Communications On Pure & Applied Mathematics [SJR: 4.177] [H-I: 74] [3 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 0010-3640 - ISSN (Online) 1097-0312 Published by John Wiley and Sons [1589 journals] |
- Issue Information
- Abstract: No abstract is available for this article.
PubDate: 2017-04-05T12:49:47.464013-05:
DOI: 10.1002/cnm.2883
- Abstract: No abstract is available for this article.
- What Is Variable Bandwidth?
- Authors: Karlheinz Gröchenig; Andreas Klotz
Abstract: We propose a new notion of variable bandwidth that is based on the spectral subspaces of an elliptic operator Apf=−ddx(p(x)ddx)f where p > 0 is a strictly positive function. Denote by cΛ(Ap) the orthogonal projection of Ap corresponding to the spectrum of Ap in Λ⊂ ℝ+; the range of this projection is the space of functions of variable bandwidth with spectral set in Λ.We will develop the basic theory of these function spaces. First, we derive (nonuniform) sampling theorems; second, we prove necessary density conditions in the style of Landau. Roughly, for a spectrum Λ=[0,Ω] the main results say that, in a neighborhood of x∈ ℝ, a function of variable bandwidth behaves like a band-limited function with local bandwidth (Ω/p(x))1/2.Although the formulation of the results is deceptively similar to the corresponding results for classical band-limited functions, the methods of proof are much more involved. On the one hand, we use the oscillation method from sampling theory and frame-theoretic methods; on the other hand, we need the precise spectral theory of Sturm-Liouville operators and the scattering theory of one-dimensional Schrödinger operators. © 2017 Wiley Periodicals, Inc.
PubDate: 2017-03-28T05:11:11.432927-05:
DOI: 10.1002/cpa.21694
- Authors: Karlheinz Gröchenig; Andreas Klotz
- Large Deviations for Stationary Measures of Stochastic Nonlinear Wave
Equations with Smooth White Noise- Authors: Davit Martirosyan
PubDate: 2017-03-17T05:25:45.4721-05:00
DOI: 10.1002/cpa.21693
- Authors: Davit Martirosyan
- Pointwise Estimates and Regularity in Geometric Optics and Other Generated
Jacobian Equations- Authors: Nestor Guillen; Jun Kitagawa
Abstract: The study of reflector surfaces in geometric optics necessitates the analysis of certain nonlinear equations of Monge-Ampère type known as generated Jacobian equations. This class of equations, whose general existence theory has been recently developed by Trudinger, goes beyond the framework of optimal transport. We obtain pointwise estimates for weak solutions of such equations under minimal structural and regularity assumptions, covering situations analogous to those of costs satisfying the A3-weak condition introduced by Ma, Trudinger, and Wang in optimal transport. These estimates are used to develop a C1,α regularity theory for weak solutions of Aleksandrov type. The results are new even for all known near-field reflector/refractor models, including the point source and parallel beam reflectors, and are applicable to problems in other areas of geometry, such as the generalized Minkowski problem. © 2016 Wiley Periodicals, Inc.
PubDate: 2017-03-11T02:15:25.448477-05:
DOI: 10.1002/cpa.21691
- Authors: Nestor Guillen; Jun Kitagawa
- Uniqueness of Tangent Cones for Two-Dimensional Almost-Minimizing Currents
- Authors: Camillo De Lellis; Emanuele Spadaro, Luca Spolaor
Abstract: We consider two-dimensional integer rectifiable currents that are almost area minimizing and show that their tangent cones are everywhere unique. Our argument unifies a few uniqueness theorems of the same flavor, which are all obtained by a suitable modification of White's original theorem for area-minimizing currents in the euclidean space. This note is also the first step in a regularity program for semicalibrated two-dimensional currents and spherical cross sections of three-dimensional area-minimizing cones.© 2016 Wiley Periodicals, Inc.
PubDate: 2017-03-01T03:15:44.210435-05:
DOI: 10.1002/cpa.21690
- Authors: Camillo De Lellis; Emanuele Spadaro, Luca Spolaor
- Riemann-Hilbert Problems for the Shapes Formed by Bodies Dissolving,
Melting, and Eroding in Fluid Flows- Authors: M. Nicholas J. Moore
Abstract: The classical Stefan problem involves the motion of boundaries during phase transition, but this process can be greatly complicated by the presence of a fluid flow. Here we consider a body undergoing material loss due to either dissolution (from molecular diffusion), melting (from thermodynamic phase change), or erosion (from fluid-mechanical stresses) in a fast-flowing fluid. In each case, the task of finding the shape formed by the shrinking body can be posed as a singular Riemann-Hilbert problem. A class of exact solutions captures the rounded surfaces formed during dissolution/melting, as well as the angular features formed during erosion, thus unifying these different physical processes under a common framework. This study, which merges boundary-layer theory, separated-flow theory, and Riemann-Hilbert analysis, represents a rare instance of an exactly solvable model for high-speed fluid flows with free boundaries.© 2017 Wiley Periodicals, Inc.
PubDate: 2017-03-01T03:10:34.407137-05:
DOI: 10.1002/cpa.21689
- Authors: M. Nicholas J. Moore
- Compactness of Alexandrov-Nirenberg Surfaces
- Authors: Qing Han; Jiaxing Hong, Genggeng Huang
Abstract: We study a class of compact surfaces in ℝ3 introduced by Alexandrov and generalized by Nirenberg and prove a compactness result under suitable assumptions on induced metrics and Gauss curvatures. © 2016 Wiley Periodicals, Inc.
PubDate: 2017-02-16T02:00:34.949701-05:
DOI: 10.1002/cpa.21686
- Authors: Qing Han; Jiaxing Hong, Genggeng Huang
- Arithmetic Spectral Transitions for the Maryland Model
- Authors: Svetlana Jitomirskaya; Wencai Liu
Abstract: We give a precise description of spectra of the Maryland model(hλ,α,θu)n=un+1+un−1+λtanπ(θ+nα)un for all values of parameters. We introduce an arithmetically defined index δ(α,θ) and show that for α∉ℚ,σsc(hλ,α,θ)={e:γλ(e)
PubDate: 2017-02-16T01:40:24.978002-05:
DOI: 10.1002/cpa.21688
- Authors: Svetlana Jitomirskaya; Wencai Liu
- Spectral Approach to D-bar Problems
- Authors: Christian Klein; Kenneth D. T-R McLaughlin
Abstract: We present the first numerical approach to D-bar problems having spectral convergence for real analytic, rapidly decreasing potentials. The proposed method starts from a formulation of the problem in terms of an integral equation that is numerically solved with Fourier techniques. The singular integrand is regularized analytically. The resulting integral equation is approximated via a discrete system that is solved with Krylov methods. As an example, the D-bar problem for the Davey-Stewartson II equations is considered. The result is used to test direct numerical solutions of the PDE.© 2016 Wiley Periodicals, Inc.
PubDate: 2017-02-16T01:35:27.991023-05:
DOI: 10.1002/cpa.21684
- Authors: Christian Klein; Kenneth D. T-R McLaughlin
- Mutual Absolute Continuity of Interior and Exterior Harmonic Measure
Implies Rectifiability- Authors: Jonas Azzam; Mihalis Mourgoglou, Xavier Tolsa
Abstract: We show that, for disjoint domains in the euclidean space whose boundaries satisfy a nondegeneracy condition, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries. © 2016 Wiley Periodicals, Inc.
PubDate: 2017-02-15T01:16:04.044808-05:
DOI: 10.1002/cpa.21687
- Authors: Jonas Azzam; Mihalis Mourgoglou, Xavier Tolsa
- Experiment for validation of fluid-structure interaction models and
algorithms- Authors: A. Hessenthaler; N. R. Gaddum, O. Holub, R. Sinkus, O. Röhrle, D. Nordsletten
Abstract: In this paper a fluid-structure interaction (FSI) experiment is presented. The aim of this experiment is to provide a challenging yet easy-to-setup FSI test case that addresses the need for rigorous testing of FSI algorithms and modeling frameworks. Steady-state and periodic steady-state test cases with constant and periodic inflow were established. Focus of the experiment is on biomedical engineering applications with flow being in the laminar regime with Reynolds numbers 1283 and 651. Flow and solid domains were defined using computer-aided design (CAD) tools. The experimental design aimed at providing a straightforward boundary condition definition. Material parameters and mechanical response of a moderately viscous Newtonian fluid and a nonlinear incompressible solid were experimentally determined. A comprehensive data set was acquired by using magnetic resonance imaging to record the interaction between the fluid and the solid, quantifying flow and solid motion.A fluid-structure interaction (FSI) experiment is presented with the aim to provide a challenging yet easy-to-setup FSI test case that addresses the need for rigorous testing of FSI algorithms and modeling frameworks. Focus of the experiment is on biomedical engineering applications. A comprehensive data set was acquired by employing magnetic resonance imaging to record the interaction between the fluid and the solid, quantifying flow and solid motion for steady-state and periodic steady-state test cases.
