Finite volume effects in chiral perturbation theory with twisted boundary conditions

We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We apply Chiral Perturbation Theory in the p-regime and introduce the twist by means of a constant vector field. The corrections of masses, decay constants, pseudoscalar coupling constants and form factors are calculated at next-to-leading order. We detail the derivations and compare with results available in the literature. In some case there is disagreement due to a different treatment of new extra terms generated from the breaking of the cubic invariance. We advocate to treat such terms as renormalization terms of the twisting angles and reabsorb them in the on-shell conditions. We confirm that the corrections of masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. Furthermore, we show that the matrix elements of the scalar (resp. vector) form factor satisfies the Feynman–Hellman Theorem (resp. the Ward–Takahashi identity). To show the Ward–Takahashi identity we construct an effective field theory for charged pions which is invariant under electromagnetic gauge transformations and which reproduces the results obtained with Chiral Perturbation Theory at a vanishing momentum transfer. This generalizes considerations previously published for periodic boundary conditions to twisted boundary conditions. Another method to estimate the corrections in finite volume are asymptotic formulae. Asymptotic formulae were introduced by Lüscher and relate the corrections of a given physical quantity to an integral of a specific amplitude, evaluated in infinite volume. Here, we revise the original derivation of Lüscher and generalize it to finite volume with twisted boundary conditions. In some cases, the derivation involves complications due to extra terms generated from the breaking of the cubic invariance. We isolate such terms and treat them as renormalization terms just as done before. In that way, we derive asymptotic formulae for masses, decay constants, pseudoscalar coupling constants and scalar form factors. At the same time, we derive also asymptotic formulae for renormalization terms. We apply all these formulae in combination with Chiral Perturbation Theory and estimate the corrections beyond next-to-leading order. We show that asymptotic formulae for masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. A similar relation connects in an independent way asymptotic formulae for renormalization terms. We check these relations for charged pions through a direct calculation. To conclude, a numerical analysis quantifies the importance of finite volume corrections at next-to-leading order and beyond. We perform a generic Analysis and illustrate two possible applications to real simulations.

An experimentally validated finite element method for augmented vertebral bodies

Background Finite element models of augmented vertebral bodies require a realistic modelling of the cement infiltrated region. Most methods published so far used idealized cement shapes or oversimplified material models for the augmented region. In this study, an improved, anatomy-specific, homogenized finite element method was developed and validated to predict the apparent as well as the local mechanical behavior of augmented vertebral bodies. Methods Forty-nine human vertebral body sections were prepared by removing the cortical endplates and scanned with high-resolution peripheral quantitative CT before and after injection of a standard and a low-modulus bone cement. Forty-one specimens were tested in compression to measure stiffness, strength and contact pressure distributions between specimens and loading-plates. From the remaining eight, fourteen cylindrical specimens were extracted from the augmented region and tested in compression to obtain material properties. Anatomy-specific finite element models were generated from the CT data. The models featured element-specific, density-fabric-based material properties, damage accumulation, real cement distributions and experimentally determined material properties for the augmented region. Apparent stiffness and strength as well as contact pressure distributions at the loading plates were compared between simulations and experiments. Findings The finite element models were able to predict apparent stiffness (R2 > 0.86) and apparent strength (R2 > 0.92) very well. Also, the numerically obtained pressure distributions were in reasonable quantitative (R2 > 0.48) and qualitative agreement with the experiments. Interpretation The proposed finite element models have proven to be an accurate tool for studying the apparent as well as the local mechanical behavior of augmented vertebral bodies.

