Introduction

The Variable Flip Angle (VFA) approach estimating the longitudinal relaxation time (T₁) assumes perfect spoiling of the transverse magnetization across TR. Despite gradient and radiofrequency (RF) spoiling, this condition is rarely met resulting in error in the estimated T₁ times (T₁^app). Given that the error is dependent on B₁⁺ efficiency, correction based on a transmit field map has been proposed¹. Although comparatively small, T₂ dependence is also expected in T₁^app. We investigate the amplitude of the T₂ dependent bias observed in T₁ times estimated with the VFA approach at 7T in different spoiling conditions. Unlike B₁⁺ efficiency, a T₂ map cannot be easily or rapidly acquired preventing a correction scheme from being used. An interesting alternative would consist of carefully choosing an RF spoiling increment that minimizes T₂ dependence. We attempt in this work to provide guidelines regarding the choice of spoiling parameters in the Multi-parameter Mapping protocol² to most accurately estimate T₁ times at 7T.

Methods

In-vivo acquisitions
Eight T₁^app maps were acquired on one healthy volunteer on a 7T Terra Siemens scanner with the MPM protocol using 4 RF spoiling increments (φ₀), carefully chosen for their distinct behaviour observed in simulations: 50°, 117°, 120° and 144°, and 2 spoiling gradient moments resulting in 2π and 6π dephasing per TR. Key parameters are: multi-echo spoiled gradient echo with TR=19.5ms, flip angles of α₁=6° and α₂=26°, 6 echoes with TE between 2.56 and 11.66ms, isotropic resolution of 1mm³. Additionally, transmit field maps (f_B1+) were acquired with the Bloch-Siegert approach³ to compute T₁^app maps as follows⁴:
$$T_1^{app}=-\frac{TR}{ln⁡(E_1)}\space with \space E_1=\frac{S_2-S_1.\frac{sin⁡(α_2^c)}{sin⁡(α_1^c)}}{S_2.cos⁡(α_2^c)-S_1.cos⁡(α_1^c)\frac{sin⁡(α_2^c)}{sin⁡(α_1^c)}}and\begin{cases}α_1^c=α_1.\frac{f_{B_1^+}}{100} \\ α_2^c=α_2.\frac{f_{B_1^+}}{100} \end{cases}\space(Eq.1)$$
Reference T₁ and T₂ maps were obtained from the mono-exponential fitting of 10 single-slice spin-echo acquisitions with and without pre-inversion pulse respectively and variable TIs or TEs respectively. Relevant parameters are: TR=10s, voxel size of 1.2×1.2×3.5mm³, TEs between 29 and 129ms for the T₂ measurement, TE=29ms and TIs between 100 and 5000ms for the T₁ measurement. An estimate of the apparent diffusion coefficient (ADC) was also obtained with diffusion-weighted spin-echo EPI acquisitions. T₁^app maps were co-registered to the reference T₁ and T₂ maps with SPM12.6 (https://www.fil.ion.ucl.ac.uk/spm/) to assess the T₂ dependency of T₁^app in a region with comparatively homogeneous T₁ (1100<T₁<1350ms) as estimated in the reference T₁ map, thereby minimizing the potential confounding factor of anatomical variability.

Numerical simulations
Numerical simulations of the MPM protocols were performed with the Extended Phase Graph (EPG) framework (https://sycomore.readthedocs.io/⁵), including diffusion effects⁶, for a range of expected T₂ and T₁ times and transmit field efficiency (f_B1+). The diffusion coefficient D was fixed to 0.8µm²/ms. Correction factors for imperfect spoiling were computed from these simulations as described in¹:
$$T_1=A(f_{B_1^+})+B(f_{B_1^+}).T_1^{app}\space with\begin{cases}A(f_{B_1^+})=a_2.f_{B_1^+ }^2+a_1.f_{B_1^+}+a_0\\B(f_{B_1^+})=b_2.f_{B_1^+}^2+b_1.f_{B_1^+}+b_0\end{cases}\space (Eq.2)$$
Three sets of correction factors for each spoiling condition were computed with T₂ fixed to 35, 45 and 55ms and applied to T₁^app maps to correct for imperfect spoiling.

Results

Reference T₂, T₁ and ADC values in the region of interest were estimated to be 47±6ms, 1260±50ms and 0.7±0.1mm²/ms respectively. The T₂ dependence of T₁^app obtained from the MPM protocols was observed in-vivo at 7T as was the impact of the spoiling conditions (Fig.1b,d). The T₂ dependence generally followed the predictions of numerical simulations (Fig.1a,c)).
φ₀ of 50° and 120° were the most sensitive to T₂ as predicted by numerical simulations (+30ms and -51ms respectively). 117° and 144° showed the smallest T₂ dependence (variation smaller than 10ms). In line with simulations, the in-vivo T₂ dependence decreased for 120° and was negligibly impacted for 117° and 50° when increasing gradient spoiling. As predicted, the T₂ dependence of 144° was also impacted but the measured dependence was not as low as predicted. Difference across T₁^app maps (Fig.2a) were visible and highlighted by the map of the standard deviation (σ) across φ₀ (Fig.2b). The variability across φ₀ generally decreased with higher spoiling gradient. After correction for imperfect spoiling, the variability decreased when assuming a global T₂ of 45ms in the correction factors, and decreased even further with a T₂ of 35ms. However, it increased with correction factors assuming a T₂ of 55ms.

Discussion

Although T₂ shortens at 7T, and the diffusion spoiling is increased with a multi-echo protocol, a remaining T₂ dependence of the estimated T₁ times due to imperfect spoiling was observed. Ultimately, this resulted in a dependence of the corrected T₁ maps on the choice of T₂ used to compute the correction factors. A T₂ of 35ms reduced the variability across φ₀ although the estimated T₂ with a spin-echo sequence was slightly longer. Given that only a global T₂ is used, the residual spatial T₂ dependency will remain after correction. A careful choice of the RF spoiling increment and the spoiling gradient moment is therefore recommended to minimize the T₂ dependency. Although 50° is commonly used, 117° or 144° with relatively high spoiling gradient. would be preferable.

Conclusion

We demonstrated the T₂ dependent bias of T₁ estimated with VFA at 7T resulting from imperfect spoiling. We observed a manifestation of the diffusion effect at 7T in-vivo with reasonable gradient amplitude and commonly used protocols. We recommend the use of an RF spoiling increment that minimizes T₂ dependency in combination with a relatively high spoiling gradient moment.

Acknowledgements

The Wellcome Centre for Human Neuroimaging is supported by core funding from the Wellcome [203147/Z/16/Z].