Oscar Jalnefjord^{1,2}, Mikael Montelius^{1}, Jonathan Arvidsson^{1,2}, Eva Forssell-Aronsson^{1,2}, GĂ¶ran Starck^{1,2}, and Maria Ljungberg^{1,2}

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 vivo^{1}. The ability to quantify tumor heterogeneity has been shown useful for, e.g., prediction of clinical outcome^{2}.

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
information^{3}. To enable
a more localized, but still comprehensible, analysis, the tumors can be partition into smaller subregions for further analysis^{4}. 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
evaluation^{1,5}.

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 ^{177}Lu-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/mm^{2} (5 animals) or 1.4,5,10,20,35,50,75,100,201,401,602,802s/mm^{2} (9
animals), TE=22ms, pixel size=320×320μm^{2}, slice thickness=1000μm.

**IVIM model fitting**

IVIM parameter maps were obtained by Bayesian model fitting^{6} of the IVIM model:

$$S(b)=S_0((1-f)e^{-bD}+fe^{-bD^*})\quad[1]$$

where *S*(*b*) is the signal with
b-value *b*, *S*_{0} is the signal without diffusion weighting, *f* is the perfusion fraction, *D* is the diffusion coefficient and *D** is the pseudo-diffusion coefficient^{5}.

**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 (* μ_{l}*)
and covariance matrices (

Similarly, data were also
clustered with a Gaussian hidden Markov random field model (GHMRFM) as
described previously^{7}. 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 performance^{8}.

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 0.25×0.25μm^{2} 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.

**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).

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