Effect of protocol parameters on contrast agent washout curve separability in breast dynamic contrast enhanced MRI: A simulation study

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(1)Magnetic Resonance in Medicine 68:516–522 (2012). Effect of Protocol Parameters on Contrast Agent Washout Curve Separability in Breast Dynamic Contrast Enhanced MRI: A Simulation Study Melanie Freed* Variability in diagnostic performance of breast dynamic contrast-enhanced MRI has highlighted the need for improved standardization. While guidance exists on some aspects of the technique, currently, there is no standardized method for selecting repetition time and flip angle, which are important determinants of image contrast. This study develops a theoretical framework for quantitative optimization of temporal aspects of dynamic contrast-enhanced MRI based on area under the receiver operating curve. Optimizations in simulation demonstrate the potential for increases in area under the receiver operating characteristic curve by up to 0.20 and specificity at a sensitivity of 90% by up to 19%, depending on the protocol. These results suggest that careful selection of repetition time and flip angle can improve diagnostic performance and identify these quantities as potentially important parameters for future standardization. Magn Reson Med 68:516–522, 2012. © 2011 Wiley Periodicals, Inc. Key words: breast DCE-MRI; optimization; protocol; ROC. Dynamic contrast-enhanced (DCE)-MRI has been rapidly gaining traction as a tool for the diagnosis of breast cancer. In 2007, the American Cancer Society released guidelines recommending screening MRI as an adjunct to X-ray mammography for women with a 20–25% lifetime risk of developing breast cancer (1). The use of DCE-MRI in the clinic has been increasing (2,3), and as of 2008, breast MRI is offered at about three quarters of radiology practices in the United States (4). Although DCE-MRI shows promise as a diagnostic tool, variability in performance still needs to be addressed. While DCE-MRI has demonstrated high sensitivity, it has a low and variable specificity (26–97%; Refs. 5–7) that is likely due to lack of standardization of the method. Kinetic. Division of Imaging and Applied Mathematics, Center for Devices and Radiological Health, Office of Science and Engineering Laboratories, U.S. Food and Drug Administration, Silver Spring, Maryland, United States Grant sponsors: FDA’s Office of Womens Health and an appointment to the Research Participation Program at the Center for Devices and Radiological Health administered by the Oak Ridge Institute for Science and Education through an interagency agreement between the U.S. Department of Energy and the U.S. Food and Drug Administration *Correspondence to: Melanie Freed, Ph.D., Facultad de Fĺsica, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Macul, 7820436, Santiago, Chile. E-mail: freed@fis.puc.cl The mention of commercial products in this article is not to be construed as either an actual or implied endorsement of such products by the Department of Health and Human Services. This is a contribution of the U.S. Food and Drug Administration and is not subject to copyright. Received 25 April 2011; revised 09 August 2011; accepted 06 September 2011. DOI 10.1002/mrm.23234 Published online 5 December 2011 in Wiley Online Library (wileyonlinelibrary. com). © 2011 Wiley Periodicals, Inc.. curve data of malignant lesions has been shown to vary across systems (8). Efforts to improve the standardization of DCE-MRI include the development of a breast MR lexicon published by the American College of Radiology (9,10) and practice guidelines and technical standards by the American College of Radiology1 and the European Society of Breast Imaging (11). There are also a number of review articles that discuss technical considerations for DCE-MRI examinations (12–15). While a range of parameters are considered in these references, there is almost no discussion of the protocol parameters repetition time (TR) and flip angle–the primary determinants of image contrast—and how these parameters are selected in the clinic. The lack of guidance for selection of these protocol parameters is evident in clinical practice, where values range from 5 to 60◦ for flip angle and 3.59 to 50 ms for repetition time (16–20)2 . Attempts to improve the separation of benign and malignant lesions based on washout curve data have generally focused on increasing temporal resolution and have reported mixed results with regard to the benefits of higher temporal resolution (20–22). In this study, we explore the possibility that diagnostic performance of washout curve data is affected not only by temporal resolution but also by flip angle and repetition time as well. We develop a preliminary framework for quantitative optimization of temporal, T1 -weighted, DCE-MRI data and apply that framework to representative clinical protocols from the literature. The impact of the protocol parameters on evaluation of morphological lesion features is not discussed. MATERIALS AND METHODS The following subsections describe the calculation of the figure-of-merit and the optimizations performed in simulation. Figure-of-Merit The separability of benign and malignant washout curves was quantified by considering the decision problem of discriminating between two random signals in additive Rician noise and using an ideal observer approach (23). Noise in MR magnitude images is well described by a Rician distribution (24). The two hypotheses were that the object being imaged is a benign lesion, H1 , or a malignant lesion, H2 .. 1 http://www.acr.org/SecondaryMainMenuCategories/quality_safety/ guidelines/breast/mri_breast.aspx. 2 and the U.S. National Cancer Institute’s Clinical Genetic Branch’s Breast Imaging Study (http://breastimaging.cancer.gov).. 516.

