کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10712651 | 1025217 | 2013 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A theoretical and numerical consideration of the longitudinal and transverse relaxations in the rotating frame
ترجمه فارسی عنوان
بررسی نظری و عددی از آرامش طولی و عرضی در قاب چرخشی
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کلمات کلیدی
معادلات بلوخ، آرامش طولی آرامش عرضی، قاب در حال چرخش قفل چرخش انتقال اشباع تبادل شیمیایی،
موضوعات مرتبط
مهندسی و علوم پایه
فیزیک و نجوم
فیزیک ماده چگال
چکیده انگلیسی
We previously derived a simple equation for solving time-dependent Bloch equations by a matrix operation. The purpose of this study was to present a theoretical and numerical consideration of the longitudinal (R1Ï = 1/T1Ï) and transverse relaxation rates in the rotating frame (R2Ï = 1/T2Ï), based on this method. First, we derived an equation describing the time evolution of the magnetization vector (M(t)) by expanding the matrix exponential into the eigenvalues and the corresponding eigenvectors using diagonalization. Second, we obtained the longitudinal magnetization vector in the rotating frame (M1Ï(t)) by taking the inner product of M(t) and the eigenvector with the smallest eigenvalue in modulus, and then we obtained the transverse magnetization vector in the rotating frame (M2Ï(t)) by subtracting M1Ï(t) from M(t). For comparison, we also computed the spin-locked magnetization vector. We derived the exact solutions for R1Ï and R2Ï from the eigenvalues, and compared them with those obtained numerically from M1Ï(t) and M2Ï(t), respectively. There was excellent agreement between them. From the exact solutions for R1Ï and R2Ï, R2Ï was found to be given by R2Ï = (2R2 + R1)/2 â R1Ï/2, where R1 and R2 denote the conventional longitudinal and transverse relaxation rates, respectively. We also derived M1Ï(t) and M2Ï(t) for bulk water protons, in which the effect of chemical exchange was taken into account using a 2-pool chemical exchange model, and we compared the R1Ï and R2Ï values obtained from the eigenvalues and those obtained numerically from M1Ï(t) and M2Ï(t). There was also excellent agreement between them. In conclusion, this study will be useful for better understanding of the longitudinal and transverse relaxations in the rotating frame and for analyzing the contrast mechanisms in T1Ï- and T2Ï-weighted MRI.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Magnetic Resonance Imaging - Volume 31, Issue 9, November 2013, Pages 1544-1558
Journal: Magnetic Resonance Imaging - Volume 31, Issue 9, November 2013, Pages 1544-1558
نویسندگان
Kenya Murase,