Image homogenization using pre-emphasis method for high field MRI

Introduction

High field (≥3T) magnetic resonance imaging (MRI) has been increasingly used to improve image resolution, imaging speed, signal-to-noise ratio (SNR) (1) and blood-oxygen-level dependence (BOLD) contrast in functional MRI (2,3). However, high static field strength, corresponding to high resonance frequency, reduces the wavelength of the electromagnetic field which is produced by radiofrequency (RF) coils to the order of the dimension of biological samples such as human body and head (4). The shortened wavelength leads to increased phase variation of the RF field in the subjects. Thus the high frequency interference effect (or high frequency wave behavior), related to the electromagnetic properties of the imaging subjects, causes RF field perturbation and decreases the field homogeneity from the intrinsic B₁ field of unloaded RF coils (5), particularly for ultrahigh field MRI (6-9).

Various methods have been proposed to alleviate RF field inhomogeneity effects, including utilizing high permittivity padding (10-12) or multiple absorbing layers (13), tailored pulses (14,15) and parallel transmit methods. By using transmit/receive arrays (16,17), the current amplitudes and phases of each transmit element are capable to be adjusted individually to achieve homogenous transmit field (18-22). In addition, the RF pulses in each element can be modified for spatially-selective excitation (23-25) in the transmit sense frame work (26-28).

Studies also show that the intrinsic B₁ distribution of microstrip transmission line (MTL) volume coils can be used to compensate for the high frequency wave behavior in high permittivity samples at high fields (29-36). In this work, a novel method to improve image homogeneity based on pre-emphasis method was proposed. The possibility of using pre-emphasized intrinsic B₁ fields to address the image inhomogeneity issue in conductive and high dielectric biological samples, such as human body, at high fields was investigated. In the study, the intrinsic RF field distribution of the MTL coil was pre-emphasized in the sample’s periphery region of interest to compensate for the central brightness of high permittivity samples induced by the high frequency interference effect. Uniform images at high fields can be achieved by using appropriately pre-emphasized B₁ fields generated from a MTL volume coil. Numerical simulations using the finite difference time domain (FDTD) method (32,37-41) were performed to investigate the image homogeneity change due to the distribution of the intrinsic B₁, and also to demonstrate MTL volume coils’ capability of generating different B₁ patterns by changing the dielectric substrate thickness of the coils. Phantom experiments were carried out to verify the simulation results and the feasibility of proposed method to alleviate the high field image inhomogeneity problems.

Methods

Pre-emphasis method

Due to the high frequency interference effect, the RF volume coils provide higher B₁ in the central region of human head compared with the periphery region. Therefore, a RF volume coil with homogeneous intrinsic B₁ distribution leads to inhomogeneous image when the coil is loaded. Previous work shows the intrinsic B₁ field pattern of MTL coil can be manipulated by changing the microstrip element parameters (16,29,30,33,36,42,43), such as copper width and substrate thickness. Generally MTL volume coils with thinner substrate thickness provide higher intrinsic B₁ in the periphery region than central region. By using this effect, the B₁ in periphery region can be pre-emphasized to compensate central enhancement caused by high frequency interference effect. Therefore the substrate thickness can be optimized to provide uniform loaded B₁ distribution and ultimately achieve homogenous brain images.

Numerical simulation

In order to optimize the element parameters of the MTL coil to achieve homogeneous signal intensity distribution in the solution phantom, B₁ field distribution of 16-element MTL volume coils (25.4 cm of inner diameter and 21 cm of length) with different substrate thickness were investigated. The thickness of substrate of the MTL coil varied from 3 to 21 mm. The phantom used in this work was a 15 cm diameter sphere (58.255 of relative permittivity and 0.4915 S/m of conductivity) for mimicking the human brain load at 4T. All MTL coils with different thickness of substrate were tuned to 170 MHz, corresponding to the proton resonance frequency at 4T, and driven linearly. The unloaded and loaded B₁ field distributions of MTL coils were numerically simulated by FDTD method. In this work, Yee cell size was 1.5 mm in x and y direction, and 5 mm in z direction. Region of interest (ROI), 36 cm × 36 cm × 41 cm, was divided into 4,723,200 Yee cells. The time step was set to 3.46 picoseconds. The convergence criterion was set to –35 dB. The 7-layer perfect matching layer (PML) was used for the outer boundary truncation of the grid. The homogeneity of the B₁ field was quantified to evaluate the homogeneity improvement of the proposed pre-emphasis method. The B₁ homogeneity was defined as

