A retrospective study was conducted with 62 patients who received RT for liver cancer in Shandong Cancer Hospital from February 2022 to February 2023. This study was approved by the Ethics Review Committee of Shandong Cancer Hospital (SDTHEC2022012021), and informed consent was obtained from all patients and their families. To better describe the relationship between the plan and the location of the mass, the liver was divided into four quadrants (Fig. 1). According to the distribution of the portal vein and hepatic vein in the liver, anatomical segmentation and lobulation was carried out, generally dividing the liver into 5 leaves and 8 segments. The liver was divided into four quadrants: 1, 2, 4a as the I quadrant, 7, 8 as the II quadrant, 5, 6 as the III quadrant, and 3, 4b as the IV quadrant (Fig. 2).

Schematic diagram of the anatomical division of the liver

Schematic representation of liver masses in four patient quadrants. A Mass in the I quadrant; B mass in the II quadrant; C mass in the III quadrant; and D mass in the IV quadrant

Patients treated on the Elekta Unity MR-linac (Elekta Unity, Elekta AB, Stockholm, Sweden) received the Brilliance large-aperture CT (Royal Philips, Amsterdam, Netherlands) simulation with a tube voltage of 120 kV, a layer thickness of 1 mm, and a scan cycle of approximately 2 min. And using T2-weighted MRI (Siemens, Munich, Germany) scans (repetition time: 2100 ms, echo time: 205.585 ms, layer thickness: 1.2 mm) simulation on the same day. The supine position was fixed, the patient was in a state of free breathing, and the abdominal pressure band (Hymnsum, Shandong, China) was employed to lessen the effect of breathing. MR-LINAC can only carry out static intensity modulation scheme. (Fig. 3).

Radiation oncologists with expertise in the treatment of liver cancer carried out the PTV and OARs drawings. The PTV was obtained by enlarging the gross target volume (GTV) of liver cancer patients treated using both machines by 3 mm, and the radiation dose was 95% of the PTV, V10 < 33.9 Gy. Table 1 lists the OARs restriction. The study did not include the lungs and hearts since the chest was not completely scanned in some participants. The prescribed dose for 32.3% of patients was 63 Gy/9 fractions/qd; for the remaining patients receiving conventional radiation, the prescribed doses were 19.4% 45 Gy/15 fractions/qd, 25.8% 40 Gy/8 fractions/qd, and 8.1% 50 Gy/25 fractions/qd. Based on the idea of equal distribution of the closest, the field is distributed. The dose rate of MR-LINAC is fixed at 400 MU/min.

The program evaluation was conducted by attending physicians and medical physicists using dose-volume histogram (DVH) indicators based on the same regimen. The uniformity and consistency of the dose in the target area were evaluated by the conformity index (CI) [19] and homogeneity index (HI) [20]. The dose distribution to the PTV and OARs was evaluated by average dose (Dmean), minimum dose (Dmin), maximum dose (Dmax) and Vx (percentage of volume accepted xGy). This study is normalized and compared with the percentage of the target dose of DVH in the corresponding prescription dose because the patients' tumor sizes, shapes, and prescription doses varied.

HI and CI are defined as:

$$} = \frac}_}}} }}}_}}} }}$$

$$} = \frac}_},}}} }}}_}}} }}$$

D2% and D98% represent the minimum dose covering 2% and 98% of the target volume, respectively; VT,ref refers to the target volume where the accepted dose is equal to or greater than the reference dose, and Vref is the prescription equivalent dose volume.

On the basis of each patient's original customized intensity modulation reference plan (plan1.5 T), only the magnetic field setting was disabled, and the static intensity modulation plan without a magnetic field (plan0 T) was generated in order to compare the impact of magnetic field on the quality of the plan. Dosimetric parameter discrepancies between plans 1.5 T and 0 T were studied.

Four optimization strategies are developed to observe the impact of maximum subfield number and field density on fading magnetic field. The maximum subfield number is designed as "30, 60, 80" three critical values, and 15°uniform distribution of fields, according to clinical experience.

The first optimization scheme is designed to control only the static intensity modulation scheme (plan30), in which the maximum number of subfields is set to 30, which represents the low subfield number plan; the second optimization scheme is designed to control only the static intensity modulation scheme (plan60), in which the maximum number of subfields is set to 60, which represents the median subfield number plan; the second optimization scheme is designed to control only the static intensity modulation scheme (plan80), in which the maximum number of subfields is set to 80, which represents the high subfield number plan; the fourth is the multi-field static intensity modulation plan (planangle), which raises the field angle to about 15°, with the exception of the direction in which the lead dose limit and OARs cannot be added. Table 2 displays the planning information for each plan. The dosimetric indices with a significant influence of the magnetic field are found by comparing the dosimetric characteristics between plan1.5 T and plan0 T. Only these indexes are compared between plan0 T and optimization plan to determine which optimization strategy is comparable to or superior to the non-magnetic field plan.

IBM SPSS (Version 25.0) statistical software (IBM Corporation, Armonk, NY, USA) was used for statistical analysis. Prior to comparing the dose parameters, the data's normality was assessed using the Shapiro–Wilk test. The dosimetry parameters were compared by paired t test and Wilcoxon signed rank sum test.