Introduction
Dynamic contrastenhanced magnetic resonance imaging (DCEMRI) is a common method for evaluating tumor response to therapy in a variety of cancers (1–3), including breast (4, 5). DCEMRI acquires images before, during, and after injection of a contrast agent to characterize, for example, tumorrelated perfusion. To perform a quantitative analysis of DCEMRI data, knowledge of the precontrast longitudinal relaxation time (T_{1}) is required to convert the measured dynamic signal intensity into a time course of the concentration of the contrast agent (6). A popular technique used to measure the precontrast T_{1} is the variable flip angle (VFA) approach, which uses a series of spoiled gradient echo (SPGE) images acquired with a short, fixed repetition time (TR) and a varying flip angle (7, 8). The resulting data are then fit to the signal intensity equation describing the SPGE acquisition with T_{1} as a fit parameter for each voxel or region of interest (ROI). Although this technique allows for rapid 3dimensional (3D) T_{1} mapping, it is not without limitations, chief of which is that its accuracy is dependent on the uniformity of the transmit radiofrequency (B_{1}) field. It should be noted that other T_{1} mapping methods exist that are less sensitive to variations in the transmit field (9); however, VFA sequences are the preferred method in the clinical setting, as these acquisitions enable a large field of view (FOV) to be measured in a relatively short period.
Inhomogeneities in the B_{1} field cause variations in the prescribed flip angles, leading to inaccurate measurements of T_{1}, which can subsequently induce large errors in the DCEMRI parameters (eg, the volume transfer rate constant, K^{trans}) (10). Indeed, simulation results indicated that errors in K^{trans} ranged from 15% to 500% as the error in the T_{1} measurement ranged from 14% to 65% of the nominal value (11). Therefore, an inaccurate estimation of the precontrast T_{1} could potentially lower the sensitivity of DCEMRI for characterizing tumor vascular properties, thereby limiting the utility of the technique.
The B_{1} field experienced by spins within the body is influenced by several factors, including the distance of the spins from the radiofrequency transmit coil, the dielectric properties of the tissues, and the factors related to body size and wavelength of the radiofrequency (12). The severity of the nonuniformity in the B_{1} field increases at higher field strengths (13), and noticeable B_{1} inhomogeneities have been observed in the breast at 3 T (14–17). In particular, a substantial variation in the B_{1} field from left to right across the imaging FOV has been observed, which may artificially decrease the contrast enhancement in specific lesions (18). Thus, Kuhl et al. have suggested that B_{1} mapping in the breast should be a standard practice (14). Although several different methods for B_{1} mapping have been developed (12, 19–22), no single method has emerged for widespread application.
A technique using the Bloch–Siegert shift to map the B_{1} field has recently been developed, and it is an area of active investigation (23–26). The Bloch–Siegert shift is a term used to describe the shift in resonance frequency of a nucleus when an offresonance radiofrequency field is applied (27). Although Sacolick et al. (24) provide the details, the salient information is mentioned here. If a radiofrequency pulse is applied either far enough offresonance and/or with a pulse shape such that it does not cause spin excitation, the spins experience a change in precession frequency without excitation (28). The spin precession frequency shifts away from the offresonance irradiation and is dependent on the magnitude of the B_{1} field, as well as the difference between the spin resonance frequency and radiofrequency field. The shift in frequency results in a phase shift in the images that can be used to spatially map the B_{1} magnitude. This phasebased method generates a B_{1} map that is not significantly biased by TR, T_{1} relaxation, flip angle, chemical shift, background field inhomogeneity, or magnetization transfer (24). The insensitivity to TR is especially important in a clinical setting, as it allows for the prompt acquisition of image data with a short TR. In the current study, we present an approach to rapidly, accurately, and precisely map B_{1} and T_{1} values in the breast using the Bloch–Siegert method with a VFA sequence.
Methodology
All imaging data were acquired with a 3 T Achieva magnetic resonance scanner (Philips Healthcare, Best, The Netherlands) equipped with a 2channel multitransmit body coil and a MammoTrak table including a 16channel receive doublebreast coil (Philips Healthcare, Best, The Netherlands).
Phantom Scans
To investigate the feasibility of the approach, 8 gel phantoms (The Eurospin II Test System, Diagnostic Sonar, Livingston, Scotland, UK) submerged in water were scanned at room temperature. The T_{1} values of the phantoms ranged from 300 to 1600 milliseconds. A coronal image volume was placed in the center of the breast coil containing the phantoms, and VFA, Bloch–Siegert, and inversion recovery (IR) data were collected. VFA data with 10 flip angles (2, 4, 6, . . . 20) were acquired using a 3D SPGE sequence with the following parameters: TR/echo time (TE) = 7.9/4.6 milliseconds, sensitivity encoding parallel imaging factor of 2, acquisition matrix of 192 × 192 over a FOV of 256 × 256 mm^{2}, yielding a voxel size of 1.33 × 1.33 mm^{2}, and 15 slices with a thickness of 4 mm for a total scan time of 66 seconds. The Bloch–Siegert data were collected using a gradient echo sequence with a 2millisecond frequencyswept B_{1} phase imparting pulse (25) over the same FOV as the VFA data with the following parameters: TR/TE = 491/5.4 millisecond, acquisition matrix of 104 × 102, reconstruction voxel size of 1.33 × 1.33 mm^{2}, and root mean square B_{1} field = 2.29 μT for a total scan time of 104 seconds. As is required with the Bloch–Siegert B_{1} mapping, 2 images were collected at opposite frequency offsets. As a gold standard, a 2dimensional IRprepared turbospin echo (IRTSE) sequence was used to acquire a single slice corresponding to the center of the VFA image volume with the following parameters: 12 inversion times of 25, 50, 75, 100, 200, 300, 400, 500, 1000, 2000, 4000, and 10 000 milliseconds, acquisition matrix of 128 × 96 over an FOV of 256 × 256 mm^{2}, reconstruction voxel size of 1.33 × 1.33 mm^{2}, predelay before inversion pulse of 2500 milliseconds, and TSE factor of 24 with an echo spacing of 5.9 milliseconds for a total scan time of 125 seconds.
Subject Scans
Test–retest MRI sessions were performed on 16 women (median: 42 years, range: 25–67) with no history of breast disease. Because of age, body habitus, or hormonal status, 4 of these women did not have appreciable fibroglandular tissue (FGT) in either breast; thus, measurements for these women included data only from the adipose tissue (AT). The imaging protocol consisted of 2 scan sessions each lasting ∼30 minutes separated by a 10minute rest period. During the rest period, the subjects were removed from the scanner and allowed to stretch. All subjects were consented as part of an ongoing study approved by the local Institutional Review Board.
For each test–retest session, 2 separate sagittal imaging volumes were centered on each breast with an attempt to approximately match the stack placement between each imaging session. Subsequent VFA, Bloch–Siegert, and IR data were then collected separately for each breast. The imaging parameters for each sequence were identical to the phantom scans, except that the slice thickness was 5 mm and the number of slices for the VFA and Bloch–Siegert sequences was 10. These 2 parameters were changed to match our ongoing clinical imaging trial (29). In addition, we applied the T_{1} and Bloch–Siegert B_{1} mapping methods described herein on 3 patients with breast cancer. Each patient provided written consent to participate in the study.
Image Analysis
All image data were exported to MATLAB R2013b (The MathWorks, Natick, Massachusetts) for analysis. Bloch–Siegert B_{1} maps were calculated as described previously (25). In brief, the actual flip angle at each image voxel was obtained via linear interpolation of the entries of a phase differenceversusB_{1} strength lookup table generated using Bloch equation simulations of the offresonant Bloch–Siegert pulse. The flip angle correction map was then calculated as the ratio of the actual flip angle to the prescribed flip angle.
VFA T_{1} maps with and without B_{1} correction were obtained by fitting signal intensity (S) data to equation 1 as follows:
where
S_{0} is a constant related to scanner gain and proton density, α is the prescribed flip angle, and
f is the Bloch–Siegertderived flip angle correction factor (set to 1 for the uncorrected
T_{1} map), and we have taken TE ≪
T_{2}*. In addition,
T_{1} maps were calculated by fitting the IRTSE data (
30) to equation 2 as follows:
For the phantom scans, circular ROIs were manually drawn within each gel phantom using the IR data as a guide. The average T_{1} from each phantom was recorded from the IR T_{1} map. The same ROIs were then subsequently used to calculate the average T_{1} from the central slice of the VFAderived T_{1} maps with and without B_{1} correction. Statistical analyses were performed on the average T_{1} values calculated from each ROI. To evaluate the accuracy of the proposed B_{1} mapping technique, the percent error (%err) between the IR and VFAderived T_{1} values (with and without B_{1} correction) was calculated.
For healthy volunteers, segmentation masks for AT were automatically generated from the IR data (inversion times = 500 milliseconds), where the signal intensity for the FGT was close to 0. A representative example of the segmentation masks for each tissue is presented in Supplemental Figure 3. FGT segmentation masks were subsequently generated as the opposite of the AT mask after manually segmenting the skin and chest wall from the FOV. The average T_{1} from each tissue segmentation mask was recorded from the IR T_{1} maps for each breast and imaging session. The same tissue masks were then used to calculate the average T_{1} from the central slice of the VFAderived T_{1} maps (with and without B_{1} correction). The %err between the VFAderived T_{1} values (with and without B_{1} correction) and the IR T_{1} values was calculated to evaluate the accuracy, and the agreement between the different T_{1} values was assessed via the concordance correlation coefficient (CCC). Furthermore, the bootstrap 95% confidence interval (CI) of the mean differences in absolute deviation between IR and VFAderived T_{1} values (with and without B_{1} correction) was computed as previously described (31) using equation 3 as follows:
where
VFA and
VFA_{B1} are VFAderived
T_{1} values without and with
B_{1} correction, respectively. Equation 3 is first computed with all
T_{1} values (ie, 2 scan sessions per subject equals 32 and 26
T_{1} values for AT and FGT, respectively, in each breast). Next, the
n ×
m matrix of data is randomly resampled with replacement from the original data set (such that data from a subject(s) could be included more than once) and then equation 3 is recomputed. In the AT case, for example, the
m ×
n matrix size is 16 × 2, as there are 16 patients with 2 data points each. This process is repeated 1000 times, generating a new matrix of
m ×
n data points, which are then used to calculate the upper and lower bounds of the bootstrap 95% CIs. The number of data points
n is the total number of subjects.
To illustrate the application of the T_{1} and B_{1} mapping techniques described herein, manual ROIs were drawn in the AT, FGT (if appreciable), and tumor of 3 patients with breast cancer. Average T_{1} from each ROI was calculated, and the %err between the VFAderived T_{1} values (with and without B_{1} correction) and the IR T_{1} values was compared.
Reproducibility Statistics
Reproducibility statistics used in this test–retest study follow the methods previously described by Bland and Altman (32) and are similar to what was previously implemented in the breast of healthy volunteers (33, 34). First, the difference, d, was calculated between the 2 VFA T_{1} data sets obtained for each subject and then the distribution of those differences was tested for normality using the Shapiro–Wilk test. The Kendall's Tau test was used to ensure that the magnitude of the difference values was not correlated with the parameter mean of the repeated measurements. The Wilcoxon signedrank test was used to test the null hypothesis of no bias (ie, average difference is 0) between repeated measurements.
The statistical measurements of reproducibility were calculated as follows:
(1) The rootmeansquare deviation (rMSD) is computed using the differences, d, as follows:
(2) The 95% CI for a group of n subjects is shown as follows:
where std(d) is the standard deviation of d. The confidence interval indicates the range of expected measurement variability in a group of n subjects.
(3) The withinsubject standard deviation (wSD) is as follows:
(4) The repeatability coefficient (r) is shown as follows:
Or, equivalently, as follows:
The repeatability coefficient defines the magnitude of the maximum difference expected in 95% of paired observations; for example, r defines the expected measurement variability for an individual. Because of our moderate sample sizes, we replaced 1.96 in equation 5 with the appropriate tstatistic for our sample size, which was 2.131 (n = 16) and 2.179 (n = 13) for AT and FGT, respectively.
Statistical analyses were performed using the statistical toolbox in MATLAB^{®}. A significance value of P ≤ .05 was used for all statistical tests. In addition, we quantified the coefficient of variation (CV) between the repeated measurements, which is the ratio of the standard deviation of the repeated measurements over the mean of the repeated measurements.
Results
Gel Phantoms
A set of image data for the gel phantom experiment is displayed in Figure 1. The Bloch–Siegert B_{1} map is displayed in Figure 1A, where each voxel represents the Bloch–Siegertderived flip angle correction factor (ie, ratio of the actual flip angle to the nominal flip angle) that is incorporated into equation 1. T_{1} parametric maps generated from the IR, uncorrected VFA, and B_{1}corrected VFA data are displayed in panels B, C, and D, respectively, of Figure 1. The mean (±standard deviation) T_{1} value for each gel phantom ROI, along with the %err from the IR data, is listed in Table 1. Compared with the uncorrected VFA data, the B_{1}corrected VFAderived T_{1} estimates have a significantly lower %err (P = .016, Wilcoxon signedrank).
Figure 1.
A Bloch–Siegert B_{1} map (A) with T_{1} parametric maps calculated from inversion recovery (IR) (B) and uncorrected variable flip angle (VFA) (C), and B_{1}corrected VFA data (D) are shown for the gel phantoms. The Bloch–Siegert B_{1} map shown is the correction factor, which is the ratio of the actual and nominal flip angles. Note the large spatial variation across the B_{1} map; this variation is a representation of the B_{1} inhomogeneity across the imaging field of view (FOV). After B_{1} correction, the VFAderived T_{1} values (D) are more similar to the IR T_{1} values (B) in each gel phantom.
Table 1.
Average ± Standard T_{1} (milliseconds) Values and %err in the Gel Phantoms
Tube No. 
IR 
VFA w/o B_{1}