(2) 517. . N. Λ(g) = . gi i=1 σ2. N. gi i=1 σ2. 2 gi +s2i (θ2 )2 s2i (θ2 )gi exp − I o 2 2 2σ σ 2 2 g +s1i (θ1 ) s (θ )g exp − i 2σ2 Io 1i σ21 i. θ2. ,. [4]. θ1. where σ2 is the variance of the gaussian noise in the real and imaginary MR images, N is the number of time points in the data set, and i is an index that runs over all time points in the data set. The ideal decision rule applies a threshold to the likelihood ratio to decide which hypothesis a data set belongs to. A receiver operating characteristic (ROC) curve can be generated by varying the threshold and plotting the fraction of malignant lesions correctly identified (TMR, true malignant rate) as a function of the fraction of lesions incorrectly identified as malignant (FMR, false malignant rate). The values TMR and FMR are analogous to the quantities “True Positive Rate” and “False Positive Rate” typically used for ROC curves and signal-present versus signal-absent detection problems. We chose our figure-of-merit to be the area under the receiver operating characteristic curve (AUC) to maximize the overall performance. The specificity at a sensitivity of 0.90 is also reported. The following subsections describe our object, system, and noise models.. Echo time (ms) TR (ms). where pr(g|H1 ) and pr(g|H2 ) are the probability distribution functions for the data under the hypotheses that the object is benign and malignant, respectively, and the angled brackets with the subscript θj indicate calculation of the mean over the random variable, θj . For magnitude MRI data, we assume that the noise is independent for each time point and Rician-distributed. In this case, the likelihood ratio can be written as. Flip angle (◦ ). [3]. Bandwidth/ pixel (Hz). pr(g|H2 ) pr(g|H2 , θ2 )θ2 , = pr(g|H1 ) pr(g|H1 , θ1 )θ1. Table 1 Example 3D Spoiled Gradient-Echo Dynamic Imaging Sequences From the Literature.. Λ(g) =. Temp. Res.a (s). where g(ti ) is a MR magnitude image value for a single voxel at time ti , v is a vector of non-random parameters that describes the system, Hv,θj is the operator that transforms the object, fj (t, θj ), into data space, θj is a vector of random parameters with probability density prθj (θj ) that describes the object, n(v) is the additive Rician noise, and sj (ti , θj , v) is the noise-free signal in data space resulting from the imaging operator, Hv,θj , acting on the object function, fj (t, θj ). Here, we assume that the noise in the image is determined only by system parameters and that the object is larger than a single voxel. The ideal observer uses the likelihood ratio to decide which object type (benign or malignant) generated the data. The likelihood ratio can be written as. Number averages. [2]. Acquisition matrix. H2 : g(ti ) = Hv,θ2 f2 (t, θ2 ) + n(v) = s2 (ti , θ2 , v) + n(v),. Resolution (mm3 ). [1]. Sequence label. H1 : g(ti ) = Hv,θ1 f1 (t, θ1 ) + n(v) = s1 (ti , θ1 , v) + n(v),. Reference based on. Following the notation used by Barrett and Myers (23), under these two hypotheses, the system can be described by. A 0.625 × 0.625 × 5.0 480 × 480 × 34 3 540 6.09 4.2 5 298 Loud et al. (32)b B1 1.4 × 1.4 × 5.0 256 × 254 × 63 1c 390d 3.59 1.83 10 57 El Khouli et al. (20) “high temporal resolution” protocol 0.7 × 0.7 × 2.5 512 × 512 × 125 1c 390d 7.08 3.56 10 453 El Khouli et al. (20) “high spatial resolution” protocol B2 c C 1.4 × 1.4 × 3 256 × 256 × 84 1 390d 13 4.2 25 280 Sardanelli et al. (19) 1.33 × 1.33 × 2.5 256 × 256 × 60 1c 244 12 4.2 35 184 Brown et al. (16) “high-sensitivity” protocol D1 D2 1.33 × 1.33 × 5.0 256 × 256 × 8 1c 244 12 4.2 35 25 Brown et al. (16) “high-specificity” protocol 390d 18.4 4.3 40 132 Warner et al. (18) E 0.75 × 0.75 × 2.5 256 × 256 × 28 1c F 0.625 × 0.625 × 3.0 256 × 128 × 45 1c 390d 50 4.5 60 288 Lehman et al. (17) When ranges of parameters were provided in the references, representative values were selected. Radio frequency spoiling was not specified for protocols B1 , B2 , or F but was assumed for the purposes of this study. Exact phase encoding order was not reported for any of the protocols. a Calculated using Temp. Res. = TR × N × N × N z y avg . b Study website: http://breastimaging.cancer.gov. Patient population described in Loud et al. (32). MRI protocol provided by J.T. Loud and M.H. Greene via private communication. c Not specified in citation, one average assumed. d Not specified in citation, 390 Hz assumed.. Washout Curve Separability in Breast DCE-MRI.

