Discrete transparent boundary conditions for the mixed KDV-BBM equation

International audienceIn this paper, we consider artificial boundary conditions for the linearized mixed Korteweg-de Vries (KDV) Benjamin-Bona-Mahoney (BBM) equation which models water waves in the small amplitude, large wavelength regime. Continuous (respectively discrete) artificial boundary conditions involve non local operators in time which in turn requires to compute time convolutions and invert the Laplace transform of an analytic function (respectively the Z-transform of an holomor-phic function). In this paper, we propose a new, stable and fairly general strategy to carry out this crucial step in the design of transparent boundary conditions. For large time simulations, we also introduce a methodology based on the asymptotic expansion of coefficients involved in exact direct transparent boundary conditions. We illustrate the accuracy of our methods for Gaussian and wave packets initial data

Charakterisierung der Platinsensitivität von cisplatinsensitiven und -resistenten Tumorzellen

Die DNA-Platinierung spielt eine wichtige Rolle bei der antitumoralen Wirkung von Cisplatin. Das Ausmaß der gebildeten Platin-DNA-Addukte hat einen prädiktiven Wert im Hinblick auf das Tumoransprechen gezeigt und gilt als zentraler Parameter bei der Charakterisierung der Platinsensitivität. In der vorliegenden Arbeit wurde die Platinsensitivität mittels verschiedener Parameter in cisplatinsensitiven und -resistenten humanen Tumorzelllinien (2102 / 2102 KlonB, A2780 / A2780 cis und HeLa / HeLa CK) charakterisiert. Nach Bestimmung des Resistenzgrades der verschiedenen Tumorzelllinien gegenüber Cisplatin mittels MTT-Assay wurden neben der DNA-Platinierung die Adduktreparatur, intrazelluläre Platinkonzentrationen (Uptake und Efflux) sowie intrazelluläre Glutathionkonzentrationen untersucht. Zur Quantifizierung der Glutathionkonzentrationen wurde eine kapillarelektrophoretische Methode mit Laser-induzierter Fluoreszenz-Detektion etabliert und validiert. Für die Bestimmung sämtlicher Sensitivitätsparameter wurden in dieser Arbeit Versuchsbedingungen entwickelt und die Unterschiede in den cisplatinsensitiven und -resistenten Zelllinien quantifiziert. Bei der DNA-Platinierung zeigten sich deutliche Unterschiede zwischen cisplatinsensitiven und -resistenten Zelllinien, die mit dem Resistenzgrad korrelierten. Die Untersuchungen zum Uptake zeigten, dass die intrazellulären Platinkonzentrationen während der Inkubation mit Cisplatin in den untersuchten cisplatinresistenten Zelllinien deutlich erniedrigt waren im Vergleich zu ihrer parentalen Zelllinie. Dahingegen gab es bei dem Efflux kaum Unterschiede. Ebenso war die DNA-Reparaturgeschwindigkeit in den cisplatinsensitiven und resistenten Zelllinien nicht wesentlich unterschiedlich. Die Bestimmung der intrazellulären Glutathionkonzentrationen zeigte, dass diese in der untersuchten cisplatinresistenten Zelllinie erhöht waren. Die Ergebnisse deuten an, dass neben der DNA-Platinierung besonders der Uptake und die intrazellulären Glutathionkonzentrationen für die Charakterisierung der Platinsensitivität wichtig sind. Daraus ergeben sich neue Ansatzpunkte zur Charakterisierung der Platinsensitivität, mit denen durch die gemeinsame Betrachtung verschiedener Resistenzmechanismen die Platinsensitivität quantitativ beurteilt werden kann. Die Ergebnisse können einen Beitrag zur Entwicklung neuer Strategien zur Überwindung von Platinresistenz und Individualisierung platinhaltiger Chemotherapie leisten.Characterization of platinum sensitivity of cisplatin sensitive and resistant tumor cells DNA platination plays an important role in the antitumoral effect of cisplatin. The extent of the formed platinum-DNA adducts has a predictive value with regard to tumor response and is considered as central parameter in the characterization of platinum sensitivity. In this thesis platinum sensitivity was characterized in cisplatin-sensitive and resistant human tumor cell lines (2102 / 2102 KlonB, A2780 / A2780 cis and HeLa / HeLa CK). After determination of the degree of resistance of the different tumor cell lines using the MTT assay DNA platination, adduct repair, intracellular platinum concentrations (uptake and efflux) as well as intracellular glutathione concentrations were investigated. For the quantification of glutathione concentrations a capillary zone electrophoresis (CZE) method with laser-induced fluorescence detection was established and validated. In this thesis test conditions were developed for the determination of all sensitivity parameters and the differences in cisplatin-sensitive and resistant cell lines were quantified. DNA platination exhibited considerable differences between cisplatin-sensitive and -resistant cell lines which correlated closely with the degree of resistance. Investigations on uptake revealed that the intracellular platinum concentrations were lower during incubation with cisplatin in the resistant cells compared to the sensitive cells. No difference with regard to efflux was observed. Moreover, DNA repair did not differ between sensitive and resistant cell lines. Intracellular glutathione concentrations were found to be higher in the resistant cells. The results suggest that - beside the DNA platination - also other parameters like uptake and intracellular glutathione concentrations seem to be suitable to assess cisplatin sensitivity in tumor cells. Future studies will reveal which parameters are most predictive and can be used for a quantitative assessment of platinum sensitivity of human tumor cells. The results can contribute to the development of new strategies to overcome platinum resistance and individualize platinum-based chemotherapy

