MR-Linac Dosimetry: Current Approaches and Challenges

The use of MR-integrated linacs (MR-linac) in clinical radiation oncology applications are becoming more prevalent. However, given the novel and radically different designs of these systems from conventional linacs, current radiation dosimetry protocols for high energy photons are no longer appropriate for use in modern MR-linac systems: First, given the presence of the magnetic field and the linac design, traditional reference conditions defined by previous high energy photon dosimetry protocols cannot be met; Second, the presence of the strong magnetic field can affect the performance of conventional equipment used for dosimetry. In this manuscript, we describe some of the challenges faced in radiation dosimetry in external MR-guided radiotherapy delivery systems, summarize some of the publications in this area, and finally discuss the early work by the American Association of physicists in Medicine (AAPM) Task Group 351 which is mandated with producing a protocol for reference dosimetry in MR-linac units.


Introduction
The phrase "adaptive radiation therapy" (ART) was described in an article by Di Yan et al [1] in 1997 as "a radiation treatment process where the treatment plan can be modified using a systematic feedback of measurements".ART was performed off-line in its early conception, by introducing changes to the treatment plan between treatment fractions.Magnetic Resonance image-guided radiation therapy (MRgRT) systems have allowed changes to a treatment plan to be made based on imaging immediately prior to treatment.An adapted plan created in this way not only accounts for changes in target size or position, but also changes to organs at risk in the vicinity of the target, and to the position of the patient on the treatment couch.On-line ART requires that high quality imaging of the patient be performed while the patient is in the treatment position, and that changes to the treatment plan be made quickly, before the patient's position alters.This is only possible when the imaging system is integrated with the treatment device.
However, the integration of the magnetic fields with a conventional high energy linac has been filled with challenges, not only from a technical and construction point of view, but also in other areas including radiation dosimetry and treatment planning.Magnetic fields can impact both the overall dose distribution in water as well as the radiation dosimeters we currently employ to measure this dose [2].Furthermore, MR-linac delivery systems must be paired with accurate treatment planning systems that appropriately model the modified dose distribution due to the effects of Lorentz force on the high energy

Dose distribution in the presence of magnetic field
In the presence of strong magnetic fields, the Lorentz force will impact the trajectories of the charged particles.Given the perpendicular orientation of the magnetic field and radiation beam in both commercially available systems, the Lorentz force results in a change of some of the characteristics of the radiation dose distribution relative to what it would be in the absence of the magnetic field.This is evident in both the percent depth dose curve as well as profile shapes [10].
The Lorentz force will result in removal of contamination electrons, from air or the linac/cryostat itself, that would otherwise reach surface.These will spiral back due to feeling the Lorentz force of a perpendicularly oriented strong magnetic field to the direction of their travel [11,12].This would result in a lowering of the surface dose [13].Inside the medium, the same effect results in charged particle created from photon interactions with the medium to spiral back and in general have a shorter range of travel.This means that there is a shift upstream of dose deposition by charged particles created in the medium, directly resulting in depth of maximum dose occurring closer to the surface [14].Finally, as the charged particles exit the medium, they quickly spiral back in the lower density air (the so-called electron return effect, ERE) and contribute to additional dose inside the phantom and near the exit surface [14].As a result of same phenomenon, the shape of an offaxis profile curve becomes asymmetric in the direction of the magnetic field, while remains symmetric in the other direction.The shape of percent depth dose curves for a Unity MR-linac spectrum simulated in presence and absence of the strong 1.5 T magnetic field for several field sizes are shown in figure 1.All the impacts described above are exaggerated at higher magnetic fields [2,3,14].