(3) 518. Freed. FIG. 1. Receiver operating curves for each protocol in Table 1. The gray solid line indicates where the true malignant rate equals the false malignant rate. ROC curves are shown for the protocol in Table 1 (dotted black line), the optimized protocol with TR fixed to the value in Table 1 (dashed black line), and the optimized protocol with both TR and φ as free parameters (solid black line).. Object Model We use the empirical mathematical model described in Fan et al. (25) as our object model, fj (t, θj ). In that study, high temporal resolution DCE-MRI data at 1.5 T were acquired of 22 patients with benign and malignant lesions, and the measured signal intensities were converted to contrast agent concentration and fitted to an empirical mathematical model. The vector θj consists of five coefficients that parameterize the empirical mathematical model. The probability distribution function for each of the coefficients was assumed to be Gaussian with the mean and standard deviation set equal to the experimental values reported in Fan et al. (25). In cases where negative coefficient values were non-physical, the probability distribution functions were set to modified Gaussian distributions where only positive coefficient values were allowed.. System Model Our system model takes into account acquisition time of the imaging sequence and conversion of concentration of contrast agent to MRI signal. The time to acquire a single 3D data set was set equal to the product of the repetition time, the number of phase encoding steps in the z and y directions, and the number of signal averages (26). To account for this finite acquisition time, the contrast agent concentration as a function of time, fj (t, θj ), was averaged to produce a curve with an appropriate time resolution. Note that this approach does not take into account phase encoding ordering. The temporally averaged contrast agent concentration washout curve was converted to MRI signal using the signal equation for a. spoiled gradient-echo sequence assuming steady-state and the fast-exchange limit apply (27). This equation has been shown to provide excellent agreement with experimental data (28). To account for voxel size, the relative proton density (Mo ) was set proportional to the product of the image voxel dimensions (29). Noise Model The randomly distributed noise values, n, were generated using a Rician distribution function with the noise parameter inversely proportional to the product of the number of k-space samples in the x, y , and z directions, the number of averages, and the dwell time (29). The relative proton density and its error were measured experimentally on a vial of tissue-mimicking material with no contrast agent using a 1.5 T Siemens scanner, an extremity coil, and a 3D spoiled gradient-echo sequence (resolution = 1.0 × 1.0 × 1.0 mm3 , matrix size = 256 × 64 × 60, readout bandwidth/pixel = 390 Hz, flip angle = 90◦ , echo time = 1.24 ms, repetition time = 2000 ms). The tissue-mimicking material was prepared according to the procedures described in Tofts et al. (30) and the actual T1 and T2 values of the tissue-mimicking material were measured (T1 = 796.8 ± 1.5 ms, T2 = 47.83 ± 0.18 ms) on the prepared vial using methods previously described (31). The measured signal value in a hand-selected region-ofinterest was 0.34 ± 0.08. After correcting with the signal equation, we estimated Mo = 0.39 ± 0.09. This experimentally measured value for Mo and its error was incorporated in the simulations to ensure that the derived AUC values were of a realistic magnitude..

(4) AUCopt. 0.709 ± 0.006 0.807 ± 0.005 0.674 ± 0.005 0.781 ± 0.006 0.776 ± 0.005 0.736 ± 0.008 0.652 ± 0.007 0.642 ± 0.007 52 87 57 87 90 90 89 56. φ TR (ms). 8 37 9 27 39 39 31 9 0.28 0.34 0.22 0.36 0.32 0.27 0.20 0.18. Spec.@ Sens. = 0.9 AUCoptfa. 0.705 ± 0.028 0.750 ± 0.034 0.666 ± 0.026 0.762 ± 0.027 0.745 ± 0.027 0.708 ± 0.041 0.645 ± 0.040 0.621 ± 0.023 47 39 52 64 70 61 69 90. φ. 0.11 0.26 0.14 0.25 0.29 0.25 0.18 0.17. TR (ms) Spec.@ Sens. = 0.9 AUCnoopt. 6.09 3.59 7.08 13 12 12 18.4 50 A B1 B2 C D1 D2 E F. Protocol (fixed TR/φ). 0.507 ± 0.008 0.654 ± 0.033 0.539 ± 0.012 0.658 ± 0.024 0.713 ± 0.025 0.674 ± 0.039 0.626 ± 0.026 0.589 ± 0.018. TR (ms) Sequence label. φ. (◦ ). Table 2 Optimization Results for Protocols in Table 1. Figure 1 shows the ROC curves generated for each protocol in Table 1 using the three different optimization approaches. Table 2 gives the corresponding TR, φ, AUC, and specificity at a sensitivity of 0.90. For all of the investigated protocols, the AUCnoopt value was the lowest, and the AUCopt value was the highest. The amount of improvement of the AUC varied for each of the different protocols. The greatest improvement in AUC was found for protocols A, B1 , B2 , and C, while the least improvement was seen for protocols D1 , D2 , E, and F. In almost all cases, the AUC was improved by increasing both TR and φ. This suggests that perhaps protocols A, B1 , B2 , and C received most benefit from the optimization because they started with smaller flip angles and repetition times. The trends in specificity values are similar to those for AUC. Figure 2 examines the specific case of protocol C as an example to demonstrate the reasons for the optimization results. The far left plot in Fig. 2 shows the average benign and malignant object models, which are the objects before being modified by the imaging system. The top row of Fig. 2 shows MR signal versus time for average benign and malignant lesions for the protocol in Table 1 and the two different optimization methods. For the case of fixed TR and φ, with AUCnoopt = 0.658 ± 0.024, it is possible to distinguish the average benign and malignant curves, but the difference between the two curves is within their measurement errors. When the protocol is optimized by. (◦ ). Optimal (fixed TR, varying φ). RESULTS. 6.09 3.59 7.08 13 12 12 18.4 50. (◦ ). Optimal (varying TR/φ). The AUC was estimated using 100 randomly selected θ1 and θ2 values and 100 randomly generated noise values, n, for each set of 100 coefficients. This procedure was repeated 20 times for each protocol, and the mean and standard deviation of the results were taken as the mean AUC and its error. Optimizations were performed for each of the protocols listed in Table 1, which were selected from the literature. For each protocol, the AUC was calculated for three different conditions; TR and φ fixed to values in Table 1 (AUCnoopt ), TR fixed to value in Table 1 and φ allowed to vary (AUCoptfa ), and TR and φ both allowed to vary (AUCopt ). When not fixed, the TR and φ were allowed to vary between 3 and 55 ms and 5 and 90◦ , respectively. When TR was allowed to vary, echo time was set to 4.6 ms for TR > 9.2 ms and 1.2 ms otherwise. The object function was evaluated for a total time of 20 min for all protocols. For all simulations, values of T1,0 = 796.8 ms and T2,0 = 47.83 ms, as measured on the tissue-mimicking material in the “Noise Model” section, were used. These values are similar to glandular breast tissue values and breast lesions (31,33). The relaxation values of benign and malignant lesions do not differ significantly (33). The value * T2,0 was arbitrarily set to half of the T2,0 value. The contrast relaxivity values were assumed to be equal to r1 = 4.5 ± 0.04 s−1 mM−1 and r2 = 5.49 ± 0.06 s−1 mM−1 as measured on aqueous Gd–DTPA solutions at 1.5 T (30). Note that these relaxivity values may be different in human tissue.. 5 10 10 25 35 35 40 60. Optimizations. 0.28 0.45 0.23 0.40 0.40 0.31 0.20 0.19. 519. Spec.@ Sens. = 0.9. Washout Curve Separability in Breast DCE-MRI.

(5) 520. Freed. FIG. 2. Example washout curves and signal equations for protocol C. a: Average benign (solid line) and malignant (dotted line) object models, fj (t, θj ). Top row: MR signal curves for average benign (solid line) and malignant (dotted line) lesions, sj (ti , θj , v), for the unmodified protocol and the two optimization schemes: b: fixed TR and φ, c: fixed TR, variable φ, and d: variable TR and φ. Bottom row: Relationship between MR signal and contrast agent concentration for the protocol parameters for the unmodified protocol and the two optimization schemes: e: fixed TR and φ, f: fixed TR, variable φ, and g: variable TR and φ.. allowing φ to vary but keeping TR fixed, the AUC increases to AUCoptfa = 0.762 ± 0.027 due to an increased separation of the two curves, although the signal-to-noise ratio (SNR) is similar. Finally, for the case where both TR and φ are allowed to vary, the AUC increases even further to AUCopt = 0.781 ± 0.006 due to further separation of the two curves and an increased SNR. The reason for these changes is illustrated in the bottom row of Fig. 2, where the MR signal as a function of concentration of contrast agent is plotted for each of the three cases. For the case of fixed TR and φ, the poor separation of the average benign and malignant curves is due to the saturation of the signal equation above a contrast agent concentration of about 1 mM. The separation of the curves is improved for the case where φ is allowed to vary, and TR is fixed, because the signal equation becomes more linear. The maximum MR signal is comparable to the case where TR and φ are both fixed, which explains the similar SNR values for these two cases. Finally, for the case where both TR and φ are allowed to vary, the signal equation is more linear, and the MR signal is larger for a given contrast agent concentration. This behavior explains the large separation of the average benign and malignant curves for this case as well as the increased SNR. In general, the signal equation becomes more linear as the flip angle increases and TR decreases. The SNR increases (and the temporal resolution decreases) as TR increases. The optimization tends to increase both the TR and the flip angle in an attempt to increase both the SNR and the signal equation linearity. In the process, the temporal resolution is generally decreased. DISCUSSION There is little guidance in the literature on how to select TR and flip angle values, the primary determinants of image contrast, for dynamic breast MRI protocols. As a result,. these parameters vary widely across studies, and the motivation for their selection is not well described. In this study, we have developed a preliminary framework for optimization of TR and flip angle based on the resultant AUC values of the protocol for separation of benign and malignant lesions using kinetic information only. By applying this framework to protocols in the literature, we found that diagnostic performance could be improved by determining the optimal TR/flip angle combination for the given protocol. Improved performance was also found when TR was fixed and the flip angle was allowed to vary. In the clinic, high temporal resolution sequences are frequently alternated with high spatial resolution sequences during a dynamic data acquisition to take advantage of both types of information. Our results suggest that it may be possible to improve diagnostic performance by simply adjusting the flip angle of the high temporal resolution