Gel dosimetry: MRI

While a vast amount of scientific literature is available on the topic of gel dosimetry with MRI readout, this wealth of information may seem at first overwhelming for medical physicists and newcomers in this rapidly evolving field of research. With this review, my mission is to streamline the wealth of information in the scientific literature and provide a quick guideline for those making their first steps in implementing gel dosimetry in a clinical environment, while still providing a lookout to new and emerging evolutions in the field. In a first section, the physical mechanisms behind the MRI contrast are briefly explained for both Fricke gels and polymer gels. In a subsequent section, an overview is given of the different MRI pulse sequences and pulse sequence optimization will be discussed. Emphasize is placed on the framework and formalism to calculate optimal parameters. The reliability of MRI-based polymer gel dosimetry will be discussed, and a quick beginner’s guide is provided. Finally, a lookout to new and future developments of polymer gel dosimetry will be given.


Introduction
The paradigm of modern radiotherapy to deliver radiation to a target volume with high precision while sparing the surrounding healthy tissues, has been the practical motivation behind the rapidly emerging field of gel dosimetry.Gel dosimeters have never been aimed at replacing other radiation dosimeters, but because of their three-dimensional character they have a unique role to play in end-to-end verification of modern radiotherapy, especially where dose registration with other dosimeters is problematic because of steep dose gradients in all three dimensions [1].
While some early papers in the first half of the 20 th century already mentioned the potential of using chemical dosimeters [2], gel systems [3][4] and polymers [5][6][7] for radiation dosimetry, the field of research into gel systems for 3D radiation dosimetry only took off when a research team at Yale university discovered that the radiation induced oxidation of ferrous (Fe 2+ ) ions in ferrous sulphate dosimeters, initially developed by Fricke and Morse [2], can be read out with NMR relaxometry [8].A major obstacle for the use of Fricke gel dosimeters in radiotherapy hospitals is the diffusion of the ferrous (Fe 2+ ) and ferric (Fe 3+ ) ions in the gel matrix.Many studies have focussed on reducing the diffusivity of the ions by using different hydrogel materials and by use of chelators.While some methods have been able to reduce the diffusivity [9], none of the methods has been able to completely stop the diffusion.In 1993, the Yale group also suggested the use of polymer gel dosimeters with MRI readout [10].Polymer gel dosimeters are hydrogels that contain vinyl monomers and often also a cross-linker monomer.When exposed to ionizing radiation, radiation induced water radicals will initiate a polymerization reaction which results in the formation of small polymer aggregates that become entangled with the hydrogel matrix.The drastic change in polymer mobility has an effect on the NMR transverse relaxation rate which can be exploited to acquire absorbed dose related quantitative R2 maps.While the first dose maps acquired with Fricke gel dosimeters and polymer gel dosimeters demonstrated the potential of 3D dosimetry, gel dosimetry in the early days lacked robustness in many aspects.As the spatial integrity of polymer gel dosimeters appeared superior to the Fricke gel dosimeters, the interest in Fricke gel dosimeters declined over the years.
The challenge of increasing the accuracy and precision of 3D gel dosimetry has led to an active field of multi-disciplinary research which involved contributions from chemists, material scientists, medical physicists, engineers and MRI physicists.Scholars in the field gathered at biennial international conferences under the name "DOSGEL" (1999 -2008) and "IC3DDose" (from 2010) to exchange ideas and collaborate.The conference proceedings are a valuable source of information on the topic and is comprised of proffered papers and elaborate review papers.Since 2004, the conference proceedings are published by the Institute of Physics [11][12][13][14][15][16][17][18][19].A comprehensive review of polymer gel dosimetry has also been published by the journal Physics in Medicine and Biology [20] and in the form of book chapters [1,9].
In order to conduct reliable polymer gel dosimetry, several experimental aspects need to be taken care of.The many parameters that need to be controlled in MRI-based polymer gel dosimetry often leads to the perception that polymer gel dosimetry is a time-intensive and labour-intensive technique and the comparison is often made with non-3D faster dosimetry techniques such as film dosimetry, TLD or OSL.While the author will not refute the claim that many aspects are involved in polymer gel dosimetry, the comparison with off-the-shelf dosimeters is not a fair comparison as the fabrication and calibration of other dosimeters is often taken out of the equation.Others also claimed that polymer gel dosimetry with MRI readout would be less accurate than optical CT and refer hereby to the many publications on MRI artefacts and studies of uncertainties in polymer gel dosimetry.A word of caution is here also pertinent as the large scale of studies on the uncertainty of a particular technique is not necessarily correlated with the uncertainty itself.It is the author's opinion that with enough expertise, MRI-based polymer gel dosimetry can be used as a well-established method in the hospital.At the same time, the author also advocates for a better understanding of the principles of MRI among medical radiation physicists.