PubDate: 2017-01-27T03:31:43.428518-05:
DOI: 10.1002/cnm.2848
- Authors: A. Hessenthaler; N. R. Gaddum, O. Holub, R. Sinkus, O. Röhrle, D. Nordsletten
- Direct numerical simulation of transitional hydrodynamics of the
cerebrospinal fluid in Chiari I malformation: The role of cranio-vertebral
junction- Authors: Kartik Jain; Geir Ringstad, Per-Kristian Eide, Kent-André Mardal
Abstract: Obstruction to the cerebrospinal fluid (CSF) outflow caused by the herniation of cerebellar tonsils as a result of Chiari malformation type I leads to altered CSF hydrodynamics. This contribution explores the minutest characteristics of the CSF hydrodynamics in cervical subarachnoid space (SAS) of a healthy subject and 2 Chiari patients by performing highly resolved direct numerical simulation. The lattice Boltzmann method is used for the simulations because of its scalability on modern supercomputers that allow us to simulate up to approximately 109 cells while resolving the Kolmogorov microscales. The results depict that whereas the complex CSF flow remains largely laminar in the SAS of a healthy subject, constriction of the cranio-vertebral junction in Chiari I patients causes manifold fluctuations in the hydrodynamics of the CSF. These fluctuations resemble a flow that is in a transitional regime rather than laminar or fully developed turbulence. The fluctuations confine near the cranio-vertebral junction and are triggered due to the tonsillar herniation, which perturbs the flow as a result of altered anatomy of the SAS.Chiari malformation type I obstructs the outflow of the cerebrospinal fluid near the foramen magnum. We conducted direct numerical simulations with meshes containing up to 1 billion cells on case specific subarachnoid spaces of one control subject and 2 Chiari patients on a modern supercomputer. We found the onset of transitional-like hydrodynamics of CSF in 2 Chiari patients whereas the flow remained laminar in the control subject.
PubDate: 2017-01-13T04:35:34.389861-05:
DOI: 10.1002/cnm.2853
- Authors: Kartik Jain; Geir Ringstad, Per-Kristian Eide, Kent-André Mardal
- Assessment of reduced-order unscented Kalman filter for parameter
- Authors: A. Caiazzo; Federica Caforio, Gino Montecinos, Lucas O. Muller, Pablo J. Blanco, Eluterio F. Toro
Abstract: This work presents a detailed investigation of a parameter estimation approach on the basis of the reduced-order unscented Kalman filter (ROUKF) in the context of 1-dimensional blood flow models. In particular, the main aims of this study are (1) to investigate the effects of using real measurements versus synthetic data for the estimation procedure (i.e., numerical results of the same in silico model, perturbed with noise) and (2) to identify potential difficulties and limitations of the approach in clinically realistic applications to assess the applicability of the filter to such setups. For these purposes, the present numerical study is based on a recently published in vitro model of the arterial network, for which experimental flow and pressure measurements are available at few selected locations. To mimic clinically relevant situations, we focus on the estimation of terminal resistances and arterial wall parameters related to vessel mechanics (Young's modulus and wall thickness) using few experimental observations (at most a single pressure or flow measurement per vessel). In all cases, we first perform a theoretical identifiability analysis on the basis of the generalized sensitivity function, comparing then the results owith the ROUKF, using either synthetic or experimental data, to results obtained using reference parameters and to available measurements.This work considers a parameter estimation approach on the basis of the reduced-order unscented Kalman filter in the context of one-dimensional blood flow models, investigating the effects of using real measurements versus synthetic data for the estimation procedure. The filter is assessed considering the results of an in vitro model of the human arterial network and the available experimental measurements, comparing the estimation results with an identifiability analysis on the basis of the generalized sensitivity function and considering flow and pressure observations.
PubDate: 2017-01-13T04:10:37.92513-05:0
DOI: 10.1002/cnm.2843
- Authors: A. Caiazzo; Federica Caforio, Gino Montecinos, Lucas O. Muller, Pablo J. Blanco, Eluterio F. Toro
- Multiphase fluid-solid coupled analysis of shock-bubble-stone interaction
in shockwave lithotripsy- Authors: Kevin G. Wang
Abstract: A novel multiphase fluid-solid–coupled computational framework is applied to investigate the interaction of a kidney stone immersed in liquid with a lithotripsy shock wave (LSW) and a gas bubble near the stone. The main objective is to elucidate the effects of a bubble in the shock path to the elastic and fracture behaviors of the stone. The computational framework couples a finite volume 2-phase computational fluid dynamics solver with a finite element computational solid dynamics solver. The surface of the stone is represented as a dynamic embedded boundary in the computational fluid dynamics solver. The evolution of the bubble surface is captured by solving the level set equation. The interface conditions at the surfaces of the stone and the bubble are enforced through the construction and solution of local fluid-solid and 2-fluid Riemann problems. This computational framework is first verified for 3 example problems including a 1D multimaterial Riemann problem, a 3D shock-stone interaction problem, and a 3D shock-bubble interaction problem. Next, a series of shock-bubble-stone–coupled simulations are presented. This study suggests that the dynamic response of a bubble to LSW varies dramatically depending on its initial size. Bubbles with an initial radius smaller than a threshold collapse within 1 μs after the passage of LSW, whereas larger bubbles do not. For a typical LSW generated by an electrohydraulic lithotripter (pmax = 35.0MPa, pmin =− 10.1MPa), this threshold is approximately 0.12mm. Moreover, this study suggests that a noncollapsing bubble imposes a negative effect on stone fracture as it shields part of the LSW from the stone. On the other hand, a collapsing bubble may promote fracture on the proximal surface of the stone, yet hinder fracture from stone interior.A 3D computational fluid dynamics (CFD)-computational solid dynamics (CSD) coupled computational framework is applied to investigate the interaction of model kidney stones immersed in liquid with a lithotripsy shock wave (LSW) and a gas bubble near the stone. The simulation results suggest that bubbles smaller than a certain threshold may collapse violently during the process, thereby promoting fracture on stone surface, yet hindering fracture in the interior.
PubDate: 2017-01-13T04:05:46.50725-05:0
DOI: 10.1002/cnm.2855
- Authors: Kevin G. Wang
- Mean-Field Interaction of Brownian Occupation Measures II: A Rigorous
Construction of the Pekar Process- Authors: Erwin Bolthausen; Wolfgang König, Chiranjib Mukherjee
Abstract: We consider mean-field interactions corresponding to Gibbs measures on interacting Brownian paths in three dimensions. The interaction is self-attractive and is given by a singular Coulomb potential. The logarithmic asymptotics of the partition function for this model were identified in the 1980s by Donsker and Varadhan in terms of the Pekar variational formula, which coincides with the behavior of the partition function of the polaron problem under strong coupling. Based on this, in 1986 Spohn made a heuristic observation that the strong coupling behavior of the polaron path measure, on certain time scales, should resemble a process, named as the Pekar process, whose distribution could somehow be guessed from the limiting asymptotic behavior of the mean-field measures under interest, whose rigorous analysis remained open. The present paper is devoted to a precise analysis of these mean-field path measures and convergence of the normalized occupation measures towards an explicit mixture of the maximizers of the Pekar variational problem. This leads to a rigorous construction of the aforementioned Pekar process and hence is a contribution to the understanding of the “mean-field approximation” of the polaron problem on the level of path measures.The method of our proof is based on the compact large deviation theory developed by Mukherjee and Varadhan in 2016; its extension to the uniform strong metric for the singular Coulomb interaction was carried out by König and Mukherjee in 2015, as well as an idea inspired by a partial path exchange argument appearing in 1997 in work by Bolthausen and Schmock. © 2016 Wiley Periodicals, Inc.
PubDate: 2017-01-11T06:10:20.055249-05:
DOI: 10.1002/cpa.21682
- Authors: Erwin Bolthausen; Wolfgang König, Chiranjib Mukherjee
- Characterization of Metal Artifacts in X-Ray Computed Tomography
- Authors: Hyoung Suk Park; Jae Kyu Choi, Jin Keun Seo
Abstract: Metal streak artifacts in X-ray computerized tomography (CT) are characterized here using the notion of the wavefront set from microlocal analysis. The metal artifacts are caused mainly from the mismatch of the forward model of the filtered back-projection; the presence of metallic subjects in an imaging subject violates the model's assumption of the CT sinogram data being the Radon transform of an image. The increasing use of metallic implants has increased demand for the reduction of metal artifacts in the field of dental and medical radiography. However, it is a challenging issue due to the serious difficulties in analyzing the X-ray data, which depends nonlinearly on the distribution of the metallic subject. In this paper, we, for the first time, provide a mathematical analysis to characterize the structure of metal streaking artifacts. The metal streaking artifacts are produced along the line tangent to boundaries of the metal region touching at least two different boundaries. We also found a sufficient condition for the nonexistence of the metal streaking artifacts.© 2016 Wiley Periodicals, Inc.
