In Roeloffs et al, there were incorrect matrix elements in equations in the appendix of the original article. This flaw had no influence on other results. The corrected terms for equations are given below.C2‐4daa=λ1+R1b+kb⋅eλ1td−λ2+R1b+kb⋅eλ2tdλ1−λ2dab=kb⋅eλ1td−eλ2tdλ1−λ2dba=fb⋅dabdbb=−λ2+R1b+kb⋅eλ1td−λ1+R1b+kb⋅eλ2tdλ1−λ2In addition, more detailed derivations of previously presented useful approximations are given below.Derivation for dabdab=kb⋅eλ1td−eλ2tdλ1−λ2Assuming kb ≫ ka, R1a, R1b allows to approximate λ1 ≈ − (ka + kb + R1b) and λ2 ≈ − R1a. Consequently, |λ1| ≫ |λ2| holds and the term eλ1td can be neglected.dab=kb⋅0−eλ2tdR1a‐ka+kb+R1b=eλ2td1fb+1+R1b‐R1a/kb≈R1b‐R1a/kb<<1eλ2td11+fbDerivation for daadaa=λ1+R1b+kb⋅eλ1td−λ2+R1b+kb⋅eλ2tdλ1−λ2Neglecting the term eλ1td (see above) yieldsdaa=−−R1a+R1b+kb⋅eλ2tdR1a−ka+kb+R1bwhere−−R1a+R1bR1a−ka+kb+R1b≈0⇒daa≈−kb⋅eλ2td−kb−ka−R1b−R1a=eλ2td1fb+1+R1b‐R1a/kb=eλ2td1fb+1+R1b‐R1a/kb≈R1b‐R1a/kb<<1eλ2td11+fb≈dabDerivation for daa + ψdabdaa+ψdab≈daa1+ψ=eλ2td1+ψ1+fb=eλ2td1+fb−fb⋅α1+fb=eλ2td1−fb⋅α1+fb≈fb<<1eλ2td1−fb⋅α=eλ2td1−Rex/kbACKNOWLEDGEMENTWe want to thank Aaron Kujawa for pointing out the erroneous terms.REFERENCESRoeloffs V, Meyer C, Bachert P, Zaiss M. Towards quantification of pulsed spinlock and CEST at clinical MR scanners: an analytical interleaved saturation–relaxation (ISAR) approach. NMR in Biomedicine. 2015;28(1):40‐53. https://doi.org/10.1002/nbm.3192
NMR in Biomedicine (Electronic) – Wiley
Published: Jan 1, 2018
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