Clinical applications -The Ghent University experience
Polymer gel dosimetry has been proven to have significant impact in radiotherapy treatment validation as is illustrated in figures 1-3 which shows some typical examples of clinical applications that have made significant impact in the Ghent University radiotherapy centre or changed the course of action of the treatment.
Figure 1 shows gel dosimetry in an anthropomorphic shaped phantom for the verification of an intensity modulated radiotherapy (IMRT) class solution for patients with nasopharyngeal carcinoma either as the result of loco-regional relapses or new primary tumours [86].Gel dosimetry was still in its infancy at that stage (1998-1999) and the PAG gel was deoxygenated by bubbling the gel with nitrogen gas.In this experiment, a PVC head shaped cast was used and some penetration of oxygen through the plastic cast resulted in some inhibition near the cast.Despite, these physico-chemical artefacts, gel dosimetry experiments like the ones shown in figures 1-2 helped in establishing IMRT and gel dosimetry at the Ghent University Hospital and in benchmarking and creating confidence in the treatment planning.The treatment planning software was a beta-release of GRATIS that was developed by George Sherouse [87] and was systematically complemented by in-house software [88][89] to accommodate IMRT treatment optimization.In the process of implementing IMRT in the centre, gel dosimetry was used next to a variety of other dosimeters such as TLD's and radiographic film in combination with the Rando phantom.Gel dosimetry was recognised for its full 3D capability that is perceived as crucial because of steep dose gradients in all three dimensions.[90] with permission of the publisher.
Figure 2 shows the use of polymer gel dosimetry in the verification of a non-coplanar IMRT treatment class solution of a mediastinal carcinoma [90] around the same period.Some improvements were made to the gel dosimetry approach in terms of MRI scanning and in avoiding oxygen permeation by use of a glass recipient.Here, a cylindrical gel dosimeter insert was used that could be easily replaced with a cylindrical insert containing a stack of 20 circular radiographic films.This way, we were able to compare the gel dosimetry dose maps with film dosimetry in a reproducible manner in full 3D.It also enabled us to study the effect of photon energy (6 MV and 25 MV) on the treatment outcome by inserting different bottles of polymer gel without moving the thoracic cast.In a later study, a similar phantom was used but including a lung cavity that could be filled with either air or water to study the effect of air cavities on the dose distribution [91].
It became generally accepted within the same centre that gel dosimetry fitted the purpose of validating class solutions of patients very well but was not cost-effective to validate individual patient plans.Since then, polymer gel dosimetry has been applied in a few cases were a new critical IMRT treatment was introduced such as the one shown in figure 3 which involved a sliding window IMRT treatment of a pituitary gland adenoma that was located very close to the optic chiasm [92].Also in this case, a cylindrical insert was used and a comparison was made with both treatment planning and radiochromic micelle gel dosimetry using an in house built laser optical CT scanner [93].Aside from some isolated spots in the gamma-maps, the gamma-index was below 1 in the entire 3D volume for both the MRI-acquired dose distribution and the optical CT-acquired dose distribution which provided sufficient confidence that the treatment plan matched with the actual dose distribution and gave 'green light' to start the treatment.
Not documented in the literature, but relevant to mention, is that in a particular case, a deviation between treatment plan and polymer gel dosimetry triggered further investigation into its cause.It was found that the deviation was caused by a misalignment error caused by a dislocation of one of the positioning lasers which was immediately corrected.[92] with permission of the publisher.
In the same centre, the use of MRI-based gel dosimetry has also played a similar role in the commissioning, validation and implementation of dynamic techniques such as intensity modulated arc therapy (IMAT) (Figures 4 and 5) and Tomotherapy (Figure 6).
One of the advantages of MRI-based polymer gel dosimetry is that the dose distribution can be obtained in a large anthropomorphic volume as shown in figure 4 in the case of a whole abdominopelvic IMAT treatment of relapsed ovarian cancer [94].To obtain reliable dose maps in such a large volume, compensation of B1-field heterogeneity is required and compensation of temperature drift as a result of radiofrequency (RF) energy was compensated on the pulse sequence level [95].The abdominopelvic gel dosimeter phantom consists of a vacuum moulded Barex™ cast filled with a normoxic PAGAT gel and was surrounded by slaps of the Rando® phantom.The yellow shaded area corresponds to the liver, the green shaded areas to the kidneys and the pink shaded area corresponds to the planning target volume (PTV).The red regions in the gamma map are regions where gamma exceeds 1. Figure adapted from Vergote et al 2004 [92] with permission of the publisher.
In a European effort to consolidate the quality assurance of IMRT and IMAT (QUASIMODO-ESTRO), eight European institutions designed an IMRT plan for a horseshoe-shaped PTV surrounding a cylindrical organ-at-risk (OAR) in a simplified pelvic phantom [96].Figure 5 shows a dose map obtained with polymer gel dosimetry and the corresponding treatment plan calculated using the GRATIS treatment planning system that was complemented by in house software.

Figure 5.
Pelvic phantom from the QUASIMODO-ESTRO audit with polymer gel dosimetry acquired dose map and treatment plan after IMAT.The first treatment plan showed some angular ripple which was not present in the gel acquired dose maps.Based on these results, it was concluded that the treatment plan had to be recalculated with a finer angular discretization.The polymer gel was a normoxic PAGAT gel that was poured in a vacuum moulded Barex™ cast.
Figure 6 shows polymer gel dosimetry of a Tomotherapy treatment delivered at the Free University of Brussels.Because we were not satisfied with the absolute calibration, the data was not published but the dose distribution corresponded at least qualitatively well with the treatment plan.Gel dosimetry is also very well suited to acquire the dose distribution of treatment techniques that are difficult to evaluate with other dosimetry, such as in spatially fractionated grid radiotherapy.The three dimensional nature of the dose distribution of a GRID treatment can be appreciated in figure 7. Polymer gel dosimetry has also been useful in other spatially challenging dosimetry applications as illustrated in figures 8 and 9. Figure 8 shows a situation of electronic disequilibrium around a 25 mm diameter spherical air cavity that was inserted in a gel.The spherical hollow glass sphere was suspended in the gel by use of a glass rod.To investigate the dose disturbance caused by a tray containing lead markers for EPID spatial registration, a gel dosimetry experiment was performed which demonstrated a dose attenuation in the order of 10% (figure 9).From this experiment, it was concluded that the tray had to be removed before the start of the treatment beam delivery.Polymer gel dosimetry was used to evaluate if the tray also created a dosimetric effect in treatment beams.As a dose attenuation of 10% was measured underneath the lead markers, it was concluded that the tray had to be removed before every treatment beam delivery.It is recognised that polymer gel dosimetry with MRI has some limitations as compared to optical CTbased radiochromic dosimetry; First of all, some knowledge and expertise on quantitative MRI is required to assess the presence of imaging artefacts and to implement adequate compensation methods.In addition, access to an MRI scanner can be problematic in some centres.Secondly, the treatment of the gel is more delicate as temperature fluctuations during scanning may have a significant influence on the acquired R2 values and thus on the dose maps.Thirdly, oxygen infiltration in the gel may result in a physico-chemical induced error in the acquired dose maps.In the next sections, we will elaborate more on these effects and provide some compensation strategies.Despite these difficulties, from the abovementioned examples it will be clear that MRI-based polymer gel dosimetry (and X-ray CT based polymer gel dosimetry) has some inherent application-specific advantageous above optical CT based radiochromic dosimetry: 1. Polymer gel dosimetry can be performed in large anthropomorphic phantoms such as in the thorax and abdomen.The limitation is mostly from a practical perspective such as the manufacturing of the gel.An example of 11 L of gel is provided in figure 4, which was only limited by the size of the recipients in which the gel was prepared.However, care is required in imaging large phantoms as gradient non-linearity may give rise to geometrical distortions and the B1-field non-uniformity can lead to dose uncertainties.Both effects can be compensated.2. With the move towards MR-only simulators in radiotherapy, the co-registration of the anthropomorphic gel dosimeter with a pseudo-CT becomes more straightforward and accessibility to MRI is increased.3. Polymer gel dosimeters can be beaten into a foam to make lung-equivalent gel dosimeters [97] that can be readout with magnetization transfer (MT) MRI. 4. Recently, the potential of polymer gel dosimetry for real time dosimetry on an MRI-Linac has been demonstrated where MRI scans are taken during radiation delivery [98].Figure 10 shows a series of MRI recorded dose maps during radiation on the experimental Australian MRI-Linac.
Whether MRI-based, optical-CT based or X-ray CT based gel dosimetry is the optimal choice depends on the application and is site dependent (i.e.accessibility to an MRI scanner or CT-scanner).

Physical mechanisms of NMR relaxation and MRI contrast
A comprehensive overview of the physical mechanisms of NMR relaxation and MRI contrast of Fricke and polymer gel systems can be found elsewhere [9].We here suffice with describing the main mechanisms with a focus on those aspects that affect the ultimate reliability.