A patient-specific study of type-B aortic dissection: evaluation of true-false lumen blood exchange

BACKGROUND Aortic dissection is a severe pathological condition in which blood penetrates between layers of the aortic wall and creates a duplicate channel - the false lumen. This considerable change on the aortic morphology alters hemodynamic features dramatically and, in the case of rupture, induces markedly high rates of morbidity and mortality. METHODS In this study, we establish a patient-specific computational model and simulate the pulsatile blood flow within the dissected aorta. The k-ω SST turbulence model is employed to represent the flow and finite volume method is applied for numerical solutions. Our emphasis is on flow exchange between true and false lumen during the cardiac cycle and on quantifying the flow across specific passages. Loading distributions including pressure and wall shear stress have also been investigated and results of direct simulations are compared with solutions employing appropriate turbulence models. RESULTS Our results indicate that (i) high velocities occur at the periphery of the entries; (ii) for the case studied, approximately 40% of the blood flow passes the false lumen during a heartbeat cycle; (iii) higher pressures are found at the outer wall of the dissection, which may induce further dilation of the pseudo-lumen; (iv) highest wall shear stresses occur around the entries, perhaps indicating the vulnerability of this region to further splitting; and (v) laminar simulations with adequately fine mesh resolutions, especially refined near the walls, can capture similar flow patterns to the (coarser mesh) turbulent results, although the absolute magnitudes computed are in general smaller. CONCLUSIONS The patient-specific model of aortic dissection provides detailed flow information of blood transport within the true and false lumen and quantifies the loading distributions over the aorta and dissection walls. This contributes to evaluating potential thrombotic behavior in the false lumen and is pivotal in guiding endovascular intervention. Moreover, as a computational study, mesh requirements to successfully evaluate the hemodynamic parameters have been proposed.

Hemodynamics analyses in treated and untreated carotid arteries of the same patient: A preliminary study based on three patient cases

Carotid atherosclerotic disease is highly related to cerebrovascular events. Carotid endarterectomy is the common operation method to treat this disease. In this study, hemodynamics analyses are performed on the carotid arteries in three patients, whose right carotid artery had been treated by carotid endarterectomy and the left carotid artery remained untreated. Flow and loading conditions are compared between these treated and untreated carotid arteries and evaluation of the operative results is discussed. Patient-specific models are reconstructed from MDCT data. Intraoperative ultrasound flow measurements are performed on the treated carotid arteries and the obtained data are used as the boundary conditions of the models and the validations of the computational results. Finite volume method is employed to solve the transport equations and the flow and loading conditions of the models are reported. The results indicate that: (i) in two of the three patients, the internal-to-external flow rate ratio in the untreated carotid artery is larger than that in the treated one, and the average overall flow split ratio by summing up the data of both the left and right carotid arteries is about 2.15; (ii) in the carotid bulb, high wall shear stress occurs at the bifurcation near the external carotid artery in all of the cases without hard plaques; (iii) the operated arteries present low time-averaged wall shear stress at the carotid bulb, especially for the treated arteries with patch technique, indicating the possibility of the recurrence of stenosis; (iv) high temporal gradient of wall shear stress (>35 Pa/s) is shown in the narrowing regions along the vessels; and (v) in the carotid arteries without serious stenosis, the maximum velocity magnitude during mid-diastole is 32~37% of that at systolic peak, however, in the carotid artery with 50% stenosis by hard plaques, this value is nearly doubled (64%). The computational work quantifies flow and loading distributions in the treated and untreated carotid arteries of the same patient, contributing to evaluation of the operative results and indicating the recurrent sites of potential atheromatous plaques.

The pollen tube: a soft shell with a hard core

Plant cell expansion is controlled by a fine-tuned balance between intracellular turgor pressure, cell wall loosening and cell wall biosynthesis. To understand these processes, it is important to gain in-depth knowledge of cell wall mechanics. Pollen tubes are tip-growing cells that provide an ideal system to study mechanical properties at the single cell level. With the available approaches it was not easy to measure important mechanical parameters of pollen tubes, such as the elasticity of the cell wall. We used a cellular force microscope (CFM) to measure the apparent stiffness of lily pollen tubes. In combination with a mechanical model based on the finite element method (FEM), this allowed us to calculate turgor pressure and cell wall elasticity, which we found to be around 0.3 MPa and 20–90 MPa, respectively. Furthermore, and in contrast to previous reports, we showed that the difference in stiffness between the pollen tube tip and the shank can be explained solely by the geometry of the pollen tube. CFM, in combination with an FEM-based model, provides a powerful method to evaluate important mechanical parameters of single, growing cells. Our findings indicate that the cell wall of growing pollen tubes has mechanical properties similar to rubber. This suggests that a fully turgid pollen tube is a relatively stiff, yet flexible cell that can react very quickly to obstacles or attractants by adjusting the direction of growth on its way through the female transmitting tissue.

