@misc{oai:repo.qst.go.jp:00065000,
 author = {Kawaguchi, Hiroshi and Hirano, Yoshiyuki and Yoshida, Eiji and Tanigawa, Asuka and Suga, Mikio and Shiraishi, Takahiro and Tanimoto, Katsuyuki and Kimura, Yasuyuki and Obata, Takayuki and Ito, Hiroshi and 川口 拓之 and 平野 祥之 and 吉田 英治 and 谷川 明日香 and 菅 幹生 and 白石 貴博 and 谷本 克之 and 木村 泰之 and 小畠 隆行 and 伊藤 浩},
 month = {May},
 note = {The ability to make quantitative measurements of radioactivity is extremely essential for human brain PET. Recently, several MRI-based attenuation correction methods that estimate the spatial distribution of the attenuation coefficient (mu-map) for a PET/MRI scan have been reported. The accuracy of mu-map from an MRI image depends on correctness of tissue segmentation and attenuation coefficients to be assigned (mu-values). In our previous study, we developed a hybrid segmentation-atlas method for PET attenuation correction in PET/MRI and demonstrated that can provide the accurate tissue segmentation reflecting mu-value differences [1]. In this study, we focused on the estimation of mu-values to construct the proper mu-map for human brain PET/MRI. 
Figure 1 shows the brief procedure and schematic diagram of the proposed method. An external radiation source was placed at the fixed position and the radioactive attenuation by tissue was acquired with PET detectors. In addition, partial pathlengths of tissues are calculated from the simulation on the virtual scanner with the segmented MR image. The mu-values of tissues are calculated by inverting the linear system; y=Ax, where y is the radioactive attenuation vector of m detectors ln(I0/I), x is the mu-value vector of n tissues and each element of matrix A is the partial pathlength of radiation ray in n-th tissue from the source to the m-th detector. 
The proposed method was evaluated on the simulation with the mu-map and T1-weighted image (T1WI) of a human head acquired. The T1WI was segmented into air, bone, brain and soft tissues other than brain. The simulation of the transmission scan was performed by Geant 4.9.6. The bore of virtual HR+ scanner was divided into elements that equal to the voxel size of acquired mu-map. The intra-voxel radiation pathlength were calculated from the source to every detector. The radioactive attenuation was calculated from the sum of products between the acquired mu-map and intra-voxel radiation pathlength on the way to each detector. The partial pathlength of each tissue was calculated on the segmented T1WI. 
Figure 2 shows the acquired mu-map and T1WI and the segmented image. Figure 3 shows histograms of error rates on estimated and actual mu-values for bone, brain and soft tissue. The error rate is defined as (muact.(r)-muest.)/muact.(r), where r is the position vector of voxels. The estimated mu-value of brain agrees well with actual value. However, the estimated mu-values of bone and soft tissue are over- and under estimated, respectively. The accuracy of the estimation may depend on the length of radiation pathrength for each tissue. Our previous study showed the accuracy of brain mu-value strongly affects on quantitative measurements of radioactivity for the human brain PET, while that of bone and soft tissue affects a little [2]. 
In conclusion, the proposed method contributes to quantitative measurements of radioactivity for the human brain PET/MRI. Additionally, this method can decrease the production cost for rotation system, increase the freedom of mechanical design and reduce additional several minutes for every PET scan compared with the conventional transmission scan.
\nReferences
[1] A. Tanigawa, et al. "Hybrid segmentation-atlas method for PET-MRI attenuation correction"
, IEEE NSS-MIC 2012, M10-54. Anaheim, USA, 2012.
[2] Kawaguchi et al., "Evaluation of MRI-based attenuation correction methods for quantitative human brain PET", International Forum on Medical Imaging in Asia 2012, O6-4, Daegeon, Korea, 2012., PSMR 2013 / 4th Julich MR-PET Workshop},
 title = {An MRI-based estimation of gamma-ray attenuation coefficients with a motionless radiation source for quantitative PET/MRI on human brain},
 year = {2013}
}