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Computerized Medical Imaging and Graphics 36 (2012) 108– 118
Contents lists available at ScienceDirect
Computerized Medical Imaging and Graphics
journa l h o me pa g e: www.elsev ier .com/ locate /compmedimag
avelet-based segmentation of renal compartments in DCE-MRI of humanidney: Initial results in patients and healthy volunteers
heng Lia,b,1, Frank G. Zöllnera,c,∗,1, Andreas D. Merrema, Yinghong Pengb,arle Roervikc,d, Arvid Lundervoldd,e, Lothar R. Schada
Computer Assisted Clinical Medicine, Medical Faculty Mannheim, Heidelberg University, GermanyInstitute of Knowledge Based Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, ChinaSection for Radiology, Department of Surgical Sciences, University of Bergen, NorwayDepartment of Radiology, Haukeland University Hospital, Bergen, NorwayDepartment of Biomedicine, Neuroinformatics and Image Analysis Laboratory, University of Bergen, Norway
r t i c l e i n f o
rticle history:eceived 15 October 2010eceived in revised form 31 March 2011ccepted 1 June 2011
eywords:CE-MRIavelet analysis
a b s t r a c t
Renal diseases can lead to kidney failure that requires life-long dialysis or renal transplantation. Earlydetection and treatment can prevent progression towards end stage renal disease. MRI has evolved intoa standard examination for the assessment of the renal morphology and function. We propose a wavelet-based clustering to group the voxel time courses and thereby, to segment the renal compartments. Thisapproach comprises (1) a nonparametric, discrete wavelet transform of the voxel time course, (2) thresh-olding of the wavelet coefficients using Stein’s Unbiased Risk estimator, and (3) k-means clustering of thewavelet coefficients to segment the kidneys. Our method was applied to 3D dynamic contrast enhanced
-meansidneyegmentation
(DCE-) MRI data sets of human kidney in four healthy volunteers and three patients. On average, the renalcortex in the healthy volunteers could be segmented at 88%, the medulla at 91%, and the pelvis at 98%accuracy. In the patient data, with aberrant voxel time courses, the segmentation was also feasible withgood results for the kidney compartments. In conclusion wavelet based clustering of DCE-MRI of kidneyis feasible and a valuable tool towards automated perfusion and glomerular filtration rate quantification.
. Introduction
The kidneys serve homeostatic functions by regulation of elec-rolytes, maintenance of acid–base balance, and regulation of bloodressure. The kidneys filter the blood, and remove waste-productsnd water which are passed to the urinary bladder [1]. There areany causes of chronic kidney disease (CKD), such as diabetes mel-
itus, long-standing hypertension, polycystic kidney disease andarenchymal diseases [2]. Renal diseases can lead to kidney fail-re that requires life-long dialysis or renal transplantation. Earlyetection and treatment can prevent this progression towards endtage renal disease (ESRD). Therefore, it is important to monitor
enal function precisely, for the assessment of disease progressionnd follow-up of therapy.∗ Corresponding author at: Computer Assisted Clinical Medicine, Medical Fac-lty Mannheim, Heidelberg University, Theodor-Kutzer-Ufer 1-3, 68167 Mannheim,ermany. Tel.: +49 0621 383 5117; fax: +49 0621 383 5123.
E-mail address: [email protected] (F.G. Zöllner).1 Both authors contributed equally.
895-6111/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.oi:10.1016/j.compmedimag.2011.06.005
© 2011 Elsevier Ltd. All rights reserved.
Indirect measurements, such as creatinine, urea, and elec-trolytes, as well as creatinine clearance, have low sensitivity [3] toassess and detect renal disease in early stage. MRI has evolved intoa standard examination for the assessment of the renal morphologyand function. Especially, dynamic contrast-enhanced MR imaging(DCE-MRI) has shown to be a promising technique for the moreaccurate assessment of regional renal function [4–7]. By DCE-MRI,important physiological parameters like renal blood flow (RBF) andthe glomerular filtration rate (GFR) can be measured non-invasively[8–11].
Segmentation of the kidney and its compartments is therebyan important step towards automated analysis of the 3D DCE-MR images [12], cortical-medullary differentiation [13], and alsowhole kidney GFR estimation [14]. Segmentation of the kidney andits compartments, however, is often performed by manual draw-ing of region of interests or outlining the organ. Only few (semi-)automated approaches exits, like thresholding [15,16], graph cuts[14], or clustering [17]. Various types of cluster analysis have been
applied to MRI data in the past, mainly in MRI of the brain [18–20].Methods utilized comprises fuzzy clustering, k-means and prin-cipal component analysis (PCA), dynamic cluster analysis usingk-means clustering (adaptive clustering) [21], k-means clustering
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S. Li et al. / Computerized Medical I
nd smoothed time series by a spectral density function [22], orierarchical clustering [23].