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.

Mechanical constraints imposed by 3D cellular geometry and arrangement modulate growth patterns in the Arabidopsis embryo

Morphogenesis occurs in 3D space over time and is guided by coordinated gene expression programs. Here we use postembryonic development in Arabidopsis plants to investigate the genetic control of growth. We demonstrate that gene expression driving the production of the growth-stimulating hormone gibberellic acid and downstream growth factors is first induced within the radicle tip of the embryo. The center of cell expansion is, however, spatially displaced from the center of gene expression. Because the rapidly growing cells have very different geometry from that of those at the tip, we hypothesized that mechanical factors may contribute to this growth displacement. To this end we developed 3D finite-element method models of growing custom-designed digital embryos at cellular resolution. We used this framework to conceptualize how cell size, shape, and topology influence tissue growth and to explore the interplay of geometrical and genetic inputs into growth distribution. Our simulations showed that mechanical constraints are sufficient to explain the disconnect between the experimentally observed spatiotemporal patterns of gene expression and early postembryonic growth. The center of cell expansion is the position where genetic and mechanical facilitators of growth converge. We have thus uncovered a mechanism whereby 3D cellular geometry helps direct where genetically specified growth takes place.

Cell therapy for intervertebral disc repair: advancing cell therapy from bench to clinics

Intervertebral disc (IVD) degeneration is a major cause of pain and disability; yet therapeutic options are limited and treatment often remains unsatisfactory. In recent years, research activities have intensified in tissue engineering and regenerative medicine, and pre-clinical studies have demonstrated encouraging results. Nonetheless, the translation of new biological therapies into clinical practice faces substantial barriers. During the symposium "Where Science meets Clinics", sponsored by the AO Foundation and held in Davos, Switzerland, from September 5-7, 2013, hurdles for translation were outlined, and ways to overcome them were discussed. With respect to cell therapy for IVD repair, it is obvious that regenerative treatment is indicated at early stages of disc degeneration, before structural changes have occurred. It is envisaged that in the near future, screening techniques and non-invasive imaging methods will be available to detect early degenerative changes. The promises of cell therapy include a sustained effect on matrix synthesis, inflammation control, and prevention of angio- and neuro-genesis. Discogenic pain, originating from "black discs" or annular injury, prevention of adjacent segment disease, and prevention of post-discectomy syndrome were identified as prospective indications for cell therapy. Before such therapy can safely and effectively be introduced into clinics, the identification of the patient population and proper standardisation of diagnostic parameters and outcome measurements are indispensable. Furthermore, open questions regarding the optimal cell type and delivery method need to be resolved in order to overcome the safety concerns implied with certain procedures. Finally, appropriate large animal models and well-designed clinical studies will be required, particularly addressing safety aspects.

Critical point and scale setting in SU(3) plasma: An update

We explore a method developed in statistical physics which has been argued to have exponentially small finite-volume effects, in order to determine the critical temperature Tc of pure SU(3) gauge theory close to the continuum limit. The method allows us to estimate the critical coupling βc of the Wilson action for temporal extents up to Nτ∼20 with ≲0.1% uncertainties. Making use of the scale setting parameters r0 and t0−−√ in the same range of β-values, these results lead to the independent continuum extrapolations Tcr0=0.7457(45) and Tct0−−√=0.2489(14), with the latter originating from a more convincing fit. Inserting a conversion of r0 from literature (unfortunately with much larger errors) yields Tc/ΛMS¯¯¯¯¯=1.24(10).