Magnetic Resonance in Medicine 73:273–283 (2015)
0 Simultaneous R*, 2 R2, and R2 Quantification by Combining S0 Estimation of the Free Induction Decay with a Single Spin Echo: A Single Acquisition Method for R2 Insensitive Quantification of Holmium-166–Loaded Microspheres G. H. van de Maat,1* H. de Leeuw,1 P. R. Seevinck,1 M. A. A. J. van den Bosch,2 J. F. W. Nijsen,2 and C. J. G. Bakker2 Purpose: To present a new method, S0 estimation of the free induction decay combined with a single spin echo measurement (SOFIDSE), that enables simultaneous measurements of R*2 , R2, and R20 in order to quantify the local concentration of holmium microspheres (Ho-MS) for radioembolization. Theory and Methods: SOFIDSE estimates R*2 and the signal magnitude at time point 0, S0, from a multigradient echo readout of the free induction decay and subsequently estimates R2 using S0 and a single spin echo, from which R20 is deducted. The method was evaluated by comparing SOFIDSE R2 values with values obtained from shifted spin echo (SSE) measurements on a phantom setup containing Ho-MS and from dual spin echo measurements on a healthy volunteer. Results: On average, SOFIDSE showed a small overestimation of R2 values compared with SSE independent of the microsphere concentration. R20 values determined by subtraction of either SOFIDSE R2 or SSE R2 from R*2 showed excellent agreement (correlation coefficient ¼ 1; P ¼ 9 1011). The HoMS–induced R20 values obtained by SOFIDSE were insensitive to the R2 value of the tissue in which they resided. Conclusion: SOFIDSE enables quantification of Ho-MS, in media with spatially or temporally varying R2 values, in a single C 2014 acquisition. Magn Reson Med 73:273–283, 2015. V Wiley Periodicals, Inc. Key words: SOFIDSE; holmium microspheres; R*; 2 R2; S0 estimation; quantification
INTRODUCTION MRI-based biodistribution measurement of paramagnetic holmium-166 poly(L-lactic acid) microspheres (Ho-MS) (1–5) is, like detection of other clinically applicable (super)-paramagnetic particles (6, 7), primarily based on R* 2 dephasing effects the microspheres induce. In general, the R* 2 relaxation rate increases for increasing parti-
1 Image Sciences Institute, University Medical Center Utrecht, Utrecht, The Netherlands. 2 Department of Radiology and Nuclear Medicine, University Medical Center Utrecht, Utrecht, The Netherlands.
*Correspondence to: Gerrit H. van de Maat, Q S.459, P.O. Box 85500, 3508 GA Utrecht, The Netherlands. E-mail: [email protected]. Received 3 October 2013; revised 19 December 2013; accepted 31 December 2013 DOI 10.1002/mrm.25138 Published online 7 March 2014 in Wiley Online Library (wileyonlinelibrary. com). C 2014 Wiley Periodicals, Inc. V
cle concentration, enabling changes in R* 2 to be related to the local particle amount. Common methods to measure R* 2 relaxation rates sample either the free induction decay (FID) or the spin echo (SE) by using a multigradient echo sequence. The preferred method of quantifying the local amount of Ho-MS is by sampling the FID, as this has been shown to provide a more accurate quantitative measure than sampling the SE due to non-monoexponential signal behavior of the latter as a consequence of diffusion effects (8). R* 2 values are estimated by a monoexponential fit to the FID data and are linearly related to the local microsphere concentration by their relaxivity r*. The 2 major drawback of this approach is that both the HoMS–induced signal decay and the intrinsic R2 signal decay of the tissue in which the microspheres reside contribute to the observed R* 2 values. The presence of this tissue R2 component requires acquisition of a baseline R* 2 value prior to administration of the microspheres to subtract from the postadministration value in order to obtain the holmium-induced DR*. 2 Although this strategy has been shown to provide a good measure of the Ho-MS biodistribution (3, 9), it makes quantification sensitive to two types of errors. First, subtraction of post- and pretreatment R* 2 values has to be performed voxel-wise to prevent the influence of spatial variations in R* 2 due to tissue-specific R2 values and global field variations and thus necessitates coregistration of pre- and posttreatment images. Such a coregistration puts requirements on patient position and demands changes in size and shape of the tissue between the two imaging sessions to be minimal. Second, using pretreatment R* 2 values, which are dominated by the tissue R2 value in the absence of field inhomogeneities, as a baseline for DR* 2 measurements makes the method sensitive to changes in tissue R2 values occurring in the interval between the pre- and postimage acquisition. Such R2 changes are expected to occur because of development of necrotic, edematous, or hemorrhagic changes as a consequence of the therapy (10). Considering the influence of tissue R2 values, inclusion of R2 measurements may be expected to improve quantification of Ho-MS. The classical approach for measuring R2 values is to collect a series of Carr-Purcell-Meiboom-Gill echoes (11, 12) and apply a monoexponential fit to the SE signal intensities. However, Carr-Purcell-Meiboom-Gill echo signal behavior of diffusive systems containing
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paramagnetic objects deviates from monoexponential behavior due to diffusion effects (13, 14), which has been demonstrated to also occur in Ho-MS containing systems (15), complicating quantification of R2. Acquisition of single Hahn echoes (16) with shifted echo times suffers less from this effect but increases acquisition time, limiting clinical use. Another disadvantage of these methods is that the R2 values are acquired separately from R* 2 values, necessitating image coregistration. For these reasons, other methods have been proposed, 0 dedicated to simultaneously measuring R*, 2 R2, and R2; for example, gradient echo sampling of FID and echo (GESFIDE) (17), which samples the downslope of the FID and the upslope of a single SE, or gradient echo sampling of the SE (GESSE) (18), which samples the upslope and the downslope of a SE. However, since both methods include (partial) sampling of the SE, they suffer from the non-monoexponential signal behavior of the SE envelope due to diffusion (8). In this study, we propose a method, S0 estimation of the free induction decay combined with a single SE measurement (SOFIDSE), that can be used to simultane0 ously measure R*, 2 R2 and R2 in diffusive systems containing paramagnetic Ho-MS within a relatively short acquisition time. The method uses a multigradient echo readout of the FID followed by a 180 refocusing pulse and a single SE readout. By monoexponential fitting the FID data, R* 2 and the signal amplitude at time point 0, S0, are estimated. Subsequently, the estimated S0 together with the signal amplitude of the SE are used to estimate R2 using a monoexponential fit. By subtracting 0 R2 from R*, 2 the microsphere induced R2 is obtained. We will show that SOFIDSE can be used to accurately estimate R2 values, that SOFIDSE is more robust than GESFIDE and GESSE when diffusion effects influence the shape of the SE envelope, and that Ho-MS–induced R20 values obtained by SOFIDSE are independent of the R2 value of the tissue in which the microspheres reside and thus constitute a valuable tool for Ho-MS quantification in tissue that is subjected to R2 changes as a consequence of therapy. THEORY In general, in the absence of proton diffusion, the MR signal decay can be described in terms of a monoexponential function, where the envelope of the FID is characterized by
SðtÞ ¼ Sð0Þ eR2 t with R2 ¼ R2 þ R20
[1]
and the signal amplitude of the SE by SðtÞ ¼ Sð0Þ eR2 t
[2]
where R2 represents the tissue dependent thermodynamic decay component and R20 represents the component induced by system- or object-related external field inhomogeneities (19). In case of proton diffusion, the MR signal behavior in the presence of field inhomogeneities changes, and Eqs. 1 and 2 no longer fully describe the observed signal. To
what extent the signal behavior changes primarily depends on the water diffusion coefficient, the strength of the main magnetic field, and the size, volume fraction, and susceptibility of the field perturbing objects. In the limiting case where the system is in the socalled static dephasing regime, R20 dephasing effects can be refocused by a 180 pulse, and Eqs. 1 and 2 hold (20). In the other limiting case, known as motional narrowing (21), proton diffusion results in an effectively lower, mainly irreversible, R*. In the intermediate 2 regime, signal behavior is complex but has been investigated by means of Monte Carlo–based simulations and experiments (22). Moreover, analytical models have been developed for systems that satisfy certain criteria—for example, the model of Kiselev and Posse for microvascular networks (23, 24) and the strong- and weak-field behavior models of Jensen and Chandra (25, 26). In particular, Monte Carlo results demonstrate that in general, starting from negligible diffusion, R* 2 starts at a maximum plateau and decreases toward a minimum due to motional narrowing—whereas R2, given by the SE signal, starts at a minimum in the static dephasing regime, reaches a peak value in the intermediate regime, and decreases again toward the motional narrowing regime. Over the entire range, R* 2 is larger than R2, but the ratio between the two depends on the system (22). It has been shown that for aqueous systems, the presence of paramagnetic Ho-MS leads to a faster free induction decay and a decrease in SE amplitude (5), which means that both R* 2 and R2 are influenced by the presence of Ho-MS. It has also been shown that the change in FID is dominated by static dephasing effects, leading to a diffusion-independent relaxation rate R*, 2 whereas for the SE case, the induced signal change is the result of diffusion effects (8). Because quantification of Ho-MS using SOFIDSE is based on a subtraction of the diffusion-independent FID relaxation rate and the diffusion-dependent SE decay rate, we have to define a relaxivity parameter that relates SOFIDSE signal decay to the concentration Ho-MS. This parameter, which we call r20 SOFIDSE, is derived as follows. Based on the previous findings (8), i.e. there is no effective influence of diffusion on R*, 2 we define the FID relaxation rate of a Ho-MS containing system as: 0 0 0 R2 ¼ R2;tissue þ R2;tissue þ R2;holm þ R2;B0
[3]
following the definition for static dephasing (18). Here R2,tissue represents the tissue-dependent thermodynamic decay and R20 ,tissue represents a transverse dephasing component related to local field inhomogeneities, which may be present because of, for example, iron deposition in the liver. R20 ,holm is the Ho-MS–induced dephasing component that depends on the shape, volume fraction, and susceptibility of the microspheres and on the main magnetic field B0. R20 , B0 represents dephasing by macroscopic background gradients. For the SE decay, measured at a single SE time (TE), we adopt the monoexponential approach from Eq. 2 but include a relaxation rate term R2, holm diff, which
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represents the microsphere induced irreversible loss of signal due to proton diffusion R2 ¼ R2;tissue þ R2;holm
[4]
diff
It should be noticed that this R2,holm diff component does not appear in Eq. 3 because, although diffusion is present during both the FID and SE, the effective influence of diffusion on the MR signal is different because of the 180 pulse that is applied (22, 25, 26) in the SE case. However, R2,holm diff does depend on R20 holm (since it is a consequence of protons diffusing in the microsphere induced field deviations) and thus also depends on the volume fraction and susceptibility of the microspheres, and on the main magnetic field B0. Although the monoexponential approach of Eq. 4 does not accord with the nonlinear signal description that has been analytically derived for the SE decay of heterogeneous systems subjected to diffusion (24), in this work we will experimentally show that for a clinically interesting range of Ho-MS concentrations this approach suffices. Now that both R* 2 and R2 are defined, the SOFIDSE relaxation rate R20 ,SOFIDSE is given by subtraction of Eqs. 3 and 4: 0 0 0 0 R2;SOFIDSE ¼ ðR2;tissue þ R2;tissue þ R2;holm þ R2;B0 Þ
ðR2;tissue þ R2;holm
diff Þ
0 0 þ R2;holm R2;holm R2;B0
0 ¼ R2;tissue þ
For the proof of principle, we further neglect the presence of B0-related macroscopic and tissue-related intrinsic microscopic field inhomogeneities resulting in diff
[6]
Using Eq. 6, the SOFIDSE holmium relaxivity is given by 0 r2;SOFIDSE ¼
Phantom Three agarose gel series were prepared in 25-mL plastic tubes (length 65 mm; inner diameter ¼ 20 mm). The first series of six gel samples was prepared with 2% agarose (wt/wt) in MnCl2 4H2O doped water (30 mg per liter distilled water). During preparation of the gel, nonradioactive Ho-MS, prepared as described by Nijsen et al. (1), were added in concentrations of 0.96, 2.24, 3.03, 4.16, and 4.99 mg/mL. One sample was left blank (0 mg/mL). The microspheres had a density of 1.4 g/mL and a holmium content of 18.9% (wt/wt), whereas the microsphere diameter ranged between 20 and 50 mm with a mean diameter of 30 mm. The second series consisted of six gel samples with different agarose content: 1.00, 1.26, 1.51, 1.73, 2.01, and 2.26 % agarose (wt/wt) in MnCl2 4H2O doped water (27 mg per liter distilled water). No Ho-MS were added. The third series of six gel samples was identical to the second series with respect to the agarose content but now Ho-MS were added with an intended concentration of 1 mg/mL. Actual Ho-MS concentrations were 1.01, 1.08, 1.08, 1.04, 1.08, and 0.99 mg/mL. Healthy Volunteer
[5]
diff
0 0 R2;SOFIDSE ¼ R2;holm R2;holm
Preparation
0 0 DðR2;holm R2;holm diff Þ DR2;SOFIDSE ¼ D½Ho-PLLA-MS D½Ho-PLLA-MS [7]
From Eq. 6, it is observed that the here-defined SOFIDSE relaxation rate and thus relaxivity defined in Eq. 7 include only Ho-MS–induced dephasing effects and do not depend on tissue characteristics.