Fricke gel dosimeters
Fricke gel dosimeters are based on the Fricke dosimeter [2] which consists of a ferrous (Fe 2+ ) sulphate in a 0.8 N sulfuric acid solution.Upon radiation, the Fe 2+ ions are oxidized to Fe 3+ ions, which results in a measurable physical change, either by electrometric titration or absorption spectrophotometry with a selective absorption peak of Fe 3+ at a wavelength of 304 nm [99,100].An interesting observation was that the amount of radiation induced oxidation was independent of the concentration of ferrous ions in the solution.Fricke dosimeters have played an important role in the development of the field of radiochemistry [101] and have been used for several decades as a dosimetry standard in many laboratories [102].However, because of the strong dependence of radiochemical yield on the linear energy transfer (LET) of the radiation, the Fricke dosimeter fell into disuse [103] and has been replaced by other dosimetry standards such as calorimetry and ionization chambers as primary standards.For a more in-depth explanation of the radiation chemistry the reader is referred to textbooks [9,104].
The radiation induced conversion of ferrous ions to ferric ions by ionising radiation also alters the magnetic moment and electron spin relaxation times of the metal ion.These changes result in a change in NMR relaxation rates.In 1984, it was demonstrated that the change in magnetic moment and electron spin moment resulted in a change of the transverse relaxation rate with radiation dose of 1.13 10 −2 s −1 Gy −1 and a similar change in transverse relaxation rate of 1.21 ± 0.27 10 −2 s −1 Gy −1 [8].It was also suggested that infusion of a hydrogel with the Fricke solution could result in a 3D dosimeter.Since then, several Fricke gel systems have been proposed.However, a major obstacle in Fricke gel dosimeters is the diffusion of Fe 2+ and Fe 3+ ions within the gel matrix and many studies have focussed on reducing the diffusivity of the ions through modification of the hydrogel matrix or the use of chelates.
The MRI dose sensitivity of a Fricke solution can be calculated by calculating the molar change with absorbed radiation dose and then by using the T1 and T2 relaxivity of Fe 2+ and Fe 3+ ions, the change in relaxation rate.The radiochemical yield () in the standard Fricke solution can be calculated from the chemical yields of the different water radical species [9,104] and amounts to about 15.6 Fe 3+ ions per 100 eV of imparted radiation energy.The molar concentration of ferric ions created per unit of dose can then be obtained by multiplying the G factor in SI units (1.62 µmol/J) with the mass density (ρ): The theoretical calculation of the relaxivity of ions in solution involves a deeper understanding of the mechanisms of nuclear magnetic interactions which is beyond the scope of this paper but the reader is referred to other works for a full quantitative description of the different interaction terms [9, 105 -108].The NMR relaxation rate for an absorbed radiation dose D can eventually be written as: where the index k refers to the longitudinal (k = 1) and transverse relaxation rate (k = 2) respectively.R k,0 is the relaxation rate in free water, r k Fe 2+ is the relaxivity of ferrous ions and [Fe 2+ ] 0 is the initial concentration of ferrous ions (ferrous sulphate).The coefficient κ is a proportionality constant that is determined by the number of water molecules in the hydration sphere (i.e. the region where water is in immediate contact with the Fe 2+ and Fe 3+ ions.The relaxation dose sensitivity r k D is given by the factor preceding the radiation dose D in equation 2: After substitution of the theoretical values for κ, one finds for a field strength of 0.47 T, r 1 D = 0.013 s −1 Gy −1 and r 2 D = 0.0178 s −1 Gy −1 .These values correspond very well with measured values by Gore et al: In Fricke gel dosimeters, the Fricke solution is dissolved in a hydrogel matrix.Both agarose, gelatine and polyvinyl alcohol (PVA) have been used as gelling agents.The requirement to obtain a solid gel matrix places constraints on the concentration of sulphuric acid [109].Overall, a higher radiochemical yield is found in Fricke gel dosimeters as compared to Fricke solutions [110] with a 4fold increase in the R1-dose sensitivity in a 1% (w/w) agarose Fricke gel dosimeter and an increase in dose-sensitivity with a factor of 2.2 in a 4% (w/w) gelatine Fricke gel dosimeter [111,112].Additives such as benzoic acid [113], saccharides [116] and salt [117] have been added in an attempt to increase the sensitivity and/or to limit the diffusion of ions in the hydrogel after radiation exposure.Xylenol orange can be used as an optical indicator opening up the possibility for Fricke gel dosimeters to be scanned with optical CT [114] but comes at the cost of a decrease in the R1-dose sensitivity [115].
In a Fricke gel dosimeter, the relaxation rate can be expressed by equation 4: where R k,0 is the relaxation in free water, r k gel is the relaxivity of the gel and r k D is the relaxation dose sensitivity.Note that as discussed above, the relaxation dose sensitivity is dependent on several chemical properties and thus also on the gel agent.
To compensate for the aforementioned drawback of ion diffusion, many attempts have been made to decrease the ion diffusion coefficient [9], either by adding a chelating agent or by changing the morphology of the gel [118,119].Strategies to further reduce the diffusion coefficient could focus on anionic hydrogels, the addition of viscosity increasing substances, the dispersion of ferrous ions in liposomes, the use of sorbent polymers and functionalization of the hydrogel backbone with complex forming groups.Challenges that come with these strategies are that the radiation induced oxidation reaction should not be compromised, that the gel dosimeter remains tissue-equivalent, that there is no significant loss in dose sensitivity, that the gel dosimeter is dose rate independent and that the resulting dosimeter remains affordable.

Polymer gel dosimeters
Polymer gel dosimeters consist of a gel matrix that is immersed with vinyl monomers (and a cross-linker monomer.When exposed to ionizing radiation, reactive water radical species will initiate a polymerization reaction that results in either the creation of highly cross-linked polymer aggregates that are entangled with the gel matrix or polymer chains that graft onto the gel matrix.For a more profound discussion on the radiation chemistry of polymer gel dosimeters, the reader is referred to other work [9, 33, and 34].The spatial integrity of polymer gel dosimeters is superior to that of Fricke gel dosimeters.The change in molecular mobility of the hydrogen protons on the polymer and of bound water molecules is significantly reduced upon polymerization, which results in a significant increase of the relaxation rate, in particular of the transverse relaxation rate R 2. The fast exchange of hydrogen atoms between water molecules and polymer results in an average measured R2 that carries the signature of the restricted mobility of polymer chains [9,120].Several monomers have been used as active components of the polymer gel dosimeter.The R2-dose response follows typically a sigmoidal response (figure 11) which can be characterized by a half-value dose value (D1/2), an R2-dose sensitivity and a dynamic R2-range depending on the monomer.
The uncertainty of any dosimeter is to a large degree determined by its radiation properties such as the dependence of the dose response on the dose rate, energy, LET, the stability and environmental factors such as temperature and pressure.The radiation properties of several polymer gel dosimeters have been studied extensively.