%err 
VFA w/B_{1}

%err 
1 
322 ± 25 
364 ± 14 
13 
319 ± 8 
1 
2 
328 ± 37 
401 ± 10 
22 
331 ± 9 
1 
3 
835 ± 37 
889 ± 39 
7 
816 ± 20 
2 
4 
843 ± 39 
963 ± 40 
14 
822 ± 22 
3 
5 
1004 ± 51 
1160 ± 21 
15 
940 ± 43 
6 
6 
1478 ± 54 
1573 ± 59 
6 
1357 ± 56 
8 
7 
1500 ± 19 
1412 ± 64 
6 
1454 ± 87 
3 
8 
1558 ± 22 
1727 ± 62 
8 
1558 ± 50 
3 
In Vivo Scans
A representative set of image data is displayed for the right breast of 1 subject in Figure 2. (Identical data for the left breast in the same subject are displayed in Supplemental Figure 1.) The Bloch–Siegert B_{1} maps from both scans are displayed in Figure 2, A and E, where each voxel displays the Bloch–Siegertderived flip angle correction factor. Also shown, are test–retest T_{1} parametric maps generated from the IR (panels B and F), uncorrected VFA (panels C and G), and B_{1}corrected VFA (panels D and H) data. Average T_{1} values from each tissue ROI and T_{1} mapping technique are tabulated for the right and left breast from each subject in Supplemental Tables 1 and 2, respectively.
Figure 2.
A representative test–retest set of B_{1} and T_{1} parametric maps displayed for the right breast of a healthy volunteer. Bloch–Siegert B_{1} maps (A and E) correspond to the correction between the actual and the nominal flip angles. Note the spatial variation of the correction factors in the B_{1} maps and the difference in B_{1} maps between repeated scans; together, these images provide evidence that a B_{1} map should be incorporated into routine breast imaging if a quantitative analysis of the collected data is desired. T_{1} parametric maps include: IR maps (B and F), uncorrected VFA maps (C and G), and B_{1}corrected VFA maps (D and H). The spatial variations in T_{1} of the FGT are minimized after B_{1} correction, and the T_{1} map more closely matches the IR T_{1} map. Furthermore, the B_{1}corrected T_{1} maps are visually more similar between repeated measurements compared with the uncorrected data. Observe how the orientation is slightly different between repeated scans, which might negatively affect the T_{1} reproducibility, as the same tissue sections from each scan might not be analyzed.
Table 2 lists the accuracy results for each ROI and breast. In the right breast, %err in the FGT using the VFA method significantly (P < .001, Wilcoxon signedrank) decreased from 17.0% to 8.6% and the CCC increased from 0.55 to 0.83 after B_{1} correction. Similar trends in accuracy were observed in the AT (Table 2). Bootstrap 95% CIs for FGT and AT were 57.8–139 milliseconds and 17.2–42.2 milliseconds, respectively. The range of CIs for each tissue includes all positive numbers, and by referring to equation 3, it can be seen that the absolute difference from the gold standard IR T_{1} is smaller after B_{1} correction for both tissue ROIs. In the left breast, %err in the FGT using the VFA method significantly (P = .002, Wilcoxon signedrank) decreased from 15.0% to 8.7% and the CCC increased from 0.60 to 0.83 after B_{1} correction. Similar trends in accuracy were observed in the AT (Table 2). The bootstrap 95% CIs for FGT and AT were 35.8–104.8 milliseconds and 2.4–26.7 milliseconds, respectively; again, both values for each CI were positive, indicating that the absolute difference from gold standard IR T_{1} is smaller after B_{1} correction for both ROIs.
Table 2.
Accuracy Results for Both Breasts and ROI

