not for images of the abdomen, which are difficult to segment (Fig. 8. (d, VI), and Fig. 9. (d, VI)). The N4ITK algorithm exhibited an acceptable performance when correcting head images but not abdominal images.

Figure 9.

Intensity inhomogeneity correction of the abdomen images with different contrast, different orientation, and different resolutions. Row a: volume coil image; row b: Surface coil image; row c: VSSR corrected images; row d: MICO corrected images; row e: N4ITK corrected. Column I: T1 GRE In-Phase, Axial, 2.0 mm $\times$ 1.8 mm resolution; Column II: T1 GRE Out-Phase, Axial, 2.0 mm $\times$ 1.8 mm resolution; Column III: T1 GRE, Axial, 2.2 mm $\times$ 1.7 mm resolution; Column IV: T2 Balanced SSFP, Coronal, 2.5 mm $\times$ 2.0 mm resolution; column V: T2 Double Shot FSE, Axial, 1.5 mm $\times$ 1.5 mm resolution; VI: T2 FSE with fat saturation, 1.5 mm $\times$ 1.5 mm resolution.

Figure 10.

MSSIM values of corrected images by VSSR, MICO, and N4TIK, respectively. Coordinate figure a.-f represent the head images and coordinate figure g.-l. the abdomen images. Coordinate fig. a: T1 GRE, Axial, 1 mm $\times$ 1 mm resolution; coordinate fig. b: T1 GRE, Coronal, 1 mm $\times$ 1 mm resolution; coordinate fig. c: T1 GRE, Sagittal, 1 mm $\times$ 1 mm resolution; coordinate fig. d: T2 FSE, Axial, 1 mm $\times$ 1 mm resolution; coordinate fig. e: T2 FSE, Coronal, 1 mm $\times$ 1 mm resolution; coordinate fig. f: T2 FSE, Sagittal, 1 mm $\times$ 1 mm resolution; coordinate fig. g: T1 In-Phase, Axial, 1.5 mm $\times$ 1.8 mm, resolution; coordinate fig. h: T1 Out-Phase, Axial, 1.5 mm $\times$ 1.8 mm resolution; coordinate fig. i: T1 GRE Axial, 1.8 mm $\times$ 1.5 mm resolution; coordinate fig. j: T2 Balanced SSFP, Coronal, 2.0 mm $\times$ 1.5 mm resolution; coordinate fig. k: T2 Double Shot FSE, Axial, 1.2 mm $\times$ 1.2 mm resolution; coordinate fig. l: T2 FSE Fat Saturation, Axial, 1.2 mm $\times$ 1.2 mm.

One critical merit of the proposed intensity inhomogeneity correction method is that it retains the inherent inter-tissue contrast after correction. For a quantitative evaluation, the mean structural similarity (MSSIM) index, as defined below, is used:

$\displaystyle\textit{MSSIM}\left({s,b}\right)=\frac{1}{M}\sum_{i=0}^{M}\frac{% \left({2\mu_{s}\mu_{b}+C_{1}}\right)\left({2\sigma_{sb}+C_{2}}\right)}{\left({% \mu_{s}^{2}+\mu_{b}^{2}+C_{1}}\right)\left({\sigma_{s}^{2}+\sigma_{b}^{2}+C_{2% }}\right)},$ (7)

where $s$ is the corrected image; $b$ is the ground-truth image; $\mu_{s}$ , $\mu_{b}$ , $\sigma_{s}$ , and $\sigma_{b}$ are the mean of the corrected image, the mean of the standard image, the standard deviation of the standard image, and the standard deviation of the corrected image, respectively; $\sigma_{sb}$ is the covariance of the standard image and the corrected image; $M$ is the number of local windows; and $C_{1}$ and $C_{2}$ are constants. The closer the MSSIM index is to 1, the better the inter-tissue contrast is retained [32]. Here, we consider the volume coil image as the ground truth image with inherent inter-tissue contrast. This is true if the intensity inhomogeneity due to the imaged object itself, i.e., shape, orientation, permeability, and dielectric properties, can be ignored. As shown in Fig. 10, compared with MICO and N4TIK, the proposed VSSR method has an MSSIM closer to 1 and, more importantly, a much smaller standard deviation. Thus, VSSR was able to better retain the inherent inter-tissue contrast after intensity correction and was more robust to varying anatomical areas, imaging orientations, resolutions, and acquisition sequences.

4. Discussion and conclusion

In this study, we proposed an improved intensity inhomogeneity correction method based on the simultaneous acquisition of volume and surface coil images. This method has considerable advantages of relatively shorter acquisition time for additional volume coil images, and it avoids the need for tedious and erroneous image registration and fusion between the volume coil and surface coil images. The results of extensive in vivo experiments demonstrate that the proposed VSSR method is more effective and robust than existing algorithms. The correction performance of the proposed method was consistently satisfactory for different anatomical regions, imaging orientations, resolutions, and acquisition sequences. Images corrected using the VSSR method were able to better retain the inherent contrast between tissues. However, the VSSR method is not without limitations. As is, it cannot correct intensity inhomogeneity caused by characteristics of the imaged object itself, such as its shape, orientation, position within the magnetic field, and its specific magnetic permeability and dielectric properties. However, the impact of the imaged object is rather small at the magnetic field strength of most clinical MR scanners.

Footnotes

Acknowledgments

This work was supported by the Sichuan Science and Technology Program under Grant 2019YJ0181; the Sichuan Province Academic and Technical Leader Training Funded Projects under Grant 13XSJS002; the National Key Research and Development Program of China under Grants 2016YFC0100800 and 2016YFC0100802; the Foundation of Ph.D. Scientific Research of Neijiang Normal University under Grant 18B19; the China Postdoctoral Science Foundation funded under Grant 2020M683294; and the Sichuan applied psychology research center of Chengdu Medical College Funded Projects under Grant CSXL-21103.

Conflict of interest

The authors declare no conflict of interest.

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