1 Introduction

The value of whole-body magnetic resonance imaging (MRI) in skeletal imaging is constantly growing and is currently getting more interest in investigation of several bone pathologies, including diagnosis and prognosis of multiple myeloma [1], bone marrow in paediatric age [3], musculoskeletal imaging [6] and evaluation of treatment response assessment in bone metastases [2, 8, 11].

Due to its high resolution, whole-body coverage and high sensitivity MRI can provide excellent definition of anatomical structures and underlying skeletal pathologies. Additionally, in combination with a follow-up scan, it allows for monitoring of changes in patients body composition and disease involvement providing reliable treatment response assessment parameters (i.e. change in cancer volume, number of metastases) and image response maps.

Follow-up MR images acquired in the same scanner do not only suffer from spatial misalignments caused by different patient positioning and changes in patients’ body composition over time, but also intensity inhomogeneities, making the absolute MR intensity values inherently non-comparable. Therefore, due to the non-quantitative nature of MRI, intensities cannot be compared from one acquisition to another making it impossible to derive reproducible intensity measurements containing interpretable information. Standardized images can not be displayed with fixed windows without the need of per-case adjustment. Additionally, they limit the use of treatment response maps only to quantitative MR modalities, such as MR apparent diffusion coefficient (ADC) calculated using diffusion-weighted images. In order to successfully compare a baseline and a follow-up whole-body scan, both limiting factors have to be overcome, usually via the means of image post-processing techniques.

Whereas, intra-patient whole-body spatial image misalignment can be compensated by image registration [6, 17], inter-scan intensity inhomogeneities bring a challenging problem. In the literature, few authors have described different intensity standardization methods for MR images, however most of the work was done in the field of neuroimaging, limiting the application perspective to a very specific domain and much smaller field of view.

Nyúl et al. [10] proposed a linear piecewise method of matching image histograms of brain images. First, a number of intensity landmarks representing statistical points (percentiles, modes) are found in the reference and target image histogram. Secondly, both image landmarks are mapped on the common reference intensity space using a piecewise linear transform.

Robitaille et al. [14] proposed a method similar to Nuyl with a different landmark detection algorithm. The method incorporates tissue spatial intensity information derived from the segmentation image allowing for detection of more precise, tissue specific landmarks.

Jäger et al. [5] represented a group of multi-modal reference and target brain images as an n-D joint probability histogram. The next step involved deformable registration of obtained n-D histograms, which provided the deformation field matrix. The latter was used to standardize intensity inhomogeneities between the reference and target image stack. Additionally, a method was adapted for whole-body MRI images.

In this work, we propose an extension of existing intensity standardization methods maximizing the intensity similarity of skeletal structures in whole-body MRI together with an extensive quantitative evaluation. A strong validation criterion of mean absolute difference is introduced, allowing for direct quantification of intensity profile separation. The performance of the proposed algorithm was compared with the state-of-the-art methods.

2 Materials and Methods

The skeleton standardization methodology consist of two steps. First, the follow-up whole-body image is spatially registered to a baseline image. Accurate alignment of baseline and follow-up images improves the similarity of the intensity histograms limiting the influence of intra-scan anatomical differences. Additionally, it allows for the introduction of strong validation criteria based on voxelwise intensity comparison, such as the mean absolute intensity difference. Secondly, four different image intensity standardization methods were implemented and validated, aiming for equalization of skeleton intensity profiles.

2.1 Spatial Registration

In order to spatially align the baseline and the follow-up whole-body image and compensate for the aforementioned spatial misalignment, image registration was used.

Registration was performed in a pairwise manner, taking the baseline whole-body image as the reference image, f, and a follow-up image as a moving image, g. The aim was to solve an optimization problem finding a spatial transformation \(\mathcal {T}\) over the parameters \(\varvec{\mu }\), according to the following equation:

$$\begin{aligned} \hat{\varvec{\mu }} = \text {arg}~\underset{\varvec{\mu }}{\text {min}}~\underset{\varvec{x}\in \varOmega }{\mathcal {C}} \Big ( f ( \varvec{x}), g \big (\mathcal {T}_{\varvec{\mu }}( \varvec{x}) \big ) \Big ) \,. \end{aligned}$$
(1)

In (1), the spatial coordinate \(\varvec{x}\) is taken from the overlapping region \(\varOmega \), in which we assumed an intensity interpolation scheme for the discrete images f and g. The registration is guided by the minimization of the chosen cost function \(\mathcal {C}\). Due to non-quantitative nature of the MRI before intensity standardization, a mutual information (MI) cost function [9] was used:

$$\begin{aligned} \mathcal {D}_{MI}(f,g(\mathcal {T}_{\varvec{\mu }}) = - \sum \limits _{a,b} p_{fg}(a,b) \text {log}~\frac{p_{fg}(a,b)}{p_{f}(a) p_{g}(b)} \, , \end{aligned}$$
(2)

where \(p_{fg}\) is the joint probability density function (PDF) of the images f and g, and \(p_f\) and \(p_g\) are the marginalised PDFs for the respective images. a and b are the image intensity values.