Wavelet analysis has a wide application in image and signalrocessing [24,25]. The discrete wavelet transformation (DWT)roduces a vector of wavelet coefficients associated with tempo-al scales and specific locations in time. The DWT is well knowno track transient events in time series and thus presents itself as
reasonable candidate to decompose voxel time series in imag-ng experiments such as perfusion-weighted imaging. The DWTsolates a deterministic signal into a few large coefficients whilehe background noise is spread across most, if not all, of theavelet coefficients. Testing a subset of wavelet coefficients against
threshold is the most common way to separate the signal andoise, commonly known in the literature as wavelet shrinkage orenoising [26,27]. Recently, wavelet analysis of perfusion weightedR images of the rat brain has been demonstrated [28].In this paper, we investigate the wavelet-based segmentation of
D DCE-MRI time course in human kidney which aims at detect-ng and segmenting the renal compartments by their differentatterns of perfusion time courses. This approach comprises (1)
nonparametric, discrete wavelet transform of the voxel timeourse, (2) thresholding of the wavelet coefficients using Stein’snbiased Risk estimator, and (3) k-means clustering of the waveletoefficients to segment the kidneys. Our method provides an auto-ated approach to renal compartment segmentation which can be
irectly combined with further data analysis towards estimatingenal physiological parameters.
. Materials and methods
.1. Data acquisition
In the present study we have used two different pulse-equences for the acquisition of 3D perfusion time series having
different temporal and spatial resolution as well as a differentength [17]. On the 1.5 T Siemens Symphony scanner and 3.0 Tigma Excite GE we used a 3D volumetric interpolated breath-holdxamination (VIBE) and a 3D liver acceleration volumetric acquisi-ion (LAVA), respectively. Altogether, four data sets were obtainedn four exams of healthy volunteers, one female (exams 2 and 3)nd two males (exams 1 and 4). Table 1 gives the main spatialarameters for the acquisitions.
Exams 1 and 2 used the VIBE protocol with flip angle = 9◦,R = 3.3 ms, and TE = 1.79 ms. Exam 3 used the LAVA protocol withip angle = 12◦, TR = 2.59 ms, TE = 1.10 ms, whereas exam 4 used theAVA protocol with flip angle = 12◦, TR = 2.74 ms, and TE = 1.14 ms.n all examinations a paramagnetic contrast agent was used. A dosef 2 ml (0.5 mmol/ml Gadodiamide) of contrast agent was injectedfter recording the fifth 3D volume.
In addition, three patients (two female, one male, mean age 55ears old), were examined on a 1.5 T Siemens Symphony Visioncanner using a 3D VIBE sequence with TR = 3.3 ms, TE = 1.76msnd FA = 9◦. Similar to the volunteers’ examinations, also 2 ml ofadolinium based contrast agent was administered after 5 volumes.mage resolution and matrix sizes for the data sets (P1, P2, P3) areiven in Table 1. The study was approved by the regional Ethicalommittee of Western Norway and all volunteers and patients gave
written consent.
.2. Registration
The volunteer data have been registered by a non-rigid reg-stration algorithm [17]. The patient data were registered withn algorithm based on a variational framework proposed by
g and Graphics 36 (2012) 108– 118 109
Chefd’Hotel et al. [29]. The algorithm was implemented in C++ usingthe Insight Toolkit library (ITK) [30].
The basic idea is the following: to align a source image with areference image, the source image is warped with a displacementfield, e.g. a 3D displacement vector for each voxel. This displace-ment field maximizes cross correlation between the two images.For optimization, a gradient descent strategy is used. In each iter-ation, the gradient of the cross correlation is computed in a highdimensional space described by all displacement field coordinates.The resulting displacement field is multiplied by an exponentiallydecreasing step factor, smoothed by convolution with an isotropicGaussian kernel and added to the sum of displacement fields com-puted in all prior iterations. In the next iteration, the gradientof the cross correlation at the current total displacement field iscomputed. The algorithm stops when mean values of cross corre-lation for ten subsequent iterations cease to increase. For imageinterpolation, cubic B-splines [31] are used for the final iterations,otherwise linear functions are used. The computation scheme isshown in Fig. 1. Smoothing the displacement field is not only a cor-rection for the distortion caused by noise but also a solution to theproblem which contrast enhancement causes for registration. Theintensity patterns within the kidneys differ between the images ofa time series. This leads to a risk of misregistration, since a dis-torted and thus false intensity pattern within the kidneys can insome cases lead to a higher cross correlation than the original pat-tern. To prevent these local distortions, the standard deviation ofthe smoothing kernel was set to values between 14 and 22 mm [32].Due to breathing, the kidneys mainly move up and down. Therefore,the vertical motion of the kidneys before and after registration wasmeasured to quantify registration accuracy. A well visible anatom-ical reference point in the kidneys was selected for each datasetand the standard deviation of the position on the vertical axis wascomputed [33].
2.3. Wavelet based clustering
To segment different parts of the kidney from 3D DCE-MR image,we applied the wavelet analysis to the time series of each voxeland used k-means to cluster the coefficients to partition differentparts of the kidney. Fig. 2 shows the scheme of the procedure of ourproposed method. For processing the perfusion data by our waveletbased clustering approach, the initial image matrix was croppedand splitted into two subsets each containing a single kidney. Foruse with the k-means clustering as well as for wavelet analysis, eachof these 3D+t matrices were then transformed into 2D matrices ofdimension n × p, with n the number of voxel in the 3D volume andp the number of acquired time points.
