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Magn Reson Imaging. Author manuscript; available in PMC 2010 November 1.

Published in final edited form as:

Published online 2009 June 13. doi: 10.1016/j.mri.2009.05.007

PMCID: PMC2763059

NIHMSID: NIHMS118893

Xia Li,^{1,}^{2} Benoit M. Dawant,^{2,}^{3} E. Brian Welch,^{1,}^{4} A. Bapsi Chakravarthy,^{5} Darla Freehardt,^{5} Ingrid Mayer,^{6} Mark Kelley,^{7} Ingrid Meszoely,^{7} John C. Gore,^{1,}^{2,}^{7,}^{9,}^{10} and Thomas E. Yankeelov^{1,}^{2,}^{8,}^{9,}^{11}

Please address correspondence to: Thomas E. Yankeelov, Ph.D. Vanderbilt University Institute of Imaging Science, Vanderbilt University Medical Center, AA-1105 Medical Center North, 1161 21^{st} Avenue South, Nashville, Tennessee 37232-2310, Email: ude.tlibrednav@voleeknay.samoht

The publisher's final edited version of this article is available at Magn Reson Imaging

See other articles in PMC that cite the published article.

Dynamic contrast enhanced MRI (DCE-MRI) can estimate parameters relating to blood flow and tissue volume fractions and therefore may be used to characterize the response of breast tumors to treatment. To assess treatment response, values of these DCE-MRI parameters are observed at different time points during the course of treatment. We propose a method whereby DCE-MRI data sets obtained in separate imaging sessions can be co-registered to a common image space, thereby retaining spatial information so that serial DCE-MRI parameter maps can be compared on a voxel-by-voxel basis. In performing inter-session breast registration, one must account for patient repositioning and breast deformation, as well as changes in tumor shape and volume relative to other imaging sessions. One challenge is to optimally register the normal tissues while simultaneously preventing tumor distortion. We accomplish this by extending the adaptive bases algorithm (ABA) through adding a tumor-volume preserving constraint in the cost function. We also propose a novel method to generate the simulated breast MR images, which can be used to evaluate the proposed registration algorithm quantitatively. The proposed nonrigid registration algorithm is applied to both simulated and real longitudinal 3D high resolution MR images and the obtained transformations are then applied to lower resolution physiological parameter maps obtained *via* DCE-MRI. The registration results demonstrate the proposed algorithm can successfully register breast MR images acquired at different time points and allow for analysis of the registered parameter maps.

Breast cancer is the second leading cause of cancer death among American women. The American Cancer Society reports that in 2008 approximately 178,480 women will be diagnosed with breast cancer and there are currently no available methods to assess the response of breast tumors to therapy both quantitatively and specifically [1]. The current methods of monitoring treatment response rely on frank changes in tumor morphology (such as size) as measured by physical exam, mammography and/or ultrasound. Unfortunately, these methods are difficult to quantify and often do not correlate with each other nor with tumor activity [2]. Although useful for screening and detection of cancer, X-ray mammography and other conventional imaging methods do not provide adequate information on the status of malignancies or their response to therapy. Additionally, the 2-dimensional nature of planar X-ray mammography makes it difficult to assess both the location and extent of a potentially complex 3-dimensional lesion, thus making it very difficult to employ in quantitative longitudinal studies. Due to their invasive nature, biopsies can be obtained only infrequently to assess treatment response during chemotherapy. Additionally, their spatial sampling may be poor and may provide misleading results. Therefore this method is not acceptable for routine patient care ([3]–[6]). The net result of these limitations is that current methods of assessing tumor response are subjective and prone to error. The most widely used method of measuring tumor response is based on the Response Evaluation Criteria in Solid Tumors (RECIST). RECIST offers a simplified, practical method for extracting the salient features of anatomical imaging data [7]. However, it is well recognized that this approach needs to be significantly improved.

Dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) has matured to the point where it offers quantitative information on tumor status. DCE-MRI involves the serial acquisition of MR images of a tissue of interest (e.g., a tumor) before and after an intravenous injection of contrast agent (CA) ([8], [9]). As the CA enters into the tissue under investigation, the *T _{1}* and

There are many papers in the literature regarding the use of dynamic MRI as a surrogate biomarker for predicting response to neoadjuvant chemotherapy (see, e.g., [18]–[27]). Currently, the most frequently applied methods include tracking changes during the course of treatment in pharmacokinetic parameter values obtained from the tumor region of interest (ROI), or histograms describing their distributions. However, both of these methods are limited. The first does not capture the tissue heterogeneity as observed in distributions of parameter values. Both discard the information on spatial localization and therefore suffer from a similar limitation as the RECIST criteria. We propose a method whereby DCE-MRI data sets obtained at separate imaging sessions (during the course of treatment) can be registered so that parameter values associated with individual voxels can be compared, thereby retaining spatial information. Various registration algorithms for breast images have been proposed and applied to a wide range of imaging data. Examples include registration of MR images obtained pre- and post-contrast agent injection, 3D breast ultrasound registration, speckle tracking, positron emission mammography (PEM)/Mammography registration, MR/ultrasound registration, PEM/PET/CT registration, and X-ray/ultrasound image registration. For a review of these methods, see [30] and [31].

Typically methods, which are used for the registration of intra-session dynamic images (i.e., images acquired before and after the injection of contrast agents) include a succession of rigid and non-rigid registration steps. Mutual-Information is commonly used as the similarity measure to compute these transformations. In [32], Rueckert et al. propose to use a B-spline based free form deformation (FFD). Tanner et al. [33] and Rohlfing et al. [34] observe that registering pre- and post-contrast images with FFDs tend to shrink the tumor because of the change in image contrast. Tanner et al. propose to couple the control point of the splines, which cover the enhancing region. This results in a transformation that permits only the translation of the tumor between image volumes. Rohlfing et al. address the problem by adding an incompressibility constraint to penalize transformations, which locally compress or stretch the images. Other methods involve finite element method based registration algorithms (e.g., [35]–[37]), elastic matching models [38], or wavelet based nonrigid registration [39].

While intra-session registration is concerned with correction of relatively slight movements caused by respiratory and cardiac motion, and minor patient movements, inter-session registration must account for patient repositioning and large deformations of the breasts relative to the other imaging sessions. Moreover, in most cases, the chemotherapeutic regimen will result in substantial changes in both tumor shape and volume. Longitudinal breast registration for DCE-MR image analysis thus presents two main challenges. First, the transformation must be such that it accommodates large differences in the overall shape of the breast. Second, while it may allow re-orientation of the tumor between acquisitions, it should not permit the tumor to be deformed to match shapes even though it may have, in fact, changed shape between acquisitions. Overcoming these two challenges permits voxel-by-voxel analysis of the tumor region and allows for the application of more quantitative methods to determine whether or not a section of tissue responds to the therapy.

Currently, there is a paucity of studies regarding the registration of breast MR images obtained at different time points throughout treatment. To the best of our knowledge, there is only one such investigation, the work proposed by Chittineni et al. [40]. Their work uses a B-spline based methods to register longitudinal anatomic images. They also force the control points of the splines that cover the tumor to remain equidistant, which is similar to the constraint used by Tanner et al. [33]. In this contribution, we present results we have obtained with a non-rigid registration that we have previously developed. We study the effect of a rigidity constraint based on the value of the Jacobian determinant inspired by the work of Rohlfing et al. [34], and we use our method to register parametric maps computed at each time point. This permits visualizing the spatial distribution of tumor response. We also propose a novel validation method to assess the proposed algorithm quantitatively.

