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While many algorithms have been proposed to estimate blood flow velocities based on the transport information of contrast agent acquired by digital subtraction angiography (DSA), most relevant studies focused on a single vessel, leaving a question open as to whether the algorithms would be suitable for estimating blood flow velocities in arterial systems with complex topological structures. In this study, a one-dimensional (1-D) modeling method was developed to simulate the transport of contrast agent in cerebral arterial networks with various anatomical variations or having occlusive disease, thereby generating an in silico database for examining the accuracies of some typical algorithms (i.e., time-of-center of gravity (TCG), shifted least-squares (SLS), and cross correlation (CC) algorithms) that estimate blood flow velocity based on the concentration-time curves (CTCs) of contrast agent. The results showed that the TCG algorithm had the best performance in estimating blood flow velocities in most cerebral arteries, with the accuracy being only mildly affected by anatomical variations of the cerebral arterial network. Nevertheless, the presence of a stenosis of moderate to high severity in the internal carotid artery could considerably impair the accuracy of the TCG algorithm in estimating blood flow velocities in some cerebral arteries where the transport of contrast agent was disturbed by strong collateral flows. In summary, the study suggests that the TCG algorithm may offer a promising means for estimating blood flow velocities based on CTCs of contrast agent monitored in cerebral arteries, provided that the shapes of CTCs are not highly distorted by collateral flows.

Abstract Scorpion α-toxins are small proteins inhibiting the inactivation of voltage-gated sodium channels. They can selectively act on either mammalian (mammal toxins) or insect channels (insect toxins), or affect both types of channels (α-like toxins). Currently no model has been proposed that fully explains the dependence of selectivity upon amino acid sequence, but some patterns have already been established. Thus, most mammal toxins have an aspartic acid residue in position 8, which is involved in the formation of the nest motif, but it is still not clear whether this residue interacts directly with channels. The objective of our study was to obtain a derivative of the α-like toxin BeM9 with the replacement of lysine in position 8 by glutamate (K8E), changing the charge, but excluding the formation of the nest motif. In addition, we replaced the tyrosine in position 17 with glycine (Y17G), which is characteristic of mammal toxins. Surprisingly, the double-mutant derivative BeM9EG lost its activity on mammalian channels, becoming an insect toxin. To explain these changes, we constructed models of BeM9 and BeM9EG complexes with channels, and also performed molecular dynamics of isolated toxins. Analysis of intermolecular contacts in the complexes did not explain the reason for the selectivity change. Nevertheless, the structure of intramolecular contacts and data on molecular mobility indicate an important role of residues K8 and Y17 in stabilizing a certain conformation of BeM9 loops. We assume that the replacement of these residues allosterically affects the efficiency of toxin binding to channels.

Human knee is one of the most complex joints. Different reasons may lead to knee instability. A personalized mathematical model of the knee may improve both diagnostic procedure and knee surgery outcomes. Such models require accurate geometric representation of bones and attachment sites of ligaments and tendons. This paper addresses automatic segmentation of knee bones and detection of origins and insertions for tendons and ligaments. The approach is based on anatomical features of bones and landmarks of tendons/ligaments attachments on the CT images. It provides a tool for the design of patient-specific geometrical knee models.

Tk-hefu is an artificial peptide designed based on the α-hairpinin scaffold, which selectively blocks voltage-gated potassium channels K(v)1.3. Here we present its spatial structure resolved by NMR spectroscopy and analyze its interaction with channels using computer modeling. We apply protein surface topography to suggest mutations and increase Tk-hefu affinity to the K(v)1.3 channel isoform. We redesign the functional surface of Tk-hefu to better match the respective surface of the channel pore vestibule. The resulting peptide Tk-hefu-2 retains K(v)1.3 selectivity and displays ∼15 times greater activity compared with Tk-hefu. We verify the mode of Tk-hefu-2 binding to the channel outer vestibule experimentally by site-directed mutagenesis. We argue that scaffold engineering aided by protein surface topography represents a reliable tool for design and optimization of specific ion channel ligands.

Aortic valve disease accounts for 45% of deaths from heart valve diseases.% \cite{Coffey2015}. An appealing approach to treat aortic valve disease is surgical replacement of the valve leaflets based on chemically treated autologous pericardium. This procedure is attractive due to its low cost and high effectiveness. We aim to develop a computational technology for patient-specific assessment of reconstructed aortic valve function that can be used by surgeons at the preoperative stage. The framework includes automatic computer tomography image segmentation, mesh generation, simulation of valve leaflet deformation. The final decision will be based on uncertainty analysis and leaflet shape optimization. This paper gives a proof of concept of our methodology: simulation methods are presented and studied numerically.

The article introduces a finite-volume method for the Darcy problem in heterogeneous anisotropic media. The method is based on the mixed formulation for the pressure and its gradient. The method is stable despite collocation of both pressure and its gradient at cell centers and demonstrates the first order convergence on numerous benchmarks as well as good monotonicity property. The method produces quasi-definite matrix, which is numerically shown to have good asymptotics of the condition number. Our flux discretization method is a realization of our more general concept of stable flux discretization for saddle-point systems with vector of several unknowns. In this paper this vector is composed of pressure and its gradient and the saddle-point system is the mixed formulation of the Darcy problem.

