The formally exact framework of equilibrium Density Functional Theory (DFT) is capable of simultaneously and consistently describing thermodynamic and structural properties of interacting many-body systems in arbitrary external potentials. In practice, however, DFT hinges on approximate (free-)energy functionals from which density profiles (and hence the thermodynamic potential) follow via an Euler–Lagrange equation. Here, we explore a relatively simple Machine-Learning (ML) approach to improve the standard mean-field approximation of the excess Helmholtz free-energy functional of a 3D Lennard-Jones system at a supercritical temperature. The learning set consists of density profiles from grand-canonical Monte Carlo simulations of this system at varying chemical potentials and external potentials in a planar geometry only. Using the DFT formalism, we nevertheless can extract not only very accurate 3D bulk equations of state but also radial distribution functions using the Percus test-particle method. Unfortunately, our ML approach did not provide very reliable Ornstein–Zernike direct correlation functions for small distances.
Background and purposeTo quantify the increase in bladder and rectum dose of a bone marrow sparing (BMS) VMAT strategy for primary treatment of locally advanced cervical cancer (LACC).Materials and methodsTwenty patients with stage IB-IVA cervical cancer were selected for this study. The whole Pelvic Bones (PB) was taken as substitute for bone marrow. For every patient, Pareto-optimal plans were generated to explore the trade-off between rectum, bladder, and PB mean dose. The PB mean dose was decreased in steps of 1 Gy. For each step, the increase in rectum and bladder mean dose was quantified. The increase in mean dose of other OAR compared to no BMS was constrained to 1 Gy.ResultsIn total, 931 plans of 19 evaluable patients were analyzed. The average [range] mean dose of PB without BMS was 22.8 [20.7-26.2] Gy. When maximum BMS was applied, the average reduction in mean PB dose was 5.4 [3.0-6.8] Gy resulting in an average mean PB dose of 17.5 [15.8-19.8] Gy. For <1 Gy increase in both the bladder and the rectum mean dose, the PB mean dose could be decreased by >2 Gy, >3 Gy, >4 Gy, and >5 Gy for 19/19, 13/19, 5/19, and 1/19 patients, respectively.ConclusionBased on the comprehensive three-dimensional Pareto front analysis, we conclude that 2-5 Gy BMS can be implemented without a clinically relevant increase in mean dose to other OAR. If BMS is too dominant, it results in a large increase in mean dose to other OAR. Therefore, we recommend implementing moderate BMS for the treatment of LACC patients with VMAT.
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