%

[1]

in which the B_1max and B_1min were the maximum and minimum magnitude of B₁ within the ROI, respectively. Based on the simulation results, signal intensity images were calculated as shown in Supplementary material to evaluate image homogeneity. In defining appropriate distribution of pre-emphasized B₁ fields in order to obtain uniform images of high dielectric and conductive samples, the transmit B₁ field or B₁+ should be the metric to be used. Since the distribution of B₁- and B₁+ have a similar distribution at 170 MHz range (unlike that at 300 MHz or higher), to be simple, the MR image intensity uniformity was used to determine the appropriate pre-emphasized B₁.

In practice, it would be costly and time-consuming to build a large number of volume coils with different substrate thickness so that different B₁ patterns can be obtained and evaluated. However, it is known that given an intrinsic B₁ distribution of a RF coil, the B₁ distribution in a high dielectric sample (or image distribution) varies with the ion concentration (or conductivity) and dielectric constant of the sample. Therefore, to investigate the possibility of B₁ shimming using the pre-emphasis method at high fields, an equivalent method is to investigate the possibility of a MTL volume coil with pre-emphasized intrinsic B₁ pattern to achieve uniform images in a phantom at certain ion concentration. Based on this method, a 16-element MTL volume coil with the same dimension as mentioned above was modeled. The widths of the strip conductors of the MTL resonant elements were 2.54 cm while the substrate thickness was 0.6 cm. Copper was modeled as a conductor with conductivity of 5.95×10⁷ S/m. The MTL coil was linearly driven by a voltage source. The phantoms were modeled as a 15 cm diameter sphere with dielectric properties of five different amounts of NaCl, 50, 80, 100, 115 and 125 mM respectively. The electromagnetic properties of the phantoms were interpolated from the published experimental measurements (8,11). The resonant frequencies of the coils were found by using a Gaussian excitation and a Fourier transform of the time domain response and tuned to 170 MHz. The tuning was performed with the phantom loaded to ensure that interactions between the coil and load, which can alter the coil’s frequency response, were taken into consideration.

Phantom MRI experiment

A 16-element MTL volume coil with the same dimension (6 mm substrate thickness, 25.4 cm of inner diameter and 21 cm of length) as the simulation setup was fabricated. The widths of the strip conductors of the MTL resonant elements were 2.54 cm. The MTL coil was tuned and matched at 170 MHz. MRI experiments were carried out in a Varian 4T MRI scanner with five phantoms containing different amount of NaCl (50, 80, 100, 115 and 125 mM) respectively.

The MRI experiments were conducted on a 4T/90 cm human MRI scanner (Magnex Scientific, UK) interfaced to the Varian INOVA console (Varian Associates, Palo Alto, California). Noticed that the T1 of water proton at 4T is ~1.4 seconds, gradient echo sequence with small flip angle (~11 degree) and long repetition time (TR =5 s) was used to reduce the signal saturation effect. Echo time (TE) used was 3.2 ms. The phantom images were then compared with calculated signal intensity images to verify the simulation results.

Results

Numerical simulation

The 1D profiles of B₁ field distribution on the central transverse plane of unloaded MTL coils with different substrate thickness were shown in Figure 1. The maximum B₁ field magnitude of each profile was normalized to 1. As shown in Figure 1, the intrinsic B₁ homogeneity gradually increases with the substrate thickness increasing. Within the central transverse plane, the B₁ field magnitude variation over distance of 15 cm are 20.3% for MTL coil with 3 mm substrate thickness, while it is 14.7% for MTL coil with 21 mm substrate thickness.