PubDate: 2017-01-04T07:25:36.23014-05:0
DOI: 10.1002/cpa.21680
- Authors: Hyoung Suk Park; Jae Kyu Choi, Jin Keun Seo
- Issue Information – TOC
- Pages: 1023 - 1023
PubDate: 2017-04-18T04:56:58.465111-05:
DOI: 10.1002/cpa.21661
- Pages: 1023 - 1023
- Numerical simulation of volume-controlled mechanical ventilated
respiratory system with 2 different lungs- Authors: Yan Shi; Bolun Zhang, Maolin Cai, Xiaohua Douglas Zhang
Abstract: Mechanical ventilation is a key therapy for patients who cannot breathe adequately by themselves, and dynamics of mechanical ventilation system is of great significance for life support of patients. Recently, models of mechanical ventilated respiratory system with 1 lung are used to simulate the respiratory system of patients. However, humans have 2 lungs. When the respiratory characteristics of 2 lungs are different, a single-lung model cannot reflect real respiratory system. In this paper, to illustrate dynamic characteristics of mechanical ventilated respiratory system with 2 different lungs, we propose a mathematical model of mechanical ventilated respiratory system with 2 different lungs and conduct experiments to verify the model. Furthermore, we study the dynamics of mechanical ventilated respiratory system with 2 different lungs. This research study can be used for improving the efficiency and safety of volume-controlled mechanical ventilation system.Because coupling effects of 2 lungs has a significant influence on safety and efficiency of mechanical ventilation, a pneumatic model with 2 lungs has been built in this paper to study the coupling effects of 2 lungs in volume-controlled ventilation. It can be concluded that a change of compliance or air resistance of one lung can affect both lungs and an unbalance of 2 lungs may result in overly high pressure in the trachea and overventilation.
PubDate: 2016-12-29T10:30:32.441507-05:
DOI: 10.1002/cnm.2852
- Authors: Yan Shi; Bolun Zhang, Maolin Cai, Xiaohua Douglas Zhang
- A novel approach to the quantification of aortic root in vivo structural
mechanics- Authors: E. Votta; M. Presicce, A. Della Corte, S. Dellegrottaglie, C. Bancone, F. Sturla, A. Redaelli
Abstract: Understanding aortic root in vivo biomechanics can help in elucidating key mechanisms involved in aortic root pathologies and in the outcome of their surgical treatment. Numerical models can provide useful quantitative information. For this to be reliable, detailed aortic root anatomy should be captured. Also, since the aortic root is never unloaded throughout the cardiac cycle, the modeled geometry should be consistent with the in vivo loads acting on it. Achieving such consistency is still a challenge, which was tackled only by few numerical studies.Here we propose and describe in detail a new approach to the finite element modeling of aortic root in vivo structural mechanics. Our approach exploits the anatomical information yielded by magnetic resonance imaging by reconstructing the 3-dimensional end-diastolic geometry of the aortic root and makes the reconstructed geometry consistent with end-diastolic loading conditions through the estimation of the corresponding prestresses field.We implemented our approach through a semiautomated modeling pipeline, and we applied it to quantify aortic root biomechanics in 4 healthy participants. Computed results highlighted that including prestresses into the model allowed for pressurizing the aortic root to the end-diastolic pressure while matching the image-based ground truth data. Aortic root dynamics, tissues strains, and stresses computed at relevant time points through the cardiac cycle were consistent with a broad set of data from previous computational and in vivo studies, strongly suggesting the potential of the method. Also, results highlighted the major role played by the anatomy in driving aortic root biomechanics.We simulated aortic root (AR) dynamics combining subject-specific anatomical reconstructions, based on in vivo medical imaging, with a realistic modeling of AR loading conditions. This novel approach aimed for the consistency between AR geometry and pressure loads loading it, and hence at a reliable computation of tissues strains and stresses. The proposed strategy was successfully applied to 4 subject-specific AR models; simulations highlighted the key role of both geometrical features and tissues prestresses and suggested the potential of our method.
PubDate: 2016-12-28T09:40:46.544795-05:
DOI: 10.1002/cnm.2849
- Authors: E. Votta; M. Presicce, A. Della Corte, S. Dellegrottaglie, C. Bancone, F. Sturla, A. Redaelli
- Gluing Eguchi-Hanson Metrics and a Question of Page
- Authors: Simon Brendle; Nikolaos Kapouleas
Abstract: In 1978, Gibbons-Pope and Page proposed a physical picture for the Ricci flat Kähler metrics on the K3 surface based on a gluing construction. In this construction, one starts from a flat torus with 16 orbifold points and resolves the orbifold singularities by gluing in 16 small Eguchi-Hanson manifolds that all have the same orientation. This construction was carried out rigorously by Topiwala, LeBrun-Singer, and Donaldson.In 1981, Page asked whether the above construction can be modified by reversing the orientations of some of the Eguchi-Hanson manifolds. This is a subtle question: if successful, this construction would produce Einstein metrics that are neither Kähler nor self-dual.In this paper, we focus on a configuration of maximal symmetry involving eight small Eguchi-Hanson manifolds of each orientation that are arranged according to a chessboard pattern. By analyzing the interactions between Eguchi-Hanson manifolds with opposite orientation, we identify a nonvanishing obstruction to the gluing problem, thereby destroying any hope of producing a metric of zero Ricci curvature in this way. Using this obstruction, we are able to understand the dynamics of such metrics under Ricci flow as long as the Eguchi-Hanson manifolds remain small. In particular, for the configuration described above, we obtain an ancient solution to the Ricci flow with the property that the maximum of the Riemann curvature tensor blows up at a rate of (−t)1/2, while the maximum of the Ricci curvature converges to 0. © 2016 Wiley Periodicals, Inc.
PubDate: 2016-12-22T06:10:22.425571-05:
DOI: 10.1002/cpa.21678
- Authors: Simon Brendle; Nikolaos Kapouleas
- Improved hybrid/GPU algorithm for solving cardiac electrophysiology
problems on Purkinje networks- Authors: M. Lange; S. Palamara, T. Lassila, C. Vergara, A. Quarteroni, A. F. Frangi
Abstract: Cardiac Purkinje fibers provide an important pathway to the coordinated contraction of the heart. We present a numerical algorithm for the solution of electrophysiology problems across the Purkinje network that is efficient enough to be used in in silico studies on realistic Purkinje networks with physiologically detailed models of ion exchange at the cell membrane. The algorithm is on the basis of operator splitting and is provided with 3 different implementations: pure CPU, hybrid CPU/GPU, and pure GPU. Compared to our previous work, we modify the explicit gap junction term at network bifurcations to improve its mathematical consistency. Due to this improved consistency of the model, we are able to perform an empirical convergence study against analytical solutions. The study verified that all 3 implementations produce equivalent convergence rates, and shows that the algorithm produces equivalent result across different hardware platforms. Finally, we compare the efficiency of all 3 implementations on Purkinje networks of increasing spatial resolution using membrane models of increasing complexity. Both hybrid and pure GPU implementations outperform the pure CPU implementation, but their relative performance difference depends on the size of the Purkinje network and the complexity of the membrane model used.We present an improved numerical algorithm to solve the cardiac electrophysiology problem on Purkinje fiber networks. It is efficient enough to be used on realistic networks with physiologically detailed membrane models and is mathematically and physiologically consistent. The algorithm was implemented on 3 different hardware configurations, including on graphic processing units. All implementations are verified to produce equivalent convergence rates using analytical solutions. Finally, we compare the efficiency of the different implementations on problems of varying size and model complexity.
PubDate: 2016-12-01T23:45:43.044452-05:
DOI: 10.1002/cnm.2835
- Authors: M. Lange; S. Palamara, T. Lassila, C. Vergara, A. Quarteroni, A. F. Frangi
- Automated femoral landmark extraction for optimal prosthesis placement in
total hip arthroplasty- Authors: Diogo F. Almeida; Rui B. Ruben, João Folgado, Paulo R. Fernandes, João Gamelas, Benedict Verhegghe, Matthieu De Beule
Abstract: The automated extraction of anatomical reference landmarks in the femoral volume may improve speed, precision, and accuracy of surgical procedures, such as total hip arthroplasty. These landmarks are often hard to achieve, even via surgical incision. In addition, it provides a presurgical guidance for prosthesis sizing and placement. This study presents an automated workflow for femoral orientation and landmark extraction from a 3D surface mesh. The extraction of parameters such as the femoral neck axis, the femoral middle diaphysis axis, both trochanters and the center of the femoral head will allow the surgeon to establish the correct position of bony cuts to restore leg length and femoral offset. The definition of the medullary canal endosteal wall is used to position the prosthesis' stem. Furthermore, prosthesis alignment and sizing methods were implemented to provide the surgeon with presurgical information about performance of each of the patient-specific femur-implant couplings. The workflow considers different commercially available hip stems and has the potential to help the preoperative planning of a total hip arthroplasty in an accurate, repeatable, and reliable way. The positional and orientation errors are significantly reduced, and therefore, the risk of implant failure and subsequent revision surgery are also reduced.The presented method provides an automated presurgical guidance for prosthesis sizing and placement. In a first stage, it is able to accurately locate key anchor points in the 3D femoral mesh volume. Moreover, optimal prosthesis alignment and sizing estimation can be achieved based on the patient-specific femoral and medullary canal dimensions in an accurate, repeatable, and reliable way. The positional and orientation errors are significantly reduced, and therefore, the risk of implant failure and consequent revision surgery are minimized.