MRI pulse sequences
An important aspect in setting up MRI-based polymer gel dosimetry is the choice of the MRI pulse sequence.This choice primarily depends on the kind of gel dosimeter (i.e Fricke or polymer gel) and is determined by the maximum achievable accuracy and precision.In 3D dosimetry, two kinds of accuracy need to be considered: spatial (geometrical) accuracy and dosimetric accuracy [9,121].In MRI, the spatial and dosimetric accuracy can be compromised by the presence of artefacts which can be scanner related such as inhomogeneity in static magnetic field (B0), magnetic field gradients and radiofrequency (RF or B1) field, or which can be object related such as magnetic susceptibility difference caused by magnetic field distortion and dielectric related standing waves.The dosimetric precision is determined by the interplay of dose response of the gel dosimeter and the sequence parameters as discussed in section 5.
Fricke gel dosimeters exhibit changes in both T1 and T2.Historically, Fricke gel dosimeters have been scanned with quantitative T1, however it is equally possible to use quantitative T2 sequences.In polymer gel dosimeters the radiation induced change in T1 is at least an order of magnitude smaller than changes in T2, hence for polymer gel dosimetry, quantitative T2 sequences are preferred.In theory, it is possible to use any pulse sequence that generates images in which the signal intensity is uniquely correlated with the absorbed radiation dose (not necessarily linear).In theory, a T1-weighted or T2weighted sequence can be used.However, in practice, as a result of B0 and B1-field heterogeneity, the uniqueness is not guaranteed which can severely compromise the accuracy.A better approach is to use quantitative T1 or T2 pulse sequences as the majority of these artefacts are canceled out.Below are some of the most common MRI pulse sequences that are applicable to acquire quantitative T1 and T2 maps.
In general, for every specific pulse sequence, the pixel signal intensity is determined on one hand by known pulse sequence specific parameters such as the flip angle of the applied RF pulses , their phase  and time intervals such as the echo time TE, the repetition time TR and inversion time TI and on the other hand by unknown gel (or tissue) specific NMR properties such as the proton density (  ), the relaxation rates R1, R2, magnetization transfer parameters, magnetic susceptibility (  ) and chemical shifts (Δ).The relationship between these parameters and the acquired pixel signal intensity is described by a signal equation S f (α k , TE k , TR k , … ,   ,   ,   ,   , , … ).For a comprehensive set of signal equations for different pulse sequences, the reader is referred to reference [9] and [122].
The unknown gel specific NMR parameters (in bold) can be determined by acquiring images for a set of k different sequence parameters and minimizing the  2 difference of the acquired signal intensity and the signal equation: where   is the standard deviation (noise) of the measured signal.
Optimal NMR pulse sequences for T1 or T2 mapping are those for which equation 5 results in a set of equations that is well-determined and where for the sake of simplicity, the dimension of the phase space is small.Ideally, only one pulse sequence parameter needs to be varied to result in a set of unique signal relations.In addition, the pulse sequence should result in images with high spatial fidelity, i.e. are not geometrically distorted.Some commonly used pulse sequence are listed here.

Spin-echo, gradient echo and rapid acquisition with relaxation enhancement (RARE)
The most basic sequence to acquire R1 or R2 maps is a spin-echo sequence.The repetitive unit of the spin echo pulse sequence consists of an excitation RF pulse with flip angle 90° and a 180° refocussing pulse at half the echo time (TE/2).The time between two successive excitation RF pulses is the repetition time TR.The signal intensity in a spin-echo sequence is weighted by T1 through the choice of the repetition time TR and by T2 through the choice of the echo time TE.Thus, by acquiring several spinecho images recorded with different repetition times, the longitudinal relaxation rate R1 can be fitted on a pixel-by-pixel basis and by acquiring spin echo-images recorded with different echo times, the transverse relaxation rate R2 can be determined.It is also convenient to apply an image threshold filter to filter out background voxels before the fitting.In addition to the parametric relaxation maps, parametric maps of fitting performance such as Pearson correlation coefficients can also be calculated.
It is sometimes also advisable to treat the flip angle α of the excitation pulse as an unknown fitting variable to account for imperfect excitation (B1 + -field).
Instead of acquiring a spin-echo, a gradient echo can also be acquired.The saturation recovery sequence is a gradient echo sequence with the flip angle of the excitation pulses equal to 90°.Here, all longitudinal magnetization that is rebuild during the repetition time TR is flipped in the transverse plane and gives way to measurable signal.Spoiler gradients are applied after each gradient echo readout to remove phase coherence in the transverse magnetization which would otherwise result in stimulated echoes.An increase in repetition time will result in an increase in signal intensity which also depends on the T1 relaxation time.Spoiled gradient recalled echo imaging (SPGRE) in which the 90° pulses are replaced by smaller α pulses can be found in a technique called DESPOT in which base images are recorded with various flip angles [123] while keeping the echo time and repetition time fixed.
The spin echo sequence is a relatively slow sequence as the excitation/read out loop needs to be repeated for at least the number of phase encoding lines to acquire a single T1/T2 -weighted image.The read out can be accelerated by applying a series of 180° refocusing pulses after the first spin echo.This will result in a series of spin echoes that can be all phase encoded differently so that in a single pulse sequence repetition loop several phase encoding lines are acquired.This is the concept of a Rapid Acquisition with Relaxation Enhancement (RARE) sequence.The acceleration is determined by the number of echoes (or refocusing pulses) in the readout echo train (N E ).Different T2 weighting of the different spin-echoes in the echo train will however lead to some broadening of the point spread function of each voxel.

The multi-spin-echo pulse sequence
The most common sequence that is used to acquire a set of T2-weighted base images is the multi-spinecho sequence [124,125].The pulse sequence scheme is very similar to the RARE sequence but instead of storing the different spin-echo signals in different k-space lines of the same k-space image, the different spin-echo signals are stored in corresponding k-space lines in separate k-space matrices (figure 12).A typical pulse sequence scheme of a multi-spin echo sequence is the Carr-Purcell Meiboom-Gill (CPMG) sequence where the 90-degree excitation RF-pulse has a 90-degree phase difference with respect to the successive 180-degree refocussing RF-pulses.By shifting the phase between the excitation and refocussing pulses, the sequence becomes more robust against B1-field nonuniformity [126].A CPMG multi-spin-echo sequence provides a series of differently T2 weighted base images on which an exponential T2-decay curve can be fitted on a pixel-by-pixel basis.Calibration vials are scanned together with the volumetric dosimetry phantom which can be used to convert the R2 values in dose values.In the saturation recovery sequence, a 90° RF pulse followed by a crusher gradient will destroy the longitudinal and transverse magnetization.The longitudinal magnetization will start to recover immediately after the 90° pulse.After a recovery time TM, the longitudinal magnetization component is turned into a measurable gradient echo signal by use of a second 90° pulse.In an inversion recovery sequence (figure 13b), a 180° inversion pulse is applied.After an inversion recovery time TI, the longitudinal magnetization is turned into a measurable signal.In the case of an inversion recovery experiment, it is important to acquire the real component of the signal instead of the magnitude of the signal.
In principle, any kind of fast read out block can be applied after the 90° pulse, such as a spin echo, fast spin echo or a combination of a gradient echo train and spin echo train, also referred to as GRASE readout.For gel dosimetry, it is not recommended to use an Echo Planar Imaging (EPI) readout because of the significant spatial distortions related to the low bandwidth in the phase encoding direction in combination with magnetic field inhomogeneity as a result of magnetic susceptibility differences between air and gel.

