Optical density based quantification of total haemoglobin concentrations with spectroscopic optical coherence tomography

Spectroscopic optical coherence tomography (sOCT) has emerged as a new possibility for non-invasive quantification of total haemoglobin concentrations [tHb]. Recently, we demonstrated that [tHb] measured in ex-vivo human whole-blood with a conventional sOCT system achieves a precision of 9.10 g/dL with a bias of 1.50 g/dL. This precision improved by acquiring data with a combination of focus tracking and zero-delay acquisition (FZA) that compensated for experimental limitations, increasing to 3.80 g/dL with a bias of 1.50 g/dL. Nevertheless, sOCT precision should improve at least to $$\sim 2$$ ∼ 2 g/dL to be clinically relevant. Therefore, sOCT-based [tHb] determinations require the development of new analysis methods that reduce the variability of [tHb] estimations. In this work, we aim to increase sOCT precision by retrieving the [tHb] content from a numerical optimisation of the optical density (OD), while considering the blood absorption flattening effect. The OD-based approach simplifies previous two-step Lambert–Beer fitting approaches to a single step, thereby reducing errors during the fitting procedure. We validated our model with ex-vivo [tHb] measurements on flowing whole-blood samples in the clinical range (7–23 g/dL). Our results show that, with the new model, conventional sOCT can determine [tHb] with a precision of 3.09 g/dL and a bias of 0.86 g/dL compared to a commercial blood analyser. We present further precision improvement by combining the OD methodology with FZA, leading to a precision of 2.08 g/dL with a bias of 0.46 g/dL.

Generalised Pattern Search Based on Covariance Matrix Diagonalisation

Pattern Search is a family of gradient-free direct search methods for numerical optimisation problems. The characterising feature of pattern search methods is the use of multiple directions spanning the problem domain to sample new candidate solutions. These directions compose a matrix of potential search moves, that is the pattern. Although some fundamental studies theoretically indicate that various directions can be used, the selection of the search directions remains an unaddressed problem. The present article proposes a procedure for selecting the directions that guarantee high convergence/high performance of pattern search. The proposed procedure consists of a fitness landscape analysis to characterise the geometry of the problem by sampling points and selecting those whose objective function values are below a threshold. The eigenvectors of the covariance matrix of this distribution are then used as search directions for the pattern search. Numerical results show that the proposed method systematically outperforms its standard counterpart and is competitive with modern complex direct search and metaheuristic methods.

Construction of All-Wood Trusses with Plywood Nodes and Wooden Pegs: A Strategy towards Resource-Efficient Timber Construction

Timber truss systems are very efficient load-bearing structures. They allow for great freedom in design and are characterised by high material use in combination with a low environmental impact. Unfortunately, the extensive effort in design and production have made the manufacturing and application of these structures, in this day and age, a rarity. In addition, the currently mainly used steel gusset plates adversely affect the costs and environmental impact of the trusses. The authors’ goals are to optimise the design of timber trusses and to solely use wood for all building components. The two research areas, (1) optimisation of the truss geometry and (2) optimisation of the joints by using solely wood–wood connections, are addressed in this paper. The numerical optimisation strategy is based on a parametric design of the truss and the use of a genetic solver for the optimisation regarding minimal material consumption. Furthermore, first results of the tensile and compression behaviour of the chosen wood–wood connections are presented. The basic idea for the joints is to use a plywood plate as a connector, which is inserted into the truss members and fixed with wooden pegs. The housing of the new robot laboratory located at BOKU Vienna is considered a special case study for the research and serves as an accompanying example for the application of the research within the present paper.

Fully and semi-automated shape differentiation in NGSolve

In this paper, we present a framework for automated shape differentiation in the finite element software . Our approach combines the mathematical Lagrangian approach for differentiating PDE-constrained shape functions with the automated differentiation capabilities of . The user can decide which degree of automatisation is required, thus allowing for either a more custom-like or black-box–like behaviour of the software. We discuss the automatic generation of first- and second-order shape derivatives for unconstrained model problems as well as for more realistic problems that are constrained by different types of partial differential equations. We consider linear as well as nonlinear problems and also problems which are posed on surfaces. In numerical experiments, we verify the accuracy of the computed derivatives via a Taylor test. Finally, we present first- and second-order shape optimisation algorithms and illustrate them for several numerical optimisation examples ranging from nonlinear elasticity to Maxwell’s equations.