Right Breast

Left Breast

%err (Std) 
CCC 
%err 
CCC 
Adipose Tissue





VFA 
13% (9.7%) 
0.26 
13% (11%) 
0.29 
VFA w/B_{1}

6.2% (4.8%) 
0.59 
9.4% (7.3%) 
0.5 
Fibroglandular Tissue




VFA 
17% (9.1%) 
0.55 
15% (11%) 
0.6 
VFA w/B_{1}

8.6% (7.4%) 
0.83 
8.7% (5.5%) 
0.83 
As a proof of principle, the T_{1} and B_{1} mapping methods were applied in 3 patients with breast cancer. Figure 3 displays T_{1} parametric maps for all 3 patients generated from IR (left column), uncorrected VFA (center column), and B_{1}corrected VFA (right column) data. From these images, it can be seen that the B_{1}corrected T_{1} values in the tumors more closely match the IR T_{1} values. This similarity is extremely important, as accurate T_{1} values are required when performing a quantitative DCEMRI analysis. The mean (±standard deviation) T_{1} value for each tissue ROI, along with the %err from the IR data, is listed in Table 3 for each patient with breast cancer. Compared with the uncorrected VFA data, the B_{1}corrected VFAderived T_{1} estimates have, on average, a lower %err. Combining all tissue ROIs for each imaging technique, a significantly lower %err was observed after B_{1} correction (P = .004, Wilcoxon signedrank).
Figure 3.
As a proof of principle, the B_{1} and T_{1} methods presented in this article were performed on 3 patients with breast cancer; each patient was a subject enrolled in our ongoing breast imaging clinical trial (29). T_{1} parametric maps are shown for IR (left center column), uncorrected VFA (right center column), and B_{1}corrected VFA (right column) data collected from each patient (shown in rows). The tumors are shown with red arrows in each image. Compared with the uncorrected VFA data, the B_{1}corrected VFA T_{1} values of the FGT, AT, and tumor in all 3 patients are more similar to the IR T_{1} values, thus suggesting a more accurate T_{1} value in each tissue after B_{1} correction. Note that circular regions in the breasts that have a lack of signal intensity are due to the presence of a breast biopsy clip.
Table 3.
Average ± Standard T_{1} (milliseconds) Values and %err from ROIs in Patients with Breast Cancer
Patient 
ROI 
IR 
VFA w/o B_{1}

%err 
VFA w/B_{1}

%err 
1 
Tumor 
1364 ± 292 
1682 ± 330 
23 
1514 ± 269 
11 
AT 
411 ± 10 
470 ± 48 
14 
384 ± 36 
7 
FGT 
1391 ± 336 
1807 ± 215 
30 
1383 ± 164 
1 
2 
Tumor 
1374 ± 376 
2104 ± 267 
53 
1721 ± 209 
25 
AT 
397 ± 10 
439 ± 34 
11 
409 ± 33 
3 
FGT 
1493 ± 224 
1725 ± 99 
16 
1578 ± 79 
6 
3 
Tumor 
1101 ± 345 
1275 ± 381 
16 
1151 ± 344 
5 
AT 
407 ± 7 
465 ± 45 
14 
415 ± 41 
2 
FGT 
1471 ± 319 
2036 ± 343 
38 
1594 ± 271 
8 
Reproducibility
Reproducibility statistics for each tissue are listed in Table 4 and Supplemental Table 3 for the right and left breast, respectively. Normality was assumed for each data set as determined by the Shapiro–Wilk test. No data sets had an average difference significantly different from 0 as determined by the Wilcoxon signedrank test. In addition, the Kendall's Tau test showed that the difference between repeat measurements d was independent of the mean for each ROI.
Table 4.
Reproducibility Results for the Right Breast

Mean 
Mean Difference 
95% CI for Mean Difference 
wSD 
Repeatability 
CV (Mean ± SD) 
Adipose Tissue






VFA 
429 
40 
±28 (6.5%) 
38 
104 
6.7% ± 6.1% 
VFA w/B_{1}

418 
19 
±14 (3.3%) 
18 
48 
3.2% ± 3.0% 
Fibroglandular Tissue






VFA 
1316 
106 
±94 (7.1%) 
100 
276 
4.7% ± 4.9% 
VFA w/B_{1}

1256 
49 
±38 (3.0%) 
40 
111 
2.6% ± 1.5% 
Bland–Altman plots for each tissue ROI are displayed in Figure 4 and Supplemental Figure 2 for the right and left breast, respectively. Each panel displays the difference in T_{1} between the repeated scans against the mean T_{1} from both scans. The mean difference and 95% CIs of the mean difference are displayed as black and blue lines, respectively. The 95% CIs of the mean difference, which define expected measurement variability for a cohort of subjects, decreased after B_{1} correction. For the right breast, the 95% CI of the mean difference of the AT ROI decreased from ±28 milliseconds (6.5%) to ±14 milliseconds (3.3%) after B_{1} correction, whereas the 95% CI of the mean difference for the FGT ROI decreased from ±94 milliseconds (7.1%) to ±38 milliseconds (3.0%). The repeatability coefficient (red lines in Figure 4 and Supplemental Figure 2), which defines the measurement variability in an individual, decreased from 104 to 48 milliseconds in AT and from 276 to 111 milliseconds in FGT after B_{1} correction. Similar trends in the 95% CI of the mean difference and r were observed for both tissues in the left breast (Supplemental Table 3).
Figure 4.
Bland–Altman plots for the right breast displaying the difference in T_{1} between repeated measurements plotted against mean T_{1} for AT before B_{1} correction (A), AT after B_{1} correction (B), FGT before B_{1} correction (C), and FGT after B_{1} correction (D). The mean difference (black line) is shown with 95% confidence intervals of the mean difference (blue lines), which defines a measure of the spontaneous variability that is expected in a cohort of subjects. Repeatability is also shown (red lines), which quantifies the maximum difference expected to be observed between 2 repeat measurements in an individual. It can be noted from the figure that the width of both the 95% CIs of the mean difference and repeatability coefficient decreases after B_{1} correction, suggesting a lower variability.
In the right breast, the CV (Table 4) significantly (P = .039, Wilcoxon signedrank) decreased from 6.7% to 3.2% in the AT after B_{1} correction. In the FGT, the CV decreased from 5.5% to 2.2% after B_{1} correction; however, the difference was not statistically significant (P = .064). In the left breast (Supplemental Table 3), the CV significantly decreased from 7.5% to 3.9% in the AT (P = .002) and 6.8% to 2.4% in the FGT (P = .016) after B_{1} correction.
Discussion
It is well known that variations in the B_{1} transmit field exist in the breast at 3 T (14, 35). Thus, applying a B_{1} correction scheme is critical—especially when measuring T_{1} with an acquisition technique that requires multiple flip angles (ie, the VFA technique). Any bias in the prescribed flip angle will lead to inaccuracies in the measured T_{1}. The observed T_{1} values in the AT and FGT in this study are not unreasonable and are similar to a recent study by Bedair et al. that investigated the effect of a Bloch–Siegert B_{1} correction technique on VFAderived measurements of T_{1} in the breast at 3 T (36). In addition, our study incorporated a comparison with the gold standard IR data and a reproducibility analysis, allowing for an evaluation of accuracy and precision of the combination of the Bloch–Siegert B_{1} and the VFA T_{1} mapping techniques. We showed that the T_{1} and B_{1} mapping methods described herein are not only appropriate for clinical applications but also produce accurate estimates of T_{1} in breast tissues, including FGT, AT, and breast cancer.
The feasibility of the presented T_{1} and B_{1} mapping techniques was shown in the gel phantom experiment. After B_{1} correction, the VFAderived T_{1} values in each gel phantom more closely matched the gold standard IR T_{1} values, which was supported by the significantly lower %err (P = .016, Wilcoxon signedrank). In addition, we observed that the Bloch–Siegert B_{1} mapping technique improved the accuracy of the VFAderived T_{1} measurements in the breast. The %err in both ROIs (ie, FGT and AT) decreased after B_{1} correction for both breasts, suggesting that a smaller difference exists between the B_{1}corrected VFA and IR T_{1} values as compared to the uncorrected VFA data. The bootstrap 95% CIs were positive for all ROIs (including both breasts), indicating that the T_{1} values after B_{1} correction are more similar to the IR T_{1} data. Furthermore, the CCC increased by ∼50% for all measurements after B_{1} correction. Although the CCC value in the AT ROIs increased after B_{1} correction, the level of agreement after B_{1} correction was minimal (ie, CCC = ∼0.5) and much lower than the CCCs in the FGT. The radiofrequency pulses for the Bloch–Siegert technique described in this study were designed to produce pure phase shifts over a ±600 Hz range (25); however, these phase shifts will have some (albeit small) sensitivity to offresonance effects over that range. In principle, ±600 Hz should be sufficient for AT alone, but it could be problematic if a chemical shift exists in the field gradients. This could explain the observed lower agreement, as measured by the CCC, between the B_{1}corrected VFA and IR T_{1} values in the AT. The potential offresonance effects should not be considered a limitation to the Bloch–Siegert method, however, and can be compensated for using a map of the static magnetic field (ie, a B_{0} map).
There have been several recent studies investigating various B_{1} correction schemes for accurate T_{1} mapping of the breast at 3 T. Sung et al. (35) evaluated the accuracy of T_{1} measurements in the AT using the doubleangle method of B_{1} mapping, which is a technique that uses the signal magnitude images at nominal flip angles α and 2α. Their results showed an average relative flip angle variation of 115% on the left breast and 82% on the right breast, which improved to 7% after B_{1} correction (35). Although the doubleangle method generates robust measurements of B_{1} inhomogeneity, it is limited by its T_{1} dependence and the requirement for long TRs to mitigate the T_{1} dependence, which provides a possible barrier to clinical applications. The same group developed a technique to simultaneously map B_{1} and T_{1} using the AT as a reference region, and compared their results to the doubleangle method (17). This technique uses a 2point Dixon algorithm (37) to generate ATonly images and then assigns a known T_{1} value to a ratio of signal magnitudes to compute the B_{1} field variation. Sung et al. observed that the B_{1} maps generated with their postprocessing technique were similar to the doubleangle method (17); therefore, they concluded that their approach, which is more timeefficient than the doubleangle method, could be used to correct B_{1} inhomogeneities in breast MRI data.
Pineda et al. also developed a reference region technique to map the B_{1} transmit field using a populationaverage T_{1} value in the AT that was measured using an inversion recovery spectroscopic technique (16). These investigators evaluated their B_{1}mapping technique by comparing VFAderived T_{1} values (before and after B_{1} correction) to IR T_{1} values in the breasts of 4 patients. Before correction, the absolute difference between VFA and IR values was 58% ± 21%, which was reduced to 8.1% ± 7.8% after the B_{1} correction (16). Although we observed similar results in our study, the Bloch–Siegert technique described herein is not limited by the necessary assumptions of a reference region technique, with the first assumption being that the T_{1} of AT in the breast is globally uniform and well characterized (16, 17). The second is the requirement for a large section of tissue in the FOV with a homogenous T_{1}, which may not always be available in, for example, women with dense breasts (17). Another B_{1} mapping technique that may show promise in breast imaging is the DREAM approach by Nehrke and Bornert (38), which is a novel approach for robust, ultrafast, multislice B_{1} mapping.
The reproducibility analysis performed in this study provides objective statistical thresholds that define the range of repeatability by quantifying the maximum difference expected to be observed between 2 repeat measurements in an individual. In addition, the 95% CIs for the mean difference provide a measure of the spontaneous variability that is expected in a cohort of subjects. Both the 95% CIs of the mean difference and repeatability coefficient are useful when defining the associated variability in a measurement so that future studies can be designed and statistically powered appropriately. We observed lower 95% CIs of the mean difference and repeatability coefficients after B_{1} correction in all ROIs (including both breasts). We also observed an ∼50% reduction in the coefficient of variation between the repeated measures, thus suggesting lower variability after B_{1} correction. Therefore, our reproducibility analysis showed that the Bloch–Siegert B_{1} mapping technique improved reproducibility, thereby also improving precision, of VFAderived T_{1} measurements in the breast at 3 T.
We attempted to be as consistent as possible when positioning each subject in the scanner and determining the imaging FOVs between repeated acquisitions. However, image registration between repeat acquisitions was not performed because the success of the registration results would be limited by the singleslice IR acquisition. We note that this is a limitation in the current study, as tests for accuracy and reproducibility were performed using only 1 slice. We would expect, however, that applying a longitudinal registration technique (39) would only improve accuracy and precision, as differences in subject position and imaging FOV would only minimally impact the results. In addition, by using the average T_{1} value from all of the AT and FGT voxels in the FOV, we felt that the accuracy and precision results would not be biased by a reader who, for example, would manually draw ROIs in the tissues. Another limitation to our study is the different number of data sets in the AT and FGT analyses. Our goal was to recruit a cohort of subjects with an age range that was representative of our ongoing clinical breast imaging study (29); however, some of the women included in this study had very little or no FGT because of either age or body habitus. We noted above that offresonance effects could limit the accuracy of the Bloch–Siegert approach in areas of the breast where a chemical shift exists in the field gradients, which, for example, could be in the AT and areas of the breast with a mixture of AT and FGT. This limitation, however, would only affect the accuracy results described herein and should not be considered as a limitation of the Bloch–Siegert method, as chemical shift effects can be minimized by incorporating a map of the static magnetic field into the correction scheme.
Conclusion
The VFA technique is often used in clinical applications of DCEMRI, as it allows for 3D T_{1} mapping in a timeefficient manner. However, the accuracy of the technique is severely affected by inhomogeneities in the B_{1} transmit field, which are known to be significant in the breast at 3 T (14). The difference in the prescribed flip angle due to B_{1} inhomogeneities leads to inaccuracies in VFAderived estimates of T_{1}, which can compound to large errors in, for example, the DCEMRI parameter K^{trans} (11, 36). Large errors in DCEMRI analyses could lower the sensitivity and specificity of the imaging technique, thereby limiting clinical adoption. Applying a B_{1} correction map is 1 technique, among others, that can be used to compensate for the inhomogeneities in the transmit field. In this study, we showed that B_{1} correction using the Bloch–Siegert shift is a viable (and attractive) option to measure accurate and precise VFAderived T_{1} values in the breast at 3 T.
Acknowledgments
We thank the National Institutes of Health for funding through NCI 1R01CA129961, NCI 1U01CA142565, NCI 1P50 098131, NIH P30 CA68485, and NIBIB K25 EB013659. We offer our sincere thanks to the women who participated in our study. We would also like to thank Dr. Jeffrey J. Luci for informative discussions on the technical aspects of the Bloch–Siegert sequence, and Ms. Leslie McIntosh and Ms. Kristen GeorgeDurrett for providing expert MRI systemspecific technical assistance.
Disclosures: No disclosures to report.
Conflict of Interest: None reported.
References

