Los números

128 páginas.La teoría de los números ocupa un peculiar y distinguido lugar entre las diversas ramas de las matemáticas. Que su objetivo principal sea el estudio de algo tan conocido y familiar como son los enteros, sus propiedades y sus relaciones, explica el interés que ha suscitado siempre entre muchos ciudadanos, quienes, aun careciendo de la formación matemática apropiada, se sienten fascinados por sus problemas, tan fáciles de enunciar y, sin embargo, tan difíciles a veces de resolver. Este libro no pretende ser, ni mucho menos, un tratado de la teoría de los números, sino tan sólo un vehículo que permita al lector pasear por algunos de sus parajes más asequibles. Una especie de guía turística para aritméticos aficionados y para todos aquellos que tengan curiosidad acerca de las propiedades de los números y aprecien el arte de engarzar las ideas que conlleva todo razonamiento matemático.Peer reviewe

Monitoring activated clotting time for combined heparin and aprotinin application: in vivo evaluation of a new aprotinin-insensitive test using Sonoclot

Objective: Kaolin-based activated clotting time assessed by HEMOCHRON (HkACT) is a clinical standard for heparin monitoring alone and combined with aprotinin during cardiopulmonary bypass (CPB). However, aprotinin is known to prolong not only celite-based but also kaolin-based activated clotting time. Overestimation of activated clotting times implies a potential hazardous risk of subtherapeutic heparin anticoagulation. Recently, a novel ‘aprotinin-insensitive' activated clotting time test has been developed for the SONOCLOT analyzer (SaiACT). The aim of our study was to evaluate SaiACT in patients undergoing CPB in presence of heparin and aprotinin. Methods: Blood samples were taken from 44 elective cardiac surgery patients at the following measurement time points: baseline (T0); before CPB after heparinization (T1 and T2); on CPB, before administration of aprotinin (T3); 15, 30, and 60min on CPB after administration of aprotinin (T4, T5, and T6); after protamine infusion (T7). On each measurement time point, activated clotting time was assessed with HkACT and SaiACT, both in duplicate. Furthermore, the rate of factor Xa inhibition and antithrombin concentration were measured. Statistical analysis was done using Bland and Altman analysis, Pearson's correlation, and ANOVA with post hoc Bonferroni-Dunn correction. Results: Monitoring anticoagulation with SaiACT showed reliable readings. Compared to the established HkACT, SaiACT values were lower at all measurement time points. On CPB but before administration of aprotinin (T3), SaiACT values (mean±SD) were 44±118s lower compared to HkACT. However, the difference between the two measurement techniques increased significantly on CPB after aprotinin administration (T4-T6; 89±152s, P=0.032). Correlation of ACT measurements with anti-Xa activity was unchanged for SaiACT before and after aprotinin administration (r2=0.473 and 0.487, respectively; P=0.794), but was lower for HkACT after aprotinin administration (r2=0.481 and 0.361, respectively; P=0.041). On CPB after administration of aprotinin, 96% of all ACT values were classified as therapeutic by HkACT, but only 86% of all values were classified therapeutic if ACT was determined by SaiACT. Test variability was comparable for SaiACT and HkACT. Conclusions: The use of SaiACT may result in more consistent heparin management that is less affected by aprotinin and a corresponding increase in heparin administration for patients receiving aprotini

Screening for Incidental Sars-Cov-2 Infection in a Neurocritical Care Unit: A Longitudinal Diagnostic Prediction Model

