Scattering states of coupled valence-band holes in point defect potential derived from variable phase theory

In this article we present a method to compute the scattering states of holes in spherical bands in the strong spin-orbit coupling regime. More precisely, we calculate scattering phase shifts and amplitudes of holes induced by defects in a semiconductor crystal. We follow a previous work done on this topic by Ralph [H. I. Ralph, Philips Res. Rept. 32 160 (1977)] to account for the p-wave nature and the coupling of valence band states. We extend Ralph's analysis to incorporate finite-range potentials in the scattering problem. We find that the variable phase method provides a very convenient framework for our purposes and show in detail how scattering amplitudes and phase shifts are obtained. The Green's matrix of the Schroedinger equation, the Lippmann-Schwinger equation and the Born approximation are also discussed. Examples are provided to illustrate our calculations with Yukawa type potentials.Comment: 16 pages and 9 figure

Coulomb singularities in scattering wave functions of spin-orbit-coupled states

We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular momenta such that $\Delta l = 0, \pm 2$. In these conditions, the two radial functions, components of a partial wave associated to two values of the angular momentum $l$, satisfy a system of two second-order ordinary differential equations. We examine the difficulties arising in the analysis of the behavior of the regular solutions near the origin because of this coupling. First, we demonstrate that for a singularity of the first kind in the potential, one of the solutions is not amenable to a power series expansion. The use of the Lippmann-Schwinger equations confirms this fact: a logarithmic divergence arises at the second iteration. To overcome this difficulty, we introduce two auxilliary functions which, together with the two radial functions, satisfy a system of four first-order differential equations. The reduction of the order of the differential system enables us to use a matrix-based approach, which generalizes the standard Frobenius method. We illustrate our analysis with numerical calculations of coupled scattering wave functions in a solid-state system

Hemoadsorption in ‘liver indication’: analysis of 109 patients’ data from the CytoSorb international registry

Background: Our aim is to report the results of the ‘liver indication’ subset of patients in the CytoSorb International Registry. Methods: Structured data were recorded. Treatment characteristics and changes from T1 (start of hemoadsorption) to T2 (termination) were evaluated with a special focus on bilirubin, C-reactive protein, procalcitonin, interleukin-6, platelet levels, SOFA scores, mortality, and subjective assessment by the attending physicians. Results: Until January 2021, from the total 1434 patients, 109 (age: 49.2 ± 17.1 years, 57.8% males) received treatment for hyperbilirubinemia. APACHE II-predicted mortality was 49.6 ± 26.8%. In the study, 91% of patients were alive at the termination of hemoadsorption and improvement was observed by the physicians in 75 cases. Overall, 65 (59.6%) patients died in the hospital, and 60 (55.0%) died in the ICU. Patients received a median of two treatments for a median of 43 h (interquartile range: 24–72 h) in total. Serum bilirubin levels reduced significantly to −4.6 (95% CI: −6.329 to −2.8) mg/dL. Thrombocytopenia was reported in four patients as an adverse event. Conclusions: We report the largest case series on hemoadsorption for ‘liver indication’ from the CytoSorb International Registry. The finding of significant bilirubin removal observed in our study could have substantial impact in designing and executing further studies on the effects of hemoadsorption in liver dysfunction, which are certainly warranted

The Functional Trajectory in Frail Compared With Non-frail Critically Ill Patients During the Hospital Stay