A 27-year-old male healthy volunteer who provided written informed consent was included in this study. The study setup was in accordance with the guidelines of the institutional review board. Data Acquisition MRI data were acquired on a 1.5T whole body scanner (Achieva, Philips Healthcare, Best, The Netherlands), using an eight-channel head receive coil for the phantom experiments and a 16-channel torso receive coil for imaging of the healthy volunteer. Data were acquired in such a way that it could be processed according to three different methods: GESFIDE, GESSE and SOFIDSE. Therefore, an acquisition scheme was used that sampled both the FID and, after applying a 180 refocusing pulse, the SE envelope by means of gradient echo images. For this purpose, a custom-built research patch (Philips Research Laboratories, Hamburg, Germany) was used, as described in Fig. 2 of reference (27), but using only one SE.
METHODS
Phantom
SOFIDSE was applied to an agarose phantom containing a range of Ho-MS concentrations, and results were compared with results obtained from a combination of FID and shifted SE measurements to validate the method. 0 SOFIDSE results (R*, 2 R2, R2) were compared with results that were obtained using the GESFIDE (17) and GESSE (18) methods. Furthermore, the independence of SOFIDSE-based Ho-MS quantification on tissue R2 was demonstrated by measurements on a phantom containing gels with varying agarose concentration and therefore different R2 values. Finally, similar experiments were performed on a healthy volunteer to investigate the in vivo applicability of the method.
For the first gel series, data were acquired using a twodimensional sequence, sampling the FID by 11 gradient echoes (TE1 ¼ 3.1 ms/DTE ¼ 0.8 ms) followed by sampling the SE envelope by 11 gradient echoes with DTE ¼ 0.8 ms, centered around the SE peak. This was repeated five times using five different SE times (20, 30, 40, 50, and 60 ms) to provide shifted SE (SSE) data. Other parameters included: repetition time (TR) ¼ 2000 ms; slice thickness ¼ 10 mm; field of view (FOV) ¼ 128 128 mm2; acquisition matrix ¼ 642; reconstruction matrix ¼ 802; and readout bandwidth ¼ 1783 Hz/pixel. For the second gel series, SSE data were acquired using a two-dimensional single SE sequence that was
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repeated for five different echo times (10, 20, 30, 40, and 50 ms). TR, slice thickness, FOV and matrix were identical to the parameters used for the first gel series, apart from a slightly different readout bandwidth (2047 Hz/ pixel). In addition, diffusion-weighted imaging with bvalues of 0, 100, 200, 300, and 400 s/mm2 (effective echo time: 48 ms) was performed for apparent diffusion coefficient (ADC) measurements to verify that varying the agarose concentration did not influence the diffusion coefficient. Other imaging parameters were identical to those of the previous experiment. For the last gel series, a single acquisition was performed, sampling both the FID (TE1 ¼ 3.1 ms) and SE (TE ¼ 30 ms) by 11 gradient echoes (DTE ¼ 0.8 ms). Healthy Volunteer Multislice SOFIDSE data were acquired using 13 gradient echoes for sampling the FID (TE1 ¼ 2.3 ms; DTE ¼ 0.8 ms) and 13 gradient echoes for sampling the SE envelope (SE time ¼ 30 ms; DTE ¼ 0.8 ms). Imaging parameters included: FOV ¼ 384 344 mm2; acquisition matrix ¼ 192 151; reconstruction matrix ¼ 192 192; slice thickness ¼ 6 mm; number of slices ¼ 45; TR ¼ 360 ms; flip angle ¼ 90 ; and readout bandwidth ¼ 1783 Hz/ pixel. Sensitivity encoding with a factor of 2.7 was used for acceleration resulting in a scan time of 5 20 s during breath hold. Dual echo (DE) SE data were acquired using a multislice DE sequence with TE1 ¼ 20 ms and TE2 ¼ 50 ms. FOV, matrix, and flip angle were identical to the SOFIDSE acquisition. A TR of 300 ms was used and the readout bandwidth was 1733 Hz/pixel. Here also sensitivity encoding was used (factor 2.7) and two signal averages were acquired resulting in a scan time of 9 20 s during breath hold. Data Analysis Phantom Signal intensities for each gel sample were measured using regions of interest (ROI) (mean size ¼ 85 6 4 pixels). Data of the first gel series were processed according to three different methods: SOFIDSE, GESFIDE, and GESSE. The sampling schemes used for these three methods are illustrated in Fig. 1. For SOFIDSE, a monoexponential fit was applied to the gradient echo signal intensities of the FID data from which R* 2 and S0 values were obtained. A threshold was applied excluding signal intensities from the fitting procedure with a signal-to-noise ratio (SNR) lower than 3, with the noise determined by the standard deviation (SD) of the ROI signal intensity of the 0 mg/mL sample. Subsequently, the estimated S0 values were combined with the signal intensities of the central SE sample for TE ¼ 30 ms and R2,SOFIDSE values were determined by R2,SOFIDSE ¼ ln((S0)/S(TE))/TE. Next, the shifted spin echo (SSE) intensities, for the range of used SE times (20, 30, 40, 50, 60 ms) were fitted by S(TE) ¼ S0 exp[R2, SSE TE] to obtain S0 and R2, SSE values from the SSE data. Finally, R20 SOFIDSE values were calculated using R20 SOFIDSE ¼ R* 2 R2 (Eq. 6) with R2 either R2,
FIG. 1. Illustration of the sampling schemes used for SOFIDSE (top), GESFIDE (middle), and GESSE (bottom). The solid lines illustrate the general MR signal in time, and the circles illustrate the sample points used for quantification of R2, R2*, and R20 by the specific method. For the SOFIDSE method, S0 is the estimated signal at time point zero, and the dashed line illustrates the R2 signal envelope
values or R2,SSE values. Correlations coefficients for both R2 values and both R20 SOFIDSE values were calcur2, and r20 SOFIDSE lated and the Ho-MS relaxivities r*, 2 were determined from a linear fit of relaxation rates versus microsphere concentration. For GESFIDE, a monoexponential fit was applied to both the FID and the upslope of the SE, including the top (central echo). The SNR threshold was determined in the same way as was done for SOFIDSE. According to Ma and Wehrli (17), a fit to the FID provides R* 2 (¼R2 þ R20 ), whereas a fit to the upslope of the SE provides a value representing R2 R20 . Therefore, R2 was obtained by addition of the FID and SE upslope: SOFIDSE
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FIG. 2. a: Signal decay of the FID part of the SOFIDSE data, on a logarithmic scale, with their monoexponential fit for three different concentrations of Ho-MS (0, 2.24 and 4.99 mg/mL). Monoexponential signal decay is observed for all concentrations, excluding signal values lower than the applied SNR threshold. b: Signal intensities measured from the SSE experiments with their monoexponential fit. Monoexponential signal decay is also observed here. c: S0 values estimated from the monoexponential fit of the FID (SOFIDSE) and of the SSE measurements for the whole range of Ho-MS concentrations. SOFIDSE values are slightly higher than SSE values for all concentrations with a mean SNR 6 SD of 429 6 9 for SOFIDSE and 393 6 13 for SSE.
