Corrigendum

Corrigendum 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png NMR in Biomedicine (Electronic) Wiley

Corrigendum

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Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2018 John Wiley & Sons, Ltd.
ISSN
0952-3480
eISSN
1099-1492
D.O.I.
10.1002/nbm.3906
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Abstract

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

Journal

NMR in Biomedicine (Electronic)Wiley

Published: Jan 1, 2018

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