Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

In vitro fabrication of autologous living tissue-engineered vascular grafts based on prenatally harvested ovine amniotic fluid-derived stem cells

Amniotic fluid cells (AFCs) have been proposed as a valuable source for tissue engineering and regenerative medicine. However, before clinical implementation, rigorous evaluation of this cell source in clinically relevant animal models accepted by regulatory authorities is indispensable. Today, the ovine model represents one of the most accepted preclinical animal models, in particular for cardiovascular applications. Here, we investigate the isolation and use of autologous ovine AFCs as cell source for cardiovascular tissue engineering applications. Fetal fluids were aspirated in vivo from pregnant ewes (n = 9) and from explanted uteri post mortem at different gestational ages (n = 91). Amniotic non-allantoic fluid nature was evaluated biochemically and in vivo samples were compared with post mortem reference samples. Isolated cells revealed an immunohistochemical phenotype similar to ovine bone marrow-derived mesenchymal stem cells (MSCs) and showed expression of stem cell factors described for embryonic stem cells, such as NANOG and STAT-3. Isolated ovine amniotic fluid-derived MSCs were screened for numeric chromosomal aberrations and successfully differentiated into several mesodermal phenotypes. Myofibroblastic ovine AFC lineages were then successfully used for the in vitro fabrication of small- and large-diameter tissue-engineered vascular grafts (n = 10) and cardiovascular patches (n = 34), laying the foundation for the use of this relevant pre-clinical in vivo assessment model for future amniotic fluid cell-based therapeutic applications. Copyright © 2013 John Wiley & Sons, Ltd.

A class of exact Navier-Stokes solutions for homogeneous flat-plate boundary layers and their linear stability

We introduce a new boundary layer formalism on the basis of which a class of exact solutions to the Navier–Stokes equations is derived. These solutions describe laminar boundary layer flows past a flat plate under the assumption of one homogeneous direction, such as the classical swept Hiemenz boundary layer (SHBL), the asymptotic suction boundary layer (ASBL) and the oblique impingement boundary layer. The linear stability of these new solutions is investigated, uncovering new results for the SHBL and the ASBL. Previously, each of these flows had been described with its own formalism and coordinate system, such that the solutions could not be transformed into each other. Using a new compound formalism, we are able to show that the ASBL is the physical limit of the SHBL with wall suction when the chordwise velocity component vanishes while the homogeneous sweep velocity is maintained. A corresponding non-dimensionalization is proposed, which allows conversion of the new Reynolds number definition to the classical ones. Linear stability analysis for the new class of solutions reveals a compound neutral surface which contains the classical neutral curves of the SHBL and the ASBL. It is shown that the linearly most unstable Görtler–Hämmerlin modes of the SHBL smoothly transform into Tollmien–Schlichting modes as the chordwise velocity vanishes. These results are useful for transition prediction of the attachment-line instability, especially concerning the use of suction to stabilize boundary layers of swept-wing aircraft.

Computational fluid dynamics modelling in cardiovascular medicine.

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards 'digital patient' or 'virtual physiological human' representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Energy harvesting through arterial wall deformation: A FEM approach to fluid–structure interactions and magneto-hydrodynamics

Engineers are confronted with the energy demand of active medical implants in patients with increasing life expectancy. Scavenging energy from the patient’s body is envisioned as an alternative to conventional power sources. Joining in this effort towards human-powered implants, we propose an innovative concept that combines the deformation of an artery resulting from the arterial pressure pulse with a transduction mechanism based on magneto-hydrodynamics. To overcome certain limitations of a preliminary analytical study on this topic, we demonstrate here a more accurate model of our generator by implementing a three-dimensional multiphysics finite element method (FEM) simulation combining solid mechanics, fluid mechanics, electric and magnetic fields as well as the corresponding couplings. This simulation is used to optimize the generator with respect to several design parameters. A first validation is obtained by comparing the results of the FEM simulation with those of the analytical approach adopted in our previous study. With an expected overall conversion efficiency of 20% and an average output power of 30 μW, our generator outperforms previous devices based on arterial wall deformation by more than two orders of magnitude. Most importantly, our generator provides sufficient power to supply a cardiac pacemaker.

Performance analysis of a miniature turbine generator for intracorporeal energy harvesting

Replacement intervals of implantable medical devices are commonly dictated by battery life. Therefore, intracorporeal energy harvesting has the potential to reduce the number of surgical interventions by extending the life cycle of active devices. Given the accumulated experience with intravascular devices such as stents, heart valves, and cardiac assist devices, the idea to harvest a small fraction of the hydraulic energy available in the cardiovascular circulation is revisited. The aim of this article is to explore the technical feasibility of harvesting 1 mW electric power using a miniature hydrodynamic turbine powered by about 1% of the cardiac output flow in a peripheral artery. To this end, numerical modelling of the fluid mechanics and experimental verification of the overall performance of a 1:1 scale friction turbine are performed in vitro. The numerical flow model is validated for a range of turbine configurations and flow conditions (up to 250 mL/min) in terms of hydromechanic efficiency; up to 15% could be achieved with the nonoptimized configurations of the study. Although this article does not entail the clinical feasibility of intravascular turbines in terms of hemocompatibility and impact on the circulatory system, the numerical model does provide first estimates of the mechanical shear forces relevant to blood trauma and platelet activation. It is concluded that the time-integrated shear stress exposure is significantly lower than in cardiac assist devices due to lower flow velocities and predominantly laminar flow.

Steady streaming in a two-dimensional box model of a passive cochlea

Acoustic stimulation of the cochlea leads to a travelling wave in the cochlear fluids and on the basilar membrane (BM). It has long been suspected that this travelling wave leads to a steady streaming flow in the cochlea. Theoretical investigations suggested that the steady streaming might be of physiological relevance. Here, we present a quantitative study of the steady streaming in a computational model of a passive cochlea. The structure of the streaming flow is illustrated and the sources of streaming are closely investigated. We describe a source of streaming which has not been considered in the cochlea by previous authors. This source is also related to a steady axial displacement of the BM which leads to a local stretching of this compliant structure. We present theoretical predictions for the streaming intensity which account for these new phenomena. It is shown that these predictions compare well with our numerical results and that there may be steady streaming velocities of the order of millimetres per second. Our results indicate that steady streaming should be more relevant to low-frequency hearing because the strength of the streaming flow rapidly decreases for higher frequencies.