Calorimetry
Calorimetry is one of the main radiation dose detection techniques used by radiation standard laboratories.Here, the radiation dose to medium Dmedium is measured directly by measuring radiationinduced temperature rises ∆Tmedium through the relationship [15]: where c is the specific heat capacity of the medium, and ki represents various often relatively small correction factors including heat transfer, heat defect, perturbation, etc.Of the many radiation detectors used in radiation dosimetry, only calorimetry can be categorized as a true primary absolute dosimeter.This is because in calorimetry, the conversion factor, specific heat capacity, relating the detector signal (i.e.temperature rise) to absorbed dose can be accurately determined in the absence of a known radiation beam, for example through electrical techniques.As seen from equation 1, calorimetry is theoretically insensitive to the presence of the magnetic field as the specific heat capacity c is independent of the magnetic field.This was later experimentally studied and verified by De Prez et al [16], D'Souza et al [17,18], and Renaud et al [19] as calorimeters were shown to nearly display no sensitivity to the presence of the magnetic field.
There are two main types of calorimeters that are currently used in high energy photon radiotherapy [15]: (1) in water calorimetry, dose to water, is measured directly and absolutely at a point in water; (2) in graphite calorimetry, the medium of the detector is graphite, and hence the dose to graphite is measured directly and absolutely, and is converted to dose to water through simulated or measured conversion factors.Although, water calorimetry measures the quantity of interest in radiation dosimetry directly, its operation is challenging because of the low signal to noise ratio involved, and the need for operation of the entire device at 4° C to minimize heat transfer effects, among other factors.Relative to water calorimeters, graphite calorimeters produce higher signal to noise ratio for the same given dose, but require dose-to-graphite to dose-to-water conversion factors that were previously discussed and would in turn add to the overall dose uncertainty.
Water calorimeters [16,18] and to a smaller extent a modified graphite calorimeter [19] have been used successfully in MR-linacs.Given the complexity of the detectors and high level of expertise required for their operation, calorimeters are not used clinically, but rather are used to characterize and calibrate other reference detectors used in clinics.

Ionometry
Ionization Detectors are the detectors of choice for radiation dosimetry in clinics.They are robust, easy to use, produce good signal to noise ratio, and their results are very reproducible.An ionization chamber is similar to a capacitor, where ionizations produced in the air volume of the cavity are separated and collected by the two electrodes defining the volume of the cavity and maintained at different polarity.Given the fact that Lorentz force changes the trajectory and affects the path length of the ions produced inside the chamber cavity, the measured signal by an ionization chamber is found to be dependent not only on the chamber type and radiation beam, but also on the orientation of the chamber with respect to both the radiation beam and the magnetic field involved [20,21].
It is therefore of great importance that modern reference class ionization chambers be well characterized inside an MR-linac environment prior to their use.A few complications with ionization chamber reference dosimetry in the presence of strong magnetic field are noteworthy: First, the electric field lines spanning the two electrodes are not perfectly homogeneous inside a cavity, and more importantly there may be so called dead volumes inside the chamber cavity in which the charge released is not collected.It has been shown that the change in trajectory of charges released, due to Lorentz force, may take them to areas where they are collected with different efficiencies, as such making the impact of dead volume on charge collection a function of chamber orientation with respect to the radiation and magnetic field [22][23][24].
Second, the effective point of the measurement (EPOM) of ionization chambers is shifted not only in the upstream-downstream direction but also laterally [25].This change in EPOM is complex and depends on detailed analysis of radiation transport, and the impact of Lorentz force on charged particles.
Third, the presence of even a small air bubble adjacent to the outside wall of the ionization chamber could result in significant difference in charge collection given the impact of the ERE and the change in trajectory of the charged particle in this small air volume.This has been studied in detail following significant issues in measurement reproducibility of ionization chambers in solid phantom materials [26].Although some have suggested the use of small amount of water or gel to fill the air gap that would have otherwise been present between the chamber and the solid water phantom cavity, the best approach is to perform dosimetry in water and visually ensure the absence of any air bubbles in close vicinity of the chamber volume to avoid dosimetric issues.

Chemical Dosimetry
Chemical dosimeters and their performance in the presence of the magnetic field have also been studied.The details of basic theory and operation of these chemical dosimeters can be found elsewhere [27].However, in general they enable dose determination through a measurement of the concentration of chemical by-products of radiation-catalyzed reactions that are stable.Although rarely used for routine clinical dosimetry, both alanine and Fricke dosimeters are used by primary standard laboratories.Specifically, alanine can be used either as mailed audit dosimeter of choice or a transfer instrument for calibration standards.Studies towards their use in the same capacity for MR-linac have yielded promising results [28].