Background: Rapid diagnosis of SARS-CoV-2 infection in patients not primarily assigned with the diagnosis of COVID-19 is highly relevant to effectively rule out virus transmission among patients and medical staff. The purpose is to develop a model for the prediction of the actual presence of a SARS-CoV-2 infection before a valid test result is available and to avoid unnecessary testing in Critical Care Units. Methods: Datasets of laboratory and blood gas analysis tests were collected retrospectively for the development and subsequent validation of machine learning (ML) based models. The data set was composed of 1. 254 SARS-CoV-2 positive cases, collected in an ICU dedicated to patients with COVID-19 pneumonia, 2a. 914 SARS-CoV-2 negative patients treated in a Neurocritical Care Unit and 2b. 32 patients treated for severe influenza pneumonia in a Medical ICU at the same hospital. The models were subsequently validated on a dataset collected from the Neurocritical Care Unit that consisted of data from 7 positive and 42 negative patients. Models were adapted to newly available laboratory values throughout their ICU stay. Extremely Randomized Trees (ERT) and Random Forest (RF) models were evaluated. A baseline model comprising fully grown trees, an optimized model including optimal values for the maximum depth, and a simplified model that only uses the 6 most important features were trained. Results: The overall best model, evaluated via crossvalidation on the development set, is an optimized ERT model with a ROC AUC value of 0.946. The model performance on the validation set is best for the simplified RF model achieving a ROC AUC value of 0.701. Gini feature and permutation importance for the simplified RF model revealed hemoglobin, procalcitonin, C-reactive protein, glomerular filtration rate based on CKD-EPI equation, creatinine, and urea as the most important input features. Using the simplified RF model and a threshold of 0.012 for the probability, a sensitivity above 80% with a specificity of 43% is achieved. Compared to a hypothetical daily testing regimen, using a threshold of 0.145, the simplified RF model detects all positive cases, and, with a false positive rate of 35%, daily tests might be reduced by two thirds. Conclusions: The model developed may support the medical staff in the ICUs by enabling faster and more reliable recognition of COVID-19. Unnecessary serial test sampling might be reduced. To ensure the quality of the model before clinical use, it should be further validated in prospective patient cohorts

Elimination of Herpes Simplex Virus-2 and Epstein-Barr Virus With Seraph 100 Microbind Affinity Blood Filter and Therapeutic Plasma Exchange: An Explorative Study in a Patient With Acute Liver Failure

OBJECTIVES Herpes simplex virus (HSV)-2 is a rare cause of hepatitis that can lead to acute liver failure (ALF) and often death. The earlier the initiation of acyclovir treatment the better the survival. With regard to ALF, controlled randomized data support the use of therapeutic plasma exchange (TPE) both as bridge to recovery or transplantation-possibly by modulating the systemic inflammatory response and by replacing coagulation factors. Seraph 100 Microbind Affinity Blood Filter (Seraph; Ex Thera Medical, Martinez, CA), a novel extracorporeal adsorption device, removes living pathogens by binding to a heparin-coated surface was shown to efficiently clear HSV-2 particles in vitro. Here, we tested the combination of Seraph with TPE to reduce a massive HSV-2 viral load to reach a situation in that liver transplantation would be feasible. DESIGN Explorative study. SETTING Academic tertiary care transplant center. PATIENT Single patient with HSV-2-induced ALF. INTERVENTIONS TPE + Seraph 100 Microbind Affinity Blood Filter. MEASUREMENTS AND MAIN RESULTS We report Seraph clearance data of HSV-2 and of Epstein-Barr virus (EBV) in vivo as well as total viral elimination by TPE. Genome copies/mL of HSV-2 and EBV in EDTA plasma were measured by polymerase chain reaction every 60 minutes over 6 hours after starting Seraph both systemically and post adsorber. Also, HSV-2 and EBV were quantified before and after TPE and in the removed apheresis plasma. We found a total elimination of 1.81 × e$^{11}$ HSV-2 copies and 2.11 × e$^{6}$ EBV copies with a single TPE (exchange volume of 5L; 1.5× calculated plasma volume). Whole blood clearance of HSV-2 in the first 6 hours of treatment was 6.64 mL/min (4.98-12.92 mL/min). Despite much lower baseline viremia, clearance of EBV was higher 36.62 mL/min (22.67-53.48 mL/min). CONCLUSIONS TPE was able to remove circulating HSV-2 copies by 25% and EBV copies by 40% from the blood. On the other hand, clearance of HSV-2 by Seraph was clinically irrelevant, but Seraph seemed to be far more effective of removing EBV, implicating a possible use in EBV-associated pathologies, but this requires further study

