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.     

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.     

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.     

In Vivo Optical Properties of Melanocytic Skin Lesions: Common Nevi, Dysplastic Nevi and Malignant Melanoma

We present an in vivo study of the optical properties of common nevi, dysplastic nevi and malignant melanoma skin lesions in human subjects. Reflectance spectra were measured on 1379 skin lesions, in the visible and near-infrared spectral regions, using a spectral imaging system, in a clinical setting. Analysis of the data using a reflectance model revealed differences between the optical properties of melanin present in nevi and melanoma lesions. These differences, which are in agreement with our previous observations on average reflectance spectra, may be potentially useful for the noninvasive characterization of pigmented skin lesions and the early diagnosis of melanoma.     

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.

     

Tumor Biochemical Heterogeneity and Cancer Radiochemotherapy: Network Breakdown Zone-Model

Breakdowns of two-zone random networks of the Erdős–Rényi type are investigated. They are used as mathematical models for understanding the incompleteness of the tumor network breakdown under radiochemotherapy, an incompleteness that may result from a tumor’s physical and/or chemical heterogeneity. Mathematically, having a reduced node removal probability in the network’s inner zone hampers the network’s breakdown. The latter is described quantitatively as a function of reduction in the inner zone’s removal probability, where the network breakdown is described in terms of the largest remaining clusters and their size distributions. The effects on the efficacy of radiochemotherapy due to the tumor micro-environment (TME)’s chemical make-up, and its heterogeneity, are discussed, with the goal of using such TME chemical heterogeneity imaging to inform precision oncology.     

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     

Equilibrium results for the M/G/k group-arrival loss system

In this paper we consider a specific M/G/k group-arrival loss system, under statistical equilibrium and two cases of acceptance policy. In the first case the system works under the partial acceptance policy. Explicit results are obtained for the corresponding stationary distribution, which extend previous relevant results. In the second case, where the system works under the all-or-nothing acceptance policy, a sufficient condition is given for the stationary distribution to have a closed-product form. In both cases customers depart individually, while the joint service time distribution of the accepted members of a group may depend both on its initial and the accepted size plus an additional condition.     

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.