Total roman domination number of graphs

In this paper a characterization of minimal total roman dominating functions has been proved. It has also been proved that if v is a pendant vertex and its neighbor u is not a pendant vertex then f(v) = 0 or 1 for any minimal total roman dominating function f. The operation of vertex removal has been considered. A necessary and sufficient condition under which the total roman domination number increases (under this operation) has been proved. Similarly a necessary and sufficient condition has been proved under which the total roman domination number decreases. Some examples has been given with miscellaneous results. We characterize those graphs for which the total roman domination number is equal to the number of vertices of the graph.Publisher's Versio

Therapeutic mammoplasty: a “wise” oncoplastic choice—lessons from the largest single-center cohort from Asia

IntroductionThe majority of breast cancer patients from India usually present with advanced disease, limiting the scope of breast conservation surgery. Therapeutic mammoplasty (TM), an oncoplastic technique that permits larger excisions, is quite promising in such a scenario and well suited to breast cancer in medium-to-large-sized breasts with ptosis and in some cases of large or multifocal/multicentric tumors. Here, we describe our TM cohort of 205 (194 malignant and 11 benign) patients from 2012 to 2019 treated at a single surgeon center in India, the largest Asian dataset for TM.MethodsAll patients underwent treatment after careful discussions by a multidisciplinary tumor board and patient counseling. We report the clinicopathological profiles and surgical, oncological, cosmetic, and patient-related outcomes with different TM procedures.ResultsThe median age of breast cancer patients was 49 years; that of benign disease patients was 41 years. The breast cancer cohort underwent simple (n = 84), complex (n = 71), or extreme (n = 44) TM surgeries. All resection margins were analyzed through intra-operative frozen-section assessment with stringent rad-path analysis protocols. The margin positivity rate was found to be 1.4%. A majority of the cohort was observed to have pT1–pT2 tumors, and the median resection volume was 180 cc. Low post-operative complication rates and good-to-excellent cosmetic scores were observed. The median follow-up was 39 months. We observed 2.07% local and 5.7% distal recurrences, and disease-specific mortality was 3.1%. At median follow-up, the overall survival was observed to be 95.9%, and disease-free survival was found to be 92.2%. The patient-reported outcome measures (PROMs) showed good-to-excellent scores for all types of TMs across BREAST-Q domains.ConclusionWe conclude that in India, a country where women present with large and locally advanced tumors, TM safely expands the indications for breast conservation surgery. Our results show oncological and cosmetic outcomes at acceptable levels. Most importantly, PROM scores suggest improved overall wellbeing and better satisfaction with the quality of life. For patients with macromastia, this technique not only focuses on cancer but also improves self-image and reduces associated physical discomfort often overlooked by women in the Indian setting. The popularization of this procedure will enable Indian patients with breast cancer to receive the benefits of breast conservation

Pre-Intubation Veno-Venous Extracorporeal Membrane Oxygenation in Patients at Risk for Respiratory Decompensation

Veno-venous extracorporeal membrane oxygenation (VV-ECMO) has emerged as a potential life-saving treatment for patients with acute respiratory failure. Given the accumulating literature supporting the use of VV-ECMO without therapeutic levels of anticoagulation, it might be feasible to use it for planned intubation before surgical procedures. Here, we report consecutive series of patients who underwent planned initiation of VV-ECMO, without anticoagulation, before induction of general anesthesia for anticipated difficult airways or respiratory decompensation. We describe the approach to safely initiate VV-ECMO in an awake patient. We retrospectively identified patients in a prospectively maintained database who underwent planned initiation of VV-ECMO before intubation. Standard statistical methods were used to determine post-procedure outcomes. Patients included were three men and one woman, with a mean age of 34.3 ± 10.4 years. Indications included mediastinal lymphoma, foreign body obstruction, hemoptysis, and tracheo-esophageal fistula. VV-ECMO was initiated electively for all patients, and no anticoagulation was used. The median duration of VV-ECMO support was 2.5 days (1–11 days), the median length of ventilator dependence and intensive care unit stay was 1 day (1–23 days) and 5 days (4–31 days), respectively. The median length of stay was 18.5 days (8–39 days). There were no thrombotic complications and no mortality at 30 days. Initiation of awake VV-ECMO is feasible and is safe before intubation and induction of anesthesia in patients at high risk for respiratory decompensation

Timing of Intubation in Coronavirus Disease 2019: A Study of Ventilator Mechanics, Imaging, Findings, and Outcomes

Objectives:. Determine the variation in outcomes and respiratory mechanics between the subjects who are intubated earlier versus later in their coronavirus disease 2019 course. Design:. Retrospective cohort study. Setting:. Northwestern Memorial Hospital ICUs. Patients:. All patients intubated for coronavirus disease 2019 between March 2020 and June 2020. Interventions:. Patients were stratified by time to intubation: 30 subjects were intubated 4–24 hours after presentation and 24 subjects were intubated 5–10 days after presentation. Baseline characteristics, hospitalization, ventilator mechanics, and outcomes were extracted and analyzed. Ten clinically available CT scans were manually reviewed to identify evidence of pulmonary vascular thrombosis and intussusceptive angiogenesis. Measurements and Main Results:. Median time from symptom onset to intubation was significantly different between the early and late intubation cohorts, with the latter being intubated later in the course of their illness (7.9 vs 11.8 d; p = 0.04). The early intubation cohort had a lower mortality rate than the late intubation cohort (6% vs 30%, p < 0.001) without significantly different respiratory mechanics at the time of intubation. The late intubation cohort was noted to have higher dead space ratio (0.40 vs 0.52; p = 0.03). On review of CT scans, the late intubation cohort also had more dilated peripheral segments on imaging (two segments vs five segments). Conclusions:. The question as to whether delaying intubation is beneficial or harmful for patients with coronavirus disease 2019-induced hypoxemic respiratory failure has yet to be answered. As our approaches to coronavirus disease 2019 continue to evolve, the decision of timing of intubation remains paramount. Although noninvasive ventilation may allow for delaying intubation, it is possible that there are downstream effects of delayed intubation that should be considered, including the potential for pulmonary vascular thrombosis and intussusceptive angiogenesis with delayed intubation