Renal Tubular Acidosis in Pregnant Critically Ill COVID-19 Patients: A Secondary Analysis of a Prospective Cohort

Background: Renal tubular acidosis (RTA) is an extremely rare cause of metabolic acidosis (10 in 100,000). RTA has been linked neither to pregnancy nor to severe coronavirus disease 2019 (COVID-19). The purpose of this study was to analyze the prevalence and clinical course of normal anion gap metabolic acidosis in critically ill pregnant COVID-19 patients and to compare them to an age-matched nonpregnant female patient cohort. Methods: Secondary analysis was conducted on a prospective observational cohort of critically ill patients suffering from COVID-19 consecutively admitted to a tertiary intensive care unit (ICU) between February 2020 and April 2021. Results: A total of 321 COVID-19 patients required admission to the ICU; 95 (30%) were female, and 18 (19%) were of childbearing age. Seven of eight (88%) pregnant women (all in the last trimester) required advanced respiratory support due to COVID-19. The estimated glomerular filtration rate was 135 (123–158) mL/min/m$^{2}$ body surface area, and six pregnant women (86%) were diagnosed with a normal, respiratory compensated, anion gap metabolic acidosis (pH$_{min}$ 7.3 (7.18–7.31), HCO3−$_{min}$ 14.8 (12.8–18.6) mmol/L, and paCO2 3.4 (3.3–4.5) kPa). Three (43%) acidotic pregnant women fulfilled diagnostic criteria for RTA. All women recovered spontaneously within less 7 days. Conclusions: Metabolic acidosis seems to be very common (85%) in pregnant critically ill COVID-19 patients, and the prevalence of RTA might be higher than normal. It remains to be demonstrated if this observation is an indirect epiphenomenon or due to a direct viral effect on the tubular epithelium

Indications and Outcomes of Patients Receiving Therapeutic Plasma Exchange under Critical Care Conditions: A Retrospective Eleven-Year Single-Center Study at a Tertiary Care Center

Background: Therapeutic plasma exchange (TPE) is frequently performed in critical care settings for heterogenous indications. However, specific intensive care unit (ICU) data regarding TPE indications, patient characteristics and technical details are sparse. Methods: We performed a retrospective, single-center study using data from January 2010 until August 2021 for patients treated with TPE in an ICU setting at the University Hospital Zurich. Data collected included patient characteristics and outcomes, ICU-specific parameters, as well as apheresis-specific technical parameters and complications. Results: We identified n = 105 patients receiving n = 408 TPEs for n = 24 indications during the study period. The most common was thrombotic microangiopathies (TMA) (38%), transplant-associated complications (16.3%) and vasculitis (14%). One-third of indications (35.2%) could not be classified according to ASFA. Anaphylaxis was the most common TPE-related complication (6.7%), while bleeding complications were rare (1%). The median duration of ICU stay was 8 ± 14 days. Ventilator support, renal replacement therapy or vasopressors were required in 59 (56.2%), 26 (24.8%), and 35 (33.3%) patients, respectively, and 6 (5.7%) patients required extracorporeal membrane oxygenation. The overall hospital survival rate was 88.6%. Conclusion: Our study provides valuable real-world data on heterogenous TPE indications for patients in the ICU setting, potentially supporting decision-making

Pulse-pressure variation and hemodynamic response in patients with elevated pulmonary artery pressure: a clinical study

Pulse-pressure variation (PPV) due to increased right ventricular afterload and dysfunction may misleadingly suggest volume responsiveness. We aimed to assess prediction of volume responsiveness with PPV in patients with increased pulmonary artery pressure

OCT, Triple H oder doch etwas anderes? OCT, Triple H or anything else?