Reference Dosimetry Formalism
The American Association of Physicists in Medicine (AAPM) Task Group 51 [29] and its addendum [30] form the current primary reference dosimetry standard for high energy photon beams in North America.The protocol recommends the use of reference class ionization chambers with a traceable calibration factor back to a primary standard laboratory or equivalent.However, given the fact that modern MR-linac systems do not satisfy much of what is traditionally considered reference setup conditions required by the protocols, the AAPM created TG-351 in 2020 and tasked it with the development of a radiation dosimetry protocol in external MR-guided radiotherapy systems.The resulting protocol will follow the same format as the previous reference dosimetry guidelines, where it introduces the formalism, the reference condition setup, and practical recommendations and guidelines for best reference dosimetry practices in MRgRT environment, in addition to a sample in-depth uncertainty budget analysis.
The impending formalism will take similar form as that of the TG-51 and its addendum, and follows closely the structure introduced previously by several authors [12,21,23].The general formalism determines dose to water at a point inside an external MRgRT system  w Q,B from a corrected chamber signal reading M through the following relation: where  D,w Co−60 is the calibration factor of the chamber from a primary standard lab which is provided in a Co-60 beam under TG-51 defined reference conditions and in the absence of an magnetic field, and kQ is the beam quality conversion factor that converts the chamber calibration factor from Co-60 to the beam quality of interest (i.e. that of the MR-linac beam) but in the absence of the magnetic field.These parameters, including the corrections necessary to convert a raw chamber signal to a corrected chamber signal M, have all been discussed in length in TG-51 and its addendum.The kQ,B quality conversion factor, however, will be introduced by the TG-351 and will convert the calibration factor of a reference class ion chamber from a zero magnetic field environment to one where the strong magnetic field is present.The kQ,B factors will be provided by the task group as a function of beam quality and the particular MRgRT system, the reference ion chamber type, and the orientation of the chamber with respect to the radiation beam and magnetic field.The data will be provided for a subset of all currently accepted reference class ion chambers that have been well studied and characterized either through repeated independent Monte Carlo studies and/or accurate experimental data.There have been a few articles as well that have summarized some of the available data for example by De Pooter et al [2], Iakovenko et al [32,33] or work currently under review by Begg et al that provides local recommendations on MR-linac dosimetry in Australia.
The TG-351 protocol will also make further recommendations with respect to reference setup conditions and will build upon the recently published AAPM WGTG51 Report 374 on practical guidelines for accurate reference dosimetry [34].Reference dosimetry must only be performed with waterproof chambers in a water phantom to avoid some of the issues discussed in section 3.3.Moreover, given that the magnetic field correction factors kQ,B have smallest magnitude when the ion chamber is oriented parallel with respect to the magnetic field, this chamber orientation is recommended for reference setup.
It is noteworthy that in strong deviation from its predecessors, TG-351 will recommend the ratio of the tissue phantom ratio at depths 20 cm and 10 cm in water, TPR20,10 , as the beam quality of interest in external MRgRT systems.Section 2 describes some of the changes to the shape of the PDD and its sensitivity to the presence of the magnetic field.TPR20,10 acts as a more robust and reproducible beam quality specifier that is less sensitive to the effects of magnetic field.
Finally, the uncertainty budget described in the protocol can serve as a template for future users to perform their own uncertainty calculations by considering their own equipment and methodologies.The uncertainty budget will focus on both user dependent and independent criteria, including the effects of both linac as well as MR stability on final reference dose measurement

Conclusion
This manuscript discusses some of the existing external MR guided radiotherapy systems, as well as the basic physics behind the impact of a strong magnetic field on electron transport.It discusses several available radiation dosimeters, and their performance under the influence of a strong magnetic field.Finally, a brief introduction of the work done by the AAPM TG-351 tasked with producing a clinical protocol for external MRgRT reference dosimetry is presented.

FIG 1 :
FIG 1: Normalized depth dose curves for various field sizes in a homogeneous water phantom.GEANT4 was used to simulate the figures using full Unity MRlinac spectrum.Top figure is with magnetic field turned off, and bottom figure is with it turned on.Images reproduced with permission from Ahmad et al [3].

Table 1 .
[7]rent MRI-linac systems/programs.Only first two systems are currently being widely used as commercial systems[7].In the table's 'orientation' column, 'ꓕ' refers to a setup with radiation being perpendicular to B field, whereas '//' refers to a parallel orientation.