An analytical description of balanced steady-state free precession with finite radio-frequency excitation

Unbiased signal equation for quantitative magnetization transfer mapping in balanced steady-state free precession MRI

Purpose

Quantitative magnetization transfer (qMT) imaging can be used to quantify the proportion of protons in a voxel attached to macromolecules. Here, we show that the original qMT balanced steady‐state free precession (bSSFP) model is biased due to over‐simplistic assumptions made in its derivation.

Theory and Methods

We present an improved model for qMT bSSFP, which incorporates finite radiofrequency (RF) pulse effects as well as simultaneous exchange and relaxation. Furthermore, a correction relating to finite RF pulse effects for sinc‐shaped excitations is derived. The new model is compared to the original one in numerical simulations of the Bloch‐McConnell equations and in previously acquired in vivo data.

Results

Our numerical simulations show that the original signal equation is significantly biased in typical brain tissue structures (by 7%‐20%), whereas the new signal equation outperforms the original one with minimal bias (<1%). It is further shown that the bias of the original model strongly affects the acquired qMT parameters in human brain structures, with differences in the clinically relevant parameter of pool‐size‐ratio of up to 31%. Particularly high biases of the original signal equation are expected in an MS lesion within diseased brain tissue (due to a low T2/T1‐ratio), demanding a more accurate model for clinical applications.

Conclusion

The improved model for qMT bSSFP is recommended for accurate qMT parameter mapping in healthy and diseased brain tissue structures.

Rapid simultaneous high-resolution mapping of myelin water fraction and relaxation times in human brain using BMC-mcDESPOT

A number of central nervous system (CNS) diseases exhibit changes in myelin content and magnetic resonance longitudinal, T₁, and transverse, T₂, relaxation times, which therefore represent important biomarkers of CNS pathology. Among the methods applied for measurement of myelin water fraction (MWF) and relaxation times, the multicomponent driven equilibrium single pulse observation of T₁ and T₂ (mcDESPOT) approach is of particular interest. mcDESPOT permits whole brain mapping of multicomponent T₁ and T₂, with data acquisition accomplished within a clinically realistic acquisition time. Unfortunately, previous studies have indicated the limited performance of mcDESPOT in the setting of the modest signal-to-noise range of high-resolution mapping, required for the depiction of small structures and to reduce partial volume effects. Recently, we showed that a new Bayesian Monte Carlo (BMC) analysis substantially improved determination of MWF from mcDESPOT imaging data. However, our previous study was limited in that it did not discuss determination of relaxation times. Here, we extend the BMC analysis to the simultaneous determination of whole-brain MWF and relaxation times using the two-component mcDESPOT signal model. Simulation analyses and in-vivo human brain studies indicate the overall greater performance of this approach compared to the stochastic region contraction (SRC) algorithm, conventionally used to derive parameter estimates from mcDESPOT data. SRC estimates of the transverse relaxation time of the long T₂ fraction, T_2,l, and the longitudinal relaxation time of the short T₁ fraction, T_1,s, clustered towards the lower and upper parameter search space limits, respectively, indicating failure of the fitting procedure. We demonstrate that this effect is absent in the BMC analysis. Our results also showed improved parameter estimation for BMC as compared to SRC for high-resolution mapping. Overall we find that the combination of BMC analysis and mcDESPOT, BMC-mcDESPOT, shows excellent performance for accurate high-resolution whole-brain mapping of MWF and bi-component transverse and longitudinal relaxation times within a clinically realistic acquisition time.

Incorporation of nonzero echo times in the SPGR and bSSFP signal models used in mcDESPOT

PURPOSE

To analyze the effect of neglecting nonzero echo times (TEs) in the conventional model of multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT).

THEORY AND METHODS

Formulations of the two-component spoiled gradient recalled echo (SPGR) and balanced steady state free precession (bSSFP) models that incorporate nonzero TE effects are presented in the context of mcDESPOT and compared with the conventionally used SPGR and bSSFP models which ignore nonzero TEs. Relative errors in derived parameter estimates from conventional mcDESPOT, omitting TE effects, are assessed using simulations over a wide range of experimental and sample parameters.

RESULTS

The neglect of nonzero TE leads to an overestimate of the SPGR signal and an underestimate of the bSSFP signal. These effects can introduce large errors in parameter estimates derived from conventional mcDESPOT under realistic imaging conditions.

CONCLUSION

SPGR and bSSFP signal models accounting for nonzero TE effects should be incorporated into quantitative mcDESPOT analyses.

Superbalanced steady state free precession

Steady state free precession (SSFP) signal theory is commonly derived in the limit of quasi-instantaneous radiofrequency (RF) excitation. SSFP imaging protocols, however, are frequently set up with minimal pulse repetition times and RF pulses can thus constitute a considerable amount to the actual pulse repetition time. As a result, finite RF pulse effects can lead to 10-20% signal deviation from common SSFP theory in the transient and in the steady state which may impair the accuracy of SSFP-based quantitative imaging techniques. In this article, a new and generic approach for intrinsic compensation of finite RF pulse effects is introduced. Compensation is based on balancing relaxation effects during finite RF excitation, similar to flow or motion compensation of gradient moments. RF pulse balancing, in addition to the refocusing of gradient moments with balanced SSFP, results in a superbalanced SSFP sequence free of finite RF pulse effects in the transient and in the steady state; irrespective of the RF pulse duration, flip angles, relaxation times, or off-resonances. Superbalancing of SSFP sequences can be used with all quantitative SSFP techniques where finite RF pulse effects are expected or where elongated RF pulses are used.