R2 þ ðR2 R20 Þ ðR2 þ R20 þ R2 R20 Þ ¼ ¼ R2 2 2
[8]
and R20 was obtained by subtraction: R2 -ðR2 R20 Þ ðR2 þ R20 R2 þ R20 Þ ¼ ¼ R20 2 2
[9]
For GESSE, a monoexponential fit was applied to both the upslope and the downslope of the SE, including the top (central echo) for both cases. Again, the SNR threshold was determined the same way as mentioned above. According to Yablonskiy and Haacke (18), a fit to the upslope provides R2 R20 , whereas a fit to the downslope provides R2 þ R20 , which represents R*. 2 Therefore, R2 was obtained by addition: ðR2 R20 Þ þ ðR2 þ R20 Þ ¼ R2 2
[10]
values were obtained by subtracting R* 2 and R2 values. Voxel-wise R2 values were also obtained from a monoexponential fit to the SE signal intensities of the DE data [R2 (DE)]. The liver was manually segmented using the tissue contrast of the SE image of the SOFIDSE data. The distribution of estimated R2 values within the liver was measured for both SOFIDSE and DE, and mean R2 values were calculated together with their SD. In addition, the mean R* 2 value of the liver, measured from the SOFIDSE data, was calculated and subtracted from the R* 2 maps in order to obtain maps that correspond to conventional DR* 2 maps. Assuming homogeneous liver tissue, and neglecting effects of, for example, the presence of iron in the liver, these DR* 2 maps will represent the variation in R* 2 induced by field inhomogeneities and, therefore, be comparable to R20 SOFIDSE values. The distribution of these DR* 2 values was compared with the distribution of R20 SOFIDSE values and the means and SDs were calculated.
whereas R20 was obtained by subtraction ðR2 R20 Þ ðR2 þ R20 Þ ¼ R20 2
RESULTS [11]
For the second gel series, signal intensities of the SSE data were monoexponentially fitted to obtain the R2 value for each agarose concentration. Signal intensities of the diffusion weighted images were also fitted using SðbÞ ¼ Sð0Þ exp½ADC b
[12]
from which ADC values were obtained. For the third gel series, R20 SOFIDSE values were determined following the same procedure used for the first gel series. Healthy Volunteer From the gradient echo images of the FID part of the SOFIDSE data, S0 values and R* 2 values were estimated for each voxel by applying a monoexponential fit. The resulting S0 images were subsequently used in combination with the central SE image of the SOFIDSE data to determine voxel-wise R2 (SOFIDSE) values. R20 SOFIDSE
Phantom Signal intensities from the gel series containing a range of Ho-MS showed monoexponential signal decay for all concentrations for both the FID of the SOFIDSE data (Fig. 2a) and the SSE data (Fig. 2b), excluding values lower than the applied SNR threshold. A monoexponential fit (R2 ¼ 1 for all concentrations and both datasets) provided S0 values for both the SOFIDSE and SSE data (Fig. 2c). Estimated S0 values were slightly higher for SOFIDSE compared with SSE, including the 0 mg/mL sample. The mean SNR 6 SD of the estimated S0 values of the entire range of Ho-MS was 429 6 9 for SOFIDSE and 393 6 13 for SSE, corresponding to an S0 overestimation of 9% on average. Variations in S0 over the range of microspheres concentrations were observed, showing similar deviations for SOFIDSE and SSE but no correlation with the concentration Ho-MS. Signal intensities of the upslope and downslope of the SE envelope obtained from the SOFIDSE data revealed obvious deviation from monoexponential signal behavior (Fig. 3), particularly for higher Ho-MS concentrations.
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FIG. 3. Upslope (a) and downslope (b) of the SE envelope of the SOFIDSE data around the SE time of 30 ms on a logarithmic scale for three different concentrations of Ho-MS (0, 2.24 and 4.99 mg/mL). The signal of both the upslope and downslope of the SE envelope deviates from monoexponential behavior.
R2 values that were obtained by either monoexponential fitting of the SSE data or determined by SOFIDSE data (with SE ¼ 30 ms) both showed a linear dependency on concentration (Fig. 4a). For SOFIDSE, slightly higher values were found compared with SSE values, which may be attributed to the higher SOFIDSE S0 values, leading to an overestimation of 5% on average for SOFIDSE. No significant relation of this overestimation with Ho-MS concentration was found. From a linear fit to the R2 values, a Ho-MS r2 relaxivity of 8.6 6 1.0 s1 and 8.7 6 1.3 s1 (95% confidence bounds) was found for, respectively, SOFIDSE and SSE at 1.5T. From a statistical analysis, a correlation coefficient of 1 (P 5 1.5 106) was found for the two methods (Fig. 4b). Figure 4c shows the R20 SOFIDSE values determined by subsequently subtracting the R2 values obtained from SSE and SOFIDSE from the R* 2 values determined from the FID of the SOFIDSE data, as a function of concentration Ho-MS. A linear relationship was found between R20 SOFIDSE values and concentration microspheres for both methods, resulting in an r20 SOFIDSE relaxivity of 99 6 5 s1 mg1 mL (95% confidence interval) for the Ho-MS at 1.5T for both methods. The R20 value of the sample containing no HoMS (0.6 s1), resulting from the meas1 ured R* and 28.7 s1 with SDs of 2 and R2 values (29.3 s 0.6 s1 and 0.3 s1, respectively) indicates negligible influence of macroscopic background gradients for the phantom setup. A correlation coefficient of 1 (P ¼ 9 1011) was found for the R20 SOFIDSE values of the two methods (Fig. 4d). Figure 4c also shows the R* 2 values determined from the FID and normalized by subtraction of the R* 2 value of the 0 mg/mL sample. By a linear fit to 1 these values, an r* mg1 mL 2 relaxivity of 108 6 7 s was found. 0 Comparing R*, 2 R2, and R2 values determined by subsequent SOFIDSE, GESFIDE, and GESSE (Fig. 5) showed that both GESFIDE and GESSE provided values that were SE time–dependent. For GESFIDE, R* 2 values showed no dependency on the SE time because R* 2 was estimated from the FID. However, R2 values determined by GESFIDE increased for increasing SE times (R2 ¼ 48– 75 s1 for SE ¼ 20–60 ms, 0.96 mg/mL HoMS; R2 ¼ 88– 160 s1 for SE ¼ 20–60 ms, 3.03 mg/mL HoMS). As a
result, GESFIDE R20 values decreased for increasing SE times (R20 ¼ 87 s1–60 s1 for SE ¼ 20–60 ms, 0.96 mg/ mL HoMS; R20 ¼ 271–200 s1 for SE ¼ 20–60 ms, 3.03 mg/mL HoMS). For GESSE, both R* 2 values and R2 values were found to depend on the used SE time, because both parameters were measured using the SE envelope. R* 2 values decreased for increasing SE times (R* 2 ¼ 97–61 s1 for SE ¼ 20–60 ms, 0.96 mg/mL HoMS; R20 ¼ 246– 148 s1 for SE ¼ 20–60 ms, 3.03 mg/mL HoMS), whereas R2 values increased for increasing echo times (R2 ¼ 29– 40 s1 for SE ¼ 20–60 ms, 0.96 mg/mL HoMS; R2 ¼ 32– 54 s1 for SE ¼ 20–60 ms, 3.03 mg/mL HoMS). As a result, also for GESSE, R20 decreased for increasing SE times (R20 ¼ 68–23 s1 for SE ¼ 20–60 ms, 0.96 mg/mL HoMS; R20 ¼ 215–94 s1 for SE ¼ 20–60 ms, 3.03 mg/mL HoMS). For SOFIDSE, no obvious dependency of R*, 2 R2, and thus R20 was found for increasing SE times. R2 values determined from the SSE data of the second gel series, containing various concentrations of agarose but no Ho-MS, are plotted in Fig. 6a. Increasing R2 values were found for increasing agarose concentrations, where R2 ranged from 17 to 29 s1, corresponding to T2 values of 58–35 ms, for the agarose concentration range of 1%–2.26% (wt/wt). ADC values of the same gel series, determined from the diffusion-weighted images, showed no dependency on agarose concentration (Fig. 6b), demonstrating that only the intrinsic R2 values of the samples differed. R20 SOFIDSE values of the third gel series, containing various concentrations of agarose and thus various R2 values, and 1 mg/mL Ho-MS, showed fluctuations that corresponded to the known fluctuations in concentration HoMS (Fig. 7a). R20 SOFIDSE values corrected for these fluctuations showed no dependency on sample R2, whereas R* 2 values showed an increase for increasing sample R2 (Fig. 7b). Healthy Volunteer R2 maps of the liver of the healthy volunteer (containing no Ho-MS) determined from the SOFIDSE data showed good agreement with R2 maps determined from the DE data (Fig. 8a,8b). Differences were observed particularly
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FIG. 4. a: R2 values, determined from a monoexponential fit to the estimated S0 in combination with a single SE measurement (SOFIDSE) and from a monoexponential fit to the repeated single spin echo (SSE) measurement as a function of concentration Ho-MS. b: R2 values determined by SOFIDSE versus R2 values determined by SSE. A good correlation is observed between the two methods, although a small overestimation is found for the SOFIDSE method when compared with unity (dashed line). c: R2* values as determined from gradient echo sampling of the FID normalized by the R2* value of the 0 mg/mL sample (R2* norm) and R20 values determined by subtraction of SOFIDSE R2 values from SOFIDSE R2* values (R20 SOFIDSE) and by subtraction of SSE R2 values from SOFIDSE R2* values (R20 SSE). d: R20 SOFIDSE values versus R20 SSE values display high correlation (correlation coefficient ¼ 1, P ¼ 3 1012)
at the locations of large blood vessels (Fig. 8d) and are probably a result of flow artifacts, since for SOFIDSE a 90 /180 excitation scheme was used, while for DE a 90 /180 /180 excitation scheme was applied. In areas where no large vessels were present, R2 values (mean 6 SD) measured in a region of interest (Fig. 8, white circle) were similar for both methods: 31 6 6 s1 and 30 6 12 s1 for, respectively, SOFIDSE and DE SE. The SOFIDSE R2 maps showed smaller variability as reflected by the SD of R2 within the ROI, despite the fact that the SOFIDE SE image was noisier than the SE image of the DE data set (as a result of using two signal averages for the latter). R20 SOFIDSE maps (Fig. 9a) and the R* 2 maps that were determined from only the FID part of the SOFIDSE data and normalized by their mean value (Fig. 9b) showed good visual resemblance and no obvious differences. A quantitative assessment, comparing the distributions of R2, R20 SOFIDSE, and R* 2 that were found in the entire liver, showed that R2 values obtained by SOFIDSE were very similar to R2 values obtained by the DE acquisition (Fig. 10a). On average, a mean R2 value of 30 s1 with an SD of 10 s1 was found for SOFIDSE, whereas for the DE acquisition these values were 28 s1 and 17 s1, respectively. A very good agreement was found between
R20 SOFIDSE values and normalized R* 2 values. Mean values of 2 s1 and 0 s1 were found with an SD of 19 s1 and 20 s1, respectively (Fig. 10b). A slight deviation from 0 was found for the SOFIDSE R20 SOFIDSE values. DISCUSSION AND CONCLUSIONS In this study, we present a new method for simultaneous 0 estimation of R*, 2 R2, and R2 values for quantification of Ho-MS, paramagnetic microspheres that can be employed for radioembolization. The method assumes that both the free induction decay and the single SE decay can be described by a monoexponential function with identical initial value S0. In that case, S0 estimated from the FID can subsequently be used in combination with a single SE to estimate the SE decay rate. Phantom experiments clearly showed that the FID as well as the shifted single SE decay of Ho-MS–containing systems are monoexponential, irrespective of the microsphere concentration. The S0 values that were obtained by SOFIDSE showed a small overestimation (9%), independent of the concentration Ho-MS, compared with the reference values obtained by SSE. This overestimation may be the result of differences in excitation and refocusing slice profiles
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FIG. 5. Comparison of R2* (a), R2 (b), and resulting R20 (c) values as a function of used SE time for samples containing 0.96 mg/mL HoMS (left) and 3.03 mg/mL HoMS (right) determined by respectively GESFIDE, GESSE, and SOFIDSE. Both GESFIDE and GESSE show SE timedependent R2 values and R20 values, whereas GESSE also shows SE timedependent R2* values. For SOFIDSE, no dependency on SE time is observed.
and nonperfect refocusing pulses, reducing the absolute signal at the SE time, which leads to lower estimated S0 values. As a consequence of this S0 overestimation, SOFIDSE R2 values showed a concentration-independent overestimation of 5% on average compared with SSE R2 values, which will be acceptable for the intended application.
