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We study a new class of time integration methods based on a s-stage linearly implicit two-step scheme. The convergence of the methods can be shown with the help of some simplifying assumption. We derive some L-and L(α)-stable two-step W-methods (TSW-methods) with s = 2 and s = 3 of order p = s and stage order q = s. Numerical comparisons show the efficiency of the methods, especially in combination with Krylov-techniques for large stiff systems. [ABSTRACT FROM AUTHOR]

The hot melt extrusion process is a widespread technique to mix viscous melts. The residence time of material in the process frequently determines the product properties. An experimental setup and a corresponding mathematical model were developed to evaluate residence time and residence time distribution in twin screw extrusion processes. The extrusion process was modeled as the convolution of a mass transport process described by a Gaussian probability function, and a mixing process represented by an exponential function. The residence time of the extrusion process was determined by introducing a tracer at the extruder inlet and measuring the tracer concentration at the die. These concentrations were fitted to the residence time model, and an adequate correlation was found. Different parameters were derived to characterize the extrusion process including the dead time, the apparent mixing volume, and a transport related axial mixing. A 2(3) design of experiments was performed to evaluate the effect of powder feed rate, screw speed, and melt viscosity of the material on the residence time. All three parameters affect the residence time of material in the extruder. In conclusion, a residence time model was developed to interpret experimental data and to get insights into the hot melt extrusion process., (Copyright © 2013 Elsevier B.V. All rights reserved.)

The aim of this study was to select a group of patients who had mild intermittent claudication and were undergoing secondary prevention measures, and record all vascular and non-vascular events over a 10-year follow-up. A total of 534 events were recorded in 109 claudicants. 25.7% of the claudicants died, 39% of them due to vascular events, 36% from cancer and 25% from other causes. 17 of the 20 cancer cases could be classified as related to smoking. Cancer occurred relatively early in the study, within the first five years, while severe vascular events occurred mainly during later periods. A clear transformation occurred in the outcome of the claudicants. Mortality was equally attributable to vascular and cancer-related comorbidities. In conclusion, the improvement of vascular outcomes due to secondary prevention measures and technological advances in the management of acute vascular events may result in a relative increase in cancer incidence and deaths.

Background and Purpose: Unclear extremity complaints are common symptoms of inpatients. In a subset of these patients, a clinical suspicion of deep vein thrombosis (DVT) results; this needs to be quickly and definitively clarified by a vascular physician. The question arose of how often a clinical suspicion of DVT was confirmed in an inpatient population and which alternative diagnoses were able to be made by angiologists., Patients and Methods: In a retrospective analysis, all inpatients in the Angiologic Vascular Diagnostics Center of the University Hospital Halle, Germany, examined in 2007 for a suspicion of DVT were evaluated with respect to the definitively made diagnosis., Results: In 213 (28.6%) of 745 suspected cases of DVT, a DVT was confirmed. In 532 patients (71.4%), DVT was excluded. In 314 of these patients, 436 alternative diagnoses were recorded in the diagnostic reports of angiologic examinations. In 38.6% (n = 168), other venous causes could be confirmed as the most common alternative diagnosis. There were chronic venous diseases in 28% (n = 122), superficial thrombophlebitis (n = 27), and tumor-related pelvic vein compression (n = 19). 17.4% (n = 76) exhibited lymphedema. In 13.3% (n = 58), a generalized edema was diagnosed. Arthrogenic causes followed with 12.8% (n = 56). Lipedema (5.3%) and hematoma (5%) could be verified as other important differential diagnoses. Rare causes were symptomatic or ruptured Baker's cysts (2.5%), erysipelas (2.5%), abscess, aneurysm, muscle tears, and tumors., Conclusion: The variety of alternative diagnoses in patients with clinical suspicion of DVT is high. The knowledge and systematic examination of potential, even rare differential diagnoses after exclusion of DVT are part of the repertoire of the vascular physician. Unnecessary and expensive, as well as onerous, diagnostic procedures on the patient can be avoided. Anticoagulation that was begun as a result of the suspicion of DVT can quickly be stopped.

