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In this paper, we present the reprentation of all operators B which are Drazin invertible and sharing the spectral projections at 0 with a given Drazin invertible operator A. Meanwhile, some related results for EP operators with closed range are obtained.

Purpose: Intensity-modulated arc therapy (IMAT) is a method for delivering intensity-modulated radiation therapy (IMRT) using rotational beams. During delivery, the field shape, formed by a multileaf collimator (MLC), changes constantly. The objectives of this study were to ( 1 ) clinically implement the IMAT technique, and ( 2 ) evaluate the dosimetry in comparison with conventional three-dimensional (3D) conformal techniques. Methods and Materials: Forward planning with a commercial system (RenderPlan 3D, Precision Therapy International, Inc., Norcross, GA) was used for IMAT planning. Arcs were approximated as multiple shaped fields spaced every 5–10° around the patient. The number and ranges of the arcs were chosen manually. Multiple coplanar, superimposing arcs or noncoplanar arcs with or without a wedge were allowed. For comparison, conventional 3D conformal treatment plans were generated with the same commercial forward planning system as for IMAT. Intensity-modulated treatment plans were also created with a commercial inverse planning system (CORVUS, Nomos Corporation). A leaf-sequencing program was developed to generate the dynamic MLC prescriptions. IMAT treatment delivery was accomplished by programming the linear accelerator (linac) to deliver an arc and the MLC to step through a sequence of fields. Both gantry rotation and leaf motion were enslaved to the delivered MUs. Dosimetric accuracy of the entire process was verified with phantoms before IMAT was used clinically. For each IMAT treatment, a dry run was performed to assess the geometric and dosimetric accuracy. Both the central axis dose and dose distributions were measured and compared with predictions by the planning system. Results: By the end of May 2001, 50 patients had completed their treatments with the IMAT technique. Two to five arcs were needed to achieve highly conformal dose distributions. The IMAT plans provided better dose uniformity in the target and lower doses to normal structures than 3D conformal plans. The results varied when the comparison was made with fixed gantry IMRT. In general, IMAT plans provided more uniform dose distributions in the target, whereas the inverse-planned fixed gantry treatments had greater flexibility in controlling dose to the critical structures. Because the field sizes and shapes used in the IMAT were similar to those used in conventional treatments, the dosimetric uncertainty was very small. Of the first 32 patients treated, the average difference between the measured and predicted doses was −0.54 ± 1.72% at isocenter. The 80%–95% isodose contours measured with film dosimetry matched those predicted by the planning system to within 2 mm. The planning time for IMAT was slightly longer than for generating conventional 3D conformal plans. However, because of the need to create phantom plans for the dry run, the overall planning time was doubled. The average time a patient spent on the table for IMAT treatment was similar to conventional treatments. Conclusion: Initial results demonstrated the feasibility and accuracy of IMAT for achieving highly conformal dose distributions for different sites. If treatment plans can be optimized for IMAT cone beam delivery, we expect IMAT to achieve dose distributions that rival both slice-based and fixed-field IMRT techniques. The efficient delivery with existing linac and MLC makes IMAT a practical choice.

A new treatment technique, intensity modulated arc therapy (IMAT), has been implemented in the authors' clinical practice. Instead of delivering intensity-modulated beams with fixed gentry angles, IMAT delivers optimized dose distributions using rotational beams. During delivery, the field shape, which is formed by a multileaf collimator (MLC), changes constantly. Treatment plans are developed with a combination of forward and inverse planning. Arcs are approximated as multiple shaped fields spaced every 10 degrees around the patient. Multiple coplanar or non-coplanar arcs are used in combination with wedges. The beam weights can be optimized outside of the commercial planning system. A leaf-sequencer is used to convert the fields from the final plan into MLC leaf sequences. Comparisons were made with conventional and inversely optimized treatment plans. Dosimetric accuracy of the entire process was verified with phantoms before IMAT was used clinically. Patient-specific verifications were performed using both the absolute and relative dose measurements in a humanoid phantom. The authors have demonstrated the clinical feasibility and accuracy of IMAT treatments on patients with head and neck cancers. Generally, no more than 3 arcs are needed to achieve a conformal dose distribution. The complexity of the IMAT is not significantly greater than existing are therapy from the point of view of the operator. The treatment time using IMAT is similar to conventional treatments. Clinical examples of IMAT treatments will be presented to illustrate the dosimetric advantage of rotational delivery.

Intensity-modulated arc therapy, or MAT, is one of the methods for delivering intensity-modulated radiation treatments to achieve high dose conformity. Instead of delivering intensity-modulated beams with fixed gantry angles [1], IMAT delivers optimized dose distributions by rotating the radiation beam around the patient. During delivery, the field shape, which is formed by a multileaf collimator (MLC), changes constantly as determined by the required intensity distributions at different beam angles. Intensity distributions at all angles around the patient are achieved with multiple overlapping arcs of different field apertures and gantry speed. Therefore, IMAT is also different from tomotherapy[2,3], which use intensity modulated fan beams rotating around the patient to delivery the treatment slice-by-slice. As with tomotherapy, IMAT combines intensity modulation and rotational delivery. Detailed description of the technique was reported by Yu in a previous article [4].