Cluster analysis of IVIM parameter maps reveals tumor subregions of different proliferative status
Oscar Jalnefjord1,2, Mikael Montelius1, Jonathan Arvidsson1,2, Eva Forssell-Aronsson1,2, Göran Starck1,2, and Maria Ljungberg1,2

1Department of Radiation Physics, University of Gothenburg, Gothenburg, Sweden, 2Department of Medical Physics and Biomedical Engineering, Sahlgrenska University Hospital, Gothenburg, Sweden


Tumors are often heterogeneous, which can be seen with various imaging techniques. Even so, analysis based on quantitative imaging is often restrained to average tumor parameter values. In this study we used cluster analysis to identify tumor subregions based on IVIM parameter maps. The tumor subregions showed strong agreement with proliferative status as derived from histological analysis.


Quantitative imaging techniques such as diffusion and perfusion MRI have potential not only to probe clinically relevant tumor characteristics, but also to provide their spatial distribution in vivo1. The ability to quantify tumor heterogeneity has been shown useful for, e.g., prediction of clinical outcome2.

Even though the heterogeneous nature of tumors is well known, analysis in most studies utilizing quantitative MRI is limited to average tumor parameter values, which may result in loss of important information3. To enable a more localized, but still comprehensible, analysis, the tumors can be partition into smaller subregions for further analysis4. The definition of such subregions can be based on functional information by applying, e.g., a clustering algorithm on parameter maps.

A quantitative MRI technique with great potential for tumor characterization is intravoxel incoherent motion (IVIM) analysis of diffusion-weighted imaging data. IVIM analysis provides information on perfusion and tissue water diffusion, both important markers for tumor evaluation1,5.

The aim of this study was to investigate if clustering based on IVIM parameter maps can be used to obtain tumor subregions with biological relevance.


Tumor model and MR imaging
Fourteen mice with human small intestine neuroendocrine tumor subcutaneous in the neck region (tumor diameter approximately 15mm) were given non-curative 15MBq 177Lu-octreotate treatment (absorbed dose 4.0Gy) resulting in responses ranging from reduced growth rate to significant tumor volume reduction.

Diffusion-weighted SE-EPI images were obtained with a Bruker 7T system thirteen days after treatment, when the tumor volume was either constant or increasing after the initial therapeutic response. Imaging parameters were: b(Δ=9ms,δ=4ms)=1.4,14,25,36,56,82,108,421,751s/mm2 (5 animals) or 1.4,5,10,20,35,50,75,100,201,401,602,802s/mm2 (9 animals), TE=22ms, pixel size=320×320μm2, slice thickness=1000μm.

IVIM model fitting
IVIM parameter maps were obtained by Bayesian model fitting6 of the IVIM model:


where S(b) is the signal with b-value b, S0 is the signal without diffusion weighting, f is the perfusion fraction, D is the diffusion coefficient and D* is the pseudo-diffusion coefficient5.

Cluster analysis
The tumors were manually delineated and the IVIM parameters D, D* and f were extracted from each voxel separately and log transformed before being fed into the clustering algorithms described below.

Data were clustered into k classes by fitting a Gaussian mixture model (GMM). The results thus consisted of k sets of prior class probabilities (P(l)), mean vectors (μl) and covariance matrices (Σl).

Similarly, data were also clustered with a Gaussian hidden Markov random field model (GHMRFM) as described previously7. The GHMRFM is similar to a GMM, but uses a prior distribution that depends on the neighboring voxels. The GHMRFM was utilized since clustering including spatial information has shown enhanced performance8.

Both clustering algorithms were also run with only D and f as input to study if D* provides additional information. Being able to exclude D* would reduce the high demands on image quality needed for estimation of D*9.

Data was chosen to be partitioned into two clusters based on goodness of fit.

Histological analysis
To study the biological relevance of the tumor subregions obtained from cluster analysis, a histological analysis was performed. After the MR examination the animals were killed and tumor sections (3µm thick) were collected. Based on the clustering results, it was hypothesized that the obtained clusters corresponded to different proliferative status. Staining was therefore performed with Ki-67 to assess cellular proliferation. The stained tissue sections were digitally imaged at 0.25×0.25μm2 resolution using a Leica SCN400 Slide Scanner. The tumor tissue regions were manually delineated and segmented into proliferating or non-proliferating regions as outlined in Figure 1.

Results and Discussion

Cluster analysis
The IVIM parameters showed distributions that were well approximated by a mixture of two Gaussian distributions (Fig. 2). The two identified classes were characterized by either high perfusion and low diffusion, or low perfusion and slightly higher diffusion (Fig. 2 and Table 1), potentially corresponding to regions of high and low degree of proliferation, respectively. The resulting cluster maps showed large spatially contiguous tumor subregions (see example in Fig. 3). Inclusion of D* or spatial information only had minor effects on the clustering results (Figs. 3 and 4, and Table 1).

Histological validation
A strong agreement was found between the tumor subregions with high perfusion (indicating high supply of nutrient and oxygen) and low diffusion (potentially a marker of high cellularity) identified by clustering, and the subregions identified as proliferating by histological analysis. These results were seen both regarding spatial distribution (example in Fig. 3) and regarding size of subregions (Fig. 4).


This study shows that clustering based on IVIM parameter maps can identify tumor subregions that are associated with proliferative activity.


The study was supported by grants from the Swedish Cancer Society and the King Gustav V Jubilee Clinic Cancer Research Foundation.


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Figure 1. Outline of the histological analysis used to identify proliferating areas in Ki-67 stained tumor section. First, Ki-67 positive (brown) pixels were identified by applying a color threshold. Second, the proportion of Ki-67 positive pixels in regions of 64×64µm2 was calculated. Finally, regions with more than 2% Ki-67 positive pixels were defined as proliferating. The threshold was confirmed by a board certified pathologist

Figure 2. Histograms showing the distribution of the complete set of IVIM parameters obtained from all tumors on linear scale (top row) and log scale (bottom row). The GMM fit based on log-transformed data is superimposed on the histograms in black. The Gaussian distributions corresponding to the individual classes are shown in green and red (the colors correspond to class 1 and 2 in Table 1, respectively)

Figure 3. Qualitative assessment of agreement between clustering and histological results. The figure shows IVIM parameter maps, cluster maps and proliferation map from one example tumor. Note the high degree of similarity between the cluster maps, which are based on MRI data, and the proliferation map, which is based on histological data (Ki-67 staining)

Figure 4. Quantitative assessment of agreement between clustering and histological results. The graphs show size of subregions belonging to the cluster with high perfusion plotted versus size of areas identified as proliferating by the histological analysis. The agreement was quantified by Lin’s concordance correlation coefficient (rc). Note the strong agreement between the sizes given by clustering, which is based on MRI data, and the sizes of proliferating areas, which are based on histological data (Ki-67 staining)

Table 1. Cluster characteristics obtained from the four different clustering approaches used in this study. P(l) is the prior class probability and μl is the mean vector of class l

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)