Look-Locker sequences
A fast sequence to acquire R1 maps is the Look-Locker sequence [127].The Look-Locker sequence is similar to the inversion recovery gradient echo sequence, but a faster readout is achieved by replacing the 90° pulse with an RF pulse train with small flip angles α.Each α-pulse transfers some recovered longitudinal magnetization in the transverse plain which is readout as gradient echoes.Also, between each -pulse, a small phase encoding gradient is applied so that each gradient echo results in a new kspace line.This means that for each inversion excitation part of k-space is sampled instead of only one k-space line in the case of the IRGE sequence.The relaxation weighting of the different k-space lines also results in broadening of the point-spread-function (PSF), thus compromising the intrinsic resolution.To avoid severe artefacts as a result of the relaxation between the different k-space lines, a k-space ordering scheme is often proposed.In this scheme the central k-space lines (close to ky = 0) are from echoes recorded immediately after the first α-pulse.
A variation on the Look-Locker sequence is the TOMROP (T1 by multiple readout pulses) sequence.In this sequence the gradient echoes are grouped and interleaved with some recovery time to allow T1 relaxation to take place.Each group of gradient echoes is used in a separate T1 weighted base image.The different T1-weighted base images are then used to reconstruct an R1 map.The Look-Locker sequence is particularly sensitive to RF pulse imperfections.Also changes in the flip angle distribution within the image (B1-field non-uniformity) will affect the signal and B1 inhomogeneity corrections may be necessary.In addition, more sophisticated numerical algorithms are required to solve for the relaxation rate R1 [128].

Steady State Free Precession (SSFP) sequence
A sequence of RF pulse excitations separated by a time TR (without spoiler gradients) will bring the NMR signal in a steady state.In between two successive pulses the frequency encoding gradients can be placed in such a way that two echoes are obtained [122].After recording images with various flip angles  and repetition times TR, R1 maps and R2 maps can be calculated.
A special case of SSFP is when the net gradient area is zero at any of the three gradient axes during one TR interval (i.e. between two successive excitations).In this case, only one echo is obtained.This sequence is called balanced SSFP.Because both the spatial and dose accuracy are important in the 3D radiation dosimeters, careful validation of the quantitative MRI protocol is essential.Indeed, any imaging artefacts may result in a misinterpretation of the dose at a specific location or of the location where the radiation dose is administered.Benchmarking the accuracy of the dosimeter involves quality assurance experiments on blank (non-irradiated) phantoms and on phantoms with a well characterized golden standard phantom containing gels with well-known R1 and R2.Eventually, corrections for RFfield inhomogeneity can be applied [63,129].

Magnetization transfer pulse sequence
The MRI contrast mechanisms indicate a strong dependence of the MRI signal on magnetization transfer which has been experimentally demonstrated in a magnetization transfer experiment [130].Magnetization transfer (MT) is preferred above R2 as imaging property in polymer gel foams which find potential use as lung equivalent dosimeters.Not only is the dynamic range much higher for MT than for R2, the measured MT ratio (MTR) is also less sensitive to variations in bubble size and density [97].Magnetization transfer images can be acquired by use of an imaging pulse sequence that consists of an MT contrast preparation block and an image acquisition block.The MT preparation block has a series of off-resonance Gaussian shaped MT saturation pulses followed by spoiler gradients to get rid of residual transverse magnetization (figure 14).The MT saturation pulses will selectively destroy the magnetization on the polymer proton pool, which through chemical exchange affects the water proton pool (figure 14).For polymer gel foam dosimeters, the acquisition block requires the use of short echo times to limit diffusion attenuation of the signal.The resulting MT-weighted signal attenuation can be compared to the signal obtained with the same sequence but without playing out the MT saturation pulses.The ratio of the signal change in each voxel, with respect to pure water and the non-MT weighted signal can be mapped in an MT map.As the size of the polymer proton pool increases with radiation dose, the MT effect will increase.The MT contrast depends on the offset frequency of the MT saturation pulses.An optimum frequency offset can be determined and an MT versus dose response curve can be extracted.The MT map can be calibrated to dose by use of a set of gel foam calibration phantoms that have been irradiated with predefined doses.[97] with permission of the publisher.

MRI pulse sequence optimization
A more extensive treatise on the uncertainty in 3D radiation dosimetry can be found elsewhere [22,23].
It is emphasized that dosimetric and spatial uncertainties are intermingled in the case of 3D gel dosimetry and it can be difficult to impossible to differentiate one from the other in a measured dose distribution.It is in this light that gamma-map comparisons have been used [131].The overall uncertainty of 3D radiation dosimetry can be achieved through a reproducibility study of the complete dosimetry experiment from gel fabrication to dose distribution analysis (type A uncertainties) and by comparison against other non-3D dosimetry standards (type B uncertainties) [75].In a clinical dose verification with gel dosimetry the uncertainty of the dose measured in each voxel comprises both the systematic inaccuracy and random errors, including stochastic image noise.To minimize systematic uncertainties, physico-chemical parameters (such as temperature and fabrication procedures) can be controlled carefully while MRI artefacts can be minimized by a careful choice of pulse sequences and artefact compensation techniques [62][63][64].Stochastic image noise can be minimized by optimizing the imaging parameters such as repetition time, echo time and flip angle.The optimal imaging parameters are dependent on the type of gel (i.e. the T1 and T2 working range of the gel dosimeter).

Optimization for 3D radiation dosimetry
The optimization problem in 3D radiation gel dosimetry can be defined as "Find the imaging parameters that minimizes the stochastic noise in the dose maps for a predefined spatial resolution within a fixed measurement time and total imaging volume."A complication is that the total measurement time will be determined by the imaging parameters.Here it is important to keep in mind that taking more image averages (NEX) will result in a scaling of the standard deviation (noise) with NEX -1/2 .So in comparing different sets of imaging parameters, it is paramount to take the measurement time into account.On the other hand, in practice, the available measurement time can be constraint by the availability of the MRI scanner for the gel dosimetry readout.Note that this does not only apply to MRI but is also valid for Xray CT and optical CT readout.Also, the total imaging volume and required spatial resolution are defined by the particular study (e.g.glioblastoma versus whole abdominopelvic radiotherapy).
Below are the general steps that can be followed to optimize the imaging parameters for a particular MRI pulse sequence and gel dosimeter (Figure 15): 1. Define the input parameters for the optimization problem: a. Select the MRI pulse sequence.Note that different pulse sequences can be selected and compared in terms of performance, both in terms of their susceptibility to artefacts and obtainable dose resolution (as to be determined).b.Define the parameter that is to be extracted from the MRI signal relation in the parameter space of one of the imaging parameters.A logical choice is R2 for polymer gel dosimeters and R1 or R2 for Fricke gel dosimeters.For example, we define the signal in the parameter space of echo time S k = S(TE k ) for a polymer gel dosimeter, when we will acquire the signal S for different echo times TEk for example by use of a multi-echo pulse sequence.However, in principle, it is not necessary to take the relaxation rates R1 or R2.A necessary condition is that the function preserves the uniqueness with respect to dose.Another logical choice could be for example: where par1 and par2 are two different values of the imaging parameter 'par' (par = TE, TR , α, …).The motivation behind this functional form is that the subtraction in the nominator will remove any additive constant artefact, while the denominator will compensate (in first order) radiofrequency heterogeneity (B1).c.Define the total volume-of-interest to be imaged and the imaging resolution.In multislice MRI, this will come down to the in-plane pixel resolution and the slice thickness.This will be translated in the matrix size (Nx, Ny) and the number of slices Nsl and voxel size (∆x, ∆y, ∆z).d.Define the operating dose range and the available measurement time   (i.e. the time in which the entire volume is to be scanned with the specified spatial resolution).
2. The signal intensity in the voxel with dimensions (∆x, ∆y, ∆z) as a function of imaging parameters and radiation dose is determined by the type of sequence.See section 4 for some examples.In the signal equation, the relaxation rates are functions of dose (Rk(D), k = 1,2), which depends on the type of gel dosimeter.In some cases, a linear relation can be assumed within a particular dose range.In other cases, a higher order functional relation (often sigmoidal) needs to be assumed.
We have found that for many polymer gel types, a bi-exponential fit with offset fits the relation R2(D).While the inverse of such a bi-exponential function D(R2) is not trivial and requires numerical methods, we found that a bi-exponential function of the form described in equation 7 is applicable in practice [98].
where the fitting variables a, b, c, d and f are real positive.
3. The error propagation can now be either calculated or simulated.For a calculation of the dose error in the case of polymer gel dosimeters scanned with a single or multi spin-echo pulse sequence we refer to the literature [72,74].Alternatively, a numerical simulation can also be performed whereby Gaussian distributed noise is added to the signal S and propagated through the variable P(S) or R2(S) and further through the dose D by use of equation 7.
4. The noise propagation is repeated for different imaging parameters (TE, TR, α) until a minimum is found for the maximum standard deviation within the dose range [0,  ].The minimum can be found by either a brute force grid search over all imaging parameters or by use of a conjugate gradient minimization.