Data were acquired from a single patient with locally advanced breast cancer who was enrolled in an ongoing clinical trial [17]. The patient provided informed consent and the study was approved by the ethics committee of our Cancer Center. DCE-MRI was performed using a Philips 3T Achieva MR scanner (Philips Healthcare, Best, The Netherlands) prior to neoadjuvant chemotherapy. A 4-channel receive double-breast coil covering both breasts was used for all imaging (In vivo Inc., Gainesville, FL). Data for a *T _{1}* map were acquired employing a 3D gradient echo multi-flip angle approach with a

Pre-contrast *T _{1}* values,

$$S={S}_{0}\u2022[sin\alpha \u2022(1-exp(-TR/{T}_{1}))/(1-exp(-TR/{T}_{1})\u2022cos\alpha )],$$

(1)

where *α* is the flip angle, *S _{0}* is a constant describing the scanner gain and proton density, and we have assumed that

$$\begin{array}{l}{R}_{1}(t)=(1/2)\u2022(2{R}_{1i}+{r}_{1}\u2022{C}_{t}(t)+({R}_{10}-{R}_{1i}+1/{\tau}_{i})/({v}_{e}/{f}_{w}))\\ -(1/2)\u2022[{(2/{\tau}_{i}-{r}_{1}\u2022{C}_{t}(t)-({R}_{10}-{R}_{1i}+1/{\tau}_{i})/{v}_{e}/{f}_{w})}^{2}+4\u2022(1-{v}_{e}/{f}_{w})/{\tau}_{i}^{2}\u2022{({v}_{e}/{f}_{w})}^{1/2}],\end{array}$$

(2)

where *R _{1i}* is the intracellular

$${C}_{t}(T)={K}^{\mathit{trans}}{\int}_{0}^{T}{C}_{p}(t)exp(-({K}^{\mathit{trans}}/{v}_{e})\phantom{\rule{0.16667em}{0ex}}(T-t))dt,$$

(3)

where *K ^{trans}* is the CA extravasation rate constant, and

First, a standard normalized mutual-information (NMI) based rigid body registration algorithm [41] is applied to the 3D high resolution *T _{1}* weighted breast MR volumes to obtain an approximate registration result. A rotation matrix

$${\mathit{x}}^{\prime}=\mathit{Rx}+\mathit{t},$$

(4)

where ** x** and

The rigid body registration results are then used as the input for the nonrigid registration algorithm. Note that we do not use an affine transformation as it includes scaling parameters, which may result in undesirable compression or expansion of the tumor regions.

The next step relies on an intensity-based registration algorithm we have proposed in the past, which we call ABA for adaptive bases algorithm [43]. This algorithm also uses normalized mutual information as the similarity measure and models the deformation field (** v**) that registers the two images as a linear combination of radial basis functions (RBFs) with finite support:

$$\mathit{v}(\mathit{x})={\sum}_{i=1}^{N}{\mathit{c}}_{\mathit{i}}\phi (\frac{\mid \mid \mathit{x}-{\mathit{x}}_{\mathit{i}}\mid {\mid}_{2}}{s}),$$

(5)

with

$$\phi \phantom{\rule{0.16667em}{0ex}}(r)={(1-r)}_{+}^{4}(3{r}^{3}+12{r}^{2}+16r+4),\text{for}\phantom{\rule{0.16667em}{0ex}}r>0.$$

(6)

(*r*) is one of Wu’s compactly supported positive radial basis functions [44], ** x** is a coordinate vector in

This algorithm is applied using a multilevel strategy. The original MR images are down-sampled into a number of low-resolution images. The algorithm starts at a low resolution level, with few basis functions. As the image resolution increases, the number of radial basis functions increases and the resulting transformation becomes more and more local. The number of resolution levels and basis functions at each level are user-selected parameters. Hence, the final deformation field is computed as

$$\mathit{v}(\mathit{x})={\mathit{v}}_{1}(\mathit{x})+{\mathit{v}}_{2}(\mathit{x})+\cdots +{\mathit{v}}_{M}(\mathit{x}),$$

(7)

where *M* is the total number of levels. We also compute both the forward and the backward transformations to constrain these transformations to be inverses of each other using the method described in [45].

