Approximate B1+ scaling of the SSFP steady state

Abstract

Purpose It is shown that the steady state of rapid, TR‐periodic steady‐state free precession (SSFP) sequences at small to moderate flip angles exhibits a universal, approximate scaling law with respect to variations of B1+$$ {B}_1^{+} $$. Implications for the accuracy and precision of relaxometry experiments are discussed. Methods The approximate scaling law is derived from and numerically tested against known analytical solutions. To assess the attainable estimator precision in a typical relaxometry experiment, we calculate the Cramér–Rao bound (CRB) and perform Monte Carlo (MC) simulations. Results The approximate universal scaling holds well up to moderate flip angles. For pure steady state relaxometry, we observe a significant precision penalty for simultaneous estimation of R1$$ {R}_1 $$ and B1+$$ {B}_1^{+} $$, whereas good R2$$ {R}_2 $$ estimates can be obtained without even knowing the correct actual flip angle. Conclusion Simultaneous estimation of R1$$ {R}_1 $$ and B1+$$ {B}_1^{+} $$ from a set of SSFP steady states alone is not advisable. Apart from separate B1+$$ {B}_1^{+} $$ measurements, the problem can be addressed by adding transient state information, but, depending on the situation, residual effects due to the scaling may still require some attention.

Robust T2 estimation with balanced steady state free precession

“…There was, however, given experimental evidence that T 2 estimation with triple‐echo steady state (TESS) 16 or using multiple pc‐bSSFP scans 9 is inert to B 1 field inhomogeneities. This rather surprising experimental finding was only recently corroborated theoretically by an approximate scaling for steady state sequences 17 . In this work, we further elaborate on this recent theoretical finding to show that balanced steady state free precession (bSSFP) theory predicts that T 2 estimation should not only be insensitive to B 1 , but also to MT.…”

“…This rather surprising experimental finding was only recently corroborated theoretically by an approximate scaling for steady state sequences. 17 In this work, we further elaborate on this recent theoretical finding to show that balanced steady state free precession (bSSFP) theory predicts that T 2 estimation should not only be insensitive to B 1 , but also to MT. All sources of bias, as introduced to the steady state bSSFP signal by B 1 field inhomogeneities and MT effects are absorbed into a large bias for T 1 .…”

“…The configuration orders can be expressed as 17 $$$$ {m}^{(n)}=\left\{\begin{array}{l}\ {A}^n\left(c,{E}_2\right)\cdotp {m}^{(0)}:n\ge 0\\ {}{A}^{\mid n\mid -1}\left(c,{E}_2\right)\cdotp {m}^{\left(-1\right)}:n<0\end{array}\right., $$$$ with the definitions $$$$ c:= \frac{\cos \alpha -{E}_1}{1-{E}_1\cos \alpha }, $$$$ $$$$ A:= \frac{1+c}{2-\left(1-c\right)d}\cdotp {E}_2, $$$$ $$$$ d\cdotp \left(1-c\right):= 1-c{E}_2^2-\sqrt{\left(1-{c}^2{E}_2^2\right)\left(1-{E}_2^2\right)}. $$$$ …”

Intra‐scan RF power amplifier drift correction

“…Please note that motion‐insensitive rapid configuration relaxometry and triple echo steady state allow the joint quantification of $$$ {\mathrm{T}}_2 $$$ alongside $$$ {\mathrm{T}}_1 $$$. In contrast to $$$ {\mathrm{T}}_1 $$$, the $$$ {\mathrm{T}}_2 $$$ estimation is largely independent of $$$ {\mathrm{B}}_1^{+} $$$ for these methods 44 . Generally, RFPA drift is expected to become the more apparent the shorter the scan times and should thus be considered especially in case of accelerated quantitative imaging with sparsely sampled data.…”

“…In contrast to T 1 , the T 2 estimation is largely independent of B + 1 for these methods. 44 Generally, RFPA drift is expected to become the more apparent the shorter the scan times and should thus be considered especially in case of accelerated quantitative imaging with sparsely sampled data.…”