Optimization for 4D radiation dosimetry with the MRI-Linac
The optimization of the parameters in a 4D measurement is similar to the optimization but here the is to obtain the smallest temporal uncertainty and the temporal resolution (number of scanned volumes within the measurement time) should match the temporal uncertainty as close as possible.Indeed, there is no advantage in having a higher scanning rate when the (stochastic) uncertainty in dose between different time frames is larger than the incremental change in dose.The temporal uncertainty (within a confidence level of p%) TU p% can be written as where D ∆ p is the dose resolution and D ̇ is the dose rate.For a confidence level of 95%,   √2 = 2.77.
Note that for a given dose rate, the temporal uncertainty is proportional to the standard deviation.The optimization problem can now be defined as "Find the minimum standard deviation within a scanning time frame that is as close as possible, but smaller than the temporal uncertainty TU p% .Note that in contrast to the 3D optimization scheme described above, the available measurement time is flexible.Such an optimization scheme has been implemented in MATLAB for both the RARE sequence and a balanced SSFP readout, where in addition also the relaxation rates of the gel can be varied by adding an MRI contrast agent.The results are presented in another proceedings abstract [132].We here describe briefly the approach and calculations for both sequences where the standard deviation on the dose is calculated (approximate) algebraically.

Rapid Acquisition with Relaxation Enhancement (RARE) sequence
The number of echoes that can fit within an effective echo time , which here also equals the echo train length (ETL) is given by   = (/∆).The function (•) returns the highest integer value for which   • ∆ < .The echo time spacing ∆ is the minimum achievable echo time spacing in the sequence.This minimum value is to some degree also determined by the receive bandwidth.A larger receive bandwidth will typically result in a smaller achievable ∆, but this also results in a lower SNR.
The optimization approach starts with a choice of N ETL .The effective echo time then becomes TE = N ETL ΔTE + τ D where τ D accounts for a dead time before another echo train can be switched.Another choice is the number of scanned slices within a single repetition time N sl in TR .The repetition time is then TR = N sl in TR • (N ETL ΔTE + τ D ) and the minimum total time required to scan one kspace line for all (N sl ) slices becomes: The measurement time for a single acquisition, is given by the product of T m 1 with the number of k-space line or phase encoding steps N ph , hence The total measurement for multiple acquisitions becomes In the optimization problem, the number of acquisitions (experiments) is considered as an optimization variable.The relaxation rates can also be varied by adding a contrast agent such as gadobutrol [132].
The signal intensity can now be calculated for this set of imaging parameters and the concentration of contrast agent.For the RARE sequence, the signal intensity is given by: In 4D radiation dosimetry, the absorbed dose D is estimated from the change in relaxation rate.Both the longitudinal relaxation rate R 1 (= 1 T 1 ⁄ ) and transverse relaxation rate R 2 (= 1 T 2 ⁄ ) depend on the dose, but R1 is significantly less dependent on dose.As a first order approximation, one can assume a linear relationship between the relaxation rate and the dose.
where R 1,0 D and R 2,0 D are the intercept in the  1 -dose plot and  2 -dose plot respectively.r 2 D is the dose relaxivity, in other words, the change of transverse relaxation rate per unit of absorbed dose.The R2-dose response is only approximately linear in the interval [0 Gy, 2 Gy], while the R1-dose response is independent of dose (R 1 = R 1,0 ).Note however that the non-linear R2-dose response can also be considered in the calculations.When the polymer gel dosimeter is doped with a contrast agent, the intercepts R 1,0 D and R 2,0 D are also dependent on the concentration of contrast agent.There is also a small dependence of the transverse relaxivity r 2 D on the concentration of contrast agent but which in a first order approximation can be neglected [132].
The change in transverse relaxation rate ∆R 2 can be (in first order, neglecting R1) obtained by taking the logarithm of the ratio of the signal intensity before radiation exposure and after radiation exposure.
where S(D) is the signal intensity in the same voxel after absorbing an amount of radiation dose D and S(0) is the signal intensity in a voxel before radiation.Note the different meaning of S0 and S(0).
The standard deviation on estimated dose can then be written as: and which results in In the derivation of equation 20, we ignored the T1-effect and assumed that the R2-dose response is linear.For a more exact approach, a numerical approach as outlined in section 5.1 can be followed.
A flow chart of the different steps in the algorithm to optimize the RARE sequence for inline MRI gel dosimetry on an MRI-Linac is shown in figure 17.First, the resolution and scanning volume are defined.This is characterized by the number of phase encoding lines (Nph), number of points in the readout direction (Nro), the number of slices (Nsl) and the voxel dimensions (∆x, ∆y, ∆z).The echo train length (NETL) is to be optimized.Also the repetition time is an optimization variable which is defined by the number of slices that are acquired within a repetition loop (N sl in TR ).The optimization algorithm will iterate and update these parameters until convergence is obtained.To account for the imaging time, it is allowed to change the number of acquisitions (NEX) that will contribute to the same image set.The three optimization variables (N ETL , N sl in TR and NEX) will determine the total imaging time T t (equations 9-11).For each set of optimization variables, the standard deviation in a predefined dose range [0, Dmax] is calculated (equation 20) or simulated by adding normal distributed noise to the signal amplitude and propagating this to the estimated dose D. The standard deviation defines the temporal uncertainty.It is important to note that for each iteration step in the inner optimization loop, both the total imaging time T t and temporal uncertainty TU p% are updated.The optimization is continued until the total imaging time becomes larger than the temporal uncertainty, which defines the number of possible acquisitions as NEX-1 for this particular set of optimization variables.The maximum standard deviation on the dose within the dose range [0, Dmax] is calculated and the corresponding temporal uncertainty is compared against the until-then obtained minimum value.The optimization of the variables N ETL and N sl in TR is continued until convergence is obtained.The optimization can be conducted by use of a conjugate gradient minimization or by scanning in a two dimensional grid of the parameter space (N ETL ,N sl in TR ).Both techniques can be combined to find the global minimum.