To regularize the transformation and keep the images transformed topologically correctly, our algorithm constrains the difference between the coefficients of adjacent basis functions through setting a threshold, ε. This difference is evaluated as

$$\mid {\mathit{c}}_{i+1}-{\mathit{c}}_{i}\mid \le \epsilon ,$$

(8)

where *c** _{i}* and

As mentioned before, intensity based registration algorithms tend to deform the tumors in the source image and force them to match the tumors in the target image. This can thus potentially lead to an inaccurate analysis of tumor status. To limit the deformation of the tumors in the MR images, we add the constraint term proposed in [34] to the cost function. However, different from the work in [34], we only compute the Jacobian determinant over the tumor or lesion regions in MR images, instead of the whole breast volume. In our experiment, based on visual assessment, using the same constraint on the entire volume led to results which were not as accurate in the regions of normal tissues as those obtained with a Jacobian constraint applied locally.

In *T _{1}* weighted MR images, tumor areas possess a higher intensity than other regions. Tumor can thus be easily segmented with an intensity threshold and the constraint term is added to the cost function to penalize the deformation of tumor areas. Hence, the new cost function becomes:

$${f}_{\text{cost}}=-\frac{H(A)+H(B)}{H(A,B)}+\alpha \frac{{\sum}_{x\in T}\mid log({J}_{T}(x))\mid}{M},$$

(9)

where the first term is the negative normalized mutual information, *H(A)* and *H(B)* are the marginal entropy, and *H(A,B)* is the joint entropy of image *A* and *B*. The second term is the tumor constraint term, in which ** x** is the coordinate vector of a voxel in the tumor area

As is done in the rigid registration step, the high resolution MR images obtained from the first two time points are registered to the one obtained at the completion of chemotherapy just prior to surgery. The exact same registration parameters are set for all MR data sets. In the study presented herein, three resolution levels used are: 128 ×128 ×32, 256 ×256 ×64, and 512 ×512 ×129. At the lowest resolution level, we use 4 ×4×4 and 8 ×8 ×4 basis functions. At the second one, we use 10×10×6 and 16×16×8 basis functions. At the highest level, we use 18×18×10 and 20×20×12 functions during the registration. The threshold ε is selected as 0.2. All parameters are determined empirically. Both the rigid and nonrigid registration algorithms were implemented in the C programming language.

After the registration of the *T _{1}* weighted high resolution isotropic MR volumes, the obtained transformations are applied to the low resolution physiological parameter maps obtained from the DCE-MRI analysis. Hence, three parametric maps,

To demonstrate the validity of the registration technique described above, we present a novel simulation scheme. The proposed method begins with experimentally measured pre-treatment data and simulates tumor deformation in a controlled way. Through this process we have complete knowledge of the deformation that occurs within the breast so that we can quantitatively assess the accuracy of the proposed registration algorithm and the original ABA algorithm.

To simulate the MR post-treatment images, the tumor in the original (pre-treatment) images is contracted by an arbitrary amount (here we perform two contractions: 70% and 95%, respectively), and the contracted area is filled using texture from nearby healthy appearing tissue. The healthy appearing tissue is selected as follows: for every voxel, ** v_{i}**, within the contracted area, the closest point

The next step is to simulate breast deformation caused by patient repositioning associated with the post-treatment scan. To achieve this, two sets of points are first extracted automatically from the breast surfaces of the simulated (contracted tumor) image and the actual post-treatment image, using a single thresholding method, which segments the whole breast surface contours from the background. The two point sets are then co-registered using a robust point matching algorithm [46]. This algorithm iteratively computes a correspondence between the points in the set and a smooth non-rigid transformation based on thin-plate splines, which registers the two image volumes. Once computed, the transformation is applied to the simulated (contracted tumor) image to generate the simulated post-treatment image for which the true deformation is known. Finally, the deformation fields estimated with the original and the modified version of the ABA algorithms are compared to these known deformation fields to study the effect of the constraint scheme.

We first present the results of the novel validation scheme before proceeding to the registration results of the patient data and the analysis of the DCE-MRI parameters.

Figure 1 shows the simulated data sets: panel a is the original pre-treatment image, while panels b and c show the simulated images with tumors contracted by 70% and 95%, respectively. Note that the simulated image appears quite realistic even when the tumor is contracted by 95%. The images with the contracted tumor (panel b and c) are then registered to the experimentally measured post-treatment image (panel d) using the robust point matching algorithm. The transformed images (panel e and f) are considered as the simulated post-treatment images, and used to evaluate the proposed registration method.