Discrete artificial boundary conditions for nonlinear Schrödinger equations

In this work we construct and analyze discrete artificial boundary conditions (ABCs) for different finite difference schemes to solve nonlinear Schrödinger equations. These new discrete boundary conditions are motivated by the continuous ABCs recently obtained by the potential strategy of Szeftel. Since these new nonlinear ABCs are based on the discrete ABCs for the linear problem we first review the well-known results for the linear Schrödinger equation. We present our approach for a couple of finite difference schemes, including the Crank-Nicholson scheme, the Duran-Sanz-Serna scheme, the DuFort-Frankel method and several split-step (fractional step) methods such as the Lie splitting, the Strang splitting and the relaxation scheme of Besse. Finally, several numerical tests illustrate the accuracy and stability of our new discrete approach for the considered finite difference schemes

Combined antitumor effects of bee venom and cisplatin on human cervical and laryngeal carcinoma cells and their drug resistant sublines

In the present study, we investigated the possible combined anticancer ability of bee venom (BV) and cisplatin towards two pairs of tumour cell lines: parental cervical carcinoma HeLa cells and their cisplatin-resistant HeLa CK subline, as well as laryngeal carcinoma HEp-2 cells and their cisplatin-resistant CK2 subline. Additionally, we identified several peptides of BV in the BV sample used in the course of the study and determined the exact concentration of MEL. BV applied alone in concentrations of 30 to 60 μg ml-1 displayed dose-dependent cytotoxicity against all cell lines tested. Cisplatin-resistant cervical carcinoma cells were more sensitive to BV than their parental cell lines (IC50 values were 52.50 μg ml-1 for HeLa vs. 47.64 μg ml-1 for HeLa CK cells), whereas opposite results were obtained for cisplatin-resistant laryngeal carcinoma cells (IC50 values were 51.98 μg ml-1 for HEp-2 vs. > 60.00 μg ml-1 for CK2 cells). Treatment with BV alone induced a necrotic type of cell death, as shown by characteristic morphological features, fast staining with ethidium-bromide and a lack of cleavage of apoptotic marker poly (ADP-ribose) polymerase (PARP) on Western blot. Combined treatment of BV and cisplatin induced an additive and/or weak synergistic effect towards tested cell lines, suggesting that BV could enhance the killing effect of selected cells when combined with cisplatin. Therefore, a greater anticancer effect could be triggered if BV was used in the course of chemotherapy. Our results suggest that combined treatment with BV could be useful from the point of minimizing the cisplatin concentration during chemotherapy, consequently reducing and/or postponing the development of cisplatin resistance

Altered localisation of the copper efflux transporters ATP7A and ATP7B associated with cisplatin resistance in human ovarian carcinoma cells

Metals in Catalysis, Biomimetics & Inorganic Material

MicroRNA-31 Regulates Chemosensitivity in Malignant Pleural Mesothelioma

YesMalignant pleural mesothelioma (MPM) is associated with an extremely poor prognosis, and most patients initially are or rapidly become unresponsive to platinum-based chemotherapy. MicroRNA-31 (miR-31) is encoded on a genomic fragile site, 9p21.3, which is reportedly lost in many MPM tumors. Based on previous findings in a variety of other cancers, we hypothesized that miR-31 alters chemosensitivity and that miR-31 reconstitution may influence sensitivity to chemotherapeutics in MPM. Reintroduction of miR-31 into miR-31 null NCI-H2452 cells significantly enhanced clonogenic resistance to cisplatin and carboplatin. Although miR-31 re-expression increased chemoresistance, paradoxically, a higher relative intracellular accumulation of platinum was detected. This was coupled to a significantly decreased intranuclear concentration of platinum. Linked with a downregulation of OCT1, a bipotential transcriptional regulator with multiple miR-31 target binding sites, we subsequently identified an indirect miR-31-mediated upregulation of ABCB9, a transporter associated with drug accumulation in lysosomes, and increased uptake of platinum to lysosomes. However, when overexpressed directly, ABCB9 promoted cellular chemosensitivity, suggesting that miR-31 promotes chemoresistance largely via an ABCB9-independent mechanism. Overall, our data suggest that miR-31 loss from MPM tumors promotes chemosensitivity and may be prognostically beneficial in the context of therapeutic sensitivity