sequence, while keeping TR the same. In general, the optimizations presented in this study improved the separation of benign and malignant lesions by increasing both the TR and the flip angle. These changes had the effect of increasing both the SNR and the signal equation linearity of the imaging protocol. In most cases, the optimal protocol had a lower temporal resolution than the original protocol investigated, indicating that simply decreasing the temporal resolution may not be adequate to improve lesion separation. The potential shortcomings of relying on temporal resolution to select imaging protocols can be demonstrated by comparing protocols B1 and B2 with D1 and D2 . Protocol B1 , identified as a high temporal resolution protocol by El Khouli et al. (20), has an AUCnoopt = 0.654 ± 0.033 and protocol B2 , identified as a high spatial resolution protocol, has an AUCnoopt = 0.539 ± 0.012. Consistent with their identification, protocol B2 has almost no ability to differentiate benign and malignant lesions, while the ability of protocol B1 to do so is improved. Therefore, even though.

(6) Washout Curve Separability in Breast DCE-MRI. the flip angle of protocols B1 and B2 is the same, improving the temporal resolution by decreasing both the TR and the spatial resolution allowed the authors to improve their ability to differentiate benign and malignant lesions. On the other hand, protocol D1 , identified as a high sensitivity protocol by Brown et al. (16), has an AUCnoopt = 0.713 ± 0.025 and protocol D2 , identified as a high specificity protocol, has an AUCnoopt = 0.674 ± 0.039. These two AUC values are the same to within their errors, and therefore, there appears to be no improvement in the ability to distinguish benign and malignant lesions for protocol D2 versus protocol D1 . While protocol D2 does have a higher temporal resolution due to a lower spatial resolution, the TR and φ values are unchanged. This indicates that higher temporal resolution may not always translate into higher specificity. The effect of morphological lesion parameters and partial volume issues on diagnostic performance was not investigated in this study. This, in combination with the fact that an ideal observer was used, means that the estimated AUC values should not be interpreted as expected performance in the clinic. Rather, results should be interpreted in terms of relative performance differences between protocols for the selected object model and consideration of kinetic information only. The fact that the simulated specificity of the protocols was lower than the specificity typically seen in the clinic is probably due to the lack of inclusion of morphological information. In the future, if considerations of lesion morphology are included, this framework could be expanded to allow more general optimizations of breast MRI protocols that include spatial resolution and region-of-interest size and placement. Until careful experimental validation has been performed, we caution the reader against using these results to select protocol parameters in patient studies. Future studies with dynamic phantoms (34) may provide appropriate experimental validation. While this study applies to evaluation of temporal data only, expansion of the framework to include morphological considerations will allow for optimization of additional parameters. This study highlights the gains that may be possible with quantitative optimizations and suggests that closer examination of TR and flip angle may be warranted. CONCLUSIONS Lack of standardization of breast DCE-MRI protocols may contribute to the well-documented variability in diagnostic performance. The preliminary framework developed in this study provides a method for quantitative optimizations of breast DCE-MRI protocol parameters without confounding issues of reader variability. 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