We applied the discrete wavelet transform (DWT) indepen-dently on each voxel [34]. The DWT of a signal x is calculated bypassing it through a series of filters. First the samples are passedthrough a low pass filter with impulse response g resulting in aconvolution of the two (cf. Eq. (1)). The signal is also decomposedsimultaneously using a high-pass filter h (cf. Eq. (2)). The outputsgive the detail coefficients (from the high-pass filter) and approxi-mation coefficients (from the low-pass).
ylow[n] =∞∑
k=−∞x[k]g[2n − k] (1)
yhigh[n] =∞∑
k=−∞x[k]h[2n + 1 − k] (2)
This requires that the number of observations in the voxel timeseries is dyadic in length. The resulting wavelet coefficients areassociated with both time and scale, and may be organized intothe vector W = [W1, W2, · · ·, WJ, VJ] where the maximum scale is
110 S. Li et al. / Computerized Medical Imaging and Graphics 36 (2012) 108– 118
Table 1Description of the pulse-sequences (VIBE or LAVA) used in this study to acquire the image data.
Exam Scanner Sequence Spatial res (mm) Matrix Temporal res
V1 1.5 T VIBE (1.48 × 1.48 × 3.0) (256 × 256 × 20 × 20) n.e.2
V2 1.5 T VIBE (1.48 × 1.48 × 3.0) (256 × 256 × 20 × 118) 2.5 sV3 3.0 T LAVA (0.86 × 0.86 × 2.4) (512 × 512 × 44 × 60) 3.0 sV4 3.0 T LAVA (1.72 × 1.72 × 2.4) (256 × 256 × 22 × 60) 3.7 sP1 1.5 T VIBE (1.56 × 1.56 × 4.0) (256 × 256 × 22 × 100) 2.8 sP2 1.5 T VIBE (1.56 × 1.56 × 4.0) (256 × 256 × 22 × 100) 2.8 s
6 × 1.
E
Jilnsoo
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P3 1.5 T VIBE (1.5
xam V1 has been recorded with non-equidistant time sampling (n.e.).
= log2(N) and each wavelet scale is associated with the frequencynterval �j = (1/2j + 1, 1/2j] for j = 1, · · ·, J. Thus, high-frequency oscil-ations are captured in the first wavelet scale �1 = (1/4, 1/2], theext high-frequency interval is captured in the second waveletcale �2 = (1/8,1/4], and so on. The final coefficient in the vectorf wavelet coefficients VJ is proportional to the sample mean of theriginal vector.
In practice, we used Daubechies 4 as the mother wavelet35]. Although the Haar wavelet algorithm has the advantagef being simple to compute and easier to understand [36], andhe Daubechies 4 algorithm has a slightly higher computationalost and is more conceptually complex, because there is overlapetween iterations in the Daubechies 4 transform step, this overlapllows the Daubechies 4 algorithm to pick up detail that is missed
y the Haar wavelet algorithm [35]. We applied a one-dimensionalavelet transform function to each voxel time courses and theoxel time courses where decomposed on the first scale J = 1.
Fig. 1. Computation scheme of t
56 × 4.0) (256 × 256 × 22 × 100) 2.8 s
2.3.1. Wavelet coefficients selectionHard thresholding is applied to the decomposed wavelet coef-
ficients, because it can preserve local characteristics, although thereconstructed signals might not be smooth. Hard thresholding canbe described as setting to zero the elements whose absolute valuesare lower than the threshold.
For threshold selection, we use the principle of Stein’s UnbiasedRisk [27]. By this method, an estimate of the risk for a particu-lar threshold value t can be obtained. Minimizing the risks in tgives than an optimal selection of the threshold value. In statis-tics, Stein’s unbiased risk estimate (SURE) is an unbiased estimatorof the mean-squared error of a given estimator, in a determinis-tic estimation scenario. In other words, it provides an indication ofthe accuracy of a given estimator. This is important since, in deter-
ministic estimation, the true mean-squared error of an estimatorgenerally depends on the value of the unknown parameter, andthus cannot be determined completely.he registration algorithm.
S. Li et al. / Computerized Medical Imagin
Fig. 2. Scheme of wavelet-based clustering of DCE-MRI time series. First, for eachvo
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ing accuracies obtained for the single slices.
oxel time series a wavelet analysis including thresholding is performed. Then, thebtained wavelet coefficients are clustered using k-means.
Let � ∈ Rn be an unknown deterministic parameter and let x be measurement vector which is distributed normally with mean �nd covariance �2I. Suppose h(x) is an estimator of � from x. Then,tein’s unbiased risk estimate is given by
URE(h) =∥∥�
∥∥2 +∥∥h(x)
∥∥2 + 2�2n∑
∂xi
∂hi
∂xi− 2
n∑
i=1
xihi(x) (3)
here hi(x) is the ith component of the estimate, and ||·|| is theuclidean norm.
The importance of SURE is that it is an unbiased estimate of theean-squared error (or squared error risk) of h(x), i.e.
{SURE(h)} = MSE(h) (4)
Thus, minimizing SURE can be expected to minimize the MSE.xcept for the first term in SURE, which is identical for all estima-ors, there is no dependence on the unknown parameter � in thexpression for SURE above. Thus, it can be manipulated (e.g., toetermine optimal estimation settings) without knowledge of �.
