IMEX finite volume methods for the shallow water equations

Die Flachwassergleichungen (SWE) sind ein hyperbolisches System von Bilanzgleichungen, die adäquate Approximationen an groß-skalige Strömungen der Ozeane, Flüsse und der Atmosphäre liefern. Dabei werden Masse und Impuls erhalten. Wir unterscheiden zwei charakteristische Geschwindigkeiten: die Advektionsgeschwindigkeit, d.h. die Geschwindigkeit des Massentransports, und die Geschwindigkeit von Schwerewellen, d.h. die Geschwindigkeit der Oberflächenwellen, die Energie und Impuls tragen. Die Froude-Zahl ist eine Kennzahl und ist durch das Verhältnis der Referenzadvektionsgeschwindigkeit zu der Referenzgeschwindigkeit der Schwerewellen gegeben. Für die oben genannten Anwendungen ist sie typischerweise sehr klein, z.B. 0.01. Zeit-explizite Finite-Volume-Verfahren werden am öftersten zur numerischen Berechnung hyperbolischer Bilanzgleichungen benutzt. Daher muss die CFL-Stabilitätsbedingung eingehalten werden und das Zeitinkrement ist ungefähr proportional zu der Froude-Zahl. Deswegen entsteht bei kleinen Froude-Zahlen, etwa kleiner als 0.2, ein hoher Rechenaufwand. Ferner sind die numerischen Lösungen dissipativ. Es ist allgemein bekannt, dass die Lösungen der SWE gegen die Lösungen der Seegleichungen/ Froude-Zahl Null SWE für Froude-Zahl gegen Null konvergieren, falls adäquate Bedingungen erfüllt sind. In diesem Grenzwertprozess ändern die Gleichungen ihren Typ von hyperbolisch zu hyperbolisch.-elliptisch. Ferner kann bei kleinen Froude-Zahlen die Konvergenzordnung sinken oder das numerische Verfahren zusammenbrechen. Insbesondere wurde bei zeit-expliziten Verfahren falsches asymptotisches Verhalten (bzgl. der Froude-Zahl) beobachtet, das diese Effekte verursachen könnte.Ozeanographische und atmosphärische Strömungen sind typischerweise kleine Störungen eines unterliegenden Equilibriumzustandes. Wir möchten, dass numerische Verfahren für Bilanzgleichungen gewisse Equilibriumzustände exakt erhalten, sonst können künstliche Strömungen vom Verfahren erzeugt werden. Daher ist die Quelltermapproximation essentiell. Numerische Verfahren die Equilibriumzustände erhalten heißen ausbalanciert.rnrnIn der vorliegenden Arbeit spalten wir die SWE in einen steifen, linearen und einen nicht-steifen Teil, um die starke Einschränkung der Zeitschritte durch die CFL-Bedingung zu umgehen. Der steife Teil wird implizit und der nicht-steife explizit approximiert. Dazu verwenden wir IMEX (implicit-explicit) Runge-Kutta und IMEX Mehrschritt-Zeitdiskretisierungen. Die Raumdiskretisierung erfolgt mittels der Finite-Volumen-Methode. Der steife Teil wird mit Hilfe von finiter Differenzen oder au eine acht mehrdimensional Art und Weise approximniert. Zur mehrdimensionalen Approximation verwenden wir approximative Evolutionsoperatoren, die alle unendlich viele Informationsausbreitungsrichtungen berücksichtigen. Die expliziten Terme werden mit gewöhnlichen numerischen Flüssen approximiert. Daher erhalten wir eine Stabilitätsbedingung analog zu einer rein advektiven Strömung, d.h. das Zeitinkrement vergrößert um den Faktor Kehrwert der Froude-Zahl. Die in dieser Arbeit hergeleiteten Verfahren sind asymptotisch erhaltend und ausbalanciert. Die asymptotischer Erhaltung stellt sicher, dass numerische Lösung das "korrekte" asymptotische Verhalten bezüglich kleiner Froude-Zahlen besitzt. Wir präsentieren Verfahren erster und zweiter Ordnung. Numerische Resultate bestätigen die Konvergenzordnung, so wie Stabilität, Ausbalanciertheit und die asymptotische Erhaltung. Insbesondere beobachten wir bei machen Verfahren, dass die Konvergenzordnung fast unabhängig von der Froude-Zahl ist.