This work introduces an effective bacterial system for the production of β-toxin Ts1, the main component of the Brazilian scorpion Tityus serrulatus venom. Recombinant toxin and its 15N-labeled analogue are obtained by direct expression of the synthetic gene in Escherichia coli, with subsequent folding from the inclusion bodies. NMR spectroscopy data assert that the recombinant toxin is structured in aqueous solution and is composed of a significant fraction of β-structure. Moreover, the formation of a stable Ts1 disulfide-bond isomer of a disordered structure is observed during folding; recombinant Ts1 blocks Na+ current through NaV1.5 channels, without affecting the processes of activation and inactivation. Simultaneously, the effect upon NaV1.4 channels is associated with a shift of the activation curve toward the more negative membrane potentials.

We study approximations of eigenvalue problems for integral operators associated with kernel functions of exponential type. We show convergence rate | λ k - λ k , h | ≤ C k ⁢ h 2 {\lvert\lambda_{k}-\lambda_{k,h}\rvert\leq C_{k}h^{2}} in the case of lowest order approximation for both Galerkin and Nyström methods, where h is the mesh size, λ k {\lambda_{k}} and λ k , h {\lambda_{k,h}} are the exact and approximate kth largest eigenvalues, respectively. We prove that the two methods are numerically equivalent in the sense that | λ k , h ( G ) - λ k , h ( N ) | ≤ C ⁢ h 2 {|\lambda^{(G)}_{k,h}-\lambda^{(N)}_{k,h}|\leq Ch^{2}} , where λ k , h ( G ) {\lambda^{(G)}_{k,h}} and λ k , h ( N ) {\lambda^{(N)}_{k,h}} denote the kth largest eigenvalues computed by Galerkin and Nyström methods, respectively, and C is a eigenvalue independent constant. The theoretical results are accompanied by a series of numerical experiments.

We propose an unified algebraic approach for static condensation and hybridization, two popular techniques in finite element discretizations. The algebraic approach is supported by the construction of scalable solvers for problems involving H(div)-spaces discretized by conforming (Raviart-Thomas) elements of arbitrary order. We illustrate through numerical experiments the relative performance of the two (in some sense dual) techniques in comparison with a state-of-the-art parallel solver, ADS, available in the software hypre and MFEM. The superior performance of the hybridization technique is clearly demonstrated with increased benefit for higher order elements., Comment: 18 pages, 9 figures

Algebraic multigrid (AMG) coarse spaces are commonly constructed so that they exhibit the so-called weak approximation (WAP) property which is necessary and sufficient condition for uniform two-grid convergence. This paper studies a modification of such coarse spaces so that the modified ones provide approximation in energy norm. Our modification is based on the projection in energy norm onto an orthogonal complement of original coarse space. This generally leads to dense modified coarse space matrices which is hence computationally infeasible. To remedy this, based on the fact that the projection involves inverse of a well-conditioned matrix, we use polynomials to approximate the projection and, therefore, obtain a practical, sparse modified coarse matrix and prove that the modified coarse space maintains computationally feasible approximation in energy norm. We present some numerical results for both, PDE discretization matrices as well as graph Laplacian ones, which are in accordance with our theoretical results.

In this paper we analyze and investigate numerically a monolithic finite element method for the incompressible Navier–Stokes equations coupled to the Saint Venant–Kirchhoff hyperelastic model. The approach strongly enforces the coupling conditions on the fluid–structure interface and treats both solid and fluid equations in a reference domain accounting for geometric motion through time-dependent coefficients. The paper derives an energy balance for the fully discrete system and proves that the finite element method is numerically stable. The performance of the method is further assessed by validating numerical results for the pressure impulse prorogation test and against the results of a recently proposed experimental 3D fluid-structure interaction benchmark problem.

Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first time. Our numerical thin shell model is based on a combination of the hyperelastic nodal forces method and the rotation-free finite elements. The shell model is verified on several popular benchmarks for thin-shell analysis. The relative error with respect to reference solutions does not exceed 1–2%. We apply our numerical shell and membrane formulations to model the closure of an idealized aortic valve varying hyperelasticity models and their shear moduli. The coaptation characteristics become almost insensitive to elastic potentials and sensitive to bending stiffness, which reduces the coaptation zone.

The diseases and injuries of the knee joint are the most common orthopedic disorders. Personalized knee models can be helpful in the process of early intervention and lasting treatment techniques development. Fully automatic reconstruction of knee joint anatomical structures from medical images (CT, MRI, ultrasound) remains a challenge. For this reason, most of state-of-the-art knee joint models contain simplifications such as representation of muscles and ligaments as line segments connecting two points which replace attachment areas. The paper presents algorithms for automatic detection of such points on knee CT images.This paper presents three approaches to automatic detection of ligaments and tendons attachment sites on the patients CT images: qualitative anatomical descriptions, analysis of bones curvature, and quantitative anatomical descriptions. Combinations of these approaches result in new automatic detection algorithms. Each algorithm exploits anatomical peculiarities of each attachment site, e.g., bone curvature and number of other attachments in a neighborhood of the site.The experimental dataset consisted of 26 anonymized CT sequences containing right and left knee joints in different resolutions. The proposed algorithms take into account bone surface curvatures and spatial differences in locations of medial and lateral parts of both knees. The algorithms for detection of quadriceps femoris, popliteus, biceps femoris tendons, and lateral collateral and medial collateral ligaments attachment sites are provided, as well as examples of their application. Two algorithms are validated by comparison with known statistics of ligaments lengths and also using ground truth annotations for anatomical landmarks approved by clinical experts.The algorithms simplify generation of patient-specific knee joint models demanded in personalized biomechanical models. The algorithms in the current implementation have two important limitations. First, the correctness of the produced results depends on the bones segmentation quality. Second, the presented algorithms detect a point of the attachment site, which is not necessarily its center. Therefore, manual correction of the attachment site location may be required for attachments with relatively large area.