Intraoperative spectral domain optical coherence tomography for vitreoretinal surgery

We demonstrate in vivo human retinal imaging using an intraoperative microscope-mounted optical coherence tomography system (MMOCT). Our optomechanical design adapts an Oculus Binocular Indirect Ophthalmo Microscope (BIOM3), suspended from a Leica ophthalmic surgical microscope, with spectral domain optical coherence tomography (SD-OCT) scanning and relay optics. The MMOCT enables wide-field noncontact real-time cross-sectional imaging of retinal structure, allowing for SD-OCT augmented intrasurgical microscopy for intraocular visualization. We experimentally quantify the axial and lateral resolution of the MMOCT and demonstrate fundus imaging at a 20Hz frame rate.     

On the Stability Analysis of Decoupled Solution Schemes

Many problems in engineering, physics or other disciplines require an integrated treatment of coupled fields. These problems are characterised by a dynamic interaction among two or more physically or computationally distinct components, where the undergoing mathematical model commonly consists of a system of coupled PDE. Considerable progress has been made in the development of appropriate computational schemes to solve such coupled PDE systems. These attempts have resulted in various monolithic and decoupled numerical solution approaches. Despite the unconditional stability offered by implicit monolithic solution strategies, their use is not always recommended. The reason mainly lies in the complexity of the resulting system of equations and the limited flexibility in choosing appropriate time integrators for individual components. This has motivated the elaboration of tailored decoupled solution schemes, which follow the idea of splitting the problem into several sub-problems. But selection of the way of splitting can have a direct influence on the stability of the resulting solution algorithm. This necessitates the stability analysis of such an algorithm. Here, we introduce a general framework for the stability analysis of decoupled solution schemes. The approach is then used to study the stability behaviour of established decoupling strategies applied to typical volume- and surface-coupled problems, namely, coupled problems of thermoelasticity, porous media dynamics and structure-structure interaction. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic Wave Propagation in Porous Media Semi-Infinite Domains

The problem of dynamic wave propagation in semi-infinite domains is of great importance, especially, in subjects of applied mechanics and geomechanics, such as the issues of earthquake wave propagation in an infinite half-space and soil-structure interaction under seismic loading. In such problems, the elastic waves are supposed to propagate to infinity, which requires a special treatment of the boundaries in initial boundary-value problems (IBVP). Saturated porous materials, e. g. soil, basically represent volumetrically coupled solid-fluid aggregates. Based on the continuum-mechanical principles and the established macroscopic Theory of Porous Media (TPM) [1, 2], the governing balance equations yield a coupled system of partial differential equations (PDE). Restricting the discussion to the isothermal and geometrically linear case, this system comprises the solid and fluid momentum balances and the overall volume balance, and can be conveniently treated numerically following an implicit monolithic approach [3]. Therefore, the equations are firstly discretised in space using the mixed Finite Element Method (FEM) together with quasi-static Infinite Elements (IE) at the boundaries that represent the extension of the domain to infinity [4], and secondly in time using an appropriate implicit time-integration scheme. Additionally, a stable implementation of the Viscous Damping Boundary (VDB) method [5] for the simulation of transient waves at infinity is presented, which implicitly treats the damping boundary terms in a weakly imposed sense. The proposed algorithm is implemented into the FE tool PANDAS and tested on a two-dimensional IBVP. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Signal‐regulated systems and networks

The article presents the use of signal regulatory networks (SRNs), a biologically inspired model based on gene regulatory networks. SRNs are a way of understanding a class of self‐organizing IT systems, signal‐regulated systems (SRSs). This article builds on the theory of SRSs and introduces some formalisms to clarify the discussion. An exemplar SRS that can be evaluated using SRNs is presented. Finally, an implementation of an adaptive and robust solution, built on a theory of SRSs and analyzed as a SRN, is shown to be plausible. © 2010 Wiley Periodicals, Inc. Complexity, 2010     

Thermal degradation of polymers with phenylene units in the chain. IV. Aromatic polyamides and polyimides

The breakdown mechanism of an aromatic polyamide and four polyimides has been studied under vacuum in the temperature range of 375–620°C, by using techniques described earlier, involving collection and analysis of volatile products as well as analyses of residues at different temperatures. The decomposition of the polyamide up to 375°C yielded predominantly carbon dioxide, while between 375 and 450°C about equal amounts of carbon dioxide and carbon monoxide formed. Hydrogen is the major product between 450 and 550°C, along with hydrogen cyanide, methane, and carbon monoxide. The major reaction at the lower temperatures seems to be the cleavage of the linkage between the carbonyl group and the ring, with subsequent formation of a carbodiimide linkage via isocyanate intermediates, and liberation of carbon dioxide. Alternatively, cleavage between the carboxyl and the NH-group leads to the formation of carbon monoxide. Carbon dioxide and carbon monoxide are also the major volatile decomposition products of the polyimides at the lower temperatures. The primary cleavage reaction is believed to be the rupture of the imide ring between a carbonyl and nitrogen, with subsequent formation of isocyanate groups. The latter react with each other to form carbodiimide linkages and carbon dioxide, while the remaining benzoyl radical is the source for carbon monoxide.     

Parallel Solution Methods for Porous Media Models in Biomechanics

We present a biomechanical application of our parallel finite element model for coupled problems in solid mechanics. This programming framework provides a very lean and flexible interface, which allows to realize time-dependent nonlinear simulations. In this context, a special variant of a stabilized local Gauß-Seidel preconditioner is introduced, which can be successfully employed to large scale computations. Finally, the efficiency of the implemented algorithm is shown by a numerical example considering the axial compression of a L4-L5 motion segment of the spine. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite Elastic Deformations in Liquid-Saturated and Empty Porous Solids

Based on the Theory of Porous Media (TPM), a formulation of a fluid-saturated porous solid is presented where both constituents, the solid and the fluid, are assumed to be materially incompressible. Therefore, the so-called point of compaction exists. This deformation state is reached when all pores are closed and any further volume compression is impossible due to the incompressibility constraint of the solid skeleton material. To describe this effect, a new finite elasticity law is developed on the basis of a hyperelastic strain energy function, thus governing the constraint of material incompressibility for the solid material. Furthermore, a power function to describe deformation dependent permeability effects is introduced.After the spatial discretization of the governing field equations within the finite element method, a differential algebraic system in time arises due to the incompressibility constraint of both constituents. For the efficient numerical treatment of the strongly coupled nonlinear solid-fluid problem, a consistent linearization of the weak forms of the governing equations with respect to the unknowns must be used.