.3.2. ClusteringIn this approach the DCE-MRI data, each voxel i is repre-
ented as a point in p-dimensional space where the dimensionsre the selected wavelet coefficients seen as a vector −→
Wi =w1
i, . . . , wP
i, . . . , wP
i) ∈ RP where p = 1, · · ·, P denotes the number of
oefficients. We apply the k-means clustering [37] to the selectedavelet coefficients. We found that the cosine distance function
38] was a good choice for the metric d: RP × RP → R, i.e.
( �Wi, �Wj) = 1 − cos ̨ (5)
g and Graphics 36 (2012) 108– 118 111
with
cos ̨ =�Wi
�Wj
| �Wi|| �Wj|(6)
the cosine of the angle between �Wi and �Wj in RP. We initializedthe algorithm with k = 5 (“cortex”, “medulla”, “pelvis”, “other parts”and “background”). The cluster centroids were initially chosen byrandom. The clustering itself was repeated ten times to not getbiased due to the initialization. From the obtained labeled list ofvoxels after clustering, a 3D volume is reconstructed again.
2.4. Patient data
The patient data were preprocessed the same way as the datafrom the healthy volunteers. At first, they were corrected for move-ments using the algorithm described in Section 2.1. Afterwards, thedata were cropped to the sizes of the kidney, obtaining two sub-sets of data for each patient. Then, wavelet based clustering wasperformed as described in before.
However, patients who suffer from kidney disease might showdifferent perfusion patterns as healthy volunteers. Therefore, wetook the previously estimated number of clusters from the healthyvolunteers’ analysis as a reference and selected the number of kclusters around this value (3–7 clusters). The optimal number ofclusters was determined by visual inspection, i.e. how good thedifferent compartments could be separated by clustering.
2.5. Evaluation
The evaluation of segmentation results is difficult due to thelack of gold standards [39]. In our case we compared the auto-matic segmentation to manual delineated (by trained experts)regions in order to quantify the segmentation error. Furthermore,we compared our results to k-means clustering of the original timeintensity courses as described in [17]. We calculate the accuracyto evaluate the segmentation results. The accuracy is calculated bythe proportion of true results (both true positives and true nega-tives) in the sample. The total number of positives and negativesrefer to the number of pixels which are compared with automaticsegmentation to manually delineated. More specificially,
accuracy = TP + TN
TP + FP + FN + TN(7)
where TP = number of true positive, TN = number of true negative,FP = number of false positive, FN = number of false negative. Obvi-ously, accuracy approaches 1 if the similarity between the sets ishigh.
Here, TP are those voxels (with the same spatial position) inboth masks that were labeled by one whereas TN are those voxelwhich are labeled zero, respectively. False positive voxels are thosevoxel that are labeled zero in the reference mask image (manualdelineation) and by one in the wavelet-based segmentation. TheFP value reflects the amount of over-segmentation error. Similar,FN are those voxels in both masks that are labeled zero in theclustering and one by the reader. Therefore, FN reflects the under-segmentation error of the algorithm.
The evaluation was carried out slice by slice similar to [17] toassess the segmentation results more specific rather than compar-ing the segmented 3D volume of interests (VOIs). The outer mostslices mostly contain no or only partly, even manually hard to delin-eate, kidney regions. Such slices were excluded from the analysis.Total segmentation accuracy per kidney was calculated by averag-
We also compared the results with a clustering approachdescribed in [17]. The authors used k-means clustering on the rawvoxel intensity time courses. A Wilcoxon rank sum test [40] on
112 S. Li et al. / Computerized Medical Imaging and Graphics 36 (2012) 108– 118
F nd the reconstructed signals (solid line) after wavelet analysis. Signals are retrieved fromd
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Table 2The iterations steps and mean calculation time of different k-means clusterings.
Methods Distance Iteration steps
k-means only Squared Euclidean 32 ± 6
inspection, the results show no significant differences.Table 3 shows the quantitative evaluation and comparison of the
methods. For all four data sets high accuracy could be obtained. On
ig. 3. Comparison between the original voxel intensity time courses (dashed line) aifferent region points (cortex, medulla, and pelvis) in the mid-slice of data 3.
he segmentation accuracies was carried out to test significanceetween segmentation results of the methods. The null hypothesishat segmentation results of the methods are independent sam-les from identical continuous distributions with equal mediansresults do not differ), against the alternative that they do not havequal medians (results differ) was tested at a significance level of.05.
Furthermore, time intensity curves of healthy volunteers andatients from the segmented VOIs were inspected. To extract theime intensity curves, the segmented VOIs were used to mask theriginal perfusion data sets and voxels belonging to these regionsere averaged to obtain a mean time intensity curve for the differ-
nt compartments or segmented VOIs, respectively.
. Results
.1. Wavelet analysis
Fig. 3 is the illustration of voxel intensity time courses and theeconstructed signals from one voxel from the different compart-ents of the kidney (cortex, medulla and pelvis). Thresholding
he wavelet coefficients results in a smoothed signal after recon-truction. For our data about 5% of the wavelet coefficients werehresholded.
The wavelet analysis including thresholding allows for a fasteromputation and therefore, segmentation. Processing time waseasured on a standard PC with an Intel CoreTM2 Duo CPU T7250
.00 GHz and 1 GB RAM. Fig. 4 depicts the average calculation timeor clustering one slice by the two methods. The mean iterationteps to find an optimal partition of the data by clustering are shownn Table 2.