Figure 1 Simulated intrinsic B₁ field distributions in the transverse direction for unloaded MTL coils with substrate thickness from 3 to 21 mm. The maximum B₁ field magnitudes of all coils are normalized to 1. Arbitrary unit (a.u.) is used to show the relative values of B₁ field

The 1D profiles of B₁ filed distribution on the central transverse plane of loaded MTL coils with different substrate thickness were shown in Figure 2. The maximum B₁ field within each spherical phantom was normalized to 1 as well. Compared with unloaded case in Figure 1, the high frequency interference effect is obvious and it can be compensated by the pre-emphasized intrinsic B₁ field of unload MTL coils. As shown in Figure 2, the homogeneity of B₁ field can be improved by decreasing the substrate thickness of MTL coils from 21 to 4.5 mm. When the substrate thickness of MTL coils decreased from 4.5 to 3 mm, the homogeneity of B₁ field decreased. The optimized B₁ homogeneity increased to 98% when the substrate thickness was 4.5 mm. The simulation results indicated that the MTL coil with 4.5 mm substrate provides optimized B₁ field distribution with the loaded phantom in terms of homogeneity. Figure 3A illustrated the pre-emphasized intrinsic (or unloaded) B₁ field pattern of the MTL coil with 4.5 mm thick substrate. Figure 3B was calculated MRI signal intensity of the spherical phantom in the MTL coil. The results indicated that relatively uniform image of the spherical phantom can be achieved by pre-emphasizing the intrinsic B₁ field in the periphery region of the phantom.

Figure 2 Simulated B₁ field distributions in the transverse direction for loaded MTL coils with substrate thickness from 3 to 21 mm. The maximum B₁ field magnitudes of all coils are normalized to 1

Figure 3 Intrinsic B₁ field pattern (A) of the MTL coil with thickness of 4.5 mm and calculated SI image (B) of the phantom with the coil

For the MTL volume coil with 0.6 cm substrate thickness, the simulated signal intensity (SI) images of five saline phantoms, which contain 50, 80, 100, 115 and 125 mM NaCl respectively, were calculated and scaled to the same input power as shown in Figure 4. The high frequency interference effect was evident in the phantom with 50 mM NaCl. With increasing NaCl concentration, the high frequency interference effect on MRI decreased. Relatively homogeneous signal intensity distribution can be obtained in the phantom with 125 mM NaCl. The 1D profile at the center line and homogeneity of each SI image was illustrated in Figure 5A,B respectively, which showed that the homogeneity of SI distribution was improved with the NaCl concentration increasing. The absolute B₁ values and transmit power were also evaluated, as shown in Table 1. There is less than 10% difference of the coil efficiency among different substrate thickness. Furthermore, the achievable field strength and SNR in the center will not decrease while the peripheral field is emphasized in this case. In other words, the stronger emphasis on peripheral fields is not at the expense of the achievable field strength and SNR in the center. The simulation results indicated for a given MTL volume coil configuration, uniform SI distribution could be achieved in certain phantom with appropriate dielectric properties within a desired range. Considering all of the simulation results, the optimal relationship between load and substrate thickness was possible for improving the image homogeneity, which demonstrated the feasibility of the pre-emphasis concept.

Table 1 Absolute B₁ values and transmit power
Full Table

Figure 4 Calculated signal intensity images of phantoms with different NaCl concentrations (axial). Top insert shows their 1D profile of each image. Relatively uniform image distribution can be achieved at 125 mm. This result demonstrates that with a given pre-emphasized B₁ field, improved uniformity of images can be possibly obtained at high fields

Figure 5 A. 1D profiles of the signal intensity; B. image homogeneity within phantoms with different NaCl concentrations

Phantom MRI experiment

In order to validate the simulation results, MRI phantom experiments were performed at 4T. Figure 6 shows the phantom (15 cm diameter) images of the NaCl solution with different concentrations acquired using the MTL volume coil (30). When the concentration of NaCl increased to 125 mM, relatively homogeneous image was obtained. The good agreement between experimental results in Figure 6 and simulation results in Figure 4 demonstrated the accuracy of the calculation method and the feasibility of the proposed method. Subtle differences between experiment and simulation were probably induced by the slight electromagnetic property difference between the simulation model and saline phantom.