Three stage multi-resolution image registration consisting of a rigid, affine and deformable B-Spline [15] deformation was implemented in the freeware software package elastix [7]. For a deformable step, a bending energy penalty (BEP) was used [15]. Detailed registration parameters are provided in Table 1.

Table 1. Parameters used in the spatial registration step.
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The registration was driven by high resolution 3D \(T_{1}\) whole-body image and the resulting transformation field was used to map other modalities of lower image quality, i.e. diffusion-weighted images.

2.2 Intensity Standardization

We compared 5 different intensity standardization algorithms with increasing complexity based on histogram matching principle.

Method 1. Linear Scaling: Target image is linearly scaled to match the intensity distribution in a reference image. Because of the signal intensity outliers, we use the intensity range up the the 99.9% intensity percentile, which according to the Eq. 3 gives:

$$\begin{aligned} I_{LS}=I_{R min}\frac{I_{T}-I_{Tmin}}{I_{ToutlierPerc} - I_{Tmin}}(I_{RoutlierPerc}-I_{Rmin}). \end{aligned}$$
(3)

Here, we denote \(I_{R}\), \(I_{T}\) and \(I_{LS}\) as the reference, target and linearly scaled output image. \(I_{Rmin}\), \(I_{Tmin}\), \(I_{RoutlierPerc}\) and \(I_{ToutlierPerc}\) are the minimum intensity values and 99.9% intensity outlier percentile values of the reference and target image, respectively. Additionally, all other compared methods were initialized from the linearly scaled result in order to roughly align image intensity profiles before allowing for standardization with more degrees of freedom. Experiment was performed, showing a benefit of initialization by linear scaling.

Method 2. Piecewise Linear Matching of Intensity Histograms: The method is implemented similar to [10], where the basic idea is to find a linear piecewise mapping that deforms the follow-up image intensity histogram so that it matches a baseline image histogram using intensity landmarks. In the first step, five landmarks, L, representing intensity percentiles of the baseline and follow-up image are calculated. Here, a number of \(n=5\) evenly spaced percentile values was chosen, \(L = [0, 20, 40, 60, 99.9]\). Second, a piecewise linear normalization is applied, mapping a follow-up image landmarks to corresponding baseline image landmarks, creating \(n-1\) linear and independent transformations, each between two landmarks (see Fig. 1).

Fig. 1.
figure 1

Schematic representation of a linear piecewise transform. Two sets of landmarks \(L_{1-5}\) are detected in a reference and target image. Linear transformations \(T_{1-4}\) are used to standardize intensities between the images, mapping follow-up image intensities onto baseline image intensity profile.

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Method 2.1. Piecewise Linear Matching of Masked Intensity Histograms: We propose a modification to the linear piecewise method by the introduction of the whole-body skeleton mask (see Sect. 2.3). Instead of taking all whole-body image voxels into account while calculating the intensity landmarks, only the masked tissues of interest will be used. Here, a 3D binary mask of the skeletal tissues is introduced, limiting excess of image information and focusing algorithm performance only on the chosen masked structure. Similar to method 2, five evenly spaced intensity percentiles were chosen as landmarks in the baseline and follow-up image, \(L = [0, 20, 40, 60, 100]\), however, the range of intensities used was limited to the intensity range of the masked skeleton tissue. Later, as in method 2, piecewise normalization is performed taking into account updated landmark positions.

Method 3: Deformable Registration of Intensity Histograms: An image intensity histogram can be represented as a 1D image, where intensity values represent voxel count at each specific histogram bin. Therefore, the intensity standardization problem can be treated as a deformable image registration problem, aiming at finding a spatial transformation, \(\mathcal {T}_{\varvec{\mu }}\), mapping a follow-up histogram image, H(g), to a baseline intensity profile, H(f), according to Eq. 1 (see Fig. 2). The resulting deformation field is used to correct intensities in the follow-up image [5]. Such method, gives more degrees of freedom compared to Method 2, allowing for smooth transformation and closer alignment of two intensity profiles. Here, a single-resolution deformable image registration with mean square difference cost function, bending energy penalty regularizer, histogram with 128 bins and a final B-Spline grid spacing of 30 pixels was used.