The monoexponential behavior of both FID and SSE, for the entire investigated range of Ho-MS concentrations, demonstrated that the signal decay of Ho-MS– containing systems can be characterized by an addition of monoexponential components as given by Eqs. 3 and 4. Therefore, the Ho-MS–induced signal decay in SOFIDSE measurements, R20 SOFIDSE, can be determined
FIG. 6. a: R2 values as a function of agarose content measured from the gel series containing no Ho-MS. An increase of R2 is observed for increasing agarose content. b: ADC values as a function of agarose content measured from the same gel series. No changes in ADC value are observed for changes in agarose content.
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FIG. 7. a: R20 values (w) and corresponding Ho-MS concentrations (•) as a function of baseline R2 value, measured from the gel series with varying agarose content and on average 1 mg/mL Ho-MS. No influence of the baseline R2 value on R20 is visible. Fluctuations that are observed clearly correspond to fluctuations in Ho-MS concentrations. b: R2* and R20 values normalized for Ho-MS concentration as a function of baseline R2. R2* depends on R2 gel, whereas for R20 , no such dependency is found
by a subtraction of R* 2 and R2 as given by Eq. 5, and this R20 SOFIDSE value is, unlike R*, independent of the R2 2 value of the tissue, as was clearly demonstrated by the measurements performed on the phantom with varying intrinsic R2 values (Fig. 7). The introduction of this R20 SOFIDSE value that only characterizes the reversible dephasing effect of the microspheres leads to the intro-
duction of the Ho-MS relaxivity parameter r20 SOFIDSE, which linearly relates the local R20 SOFIDSE to the microsphere concentration (Eq. 6). This r20 SOFIDSE value was empirically found to be 99 6 5 s1 mg1 mL at 1.5T for the used microspheres with a holmium content of 1 18.9%, whereas the r* 2 relaxivity was found to be 108 s 1 6 7 mg mL.
FIG. 8. Top row: R2 maps on a scale of 10 to 76 s1 determined from SOFIDSE data (left) and DE data (right). On average, similar values are found for both methods, but DE data show differences at locations where large vessels are present. These differences are also clearly visible in the corresponding SE images (bottom row) where hypo- and hyperintense areas are observed in the first SE image (20 ms) of the DE data (right). These hypo- and hyperintense areas are much less visible in the central SE image (20 ms) of the SE envelope of the SOFIDSE data (left). From an ROI analysis (white circle), similar R2 values were found for normal liver tissue for both methods (R2 ¼ 31 6 6 s1 for SOFIDSE and R2 ¼ 30 6 12 s1 for DE SE).
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FIG. 9. One slice of the R20 maps determined by SOFIDSE (a) and the same slice of the normalized R2* map, determined from the FID of the SOFIDSE data and normalized by the mean R2* value of the entire liver (b). The normalized map mimics a DR2* map that would have been estimated using the conventional quantification method. No obvious differences are observed between the two maps.
In vivo, R2 values obtained by SOFIDSE closely corresponded with R2 values obtained by a dual SE technique, demonstrating the clinical applicability of the method. For Ho-MS quantification in clinical practice, SOFIDSE adds value for several reasons. First, it allows for R2 measurements using a short acquisition time, since only a single SE is required. Second, within the same time, R* 2 is measured, which was shown to enable Ho-MS quantification purely based on R20 dephasing effects. By combining FID and SE in a single acquisition, SOFIDSE basically eliminates the need for acquisition of baseline MRI data prior to administration of the microspheres, preventing errors due to misalignment of preand posttherapy images and errors invoked by tissue changes. This will especially create possibilities for quantitative imaging during the radioembolization procedure, since image processing and user intervention are minimal and R20 SOFIDSE maps can be calculated rapidly on site. A third benefit of the method is that the R* 2 or R20 SOFIDSE maps are intrinsically coregistered to the anatomical SE image, facilitating segmentation of the maps based on the contrast of the SE image. Since the quantitative MRI maps can be used to determine the absorbed radiation dose of both liver and tumor tissue (3, 9), SOFIDSE enables fast verification of safety and potential efficacy of holmium microsphere radioembolization. Field inhomogeneities other than those induced by the Ho-MS may influence the SOFIDSE measurements. For
the phantom setup, macroscopic field effects were negligible according to the minimal differences that were measured between R* 2 and R2 of the blank gel sample. However, in vivo, these effects may be comparable to those familiar from other R*-based quantification meth2 ods and will mostly be present near the lungs and stomach as a result of air–tissue interfaces. Another source of error may be the presence of iron in liver tissue, which will also lead to increased R20 SOFIDSE values that may be misinterpreted as concentrations of Ho-MS. Correcting for the macroscopic effects induced by air–tissue interfaces may be done by using postprocessing techniques (28). Correcting for the presence of iron may require pretreatment imaging for comparison, but that will negate one of the benefits of SOFIDSE (ie, quantification based on posttreatment imaging only). Future clinical studies have to show the extent of iron-induced errors in clinical practice. In the present study, we show the applicability of SOFIDSE for quantification of Ho-MS. However, its use is not restricted to Ho-MS. If the system under investigation complies with the condition described in this study (ie, if it can be assumed that S0 is identical for both FID and SE decay), then SOFIDSE can be used to estimate R* 2 and R2. Whether SOFIDSE is superior to other methods proposed in the literature, such as GESFIDE and GESSE (17, 18), will depend on the clinical context and the expected MR signal characteristics of the tissue of interest. We showed that, in case diffusion effects lead to
FIG. 10. a: Distributions of R2 values found in the entire liver for the SOFIDSE method (solid line) and the DE method (dashed line). b: R20 values, determined by SOFIDSE, and normalized R2* values, determined by subtraction of the mean R2* value of the liver from the voxel R2* values, that were found in the entire liver of the subject.
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non-monoexponential signal behavior of the SE envelope, SOFIDSE provides a more robust R20 estimate than the existing methods. Furthermore, compared with GESSE, data can be acquired more quickly, since SOFIDSE does not sample the downslope of the SE envelope, saving acquisition time. In conclusion, S0 estimation of the free induction decay combined with a single SE measurement can be 0 used to simultaneously measure R*, 2 R2, and R2 for R2 insensitive quantification of Ho-MS within a single acquisition. REFERENCES 1. Nijsen JF, Zonnenberg BA, Woittiez JR, Rook DW, Swildens-van Woudenberg IA, van Rijk PP, van het Schip AD. Holmium-166 poly lactic acid microspheres applicable for intra-arterial radionuclide therapy of hepatic malignancies: effects of preparation and neutron activation techniques. Eur J Nucl Med 1999;26:699–704. 2. Nijsen JFW, van Steenbergen MJ, Kooijman H, Talsma H, KroonBatenburg LM, van de Weert M, van Rijk PP, De Witte A, van het Schip AD. Characterization of poly(L-lactic acid) microspheres loaded with holmium acetylacetonate. Biomaterials 2001;22:3073–3081. 3. van de Maat GH, Seevinck PR, Elschot M, et al. MRI-based biodistribution assessment of holmium-166 poly (L-lactic acid) microspheres after radioembolisation. Eur Radiol 2013;23:827–835. 4. Nijsen JFW, Seppenwoolde JH, Havenith T, Bos C, Bakker CJ, van het Schip AD. Liver tumors: MR imaging of radioactive holmium microspheres—phantom and rabbit study. Radiol 2004;231:491–499. 5. Seppenwoolde JH, Nijsen JFW, Bartels LW, Zielhuis SW, van het Schip AD, Bakker CJ. Internal radiation therapy of liver tumors: qualitative and quantitative magnetic resonance imaging of the biodistribution of holmium-loaded microspheres in animal models. Magn Reson Med 2005;53:76–84. 6. Gupta T, Virmani S, Neidt TM, et al. MR tracking of iron-labeled glass Radioembolization microspheres during transcatheter delivery to rabbit VX2 liver tumors: feasibility study. Radiol 2008;249: 845–854. 7. Bulte JWM, Duncan ID, Frank JA. In vivo magnetic resonance tracking of magnetically labeled cells after transplantation. J Cereb Blood Flow Met 2002;22:899–907. 8. Seevinck PR, Seppenwoolde JH, Zwanenburg JJ, Nijsen JF, Bakker CJ. FID Sampling superior to spin-echo sampling for T2*-based quantification of holmium-loaded microspheres: theory and experiments. Magn Reson Med 2008;60:1466–1476. 9. Seevinck PR, van de Maat GH, de Wit TC, Vente MA, Nijsen JF, Bakker CJ. Magnetic resonance imaging-based radiation-absorbed dose estimation of 166Ho microspheres in liver radioembolization. Int J Radiation Oncol Biol Phys 2012;83:e437–e444. 10. Kamel IR, Bluemke DA. Imaging evaluation of hepatocellular carcinoma. J Vasc Interv Radiol 2002;13:S173–S183.