Petrillo M, Fusco R, Catalano O, Sansone M, Avallone A, Delrio P, Pecori B, Tatangelo F, Petrillo A. MRI for assessing response to neoadjuvant therapy in locally advanced rectal cancer using DCEMR and DWMR data sets: a preliminary report. Biomed Res Int. 2015;2015:514740.

Piludu F, Marzi S, Pace A, Villani V, Fabi A, Carapella CM, Terrenato I, Antenucci A, Vidiri A. Early biomarkers from dynamic contrastenhanced magnetic resonance imaging to predict the response to antiangiogenic therapy in highgrade gliomas. Neuroradiology. 2015;57(12):1269–1280.

Chawla S, Kim S, Dougherty L, Wang S, Loevner LA, Quon H, Poptani H. Pretreatment diffusionweighted and dynamic contrastenhanced MRI for prediction of local treatment response in squamous cell carcinomas of the head and neck. AJR Am J Roentgenol. 2013;200(1):35–43.

Abramson RG, Li X, Hoyt TL, Su PF, Arlinghaus LR, Wilson KJ, Abramson VG, Chakravarthy AB, Yankeelov TE. Early assessment of breast cancer response to neoadjuvant chemotherapy by semiquantitative analysis of hightemporal resolution DCEMRI: preliminary results. Magn Reson Imaging. 2013;31(9):1457–1464.

Li X, Arlinghaus LR, Ayers GD, Chakravarthy AB, Abramson RG, Abramson VG, Atuegwu N, Farley J, Mayer IA, Kelley MC, Meszoely IM, MeansPowell J, Grau AM, Sanders M, Bhave SR, Yankeelov TE. DCEMRI analysis methods for predicting the response of breast cancer to neoadjuvant chemotherapy: pilot study findings. Magn Reson Med. 2014;71(4):1592–1602.

Yankeelov TE, Gore JC. Dynamic contrast enhanced magnetic resonance imaging in oncology: theory, data acquisition, analysis, and examples. Curr Med Imaging Rev. 2009;3(2):91–107.

Brookes JA, Redpath TW, Gilbert FJ, Murray AD, Staff RT. Accuracy of T1 measurement in dynamic contrastenhanced breast MRI using two and threedimensional variable flip angle fast lowangle shot. J Magn Reson Imaging. 1999;9(2):163–171.

Wang HZ, Riederer SJ, Lee JN. Optimizing the precision in T1 relaxation estimation using limited flip angles. Magn Reson Med. 1987;5(5):399–416.

Yankeelov TE, Pickens DR, Price RR. Quantitative MRI in Cancer. Hendee WR, editor. Boca Raton, Florida: Taylor & Francis Group, LLC, 2012.

Tofts PS, Berkowitz B, Schnall MD. Quantitative analysis of dynamic GdDTPA enhancement in breast tumors using a permeability model. Magn Reson Med. 1995;33(4):564–568.

Di Giovanni P, Azlan CA, Ahearn TS, Semple SI, Gilbert FJ, Redpath TW. The accuracy of pharmacokinetic parameter measurement in DCEMRI of the breast at 3 T. Phys Med Biol. 2010;55(1):121–132.

Cunningham CH, Pauly JM, Nayak KS. Saturated doubleangle method for rapid B1+ mapping. Magn Reson Med. 2006;55(6):1326–1333.

Cohen MS, DuBois RM, Zeineh MM. Rapid and effective correction of RF inhomogeneity for high field magnetic resonance imaging. Hum Brain Mapp. 2000;10(4):204–211.

Kuhl CK, Kooijman H, Gieseke J, Schild HH. Effect of B1 inhomogeneity on breast MR imaging at 3.0 T. Radiology. 2007;244(3):929–930.

Azlan CA, Di Giovanni P, Ahearn TS, Semple SI, Gilbert FJ, Redpath TW. B1 transmissionfield inhomogeneity and enhancement ratio errors in dynamic contrastenhanced MRI (DCEMRI) of the breast at 3T. J Magn Reson Imaging. 2010;31(1):234–239.

Pineda FD, Medved M, Fan X, Karczmar GS. B1 and T1 mapping of the breast with a reference tissue method. Magn Reson Med. 2015;75(4):1565–1573.

Sung K, Saranathan M, Daniel BL, Hargreaves BA. Simultaneous T(1) and B(1) (+) mapping using reference region variable flip angle imaging. Magn Reson Med. 2013;70(4):954–961.

Kuhl CK, Jost P, Morakkabati N, Zivanovic O, Schild HH, Gieseke J. Contrastenhanced MR imaging of the breast at 3.0 and 1.5 T in the same patients: initial experience. Radiology. 2006;239(3):666–676.

Hornak JP, Szumowski J, Bryant RG. Magnetic field mapping. Magn Reson Med. 1988;6(2):158–163.

Yarnykh VL. Actual flipangle imaging in the pulsed steady state: a method for rapid threedimensional mapping of the transmitted radiofrequency field. Magn Reson Med. 2007;57(1):192–200.

Morrell GR. A phasesensitive method of flip angle mapping. Magn Reson Med. 2008;60(4):889–894.

Jiru F, Klose U. Fast 3D radiofrequency field mapping using echoplanar imaging. Magn Reson Med. 2006;56(6):1375–1379.

Duan Q, van Gelderen P, Duyn J. Improved BlochSiegert based B1 mapping by reducing offresonance shift. NMR Biomed. 2013;26(9):1070–1078.

Sacolick LI, Wiesinger F, Hancu I, Vogel MW. B1 mapping by BlochSiegert shift. Magn Reson Med. 2010;63(5):1315–1322.

Jankiewicz M, Gore JC, Grissom WA. Improved encoding pulses for BlochSiegert B1(+) mapping. J Magn Reson. 2013;226:79–87.

Park DJ, Bangerter NK, Javed A, Kaggie J, Khalighi MM, Morrell GR. A statistical analysis of the BlochSiegert B1 mapping technique. Phys Med Biol. 2013;58(16):5673–5691.

Bloch F, Siegert A. Magnetic resonance for nonrotating fields. Phys Rev. 1940;57(6):522–527.

Steffen M, Vandersypen LM, Chuang IL. Simultaneous soft pulses applied at nearby frequencies. J Magn Reson. 2000;146(2):369–374.

Li X, Abramson RG, Arlinghaus LR, Kang H, Chakravarthy AB, Abramson VG, Farley J, Mayer IA, Kelley MC, Meszoely IM, MeansPowell J, Grau AM, Sanders M, Yankeelov TE. Multiparametric magnetic resonance imaging for predicting pathological response after the first cycle of neoadjuvant chemotherapy in breast cancer. Invest Radiol. 2015;50(4):195–204.

Li K, Zu Z, Xu J, Janve VA, Gore JC, Does MD, Gochberg DF. Optimized inversion recovery sequences for quantitative T1 and magnetization transfer imaging. Magn Reson Med. 2010;64(2):491–500.

Efron B. Bootstrap methods: another look at the jackknife. Ann Stat. 1979;7(1):1–26.

Bland JM, Altman DG. Measuring agreement in method comparison studies. Stat Methods Med Res. 1999;8(2):135–160.

Dula AN, Arlinghaus LR, Dortch RD, Dewey BE, Whisenant JG, Ayers GD, Yankeelov TE, Smith SA. Amide proton transfer imaging of the breast at 3 T: establishing reproducibility and possible feasibility assessing chemotherapy response. Magn Reson Med. 2013;70(1):216–224.

Zhu H, Arlinghaus LR, Whisenant JG, Li M, Gore JC, Yankeelov TE. Sequence design and evaluation of the reproducibility of waterselective diffusionweighted imaging of the breast at 3 T. NMR Biomed. 2014;27(9):1030–1036.

Sung K, Daniel BL, Hargreaves BA. Transmit B1+ field inhomogeneity and T1 estimation errors in breast DCEMRI at 3 tesla. J Magn Reson Imaging. 2013;38(2):454–459.

Bedair R, Graves MJ, Patterson AJ, McLean MA, Manavaki R, Wallace T, Reid S, Mendichovszky I, Griffiths J, Gilbert FJ. Effect of radiofrequency transmit field correction on quantitative dynamic contrastenhanced MR imaging of the breast at 3.0 T. Radiology. 2015;279(2):150920.

Ma J. Breathhold water and fat imaging using a dualecho twopoint Dixon technique with an efficient and robust phasecorrection algorithm. Magn Reson Med. 2004;52(2):415–419.

Nehrke K, Börnert P. DREAM–a novel approach for robust, ultrafast, multislice B(1) mapping. Magn Reson Med. 2012;68(5):1517–1526.