Balanced Steady State Free Precession (bSSFP, trueFISP)
For the bSSFP pulse sequence the optimization is With bSSFP, it is a reasonable choice to consider the relative signal change R = S(0)−S(D) S(0) as the dose correlating metric.The signal intensity in a voxel of a bSSFP image with TR << T 1 , T 2 is given by: A similar derivation leads to the expression for σ D : Minimization of the objective function   towards concentrations of contrast agent and different flip angles can be performed numerically.
Note that with the bSSFP sequence, the scanning time is immediately defined by the minimum TR that is achievable in the sequence, the number of lines in the phase encoding direction and the number of slices.

How to start with gel dosimetry and MRI readout: Do's and don'ts
There are many different kinds of gel dosimeters and there exists a vast amount of scientific literature on the subject which may appear overwhelming at first and not all information is as valuable when starting with implementing gel dosimetry.The sequence below is not scientific but can be seen as a piece of advice that may help in bridging some obstacles in establishing gel dosimetry in a clinical setting.

Choose a gel dosimeter:
The choice of the gel dosimeter may depend on the application and practical considerations such as availability (e.g.commercial versus in-house fabrication).Paramount in the choice of a gel dosimeter are the physico-chemical and radiation properties, such as stability, temperature sensitivity and dose rate dependence.Some of the sensitivities such as temperature sensitivity can be compensated in the experimental design but requires a careful control during storage, irradiation and/or scanning.Not all the properties have been reported for all types of gel dosimeters (including commercial gel dosimeters) and it is important to be aware of possible related uncertainties.
Gel dosimeters with the highest dose sensitivity are not always the best.Other properties of the gel dosimeter may result in higher dose uncertainties and stochastic uncertainties depend in a rather non-intuitive way on the interplay between dose response and MRI scanning parameters.2. Choose an MR imaging sequence: Several pulse sequences are available on standard clinical MRI scanners.However, most pulse sequences are designed for diagnostic imaging purposes where image uniformity and geometrical distortions are less of a concern.It is important to spend some time in optimizing the imaging protocol to acquire reliable quantitative MR images.For 3D polymer gel dosimetry, the most used pulse sequence is a multi-spin-echo (CPMG) sequence.To process the images in a quantitative MRI map, a pixel-wise fitting algorithm is required.Commercial and freeware software can be applied but it is important to keep in mind that the fitting algorithm also has an influence on stochastic dose uncertainties.For larger phantoms (such as whole abdominopelvic), correction for image non-uniformity may be required.In the case of gel dosimetry in regions with magnetic susceptibility differences such as air cavities or implants, B 0-field corrections may be required.For lung-equivalent gel dosimetry, a magnetization transfer imaging sequence may be required [97].Do not treat MRI as a black box.It is more efficient to obtain a good understanding of the inner workings of MRI, than trying to optimize the imaging design by trial-and-error.3. Choose optimal sequence parameters: Optimization strategies are discussed in section 5 and the corresponding literature for both 3D [72,74] and 4D [98] imaging.The importance of sequence parameter optimization should not be underestimated as the stochastic dose uncertainty can be decreased significantly by optimization.4. Choose a recipient: Two kinds of approaches can be taken.If the dose distribution towards the skin of the patient is not important, one may choose to use a phantom with a cylindrical gel insert and the gel dosimeter can be poured in a glass recipient.This is the approach that is mostly used with optical CT.However, if the entire dose distribution up to the skin is needed, a humanoid shaped cast is needed.Such a cast is preferably made from Barex  , glass or any other material with very low oxygen permeability.5. Investigative testing: It is important to obtain a good sense of the expected uniformity and geometrical distortions.The recipient can be filled with a 'blank'-gel.The blank gel should have NMR relaxation rates close to the gel dosimetry phantom.Fiducial markers can be placed on the phantom.The phantom can then be scanned with MRI and/or CT and the image data set can be used as the template for the treatment planning (simulation).As the gel dosimeter will not have anatomical structures to use in the treatment planning (i.e.critical organs and CTV), anatomical structures can be virtually created by transferring them from a patient data set onto the planning template by use of a morphological affine transformation.The treatment should be planned on the basis of this data set and not on any other anatomical data set which may have a different geometry compared to the gel dosimeter phantom.6. Fabricate the gel dosimeter: In fabricating the gel dosimeter make sure to control the temperature and storage conditions as much as possible.This will facilitate the reproducibility of the experiment.If a large volume of gel is used (e.g.> 10 L), it is important to make sure that temperature changes within the phantom occur relatively uniform.Avoid air pockets in the gel dosimeter.Even normoxic gel dosimeters are still sensitive to oxygen [21].7. Perform the polymer gel dosimetry experiment: It may be necessary to scale the radiation output (MU) to optimize the response (relative dose resolution).However, such approach may not be possible in applications where the absolute dose as delivered to the patient needs to be matched, such as inline MRI-Linac treatments.In these cases, a highly dose sensitive gel dosimeter is required.The maximum delivered radiation dose may be limited as a result of loss of spatial integrity [45].Some temperature stabilization and/or control may be required during the radiation and scanning.When scanning the gel dosimeter, it is advisable to scan both the phantom and calibration vials together to minimize any uncertainties as a result of instability.Calibration vials can be taped onto the phantom during scanning.

Compare the gel dosimetry acquired dose maps with the treatment plan:
A gamma-evaluation can be used to assess the correspondence between the intended dose distribution and the delivered dose distribution.Use gamma pass rates with great care!The main purpose of a gamma evaluation is to highlight regions where the difference between both dose distributions exceeds an acceptable level.The spatial information on where gamma > 1 is important.In some regions one can tolerate a larger gamma-deviation than in others.Gamma pass rates depend strongly on the volume in which gamma is evaluated.For inter-comparisons of treatment approaches within the same centre and same treatment site (brain, H&N, abdominopelvic), a valid approach may be to extract gamma pass rates in a region defined by a lower isodose boundary.However, much care is needed to use gamma pass rates as absolute instruments or for the comparison between different treatment sites as the location and size of the target may have a significant influence on the expected pass rate.