Figure 6 Phantoms images of the phantom filled with NaCl solution with different concentrations acquired using the MTL volume coil. Top insert shows their 1D profile along the middle line of each image. This imaging experiment verifies the simulation results shown in Figure 4

Conclusions

This study demonstrates that image inhomogeneity in conductive, high permittivity samples (e.g., human body) caused by high frequency interference effect or high frequency wave behavior at high magnetic fields can be corrected using appropriately pre-emphasized B₁ fields generated by a RF volume coil. With the proposed pre-emphasis method, relatively uniform MR images can be achieved as shown in both the numerical simulations and the MR imaging experiments. The required pre-emphasized B₁ fields may not be readily realized in regular volume coils, e.g., birdcage coils. The unique structure of microstrip transmission line volume coils provides the possibility and flexibility for generating and also optimizing the pre-emphasized B₁ field distribution by changing the thickness of their dielectric substrates. There are different approaches to changing the B₁ field distributions of a volume coil. In this study, we change B₁ field distribution by varying the dielectric substrate thickness, as an example, to demonstrate the image homogeneity at high fields can be improved by using the pre-emphasis method. This study also suggests that at high magnetic fields, uniform intrinsic (or unloaded) B₁ fields will not necessarily give uniform images of conductive, high permittivity samples such as human bodies.

A common approach to parallel imaging acquisitions in humans at high fields is to use a multi-channel coil array for signal reception and a conventional volume coil for spin excitation, particularly in the case where the body coil is not available. Apparently, this setup has no capacity of parallel excitation for performing B₁ shimming (16,26,27,44-46) in order to achieve uniform images. Usually images acquired by using this method are fairly inhomogeneous unless an intensity correction post-processing is applied at the expense of SNR degradation. With the use of a volume excitation coil with the pre-emphasis method proposed in this work, more uniform images in such parallel acquisitions can be expected.

Acknowledgements

This work was partially supported by NIH grants EB004453, EB008699, NS070839 and P41 EB013598, a QB3 Research Award, and a Springer Med Fund Award.

Disclosure: The authors declare no conflict of interest.

Supplementary Material

In this work, the B₁ field distribution with and without load was numerically simulated by using FDTD method (47), which calculated electrical and magnetic fields in samples by solving time-dependent Maxwell’s curl equations in time domain. All FDTD calculations were performed with a commercially available software package XFDTD (Remcom, Inc., State College, PA), whereas the post-processing of the electromagnetic field data for calculating circularly-polarized component of the B1 field, and mapping signal intensity distribution were performed by using MATLAB (MathWorks, Inc., Natick, MA) program.

To minimize the errors caused by stair stepping, the Yee cells, which are the basic elements of 3D meshes in FDTD method, should be chosen small enough to characterize the structure of the coils. Based on the Courant stability condition (48), the time step should satisfy the requirement as:

[S1]

where Δt and c are time step and light speed in free space respectively. Δx, Δy, Δz are Yee cell side dimensions.

The positive () and negative () circularly polarized magnetic field component were calculated by the principle of reciprocity (49).

[S2]

[S3]

where and are complex magnitude of the x- and y-oriented RF magnetic fields created by the coil, i is the imaginary unit, the asterisk denotes a complex conjugate. The rotation direction of is assumed as the same as the spin.

For a rectangular pulse, the flip angle of the nuclear magnetization can be represented as

[S4]

where γ is the gyromagnetic ratio and τ is the pulse duration. The factor V is proportional to coil driving voltage in a given experiment (32). The magnitude of the signal induced by the spins in the voxel is proportional to the magnitude of at that point when the coil is driven by unit voltage (50). Then the signal intensity (SI) is calculated as

[S5]

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