PubDate: 2016-11-25T06:00:33.338561-05:
DOI: 10.1002/cnm.2844
- Authors: Diogo F. Almeida; Rui B. Ruben, João Folgado, Paulo R. Fernandes, João Gamelas, Benedict Verhegghe, Matthieu De Beule
- An atlas- and data-driven approach to initializing reaction-diffusion
systems in computer cardiac electrophysiology- Authors: Corné Hoogendoorn; Rafael Sebastian, José Félix Rodriguez, Karim Lekadir, Alejandro F. Frangi
Abstract: The cardiac electrophysiology (EP) problem is governed by a nonlinear anisotropic reaction-diffusion system with a very rapidly varying reaction term associated with the transmembrane cell current. The nonlinearity associated with the cell models requires a stabilization process before any simulation is performed. More importantly, when used in a 3-dimensional (3D) anatomy, it is not sufficient to perform this stabilization on the basis of isolated cells only, since the coupling of the different cells through the tissue greatly modulates the dynamics of the system. Therefore, stabilization of the system must be performed on the entire 3D model. This work develops a novel procedure for the initialization of reaction-diffusion systems for numerical simulations of cardiac EP from steady-state conditions. We exploit surface point correspondence to establish volumetric point correspondence. Upon introduction of a new 3D anatomy with surface point correspondence, a prediction of the cell model steady states is derived from the set of earlier biophysical simulations. We show that the prediction error is typically less than 10% for all model variables, with most variables showing even greater accuracy. When initializing simulations with the predicted model states, it is demonstrated that simulation times can be cut by at least two-thirds and potentially more, which saves hours or days of high-performance computing. Overall, these results increase the clinical applicability of detailed computational EP studies on personalized anatomies.In cardiac electrophysiology modeling and simulation, the nonlinearity associated with the cell models requires a stabilization process in the entire 3D domain. This work develops a novel procedure for the initialization of reaction-diffusion systems for simulations of cardiac electrophysiology from steady-state conditions. Obtained prediction error was typically less than 10% for all model variables. Simulation times could be cut by at least two-thirds and potentially more, which saves hours or days of high-performance computing.
PubDate: 2016-11-23T02:13:26.103421-05:
DOI: 10.1002/cnm.2846
- Authors: Corné Hoogendoorn; Rafael Sebastian, José Félix Rodriguez, Karim Lekadir, Alejandro F. Frangi
- Long Time Stability for Solutions of a β-Plane Equation
- Authors: Tarek M. Elgindi; Klaus Widmayer
Abstract: We prove stability for arbitrarily long times of the zero solution for the so-called β-plane equation, which describes the motion of a two-dimensional inviscid, ideal fluid under the influence of the Coriolis effect. The Coriolis force introduces a linear dispersive operator into the two-dimensional incompressible Euler equations, thus making this problem amenable to an analysis from the point of view of nonlinear dispersive equations. The dispersive operator, L1 ≔ ∂1/ ∇ 2, exhibits good decay, but has numerous unfavorable properties, chief among which are its anisotropy and its behavior at small frequencies.© 2016 Wiley Periodicals, Inc.
PubDate: 2016-11-15T01:51:39.011201-05:
DOI: 10.1002/cpa.21676
- Authors: Tarek M. Elgindi; Klaus Widmayer
- Local Regularity for the Modified SQG Patch Equation
- Authors: Alexander Kiselev; Yao Yao, Andrej Zlatoš
Abstract: We study the patch dynamics on the whole plane and on the half-plane for a family of active scalars called modified surface quasi-geostrophic (SQG) equations. These involve a parameter α that appears in the power of the kernel in their Biot-Savart laws and describes the degree of regularity of the equation. The values α=0 and α=½ correspond to the two-dimensional Euler and SQG equations, respectively. We establish here local-in-time regularity for these models, for all α ∊ (0,½) on the whole plane and for all small α > 0 on the half-plane. We use the latter result in [16], where we show existence of regular initial data on the half-plane that lead to a finite-time singularity.© 2016 Wiley Periodicals, Inc.
PubDate: 2016-11-11T08:35:22.499299-05:
DOI: 10.1002/cpa.21677
- Authors: Alexander Kiselev; Yao Yao, Andrej Zlatoš
- An implicit solver for 1D arterial network models
- Authors: Jason Carson; Raoul Van Loon
Abstract: In this study, the 1D blood flow equations are solved using a newly proposed enhanced trapezoidal rule method (ETM), which is an extension to the simplified trapezoidal rule method. At vessel junctions, the conservation of mass and conservation of total pressure are held as system constraints using Lagrange multipliers that can be physically interpreted as external flow rates. The ETM scheme is compared with published arterial network benchmark problems and a dam break problem. Strengths of the ETM scheme include being simple to implement, intuitive connection to lumped parameter models, and no restrictive stability criteria such as the Courant-Friedrichs-Lewy (CFL) number. The ETM scheme does not require the use of characteristics at vessel junctions, or for inlet and outlet boundary conditions. The ETM forms an implicit system of equations, which requires only one global solve per time step for pressure, followed by flow rate update on the elemental system of equations; thus, no iterations are required per time step. Consistent results are found for all benchmark cases, and for a 56-vessel arterial network problem, it gives very satisfactory solutions at a spatial and time discretization that results in a maximum CFL of 3, taking 4.44 seconds per cardiac cycle. By increasing the time step and element size to produce a maximum CFL number of 15, the method takes only 0.39 second per cardiac cycle with only a small compromise on accuracy.In this study, the 1D blood flow equations are solved using the enhanced trapezoidal rule method (ETM). The ETM is an implicit scheme and uses Lagrange multipliers, which are physically interpreted as external flow rates, to impose conservation of total pressure and conservation of mass at vessel junctions. The method is compared with benchmark problems and a shock problem.
PubDate: 2016-11-10T06:45:37.377709-05:
DOI: 10.1002/cnm.2837
- Authors: Jason Carson; Raoul Van Loon
- Non-Newtonian versus numerical rheology: Practical impact of
shear-thinning on the prediction of stable and unstable flows in
intracranial aneurysms- Authors: M. O. Khan; D. A. Steinman, K. Valen-Sendstad
Abstract: Computational fluid dynamics (CFD) shows promise for informing treatment planning and rupture risk assessment for intracranial aneurysms. Much attention has been paid to the impact on predicted hemodynamics of various modelling assumptions and uncertainties, including the need for modelling the non-Newtonian, shear-thinning rheology of blood, with equivocal results. Our study clarifies this issue by contextualizing the impact of rheology model against the recently demonstrated impact of CFD solution strategy on the prediction of aneurysm flow instabilities. Three aneurysm cases were considered, spanning a range of stable to unstable flows. Simulations were performed using a high-resolution/accuracy solution strategy with Newtonian and modified-Cross rheology models and compared against results from a so-called normal-resolution strategy. Time-averaged and instantaneous wall shear stress (WSS) distributions, as well as frequency content of flow instabilities and dome-averaged WSS metrics, were minimally affected by the rheology model, whereas numerical solution strategy had a demonstrably more marked impact when the rheology model was fixed. We show that point-wise normalization of non-Newtonian by Newtonian WSS values tended to artificially amplify small differences in WSS of questionable physiological relevance in already-low WSS regions, which might help to explain the disparity of opinions in the aneurysm CFD literature regarding the impact of non-Newtonian rheology. Toward the goal of more patient-specific aneurysm CFD, we conclude that attention seems better spent on solution strategy and other likely “first-order” effects (eg, lumen segmentation and choice of flow rates), as opposed to “second-order” effects such as rheology.Computational fluid dynamics shows promise for rupture risk assessment of intracranial aneurysms, and the need for modelling the non-Newtonian behavior of blood has been questioned; with equivocal results. We sought to clarify this issue by contextualizing the impact of rheology (HR-NN vs HR-N) against impact of computational fluid dynamics solution strategy (NR-N). Based on Figure (showing commonly computed hemodynamic indices), we conclude that attention seems better spent on solution strategy, as opposed to “second-order” effects such as rheology.
PubDate: 2016-11-09T15:17:24.990996-05:
DOI: 10.1002/cnm.2836
- Authors: M. O. Khan; D. A. Steinman, K. Valen-Sendstad
- Modeling the mechanics of axonal fiber tracts using the embedded finite
element method- Authors: Harsha T. Garimella; Reuben H. Kraft
Abstract: A subject-specific human head finite element model with embedded axonal fiber tractography obtained from diffusion tensor imaging was developed. The axonal fiber tractography finite element model was coupled with the volumetric elements in the head model using the embedded element method. This technique enables the calculation of axonal strains and real-time tracking of the mechanical response of the axonal fiber tracts. The coupled model was then verified using pressure and relative displacement-based (between skull and brain) experimental studies and was employed to analyze a head impact, demonstrating the applicability of this method in studying axonal injury. Following this, a comparison study of different injury criteria was performed. This model was used to determine the influence of impact direction on the extent of the axonal injury. The results suggested that the lateral impact loading is more dangerous compared to loading in the sagittal plane, a finding in agreement with previous studies. Through this analysis, we demonstrated the viability of the embedded element method as an alternative numerical approach for studying axonal injury in patient-specific human head models.A human head finite element model with embedded axonal tractography (developed using DTI) was developed using the “embedded element method.” The model was verified and was used to analyze a concussive head impact, demonstrating the applicability of this method in studying axonal injury. Effects of different loading directions and the importance of axonal orientation were studied, and the results show that the axonal tract arrangement could be one of the reasons for differences in axonal damage under different loading directions.