283 11. Carr HY, Purcell EM. Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys Rev 1954;94:630–638. 12. Meiboom S, Gill D. Modified spin-echo method for measuring nuclear relaxation times. Rev Sci Instr 1958;29:688–691. 13. Rozenman Y, Zou X, Kantor HL. Signal loss induced by superparamagnetic iron oxide particle in NMR spin-echo images: the role of diffusion. Magn Reson Med 1990;14:31–39. 14. Bulte JWM, Miller GF, Vymazal J, Brooks RA, Frank JA. Hepatic hemosiderosis in non-human primates: quantification of liver iron using different field strengths. Magn Reson Med 1997;37:530–536. 15. GH van de Maat, PR Seevinck, KL Vincken, Vincken KL, de Leeuw H, Bakker CJ. Multi-echo spin-echo (MESE) signal behavior of paramagnetic holmium-166 loaded microspheres for radiotherapy: experiment and simulation. In Proceedings of the 17th Annual Meeting of ISMRM, Honolulu, Hawaii, USA, 2009. p. 4468. 16. Hahn EL. Spin echoes. Phys Rev 1950;80:580–594. 17. Ma J, Wehrli FW. Method for image-based measurement of the reversible and irreversible contribution to the transverse-relaxation rate. J Magn Reson Ser B 1996;111:61–69. 18. Yablonskiy DA, Haacke EM. An MRI method for measuring T2 in the presence of static and RF magnetic field inhomogeneities. Magn Reson Med 1997;37:872–876. 19. Haacke EM, Brown RW, Thompson MR, Venkatesan R. Magnetic resonance imaging: physical principles and sequence design. New York: John Wiley & Sons, Inc; 1999. 20. Yablonski DA, Haacke EM. Theory of NMR signal behavior in magnetically inhomogeneous tissues: the static dephasing regime. Magn Reson Med 1994;32:749–763. 21. Gillis P, Koenig SH. Transverse relaxation of solvent protons induced by magnetized spheres: application to ferritin, erythrocytes, and magnetite. Magn Reson Med 1987;5:323–345. 22. Boxerman JL, Hamberg LM, Rosen BR, Weisskoff RM. MR contrast due to intravascular magnetic susceptibility perturbations. Magn Reson Med 1995;34:555–566. 23. Kiselev VG, Posse S. Analytical theory of susceptibility induced NRM signal dephasing in a cerebrovascular network. Phys Rev Lett 1998;81:5696–5699. 24. Kiselev VG, Posse S. Analytical model of susceptibility-induced MR signal dephasing: effect of diffusion in a microvascular network. Magn Reson Med 1999;41:499–509. 25. Jensen JH, Chandra R. Strong field behavior of the NMR signal from magnetically heterogeneous tissues. Magn Reson Med 2000;43: 226–236. 26. Jensen JH, Chandra R. NMR relaxation in tissues with weak magnetic inhomogeneities. Magn Reson Med 2000;44:144–156. 27. Remmele S, Ring J, S en egas J, Heindel W, Mesters RM, Bremer C, Persigehl T. Concurrent MR blood volume and vessel size estimation in tumors by robust and simultaneous DR2 and DR2* quantification. Magn Reson Med 2011;66:144–153. 28. de Leeuw H, Bakker CJG. Correction of gradient echo images for first and second order macroscopic signal dephasing using phase derivative mapping. Neuroimage 2012;60:818–829.
0 Simultaneous R*, 2 R2, and R2 Quantification by Combining S0 Estimation of the Free Induction Decay with a Single Spin Echo: A Single Acquisition Method for R2 Insensitive Quantification of Holmium-166–Loaded Microspheres G. H. van de Maat,1* H. de Leeuw,1 P. R. Seevinck,1 M. A. A. J. van den Bosch,2 J. F. W. Nijsen,2 and C. J. G. Bakker2 Purpose: To present a new method, S0 estimation of the free induction decay combined with a single spin echo measurement (SOFIDSE), that enables simultaneous measurements of R*2 , R2, and R20 in order to quantify the local concentration of holmium microspheres (Ho-MS) for radioembolization. Theory and Methods: SOFIDSE estimates R*2 and the signal magnitude at time point 0, S0, from a multigradient echo readout of the free induction decay and subsequently estimates R2 using S0 and a single spin echo, from which R20 is deducted. The method was evaluated by comparing SOFIDSE R2 values with values obtained from shifted spin echo (SSE) measurements on a phantom setup containing Ho-MS and from dual spin echo measurements on a healthy volunteer. Results: On average, SOFIDSE showed a small overestimation of R2 values compared with SSE independent of the microsphere concentration. R20 values determined by subtraction of either SOFIDSE R2 or SSE R2 from R*2 showed excellent agreement (correlation coefficient ¼ 1; P ¼ 9 1011). The HoMS–induced R20 values obtained by SOFIDSE were insensitive to the R2 value of the tissue in which they resided. Conclusion: SOFIDSE enables quantification of Ho-MS, in media with spatially or temporally varying R2 values, in a single C 2014 acquisition. Magn Reson Med 73:273–283, 2015. V Wiley Periodicals, Inc. Key words: SOFIDSE; holmium microspheres; R*; 2 R2; S0 estimation; quantification
INTRODUCTION MRI-based biodistribution measurement of paramagnetic holmium-166 poly(L-lactic acid) microspheres (Ho-MS) (1–5) is, like detection of other clinically applicable (super)-paramagnetic particles (6, 7), primarily based on R* 2 dephasing effects the microspheres induce. In general, the R* 2 relaxation rate increases for increasing parti-
1 Image Sciences Institute, University Medical Center Utrecht, Utrecht, The Netherlands. 2 Department of Radiology and Nuclear Medicine, University Medical Center Utrecht, Utrecht, The Netherlands.
*Correspondence to: Gerrit H. van de Maat, Q S.459, P.O. Box 85500, 3508 GA Utrecht, The Netherlands. E-mail: [email protected]. Received 3 October 2013; revised 19 December 2013; accepted 31 December 2013 DOI 10.1002/mrm.25138 Published online 7 March 2014 in Wiley Online Library (wileyonlinelibrary. com). C 2014 Wiley Periodicals, Inc. V
cle concentration, enabling changes in R* 2 to be related to the local particle amount. Common methods to measure R* 2 relaxation rates sample either the free induction decay (FID) or the spin echo (SE) by using a multigradient echo sequence. The preferred method of quantifying the local amount of Ho-MS is by sampling the FID, as this has been shown to provide a more accurate quantitative measure than sampling the SE due to non-monoexponential signal behavior of the latter as a consequence of diffusion effects (8). R* 2 values are estimated by a monoexponential fit to the FID data and are linearly related to the local microsphere concentration by their relaxivity r*. The 2 major drawback of this approach is that both the HoMS–induced signal decay and the intrinsic R2 signal decay of the tissue in which the microspheres reside contribute to the observed R* 2 values. The presence of this tissue R2 component requires acquisition of a baseline R* 2 value prior to administration of the microspheres to subtract from the postadministration value in order to obtain the holmium-induced DR*. 2 Although this strategy has been shown to provide a good measure of the Ho-MS biodistribution (3, 9), it makes quantification sensitive to two types of errors. First, subtraction of post- and pretreatment R* 2 values has to be performed voxel-wise to prevent the influence of spatial variations in R* 2 due to tissue-specific R2 values and global field variations and thus necessitates coregistration of pre- and posttreatment images. Such a coregistration puts requirements on patient position and demands changes in size and shape of the tissue between the two imaging sessions to be minimal. Second, using pretreatment R* 2 values, which are dominated by the tissue R2 value in the absence of field inhomogeneities, as a baseline for DR* 2 measurements makes the method sensitive to changes in tissue R2 values occurring in the interval between the pre- and postimage acquisition. Such R2 changes are expected to occur because of development of necrotic, edematous, or hemorrhagic changes as a consequence of the therapy (10). Considering the influence of tissue R2 values, inclusion of R2 measurements may be expected to improve quantification of Ho-MS. The classical approach for measuring R2 values is to collect a series of Carr-Purcell-Meiboom-Gill echoes (11, 12) and apply a monoexponential fit to the SE signal intensities. However, Carr-Purcell-Meiboom-Gill echo signal behavior of diffusive systems containing
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paramagnetic objects deviates from monoexponential behavior due to diffusion effects (13, 14), which has been demonstrated to also occur in Ho-MS containing systems (15), complicating quantification of R2. Acquisition of single Hahn echoes (16) with shifted echo times suffers less from this effect but increases acquisition time, limiting clinical use. Another disadvantage of these methods is that the R2 values are acquired separately from R* 2 values, necessitating image coregistration. For these reasons, other methods have been proposed, 0 dedicated to simultaneously measuring R*, 2 R2, and R2; for example, gradient echo sampling of FID and echo (GESFIDE) (17), which samples the downslope of the FID and the upslope of a single SE, or gradient echo sampling of the SE (GESSE) (18), which samples the upslope and the downslope of a SE. However, since both methods include (partial) sampling of the SE, they suffer from the non-monoexponential signal behavior of the SE envelope due to diffusion (8). In this study, we propose a method, S0 estimation of the free induction decay combined with a single SE measurement (SOFIDSE), that can be used to simultane0 ously measure R*, 2 R2 and R2 in diffusive systems containing paramagnetic Ho-MS within a relatively short acquisition time. The method uses a multigradient echo readout of the FID followed by a 180 refocusing pulse and a single SE readout. By monoexponential fitting the FID data, R* 2 and the signal amplitude at time point 0, S0, are estimated. Subsequently, the estimated S0 together with the signal amplitude of the SE are used to estimate R2 using a monoexponential fit. By subtracting 0 R2 from R*, 2 the microsphere induced R2 is obtained. We will show that SOFIDSE can be used to accurately estimate R2 values, that SOFIDSE is more robust than GESFIDE and GESSE when diffusion effects influence the shape of the SE envelope, and that Ho-MS–induced R20 values obtained by SOFIDSE are independent of the R2 value of the tissue in which the microspheres reside and thus constitute a valuable tool for Ho-MS quantification in tissue that is subjected to R2 changes as a consequence of therapy. THEORY In general, in the absence of proton diffusion, the MR signal decay can be described in terms of a monoexponential function, where the envelope of the FID is characterized by
SðtÞ ¼ Sð0Þ eR2 t with R2 ¼ R2 þ R20
[1]
and the signal amplitude of the SE by SðtÞ ¼ Sð0Þ eR2 t
[2]
where R2 represents the tissue dependent thermodynamic decay component and R20 represents the component induced by system- or object-related external field inhomogeneities (19). In case of proton diffusion, the MR signal behavior in the presence of field inhomogeneities changes, and Eqs. 1 and 2 no longer fully describe the observed signal. To