Diskrete transparente Randbedingungen für Evolutionsgleichungen

Die vorliegende Doktorarbeit befasst sich mit der Herleitung und Implementierung von diskreten transparenten Randbedingungen für Systeme von Evolutionsgleichungen. Transparente Randbedingungen (TRBen) sind spezielle künstliche Randbedingungen, durch die die Lösung der Gleichung auf beschränktem und mit TRBen versehenem Gebiet mit der exakten Lösung des Ganzraumproblems (auf diesem beschränkten Gebiet) übereinstimmt. Die Differentialgleichungen werden durch ein Finite-Differenzen-Verfahren (theta-Schema) diskretisiert. Für die entstandene diskrete Gleichung werden diskrete transparente Randbedingungen (DTRBen) hergeleitet, wodurch die DTRBen besonders gut an das numerische Verfahren angepasst sind. Für skalare Gleichungen sind diese DTRBen bereits länger bekannt und man weiß, dass im Gegensatz zur ad-hoc Diskretisierung der analytischen TRBen Stabilitätsprobleme und künstliche Reflektionen am Rand vermieden werden können. Wir werden uns hier mit Systemen von Differentialgleichungen (parabolisch und Schrödinger Typ) befassen. Für diese Systeme ist der Ansatz der DTRBen gänzlich neu und wirft zusätzliche Probleme auf, die für skalare Gleichungen nicht auftreten. Nachdem wir uns eingehend mit den TRBen und DTRBen für schwach gekoppelte Systeme von parabolischen Differentialgleichungen beschäftigt haben, die das Verhalten von fluiden stochastischen Petri-Netzen beschreiben, verallgemeinern wir unser Vorgehen auf ein beliebiges lineares parabolisches System. Im Anschluss daran betrachten wir ein System von Schrödinger-Gleichungen, wie es z.B. in der Halbleiterphysik als sogenannte k·p-Schrödinger Gleichung der Quantenmechanik auftritt. Die angeführten numerischen Beispiele zeigen, dass sowohl für parabolische als auch für Systeme von Schrödinger Gleichungen die DTRBen nur sehr kleine Fehler verursachen.This dissertation is concerned with the derivation and implementation of discrete transparent boundary conditions for systems of evolution equations. Transparent boundary conditions (TBCs) are a special kind of artificial boundary conditions, that are constructed in such a way, that the solution on a bounded domain with TBCs is equal to the solution of the whole-space problem restricted to the bounded (computational) domain. The partial differential equations are discretised by finite differences (theta-scheme) and discrete transparent boundary conditions (DTBCs) are constructed for the discrete equation. Therefore, the DTBCs are well adapted to the numerical scheme. For scalar equations these DTBCs are well established. Compared to discretising the analytical TBC, in the scalar case it is known that these DTBCs have the advantage, not to destroy the stability properties of the underlying discrete scheme and to avoid any numerical reflections. In this dissertation we will deal with systems of partial differ ential equations (parabolic and Schrödinger type). For these systems the approach of DTBCs is completely new and involves additional problems not encountered in the scalar case. Since the numerical computation of these DTBCs is very costly, we give an approximation which greatly reduces the effort. After a concise construction of the TBCs and DTBCs for the weakly coupled system of parabolic equations arising from the mathematical description of fluid stochastic Petri nets, we proceed to extend the results to a system of general parabolic equations. Finally we will consider DTBCs for a system of Schrödinger-type equations, which arise e.g. in the physics of layered semiconductor devices as the so called k·p-Schrödinger equation of quantum mechanics. For both kinds of systems we will give numerical examples, which show the very small error caused by the DTBC

On Markov reward modelling with FSPNs

In this paper fluid stochastic Petri nets (FSPNs) will be used for modelling reward in a performability model. Two variations of a known performability model are presented in order to demonstrate the ability of FSPNs in modelling accumulated rate reward as well as accumulated impulse reward. In the first model two fluid places are used, one of which represents the profit (reward) obtained by operating the system and the other one the buffer, that is approximated continuously. In the second model only one fluid place is used, representing the costs (negative reward) arising due to repair of system components. The costs increase continuously at deterministic rate while the system is in state of repair (which is a rate reward in the model). Additional costs incur each time the buffer fails (which is an impulse reward in the model). With a numerical solution algorithm the distribution of the reward and its mean are computed. The accuracy of the numerical algorithm is studied by showing for the first model the impact of the choice of the discretization stepsizes on the obtained solution. Different boundary conditions are discussed for the second model