The registration algorithms with and without the constraint are applied to the simulated images. Figure 2 shows the histograms of the differences between the true and the estimated magnitude of the displacements with and without the constraint, when the proposed algorithm and the original ABA algorithm are compared with the true displacement, for both cases of 70% and 95%. Note that the proposed method leads to a more accurate registration, as well as a smaller mean error and smaller standard deviation (0.59 ± 0.25 mm for the tumor contracted by 70%; 0.58 ± 0.27 mm for the tumor contracted by 95%), compared with the unconstrained ABA algorithm (1.13 ± 0.42 mm for the tumor contracted by 70%; 1.49 ± 0.65 mm for the tumor contracted by 95%). The maximum error generated by the proposed method is also much smaller than by the original ABA algorithm. Furthermore, with the tumor contracted more, the original ABA algorithm performs worse, because without the constraint on tumor area, the algorithm compresses the tumor in source image as much as possible to match the tumor in the target image. However, the proposed algorithm performs well even when the tumor is contracted by 95%.

The registration results on the simulated images show the proposed algorithm leads to a more accurate performance, compared with the original ABA algorithm. Next, we apply the proposed method and the original ABA algorithm to the real longitudinal breast MR images.

Figure 3 shows the maximum intensity projection of breast MR volumes with tumors for the patient. The MR images correspond to the pre-treatment (panel a, denoted as time *t _{1}*), after one cycle of treatment (panel b, denoted as time

Maximum Intensity Projection (MIP) figures from breast MR volumes with tumors acquired at three different time points: a) pre-treatment, b) post-one cycle of neoadjuvant chemotherapy, c) after completion of chemotherapy. The green arrows show the location **...**

Figure 4 shows registration results obtained on the 3D high resolution MR images of the same patient. The first column shows the corresponding slice (i.e., the slice with the same index) in the volumes acquired at time *t _{1}*,

Three axial slices at three different time points after rigid body registration (col. 1), after nonrigid registration without the constraint (col. 2), and with the constraint (col. 3). In the 4^{th} row, the zoom-in deformation field without and with the **...**

The deformation fields generated with different algorithms are also shown in Figure 4. In the fourth row, the first two panels are the deformation fields registering the image at *t _{1}* to

We have experimented with a range of values for the parameter α. Very large values of α lead to transformations that are very rigid. This produces transformations for which the shape of the tumor does not change at all but for which the breast as a whole is not registered correctly. Very small values of α produce transformations similar to those obtained with the original ABA algorithm. The influence of the constraint parameter α on the tumor volume is shown in Figure 5. The smaller the parameter α is, the smaller the constraint term weighs in the cost function, and, consequently, the less the tumor area is constrained. Through experimentation, we have determined that a value of 0.15 for alpha is a good compromise for the images we have dealt with so far.

Breast volume change with different constraint parameters α. In this study, 0.15 is selected as the optimal value of α.

As described above, after registering the high resolution breast MR images and generating the transformations, we apply the obtained transformations to the low resolution parametric images. Figure 6 displays a central slice of the low resolution breast MR images at three time points and at different registration stages. It shows that after the proposed registration algorithm, the images pre-treatment and after the first cycle of treatment are aligned to the corresponding images acquired after all cycles of treatment accurately. These results also show that the tumor volume is preserved even though it has clearly changed when the data from *t _{1}* and

Figure 7 shows one central slice of the tumor at three time points after the proposed registration algorithm, with the parameters, *K ^{trans}*,

The central slice of low resolution breast MR image volume at three time points after the proposed registration algorithm, with *K*^{trans}, *v*_{e}, *τ*_{i}, color-coded and superimposed (columns 1–3). The *T*_{1} maps at different time points are shown **...**

Figure 8 displays the central slice with two kinds of difference images of the three parameters, *K ^{trans}*,

