In time-series of single-shot diffusion weighted (DW) images signal voids in different muscle groups have been observed ¹. Due to the random appearance of these signal voids in the time domain and a large number of images, an automatic segmentation is desired to expedite the time-consuming evaluation and thus enable larger studies for revealing the underlying processes of this phenomenon. To prevent an underestimation of the size of the signal voids caused by ignoring regions with partial volume effects, a two-class detection and segmentation approach is proposed. Furthermore, a-priori knowledge about the location of vessels, which are responsible for signal fluctuations due to blood flow and pulsation ¹, is directly incorporated into the segmentation instead of using an extra processing step ².

The DW images were acquired on a 3 T MR scanner (Magnetom Skyra, Siemens Healthcare, Erlangen, Germany) with a stimulated echo DW EPI sequence (matrix size: 64 x 64, FoV = 200 x 200 mm², TE = 31 ms, TR = 500 ms, BW = 2004 Hz/px, TM = 145 ms, 500 repetitions and 15 channel Tx/Rx knee coil). The segmentation procedure is depicted in Fig. 1 and was implemented in MATLAB^® (The Mathworks, Inc., USA). In the first step, bias-field and long-term variations were estimated and corrected by the BCFCM ³ (bias-corrected fuzzy c-means) and RLOESS ^1,4 (robust local regression with a span of 5 %) algorithm. Repetitions with high signal energy were averaged to calculate a reference image without signal voids as input image for the bias-field correction algorithm. The BCFCM algorithm was utilized to get the bias-field of the muscle tissue and to determine a tissue mask to reduce the computational load in subsequent calculations. After these processing steps, the image x_i is converted in a time-difference representation by using two temporally adjacent images x_i-1 and x_i+1 according to (1).

$$I_t(x_i)=x_i-\frac{x_{i-1}+x_{i+1}}{2} \quad \quad \quad \quad (1)$$

This simple high pass filtering enhances the temporal changes in signal intensity and emphasizes the starting points and endpoints of the signal void events. The event detection step is based on a standard two class Fuzzy C-Means algorithm ^5,6 with an additional grey-level based rejection term to suppress false positive detections in noisy images. For the segmentation the variation corrected DW images are transformed in an undirected graph-based representation, while the edge weighting is derived from the grey-level of the connected voxels ⁷, the distance to the seed points and from the time-difference representation. To prevent detections at pulsation sources like vessels, the vessel locations are estimated from a flow compensated GRE image and are integrated as an additional weighting term in the weighting function. For the intra-slice weighting (in one DW image), an 8-point, and for the inter-slice weighting (over time), a 2-point neighborhood connection is utilized as shown in Fig. 2. For an automatic seed point placement, the derivation of an Euclidean distance map is calculated ^8,9 (Fig. 3 c) and d)) to iteratively shift the equidistantly placed seed points of the “no event” class away from the event seed points. This approach determines a region between already segmented points (from the event detection) and the shifted seed points to reduce again the computational load (Fig. 3 e)). With the weighting between the voxels, a graph-based optimization problem had to be solved for the voxel classification. This optimization problem is solved by the random walker algorithm ⁷ (Fig. 3 f)), which reformulates the classification task into the solution of a linear system based on a combinatorial Dirichlet problem.

In Fig. 3 partial results along the entire whole segmentation workflow are shown. Segmentation steps from the original DW image in a) to the final segmentation result in f) are included. Three original DW images with overlaid segmentation results are depicted in Fig. 4 showing signal voids in the m. gastrocnemius medialis and in the m. soleus. It can be seen that the vessel region between the m. soleus and the m. tibialis posterior as well as the fibula is not considered as signal void (marked in the middle and right DW image).The proposed segmentation procedure enables a fast and accurate segmentation of signal voids in musculature of the human calf with considerations of the partial volume affected as well as vessel and bone regions. Moreover, the segmentation can be extended to a 3D + t approach for the segmentation of time series data of 3D or multi-slice diffusion weighted images by an extension of the graph construction step.