what extent the signal behavior changes primarily depends on the water diffusion coefficient, the strength of the main magnetic field, and the size, volume fraction, and susceptibility of the field perturbing objects. In the limiting case where the system is in the socalled static dephasing regime, R20 dephasing effects can be refocused by a 180 pulse, and Eqs. 1 and 2 hold (20). In the other limiting case, known as motional narrowing (21), proton diffusion results in an effectively lower, mainly irreversible, R*. In the intermediate 2 regime, signal behavior is complex but has been investigated by means of Monte Carlo–based simulations and experiments (22). Moreover, analytical models have been developed for systems that satisfy certain criteria—for example, the model of Kiselev and Posse for microvascular networks (23, 24) and the strong- and weak-field behavior models of Jensen and Chandra (25, 26). In particular, Monte Carlo results demonstrate that in general, starting from negligible diffusion, R* 2 starts at a maximum plateau and decreases toward a minimum due to motional narrowing—whereas R2, given by the SE signal, starts at a minimum in the static dephasing regime, reaches a peak value in the intermediate regime, and decreases again toward the motional narrowing regime. Over the entire range, R* 2 is larger than R2, but the ratio between the two depends on the system (22). It has been shown that for aqueous systems, the presence of paramagnetic Ho-MS leads to a faster free induction decay and a decrease in SE amplitude (5), which means that both R* 2 and R2 are influenced by the presence of Ho-MS. It has also been shown that the change in FID is dominated by static dephasing effects, leading to a diffusion-independent relaxation rate R*, 2 whereas for the SE case, the induced signal change is the result of diffusion effects (8). Because quantification of Ho-MS using SOFIDSE is based on a subtraction of the diffusion-independent FID relaxation rate and the diffusion-dependent SE decay rate, we have to define a relaxivity parameter that relates SOFIDSE signal decay to the concentration Ho-MS. This parameter, which we call r20 SOFIDSE, is derived as follows. Based on the previous findings (8), i.e. there is no effective influence of diffusion on R*, 2 we define the FID relaxation rate of a Ho-MS containing system as: 0 0 0 R2 ¼ R2;tissue þ R2;tissue þ R2;holm þ R2;B0
[3]
following the definition for static dephasing (18). Here R2,tissue represents the tissue-dependent thermodynamic decay and R20 ,tissue represents a transverse dephasing component related to local field inhomogeneities, which may be present because of, for example, iron deposition in the liver. R20 ,holm is the Ho-MS–induced dephasing component that depends on the shape, volume fraction, and susceptibility of the microspheres and on the main magnetic field B0. R20 , B0 represents dephasing by macroscopic background gradients. For the SE decay, measured at a single SE time (TE), we adopt the monoexponential approach from Eq. 2 but include a relaxation rate term R2, holm diff, which
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represents the microsphere induced irreversible loss of signal due to proton diffusion R2 ¼ R2;tissue þ R2;holm
[4]
diff
It should be noticed that this R2,holm diff component does not appear in Eq. 3 because, although diffusion is present during both the FID and SE, the effective influence of diffusion on the MR signal is different because of the 180 pulse that is applied (22, 25, 26) in the SE case. However, R2,holm diff does depend on R20 holm (since it is a consequence of protons diffusing in the microsphere induced field deviations) and thus also depends on the volume fraction and susceptibility of the microspheres, and on the main magnetic field B0. Although the monoexponential approach of Eq. 4 does not accord with the nonlinear signal description that has been analytically derived for the SE decay of heterogeneous systems subjected to diffusion (24), in this work we will experimentally show that for a clinically interesting range of Ho-MS concentrations this approach suffices. Now that both R* 2 and R2 are defined, the SOFIDSE relaxation rate R20 ,SOFIDSE is given by subtraction of Eqs. 3 and 4: 0 0 0 0 R2;SOFIDSE ¼ ðR2;tissue þ R2;tissue þ R2;holm þ R2;B0 Þ
ðR2;tissue þ R2;holm
diff Þ
0 0 þ R2;holm R2;holm R2;B0
0 ¼ R2;tissue þ
For the proof of principle, we further neglect the presence of B0-related macroscopic and tissue-related intrinsic microscopic field inhomogeneities resulting in diff
[6]
Using Eq. 6, the SOFIDSE holmium relaxivity is given by 0 r2;SOFIDSE ¼
Phantom Three agarose gel series were prepared in 25-mL plastic tubes (length 65 mm; inner diameter ¼ 20 mm). The first series of six gel samples was prepared with 2% agarose (wt/wt) in MnCl2 4H2O doped water (30 mg per liter distilled water). During preparation of the gel, nonradioactive Ho-MS, prepared as described by Nijsen et al. (1), were added in concentrations of 0.96, 2.24, 3.03, 4.16, and 4.99 mg/mL. One sample was left blank (0 mg/mL). The microspheres had a density of 1.4 g/mL and a holmium content of 18.9% (wt/wt), whereas the microsphere diameter ranged between 20 and 50 mm with a mean diameter of 30 mm. The second series consisted of six gel samples with different agarose content: 1.00, 1.26, 1.51, 1.73, 2.01, and 2.26 % agarose (wt/wt) in MnCl2 4H2O doped water (27 mg per liter distilled water). No Ho-MS were added. The third series of six gel samples was identical to the second series with respect to the agarose content but now Ho-MS were added with an intended concentration of 1 mg/mL. Actual Ho-MS concentrations were 1.01, 1.08, 1.08, 1.04, 1.08, and 0.99 mg/mL. Healthy Volunteer
[5]
diff
0 0 R2;SOFIDSE ¼ R2;holm R2;holm
Preparation
0 0 DðR2;holm R2;holm diff Þ DR2;SOFIDSE ¼ D½Ho-PLLA-MS D½Ho-PLLA-MS [7]
From Eq. 6, it is observed that the here-defined SOFIDSE relaxation rate and thus relaxivity defined in Eq. 7 include only Ho-MS–induced dephasing effects and do not depend on tissue characteristics.
A 27-year-old male healthy volunteer who provided written informed consent was included in this study. The study setup was in accordance with the guidelines of the institutional review board. Data Acquisition MRI data were acquired on a 1.5T whole body scanner (Achieva, Philips Healthcare, Best, The Netherlands), using an eight-channel head receive coil for the phantom experiments and a 16-channel torso receive coil for imaging of the healthy volunteer. Data were acquired in such a way that it could be processed according to three different methods: GESFIDE, GESSE and SOFIDSE. Therefore, an acquisition scheme was used that sampled both the FID and, after applying a 180 refocusing pulse, the SE envelope by means of gradient echo images. For this purpose, a custom-built research patch (Philips Research Laboratories, Hamburg, Germany) was used, as described in Fig. 2 of reference (27), but using only one SE.
METHODS
Phantom
SOFIDSE was applied to an agarose phantom containing a range of Ho-MS concentrations, and results were compared with results obtained from a combination of FID and shifted SE measurements to validate the method. 0 SOFIDSE results (R*, 2 R2, R2) were compared with results that were obtained using the GESFIDE (17) and GESSE (18) methods. Furthermore, the independence of SOFIDSE-based Ho-MS quantification on tissue R2 was demonstrated by measurements on a phantom containing gels with varying agarose concentration and therefore different R2 values. Finally, similar experiments were performed on a healthy volunteer to investigate the in vivo applicability of the method.
For the first gel series, data were acquired using a twodimensional sequence, sampling the FID by 11 gradient echoes (TE1 ¼ 3.1 ms/DTE ¼ 0.8 ms) followed by sampling the SE envelope by 11 gradient echoes with DTE ¼ 0.8 ms, centered around the SE peak. This was repeated five times using five different SE times (20, 30, 40, 50, and 60 ms) to provide shifted SE (SSE) data. Other parameters included: repetition time (TR) ¼ 2000 ms; slice thickness ¼ 10 mm; field of view (FOV) ¼ 128 128 mm2; acquisition matrix ¼ 642; reconstruction matrix ¼ 802; and readout bandwidth ¼ 1783 Hz/pixel. For the second gel series, SSE data were acquired using a two-dimensional single SE sequence that was
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repeated for five different echo times (10, 20, 30, 40, and 50 ms). TR, slice thickness, FOV and matrix were identical to the parameters used for the first gel series, apart from a slightly different readout bandwidth (2047 Hz/ pixel). In addition, diffusion-weighted imaging with bvalues of 0, 100, 200, 300, and 400 s/mm2 (effective echo time: 48 ms) was performed for apparent diffusion coefficient (ADC) measurements to verify that varying the agarose concentration did not influence the diffusion coefficient. Other imaging parameters were identical to those of the previous experiment. For the last gel series, a single acquisition was performed, sampling both the FID (TE1 ¼ 3.1 ms) and SE (TE ¼ 30 ms) by 11 gradient echoes (DTE ¼ 0.8 ms). Healthy Volunteer Multislice SOFIDSE data were acquired using 13 gradient echoes for sampling the FID (TE1 ¼ 2.3 ms; DTE ¼ 0.8 ms) and 13 gradient echoes for sampling the SE envelope (SE time ¼ 30 ms; DTE ¼ 0.8 ms). Imaging parameters included: FOV ¼ 384 344 mm2; acquisition matrix ¼ 192 151; reconstruction matrix ¼ 192 192; slice thickness ¼ 6 mm; number of slices ¼ 45; TR ¼ 360 ms; flip angle ¼ 90 ; and readout bandwidth ¼ 1783 Hz/ pixel. Sensitivity encoding with a factor of 2.7 was used for acceleration resulting in a scan time of 5 20 s during breath hold. Dual echo (DE) SE data were acquired using a multislice DE sequence with TE1 ¼ 20 ms and TE2 ¼ 50 ms. FOV, matrix, and flip angle were identical to the SOFIDSE acquisition. A TR of 300 ms was used and the readout bandwidth was 1733 Hz/pixel. Here also sensitivity encoding was used (factor 2.7) and two signal averages were acquired resulting in a scan time of 9 20 s during breath hold. Data Analysis Phantom Signal intensities for each gel sample were measured using regions of interest (ROI) (mean size ¼ 85 6 4 pixels). Data of the first gel series were processed according to three different methods: SOFIDSE, GESFIDE, and GESSE. The sampling schemes used for these three methods are illustrated in Fig. 1. For SOFIDSE, a monoexponential fit was applied to the gradient echo signal intensities of the FID data from which R* 2 and S0 values were obtained. A threshold was applied excluding signal intensities from the fitting procedure with a signal-to-noise ratio (SNR) lower than 3, with the noise determined by the standard deviation (SD) of the ROI signal intensity of the 0 mg/mL sample. Subsequently, the estimated S0 values were combined with the signal intensities of the central SE sample for TE ¼ 30 ms and R2,SOFIDSE values were determined by R2,SOFIDSE ¼ ln((S0)/S(TE))/TE. Next, the shifted spin echo (SSE) intensities, for the range of used SE times (20, 30, 40, 50, 60 ms) were fitted by S(TE) ¼ S0 exp[R2, SSE TE] to obtain S0 and R2, SSE values from the SSE data. Finally, R20 SOFIDSE values were calculated using R20 SOFIDSE ¼ R* 2 R2 (Eq. 6) with R2 either R2,
FIG. 1. Illustration of the sampling schemes used for SOFIDSE (top), GESFIDE (middle), and GESSE (bottom). The solid lines illustrate the general MR signal in time, and the circles illustrate the sample points used for quantification of R2, R2*, and R20 by the specific method. For the SOFIDSE method, S0 is the estimated signal at time point zero, and the dashed line illustrates the R2 signal envelope
values or R2,SSE values. Correlations coefficients for both R2 values and both R20 SOFIDSE values were calcur2, and r20 SOFIDSE lated and the Ho-MS relaxivities r*, 2 were determined from a linear fit of relaxation rates versus microsphere concentration. For GESFIDE, a monoexponential fit was applied to both the FID and the upslope of the SE, including the top (central echo). The SNR threshold was determined in the same way as was done for SOFIDSE. According to Ma and Wehrli (17), a fit to the FID provides R* 2 (¼R2 þ R20 ), whereas a fit to the upslope of the SE provides a value representing R2 R20 . Therefore, R2 was obtained by addition of the FID and SE upslope: SOFIDSE
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FIG. 2. a: Signal decay of the FID part of the SOFIDSE data, on a logarithmic scale, with their monoexponential fit for three different concentrations of Ho-MS (0, 2.24 and 4.99 mg/mL). Monoexponential signal decay is observed for all concentrations, excluding signal values lower than the applied SNR threshold. b: Signal intensities measured from the SSE experiments with their monoexponential fit. Monoexponential signal decay is also observed here. c: S0 values estimated from the monoexponential fit of the FID (SOFIDSE) and of the SSE measurements for the whole range of Ho-MS concentrations. SOFIDSE values are slightly higher than SSE values for all concentrations with a mean SNR 6 SD of 429 6 9 for SOFIDSE and 393 6 13 for SSE.
