Implementations of modulation complexity scores and their correlations with treatment plan quality in stereotactic...

During the delivery of contemporary stereotactic radiation therapy treatment, the radiation dose is dynamically shaped by the multileaf collimator (MLC). The modulation complexity score (MCS) is a metric that quantifies MLC apertures. However, inconsistent definitions of the MCS have been introduced in the literature. Furthermore, investigations of correlations between complexity metrics and dosimetric plan quality remain scarce.

We aim to highlight differences between MCS definitions and assess their correlation with treatment plan quality in curated datasets of stereotactic radiation therapy treatment plans.

Volumetric modulated arc therapy treatment plans from planning challenges of multi-metastasis stereotactic radiosurgery (SRS), pancreas stereotactic ablative body radiotherapy (SABR), and vertebral SABR were considered. According to the challenge guidelines, the quality of each plan was scored from 0 to 150. To quantify complexity, the two most used interpretations of the MCS were computed. In the first interpretation (beamMCS), the area aperture variability (AAV) was normalized by a virtual area constructed with the most open position of each leaf over all control points of the arc. In the second interpretation (cpMCS), the AAV was normalized by the virtual maximal leaf opening in each control point. Each quantity ranged between 0 (complex plan) and 1 (not complex plan). The Spearman correlation coefficient ( $r_s$ ) and its associated p-value were calculated between MCS and plan score. The process was repeated by stratifying the data per site, treatment planning system (TPS), and MLC type (conventional versus high definition).

The plans of 366 treatments were considered in the SRS (n = 107), pancreas (n = 137), and vertebral (n = 122) planning challenge. The plan score ranged from 86.2 to 148.3 (median = 135). All plans considered, the complexity was higher with beamMCS than cpMCS (median $\pm$ interquartile range IQR) = 0.13 $\pm$ 0.11/0.19 $\pm$ 0.11 with beamMCS/cpMCS, p-value 0.001). The beamMCS was weakly correlated with plan score ( $r_s$ = 0.14, p-value 0.01) whilst the correlation was not statistically significant with cpMCS (p-value $>$ 0.17). SRS plans were the more complex whilst vertebral plans were the less complex in both interpretations. The beamMCS and the score were positively correlated in 2/5 TPS and with the conventional MLC. The cpMCS and the score were negatively correlated in the three challenges and 1/5 TPS. All other correlations were not statistically significant.

The two MCS interpretations yielded conflicting correlations with plan scores. The cpMCS was superior in assessing plan quality in this set of SRS and SABR plans. As complexity metrics may be useful tools in treatment planning optimization, standardization in their numerical implementation would be preferable.