Assessing intravascular volume by difference in pulse pressure in pigs submitted to graded hemorrhage

We assessed changes in intravascular volume monitored by difference in pulse pressure (dPP%) after stepwise hemorrhage in an experimental pig model. Six pigs (23-25 kg) were anesthetized (isoflurane 1.5 vol%) and mechanically ventilated to keep end-tidal CO2 (etCO2) at 35 mmHg. A PA-catheter and an arterial catheter were placed via femoral access. During and after surgery, animals received lactated Ringer's solution as long as they were considered volume responders (dPP>13%). Then animals were allowed to stabilize from the induction of anesthesia and insertion of catheters for 30 min. After stabilization, baseline measurements were taken. Five percent of blood volume was withdrawn, followed by another 5%, and then in 10%-increments until death from exsanguination occurred. After withdrawal of 5% of blood volume, all pigs were considered volume responders (dPP>13%); dPP rose significantly from 6.1+/-3.3% to 19.4+/-4.2%. The regression analysis of stepwise hemorrhage revealed a linear relation between blood loss (hemorrhage in %) and dPP (y=0.99*x+14; R2=0.7764; P<.0001). In addition, dPP was the only parameter that changed significantly between baseline and a blood loss of 5% (P<0.01), whereas cardiac output, stroke volume, heart rate, MAP, central venous pressure, pulmonary artery occlusion pressure, and systemic vascular resistance, respectively, remained unchanged. We conclude that in an experimental hypovolemic pig model, dPP correlates well with blood loss.

Arterial stiffness assessed by digital volume pulse correlates with comorbidity in patients with ESRD

BACKGROUND: Digital volume pulse (DVP), a noninvasive method for indirect assessment of arterial stiffness, was not tested previously in patients with end-stage renal disease (ESRD). Therefore, we compared the DVP-derived stiffness index (SI(DVP)) with aortic pulse wave velocity (PWV) determined by means of Doppler ultrasonography in 2 groups of patients with ESRD and analyzed the correlation between SI(DVP) and comorbidity. METHODS: Photoplethysmography was performed on the index finger of the dominant hand or the hand from the nonfistula arm in 49 renal transplant (TX) recipients and 48 hemodialysis (HD) patients. Pulse curves were analyzed with computer assistance. Comorbidity was assessed by using an established index. RESULTS: The intrasubject variability of SI(DVP) was 5.7%. SI(DVP) and aortic PWV values correlated significantly (r = 0.66; P = 0.001) in patients with ESRD. SI(DVP) could not be assessed reliably in 25% and 6% of HD patients and TX recipients, respectively. Multivariate regression analyses showed that SI(DVP) increased with age in both HD patients and TX recipients (r = 0.61; P < 0.001) and with systolic blood pressure (r = 0.53; P < 0.025), mean arterial pressure (r = 0.47; P < 0.05), and pulse pressure (r = 0.52; P = 0.02) in TX recipients. Severity of comorbid status was associated highly with individual residuals of age-adjusted SI(DVP) in HD patients and TX recipients (P < 0.001). CONCLUSION: DVP allows the measurement of arterial stiffness in most, but not all, patients with ESRD. SI(DVP) values correlate with comorbidity in HD patients and TX recipients.

Lung volume reduction surgery for severe emphysema

BACKGROUND: We report mid-term results after 25 consecutive lung volume reduction operations (LVRS) for the treatment of severe dyspnea due to advanced emphysema. METHODS: Study design: patients were studied prospectively up to 12 months after surgery. Setting: preoperative evaluation, surgery and postoperative care took place in our university hospital. Patients: patient selection was based on severe dyspnea and airway obstruction despite optimal medical treatment, lung overinflation and completed rehabilitation programme. Patients with severe hypercarbia (PCO2>50 mmHg) were excluded. Nineteen rehabilitated patients who fulfilled our inclusion criteria but postponed or denied LVRS were followed up clinically. Interventions: LVRS was performed bilaterally in 22 patients (median sternotomy) and unilaterally in 3 patients (limited thoracotomy). Measures: Outcome was measured by dyspnea evaluation, 6-minute-walking distance and pulmonary function tests. RESULTS: Twelve months postoperatively dyspnea and mobility improved significantly (MRC score from 3.3+/-0.7 to 2.12+/-0.8, 6-min-walk from 251+/-190 to 477+/-189 m). These results were superior compared to the results of the conservatively treated patients. Significant improvement could also be documented in airway obstruction (FEV1 from 960+/-369 to 1438+/-610 ml) and overinflation (TLC from 133+/-14 to 118+/-21% predicted and RV from 280+/-56 to 186+/-59% predicted). CONCLUSIONS: LVRS is an effective and promising treatment option for selected patients with end-stage emphysema and could be offered as an alternative and / or bridge to lung transplantation.