PubDate: 2016-11-08T15:16:10.632292-05:
DOI: 10.1002/cnm.2823
- Authors: Harsha T. Garimella; Reuben H. Kraft
- A quasi-3D wire approach to model pulmonary airflow in human airways
- Authors: Ravishekar Kannan; Z. J. Chen, Narender Singh, Andrzej Przekwas, Renishkumar Delvadia, Geng Tian, Ross Walenga
Abstract: The models used for modeling the airflow in the human airways are either 0-dimensional compartmental or full 3-dimensional (3D) computational fluid dynamics (CFD) models. In the former, airways are treated as compartments, and the computations are performed with several assumptions, thereby generating a low-fidelity solution. The CFD method displays extremely high fidelity since the solution is obtained by solving the conservation equations in a physiologically consistent geometry. However, CFD models (1) require millions of degrees of freedom to accurately describe the geometry and to reduce the discretization errors, (2) have convergence problems, and (3) require several days to simulate a few breathing cycles. In this paper, we present a novel, fast-running, and robust quasi-3D wire model for modeling the airflow in the human lung airway. The wire mesh is obtained by contracting the high-fidelity lung airway surface mesh to a system of connected wires, with well-defined radii. The conservation equations are then solved in each wire. These wire meshes have around O(1000) degrees of freedom and hence are 3000 to 25 000 times faster than their CFD counterparts. The 3D spatial nature is also preserved since these wires are contracted out of the actual lung STL surface. The pressure readings between the 2 approaches showed minor difference (maximum error = 15%). In general, this formulation is fast and robust, allows geometric changes, and delivers high-fidelity solutions. Hence, this approach has great potential for more complicated problems including modeling of constricted/diseased lung sections and for calibrating the lung flow resistances through parameter inversion.Schematic showing the CFD to Q3D conversion, pressure distribution for a sample simulation. Q3D is 3000–27000 times faster than the CFD approach.
PubDate: 2016-11-04T10:05:40.929872-05:
DOI: 10.1002/cnm.2838
- Authors: Ravishekar Kannan; Z. J. Chen, Narender Singh, Andrzej Przekwas, Renishkumar Delvadia, Geng Tian, Ross Walenga
- A review of personalized blood glucose prediction strategies for T1DM
patients- Authors: Silvia Oviedo; Josep Vehí, Remei Calm, Joaquim Armengol
Abstract: This paper presents a methodological review of models for predicting blood glucose (BG) concentration, risks and BG events. The surveyed models are classified into three categories, and they are presented in summary tables containing the most relevant data regarding the experimental setup for fitting and testing each model as well as the input signals and the performance metrics. Each category exhibits trends that are presented and discussed. This document aims to be a compact guide to determine the modeling options that are currently being exploited for personalized BG prediction.This paper presents a methodological review of models for predicting blood glucose (BG) concentration, risks, and BG events. The surveyed models are classified into three categories, and they are presented in summary tables containing the most relevant data regarding the experimental setup for fitting and testing each model as well as the input signals and the performance metrics. Each category exhibits trends that are presented and discussed. This document aims to be a compact guide to determine the modeling options that are currently being exploited for personalized BG prediction.
PubDate: 2016-10-28T16:05:29.778773-05:
DOI: 10.1002/cnm.2833
- Authors: Silvia Oviedo; Josep Vehí, Remei Calm, Joaquim Armengol
- Modeling of light propagation in the human neck for diagnoses of thyroid
cancers by diffuse optical tomography- Authors: H. Fujii; Y. Yamada, K. Kobayashi, M. Watanabe, Y. Hoshi
Abstract: Diffuse optical tomography using near-infrared light in a wavelength range from 700 to 1000 nm has the potential to enable non-invasive diagnoses of thyroid cancers; some of which are difficult to detect by conventional methods such as ultrasound tomography. Diffuse optical tomography needs to be based on a physically accurate model of light propagation in the neck, because it reconstructs tomographic images of the optical properties in the human neck by inverse analysis. Our objective here was to investigate the effects of three factors on light propagation in the neck using the 2D time-dependent radiative transfer equation: (1) the presence of the trachea, (2) the refractive-index mismatch at the trachea-tissue interface, and (3) the effect of neck organs other than the trachea (spine, spinal cord, and blood vessels). There was a significant influence of reflection and refraction at the trachea-tissue interface on the light intensities in the region between the trachea and the front of the neck surface. Organs other than the trachea showed little effect on the light intensities measured at the front of the neck surface although these organs affected the light intensities locally. These results indicated the necessity of modeling the refractive-index mismatch at the trachea-tissue interface and the possibility of modeling other neck organs simply as a homogeneous medium when the source and detectors were far from large blood vessels.A significant influence of reflection and refraction at the trachea (void region)-tissue interface on the light propagation. Only little influence of other organs (spine, spinal cord, and blood vessels) than the trachea on the light detected at the front surface of the neck in a case of source and detector locations far from the organs.
PubDate: 2016-10-27T07:40:36.54234-05:0
DOI: 10.1002/cnm.2826
- Authors: H. Fujii; Y. Yamada, K. Kobayashi, M. Watanabe, Y. Hoshi
- Stochastic Homogenization of Nonconvex Hamilton-Jacobi Equations: A
Counterexample- Authors: Bruno Ziliotto
Abstract: This paper provides a counterexample to Hamilton-Jacobi homogenization in the nonconvex case for general stationary ergodic environments.© 2016 Wiley Periodicals, Inc.
PubDate: 2016-10-25T09:20:23.951907-05:
DOI: 10.1002/cpa.21674
- Authors: Bruno Ziliotto
- Linear Inviscid Damping for a Class of Monotone Shear Flow in Sobolev
Spaces- Authors: Dongyi Wei; Zhifei Zhang, Weiren Zhao
Abstract: In this paper, we prove the decay estimates of the velocity and H1 scattering for the two-dimensional linearized Euler equations around a class of monotone shear flow in a finite channel. Our result is consistent with the decay rate predicted by Case in 1960.© 2016 Wiley Periodicals, Inc.
PubDate: 2016-10-24T01:10:26.513651-05:
DOI: 10.1002/cpa.21672
- Authors: Dongyi Wei; Zhifei Zhang, Weiren Zhao
- Computational design and engineering of polymeric orthodontic aligners
- Authors: S. Barone; A. Paoli, A. V. Razionale, R. Savignano
Abstract: Transparent and removable aligners represent an effective solution to correct various orthodontic malocclusions through minimally invasive procedures. An aligner-based treatment requires patients to sequentially wear dentition-mating shells obtained by thermoforming polymeric disks on reference dental models. An aligner is shaped introducing a geometrical mismatch with respect to the actual tooth positions to induce a loading system, which moves the target teeth toward the correct positions. The common practice is based on selecting the aligner features (material, thickness, and auxiliary elements) by only considering clinician's subjective assessments.In this article, a computational design and engineering methodology has been developed to reconstruct anatomical tissues, to model parametric aligner shapes, to simulate orthodontic movements, and to enhance the aligner design. The proposed approach integrates computer-aided technologies, from tomographic imaging to optical scanning, from parametric modeling to finite element analyses, within a 3-dimensional digital framework.The anatomical modeling provides anatomies, including teeth (roots and crowns), jaw bones, and periodontal ligaments, which are the references for the down streaming parametric aligner shaping. The biomechanical interactions between anatomical models and aligner geometries are virtually reproduced using a finite element analysis software. The methodology allows numerical simulations of patient-specific conditions and the comparative analyses of different aligner configurations.In this article, the digital framework has been used to study the influence of various auxiliary elements on the loading system delivered to a maxillary and a mandibular central incisor during an orthodontic tipping movement. Numerical simulations have shown a high dependency of the orthodontic tooth movement on the auxiliary element configuration, which should then be accurately selected to maximize the aligner's effectiveness.This article presents a digital methodology to study patient-specific orthodontic treatments based on the use of polymeric aligners. The approach integrates computer-aided technologies, from tomographic imaging to optical scanning, from parametric modeling to finite element analyses. Numerical analyses proved to be a powerful tool to study different aligner's configurations evidencing how auxiliary elements features might affect the loading system delivered by the aligner. For instance, results pointed out that the loads elicited by divot geometries are higher than those provided by using attachment geometries.