R2 þ ðR2 R20 Þ ðR2 þ R20 þ R2 R20 Þ ¼ ¼ R2 2 2
[8]
and R20 was obtained by subtraction: R2 -ðR2 R20 Þ ðR2 þ R20 R2 þ R20 Þ ¼ ¼ R20 2 2
[9]
For GESSE, a monoexponential fit was applied to both the upslope and the downslope of the SE, including the top (central echo) for both cases. Again, the SNR threshold was determined the same way as mentioned above. According to Yablonskiy and Haacke (18), a fit to the upslope provides R2 R20 , whereas a fit to the downslope provides R2 þ R20 , which represents R*. 2 Therefore, R2 was obtained by addition: ðR2 R20 Þ þ ðR2 þ R20 Þ ¼ R2 2
[10]
values were obtained by subtracting R* 2 and R2 values. Voxel-wise R2 values were also obtained from a monoexponential fit to the SE signal intensities of the DE data [R2 (DE)]. The liver was manually segmented using the tissue contrast of the SE image of the SOFIDSE data. The distribution of estimated R2 values within the liver was measured for both SOFIDSE and DE, and mean R2 values were calculated together with their SD. In addition, the mean R* 2 value of the liver, measured from the SOFIDSE data, was calculated and subtracted from the R* 2 maps in order to obtain maps that correspond to conventional DR* 2 maps. Assuming homogeneous liver tissue, and neglecting effects of, for example, the presence of iron in the liver, these DR* 2 maps will represent the variation in R* 2 induced by field inhomogeneities and, therefore, be comparable to R20 SOFIDSE values. The distribution of these DR* 2 values was compared with the distribution of R20 SOFIDSE values and the means and SDs were calculated.
whereas R20 was obtained by subtraction ðR2 R20 Þ ðR2 þ R20 Þ ¼ R20 2
RESULTS [11]
For the second gel series, signal intensities of the SSE data were monoexponentially fitted to obtain the R2 value for each agarose concentration. Signal intensities of the diffusion weighted images were also fitted using SðbÞ ¼ Sð0Þ exp½ADC b
[12]
from which ADC values were obtained. For the third gel series, R20 SOFIDSE values were determined following the same procedure used for the first gel series. Healthy Volunteer From the gradient echo images of the FID part of the SOFIDSE data, S0 values and R* 2 values were estimated for each voxel by applying a monoexponential fit. The resulting S0 images were subsequently used in combination with the central SE image of the SOFIDSE data to determine voxel-wise R2 (SOFIDSE) values. R20 SOFIDSE
Phantom Signal intensities from the gel series containing a range of Ho-MS showed monoexponential signal decay for all concentrations for both the FID of the SOFIDSE data (Fig. 2a) and the SSE data (Fig. 2b), excluding values lower than the applied SNR threshold. A monoexponential fit (R2 ¼ 1 for all concentrations and both datasets) provided S0 values for both the SOFIDSE and SSE data (Fig. 2c). Estimated S0 values were slightly higher for SOFIDSE compared with SSE, including the 0 mg/mL sample. The mean SNR 6 SD of the estimated S0 values of the entire range of Ho-MS was 429 6 9 for SOFIDSE and 393 6 13 for SSE, corresponding to an S0 overestimation of 9% on average. Variations in S0 over the range of microspheres concentrations were observed, showing similar deviations for SOFIDSE and SSE but no correlation with the concentration Ho-MS. Signal intensities of the upslope and downslope of the SE envelope obtained from the SOFIDSE data revealed obvious deviation from monoexponential signal behavior (Fig. 3), particularly for higher Ho-MS concentrations.
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FIG. 3. Upslope (a) and downslope (b) of the SE envelope of the SOFIDSE data around the SE time of 30 ms on a logarithmic scale for three different concentrations of Ho-MS (0, 2.24 and 4.99 mg/mL). The signal of both the upslope and downslope of the SE envelope deviates from monoexponential behavior.
R2 values that were obtained by either monoexponential fitting of the SSE data or determined by SOFIDSE data (with SE ¼ 30 ms) both showed a linear dependency on concentration (Fig. 4a). For SOFIDSE, slightly higher values were found compared with SSE values, which may be attributed to the higher SOFIDSE S0 values, leading to an overestimation of 5% on average for SOFIDSE. No significant relation of this overestimation with Ho-MS concentration was found. From a linear fit to the R2 values, a Ho-MS r2 relaxivity of 8.6 6 1.0 s1 and 8.7 6 1.3 s1 (95% confidence bounds) was found for, respectively, SOFIDSE and SSE at 1.5T. From a statistical analysis, a correlation coefficient of 1 (P 5 1.5 106) was found for the two methods (Fig. 4b). Figure 4c shows the R20 SOFIDSE values determined by subsequently subtracting the R2 values obtained from SSE and SOFIDSE from the R* 2 values determined from the FID of the SOFIDSE data, as a function of concentration Ho-MS. A linear relationship was found between R20 SOFIDSE values and concentration microspheres for both methods, resulting in an r20 SOFIDSE relaxivity of 99 6 5 s1 mg1 mL (95% confidence interval) for the Ho-MS at 1.5T for both methods. The R20 value of the sample containing no HoMS (0.6 s1), resulting from the meas1 ured R* and 28.7 s1 with SDs of 2 and R2 values (29.3 s 0.6 s1 and 0.3 s1, respectively) indicates negligible influence of macroscopic background gradients for the phantom setup. A correlation coefficient of 1 (P ¼ 9 1011) was found for the R20 SOFIDSE values of the two methods (Fig. 4d). Figure 4c also shows the R* 2 values determined from the FID and normalized by subtraction of the R* 2 value of the 0 mg/mL sample. By a linear fit to 1 these values, an r* mg1 mL 2 relaxivity of 108 6 7 s was found. 0 Comparing R*, 2 R2, and R2 values determined by subsequent SOFIDSE, GESFIDE, and GESSE (Fig. 5) showed that both GESFIDE and GESSE provided values that were SE time–dependent. For GESFIDE, R* 2 values showed no dependency on the SE time because R* 2 was estimated from the FID. However, R2 values determined by GESFIDE increased for increasing SE times (R2 ¼ 48– 75 s1 for SE ¼ 20–60 ms, 0.96 mg/mL HoMS; R2 ¼ 88– 160 s1 for SE ¼ 20–60 ms, 3.03 mg/mL HoMS). As a
result, GESFIDE R20 values decreased for increasing SE times (R20 ¼ 87 s1–60 s1 for SE ¼ 20–60 ms, 0.96 mg/ mL HoMS; R20 ¼ 271–200 s1 for SE ¼ 20–60 ms, 3.03 mg/mL HoMS). For GESSE, both R* 2 values and R2 values were found to depend on the used SE time, because both parameters were measured using the SE envelope. R* 2 values decreased for increasing SE times (R* 2 ¼ 97–61 s1 for SE ¼ 20–60 ms, 0.96 mg/mL HoMS; R20 ¼ 246– 148 s1 for SE ¼ 20–60 ms, 3.03 mg/mL HoMS), whereas R2 values increased for increasing echo times (R2 ¼ 29– 40 s1 for SE ¼ 20–60 ms, 0.96 mg/mL HoMS; R2 ¼ 32– 54 s1 for SE ¼ 20–60 ms, 3.03 mg/mL HoMS). As a result, also for GESSE, R20 decreased for increasing SE times (R20 ¼ 68–23 s1 for SE ¼ 20–60 ms, 0.96 mg/mL HoMS; R20 ¼ 215–94 s1 for SE ¼ 20–60 ms, 3.03 mg/mL HoMS). For SOFIDSE, no obvious dependency of R*, 2 R2, and thus R20 was found for increasing SE times. R2 values determined from the SSE data of the second gel series, containing various concentrations of agarose but no Ho-MS, are plotted in Fig. 6a. Increasing R2 values were found for increasing agarose concentrations, where R2 ranged from 17 to 29 s1, corresponding to T2 values of 58–35 ms, for the agarose concentration range of 1%–2.26% (wt/wt). ADC values of the same gel series, determined from the diffusion-weighted images, showed no dependency on agarose concentration (Fig. 6b), demonstrating that only the intrinsic R2 values of the samples differed. R20 SOFIDSE values of the third gel series, containing various concentrations of agarose and thus various R2 values, and 1 mg/mL Ho-MS, showed fluctuations that corresponded to the known fluctuations in concentration HoMS (Fig. 7a). R20 SOFIDSE values corrected for these fluctuations showed no dependency on sample R2, whereas R* 2 values showed an increase for increasing sample R2 (Fig. 7b). Healthy Volunteer R2 maps of the liver of the healthy volunteer (containing no Ho-MS) determined from the SOFIDSE data showed good agreement with R2 maps determined from the DE data (Fig. 8a,8b). Differences were observed particularly
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FIG. 4. a: R2 values, determined from a monoexponential fit to the estimated S0 in combination with a single SE measurement (SOFIDSE) and from a monoexponential fit to the repeated single spin echo (SSE) measurement as a function of concentration Ho-MS. b: R2 values determined by SOFIDSE versus R2 values determined by SSE. A good correlation is observed between the two methods, although a small overestimation is found for the SOFIDSE method when compared with unity (dashed line). c: R2* values as determined from gradient echo sampling of the FID normalized by the R2* value of the 0 mg/mL sample (R2* norm) and R20 values determined by subtraction of SOFIDSE R2 values from SOFIDSE R2* values (R20 SOFIDSE) and by subtraction of SSE R2 values from SOFIDSE R2* values (R20 SSE). d: R20 SOFIDSE values versus R20 SSE values display high correlation (correlation coefficient ¼ 1, P ¼ 3 1012)
at the locations of large blood vessels (Fig. 8d) and are probably a result of flow artifacts, since for SOFIDSE a 90 /180 excitation scheme was used, while for DE a 90 /180 /180 excitation scheme was applied. In areas where no large vessels were present, R2 values (mean 6 SD) measured in a region of interest (Fig. 8, white circle) were similar for both methods: 31 6 6 s1 and 30 6 12 s1 for, respectively, SOFIDSE and DE SE. The SOFIDSE R2 maps showed smaller variability as reflected by the SD of R2 within the ROI, despite the fact that the SOFIDE SE image was noisier than the SE image of the DE data set (as a result of using two signal averages for the latter). R20 SOFIDSE maps (Fig. 9a) and the R* 2 maps that were determined from only the FID part of the SOFIDSE data and normalized by their mean value (Fig. 9b) showed good visual resemblance and no obvious differences. A quantitative assessment, comparing the distributions of R2, R20 SOFIDSE, and R* 2 that were found in the entire liver, showed that R2 values obtained by SOFIDSE were very similar to R2 values obtained by the DE acquisition (Fig. 10a). On average, a mean R2 value of 30 s1 with an SD of 10 s1 was found for SOFIDSE, whereas for the DE acquisition these values were 28 s1 and 17 s1, respectively. A very good agreement was found between
R20 SOFIDSE values and normalized R* 2 values. Mean values of 2 s1 and 0 s1 were found with an SD of 19 s1 and 20 s1, respectively (Fig. 10b). A slight deviation from 0 was found for the SOFIDSE R20 SOFIDSE values. DISCUSSION AND CONCLUSIONS In this study, we present a new method for simultaneous 0 estimation of R*, 2 R2, and R2 values for quantification of Ho-MS, paramagnetic microspheres that can be employed for radioembolization. The method assumes that both the free induction decay and the single SE decay can be described by a monoexponential function with identical initial value S0. In that case, S0 estimated from the FID can subsequently be used in combination with a single SE to estimate the SE decay rate. Phantom experiments clearly showed that the FID as well as the shifted single SE decay of Ho-MS–containing systems are monoexponential, irrespective of the microsphere concentration. The S0 values that were obtained by SOFIDSE showed a small overestimation (9%), independent of the concentration Ho-MS, compared with the reference values obtained by SSE. This overestimation may be the result of differences in excitation and refocusing slice profiles
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FIG. 5. Comparison of R2* (a), R2 (b), and resulting R20 (c) values as a function of used SE time for samples containing 0.96 mg/mL HoMS (left) and 3.03 mg/mL HoMS (right) determined by respectively GESFIDE, GESSE, and SOFIDSE. Both GESFIDE and GESSE show SE timedependent R2 values and R20 values, whereas GESSE also shows SE timedependent R2* values. For SOFIDSE, no dependency on SE time is observed.