Fig. 2.
figure 2

Schematic representation of a deformable registration of two 1D histograms. The histogram of a follow-up image is deformably registered to the baseline image histogram. Obtained 1D deformation field (red arrows) is used to map intensities of the follow-up image onto baseline image intensity space. (Color figure online)

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Method 3.1. Deformable Registration of Masked Intensity Histograms: The proposed method is a modification of method 3, where similarly to method 2.1, intensity histograms of the baseline and follow-up image are calculated only for the voxels included in the skeleton mask. Therefore, deformable registration is based only on intensities of interest, allowing for more precise intensity standardization transformation focusing on a chosen tissue of interest (i.e. bone).

2.3 Data Description

Experiments were performed on a 3D T\(_{1}\) and diffusion-weighted whole-body images of prostate cancer patients with metastatic bone involvement and healthy volunteers. Each patient had one follow-up examination, with an approximate 3–9 months between consecutive scans. The follow-up images of healthy volunteers were acquired during the same day, in a separate scanning session. 5 whole-body image pairs (baseline + follow-up) of the same subject consisting of 4 image station covering roughly head, torso, pelvis and legs were acquired. Images were obtained as a routine examination performed in the Cliniques Universitaires Saint-Luc, Brussels and Universitair Ziekenhuis Brussel. The study was approved by the Institutional Ethics Board of both institutions.

MRI: Whole-body stations were composed after independent image station preprocessing, which involved noise filtering using anisotropic diffusion followed by bias field correction [18] both implemented as a standard Insight Segmentation and Registration Toolkit (ITK) filters. Additionally, inter-station intensity standardization was applied by scaling the intensity distribution of neighbouring stations to 99.9% intensity percentile based on the common station overlay region prior to the composition of the whole-body image from separate stations.

Anatomical whole-body image station were acquired as a T\(_{1}\) weighted spin-echo sequence [12], with the following parameters: echo time (TE) = 8 ms, repetition time (TR) = 382 ms, matrix size of 480\(\,\times \,\)480, pixel spacing 0.65 mm, slice thickness 1.19 mm. After the whole-body image reconstruction, spacing was equal to 1.2\(\,\times \,\)0.65\(\,\times \,\)0.65 mm respectively in x, y and z direction with a matrix size of 210\(\,\times \,\)1612–1705\(\,\times \,\)768. Diffusion-weighted images were acquired with axial free breathing echo-planar DWI sequence (DWIBS) with a b-value equal to 1000 s/mm\(^{2}\). Following sequence parameters were used: TR = 8421 ms, TE = 66 ms, slice thickness 6.1 mm, matrix size 192\(\,\times \,\)192, pixel spacing 2.3 mm, FOV = 440\(\,\times \,\)440 mm\(^{2}\).

Skeleton Segmentation Mask: For each whole-body image pair (baseline and follow-up image), the skeleton segmentation for a reference image was delineated using first, the ‘GrowCutEffect’ application from Slicer [4] followed by manual refinement. Additional smoothing was applied using morphological operations. Aiming at the specific applications for bone pathologies (metastatic bone disease, multiple melanoma), only a selected number of bones with high probability of involvement were considered. This involved clavicle, spine from C2 vertebra to sacrum, pelvis and both femur bones. Tubercular bone as well as the cortical bone were included. Figure 3 illustrates the anatomical reference of the bones that are considered in this study together with corresponding manual segmentations.

Fig. 3.
figure 3

(a) Anatomical reference from Bio Digital [13]. (b) Volume rendering from manual segmentation. (c) Coronal and (d) sagittal slice of a whole-body T\(_{1}\) image in overlay with bone segmentation mask (yellow). (Color figure online)

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2.4 Validation

Two validation criteria were used to asses similarity of skeletal intensity profiles between a reference baseline and target follow-up image.

Mean Absolute Difference: Corresponding voxel intensities were compared and summed into a mean absolute difference (MAD) value

$$\begin{aligned} MAD=\frac{\sum \limits _{x} |f(x)-g'((\mathcal {T}_{\mu }(x))|}{N}, \end{aligned}$$
(4)

where, f(x) and \(g'(\mathcal {T}_{\mu }(x))\) are image intensities of the reference and spatially registered - intensity standardized target image in the corresponding voxel location x and N is a number of image voxels.