PubDate: 2016-10-21T07:55:38.530121-05:
DOI: 10.1002/cnm.2839
- Authors: S. Barone; A. Paoli, A. V. Razionale, R. Savignano
- Calibration of parameters for cardiovascular models with application to
arterial growth- Authors: Sebastian Kehl; Michael W. Gee
Abstract: We present a computational framework for the calibration of parameters describing cardiovascular models with a focus on the application of growth of abdominal aortic aneurysms (AAA). The growth rate in this sort of pathology is considered a critical parameter in the risk management and is an essential indicator for the assessment of surveillance intervals. Parameters describing growth of AAAs are not measurable directly and need to be estimated from available data often given by medical imaging technologies. Registration procedures often applied in standard workflows of parameter identification to extract the image encoded information are a source of significant systematic error. The concept of surface currents provides means to effectively avoid this source of errors by establishing a mathematical framework to compare surface information, directly accessible from image data. By utilizing this concept it is possible to inversely estimate growth parameters using sophisticated numerical models of AAAs from measurements available as surface information. In this work we present a framework to obtain spatial distributions of parameters governing growth of arterial tissue, and we show how the use of surface currents can significantly improve the results. We further present the application to patient specific follow-up data resulting in a spatial map of volumetric growth rates enabling, for the first time, prediction of further AAA expansion.We present a parameter identification framework for the estimation of growth parameters of cardiovascular tissue with application to growth of abdominal aortic aneurysms (AAA). We demonstrate on a synthetic example how the application of surface currents in combination with a flexible total variation regularization allows for the accurate determination of spatial distributions of parameter estimates. Finally we present the application to patient specific follow-up data enabling prediction of further AAA expansion.
PubDate: 2016-10-21T07:45:32.074739-05:
DOI: 10.1002/cnm.2822
- Authors: Sebastian Kehl; Michael W. Gee
- Infinite Speed of Propagation and Regularity of Solutions to the
Fractional Porous Medium Equation in General Domains- Authors: Matteo Bonforte; Alessio Figalli, Xavier Ros-Oton
Abstract: We study the positivity and regularity of solutions to the fractional porous me\-dium equations ut + (−Δ)sum=0 in (0,∞) × Ω for m > 1 and s ∊ (0,1), with Dirichlet boundary data u=0 in (0,∞) × (ℝN∖Ω) and nonnegative initial condition u(0,·,)=u0 ≥ 0.Our first result is a quantitative lower bound for solutions that holds for all positive times t > 0. As a consequence, we find a global Harnack principle stating that for any t > 0 solutions are comparable to ds/m, where d is the distance to ∂Ω. This is in sharp contrast with the local case s=1, where the equation has finite speed of propagation.After this, we study the regularity of solutions. We prove that solutions are classical in the interior (C∞ in x and C1,α in t) and establish a sharp Cxs/m regularity estimate up to the boundary.Our methods are quite general and can be applied to wider classes of nonlocal parabolic equations of the form ut + ℒF(u) = 0 in Ω, both in bounded and unbounded domains.© 2016 Wiley Periodicals, Inc.
PubDate: 2016-10-19T05:20:21.903843-05:
DOI: 10.1002/cpa.21673
- Authors: Matteo Bonforte; Alessio Figalli, Xavier Ros-Oton
- A methodology for constraining power in finite element modeling of
radiofrequency ablation- Authors: Yansheng Jiang; Ricardo Possebon, Stefaan Mulier, Chong Wang, Feng Chen, Yuanbo Feng, Qian Xia, Yewei Liu, Ting Yin, Raymond Oyen, Yicheng Ni
Abstract: Radiofrequency ablation (RFA) is a minimally invasive thermal therapy for the treatment of cancer, hyperopia, and cardiac tachyarrhythmia. In RFA, the power delivered to the tissue is a key parameter. The objective of this study was to establish a methodology for the finite element modeling of RFA with constant power. Because of changes in the electric conductivity of tissue with temperature, a nonconventional boundary value problem arises in the mathematic modeling of RFA: neither the voltage (Dirichlet condition) nor the current (Neumann condition), but the power, that is, the product of voltage and current was prescribed on part of boundary. We solved the problem using Lagrange multiplier: the product of the voltage and current on the electrode surface is constrained to be equal to the Joule heating. We theoretically proved the equality between the product of the voltage and current on the surface of the electrode and the Joule heating in the domain. We also proved the well-posedness of the problem of solving the Laplace equation for the electric potential under a constant power constraint prescribed on the electrode surface. The Pennes bioheat transfer equation and the Laplace equation for electric potential augmented with the constraint of constant power were solved simultaneously using the Newton-Raphson algorithm. Three problems for validation were solved. Numerical results were compared either with an analytical solution deduced in this study or with results obtained by ANSYS or experiments. This work provides the finite element modeling of constant power RFA with a firm mathematical basis and opens pathway for achieving the optimal RFA power.It is shown that λ(P − Q) = 0, where λ is Lagrange multiplier, P denotes the delivered power of RFA, and Q is the Joule heating, which cannot be used as the power constraint equation. Instead, we used λ(P − Qs) = 0 as the power constraint equation, where Qs denotes the total power flux across boundary, solved together with Laplace equation for electric potential.The correctness proof of our method is demonstrated through solutions of test problems.
PubDate: 2016-10-14T00:40:39.670398-05:
DOI: 10.1002/cnm.2834
- Authors: Yansheng Jiang; Ricardo Possebon, Stefaan Mulier, Chong Wang, Feng Chen, Yuanbo Feng, Qian Xia, Yewei Liu, Ting Yin, Raymond Oyen, Yicheng Ni
- 3D physiological model of the aortic valve incorporating small coronary
arteries- Authors: Hossein Mohammadi; Raymond Cartier, Rosaire Mongrain
Abstract: The diseases of the coronary arteries and the aortic root are still the leading causes of mortality and morbidity worldwide. In this study, a 3D global fluid-structure interaction of the aortic root with inclusion of anatomically inspired small coronary arteries using the finite element method is presented. This innovative model allows to study the impact and interaction of root biomechanics on coronary hemodynamics and brings a new understanding to small coronary vessels hemodynamics. For the first time, the velocity profiles and shear stresses are reported in distal coronary arteries as a result of the aortic flow conditions in a global fluid-structure interaction model.This paper presents an innovative 3D global fluid-structure interaction of the aortic valve incorporating small coronary arteries using the finite element method. Inclusion of the small coronaries and incorporating realistic material properties introduced the notion of globality into the model. This global model was assessed with the results of echocardiography studies. The findings proved that decoupling the aorta and coronary structures brings non-obvious problems on how to manage the dynamic mechanical conditions at the interface during the flow cycle.
PubDate: 2016-10-13T02:36:45.106975-05:
DOI: 10.1002/cnm.2829
- Authors: Hossein Mohammadi; Raymond Cartier, Rosaire Mongrain
- Design of a numerical model of lung by means of a special boundary
condition in the truncated branches- Authors: Ana F. Tena; Joaquín Fernández, Eduardo Álvarez, Pere Casan, D. Keith Walters
Abstract: BackgroundThe need for a better understanding of pulmonary diseases has led to increased interest in the development of realistic computational models of the human lung.MethodsTo minimize computational cost, a reduced geometry model is used for a model lung airway geometry up to generation 16. Truncated airway branches require physiologically realistic boundary conditions to accurately represent the effect of the removed airway sections. A user-defined function has been developed, which applies velocities mapped from similar locations in fully resolved airway sections. The methodology can be applied in any general purpose computational fluid dynamics code, with the only limitation that the lung model must be symmetrical in each truncated branch.ResultsUnsteady simulations have been performed to verify the operation of the model. The test case simulates a spirometry because the lung is obliged to rapidly perform both inspiration and expiration. Once the simulation was completed, the obtained pressure in the lower level of the lung was used as a boundary condition. The output velocity, which is a numerical spirometry, was compared with the experimental spirometry for validation purposes.ConclusionsThis model can be applied for a wide range of patient-specific resolution levels. If the upper airway generations have been constructed from a computed tomography scan, it would be possible to quickly obtain a complete reconstruction of the lung specific to a specific person, which would allow individualized therapies.A reduced symmetrical model is used in a model lung airway geometry up to generation 16 and can be applied in any general model.A user-defined function has been developed, which applies velocities mapped from similar locations in fully resolved airway sections.If the upper airway generations have been constructed from a computed tomography scan, it would be possible to quickly obtain a complete reconstruction of the lung particularized for each person, which would allow individualized therapies.