Sirolimus-eluting stent treatment at high-volume centers confers lower mortality at 6-month follow-up: results from the prospective multicenter German Cypher Registry

BACKGROUND: Studies continue to identify percutaneous coronary intervention procedural volume both at the institutional level and at the operator level as being strongly correlated with outcome. High-volume centers have been defined as those that perform >400 percutaneous coronary intervention procedures per year. The relationship between drug-eluting stent procedural volume and outcome is unknown. We investigated this relationship in the German Cypher Registry. METHODS AND RESULTS: The present analysis included 8201 patients treated with sirolimus-eluting stents between April 2002 and September 2005 in 51 centers. Centers that recruited >400 sirolimus-eluting stent patients in this time period were considered high-volume centers; those with 150 to 400 patients were considered intermediate-volume centers; and those with <150 patients were designated as low-volume centers. The primary end point was all death, myocardial infarction, and target-vessel revascularization at 6 months. This end point occurred in 11.3%, 12.1%, and 9.0% of patients in the low-, intermediate-, and high-volume center groups, respectively (P=0.0001). There was no difference between groups in the rate of target-vessel revascularization (P=0.2) or cerebrovascular accidents (P=0.5). The difference in death/myocardial infarction remained significant after adjustment for baseline factors (odds ratio 1.85, 95% confidence interval 1.31 to 2.59, P<0.001 for low-volume centers; odds ratio 1.69, 95% confidence interval 1.29 to 2.21, P<0.001 for intermediate-volume centers). Patient and lesion selection, procedural features, and postprocedural medications differed significantly between groups. CONCLUSIONS: The volume of sirolimus-eluting stent procedures performed on an institutional level was inversely related to death and myocardial infarction but not to target-vessel revascularization at 6-month follow-up. Safety issues are better considered in high-volume centers. These findings have important public health policy implications.

End-tidal CO2 pressure: an important parameter for a correct interpretation of changes in cerebral hemodynamics and oxygenation measured with functional near infrared spectrophotometry (fNIRS)

The aim of the present study was to investigate the effects of different speech tasks (recitation of prose (PR), alliteration (AR) and hexameter (HR) verses) and a control task (mental arithmetic (MA) with voicing of the result) on endtidal CO2 (ET-CO2), cerebral hemodynamics; i.e. total hemoglobin (tHb) and tissue oxygen saturation (StO2). tHb and StO2 were measured with a frequency domain near infrared spectrophotometer (ISS Inc., USA) and ET-CO2 with a gas analyzer (Nellcor N1000). Measurements were performed in 24 adult volunteers (11 female, 13 male; age range 22 to 64 years) during task performance in a randomized order on 4 different days to avoid potential carry over effects. Statistical analysis was applied to test differences between baseline, 2 recitation and 5 recovery periods. The two brain hemispheres and 4 tasks were tested separately. Data analysis revealed that during the recitation tasks (PR, AR and HR) StO2 decreased statistically significant (p < 0.05) during PR and AR in the right prefrontal cortex (PFC) and during AR and HR in the left PFC. tHb showed a significant decrease during HR in the right PFC and during PR, AR and HR in the left PFC. During the MA task, StO2 increased significantly. A significant decrease in ET-CO2 was found during all 4 tasks with the smallest decrease during the MA task. In conclusion, we hypothesize that the observed changes in tHb and StO2 are mainly caused by an altered breathing during the tasks that led a lowering of the CO2 content in the blood provoked a cerebral CO2 reaction, i.e. a vasoconstriction of blood vessels due to decreased CO2 pressure and thereby decrease in cerebral blood volume. Therefore, breathing changes should be monitored during brain studies involving speech when using functional near infrared spectroscopy (fNIRS) to ensure a correct interpretation of changes in hemodynamics and oxygenation.

There is a place for radical cystectomy and urinary diversion, including orthotopic bladder substitution, in patients aged 75 and older: Results of a retrospective observational analysis from a high-volume center

INTRODUCTION The incidence of cancer increases with age and owing to the changing demographics we are increasingly confronted with treating bladder cancer in old patients. We report our results in patients>75 years of age who underwent open radical cystectomy (RC) and urinary diversion. MATERIAL AND METHODS From January 2000 to March 2013, a consecutive series of 224 old patients with complete follow-up who underwent RC and urinary diversion (ileal orthotopic bladder substitute [OBS], ileal conduit [IC], and ureterocutaneostomy [UCST]) were included in this retrospective single-center study. End points were the 90-day complication rates (Clavien-Dindo classification), 90-day mortality rates, overall and cancer-specific survival rates, and continence rates (OBS). RESULTS Median age was 79.2 years (range: 75.1-91.6); 35 of the 224 patients (17%) received an OBS, 178 of the 224 patients (78%) an IC, and 11 of the 224 patients (5%) an UCST. The 90-day complication rate was 54.3% in the OBS (major: Clavien grade 3-5: 22.9%, minor: Clavien Grade 1-2: 31.4%), 56.7% in the IC (major: 27%, minor: 29.8%), and 63.6% in the UCST group (major: 36.4%, minor: 27.3%); P = 0.001. The 90-day mortality was 0% in the OBS group, 13% in the IC group, and 10% in the UCST group (P = 0.077). The Glasgow prognostic score was an independent predictor of all survival parameters assessed, including 90-day mortality. Median follow-up was 22 months. Overall and cancer-specific survivals were 90 and 98, 47 and 91, and 11 and 12 months for OBS, IC, and UCST, respectively. In OBS patients, daytime continence was considered as dry in 66% and humid in 20% of patients. Nighttime continence was dry in 46% and humid 26% of patients. CONCLUSION With careful patient selection, oncological and functional outcome after RC can be good in old patients. Old age as the sole criterion should not preclude the indication for RC or the option of OBS. In old patients undergoing OBS, satisfactory continence results can be achieved.

