Investigative Magnetic Resonance Imaging

Korean Society of Magnetic Resonance in Medicine (대한자기공명의과학회)
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Quantitative Conductivity Estimation Error due to Statistical Noise in Complex $B_1{^+}$ Map

정량적 도전율측정의 오차와 $B_1{^+}$ map의 노이즈에 관한 분석

  • Shin, Jaewook (Department of Electrical and Electronic Engineering, Yonsei University) ;
  • Lee, Joonsung (SIRIC, Yonsei University) ;
  • Kim, Min-Oh (Department of Electrical and Electronic Engineering, Yonsei University) ;
  • Choi, Narae (Department of Electrical and Electronic Engineering, Yonsei University) ;
  • Seo, Jin Keun (Department of Computer Science & Engineering, Yonsei University) ;
  • Kim, Dong-Hyun (Department of Electrical and Electronic Engineering, Yonsei University)
  • 신재욱 (연세대학교 전기전자공학) ;
  • 이준성 (연세대학교 뇌심혈관질환융합연구사업단) ;
  • 김민오 (연세대학교 전기전자공학) ;
  • 최나래 (연세대학교 전기전자공학) ;
  • 서진근 (연세대학교 계산과학공학) ;
  • 김동현 (연세대학교 전기전자공학)
  • Received : 2014.08.19
  • Accepted : 2014.10.02
  • Published : 2014.12.31
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Abstract

Purpose : In-vivo conductivity reconstruction using transmit field ($B_1{^+}$) information of MRI was proposed. We assessed the accuracy of conductivity reconstruction in the presence of statistical noise in complex $B_1{^+}$ map and provided a parametric model of the conductivity-to-noise ratio value. Materials and Methods: The $B_1{^+}$ distribution was simulated for a cylindrical phantom model. By adding complex Gaussian noise to the simulated $B_1{^+}$ map, quantitative conductivity estimation error was evaluated. The quantitative evaluation process was repeated over several different parameters such as Larmor frequency, object radius and SNR of $B_1{^+}$ map. A parametric model for the conductivity-to-noise ratio was developed according to these various parameters. Results: According to the simulation results, conductivity estimation is more sensitive to statistical noise in $B_1{^+}$ phase than to noise in $B_1{^+}$ magnitude. The conductivity estimate of the object of interest does not depend on the external object surrounding it. The conductivity-to-noise ratio is proportional to the signal-to-noise ratio of the $B_1{^+}$ map, Larmor frequency, the conductivity value itself and the number of averaged pixels. To estimate accurate conductivity value of the targeted tissue, SNR of $B_1{^+}$ map and adequate filtering size have to be taken into account for conductivity reconstruction process. In addition, the simulation result was verified at 3T conventional MRI scanner. Conclusion: Through all these relationships, quantitative conductivity estimation error due to statistical noise in $B_1{^+}$ map is modeled. By using this model, further issues regarding filtering and reconstruction algorithms can be investigated for MREPT.

목적: 자기공명 영상장치(MRI)의 송신 자기장 정보를 이용한 인체 내 도전율을 측정하는 기술이 최근 제안되었다. 송신 자기장 정보의 노이즈에 따른 도전율의 오차를 측정하고 도전율과 노이즈의 관계를 모델화 하였다. 대상과 방법: 송신 자기장의 분포는 원형 모델에 대해서 시뮬레이션을 수행하였다. 시뮬레이션으로 생성된 송신 자기장의 분포에 가우시안 노이즈를 더해준 후 정량적인 도전율 측정에 어떤 영향을 주는지 공명 주파수, 물체의 크기, 송신 자기장의 신호 대 잡음 비에 대해서 수행하였다. 각 각의 변수에 따른 도전율 대 잡음 비를 측정하여 모델화 하였다. 결과: 시뮬레이션 결과 도전율 측정은 송신 주파수의 크기 오차보다 위상 오차에 더 큰 영향을 받는 것을 보였다. 또한, 송신 자기장의 신호 대 잡음 비, 공명 주파수, 도전율 값, 평균필터의 크기에 따라서 도전율 대 잡음비가 비례하는 경향성을 보였다. 하지만, 물체를 둘러싼 외부 물질의 크기는 도전율 측정에 큰 영향을 주지 않았다. 위의 시뮬레이션 결과는 3T 임상용 MRI에서 원형 모델 팬텀에 대해서 검증되었다. 결론: 시뮬레이션을 통해 얻어진 변수와 도전율 측정의 오차와의 관계를 통해서 정량적인 도전율 측정에서 발생되는 오차를 모델화 할 수 있었다. 또한 제시된 분석 방법을 통하여 자기공명 영상 장치를 이용한 도전율 측정의 필터링 및 재구성 알고리즘의 효과를 검증 할 수 있을 것으로 보인다.

Keywords

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