Conclusion -An outlook to the future
Since the early developments of polymer gel dosimetry, scholars expected a broader application of gel dosimetry in clinical practice.There are some reports where gel dosimetry has been applied successfully in clinical validation of high precision treatments and where findings had an impact on patient treatment.The limited dissemination of gel dosimetry in the hospital is multi-faceted.There has been a continuous search for more sensitive, less toxic and more reliable gel dosimeter systems and readout technologies and physico-chemical and radiation parameters have been documented for several gel dosimeters.Optical CT scanning with radiochromic plastic dosimeters has been presented as an alternative method for 3D gel dosimetry as a more accessible and easier-to-use technology.However, until now, applications with radiochromic plastics have been limited to relatively small and canonical volumes (cylindrical).While some researchers have commented on the radiation properties of some radiation sensitive plastics, there are some reports that mention that materials such as PRESAGE are not entirely immune to variations in dose response or physico-chemical induced uncertainties.The question on which dosimeter system to use depends on the application.For relatively small volumes that are confined to cylindrical shapes including inserts, radiochromic dosimeters with optical readout may be a preferred choice.However, for dosimetry in large anthropomorphic shaped regions and some emerging applications such as inline MRI-Linac with MRgRT tracking, lung dosimetry, dosimetry around deformable organs, polymer gel dosimetry with MRI readout is currently our preferred solution.However, improvements and further developments of MRI-based polymer gel dosimetry for these applications is still required.FLASH-RT poses another challenge for the entire dosimetry community.Both polymer gel dosimeters and radiochromic plastics are based on radical-induced reactions, where the equilibrium between initiation and termination reactions is responsible for dose-rate dependence.Dosimetry of FLASH-RT may be very challenging for such systems.However, gel dosimeters can be helpful in studying the mechanisms behind FLASH-RT.

Figure 1 .
Figure 1.Nasopharyngeal tumor treated with IMRT.Initial treatment planning box was only covering the area near the target volume.A hot spot was detected on gel dosimetry.Increasing the treatment planning box confirmed the presence of the hot spot.The dosimeter gel was an anoxic polyacrylamide gelatin (PAG) gel. Figure adapted from De Neve et al 1999 [86] with permission of the publisher.

Figure 2 .
Figure 2. IMRT treatment of a mediastinal tumour consisting of 6 non-coplanar beams sparing the spinal cord.Comparison with stacked radiographic film dosimetry and treatment planning revealed a good correspondence which resulted in confidence about the whole treatment chain.The dosimeter gel was an anoxic polyacrylamide gelatin (PAG) gel that was cast in a cylindrical glass bottle that

Figure 3 .
Figure 3. 3D dosimetry by both optical CT in combination with a micelle gel dosimeter (upper row) and MRI-based gel dosimetry using a normoxic PAGAT gel dosimeter (bottom row) provides confidence on the treatment plan of a pituitary gland adenoma using a sliding beam IMRT technique.Figure adapted from Vandecasteele et al 2013 [92] with permission of the publisher.

Figure 4 .
Figure 4. Whole abdominopelvic IMAT palliative treatment of patients with relapsed ovarian cancer.The abdominopelvic gel dosimeter phantom consists of a vacuum moulded Barex™ cast filled with a normoxic PAGAT gel and was surrounded by slaps of the Rando® phantom.The yellow shaded area corresponds to the liver, the green shaded areas to the kidneys and the pink shaded area corresponds to the planning target volume (PTV).The red regions in the gamma map are regions where gamma exceeds 1. Figure adapted from Vergote et al 2004[92] with permission of the publisher.

Figure 6 .
Figure 6.Polymer gel dosimetry of a Tomotherapy Head & Neck treatment at the Free University of Brussels (VUB).The polymer gel was a normoxic PAGAT gel dosimeter.

Figure 7 .
Figure 7. Polymer gel dosimetry of a GRID treatment.Normoxic PAGAT gel was used in this study.

Figure 8 .
Figure 8. Polymer gel dosimetry in a situation of electronic disequilibrium resulting in a rebuild-up behind a spherical air cavity.

Figure 9 .
Figure 9. Tray with lead-markers producing a cross-reference location on electronic portal imaging.Polymer gel dosimetry was used to evaluate if the tray also created a dosimetric effect in treatment beams.As a dose attenuation of 10% was measured underneath the lead markers, it was concluded that the tray had to be removed before every treatment beam delivery.Figure adapted from De Deene et al 2002 with permission of the publisher.
Figure 9. Tray with lead-markers producing a cross-reference location on electronic portal imaging.Polymer gel dosimetry was used to evaluate if the tray also created a dosimetric effect in treatment beams.As a dose attenuation of 10% was measured underneath the lead markers, it was concluded that the tray had to be removed before every treatment beam delivery.Figure adapted from De Deene et al 2002 with permission of the publisher.

Figure 10 .
Figure 10.Dose maps of the central slice recorded dynamically on the MRI-Linac during radiation of a head phantom.The time between two adjacent images in a row is 44 seconds (every 4 th recorded frame).Figure adapted from De Deene et al 2020 [98] with permission of the publisher.

Figure 11 .
Figure 11.Typical R2-dose response curve (a) and corresponding dose-R2 curve (b) of a PAGAT gel dosimeter, measured with a 32 echo multi-spin-echo pulse sequence on a 3T MRI scanner.Note the excellent fit.

Figure 12 .
Figure 12.Quantitative R2 maps can be obtained by using a multi-contrast CPMG spin echo sequence where several T2-weighted signals are acquired in a single repetition time.The resulting k-space images are transformed in T2-weighted base images on which a pixel-by-pixel exponential fit results in a quantitative R2 map. Figure adapted from De Deene et al [9] with permission of the publisher.

4. 3 .
Saturation and inversion recovery sequenceA second class of pulse sequences that can be employed to map R1 are the saturation and inversion recovery sequences.The pulse scheme of a saturation recovery sequence and inversion recovery sequence are displayed in figures 13a and b respectively.

Figure 13 .
Figure 13.Saturation recovery (a) and inversion recovery sequence (b) scheme with the longitudinal magnetization (  ) and transverse magnetization (  ) indicated by a solid line and dotted line respectively.A crusher gradient (  ) is added after the saturation or inversion pulse to spoil any remaining transverse magnetization.Read out and slice selection gradients are not shown.Figure adapted from De Deene et al [9] with permission of the publisher.

Figure 14 .
Figure 14.Magnetization transfer imaging of polymer gel foam can be performed by use of a series of MT saturation pulses combined with a spin echo readout (a).The spin echo readout has a relatively short TE to avoid significant R2 dispersion effects.The polymer gel foam proton pool has a relatively short T2 and thus has a broadened spectral line shape (b).Off-resonance MT saturation pulses will selectively saturate the polymer gel proton pools which exchange with the water proton pools (b) resulting in an attenuation of the liquid hydrogen pool.Figure adapted from De Deene et al 2006[97] with permission of the publisher.

Figure 15 .
Figure 15.Flow chart of the optimization of sequence parameters TE, TR, α

Figure 16
Figure 16 illustrates the calculation of the total measurement time of a single scanning frame for the situation where N ETL = 8, N sl in TR = 3, N sl = 5, TE = 8 ms, N ph = 128 and NEX = 3.

Figure 16 .
Figure 16.Sequence schematic for an example with N ETL = 8, N sl in TR = 3 and N = 5.For the situation where ∆TE = 8 ms, N ph = 128 and NEX = 3, the minimum TR is 204 ms, the measurement time for one k-space line is T m 1 = 408 ms, resulting in a measurement time for 1 acquisition T m = 52 s and a total measurement time for 3 acquisitions (NEX = 3): T t = 2 min 37 s

Figure 17 .
Figure 17.Flow chart showing the different steps in optimization of the RARE sequence: Two loops can be considered.The parameters N ETL and N sl in TR are optimized in the outer loop.