Die Hyperammonämie ist ein lebensbedrohliches Krankheitsbild, dessen Prognose von einer raschen Senkung des Ammoniaks abhängt. Ist eine hepatische Ursache ausgeschlossen, ist die Differenzialdiagnose breit und umfasst auch im Erwachsenenalter hereditäre Stoffwechselerkrankungen. Hier beschreiben wir den Fall einer 25-jährigen Patientin mit einer schweren, therapierefraktären Hyperammonämie und betonen die Relevanz der extrakorporalen Elimination des Ammoniaks

Visual Blood, Visualisation of Blood Gas Analysis in Virtual Reality, Leads to More Correct Diagnoses: A Computer-Based, Multicentre, Simulation Study

Interpreting blood gas analysis results can be challenging for the clinician, especially in stressful situations under time pressure. To foster fast and correct interpretation of blood gas results, we developed Visual Blood. This computer-based, multicentre, noninferiority study compared Visual Blood and conventional arterial blood gas (ABG) printouts. We presented six scenarios to anaesthesiologists, once with Visual Blood and once with the conventional ABG printout. The primary outcome was ABG parameter perception. The secondary outcomes included correct clinical diagnoses, perceived diagnostic confidence, and perceived workload. To analyse the results, we used mixed models and matched odds ratios. Analysing 300 within-subject cases, we showed noninferiority of Visual Blood compared to ABG printouts concerning the rate of correctly perceived ABG parameters (rate ratio, 0.96; 95% CI, 0.92–1.00; p = 0.06). Additionally, the study revealed two times higher odds of making the correct clinical diagnosis using Visual Blood (OR, 2.16; 95% CI, 1.42–3.29; p < 0.001) than using ABG printouts. There was no or, respectively, weak evidence for a difference in diagnostic confidence (OR, 0.84; 95% CI, 0.58–1.21; p = 0.34) and perceived workload (Coefficient, 2.44; 95% CI, −0.09–4.98; p = 0.06). This study showed that participants did not perceive the ABG parameters better, but using Visual Blood resulted in more correct clinical diagnoses than using conventional ABG printouts. This suggests that Visual Blood allows for a higher level of situation awareness beyond individual parameters’ perception. However, the study also highlighted the limitations of today’s virtual reality headsets and Visual Blood

Avatar-based patient monitoring improves information transfer, diagnostic confidence and reduces perceived workload in intensive care units: computer-based, multicentre comparison study

Patient monitoring is the foundation of intensive care medicine. High workload and information overload can impair situation awareness of staff, thus leading to loss of important information about patients’ conditions. To facilitate mental processing of patient monitoring data, we developed the Visual-Patient-avatar Intensive Care Unit (ICU), a virtual patient model animated from vital signs and patient installation data. It incorporates user-centred design principles to foster situation awareness. This study investigated the avatar’s effects on information transfer measured by performance, diagnostic confidence and perceived workload. This computer-based study compared Visual-Patient-avatar ICU and conventional monitor modality for the first time. We recruited 25 nurses and 25 physicians from five centres. The participants completed an equal number of scenarios in both modalities. Information transfer, as the primary outcome, was defined as correctly assessing vital signs and installations. Secondary outcomes included diagnostic confidence and perceived workload. For analysis, we used mixed models and matched odds ratios. Comparing 250 within-subject cases revealed that Visual-Patient-avatar ICU led to a higher rate of correctly assessed vital signs and installations [rate ratio (RR) 1.25; 95% CI 1.19–1.31; P < 0.001], strengthened diagnostic confidence [odds ratio (OR) 3.32; 95% CI 2.15–5.11, P < 0.001] and lowered perceived workload (coefficient − 7.62; 95% CI − 9.17 to − 6.07; P < 0.001) than conventional modality. Using Visual-Patient-avatar ICU, participants retrieved more information with higher diagnostic confidence and lower perceived workload compared to the current industry standard monitor