Once this is done for each material triplet and voxel, only the correct physical results are then counted for the final solution 17. To create this library, several material triplets from a unlimited number of basis materials are created and used, with the help of which each voxel with the information of two virtual monoE attenuation coefficients is tried to be split into the respective three materials. To this end, one concept has already been developed separating more than three materials. For this, in addition to the virtual monoE information, volume conservation must be introduced as an additional condition and at the same time a more complex method is required. Nevertheless, the determination of more than three materials is possible. A third equation at a further different energy would mean linear dependency and thus an infinite number of solutions of the system 15, 16. However, a mathematical limit is reached at a decomposition of two different materials by using two virtual monoE images and solving a simple linear equation system of two equations. Due to the fact that the total attenuation at one specific energy can be expressed as a sum of all individual mass attenuation coefficients multiplied with their densities, solving a linear equation system leads to material decomposition which has already been discussed in the scientific community regarding quantification, accuracy and methodology 11, 12, 13, 14. Using the measurement information gathered from the energy responsive detector, the detector response function and the X-ray source spectrum, virtual monoenergetic (monoE) images can then be calculated.
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In addition, due to the superimposed detector layers, both images are perfectly registered, so no post-processing registration is required. As a first proof of concept of this technique for detailed material decomposition in medicine we analyzed exact percentage composition of ex vivo clots from patients with acute ischemic stroke, using histological analysis as a reference standard. After implementation, this new multimodal method was successfully tested on self-mixed samples consisting of the aqueous base solutions iomeprol, eosin Y disodiumsalt, sodium chloride, and pure water. This method allowed both five-material decomposition and determination or optimization of the X-ray attenuation coefficients of the sample base materials via optimizations of objective functions. To address these issues, we developed a novel theoretical approach and algorithm and tested it on samples prepared in the laboratory as well as on ex-vivo medical samples. In addition, the X-ray attenuation coefficients of chemically complicated basis materials may not be known and also cannot be determined by other or previous analyses. However, when analyzing mixtures consisting of more than three individual basis materials, a physical limit is reached that no longer allows this standard analysis. In medical imaging, one method is the established analysis using dual-energy computed tomography.
The separation of mixtures of substances into their individual components plays an important role in many areas of science.
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