Li X, Dawant BM, Welch EB, Chakravarthy AB, Freehardt D, Mayer I, Kelley M, Meszoely I, Gore JC, Yankeelov TE. A nonrigid registration algorithm for longitudinal breast MR images and the analysis of breast tumor response. Magn Reson Imaging. 2009;27(9):1258–1270.
Research Articles
Download PDF (960.03 KB)
TOMOGRAPHY, December 2016, Volume 2, Issue 4:250259
DOI: 10.18383/j.tom.2016.00133
BlochSiegert B₁Mapping Improves Accuracy and Precision of Longitudinal Relaxation Measurements in the Breast at 3 T
Jennifer G. Whisenant^{1}, Richard D. Dortch^{1}, William Grissom^{1}, Hakmook Kang^{4}, Lori R. Arlinghaus^{1}, Thomas E. Yankeelov^{5}
Abstract
Variable flip angle (VFA) sequences are a popular method of calculating T_{1} values, which are required in a quantitative analysis of dynamic contrastenhanced (DCE) magnetic resonance imaging (MRI). B_{1} inhomogeneities are substantial in the breast at 3 T, and these errors negatively impact the accuracy of the VFA approach, thus leading to large errors in the DCEMRI parameters that could limit clinical adoption of the technique. This study evaluated the ability of Bloch–Siegert B_{1} mapping to improve the accuracy and precision of VFAderived T_{1} measurements in the breast. Test–retest MRI sessions were performed on 16 women with no history of breast disease. T1 was calculated using the VFA sequence, and B1 field variations were measured using the Bloch–Siegert methodology. As a gold standard, inversion recovery (IR) measurements of T1 were performed. Fibroglandular tissue and adipose tissue from each breast were segmented using the IR images, and the mean T1 was calculated for each tissue. Accuracy was evaluated by percent error (%err). Reproducibility was assessed via the 95% confidence interval (CI) of the mean difference and repeatability coefficient (r). After B1 correction, %err significantly (P < .001) decreased from 17% to 8.6%, and the 95% CI and r decreased from ±94 to ±38 milliseconds and from 276 to 111 milliseconds, respectively. Similar accuracy and reproducibility results were observed in the adipose tissue of the right breast and in both tissues of the left breast. Our data show that Bloch–Siegert B1 mapping improves accuracy and precision of VFAderived T1 measurements in the breast.
Introduction
Dynamic contrastenhanced magnetic resonance imaging (DCEMRI) is a common method for evaluating tumor response to therapy in a variety of cancers (1–3), including breast (4, 5). DCEMRI acquires images before, during, and after injection of a contrast agent to characterize, for example, tumorrelated perfusion. To perform a quantitative analysis of DCEMRI data, knowledge of the precontrast longitudinal relaxation time (T_{1}) is required to convert the measured dynamic signal intensity into a time course of the concentration of the contrast agent (6). A popular technique used to measure the precontrast T_{1} is the variable flip angle (VFA) approach, which uses a series of spoiled gradient echo (SPGE) images acquired with a short, fixed repetition time (TR) and a varying flip angle (7, 8). The resulting data are then fit to the signal intensity equation describing the SPGE acquisition with T_{1} as a fit parameter for each voxel or region of interest (ROI). Although this technique allows for rapid 3dimensional (3D) T_{1} mapping, it is not without limitations, chief of which is that its accuracy is dependent on the uniformity of the transmit radiofrequency (B_{1}) field. It should be noted that other T_{1} mapping methods exist that are less sensitive to variations in the transmit field (9); however, VFA sequences are the preferred method in the clinical setting, as these acquisitions enable a large field of view (FOV) to be measured in a relatively short period.
Inhomogeneities in the B_{1} field cause variations in the prescribed flip angles, leading to inaccurate measurements of T_{1}, which can subsequently induce large errors in the DCEMRI parameters (eg, the volume transfer rate constant, K^{trans}) (10). Indeed, simulation results indicated that errors in K^{trans} ranged from 15% to 500% as the error in the T_{1} measurement ranged from 14% to 65% of the nominal value (11). Therefore, an inaccurate estimation of the precontrast T_{1} could potentially lower the sensitivity of DCEMRI for characterizing tumor vascular properties, thereby limiting the utility of the technique.
The B_{1} field experienced by spins within the body is influenced by several factors, including the distance of the spins from the radiofrequency transmit coil, the dielectric properties of the tissues, and the factors related to body size and wavelength of the radiofrequency (12). The severity of the nonuniformity in the B_{1} field increases at higher field strengths (13), and noticeable B_{1} inhomogeneities have been observed in the breast at 3 T (14–17). In particular, a substantial variation in the B_{1} field from left to right across the imaging FOV has been observed, which may artificially decrease the contrast enhancement in specific lesions (18). Thus, Kuhl et al. have suggested that B_{1} mapping in the breast should be a standard practice (14). Although several different methods for B_{1} mapping have been developed (12, 19–22), no single method has emerged for widespread application.
A technique using the Bloch–Siegert shift to map the B_{1} field has recently been developed, and it is an area of active investigation (23–26). The Bloch–Siegert shift is a term used to describe the shift in resonance frequency of a nucleus when an offresonance radiofrequency field is applied (27). Although Sacolick et al. (24) provide the details, the salient information is mentioned here. If a radiofrequency pulse is applied either far enough offresonance and/or with a pulse shape such that it does not cause spin excitation, the spins experience a change in precession frequency without excitation (28). The spin precession frequency shifts away from the offresonance irradiation and is dependent on the magnitude of the B_{1} field, as well as the difference between the spin resonance frequency and radiofrequency field. The shift in frequency results in a phase shift in the images that can be used to spatially map the B_{1} magnitude. This phasebased method generates a B_{1} map that is not significantly biased by TR, T_{1} relaxation, flip angle, chemical shift, background field inhomogeneity, or magnetization transfer (24). The insensitivity to TR is especially important in a clinical setting, as it allows for the prompt acquisition of image data with a short TR. In the current study, we present an approach to rapidly, accurately, and precisely map B_{1} and T_{1} values in the breast using the Bloch–Siegert method with a VFA sequence.
Methodology
All imaging data were acquired with a 3 T Achieva magnetic resonance scanner (Philips Healthcare, Best, The Netherlands) equipped with a 2channel multitransmit body coil and a MammoTrak table including a 16channel receive doublebreast coil (Philips Healthcare, Best, The Netherlands).
Phantom Scans
To investigate the feasibility of the approach, 8 gel phantoms (The Eurospin II Test System, Diagnostic Sonar, Livingston, Scotland, UK) submerged in water were scanned at room temperature. The T_{1} values of the phantoms ranged from 300 to 1600 milliseconds. A coronal image volume was placed in the center of the breast coil containing the phantoms, and VFA, Bloch–Siegert, and inversion recovery (IR) data were collected. VFA data with 10 flip angles (2, 4, 6, . . . 20) were acquired using a 3D SPGE sequence with the following parameters: TR/echo time (TE) = 7.9/4.6 milliseconds, sensitivity encoding parallel imaging factor of 2, acquisition matrix of 192 × 192 over a FOV of 256 × 256 mm^{2}, yielding a voxel size of 1.33 × 1.33 mm^{2}, and 15 slices with a thickness of 4 mm for a total scan time of 66 seconds. The Bloch–Siegert data were collected using a gradient echo sequence with a 2millisecond frequencyswept B_{1} phase imparting pulse (25) over the same FOV as the VFA data with the following parameters: TR/TE = 491/5.4 millisecond, acquisition matrix of 104 × 102, reconstruction voxel size of 1.33 × 1.33 mm^{2}, and root mean square B_{1} field = 2.29 μT for a total scan time of 104 seconds. As is required with the Bloch–Siegert B_{1} mapping, 2 images were collected at opposite frequency offsets. As a gold standard, a 2dimensional IRprepared turbospin echo (IRTSE) sequence was used to acquire a single slice corresponding to the center of the VFA image volume with the following parameters: 12 inversion times of 25, 50, 75, 100, 200, 300, 400, 500, 1000, 2000, 4000, and 10 000 milliseconds, acquisition matrix of 128 × 96 over an FOV of 256 × 256 mm^{2}, reconstruction voxel size of 1.33 × 1.33 mm^{2}, predelay before inversion pulse of 2500 milliseconds, and TSE factor of 24 with an echo spacing of 5.9 milliseconds for a total scan time of 125 seconds.
Subject Scans
Test–retest MRI sessions were performed on 16 women (median: 42 years, range: 25–67) with no history of breast disease. Because of age, body habitus, or hormonal status, 4 of these women did not have appreciable fibroglandular tissue (FGT) in either breast; thus, measurements for these women included data only from the adipose tissue (AT). The imaging protocol consisted of 2 scan sessions each lasting ∼30 minutes separated by a 10minute rest period. During the rest period, the subjects were removed from the scanner and allowed to stretch. All subjects were consented as part of an ongoing study approved by the local Institutional Review Board.
For each test–retest session, 2 separate sagittal imaging volumes were centered on each breast with an attempt to approximately match the stack placement between each imaging session. Subsequent VFA, Bloch–Siegert, and IR data were then collected separately for each breast. The imaging parameters for each sequence were identical to the phantom scans, except that the slice thickness was 5 mm and the number of slices for the VFA and Bloch–Siegert sequences was 10. These 2 parameters were changed to match our ongoing clinical imaging trial (29). In addition, we applied the T_{1} and Bloch–Siegert B_{1} mapping methods described herein on 3 patients with breast cancer. Each patient provided written consent to participate in the study.
Image Analysis
All image data were exported to MATLAB R2013b (The MathWorks, Natick, Massachusetts) for analysis. Bloch–Siegert B_{1} maps were calculated as described previously (25). In brief, the actual flip angle at each image voxel was obtained via linear interpolation of the entries of a phase differenceversusB_{1} strength lookup table generated using Bloch equation simulations of the offresonant Bloch–Siegert pulse. The flip angle correction map was then calculated as the ratio of the actual flip angle to the prescribed flip angle.
VFA T_{1} maps with and without B_{1} correction were obtained by fitting signal intensity (S) data to equation 1 as follows:
1
2
For the phantom scans, circular ROIs were manually drawn within each gel phantom using the IR data as a guide. The average T_{1} from each phantom was recorded from the IR T_{1} map. The same ROIs were then subsequently used to calculate the average T_{1} from the central slice of the VFAderived T_{1} maps with and without B_{1} correction. Statistical analyses were performed on the average T_{1} values calculated from each ROI. To evaluate the accuracy of the proposed B_{1} mapping technique, the percent error (%err) between the IR and VFAderived T_{1} values (with and without B_{1} correction) was calculated.
For healthy volunteers, segmentation masks for AT were automatically generated from the IR data (inversion times = 500 milliseconds), where the signal intensity for the FGT was close to 0. A representative example of the segmentation masks for each tissue is presented in Supplemental Figure 3. FGT segmentation masks were subsequently generated as the opposite of the AT mask after manually segmenting the skin and chest wall from the FOV. The average T_{1} from each tissue segmentation mask was recorded from the IR T_{1} maps for each breast and imaging session. The same tissue masks were then used to calculate the average T_{1} from the central slice of the VFAderived T_{1} maps (with and without B_{1} correction). The %err between the VFAderived T_{1} values (with and without B_{1} correction) and the IR T_{1} values was calculated to evaluate the accuracy, and the agreement between the different T_{1} values was assessed via the concordance correlation coefficient (CCC). Furthermore, the bootstrap 95% confidence interval (CI) of the mean differences in absolute deviation between IR and VFAderived T_{1} values (with and without B_{1} correction) was computed as previously described (31) using equation 3 as follows:
3
To illustrate the application of the T_{1} and B_{1} mapping techniques described herein, manual ROIs were drawn in the AT, FGT (if appreciable), and tumor of 3 patients with breast cancer. Average T_{1} from each ROI was calculated, and the %err between the VFAderived T_{1} values (with and without B_{1} correction) and the IR T_{1} values was compared.
Reproducibility Statistics
Reproducibility statistics used in this test–retest study follow the methods previously described by Bland and Altman (32) and are similar to what was previously implemented in the breast of healthy volunteers (33, 34). First, the difference, d, was calculated between the 2 VFA T_{1} data sets obtained for each subject and then the distribution of those differences was tested for normality using the Shapiro–Wilk test. The Kendall's Tau test was used to ensure that the magnitude of the difference values was not correlated with the parameter mean of the repeated measurements. The Wilcoxon signedrank test was used to test the null hypothesis of no bias (ie, average difference is 0) between repeated measurements.
The statistical measurements of reproducibility were calculated as follows:
(1) The rootmeansquare deviation (rMSD) is computed using the differences, d, as follows:
4
(2) The 95% CI for a group of n subjects is shown as follows:
5
(3) The withinsubject standard deviation (wSD) is as follows:
6
(4) The repeatability coefficient (r) is shown as follows:
7
Or, equivalently, as follows:
8
The repeatability coefficient defines the magnitude of the maximum difference expected in 95% of paired observations; for example, r defines the expected measurement variability for an individual. Because of our moderate sample sizes, we replaced 1.96 in equation 5 with the appropriate tstatistic for our sample size, which was 2.131 (n = 16) and 2.179 (n = 13) for AT and FGT, respectively.
Statistical analyses were performed using the statistical toolbox in MATLAB^{®}. A significance value of P ≤ .05 was used for all statistical tests. In addition, we quantified the coefficient of variation (CV) between the repeated measurements, which is the ratio of the standard deviation of the repeated measurements over the mean of the repeated measurements.
Results
Gel Phantoms
A set of image data for the gel phantom experiment is displayed in Figure 1. The Bloch–Siegert B_{1} map is displayed in Figure 1A, where each voxel represents the Bloch–Siegertderived flip angle correction factor (ie, ratio of the actual flip angle to the nominal flip angle) that is incorporated into equation 1. T_{1} parametric maps generated from the IR, uncorrected VFA, and B_{1}corrected VFA data are displayed in panels B, C, and D, respectively, of Figure 1. The mean (±standard deviation) T_{1} value for each gel phantom ROI, along with the %err from the IR data, is listed in Table 1. Compared with the uncorrected VFA data, the B_{1}corrected VFAderived T_{1} estimates have a significantly lower %err (P = .016, Wilcoxon signedrank).
Figure 1.
A Bloch–Siegert B_{1} map (A) with T_{1} parametric maps calculated from inversion recovery (IR) (B) and uncorrected variable flip angle (VFA) (C), and B_{1}corrected VFA data (D) are shown for the gel phantoms. The Bloch–Siegert B_{1} map shown is the correction factor, which is the ratio of the actual and nominal flip angles. Note the large spatial variation across the B_{1} map; this variation is a representation of the B_{1} inhomogeneity across the imaging field of view (FOV). After B_{1} correction, the VFAderived T_{1} values (D) are more similar to the IR T_{1} values (B) in each gel phantom.
Table 1.
Average ± Standard T_{1} (milliseconds) Values and %err in the Gel Phantoms
i] Abbreviations: No., number; %err, percent error; IR, inversion recovery; VFA, variable flip angle.
In Vivo Scans
A representative set of image data is displayed for the right breast of 1 subject in Figure 2. (Identical data for the left breast in the same subject are displayed in Supplemental Figure 1.) The Bloch–Siegert B_{1} maps from both scans are displayed in Figure 2, A and E, where each voxel displays the Bloch–Siegertderived flip angle correction factor. Also shown, are test–retest T_{1} parametric maps generated from the IR (panels B and F), uncorrected VFA (panels C and G), and B_{1}corrected VFA (panels D and H) data. Average T_{1} values from each tissue ROI and T_{1} mapping technique are tabulated for the right and left breast from each subject in Supplemental Tables 1 and 2, respectively.
Figure 2.
A representative test–retest set of B_{1} and T_{1} parametric maps displayed for the right breast of a healthy volunteer. Bloch–Siegert B_{1} maps (A and E) correspond to the correction between the actual and the nominal flip angles. Note the spatial variation of the correction factors in the B_{1} maps and the difference in B_{1} maps between repeated scans; together, these images provide evidence that a B_{1} map should be incorporated into routine breast imaging if a quantitative analysis of the collected data is desired. T_{1} parametric maps include: IR maps (B and F), uncorrected VFA maps (C and G), and B_{1}corrected VFA maps (D and H). The spatial variations in T_{1} of the FGT are minimized after B_{1} correction, and the T_{1} map more closely matches the IR T_{1} map. Furthermore, the B_{1}corrected T_{1} maps are visually more similar between repeated measurements compared with the uncorrected data. Observe how the orientation is slightly different between repeated scans, which might negatively affect the T_{1} reproducibility, as the same tissue sections from each scan might not be analyzed.
Table 2 lists the accuracy results for each ROI and breast. In the right breast, %err in the FGT using the VFA method significantly (P < .001, Wilcoxon signedrank) decreased from 17.0% to 8.6% and the CCC increased from 0.55 to 0.83 after B_{1} correction. Similar trends in accuracy were observed in the AT (Table 2). Bootstrap 95% CIs for FGT and AT were 57.8–139 milliseconds and 17.2–42.2 milliseconds, respectively. The range of CIs for each tissue includes all positive numbers, and by referring to equation 3, it can be seen that the absolute difference from the gold standard IR T_{1} is smaller after B_{1} correction for both tissue ROIs. In the left breast, %err in the FGT using the VFA method significantly (P = .002, Wilcoxon signedrank) decreased from 15.0% to 8.7% and the CCC increased from 0.60 to 0.83 after B_{1} correction. Similar trends in accuracy were observed in the AT (Table 2). The bootstrap 95% CIs for FGT and AT were 35.8–104.8 milliseconds and 2.4–26.7 milliseconds, respectively; again, both values for each CI were positive, indicating that the absolute difference from gold standard IR T_{1} is smaller after B_{1} correction for both ROIs.
Table 2.
Accuracy Results for Both Breasts and ROI
i] Abbreviations: ROI, region of interest; %err, percent error; Std, standard deviation; CCC, concordance correlation coefficient; VFA, variable flip angle.
As a proof of principle, the T_{1} and B_{1} mapping methods were applied in 3 patients with breast cancer. Figure 3 displays T_{1} parametric maps for all 3 patients generated from IR (left column), uncorrected VFA (center column), and B_{1}corrected VFA (right column) data. From these images, it can be seen that the B_{1}corrected T_{1} values in the tumors more closely match the IR T_{1} values. This similarity is extremely important, as accurate T_{1} values are required when performing a quantitative DCEMRI analysis. The mean (±standard deviation) T_{1} value for each tissue ROI, along with the %err from the IR data, is listed in Table 3 for each patient with breast cancer. Compared with the uncorrected VFA data, the B_{1}corrected VFAderived T_{1} estimates have, on average, a lower %err. Combining all tissue ROIs for each imaging technique, a significantly lower %err was observed after B_{1} correction (P = .004, Wilcoxon signedrank).
Figure 3.
As a proof of principle, the B_{1} and T_{1} methods presented in this article were performed on 3 patients with breast cancer; each patient was a subject enrolled in our ongoing breast imaging clinical trial (29). T_{1} parametric maps are shown for IR (left center column), uncorrected VFA (right center column), and B_{1}corrected VFA (right column) data collected from each patient (shown in rows). The tumors are shown with red arrows in each image. Compared with the uncorrected VFA data, the B_{1}corrected VFA T_{1} values of the FGT, AT, and tumor in all 3 patients are more similar to the IR T_{1} values, thus suggesting a more accurate T_{1} value in each tissue after B_{1} correction. Note that circular regions in the breasts that have a lack of signal intensity are due to the presence of a breast biopsy clip.
Table 3.
Average ± Standard T_{1} (milliseconds) Values and %err from ROIs in Patients with Breast Cancer
i] Abbreviations: ROI, region of interest; %err, percent error; IR, inversion recovery; VFA, variable flip angle; AT, adipose tissue; FGT, fibroglandular tissue.
Reproducibility
Reproducibility statistics for each tissue are listed in Table 4 and Supplemental Table 3 for the right and left breast, respectively. Normality was assumed for each data set as determined by the Shapiro–Wilk test. No data sets had an average difference significantly different from 0 as determined by the Wilcoxon signedrank test. In addition, the Kendall's Tau test showed that the difference between repeat measurements d was independent of the mean for each ROI.
Table 4.
Reproducibility Results for the Right Breast
i] Abbreviations: CI, confidence interval; wSD, withinsubject standard deviation; CV, coefficient of variation; SD, standard deviation; VFA, variable flip angle.
Bland–Altman plots for each tissue ROI are displayed in Figure 4 and Supplemental Figure 2 for the right and left breast, respectively. Each panel displays the difference in T_{1} between the repeated scans against the mean T_{1} from both scans. The mean difference and 95% CIs of the mean difference are displayed as black and blue lines, respectively. The 95% CIs of the mean difference, which define expected measurement variability for a cohort of subjects, decreased after B_{1} correction. For the right breast, the 95% CI of the mean difference of the AT ROI decreased from ±28 milliseconds (6.5%) to ±14 milliseconds (3.3%) after B_{1} correction, whereas the 95% CI of the mean difference for the FGT ROI decreased from ±94 milliseconds (7.1%) to ±38 milliseconds (3.0%). The repeatability coefficient (red lines in Figure 4 and Supplemental Figure 2), which defines the measurement variability in an individual, decreased from 104 to 48 milliseconds in AT and from 276 to 111 milliseconds in FGT after B_{1} correction. Similar trends in the 95% CI of the mean difference and r were observed for both tissues in the left breast (Supplemental Table 3).
Figure 4.
Bland–Altman plots for the right breast displaying the difference in T_{1} between repeated measurements plotted against mean T_{1} for AT before B_{1} correction (A), AT after B_{1} correction (B), FGT before B_{1} correction (C), and FGT after B_{1} correction (D). The mean difference (black line) is shown with 95% confidence intervals of the mean difference (blue lines), which defines a measure of the spontaneous variability that is expected in a cohort of subjects. Repeatability is also shown (red lines), which quantifies the maximum difference expected to be observed between 2 repeat measurements in an individual. It can be noted from the figure that the width of both the 95% CIs of the mean difference and repeatability coefficient decreases after B_{1} correction, suggesting a lower variability.