and nonperfect refocusing pulses, reducing the absolute signal at the SE time, which leads to lower estimated S0 values. As a consequence of this S0 overestimation, SOFIDSE R2 values showed a concentration-independent overestimation of 5% on average compared with SSE R2 values, which will be acceptable for the intended application.
The monoexponential behavior of both FID and SSE, for the entire investigated range of Ho-MS concentrations, demonstrated that the signal decay of Ho-MS– containing systems can be characterized by an addition of monoexponential components as given by Eqs. 3 and 4. Therefore, the Ho-MS–induced signal decay in SOFIDSE measurements, R20 SOFIDSE, can be determined
FIG. 6. a: R2 values as a function of agarose content measured from the gel series containing no Ho-MS. An increase of R2 is observed for increasing agarose content. b: ADC values as a function of agarose content measured from the same gel series. No changes in ADC value are observed for changes in agarose content.
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FIG. 7. a: R20 values (w) and corresponding Ho-MS concentrations (•) as a function of baseline R2 value, measured from the gel series with varying agarose content and on average 1 mg/mL Ho-MS. No influence of the baseline R2 value on R20 is visible. Fluctuations that are observed clearly correspond to fluctuations in Ho-MS concentrations. b: R2* and R20 values normalized for Ho-MS concentration as a function of baseline R2. R2* depends on R2 gel, whereas for R20 , no such dependency is found
by a subtraction of R* 2 and R2 as given by Eq. 5, and this R20 SOFIDSE value is, unlike R*, independent of the R2 2 value of the tissue, as was clearly demonstrated by the measurements performed on the phantom with varying intrinsic R2 values (Fig. 7). The introduction of this R20 SOFIDSE value that only characterizes the reversible dephasing effect of the microspheres leads to the intro-
duction of the Ho-MS relaxivity parameter r20 SOFIDSE, which linearly relates the local R20 SOFIDSE to the microsphere concentration (Eq. 6). This r20 SOFIDSE value was empirically found to be 99 6 5 s1 mg1 mL at 1.5T for the used microspheres with a holmium content of 1 18.9%, whereas the r* 2 relaxivity was found to be 108 s 1 6 7 mg mL.
FIG. 8. Top row: R2 maps on a scale of 10 to 76 s1 determined from SOFIDSE data (left) and DE data (right). On average, similar values are found for both methods, but DE data show differences at locations where large vessels are present. These differences are also clearly visible in the corresponding SE images (bottom row) where hypo- and hyperintense areas are observed in the first SE image (20 ms) of the DE data (right). These hypo- and hyperintense areas are much less visible in the central SE image (20 ms) of the SE envelope of the SOFIDSE data (left). From an ROI analysis (white circle), similar R2 values were found for normal liver tissue for both methods (R2 ¼ 31 6 6 s1 for SOFIDSE and R2 ¼ 30 6 12 s1 for DE SE).
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FIG. 9. One slice of the R20 maps determined by SOFIDSE (a) and the same slice of the normalized R2* map, determined from the FID of the SOFIDSE data and normalized by the mean R2* value of the entire liver (b). The normalized map mimics a DR2* map that would have been estimated using the conventional quantification method. No obvious differences are observed between the two maps.
In vivo, R2 values obtained by SOFIDSE closely corresponded with R2 values obtained by a dual SE technique, demonstrating the clinical applicability of the method. For Ho-MS quantification in clinical practice, SOFIDSE adds value for several reasons. First, it allows for R2 measurements using a short acquisition time, since only a single SE is required. Second, within the same time, R* 2 is measured, which was shown to enable Ho-MS quantification purely based on R20 dephasing effects. By combining FID and SE in a single acquisition, SOFIDSE basically eliminates the need for acquisition of baseline MRI data prior to administration of the microspheres, preventing errors due to misalignment of preand posttherapy images and errors invoked by tissue changes. This will especially create possibilities for quantitative imaging during the radioembolization procedure, since image processing and user intervention are minimal and R20 SOFIDSE maps can be calculated rapidly on site. A third benefit of the method is that the R* 2 or R20 SOFIDSE maps are intrinsically coregistered to the anatomical SE image, facilitating segmentation of the maps based on the contrast of the SE image. Since the quantitative MRI maps can be used to determine the absorbed radiation dose of both liver and tumor tissue (3, 9), SOFIDSE enables fast verification of safety and potential efficacy of holmium microsphere radioembolization. Field inhomogeneities other than those induced by the Ho-MS may influence the SOFIDSE measurements. For
the phantom setup, macroscopic field effects were negligible according to the minimal differences that were measured between R* 2 and R2 of the blank gel sample. However, in vivo, these effects may be comparable to those familiar from other R*-based quantification meth2 ods and will mostly be present near the lungs and stomach as a result of air–tissue interfaces. Another source of error may be the presence of iron in liver tissue, which will also lead to increased R20 SOFIDSE values that may be misinterpreted as concentrations of Ho-MS. Correcting for the macroscopic effects induced by air–tissue interfaces may be done by using postprocessing techniques (28). Correcting for the presence of iron may require pretreatment imaging for comparison, but that will negate one of the benefits of SOFIDSE (ie, quantification based on posttreatment imaging only). Future clinical studies have to show the extent of iron-induced errors in clinical practice. In the present study, we show the applicability of SOFIDSE for quantification of Ho-MS. However, its use is not restricted to Ho-MS. If the system under investigation complies with the condition described in this study (ie, if it can be assumed that S0 is identical for both FID and SE decay), then SOFIDSE can be used to estimate R* 2 and R2. Whether SOFIDSE is superior to other methods proposed in the literature, such as GESFIDE and GESSE (17, 18), will depend on the clinical context and the expected MR signal characteristics of the tissue of interest. We showed that, in case diffusion effects lead to
FIG. 10. a: Distributions of R2 values found in the entire liver for the SOFIDSE method (solid line) and the DE method (dashed line). b: R20 values, determined by SOFIDSE, and normalized R2* values, determined by subtraction of the mean R2* value of the liver from the voxel R2* values, that were found in the entire liver of the subject.
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non-monoexponential signal behavior of the SE envelope, SOFIDSE provides a more robust R20 estimate than the existing methods. Furthermore, compared with GESSE, data can be acquired more quickly, since SOFIDSE does not sample the downslope of the SE envelope, saving acquisition time. In conclusion, S0 estimation of the free induction decay combined with a single SE measurement can be 0 used to simultaneously measure R*, 2 R2, and R2 for R2 insensitive quantification of Ho-MS within a single acquisition. REFERENCES 1. Nijsen JF, Zonnenberg BA, Woittiez JR, Rook DW, Swildens-van Woudenberg IA, van Rijk PP, van het Schip AD. Holmium-166 poly lactic acid microspheres applicable for intra-arterial radionuclide therapy of hepatic malignancies: effects of preparation and neutron activation techniques. Eur J Nucl Med 1999;26:699–704. 2. Nijsen JFW, van Steenbergen MJ, Kooijman H, Talsma H, KroonBatenburg LM, van de Weert M, van Rijk PP, De Witte A, van het Schip AD. Characterization of poly(L-lactic acid) microspheres loaded with holmium acetylacetonate. Biomaterials 2001;22:3073–3081. 3. van de Maat GH, Seevinck PR, Elschot M, et al. MRI-based biodistribution assessment of holmium-166 poly (L-lactic acid) microspheres after radioembolisation. Eur Radiol 2013;23:827–835. 4. Nijsen JFW, Seppenwoolde JH, Havenith T, Bos C, Bakker CJ, van het Schip AD. Liver tumors: MR imaging of radioactive holmium microspheres—phantom and rabbit study. Radiol 2004;231:491–499. 5. Seppenwoolde JH, Nijsen JFW, Bartels LW, Zielhuis SW, van het Schip AD, Bakker CJ. Internal radiation therapy of liver tumors: qualitative and quantitative magnetic resonance imaging of the biodistribution of holmium-loaded microspheres in animal models. Magn Reson Med 2005;53:76–84. 6. Gupta T, Virmani S, Neidt TM, et al. MR tracking of iron-labeled glass Radioembolization microspheres during transcatheter delivery to rabbit VX2 liver tumors: feasibility study. Radiol 2008;249: 845–854. 7. Bulte JWM, Duncan ID, Frank JA. In vivo magnetic resonance tracking of magnetically labeled cells after transplantation. J Cereb Blood Flow Met 2002;22:899–907. 8. Seevinck PR, Seppenwoolde JH, Zwanenburg JJ, Nijsen JF, Bakker CJ. FID Sampling superior to spin-echo sampling for T2*-based quantification of holmium-loaded microspheres: theory and experiments. Magn Reson Med 2008;60:1466–1476. 9. Seevinck PR, van de Maat GH, de Wit TC, Vente MA, Nijsen JF, Bakker CJ. Magnetic resonance imaging-based radiation-absorbed dose estimation of 166Ho microspheres in liver radioembolization. Int J Radiation Oncol Biol Phys 2012;83:e437–e444. 10. Kamel IR, Bluemke DA. Imaging evaluation of hepatocellular carcinoma. J Vasc Interv Radiol 2002;13:S173–S183.
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