Background: The known natural history of peripheral arterial disease (PAD) is determined by the generalization of atherosclerosis with resulting high cardiovascular and cerebrovascular morbidity and mortality. The aim of this prospective study was to record all vascular and non-vascular events in patients with mild intermittent claudication (IC) undergoing secondary preventive measures in a 10-year follow-up and to determine the time-points at which systemic localizations of atherosclerotic events develop., Patients and Methods: Patients who originally had an isolated Fontaine stage IIa PAD were included in the follow-up which involved assessments carried out on an annual basis. The incidence and timepoints of vascular (i.e., myocardial infarction, stroke, critical limb ischemia, vascular death), and nonvascular events (i.e., cancer, non vascular death) were recorded and compared with the known natural history., Results: 534 events (vascular: 433) concerning 109 claudicants (M/F: 88/21; 60.8 +/- 8.8 years; ABI 0.66 +/- 0.11) were recorded over an average follow-up period of 104 months. 25.7% of the claudicants died, 39% due to vascular events, 36% due to cancer disease and 25% due to other events. A deterioration of PAD (n = 108) was the most frequent event after 20 months, followed by angina pectoris (n = 41) and cancer diseases (n = 20) after 42 and 45 months, stroke (n = 19) after 58 months, myocardial infarction (n = 12) after 63 months, and finally critical limb ischemia (n = 27) and amputations (n = 10) after 80 and 114 months (median). 111 revascularizations were carried out. 62.3% of the claudicants developed a polyvascular disease, with 20% in a trivascular territory., Conclusions: A high vascular comorbidity also develops under secondary prevention as an expression of the continuing generalization of the atherosclerotic process in PAD. The causes for death are determined both by the vascular and the tumor related comorbidity.

Background and Purpose: Hemodialysis and related procedures require a reliable vascular access and the Brescia-Cimino shunt of the nondominant forearm has proven to be its most important form. Today, color Doppler sonography is regarded as the main method in the diagnosis of vascular access dysfunction. The aim of this study was to evaluate the impact of the Resistive Index (RI) of the fistula's feeding artery on the fistula's blood flow., Patients and Methods: 47 patients with arteriovenous fistulas were investigated by means of color Doppler sonography. The fistulas' blood flow, morphological details and the RI of the arteries distal as well as proximal to the fistulas were determined. Furthermore, systolic blood pressure of the second and third fingers of both hands was measured. Comparisons were made between the fistula's blood flow and the RI of the feeding artery., Results: On the arm of the fistulas, the proximal and distal RI and the systolic blood pressure were lower than on the contralateral arm. The blood flow of the upper arm fistulas was higher than that of the forearm fistulas due to a higher vascular diameter. No linear correlations existed between the RI and the fistula's blood flow. 50% of the forearm fistulas showed a proximal RI > or = 0.53 and a blood flow < 400 ml/min., Conclusion: The RI of the supplying artery of the forearm fistulas is a reliable value to detect insufficient blood flow. In such cases, further diagnostic procedures are necessary. Also, numerous influences on the measurement of the fistula's blood flow exist. Therefore, intraindividual investigations to evaluate the fistulas' further development are recommended to get better options for their control.