In the right breast, the CV (Table 4) significantly (P = .039, Wilcoxon signedrank) decreased from 6.7% to 3.2% in the AT after B_{1} correction. In the FGT, the CV decreased from 5.5% to 2.2% after B_{1} correction; however, the difference was not statistically significant (P = .064). In the left breast (Supplemental Table 3), the CV significantly decreased from 7.5% to 3.9% in the AT (P = .002) and 6.8% to 2.4% in the FGT (P = .016) after B_{1} correction.
Discussion
It is well known that variations in the B_{1} transmit field exist in the breast at 3 T (14, 35). Thus, applying a B_{1} correction scheme is critical—especially when measuring T_{1} with an acquisition technique that requires multiple flip angles (ie, the VFA technique). Any bias in the prescribed flip angle will lead to inaccuracies in the measured T_{1}. The observed T_{1} values in the AT and FGT in this study are not unreasonable and are similar to a recent study by Bedair et al. that investigated the effect of a Bloch–Siegert B_{1} correction technique on VFAderived measurements of T_{1} in the breast at 3 T (36). In addition, our study incorporated a comparison with the gold standard IR data and a reproducibility analysis, allowing for an evaluation of accuracy and precision of the combination of the Bloch–Siegert B_{1} and the VFA T_{1} mapping techniques. We showed that the T_{1} and B_{1} mapping methods described herein are not only appropriate for clinical applications but also produce accurate estimates of T_{1} in breast tissues, including FGT, AT, and breast cancer.
The feasibility of the presented T_{1} and B_{1} mapping techniques was shown in the gel phantom experiment. After B_{1} correction, the VFAderived T_{1} values in each gel phantom more closely matched the gold standard IR T_{1} values, which was supported by the significantly lower %err (P = .016, Wilcoxon signedrank). In addition, we observed that the Bloch–Siegert B_{1} mapping technique improved the accuracy of the VFAderived T_{1} measurements in the breast. The %err in both ROIs (ie, FGT and AT) decreased after B_{1} correction for both breasts, suggesting that a smaller difference exists between the B_{1}corrected VFA and IR T_{1} values as compared to the uncorrected VFA data. The bootstrap 95% CIs were positive for all ROIs (including both breasts), indicating that the T_{1} values after B_{1} correction are more similar to the IR T_{1} data. Furthermore, the CCC increased by ∼50% for all measurements after B_{1} correction. Although the CCC value in the AT ROIs increased after B_{1} correction, the level of agreement after B_{1} correction was minimal (ie, CCC = ∼0.5) and much lower than the CCCs in the FGT. The radiofrequency pulses for the Bloch–Siegert technique described in this study were designed to produce pure phase shifts over a ±600 Hz range (25); however, these phase shifts will have some (albeit small) sensitivity to offresonance effects over that range. In principle, ±600 Hz should be sufficient for AT alone, but it could be problematic if a chemical shift exists in the field gradients. This could explain the observed lower agreement, as measured by the CCC, between the B_{1}corrected VFA and IR T_{1} values in the AT. The potential offresonance effects should not be considered a limitation to the Bloch–Siegert method, however, and can be compensated for using a map of the static magnetic field (ie, a B_{0} map).
There have been several recent studies investigating various B_{1} correction schemes for accurate T_{1} mapping of the breast at 3 T. Sung et al. (35) evaluated the accuracy of T_{1} measurements in the AT using the doubleangle method of B_{1} mapping, which is a technique that uses the signal magnitude images at nominal flip angles α and 2α. Their results showed an average relative flip angle variation of 115% on the left breast and 82% on the right breast, which improved to 7% after B_{1} correction (35). Although the doubleangle method generates robust measurements of B_{1} inhomogeneity, it is limited by its T_{1} dependence and the requirement for long TRs to mitigate the T_{1} dependence, which provides a possible barrier to clinical applications. The same group developed a technique to simultaneously map B_{1} and T_{1} using the AT as a reference region, and compared their results to the doubleangle method (17). This technique uses a 2point Dixon algorithm (37) to generate ATonly images and then assigns a known T_{1} value to a ratio of signal magnitudes to compute the B_{1} field variation. Sung et al. observed that the B_{1} maps generated with their postprocessing technique were similar to the doubleangle method (17); therefore, they concluded that their approach, which is more timeefficient than the doubleangle method, could be used to correct B_{1} inhomogeneities in breast MRI data.
Pineda et al. also developed a reference region technique to map the B_{1} transmit field using a populationaverage T_{1} value in the AT that was measured using an inversion recovery spectroscopic technique (16). These investigators evaluated their B_{1}mapping technique by comparing VFAderived T_{1} values (before and after B_{1} correction) to IR T_{1} values in the breasts of 4 patients. Before correction, the absolute difference between VFA and IR values was 58% ± 21%, which was reduced to 8.1% ± 7.8% after the B_{1} correction (16). Although we observed similar results in our study, the Bloch–Siegert technique described herein is not limited by the necessary assumptions of a reference region technique, with the first assumption being that the T_{1} of AT in the breast is globally uniform and well characterized (16, 17). The second is the requirement for a large section of tissue in the FOV with a homogenous T_{1}, which may not always be available in, for example, women with dense breasts (17). Another B_{1} mapping technique that may show promise in breast imaging is the DREAM approach by Nehrke and Bornert (38), which is a novel approach for robust, ultrafast, multislice B_{1} mapping.
The reproducibility analysis performed in this study provides objective statistical thresholds that define the range of repeatability by quantifying the maximum difference expected to be observed between 2 repeat measurements in an individual. In addition, the 95% CIs for the mean difference provide a measure of the spontaneous variability that is expected in a cohort of subjects. Both the 95% CIs of the mean difference and repeatability coefficient are useful when defining the associated variability in a measurement so that future studies can be designed and statistically powered appropriately. We observed lower 95% CIs of the mean difference and repeatability coefficients after B_{1} correction in all ROIs (including both breasts). We also observed an ∼50% reduction in the coefficient of variation between the repeated measures, thus suggesting lower variability after B_{1} correction. Therefore, our reproducibility analysis showed that the Bloch–Siegert B_{1} mapping technique improved reproducibility, thereby also improving precision, of VFAderived T_{1} measurements in the breast at 3 T.
We attempted to be as consistent as possible when positioning each subject in the scanner and determining the imaging FOVs between repeated acquisitions. However, image registration between repeat acquisitions was not performed because the success of the registration results would be limited by the singleslice IR acquisition. We note that this is a limitation in the current study, as tests for accuracy and reproducibility were performed using only 1 slice. We would expect, however, that applying a longitudinal registration technique (39) would only improve accuracy and precision, as differences in subject position and imaging FOV would only minimally impact the results. In addition, by using the average T_{1} value from all of the AT and FGT voxels in the FOV, we felt that the accuracy and precision results would not be biased by a reader who, for example, would manually draw ROIs in the tissues. Another limitation to our study is the different number of data sets in the AT and FGT analyses. Our goal was to recruit a cohort of subjects with an age range that was representative of our ongoing clinical breast imaging study (29); however, some of the women included in this study had very little or no FGT because of either age or body habitus. We noted above that offresonance effects could limit the accuracy of the Bloch–Siegert approach in areas of the breast where a chemical shift exists in the field gradients, which, for example, could be in the AT and areas of the breast with a mixture of AT and FGT. This limitation, however, would only affect the accuracy results described herein and should not be considered as a limitation of the Bloch–Siegert method, as chemical shift effects can be minimized by incorporating a map of the static magnetic field into the correction scheme.
Conclusion
The VFA technique is often used in clinical applications of DCEMRI, as it allows for 3D T_{1} mapping in a timeefficient manner. However, the accuracy of the technique is severely affected by inhomogeneities in the B_{1} transmit field, which are known to be significant in the breast at 3 T (14). The difference in the prescribed flip angle due to B_{1} inhomogeneities leads to inaccuracies in VFAderived estimates of T_{1}, which can compound to large errors in, for example, the DCEMRI parameter K^{trans} (11, 36). Large errors in DCEMRI analyses could lower the sensitivity and specificity of the imaging technique, thereby limiting clinical adoption. Applying a B_{1} correction map is 1 technique, among others, that can be used to compensate for the inhomogeneities in the transmit field. In this study, we showed that B_{1} correction using the Bloch–Siegert shift is a viable (and attractive) option to measure accurate and precise VFAderived T_{1} values in the breast at 3 T.
Supplemental Materials
Supplemental Figure 1:
http://dx.doi.org/10.18383/j.tom.2016.00133.sup.01
Supplemental Figure 2:
http://dx.doi.org/10.18383/j.tom.2016.00133.sup.02
Supplemental Figure 3:
http://dx.doi.org/10.18383/j.tom.2016.00133.sup.03
Supplemental Table 1:
http://dx.doi.org/10.18383/j.tom.2016.00133.sup.04
Supplemental Table 2:
http://dx.doi.org/10.18383/j.tom.2016.00133.sup.05
Supplemental Table 3:
http://dx.doi.org/10.18383/j.tom.2016.00133.sup.06
Notes
[5] Abbreviations:
VFA
Variable flip angle
MRI
magnetic resonance imaging
DCEMRI
dynamic contrastenhanced magnetic resonance imaging
T_{1}
longitudinal relaxation time
TR
repetition time
TR
repetition time
IR
inversion recovery
SPGE
spoiled gradient echo
3D
3dimensional
TE
echo time
FOV
field of view
TSE
turbospin echo
FGT
fibroglandular tissue
ROI
region of interest
AT
adipose tissue
%err
percent error
CCC
concordance correlation coefficient
CI
confidence interval
CV
coefficient of variation
Acknowledgments
We thank the National Institutes of Health for funding through NCI 1R01CA129961, NCI 1U01CA142565, NCI 1P50 098131, NIH P30 CA68485, and NIBIB K25 EB013659. We offer our sincere thanks to the women who participated in our study. We would also like to thank Dr. Jeffrey J. Luci for informative discussions on the technical aspects of the Bloch–Siegert sequence, and Ms. Leslie McIntosh and Ms. Kristen GeorgeDurrett for providing expert MRI systemspecific technical assistance.
Disclosures: No disclosures to report.
Conflict of Interest: None reported.
References
Journal Information
Journal ID (nlmta): tom
Journal ID (publisherid): TOMOG
Title: Tomography
Subtitle: A Journal for Imaging Research
Abbreviated Title: Tomography
ISSN (print): 23791381
ISSN (electronic): 2379139X
Publisher: Grapho Publications, LLC (Ann Abor, Michigan)
Article Information
Copyright statement: © 2016 The Authors. Published by Grapho Publications, LLC
Copyright: 2016, Grapho Publications, LLC
License (openaccess, https://creativecommons.org/licenses/by/4.0/):
This is an open access article under the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).
Publication date (print): December 2016
Volume: 2
Issue: 4
Pages: 250259
Publisher ID: TOM0013316
DOI: 10.18383/j.tom.2016.00133
Supplemental Media
Supplemental Media
Supplemental Media
Supplemental Media
Supplemental Media
Supplemental Media
Supplemental Media
PDF
Download the article PDF (960.03 KB)
Download the full issue PDF (200.5 MB)
Mobileready Flipbook
View the full issue as a flipbook (Desktop and Mobileready)