Background: Long-term outcome is determined not only by the acute critical illness but increasingly by the reduced functional reserve of pre-existing frailty. The patients with frailty currently account for one-third of the critically ill, resulting in higher mortality. There is evidence of how frailty affects the intrahospital functional trajectory of critically ill patients since prehospital status is often missing. Methods: In this prospective single-center cohort study at two interdisciplinary intensive care units (ICUs) at a university hospital in Germany, the frailty was assessed using the Clinical Frailty Scale (CFS) in the adult patients with critical illness with an ICU stay >24 h. The functional status was assessed using the sum of the subdomains "Mobility" and "Transfer" of the Barthel Index (MTB) at three time points (pre-hospital, ICU discharge, and hospital discharge). Results: We included 1,172 patients with a median age of 75 years, of which 290 patients (25%) were frail. In a propensity score-matched cohort, the probability of MTB deterioration till hospital discharge did not differ in the patients with frailty (odds ratio (OR) 1.3 [95% CI 0.8-1.9], p = 0.301), confirmed in several sensitivity analyses in all the patients and survivors only. Conclusion: The patients with frailty have a reduced functional status. Their intrahospital functional trajectory, however, was not worse than those in non-frail patients, suggesting a rehabilitation potential of function in critically ill patients with frailty

International registry on the use of the CytoSorb® adsorber in ICU patients : Study protocol and preliminary results

INTRODUCTION: The aim of this clinical registry is to record the use of CytoSorb(R) adsorber device in critically ill patients under real-life conditions. METHODS: The registry records all relevant information in the course of product use, e. g., diagnosis, comorbidities, course of the condition, treatment, concomitant medication, clinical laboratory parameters, and outcome (ClinicalTrials.gov Identifier: NCT02312024). Primary endpoint is in-hospital mortality as compared to the mortality predicted by the APACHE II and SAPS II score, respectively. RESULTS: As of January 30, 2017, 130 centers from 22 countries were participating. Data available from the start of the registry on May 18, 2015 to November 24, 2016 (122 centers; 22 countries) were analyzed, of whom 20 centers from four countries provided data for a total of 198 patients (mean age 60.3 +/- 15.1 years, 135 men [68.2%]). In all, 192 (97.0%) had 1 to 5 Cytosorb(R) adsorber applications. Sepsis was the most common indication for CytoSorb(R) treatment (135 patients). Mean APACHE II score in this group was 33.1 +/- 8.4 [range 15-52] with a predicted risk of death of 78%, whereas the observed mortality was 65%. There were no significant decreases in the SOFA scores after treatment (17.2 +/- 4.8 [3-24]). However interleukin-6 levels were markedly reduced after treatment (median 5000 pg/ml before and 289 pg/ml after treatment, respectively). CONCLUSIONS: This third interim report demonstrates the feasibility of the registry with excellent data quality and completeness from 20 study centers. The results must be interpreted with caution, since the numbers are still small; however the disease severity is remarkably high and suggests that adsorber treatment might be used as an ultimate treatment in life-threatening situations. There were no device-associated side effects

Hemoadsorption in the critically ill—Final results of the International CytoSorb Registry

The aim of the current paper is to summarize the results of the International CytoSorb Registry. Data were collected on patients of the intensive care unit. The primary endpoint was actual in-hospital mortality compared to the mortality predicted by APACHE II score. The main secondary endpoints were SOFA scores, inflammatory biomarkers and overall evaluation of the general condition. 1434 patients were enrolled. Indications for hemoadsorption were sepsis/septic shock (N = 936); cardiac surgery perioperatively (N = 172); cardiac surgery postoperatively (N = 67) and "other" reasons (N = 259). APACHE-II-predicted mortality was 62.0 +/- 24.8%, whereas observed hospital mortality was 50.1%. Overall SOFA scores did not change but cardiovascular and pulmonary SOFA scores decreased by 0.4 [-0.5;-0.3] and -0.2 [-0.3;-0.2] points, respectively. Serum procalcitonin and C-reactive protein levels showed significant reduction: -15.4 [-19.6;-11.17] ng/mL; -17,52 [-70;44] mg/L, respectively. In the septic cohort PCT and IL-6 also showed significant reduction: -18.2 [-23.6;-12.8] ng/mL; -2.6 [-3.0;-2.2] pg/mL, respectively. Evaluation of the overall effect: minimal improvement (22%), much improvement (22%) and very much improvement (10%), no change observed (30%) and deterioration (4%). There was no significant difference in the primary outcome of mortality, but there were improvements in cardiovascular and pulmonary SOFA scores and a reduction in PCT, CRP and IL-6 levels