PubDate: 2016-10-07T02:01:17.72731-05:0
DOI: 10.1002/cnm.2830
- Authors: Ana F. Tena; Joaquín Fernández, Eduardo Álvarez, Pere Casan, D. Keith Walters
- Hemodynamics-driven deposition of intraluminal thrombus in abdominal
aortic aneurysms- Authors: P. Di Achille; G. Tellides, J. D. Humphrey
Abstract: Accumulating evidence suggests that intraluminal thrombus plays many roles in the natural history of abdominal aortic aneurysms. There is, therefore, a pressing need for computational models that can describe and predict the initiation and progression of thrombus in aneurysms. In this paper, we introduce a phenomenological metric for thrombus deposition potential and use hemodynamic simulations based on medical images from 6 patients to identify best-fit values of the 2 key model parameters. We then introduce a shape optimization method to predict the associated radial growth of the thrombus into the lumen based on the expectation that thrombus initiation will create a thrombogenic surface, which in turn will promote growth until increasing hemodynamically induced frictional forces prevent any further cell or protein deposition. Comparisons between predicted and actual intraluminal thrombus in the 6 patient-specific aneurysms suggest that this phenomenological description provides a good first estimate of thrombus deposition. We submit further that, because the biologically active region of the thrombus appears to be confined to a thin luminal layer, predictions of morphology alone may be sufficient to inform fluid-solid–growth models of aneurysmal growth and remodeling.Accumulating evidence suggests that intraluminal thrombus plays multiple, detrimental roles in the natural history of abdominal aortic aneurysms. Relying on a phenomenological metric for thrombus deposition potential, we introduce an optimization method to determine the growth of the thrombus into the lumen. This optimization is based on the expectation that thrombus growth will continue until increasing hemodynamically induced frictional forces prevent any further cell or protein deposition. Comparisons between predicted and actual intraluminal thrombus in 6 patient-specific aneurysms suggest that this phenomenological description provides a good first estimate of thrombus deposition
PubDate: 2016-10-07T01:37:43.535533-05:
DOI: 10.1002/cnm.2828
- Authors: P. Di Achille; G. Tellides, J. D. Humphrey
- Machine learning–based 3-D geometry reconstruction and modeling of
aortic valve deformation using 3-D computed tomography images- Authors: Liang Liang; Fanwei Kong, Caitlin Martin, Thuy Pham, Qian Wang, James Duncan, Wei Sun
Abstract: To conduct a patient-specific computational modeling of the aortic valve, 3-D aortic valve anatomic geometries of an individual patient need to be reconstructed from clinical 3-D cardiac images. Currently, most of computational studies involve manual heart valve geometry reconstruction and manual finite element (FE) model generation, which is both time-consuming and prone to human errors. A seamless computational modeling framework, which can automate this process based on machine learning algorithms, is desirable, as it can not only eliminate human errors and ensure the consistency of the modeling results but also allow fast feedback to clinicians and permits a future population-based probabilistic analysis of large patient cohorts. In this study, we developed a novel computational modeling method to automatically reconstruct the 3-D geometries of the aortic valve from computed tomographic images. The reconstructed valve geometries have built-in mesh correspondence, which bridges harmonically for the consequent FE modeling. The proposed method was evaluated by comparing the reconstructed geometries from 10 patients with those manually created by human experts, and a mean discrepancy of 0.69 mm was obtained. Based on these reconstructed geometries, FE models of valve leaflets were developed, and aortic valve closure from end systole to middiastole was simulated for 7 patients and validated by comparing the deformed geometries with those manually created by human experts, and a mean discrepancy of 1.57 mm was obtained. The proposed method offers great potential to streamline the computational modeling process and enables the development of a preoperative planning system for aortic valve disease diagnosis and treatment.We present a novel computational modeling method to automatically reconstruct the 3-D geometries of the aortic valve from computed tomographic images and build finite element models with mesh correspondence. The method was validated on clinical computed tomographic images, and the results showed good agreement with the human experts: a mean discrepancy of 0.69 mm in geometry reconstruction and a mean discrepancy of 1.57 mm in deformed geometries from finite element simulation of the aortic valve closure.
PubDate: 2016-10-07T01:22:03.662758-05:
DOI: 10.1002/cnm.2827
- Authors: Liang Liang; Fanwei Kong, Caitlin Martin, Thuy Pham, Qian Wang, James Duncan, Wei Sun
- Computational virtual evaluation of the effect of annuloplasty ring shape
- Authors: Ahnryul Choi; David D. McPherson, Hyunggun Kim
Abstract: Mitral regurgitation (MR) is a result of mitral valve (MV) pathology. Its etiology can be categorized as degenerative or functional MR. Ring annuloplasty aims to reconfigure a dilated mitral annulus to its normal size and shape. We investigated the effect of annuloplasty ring shape on MR outcome using our established 3-dimensional (3-D) echocardiography-based computational MV evaluation protocols. Virtual patient MV models were created from 3-D transesophageal echocardiographic data in patients with MR because of mitral annular dilation. Two distinct annuloplasty rings (Physio II and GeoForm) were designed and virtually implanted to the patient MVs. Dynamic finite element simulations of MV function were performed for each MV after virtual ring annuloplasty of either ring, and physiologic and biomechanical characteristics of MV function were compared. Excessive stress values appeared primarily in the midanterior and midposterior regions, and lack of leaflet coaptation was found in pre-annuloplasty patient MVs. Both rings demonstrated marked reduction of stresses and efficient leaflet coaptation. The Physio II ring demonstrated more evenly distributed stress reduction across the leaflets and annulus compared with the GeoForm ring. Conversely, the highly nonplanar curvature of the GeoForm ring more effectively increased leaflet coaptation compared with the Physio II ring. This indicates that the shape of annuloplasty ring affects post-annuloplasty physiologic and biomechanical conditions, which can lead to tissue alteration over a longer period after ring annuloplasty. This virtual ring annuloplasty simulation strategy provides detailed physiologic and biomechanical information and may help better plan the optimal ring selection and improved patient-specific MV repairs.We investigated the effect of annuloplasty ring shape on MV repair outcome using our established 3-D echocardiography-based computational MV evaluation protocols. The Physio II ring demonstrated more evenly distributed stress reduction across the leaflets compared with the GeoForm ring. Conversely, the highly nonplanar curvature of the GeoForm ring more effectively increased leaflet coaptation. This virtual ring annuloplasty strategy provides detailed physiologic and biomechanical information and may help better plan the optimal ring selection and improved patient-specific MV repairs.
PubDate: 2016-10-05T05:17:05.606832-05:
DOI: 10.1002/cnm.2831
- Authors: Ahnryul Choi; David D. McPherson, Hyunggun Kim
- Effects of walking in deep venous thrombosis: a new integrated solid and
fluid mechanics model- Authors: Josep M. López; Gerard Fortuny, Dolors Puigjaner, Joan Herrero, Francesc Marimon, Josep Garcia-Bennett
Abstract: Deep venous thrombosis (DVT) is a common disease. Large thrombi in venous vessels cause bad blood circulation and pain; and when a blood clot detaches from a vein wall, it causes an embolism whose consequences range from mild to fatal. Walking is recommended to DVT patients as a therapeutical complement. In this study the mechanical effects of walking on a specific patient of DVT were simulated by means of an unprecedented integration of 3 elements: a real geometry, a biomechanical model of body tissues, and a computational fluid dynamics study. A set of computed tomography images of a patient's leg with a thrombus in the popliteal vein was employed to reconstruct a geometry model. Then a biomechanical model was used to compute the new deformed geometry of the vein as a function of the fiber stretch level of the semimembranosus muscle. Finally, a computational fluid dynamics study was performed to compute the blood flow and the wall shear stress (WSS) at the vein and thrombus walls. Calculations showed that either a lengthening or shortening of the semimembranosus muscle led to a decrease of WSS levels up to 10%. Notwithstanding, changes in blood viscosity properties or blood flow rate may easily have a greater impact in WSS.The mechanical effects of walking on a specific patient of deep venous thrombosis was simulated by using an unprecedented integration of three elements: a real geometry, a biomechanical model of body tissues, and a computational fluid dynamics study. Computed tomography images of a patient's leg with a thrombus in the popliteal vein were employed to reconstruct a geometrical model. Then a biomechanical model was used to compute the new deformed geometry as a function of the compression state of the semimembranosus muscle. Finally, the blood flow was computed, and the wall shear stress field at the vein and thrombus walls was determined.
PubDate: 2016-09-27T06:12:42.868596-05:
DOI: 10.1002/cnm.2819
- Authors: Josep M. López; Gerard Fortuny, Dolors Puigjaner, Joan Herrero, Francesc Marimon, Josep Garcia-Bennett
- Dental implant customization using numerical optimization design and
3-dimensional printing fabrication of zirconia ceramic- Authors: Yung-Chang Cheng; Deng-Huei Lin, Cho-Pei Jiang, Yuan-Min Lin
Abstract: This study proposes a new methodology for dental implant customization consisting of numerical geometric optimization and 3-dimensional printing fabrication of zirconia ceramic. In the numerical modeling, exogenous factors for implant shape include the thread pitch, thread depth, maximal diameter of implant neck, and body size. Endogenous factors are bone density, cortical bone thickness, and non-osseointegration. An integration procedure, including uniform design method, Kriging interpolation and genetic algorithm, is applied to optimize the geometry of dental implants. The threshold of minimal micromotion for optimization evaluation was 100 μm. The optimized model is imported to the 3-dimensional slurry printer to fabricate the zirconia green body (powder is bonded by polymer weakly) of the implant. The sintered implant is obtained using a 2-stage sintering process. Twelve models are constructed according to uniform design method and simulated the micromotion behavior using finite element modeling. The result of uniform design models yields a set of exogenous factors that can provide the minimal micromotion (30.61 μm), as a suitable model. Kriging interpolation and genetic algorithm modified the exogenous factor of the suitable model, resulting in 27.11 μm as an optimization model. Experimental results show that the 3-dimensional slurry printer successfully fabricated the green body of the optimization model, but the accuracy of sintered part still needs to be improved. In addition, the scanning electron microscopy morphology is a stabilized t-phase microstructure, and the average compressive strength of the sintered part is 632.1 MPa.A new methodology for dental implant customization is proposed. It consists of numerical modeling for optimized dental shape, 3-dimensional slurry printing for fabricating the zirconia green body, and sintering to obtain high-density zirconia dental implant. Numerical results present that the Kriging interpolation and genetic algorithm can modify the initial model to obtain the optimized model. Experimental results show that the 3-dimensional slurry printer successfully fabricated the green body of the optimization model. In addition, the scanning electron microscopy morphology is a stabilized t-phase microstructure, and the average compressive strength of the sintered part is 632.1 MPa.