Kullback-Leibler Divergence: We have implemented the Kullback-Leibler divergence (KL) representing a distance measure between two discrete probability distributions (histograms)

$$\begin{aligned} KL_{D}=\sum _{i} P(i) log\frac{Q(i)}{P(i)}, \end{aligned}$$
(5)

where, P(i) and Q(i) are discrete probability distributions of a reference and standardized image at histogram bin i.

We can assume that if different tissue classes cover the same intensity range in both volumes, the histograms of a reference and target whole-body image will be as similar as possible, representing KL value close to zero.

Since not all of the data proved to be normally distributed (p > 0.05, Shapiro-Wilk Normality Test [16]), the Wilcoxon two-tailed, signed-rank test was used to investigate statistical significance of differences in validation criteria values between the non-standardized image and each of the registration strategies separately. The p-value used for the statistical significance test was equal to 0.05.

3 Results

All proposed intensity standardization methods were quantitatively validated and compared to a spatially registered and non-standardized whole-body image pair, representing a baseline value. Results of the validation criteria representing intensity standardization performance between baseline whole-body image and follow-up whole-body image, averaged over all subjects used, are presented in Table 2. Figure 4 shows the influence of the spatial registration and intensity standardization on baseline and follow-up image skeleton similarity. Figure 5 shows whole-body \(T_{1}\) and DWI baseline and follow-up images before and after intensity standardization displayed with the same window and level setting. A sample \(T_{1}\) functional response map indicating metastatic bone disease progression is shown in Fig. 6.

Table 2. Evaluation metrics averaged over 10 whole-body image pairs of \(T_{1}\) and DWI modalities for the proposed methods (± standard deviation). The best performing strategy in terms of average for each criteria is highlighted in bold. Statistical significance for each registration strategy and evaluation criterion, when compared to unregistered raw images is marked with an asterix (*).
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Fig. 4.
figure 4

Coronal overlay view of whole-body \(T_{1}\) image (top) with extracted skeleton (bottom). Pink and green colours indicate intensity difference. (a) Raw images, (b) result after rigid registration, (c) result after deformable registration, (d) result after deformable registration with linear scaling of intensities (Method 1), (e) result after deformable registration with intensity standardization (Method 2.1). (Color figure online)

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Fig. 5.
figure 5

Whole-body \(T_{1}\) (left) and DWI (right) baseline and follow-up images before and after intensity standardization (Method 2.1). Images have been spatially registered. All images are displayed with the same window and level setting.

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Fig. 6.
figure 6

From top to bottom: axial, sagittal and coronal view of functional response map calculated on \(T_{1}\) intensity standardized image showing left upper pelvis with a visible progression of focal bone metastasis (red arrow). (Color figure online)

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3.1 Computation Times

Processing was performed using a 2.5 GHz Intel® Core® i7-4870HQ processor and 16 GB RAM. Spatial registration inducing preprocessing steps and image re-sampling took around 30 min for an image pair. The entire standardization procedure (single threaded execution) for method 1 and all variations of method 2, took around 1 min. Method 3 with an execution time equal to 30 min, is considerably more expensive due to the deformable histogram registration and a higher number of intensity transformations equal to the size of the 1D deformation field.

4 Discussion and Conclusion

In this work we investigated several strategies for intra-patient whole-body intensity standardization of skeleton profiles. Five different intensity standardization methods were compared and their performance was validated. Additionally, the use of spatial registration between the baseline and follow-up volumes, allowed for the introduction of strong validation criterion based on direct intensity difference - mean absolute difference of skeleton intensity profiles. The piecewise linear method using the masked tissue of interest (Method 2.1) performed better than other evaluated methods, showing high stability and robustness of performance. Slightly worse performance of masked 1D deformable method (Method 3.1) might be caused by the limited amount of image information which corrupts the performance of deformable registration algorithms and the over-fitting of the match of the intensity profiles. Intensity standardization algorithms can be applied to any other tissue of interest if a specific mask representing a tissue type is provided.

Accurate intensity standardization of intra-patient MRI whole-body skeleton profiles, opens opportunities for whole-body quantitative follow-up, cohort comparison studies and functional response maps for non-quantitative modalities, considerably simplifying extraction of relevant quantitative information for healthy and disease.