Although Bortfeld's analytical formula is useful for describing Bragg curves, measured data can deviate from the values predicted by the model. Thus, we sought to determine the parameters of a closed analytical expression of multiple Bragg curves for scanning proton pencil beams using a simultaneous optimization algorithm and to determine the minimum number of energies that need to be measured in treatment planning so that complete Bragg curves required by the treatment planning system (TPS) can be accurately predicted. We modified Bortfeld's original analytical expression of Bragg curves to accurately describe the dose deposition resulting from secondary particles. The parameters of the modified analytical expression were expressed as the parabolic cylinder function of the ranges of the proton pencil beams in water. Thirty-nine discrete Bragg curves were measured in our center using a PTW Bragg Peak chamber during acceptance and commission of the scanning beam proton delivery system. The coefficients of parabolic function were fitted by applying a simultaneous optimization algorithm to seven measured curves. The required Bragg curves for 45 energies in the TPS were calculated using our parameterized analytical expression. Finally, the 10 cm width of spread-out Bragg peaks (SOBPs) of beams with maximum energies of 221.8 and 121.2 MeV were then calculated in the TPS and compared with measured data. Compared with Bortfeld's original formula, our modified formula improved fitting of the measured depth dose curves at depths around three-quarters of the maximum range and in the beam entrance region. The parabolic function described the relationship between the parameters of the analytic expression of different energies. The predicted Bragg curves based on the parameters fitted using the seven measured curves accurately described the Bragg curves of proton pencil beams of 45 energies configured in our TPS. When we used the calculated Bragg curves as the input to TPS, the standard deviations of the measured and calculated data points along the 10 cm SOBPs created with proton pencil beams with maximum energies of 221.8 and 121.2 MeV were 1.19% and 1.18%, respectively, using curves predicted by the algorithm generated from the seven measured curves. Our method would be a valuable tool to analyze measured Bragg curves without the need for time-consuming measurements and correctly describe multiple Bragg curves using a closed analytical expression.

Three-dimensional photography is a useful tool enabling the plastic surgeon to monitor the postoperative changes in breast morphology objectively. This study provides quantifiable data demonstrating that pseudoptosis and tissue redistribution are limited to the initial postoperative year for patients undergoing short-scar medial pedicle breast reduction. The kinetic change in the breasts during postoperative years 2 and 3 appears to be minimal. Studies comparing the changes in morphology over time with different techniques of breast reduction are underway.

Objective There are limited published data on the transmission of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus from mothers to newborns through breastfeeding or from breast milk. The World Health Organization released guidelines encouraging mothers with suspected or confirmed COVID-19 to breastfeed as the benefits of breastfeeding outweighs the possible risk of transmission. The objective of this study was to determine if SARS-CoV-2 was present in the breast milk of lactating mothers who had a positive SARS-CoV-2 nasopharyngeal swab test prior to delivery, and the clinical outcomes for their newborns. Study Design This was a single-center, observational, prospective cohort study. Maternal–newborn dyads that delivered at New York University Langone Hospital Brooklyn with confirmed maternal SARS-CoV-2 positive screen test at the time of admission were recruited for the study. Breast milk samples were collected during postpartum hospitalization and tested for the presence of SARS-CoV-2 genes N1 and N2 by two-step reverse transcription polymerase chain reaction. Additionally, the clinical characteristics of the maternal newborn dyad, results of nasopharyngeal SARS-CoV-2 testing, and neonatal follow-up data were collected. Results A total of 19 mothers were included in the study and their infants who were all fed breast milk. Breast milk samples from 18 mothers tested negative for SARS-CoV-2, and 1 was positive for SARS-CoV-2 RNA. The infant who ingested the breast milk that tested positive had a negative nasopharyngeal test for SARS-CoV-2, and had a benign clinical course. There was no evidence of significant clinical infection during the hospital stay or from outpatient neonatal follow-up data for all the infants included in this study. Conclusion In a small cohort of SARS-CoV-2 positive lactating mothers giving birth at our institution, most of their breast milk samples (95%) contained no detectable virus, and there was no evidence of COVID-19 infection in their breast milk-fed neonates. Key Points