Stable manifolds and homoclinic points near resonances in the restricted three-body problem

The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers $p$ and $q$, if its period around the heavier primary is approximately $2\pi p/q$, and by its approximate eccentricity $e$. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with $q/p$ equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any $\mu$ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for $\mu$ small enough in the unaveraged restricted three-body problem

Ethische Fallbesprechungen auf der Intensivstation: Vom Versuch zur Routine

Zusammenfassung: Hintergrund: Der Berufsalltag vieler Mitarbeitender im Gesundheitswesen ist in den letzten Jahren anspruchsvoller geworden, und die Anforderungen werden immer größer. Häufig stellen sich neben rein fachlichen auch ethische Fragen, z.B. nach der Sinnhaftigkeit einer Therapie am Lebensende. So genannte "medical futility", eine nutzlose, aussichtslose Therapie, wird von Pflegenden und Ärzten auf Intensivstationen häufig wahrgenommen. Das medizinethische Modell METAP (Akronym aus Module, Ethik, Therapieentscheidung, Allokation und Prozess) stellt Verfahren und Kriterien zur Verfügung, die es dem Behandlungsteam ermöglichen, diese Fragen gemeinsam, eigenständig und lösungsorientiert zu bearbeiten. Material und Methode: Alle Protokolle der 44 ethischen Fallbesprechungen (eFB), die zwischen Januar 2011 und Juni 2012 auf einer chirurgischen Intensivstation stattfanden, wurden zusammengefasst. Ein kurzer Fragebogen an alle Teilnehmenden erfasste deren Beurteilung des Nutzens für den Patienten und das Team sowie die Wahrnehmung der Reduktion persönlicher Belastung. Ergebnisse: Interprofessionelle eFB finden regelmäßig statt (ca. 2/Monat). Von den 41 in der eFB behandelten Patienten verstarben im Verlauf 23. Die Befragten (Rücklaufquote 52 %) schätzen den Nutzen für Patienten und Team als hoch ein (Ärzte etwas höher als Pflegende). Mehr als zwei Drittel der Pflegenden und die Hälfte der Ärzte nehmen eine Reduktion der Belastung durch die eFB wahr. Schlussfolgerungen: Eine methodisch strukturierte ethische Entscheidungsfindung kann in die klinische Routine integriert werden, wenn sie einen festen Platz im Alltag erhält, die ärztliche und die pflegerische Leitung die Implementierung unterstützen sowie die Verantwortung für die Organisation und Durchführung festgelegt ist

Klinische Alltagsethik - Unterstützung im Umgang mit moralischem Disstress?: Evaluation eines ethischen Entscheidungsfindungsmodells für interprofessionelle klinische Teams

Zusammenfassung: Hintergrund: Hochleistungsmedizin und Kostenrationierung können zu moralischem Disstress und Burn-out-Syndromen führen - mit z.T. schwerwiegenden Konsequenzen für die direkt Betroffenen, die Qualität der Patientenversorgung und die Institutionen. Das multimodale Modell METAP (Modul, Ethik, Therapieentscheide, Allokation, Prozess) wurde als maßgeschneiderte klinische Alltagsethik entwickelt und unterstützt die interprofessionelle ethische Entscheidungsfindung. Die Besonderheit des Modells liegt in der Ausbildung einer Ethikkompetenz im Umgang mit schwierigen Therapieentscheiden. METAP wurde zur Qualitätsprüfung evaluiert. Methode: Es wurde untersucht, ob METAP im Umgang mit moralischem Disstress Unterstützung bietet. Auf 3 intensivmedizinischen und 3 geriatrischen Abteilungen wurden 24 Ärzte, 44 Pflegende und 9 Personen anderer Berufsgruppen in 33 Einzel- und 9 Gruppeninterviews befragt. Ein zusätzlicher Fragebogen wurde von 122 Personen (Rücklauf: 57 %) beantwortet. Ergebnisse: Zwei Drittel der Interview- sowie 55 % der Fragebogenaussagen zeigen, dass durch METAP als klinische Alltagsethik der Umgang mit moralischem Disstress unterstützt wird. Dies gilt v.a. in der interdisziplinären Kommunikation und Zusammenarbeit sowie der Explikation und Evaluation von Behandlungszielen. METAP wirkt bei Personen, die selten mit ethischen Problemen konfrontiert sind oder das Verfahren noch nicht lange genug anwenden, nicht unterstützend. Schlussfolgerungen: Moralischer Disstress ist bis zu einem gewissen Grad unvermeidbar und muss als interprofessionelles Problem angegangen werden. Eine klinische Alltagsethik zur Förderung von ethischer Entscheidungskompetenz kann gezielte Unterstützung leisten

How to introduce medical ethics at the bedside - Factors influencing the implementation of an ethical decision-making model

BACKGROUND: As the implementation of new approaches and procedures of medical ethics is as complex and resource-consuming as in other fields, strategies and activities must be carefully planned to use the available means and funds responsibly. Which facilitators and barriers influence the implementation of a medical ethics decision-making model in daily routine? Up to now, there has been little examination of these factors in this field. METHODS: A medical ethics decision-making model called METAP was introduced on three intensive care units and two geriatric wards. An evaluation study was performed from 7 months after deployment of the project until two and a half years. Quantitative and qualitative methods including a questionnaire, semi-structured face-to-face and group-interviews were used. RESULTS: Sixty-three participants from different professional groups took part in 33 face-to-face and 9 group interviews, and 122 questionnaires could be analysed. The facilitating factors most frequently mentioned were: acceptance and presence of the model, support given by the medical and nursing management, an existing or developing (explicit) ethics culture, perception of a need for a medical ethics decision-making model, and engaged staff members. Lack of presence and acceptance, insufficient time resources and staff, poor inter-professional collaboration, absence of ethical competence, and not recognizing ethical problems were identified as inhibiting the implementation of the METAP model. However, the results of the questionnaire as well as of explicit inquiry showed that the respondents stated to have had enough time and staff available to use METAP if necessary. CONCLUSIONS: Facilitators and barriers of the implementation of a medical ethics decision-making model are quite similar to that of medical guidelines. The planning for implementing an ethics model or guideline can, therefore, benefit from the extensive literature and experience concerning the implementation of medical guidelines. Lack of time and staff can be overcome when people are convinced that the benefits justify the effort

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries