Tumor Hypoxia Heterogeneity Affects Radiotherapy: Inverse-Percolation Shell-Model Monte Carlo Simulations

Tumor hypoxia was discovered a century ago, and the interference of hypoxia with all radiotherapies is well known. Here, we demonstrate the potentially extreme effects of hypoxia heterogeneity on radiotherapy and combination radiochemotherapy. We observe that there is a decrease in hypoxia from tumor periphery to tumor center, due to oxygen diffusion, resulting in a gradient of radiative cell-kill probability, mathematically expressed as a probability gradient of occupied space removal. The radiotherapy-induced break-up of the tumor/TME network is modeled by the physics model of inverse percolation in a shell-like medium, using Monte Carlo simulations. The different shells now have different probabilities of space removal, spanning from higher probability in the periphery to lower probability in the center of the tumor. Mathematical results regarding the variability of the critical percolation concentration show an increase in the critical threshold with the applied increase in the probability of space removal. Such an observation will have an important medical implication: a much larger than expected radiation dose is needed for a tumor breakup enabling successful follow-up chemotherapy. Information on the TME’s hypoxia heterogeneity, as shown here with the numerical percolation model, may enable personalized precision radiation oncology therapy.     

Steifigkeitsmatrizen dünnwandiger Stäbe und Stabsysteme

Übersicht Die Steifigkeitsmatrizen dünnwandiger Stäbe werden nach der vereinfachten Theorie im Hauptsystem abgeleitet und auf exzentrische Knotenpunkte transformiert. Die Schubdeformation der Stabmittelfläche wird näherungsweise erfaßt. Neben der wölbfreien und wölbstarren Aussteifung wird die wölbelastische Aussteifung berücksichtigt.

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Summary The stiffness matrices of thin-walled bars are determined and transformed to excentric nodal points starting from the simplified theory. The shear strain of the middle plane of the bar is approximately included. The warping elasticity of the stiffener is considered including free warping and completely suppressed warping.

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Bericht des Instituts für Statik und Dynamik der Luft- und Raumfahrtkonstruktionen der Universität Stuttgart (ISD), Direktor: Professor Dr. Dr. h. c. J. H. Argyris.     

On the feasibility of performing non-linear autocorrelation with attosecond pulse trains

We present experimental results in which a second-order effect, namely two-photon ionization of atomic He induced by a superposition of harmonics, is observed. The harmonics are generated in a Xe gas-jet using a 790-nm 10-Hz femtosecond Ti:sapphire laser and are subsequently focused into a He gas-jet with a Kirkpatrick–Baez arrangement. The superposition is formed by using a thin In filter and it comprises the 7th to 13th harmonics. Solving the time-dependent Schrödinger equation for He in a polychromatic laser field, the He ⁺ ion yield is calculated as a function of the total XUV intensity. Using the calculated yield and taking into account the focusing and transmission properties of the arrangement, the number of He ⁺ ions produced per laser pulse is estimated and is found to be in reasonable agreement with its measured value. The total number of ions produced non-resonantly follows a nearly quadratic dependence on the harmonic intensity, thus establishing the feasibility of a second-order auto-correlation measurement of the superposition of harmonics, i.e., of a direct temporal characterization of attosecond pulse trains.     

Potential flow analysis by finite elements

Summary A finite element formulation is developed for the analysis of a general discontinuous potential field (with multiply connected regions) and leads to the solution of the Dirichlet, Neumann and Mixed Boundary Value Problems. Subcritical compressibility effects are included. The finite element model is presented in detail for the two-dimensional and axisymmetric case, but may readily be extended to the general three-dimensional case. For the representation of general boundary conditions (linear interdependencies between the unknown variables) two alternative methods are formulated. Several typical examples including compressibility, circulatory (lifting) flow and the analysis of infinite cascades demonstrate the wide applicability and accuracy of the method.

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Übersicht Für die Berechnung von allgemeinen diskontinuierlichen Potentialfeldern mit mehrfach zusammenhängenden Bereichen wird eine Formulierung für die Methode der finiten Elemente entwickelt. Dies führt zur einfachen Lösung von Randwertproblemen erster, zweiter und dritter Art, wobei auch Kompressibilitätseffekte im unterkritischen Bereich berücksichtigt werden können. Ein Finite-Element-Typ wird im Detail für den zweidimensionalen und rotationssymmetrischen Fall abgeleitet, jedoch kann die Darstellung leicht auf den allgemeinen dreidimensionalen Fall ausgedehnt werden. Für die Verwirklichung allgemeiner Randbedingungen (d. h. Berücksichtigung von linear abhängigen unbekannten Variablen) werden zwei Methoden formuliert.Mehrere typische Beispiele, welche Kompressibilität, Auftrieb und die Berechnung unendlicher Kaskadenströmung behandeln, zeigen dic Vielfalt der Anwendungsmöglichkeiten und die Genauigkeit der Methode.

     

Identifying preferred solutions to Multi-Objective Binary Optimisation problems,with an application to the Multi-Objective Knapsack Problem

In this paper we present a new framework for identifying preferred solutions to multi-objective binary optimisation problems. We develop the necessary theory which leads to new formulations that integrate the decision space with the space of criterion weights. The advantage of this is that it allows for incorporating preferences directly within a unique binary optimisation problem which identifies efficient solutions and associated weights simultaneously. We discuss how preferences can be incorporated within the formulations and also describe how to accommodate the selection of weights when the identification of a unique solution is required. Our results can be used for designing interactive procedures for the solution of multi-objective binary optimisation problems. We describe one such procedure for the multi-objective multi-dimensional binary knapsack formulation of the portfolio selection problem.     

Methods of elastoplastic analysis

Summary The paper presents a number of alternative procedures for the solution of elasto-plastic problems by the matrix displacement or finite element method. In particular, the iterative initial strain and stress approaches are fully developed. Attention is also focused on the tangent stiffness method in association with an efficient modification technique. Convergence criteria are set up for the initial strain and stress methods. It is proved that the latter will only diverge, if an actual break-down of the structure occurs. In order to speed up the eventually slow convergence of the initial stress method a procedure is suggested which has proved very useful in conjunction with the initial strain approach.The theoretically deduced convergence properties of the iterative methods are verified by the numerical results obtained for some illustrative elasto-plastic problems.

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Zusammenfassung In dieser Arbeit werden verschiedene Methoden zur Lösung elastoplastischer Probleme vorgelegt, die auf der Matrizenverschiebungsmethode (Methode finiter Elemente) beruhen. Insbesondere werden zwei iterative Verfahren vollständig hergeleitet, bei denen plastische Anfangsdehnungen bzw. Anfangsspannungen angesetzt werden. Auch die Methode der tangentialen Steifigkeit wird betrachtet, die in Verbindung mit der Modifikationstechnik besonders wirkungsvoll eingesetzt werden kann. Für die beiden iterative Verfahren mit Anfangsdehnungen bzw.-spannungen werden Konvergenzkriterien aufgestellt. Es läßt sich zeigen, daß die zweite Methode nur dann divergiert, wenn das Tragwerk tatsächlich zusammenbricht, was bei ideal plastischem Materialverhalten vorkommen kann. Um die in einigen Fällen langsame Konvergenz beim Ansatz von Anfangsspannungen zu beschleunigen, wird ein Verfahren vorgeschlagen, das sich in der Methode der Anfangsdehnungen bestens bewährt hat. Die zunächst theoretisch hergeleitelen Konvergenzeigenschaften der Iterationsverfahren werden bestätigt durch die Ergebnisse der Berechnung von einigen typischen plastisch deformierbaren Systemen.

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Dedicated to Professor Kurt Magnus on his 60th birthday     

Die Matrizentheorie der Statik

Ohne Zusammenfassung     

Toward single attosecond pulses using harmonic emission from solid-density plasmas

We report on investigations of high-order harmonic generation from solid surfaces in the coherent wake emission regime with relativistically intense few-cycle (8 fs) laser pulses. Significant spectral broadening compared to previous experiments with many-cycle pulses and the appearance of substructures on the harmonics are observed that strongly fluctuate from shot-to-shot. Measurements in which the linear polarization was rotated or ellipticity of the laser pulse was varied exhibit a strong dependence of the harmonic emission on the polarization state of the incident pulse. We show that the observed spectral features are ultimately connected to the sub-cycle electron dynamics in the laser-solid interaction and thus proof of the few-cycle nature of the observed harmonic emission. Using a simple model we have investigated the factors that play an important role in the shape of the emitted spectrum.     

Aqueous NaCl and CsCl solutions confined in crystalline slit-shaped silica nanopores of varying degree of protonation

All-atom molecular dynamics simulations were conducted to study the dynamics of aqueous electrolyte solutions confined in slit-shaped silica nanopores of various degrees of protonation. Five degrees of protonation were prepared by randomly removing surface hydrogen atoms from fully protonated crystalline silica surfaces. Aqueous electrolyte solutions containing NaCl or CsCl salt were simulated at ambient conditions. In all cases, the ionic concentration was 1 M. The results were quantified in terms of atomic density distributions within the pores, and the self-diffusion coefficient along the direction parallel to the pore surface. We found evidence for ion-specific properties that depend on ion-surface, water-ion, and only in some cases ion-ion correlations. The degree of protonation strongly affects the structure, distribution, and the dynamic behavior of confined water and electrolytes. Cl(-) ions adsorb on the surface at large degrees of protonation, and their behavior does not depend significantly on the cation type (either Na(+) or Cs(+) ions are present in the systems considered). The cations show significant ion-specific behavior. Na(+) ions occupy different positions within the pore as the degree of protonation changes, while Cs(+) ions mainly remain near the pore center at all conditions considered. For a given degree of protonation, the planar self-diffusion coefficient of Cs(+) is always greater than that of Na(+) ions. The results are useful for better understanding transport under confinement, including brine behavior in the subsurface, with important applications such as environmental remediation.     

Trace element pharmacognostical study on diuretic drugs by neutron activation analysis

Some pharmacological properties and especially diuretic action of medicinal plants are attributed to their elemental content. The elements chlorine, manganese, potassium and sodium are determined by instrumental neutron activation analysis in the dry samples of the following drugs: stigmata of Zea mays, leaves of Uva ursi, rhizome of Cynodon dactylon, whole plant of Ceterach officinarum as well as in infusions, decoction of the same drugs and in the water used for these preparations. It has been found that manganese and potassium are transferred partially into prepared solutions. Sodium is not transferred into solutions from any of these drugs while only chlorine is transferred partially into infusion of Zea mays. From these results it is concluded that the diuretic action of the examined drugs should not be attributed exclusively to the presence of their potassium and chlorine content but also to other constituents.