.2. Wavelet-based clustering
The two segmentation algorithms were tested at first on 8 kid-eys from four healthy volunteers. For all kidneys a reasonableegmentation of the renal compartments could be obtained.
Cosine 42 ± 7Wavelet-based clustering Cosine 32 ± 6
Fig. 5 is an illustration of the segmentation results obtained bywavelet-based and standard k-means clustering. The clustering candetect the renal compartments (cortex, medulla and pelvis). Sim-ilar results were retrieved for the other two data sets. By visual
Fig. 4. Mean calculation time comparison between the proposed wavelet-basedmethod and k-means only clustering.
S. Li et al. / Computerized Medical Imaging and Graphics 36 (2012) 108– 118 113
Fig. 5. Segmentation result. (a and d) the original kidney image, (b and e) the segmentation result of proposed wavelet based clustering, (c and f) the segmentation result ofk-means. The black part depicts the renal cortex, the light grey part shows the renal medulla, and the dark grey part represents the pelvis. Upper row data from data set 1,slice 10 of 20, acquired at 1.5 T, lower row middle slice of data set 3, acquired at 3.0 T.
Table 3Comparison of segmentation methods vs. manual segmentation (volunteer data). The mean accuracy over all slices and data sets are given.
Dataset Wavelet-based clustering Pure k-means
Cortex Medulla Pelvis Cortex Medulla Pelvis
V1 Left 0.89 ± 0.04 0.90 ± 0.04 0.99 ± 0.01 0.87 ± 0.04 0.90 ± 0.04 0.99 ± 0.01Right 0.89 ± 0.03 0.91 ± 0.05 0.98 ± 0.01 0.88 ± 0.03 0.92 ± 0.04 0.99 ± 0.01
V2 Left 0.88 ± 0.04 0.91 ± 0.03 0.98 ± 0.01 0.88 ± 0.04 0.91 ± 0.05 0.98 ± 0.01Right 0.88 ± 0.04 0.89 ± 0.04 0.98 ± 0.01 0.89 ± 0.03 0.91 ± 0.04 0.98 ± 0.01
V3 Left 0.90 ± 0.05 0.90 ± 0.04 0.99 ± 0.01 0.98 ± 0.05 0.91 ± 0.05 0.98 ± 0.01Right 0.87 ± 0.04 0.92 ± 0.04 0.99 ± 0.01 0.87 ± 0.05 0.90 ± 0.05 0.99 ± 0.01
0.98
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ments and their corresponding time intensity curves respectively.The clusters are depicted as black and white mask images sincethe cluster’s label is arbitrary. The kidney compartments could besuccessfully segmented by the wavelet clustering approach. For all
Table 4Registration results for three patient data sets. Given is the standard deviation inmm of the distance of the lower pole of the kidney to a fixed references point in theimage estimated in all frames of each data set. The algorithm was parameterizedwith a convolution kernel of size 14 mm.
Patient Motion before Motion after
V4 Left 0.89 ± 0.03 0.91 ± 0.03
Right 0.90 ± 0.05 0.92 ± 0.05
verage, the renal cortex could be segmented at 88%, the medullat 91%, and the pelvis at 98% accuracy. As already assumed by visualnspection, both methods perform at similar accuracy. Comparinghe quantitative segmentation results by Wilcoxon rank sum test,o significant differences in the segmentation accuracies could beetected (cortex p = 0.8, medulla p = 0.5, pelvis p = 0.4).
.3. Patients data application
.3.1. RegistrationThe registration algorithm leads to a reduction of motion in the
mages. Table 4 shows the results for the three patient data sets.or all patient datasets, the standard deviation of an anatomicaleference point’s position in the image frame was reduced to belowhe spatial resolution of 1.56 mm.
In Fig. 6, checkerboard images of the reference and source imagere depicted. The effect of registration can clearly be seen, especiallyt the lower edge and the upper left edge of the kidneys. There, dis-ontinuities at the kidney borders are removed by the registrationlgorithm.
.3.2. Wavelet-based clusteringThe segmentation algorithm was applied to MR perfusion data
f three patients. All patients had a history of known hyperten-
± 0.01 0.90 ± 0.03 0.92 ± 0.04 0.99 ± 0.01± 0.01 0.89 ± 0.04 0.93 ± 0.03 0.99 ± 0.01
sion when being examined by MRI. For the first patient no findingsrelated to kidney function was diagnosed whereas the secondpatient had a benign cyst of 3 cm diameter in the caudal part of thekidney (cf. Fig. 8a)). The third patient was diagnosed with a steno-sis in the lower segment artery of the left kidney; also no findingswere reported regarding kidney dysfunction.
Figs. 7–9 depict the segmentation results for one kidney ofeach patient data set. Each figure comprises a slice of an MRimage as reference, the obtained clusters of the renal compart-
registration (mm) registration (mm)
P1 2.47 0.74P2 2.72 1.51P3 3.32 1.44
114 S. Li et al. / Computerized Medical Imaging and Graphics 36 (2012) 108– 118
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ig. 6. Registration result of one kidney of one patient data set. Left: checker board piscontinuities are reduced after registration (see arrows).
atients, intensity time courses averaged over segmented cortexnd medullar regions showed typical contrast agent uptake pat-erns. In case of patient 2, the clustering could also discriminate theyst from the “healthy” tissue. Corresponding intensity time curveshow no contrast agent uptake for the cyst. The optimal values forhe initial number of clusters were ranging from 3 to 6 clusters.imilar results were obtained also for the second kidney of eachatient data set.
