Optimization of MRI pulse sequences and gadobutrol-doped polymer gel for real time 4D radiation dosimetry on the MRI-Linac

Different MRI pulse sequences can be applied to acquire real time dose distributions on an MRI-Linac. The temporal resolution is affected by the MRI pulse sequence type, the MRI pulse sequence parameters and the NMR relaxation-dose response of the polymer gel. To obtain a sufficiently high temporal resolution, it is crucial to optimize the MRI pulse sequence parameters such as TE, TR and flip angle. The optimization goal is to obtain the highest dose resolution within the shortest time frame, i.e. the smallest temporal uncertainty. We here also demonstrate that it is possible to further improve the temporal uncertainty of the polymer gel dosimeter by adding an MRI contrast agent. The optimization of two MRI pulse sequences in combination with a gadobutrol-doped MAGAT polymer gel dosimeter is discussed.


Introduction
In previous work on real time 4D radiation dosimetry on an MRI-Linac [1] we showed that a RARE pulse sequence (Rapid Acquisition with Relaxation Enhancement, equivalent with FSE, TSE) can be used to acquire dose maps in short time intervals, allowing dosimetry in pseudo-real time.As with any imaging technique, there is a trade-off between temporal resolution and signal-to-noise ratio (SNR), which can be comprised in the concept of temporal uncertainty.We emphasize the importance of making a clear distinction between 'temporal or imaging resolution' and 'temporal uncertainty'.'Imaging resolution' refers to the time period between two consecutive images while 'temporal uncertainty' refers to the minimum time span in which a valid dose readout can be made [1].In this paper, we provide a theoretical framework for optimizing both the sequence parameters and the gel formulation to obtain the highest imaging rate for which a significant measurable dose change applies, while minimizing the temporal uncertainty.While in this paper, two different MRI pulse sequences are considered, the concept is generally applicable to other MRI pulse sequences.

Theory
The temporal uncertainty for the different studies can be calculated using the concept of dose resolution which was introduced as a quantitative metric to define the minimal separation between two absorbed doses that can be distinguished with a given level of confidence [2,3].The relation between temporal uncertainty TP p% and dose resolution D ∆ p is given by where D ̇ is the dose rate and the dose resolution is given by: D ∆ p = k p √2σ D with k p the coverage factor for the level of confidence p. σ D is the standard deviation in the measured dose map.The standard deviation of the estimated dose is determined by the sensitivity of the gel dosimeter and the measurement parameters.In MRI, measurement parameters are determined by the pulse sequence and pulse sequence parameters such as the repetition time (TR), the echo time (TE) and flip angle (α).It is clear that for a certain dose rate, the optimum is reached when the standard deviation (σ D ) is minimal.In order to make a fair comparison, the measurement time to acquire a volumetric data set with a certain number of slices (  ) needs to be taken into account.Indeed, allowing a longer allocated measurement time frame allows more averages to be taken, hence increasing the signal-to-noise ratio (SNR) in the base images.As the SNR increases with the square root of the measurement time T m to acquire the volumetric data set, the optimization problem for the RARE pulse sequence can be written as where: R = The derivation of equation 2 can be found elsewhere [4].The last equality on the right hand side of equation 2 is only approximately valid when the longitudinal relaxation can be neglected (that is, when  ≫  1 ).Note however that this condition is not necessarily satisfied.In our optimization, we do not use this assumption and use the general applicable equation.

For the balanced Steady State Free Precession (bSSFP) pulse sequence the optimization becomes
where R = . The derivation and the expression for

∂S(D) ∂D
can be found elsewhere.
The optimization problem of a pulse sequence thus results in a two stage process: 1) finding the expression of σ D as a function of the imaging parameters and 2) finding the minimum objective function σ D �T m or the minimum temporal uncertainty TP p% in the imaging parameter space.
Minimization of the objective function towards concentrations of contrast agent and different flip angles can be performed numerically [4].

Polymer gel fabrication and irradiation
Cylindrical vials (4 ml) were filled with MAGAT gel doped with various amounts of gadobutrol (GadoVist, Bayer).The exact gel formulation and fabrication steps can be found elsewhere [1] with the exception of the addition of gadobutrol.The samples were irradiated on a 6 MV Linac (Elekta) at reference depth with a dose rate of 5.4 Gy/min.versus dose response curves are acquired with a multi-echo pulse sequence with 32 echoes (ΔTE = 9.5 ms; TR = 3 s), while R 1 versus dose response curves were obtained by use of an inversion recovery turbo spin echo sequence with different inversion times (TI = 100 ms -1500 ms in steps of 100 ms).To validate the optimization approach experimentally, MRI measurements are conducted on a 3T MRI scanner (Verio, Siemens) with both a RARE sequence where the echo time and repetition time were varied and a bSSFP sequence where the flip angle was varied.