Olfactory bulb volume predicts therapeutic outcome in major depression disorder

The volume of the olfactory bulb (OB) is strongly reduced in patients with major depressive disorder (MDD) and this group exhibits markedly decreased olfactory function. It has been suggested that olfactory input is important for maintaining balance in limbic neurocircuits. The aim of our study was to investigate whether reduced OB volume is associated with response to therapy in MDD. Twenty-four inpatients (all women, age 21-49 years, mean 38 ± 10 years SD) with MDD and 36 healthy controls (all women, age 20-52 years, mean 36 ± 10 years SD) underwent structural MRI. OB volume was compared between responders (N = 13) and non-responders (N = 11) to psychotherapy. Retest of OB volume was performed about 6 months after the end of therapy in nine of the patients. Therapy responders exhibited no significant difference in OB volume compared to healthy controls. However, average OB volume of non-responders was 23 % smaller compared to responders (p = .0011). Furthermore, OB volume was correlated with the change of depression severity (r = .46, p = .024). Volume of the OB did not change in the course of therapy. OB volume may be a biological vulnerability factor for the occurrence and/or maintenance of depression, at least in women.

Intensive care unit utilization among patients with cancer at the end of life

Over the last 2 decades, survival rates in critically ill cancer patients have improved. Despite the increase in survival, the intensive care unit (ICU) continues to be a location where end-of-life care takes place. More than 20% of deaths in the United States occur after admission to an ICU, and as baby boomers reach the seventh and eighth decades of their lives, the volume of patients in the ICU is predicted to rise. The aim of this study was to evaluate intensive care unit utilization among patients with cancer who were at the end of life. End of life was defined using decedent and high-risk cohort study designs. The decedent study evaluated characteristics and ICU utilization during the terminal hospital stay among patients who died at The University of Texas MD Anderson Cancer Center during 2003-2007. The high-risk cohort study evaluated characteristics and ICU utilization during the index hospital stay among patients admitted to MD Anderson during 2003-2007 with a high risk of in-hospital mortality. Factors associated with higher ICU utilization in the decedent study included non-local residence, hematologic and non-metastatic solid tumor malignancies, malignancy diagnosed within 2 months, and elective admission to surgical or pediatric services. Having a palliative care consultation on admission was associated with dying in the hospital without ICU services. In the cohort of patients with high risk of in-hospital mortality, patients who went to the ICU were more likely to be younger, male, with newly diagnosed non-metastatic solid tumor or hematologic malignancy, and admitted from the emergency center to one of the surgical services. A palliative care consultation on admission was associated with a decreased likelihood of having an ICU stay. There were no differences in ethnicity, marital status, comorbidities, or insurance status between patients who did and did not utilize ICU services. Inpatient mortality probability models developed for the general population are inadequate in predicting in-hospital mortality for patients with cancer. The following characteristics that differed between the decedent study and high-risk cohort study can be considered in future research to predict risk of in-hospital mortality for patients with cancer: ethnicity, type and stage of malignancy, time since diagnosis, and having advance directives. Identifying those at risk can precipitate discussions in advance to ensure care remains appropriate and in accordance with the wishes of the patient and family.^

(Table 1) Activity of strontium-90 in waters of the Northeast Atlantic at the end of 1965 and the beginning of 1966

In 1965-1966 R/V Mikhail Lomonosov conducted studies on concentrations of artificial radioactive products in the Northeast Atlantic. Concentration of strontium-90 at the end of 1965 and the beginning of 1966 was higher than the average level for the ocean and reached about 53 dpm/100 l in the surface layer. The most intense transport of artificial radioactive products out of the Irish Sea was detected in the northern and northeastern directions along the Hebrides and the Orkneys. In addition to radioactive fission products from nuclear weapons tests, radioactive wastes of atomic industrial facilities discharged into the ocean are an important source of radioactive contamination of some regions of the world ocean.