Comparing the clustering results of the patient data, especiallyhose depicted in Figs. 7 and 9 to segmentation results of healthyolunteers (Fig. 5), segmented renal cortex and renal medulla lookimilar. Fig. 10 depicts exemplarily average time intensity curves
erived from the segmented VOIs of the patient shown in Fig. 9nd the healthy volunteer shown in Fig. 5(a)–(c). The time inten-ity curve of the cortex of the patient show a later arrival of theolus and also a lower bolus amplitude than corresponding curveig. 7. Segmentation result for patient 1. (a) MR image of one slice of the data set, (b) thhe average signal over time for the segmented regions. Clustering was initialized by k = 4
of reference image and source image, right: reference image and registered image.
of the healthy volunteer. The time intensity curves of the medulla,however, are quite similar for both patient and volunteer.
4. Discussion
In this study, we proposed a wavelet-based clustering of 3DDCE-MRI image series to segment kidney compartments. Thereby,we take advantage of the signal intensities evolving over timewhich exhibit characteristic patterns [7,16] related to the func-tional anatomy of the kidney. This allows for a discrimination ofthe renal compartments in healthy volunteers as well as in patientswith hypertension as demonstrated by our study. Segmentation
accuracy in the healthy volunteers was high (about 90% for allcompartments and data sets). Significant differences to a referencemethod employing k-means clustering [17] could not be observed.However, processing time of the data decreased using wavelete cluster depicting the cortex, (c) the cluster depicting the medulla and (d) plot of.
S. Li et al. / Computerized Medical Imaging and Graphics 36 (2012) 108– 118 115
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ig. 8. Segmentation result for patient 2. (a) MR image of one slice of the data set,edulla, (d) the cluster depicting the cyst and (e) plot of the average signal over tim
ased k-means clustering. Signal intensity curves derived from seg-ented renal compartments of the patient data showed typical
erfusion patterns of the respective compartments.Wavelet analysis has a wide application in image processing,
uch as compression and denoising [23,24]. We decomposed eachoxel time series using the discrete wavelet transform (DWT) and
ebauchies 4 mother wavelet. Compared to the much simpler Haaravelet, that also have been used in for analysis time series data36], in theory, Daubechies 4 wavelet can pick up details that areissed by the Haar wavelet algorithm [35]. In practice, after explor-
ig. 9. Segmentation result for patient 1. (a) MR image of one slice of the data set, (b) thhe average signal over time for the segmented regions. Clustering was initialized by k = 6
epicting the cyst, (b) the cluster depicting the cortex, (c) the cluster depicting the the segmented regions. Clustering was initialized by k = 4.
ing different mother wavelets, including Haar, Coiflet, Symmlet andDaubechies, the results didn’t show significant differences [41].Several version of the Daubechies mother wavelet exists. Whitcheret al. reported that short wavelets (L ≤ 12) are favorable in case offew time points [28] as in some of our data sets (e.g., data set 1, 20time points).
To further process the coefficients obtained from wavelet anal-ysis, a common approach is to denoise the signal, i.e. to thresholdthe coefficients [42]. To estimate a good threshold different meth-ods exist, e.g. the universal threshold. This method aims at deriving
e cluster depicting the cortex, (c) the cluster depicting the medulla and (d) plot of.
116 S. Li et al. / Computerized Medical Imagin
Fig. 10. Time intensity curves of renal cortex and renal medulla from one healthyvolunteer and one patient. Curves were obtained by averaging the all voxel timeintensity curves within each segmented kidney compartment, respectively. Corre-sponding segmentation results are depicted in Fig. 5(a)–(c) for the volunteer andF
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Several such approaches are described in the literature [44–46].
ig. 9 for the patient.
value that is independent of the wavelet scale and takes the totalumber of coefficients and the standard deviation within the coeffi-ients into account. Furthermore, a scaling constant of magnitude 1as to be selected. We used Stein’s unbiased risk estimate (SURE) tostimate the thresholding value. The appealing advantage of SURE,sed to estimate the threshold value, is that it does not require ariori knowledge about the statistics of the unknown data.
After obtaining a threshold, we applied hard thresholding sincet can preserve local characteristics [27], although the recon-tructed signals might appear not to be smooth. As shown in Fig. 3,he reconstructed signal is smoothed as expected by the wavelethrinkage. Thereby, movement artefacts not removed by the regis-ration step could be eliminated; however, peaks related to breatholds (sharp peaks in the signal) still remain.
Soft thresholding is another possibility for wavelet shrinkage.t does not set coefficients to zero if they exceed the thresholdut assign a certain value (usually the threshold) to the coeffi-ients. However, in this study, the hard thresholding had a seconddvantage: Due to setting zero some wavelet coefficients by hardhresholding, a sparse matrix of wavelet coefficients is constructed.ilbert et al. showed that such sparse data structure or matrix can
ncrease processing speed. Thereby the gain is proportional to themount of zero elements in the data, i.e. how sparse the data is. Therocessing time for clustering the volunteer data could be reducedy ca. 50% (cf. Fig. 4 and Table 2).