The central slice with two kinds of difference images of the three parameters, *K*^{trans}, *τ*_{i}, and *v*_{e}, superimposed: the difference between the post-one cycle of chemotherapy and the pre-treatment (*t*_{2}−*t*_{1}), and the difference between the completion **...**

To analyze the change of the parameters quantitatively, the slopes of the parameter *K ^{trans}* from

We have presented an algorithm for the registration of breast MR images obtained at different time points throughout the course of neoadjuvant chemotherapy. In general, registration of images acquired before and after therapy with intensity-based nonrigid registration algorithms will result in the deformation of both normal and cancerous tissue. As tumors typically change shape and volume significantly during treatment, registration algorithms will compress or expand tumors (depending on whether the tumor has reduced or increased in size) in the images before treatment to match those acquired later. Since it merely deforms the tumor shape at one point to the tumor shape at another, such an approach can lead to an inaccurate assessment of treatment response. Hence, the challenging task for longitudinal breast MR image registration is to register the normal tissues maximally while keeping the tumor from being distorted. The proposed algorithm extended the ABA algorithm through employing an additional term, in which the compression or expansion of tumor areas is constrained. The registration results for both the simulated and real high resolution *T _{1}* weighted MR breast images and the lower resolution physiological parametric maps show the utility of this constraint term.

As described in the introduction section, an alternative approach for the longitudinal breast MR image registration is proposed in [40], using a B-spline based registration algorithm; i.e, the B-spline control knots are forced to remain equidistant to keep the transformation of control points over tumor areas rigid. However those methods are not directly applicable to our registration algorithm. For our algorithm, the control points are the center locations of radial basis functions. The distances between the control points remain constant during the registration process. It is the coefficient of each basis function that controls the magnitude of deformation, not the spatial distance between functions. In the future, we will investigate if it is feasible to fix an optimal coefficient over the tumor region to preserve the tumor deformation.

We have also proposed a novel validation method to assess the proposed registration algorithm quantitatively. After simulating the post-treatment breast MR images, we obtain the known deformations, which can be used to evaluate different registration algorithms. The results on both the simulated images and the experimental data demonstrate the proposed registration algorithm leads to a more accurate registration result, compared with the unconstrained ABA algorithm. Ongoing efforts are exploring these results in a larger patient set.

Another novel aspect is that we have introduced the ability to compare, on a voxel-by-voxel basis, the physiological parameters obtained from sequential DCE-MRI exams. In the quantitative analysis of DCE-MRI breast cancer data obtained during the course of treatment, the primary goal is to use the changes in pharmacokinetic parameters as a means to assess and, ultimately, predict treatment response. If successful, such an approach would represent a significant advance past the currently accepted and clinically employed RECIST criteria [7]. We hypothesize that a fundamental limitation in being able to execute this analysis is in the current inability to rigorously compare both the temporal and spatial features of changes within DCE-MRI parameter sets obtained at different time points. Currently, such analyses are limited to manually drawn (or computer assisted segmentation of) tumor ROIs resulting in a mean parameter value for the ROI, or a distribution of parameter values from that ROI if histogram analysis is performed. However, these methods are limited in that they discard the spatial information associated with the parameter maps. In fact, one of the principle reasons parametric maps are made in DCE-MRI (or any other analysis technique) is that they allow the inhomogeneity inherent in many pathologies to be evaluated. By performing accurate co-registration, the temporal and spatial changes of DCE-MRI parameters can be explored and important information regarding the response to treatment can be investigated. In figures 8 – 9 we display simple subtraction and slopes of the different time points to assess what percentage of voxels show an increase or decrease in a particular parameter value. It is possible that the fraction of voxels showing a decrease (or increase) in a parameter—or a combination of all available parameters—could indicate positive (or negative) response to treatment. This is a hypothesis we are currently investigating.

We thank the National Institutes of Health for funding through NCI 1R01CA129961, NIBIB 1K25 EB005936, and NCI 1P50 098131 and the Vanderbilt-Ingram Cancer Center Institutional Grant (NIH P30 CA68485). We thank Ms. Donna Butler and Ms. Wanda Smith for expert technical assistance, and Dr. John Huff, M.D., for many informative discussions.

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