Clusters of calcium-loaded sarcoplasmic reticulum (SR) vesicles in agarose gel were previously shown to behave as an excitable medium that propagates calcium waves. In a 3D-hexagonal disposition, the distance between neighboring spheres (which may stand for SR vesicles) is constant and the relationship between distance and vesicular protein concentration is expected to be nonlinear. To obtain a distribution of SR vesicles at different protein concentrations as homogeneous as possible, liquid agarose gels were carefully stirred. Electron micrographs, however, did not confirm the expected relationship between inter-SR vesicle distance and vesicular protein concentration. Light micrographs, to the contrary, resulted in a protein concentration-dependent disposition of clusters of SR vesicles, which is described by a linear function. Stable calcium waves in agarose gel occurred at SR vesicle protein concentrations between 7 and 16 g/l. At lower protein concentrations, local calcium oscillations or abortive waves were observed. The velocities of calcium waves were optimum at approximately 12 g/l and amounted to nearly 60 microm/s. The corresponding distance of neighboring calcium release units was calculated to be approximately 4 microm. The results further show that calcium signaling in the described reaction-diffusion system is optimal in a relatively small range of diffusion lengths. A change by +/-2 microm resulted in a reduction of the propagation velocity by 40%. It would appear that 1), the distance between calcium release units (clusters of ryanodine receptors in cells) is a sensitive parameter concerning propagation of Ca2+ signals; and 2), a dysfunction of the reaction-diffusion system in living cells, however, might have a negative effect on the spreading of intracellular calcium signals, thus on the cell's function.

The drug diffusion of most compounds, particularly hydrophilic molecules through the skin is limited by the permeation of the outermost cell layers of the epidermis, the stratum corneum(SC). For this reason it is of interest to characterize drug diffusion processes through this skin layer. A new FTIR-ATR cell was developed for non-invasive real time measurements of drug diffusion. The diffusion of water through an artificial polyethyleneglycol-polydimethylsiloxane membrane was studied. Additionally the diffusion of urea in human SC was analyzed. Based on a mathematical model the diffusion coefficients were derived. We could reveal that this cell associates the advantages of the Franz diffusion cell and the FTIR-ATR spectroscopy as a new powerful method for determining drug diffusion through biological membranes.

Aim: Patients suffering from peripheral arterial disease (PAD) are increasingly described as having hyperhomocysteinemia more than in patients with coronary artery or cerebrovascular disease. Cases of symptomatic PAD usually present with associated coronary artery or cerebrovascular disease and renal artery disease. It can thus be postulated that multilocular atherosclerosis is linked to hyperhomocysteinemia and that the extent of atherosclerosis has a possible correlation with homocysteine concentrations. The aim of this study was to ascertain whether fasting total homocysteine concentrations in patients with PAD are associated with the extent and the localization of systemic atherosclerosis in cerebrovascular, coronary and/or renal vascular zones., Methods: A total of 183 patients with PAD, Fontaine stages II-IV, were divided into 2 groups: Group A contained patients with isolated PAD (n=98) and Group B patients with systemic atherosclerosis in PAD (n=85). Characterization of vascular disease in various vascular zones was indication-adapted using non-invasive and/or invasive, Methods: Patients with renal insufficiency were excluded from the study., Results: Homocysteine concentrations were significantly lower in patients with isolated PAD than in patients with additional systemic atherosclerosis (10.1+/-4.4 vs 16.7+/-7.04 micromol/l, p<0.0001). There were no differences in localization or extent of concomitant systemic atherosclerosis. Logistic regression analysis indicated that elevated plasma homocysteine and decreasing ABPI served independently as significant risk indicators for systemic atherosclerosis in patients with PAD (p<0.0001)., Conclusion: Hyperhomocysteinemia is a precursoral marker of systemic atherosclerosis and thus a prognostic indicator of cardiovascular morbidity and mortality in PAD.

In this paper we develop a reaction-diffusion system describing the calcium dynamics in an agarose gel system with resuspended vesicles from the sarcoplasmic reticulum (SR vesicles). We focus on a simple model: compared with living cells (e.g. cardiac myocytes) an important property of the agarose gel system is the absence of the sarcolemma and the spatial separation of the calcium release units (CRUs). Our model includes the kinetics of ryanodine sensitive receptors (RyRs), the activity of the SERCA pumps and the diffusion of free calcium. We describe numerical simulations which show a biphasic relationship between the density of the CRUs and the propagation velocity of spreading waves. The non-monotony can be explained by changes in the amplitude of the local calcium concentration. We formulate implications for the in vitro system which could be verified in future experiments.