To further evaluate the clustering results, we compared ourpproach to a clustering using just the k-means algorithm as out-ined in [17]. The rational was to access best the impact of the
avelet analysis to the segmentation which would be more com-licated when using a complete different method like a level setpproach [43] or graph cuts [14]. Comparing the results, however,o significant differences in segmentation accuracy on the volun-eer data could be obtained. This might be to the fact that in ourtudy only decomposition into the first scale was performed. Thehoice of a wavelet scales for analysis is mostly driven by the expertnowledge. Whitcher et al. decomposed their data up to the sev-nth scale, however, which scale was finally selected for furtherrocessing remains unclear [28]. Therefore, we selected the firstcale for a start. Investigating other scales is currently a topic of ouresearch.
Although the segmentation results did not show significant dif-erences, one must also note that there was also no loss in accuracyhen thresholding about 5% of the wavelet coefficients. This sug-
g and Graphics 36 (2012) 108– 118
gests that mostly noise in the data was removed by the waveletanalysis.
Application of our method to three patients with hypertensionwas successful. In all cases a segmentation of the renal compart-ments could be obtained. Only for one patient with a cyst in lowercaudal part of one kidney, the clustering results were more dif-ficult to interpret and to identify. However time intensity curvesderived from the clusters (cf. Figs. 7–9) showed the typical shapeof kidney perfusion within the respective compartments, i.e. (i)early peak with steep up-slope corresponding to the first pass ofthe contrast agent through the vasculature of the cortex and (ii)delayed and less distinct peak, representing filtered contrast agentin the tubular and collecting system of the medulla [44,45]. Fur-thermore, the cyst in one patient was also detected and assigneda separate cluster. In patients with hypertension and renal arterystenosis (RAS) the perfusion and filtration is affected and thus, theobserved time intensity curves might change [6]. Michaely et al.analysed the influences of stenosis grade and RAS to the time inten-sity curves derived from DCE-MRI [44]. No significant differencesin low- to intermediate-grade RAS were reported; however, kid-neys with high-grade RAS showed a reduced maximum upslopeand mean transit time, i.e. delayed or dispersed bolus. In the timeintensity curves this is reflected by a broadened peak of the firstpass of the tracer and probably a later time of arrival of the con-trast agent. In our study, no renal insufficiency of the patients wasdiagnosed. However, comparing patient to volunteer time intensitycurves (cf. Fig. 10) certain differences could be detected. The shapeof the curves is similar, however, the time of bolus arrival is delayedin the patient and also the amplitude of the curve is lower than forthe healthy volunteer. Since the segmentation results show highaccuracy to manual delineations, both for healthy volunteers andpatients, we assume that these differences relate to the patients’disease. To prove this, further analysis like pharmacokinetic anal-ysis [11] or blood sampling [3] is needed which is out of the focusof this study. Certainly, further evaluation of patient data withdifferent types and degrees of renal disease will have to be per-formed.
Furthermore, it seems the employed registration algorithm forthe patient data performs similar to that used with the healthyvolunteers and has no obvious effects to the segmentation. Noiseresulting from minor motion artefacts was possibly removed viathe wavelet shrinkage as observed for the healthy volunteers, too.However, a more detailed comparison and evaluation of the reg-istration has to be performed and subject to another study in ourgroup.
The proposed wavelet-based clustering approach providesautomated processing and segmentation of the renal compart-ments. Apart from selecting a scale for the wavelets, only a secondparameter has to set by the operator: the number of clusters. Thenumber of clusters has to estimated before the start of the calcu-lations [46]. Therefore, either knowledge about a good number ofclusters is needed by the operator or the number of cluster has toestimated by iterating over a certain range of clusters supported bycluster validity measures [47]. The selection of the number of clus-ters becomes even more important, when analyzing patient data.Due to changes in the perfusion or renal masses (like cysts) newclusters should be detected. Up to know, our method was initial-ized by iterating over a certain range of k clusters. For the healthyvolunteers, similar number of clusters as given in a recent study [17]showed best results. For the patients the number of clusters var-ied between 3 and 6. Therefore, further investigations should focuson methods to determine the number of clusters automatically.
In particular, Lin et al. presented an interesting method using aniterative scheme to initialise the k-means clustering and wavelets.Clustering was performed on each scale in the multi-scale analysis
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S. Li et al. / Computerized Medical I
f the time series and the obtained clusters were used to initialisehe next, and less coarse, scale [48].
. Conclusion
From our experiments, we conclude that wavelet-based k-eans clustering is a feasible approach to segment principal renal
ompartments from DCE-MRI. Our implementation provides anutomated and fast processing of the high dimensional imagingata. Initial results in healthy volunteers and patients show promis-
ng results with high segmentation accuracy compared to manualelineations. Possible applications of the proposed method com-rises a discrimination of healthy and pathological tissue based onegmented renal compartment volumes or using the segmentedOIs for automated analysis of renal perfusion and filtration.
onflict of interest statement
Hereby the authors confirm that they do not have any conflictf interest.
