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[en] We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function. Several closely related results are also given.
[en] Purpose: The widespread use of intensity modulated radiation therapy (IMRT) for cervical cancer has been limited by internal target and normal tissue motion. Such motion increases the risk of underdosing the target, especially as planning margins are reduced in an effort to reduce toxicity. This study explored 2 adaptive strategies to mitigate this risk and proposes a new, automated method that minimizes replanning workload. Methods and Materials: Thirty patients with cervical cancer participated in a prospective clinical study and underwent pretreatment and weekly magnetic resonance (MR) scans over a 5-week course of daily external beam radiation therapy. Target volumes and organs at risk (OARs) were contoured on each of the scans. Deformable image registration was used to model the accumulated dose (the real dose delivered to the target and OARs) for 2 adaptive replanning scenarios that assumed a very small PTV margin of only 3 mm to account for setup and internal interfractional motion: (1) a preprogrammed, anatomy-driven midtreatment replan (A-IMRT); and (2) a dosimetry-triggered replan driven by target dose accumulation over time (D-IMRT). Results: Across all 30 patients, clinically relevant target dose thresholds failed for 8 patients (27%) if 3-mm margins were used without replanning. A-IMRT failed in only 3 patients and also yielded an additional small reduction in OAR doses at the cost of 30 replans. D-IMRT assured adequate target coverage in all patients, with only 23 replans in 16 patients. Conclusions: A novel, dosimetry-triggered adaptive IMRT strategy for patients with cervical cancer can minimize the risk of target underdosing in the setting of very small margins and substantial interfractional motion while minimizing programmatic workload and cost