Sequence optimization
For the RARE sequence, the imaging parameters that are optimized are the echo train length (ETL) and the repetition time (TR).The echo time spacing (∆TE) is taken as low as possible (8 ms) without compromising the receiver bandwidth (130 Hz/pixel).A current constraint in our RARE sequence is that TE eff = ETL • ∆TE.For the bSSFP sequence, the flip angle (α) is optimized while TR is taken as small as possible and TE is fixed at half the repetition time (TE = TR/2).Note that the optimal set of parameters is dependent on the relaxation rates and thus on the absorbed dose.We here consider a dose interval of [0 Gy, 4 Gy], typical for a single fraction.For the minimization objective function we consider the maximum σ D within the considered dose interval, i.e. max(σ D ()).The minimization problem is implemented in a MATLAB ® script.The optimal imaging parameters and minima are determined for different amounts of gadobutrol concentrations from which the ultimate optimum with respect to gadobutrol concentration is determined.

Gadobutrol-doped MAGAT gel response
R1 and R2 dose response plots for gadobutrol-doped MAGAT are shown in figure 1.Only a very small dependence of  1 on the dose is found (figure 1b).It is clear from figure 1c that the transverse gadobutrol relaxivity r 2 Gd increases with increasing dose for the first 2 Gy.The increase in r 2 Gd can be attributed to a decrease in the rotational correlation time of the gadobutrol contrast agent with the increased formation of the methacrylic interpenetrating network.It is not clear yet, if covalent bonds between gadolinium and methacrylic acid are also responsible for the change in relaxivity.

Optimization of the RARE pulse sequence
The signal intensity as a function of radiation dose for various echo times and repetition times is shown in figure 2. The good correspondence between measured (symbols) and theoretical (solid lines) derived signal intensity can be appreciated.

Optimization of the balanced SSFP pulse sequence
For the bSSFP sequence, the total measurement time is fixed and is given by   =  •   •  ℎ • .
Only the number of experiments NEX is considered as variable in the total measurement time.The optimum gadobutrol concentration with the bSSFP-sequence is 1.2 mM with an optimal flip angle of 90 degrees.The corresponding temporal uncertainty is 31 s (NEX = 3).

Conclusions
We here present an optimization strategy of the pulse sequence parameters in combination with a contrast agent doped polymer gel dosimeter.Two pulse sequences are considered.The parameter optimization takes into account the number of slices, the longitudinal relaxation and the measurement time.It is found that the effect of longitudinal relaxation can not be neglected in the optimization of the imaging parameters.For the RARE sequence the optimal MAGAT gel formulation is obtained for 0.58 mM gadobutrol with an optimal TR/TE of 420 ms/56 ms.The addition of 0.58 mM gadobutrol results in a reduction of the temporal uncertainty of 42%.For the bSSFP sequence, the optimal gadobutrol concentration is 1.2 mM with an optimal flip angle of 90°.The achievable temporal uncertainty is significantly higher for the bSSFP sequence than for the RARE sequence (31 s for bSSFP versus 18 s for RARE).It is concluded that the optimal imaging parameters and gadobutrol concentration is highly dependent on the pulse sequence and experimental design (e.g.number of slices).The reader is advised to conduct the optimization for their specific experimental design.Further reduction in the temporal uncertainty can be achieved by acquiring more averages of the pre-radiation reference scan.Future work will focus on the implementation of sparse sampling and a spiral keyhole imaging strategy to further reduce the temporal uncertainty.

Figure 1 .
Figure 1.R2 (a) and R1 (b) dose response of gadobutrol doped MAGAT polymer gel, ΔR2 as a function of gadobutrol concentration for various dose values (c) and the R1 and R2 relaxation rate at zero dose R1,0 and R2,0 (d) as a function of gadobutrol concentration.The R1 and R2 relaxivities for a non-irradiated MAGAT are respectively r1 = 4.908 s -1 mM -1 and r2 = 7.3941 s -1 mM -1 .The inset in (c) shows the r2 relaxivity as a function of dose.

Figure 2 .Figure 3 .
Figure 2. Signal intensity as a function of dose for various echo times (TE) with repetition time (TR) fixed at 476 ms (a-b), and for various repetition times with echo time fixed at 59 ms (c-d) for MAGAT gels doped with 0 mM gadobutrol (a,c) and 1.2 mM gadobutrol (b,d).The discrete data points are measured values while the solid lines are theoretically derived signal intensities on the basis of the experimentally derived R1 and R2 values.The optimum echo train length (ETLopt), repetition time (TRopt), temporal uncertainty and number of experiments (averages) (NEX) for the RARE sequence are shown in figure3as a function of gadobutrol concentration.The optimal gadobutrol concentration is 0.58 mM which results in a temporal uncertainty TP 95% of 18 s for an imaging volume of 7 slices and a matrix size containing 128 phase encoding lines.The corresponding optimal TR and TE are 420 ms and 56 ms (ETL = 7, ∆TE = 8 ms) respectively.A constraint in our particular RARE sequence is that the effective TE corresponds with the last recorded echo.A higher dose resolution can be obtained when this constraint is lifted but comes at the cost of a broader imaging point-spread-function (PSF).