1. Principle of multi-energy CT
Every element, such as carbon, oxygen, and nitrogen, has an eigen attenuation (absorption) coefficient and absorption edges (energies), where the absorption coefficient changes rapidly as shown in Fig. 1 . Dual- and Spectral (multi-energy) CT (SCT) calculates precise pseudo monochromatic images with CT images acquired at different X-ray energies by utilizing the absorption properties of each element. The estimation of atomic numbers and segmentation in DECT are normally performed by using absorption maps, for which the absorption coefficients of X-ray energy E1 and E2 of all pixels in CT images are plotted as shown in Fig. 2 . SCT can obtain more precise pseudo monochromatic images and segmented images because more than three absorption coefficients at different X-ray energies can be used. However, the dimensions of absorption maps can be increased to 3 and higher; therefore, estimation and segmentation done making full use of information on the absorption obtained at different X-ray energies become difficult. Instead of using an n-dimensional absorption map, we developed a novel segmentation method that uses a self-organizing neural network (SOM) and its map (SOM map).
2. Principle of SOM and its application for SCT
SOM is a kind of artificial neural network that does not require training data sets, and it simulates the visual area in the brain1. The network here was composed of many neurons as shown in Fig. 3 (a) (SOM map), and each neuron has property P of an n-dimensional vector. When signal S (n-dimensional vector) is inputted, the inner products of P and S of all neurons are calculated, and the P of the neuron having the maximum product value and its neighboring neurons are changed a little to fit S as shown in Fig. 3 (b). By iterating this procedure for every piece of input data, clusters of neurons having similar P are created in a SOM map as shown in Fig. 3 (c). Therefore, input data can be segmented by clustering on the SOM map by using a conventional method such as the k-means method2.
A CT spectrum composed of CT values of each pixel at different X-ray energies can be assumed to be an n-dimensional vector and used as input data for SOM as shown in Fig. 4 . Therefore, regions having similar CT spectrums in CT images can be segmented by using SOM without any training data set. Note that we used a SOM liability (Somoclu3) for Python for our feasibility test.
3. Imaging system for feasibility test
A feasibility test of segmentation with SCT using SOM was performed by using CT images of a phantom and biomedical sample. The CT images were obtained by using an imaging system4 at beamline 07 of the SAGA Light Source (SAGA-LS, synchrotron facility) in Japan. The system consists of a double-crystal monochromator using Si(220), sample positioner, and X-ray imager, as shown in Fig. 5 . The white synchrotron radiation (SR) emitted from a wiggler (X-ray source) installed on the storage ring of SAGA-LS was monochromated by the monochromator, irradiated on the sample, and detected by the X-ray imager. A fiber-coupled highly sensitive X-ray imager (Andor Zyla 5.5 HF) was used. Projection images were obtained with 15, 20, 25, 30, and 35-keV SR, and sectional images of each energy were reconstructed by using a conventional filtered-back projection method with a Shepp-Logan filter.
A phantom consisting of acrylic resin and an aluminum rod 2 mm in diameter, an iodine solution (diluted three times with water), and calcium powder were used. The calcium powder and iodine solution were enclosed in polyethylene tubes. All materials were packed in a polypropylene tube.