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Sheng Li received BA degree in mechanic engineering from Tongji University, Shang-hai, China, in 2006 and received MA degree in medical physics in Medical Faculty
Mannheim, Heidelberg University, Germany, in 2010. He is now pursuing the PhDdegree in Shanghai Jiaotong University, Shanghai, China. His research interests lie inthe fields of applying computational methods from image analysis, or bioinformaticsto the fields of medical image analysis. Currently, he works on magnetic resonanceimaging (MRI) of the human kidney for diagnostics of renal disease.
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munity. In 1991 he received the Venia Legendi for Medical Physics at the University
18 S. Li et al. / Computerized Medical I
rank G. Zöllner received a diploma and a PhD degree (Dr.-Ing.) in computer sciencerom Bielefeld University, Germany, in 2001 and 2004, respectively. From 2004 until006 he worked as a post-doctoral researcher in the BMBF project ALPIC. In 2006 and007 he was a researcher at the Section of Radiology, Institute for Surgical Sciences,aukeland University Hospital and Department of Biomedicine at the University ofergen, Norway. In 2008, Dr. Zöllner joined the Chair of Computer Assisted Clinicaledicine, Heidelberg University. He is head of the junior reseach group “MRI and
attern Recognition”. His research interests lie in the fields of pattern recognition,mage processing as well as bioinformatics. In particular, he is interested in applyingomputational methods from pattern recognition and medical image analysis MRIata. Dr. Zöllner is a member of the IEEE Computer Society, the ESMRMB and ISMRM.
ndreas D. Merrem is a physics student of the University of Heidelberg in his fourthear. He obtained his bachelor’s degree in physics in 2010 on delivering his thesisnder the supervision of Lothar R. Schad and Frank Zöllner at Heidelberg Univer-ity’s Institute of Computer Assisted Clinical Medicine. The topic was registrationf dynamic contrast enhanced MRI data for the measurement of kidney perfusion.urrently, he is studying physics with an emphasis on medical physics at MSc levelt University College London on an Erasmus program.
inghong Peng is the professor and the director of School of Mechanical Engineer-ng, Institute of Knowledge Engineering, Shanghai Jiaotong University. He has wonhe National Outstanding Young Teacher Award. He is also the executive director ofhe Chinese Mechanical Engineering Society, Shanghai investment consultant. Heas chaired the national “863” key projects, the National Natural Science Founda-ion research projects and more than 20 international cooperation projects. He haswice won Shanghai Science and Technology Progress Award. He has published morehan 100 articles in academic journals and conference papers. His research inter-sts include mechanical design theory and application of KBE, materials processingngineering CAD/CAE/CAM/PDM.
arle Roervik has a position as professor in radiology at the University of Bergennd physician at the department of radiology at Haukeland University Hospital,ergen, Norway. In 1998 he finished his thesis on the use of imaging for stagingrgan-confined prostate cancer prior to radical treatment. Later he continued hisesearch on prostate cancer both for detection and for staging. Currently, he and his
g and Graphics 36 (2012) 108– 118
research team is performing studies on the use of MRI with contrast and MR spec-troscopy for both detection and staging of prostate cancer. Further, he has togetherwith Arvid Lundervold established a research-group working with MRI for kidneyimaging including both morphological and functional exams. He has been a super-visor for three PhD-students (doctores medicalis) and several master students witha wide spectrum of research topics. He is in charge of the education of medical stu-dents in radiology and has received several prizes for the quality in the teaching. Aspecial interest has been the development and the use of digital teaching material.
Arvid Lundervold has a BSc in mathematics and philosophy and MD from theUniversity of Oslo. He earned his PhD at the University of Bergen. Currently, heis full professor in medical information technology at the University of Bergen,Department of Biomedicine, and head of the Neuroinformatics and Image Anal-ysis Laboratory. He has published more than 100 papers and conference reportsrelated to medical image analysis, pattern recognition, and neuroinformatics. Hehas supervised more than twenty Master and PhD students with their basic trainingfrom mathematics, computer science, medicine, or physiology. He is presently theboard chairman of the Norwegian Research School in Medical Imaging, and has beenNorwegian representative in the European COST B11 and B21 concerted actions,and the present COST BM0601 (“NEUROMATH”). He is on the Editorial board of“Computerized Medical Imaging and Graphics” and “Frontiers in Neuroinformat-ics”, and member of the Norwegian Medical Association, the International Societyfor Magnetic Resonance in Medicine, the IEEE Computer Society, and the AmericanMathematical Society.
Lothar R. Schad received his Ph.D. in Nuclear Physics from the University of Hei-delberg, Germany, in 1983. In 1984 he was postdoctoral fellow of the Max PlanckInstitute of Nuclear Physics, Heidelberg. From 1985 to 2007 he served as a researchassistant in Medical Physics at the German Cancer Research Centre, Heidelberg. From1990 to 1995 he was Heisenberg scholarship holder of the German Scientific Com-
of Heidelberg. Since 2007 he has been the Chair and Director of the Institute of Com-puter Assisted Clinical Medicine at the Medical Faculty Mannheim of the Universityof Heidelberg. His research interest lies in MRI and its applications to diagnosticsand therapy.