PubDate: 2016-09-23T03:55:45.05661-05:0
DOI: 10.1002/cnm.2820
- Authors: Yung-Chang Cheng; Deng-Huei Lin, Cho-Pei Jiang, Yuan-Min Lin
- Data assimilation for identification of cardiovascular network
characteristics- Authors: Rajnesh Lal; Bijan Mohammadi, Franck Nicoud
Abstract: A method to estimate the hemodynamics parameters of a network of vessels using an Ensemble Kalman filter is presented. The elastic moduli (Young's modulus) of blood vessels and the terminal boundary parameters are estimated as the solution of an inverse problem. Two synthetic test cases and a configuration where experimental data are available are presented. The sensitivity analysis confirms that the proposed method is quite robust even with a few numbers of observations. The simulations with the estimated parameters recovers target pressure or flow rate waveforms at given specific locations, improving the state-of-the-art predictions available in the literature. This shows the effectiveness and efficiency of both the parameter estimation algorithm and the blood flow model.An ensemble Kalman filter is use to identify the hemodynamics parameters such as Young's modulus and the terminal boundary parameters as the solution of inverse problems. The sensitivity analysis confirms that the proposed method is quite robust even with a few numbers of observations. The paper demonstrates that joint use of data assimilation and flow solution by a computational fluid dynamics code greatly improves available results in the literature for a realistic human arterial model with an available experimental reference.
PubDate: 2016-09-21T07:10:33.912164-05:
DOI: 10.1002/cnm.2824
- Authors: Rajnesh Lal; Bijan Mohammadi, Franck Nicoud
- Creation of an idealized nasopharynx geometry for accurate computational
fluid dynamics simulations of nasal airflow in patient-specific models
lacking the nasopharynx anatomy- Authors: Azadeh A.T. Borojeni; Dennis O. Frank-Ito, Julia S. Kimbell, John S. Rhee, Guilherme J.M. Garcia
Abstract: Virtual surgery planning based on computational fluid dynamics (CFD) simulations has the potential to improve surgical outcomes for nasal airway obstruction patients, but the benefits of virtual surgery planning must outweigh the risks of radiation exposure. Cone beam computed tomography (CT) scans represent an attractive imaging modality for virtual surgery planning due to lower costs and lower radiation exposures compared with conventional CT scans. However, to minimize the radiation exposure, the cone beam CT sinusitis protocol sometimes images only the nasal cavity, excluding the nasopharynx. The goal of this study was to develop an idealized nasopharynx geometry for accurate representation of outlet boundary conditions when the nasopharynx geometry is unavailable. Anatomically accurate models of the nasopharynx created from 30 CT scans were intersected with planes rotated at different angles to obtain an average geometry. Cross sections of the idealized nasopharynx were approximated as ellipses with cross-sectional areas and aspect ratios equal to the average in the actual patient-specific models. CFD simulations were performed to investigate whether nasal airflow patterns were affected when the CT-based nasopharynx was replaced by the idealized nasopharynx in 10 nasal airway obstruction patients. Despite the simple form of the idealized geometry, all biophysical variables (nasal resistance, airflow rate, and heat fluxes) were very similar in the idealized vs patient-specific models. The results confirmed the expectation that the nasopharynx geometry has a minimal effect in the nasal airflow patterns during inspiration. The idealized nasopharynx geometry will be useful in future CFD studies of nasal airflow based on medical images that exclude the nasopharynx.An idealized nasopharynx geometry was developed for accurate representation of outlet boundary conditions in nasal airflow simulations when the nasopharynx anatomy is not available. We demonstrated that the nasopharynx geometry has a negligible effect on nasal airflow patterns during inspiration, which means that the anatomically accurate nasopharynx can be replaced by an idealized geometry without significantly affecting airflow estimates in the main nasal cavity.
PubDate: 2016-09-21T07:00:46.000702-05:
DOI: 10.1002/cnm.2825
- Authors: Azadeh A.T. Borojeni; Dennis O. Frank-Ito, Julia S. Kimbell, John S. Rhee, Guilherme J.M. Garcia
- On the Two-Dimensional Muskat Problem with Monotone Large Initial Data
- Authors: Fan Deng; Zhen Lei, Fanghua Lin
Abstract: We consider the evolution of two incompressible, immiscible fluids with different densities in porous media, known as the Muskat problem [21], which in two dimensions is analogous to the Hele-Shaw cell [24]. We establish, for a class of large and monotone initial data, the global existence of weak solutions. The proof is based on a local well-posedness result for the initial data with certain specific asymptotics at spatial infinity and a new maximum principle for the first derivative of the graph function. © 2016 Wiley Periodicals, Inc.
PubDate: 2016-09-20T05:30:22.890244-05:
DOI: 10.1002/cpa.21669
- Authors: Fan Deng; Zhen Lei, Fanghua Lin
- A comparison of hemodynamic metrics and intraluminal thrombus burden in a
common iliac artery aneurysm- Authors: Lachlan J. Kelsey; Janet T. Powell, Paul E. Norman, Karol Miller, Barry J. Doyle
Abstract: Aneurysms of the common iliac artery (CIAA) are typically found in association with an abdominal aortic aneurysm (AAA). Isolated CIAAs, in the absence of an AAA, are uncommon. Similar to AAAs, CIAA may develop intraluminal thrombus (ILT). As isolated CIAAs have a contralateral common iliac artery for comparison, they provide an opportunity to study the hemodynamic mechanisms behind ILT formation.In this study, we compared a large isolated CIAA and the contralateral iliac artery using computational fluid dynamics to determine if hemodynamic metrics correlate with the location of ILT. We performed a comprehensive computational fluid dynamics study and investigated the residence time of platelets and monocytes, velocity fields, time-averaged wall shear stress, oscillatory shear index, and endothelial cell activation potential. We then correlated these data to ILT burden determined with computed tomography.We found that high cell residence times, low time-averaged wall shear stress, high oscillatory shear index, and high endothelial cell activation potential all correlate with regions of ILT development. Our results show agreement with previous hypotheses of thrombus formation in AAA and provide insights into the computational hemodynamics of iliac artery aneurysms.In this study, we compared a large isolated aneurysm of the common iliac artery and the contralateral iliac artery using computational fluid dynamics to determine if hemodynamic metrics correlate with the location of ILT. We investigated the residence behavior of particles, the velocity fields, time-averaged wall shear stress, oscillatory shear index, and endothelial cell activation potential. Our results show agreement with previous hypotheses of thrombus formation in abdominal aortic aneurysm and provide insights into the computational hemodynamics of iliac artery aneurysms.
PubDate: 2016-09-08T06:50:37.004257-05:
DOI: 10.1002/cnm.2821
- Authors: Lachlan J. Kelsey; Janet T. Powell, Paul E. Norman, Karol Miller, Barry J. Doyle
- Existence and Uniqueness for a Crystalline Mean Curvature Flow
- Authors: Antonin Chambolle; Massimiliano Morini, Marcello Ponsiglione
Abstract: An existence and uniqueness result, up to fattening, for a class of crystalline mean curvature flows with natural mobility is proved. The results are valid in any dimension and for arbitrary, possibly unbounded, initial closed sets. The comparison principle is obtained by means of a suitable weak formulation of the flow, while the existence of a global-in-time solution follows via a minimizing movement approach.© 2016 Wiley Periodicals, Inc.
PubDate: 2016-09-01T08:15:20.874762-05:
DOI: 10.1002/cpa.21668
- Authors: Antonin Chambolle; Massimiliano Morini, Marcello Ponsiglione
- Vessel segmentation from abdominal magnetic resonance images: adaptive and
reconstructive approach- Authors: Evgin Goceri; Zarine K. Shah, Metin N. Gurcan
Abstract: The liver vessels, which have low signal and run next to brighter bile ducts, are difficult to segment from MR images. This study presents a fully automated and adaptive method to segment portal and hepatic veins on magnetic resonance images. In the proposed approach, segmentation of these vessels is achieved in four stages: (i) initial segmentation, (ii) refinement, (iii) reconstruction, and (iv) post-processing. In the initial segmentation stage, k-means clustering is used, the results of which are refined iteratively with linear contrast stretching algorithm in the next stage, generating a mask image. In the reconstruction stage, vessel regions are reconstructed with the marker image from the first stage and the mask image from the second stage. Experimental data sets include slices that show fat tissues, which have the same gray level values with vessels, outside the margin of the liver. These structures are removed in the last stage. Results show that the proposed approach is more efficient than other thresholding-based methods. Copyright © 2016 John Wiley & Sons, Ltd.In this paper, we present a fully automated and adaptive method to segment portal and hepatic veins on magnetic resonance images. In the proposed approach, segmentation of these vessels is achieved in four stages: (i) initial segmentation, (ii) refinement, (iii) reconstruction, and (iv) post-processing. The proposed approach can detect boundaries of vessels by estimating potential edge pixels that belong to vessels. The proposed method has the capability to detect not only the central, larger liver vasculature but also small, peripheral vessels.
PubDate: 2016-08-02T05:50:45.811524-05:
DOI: 10.1002/cnm.2811
- Authors: Evgin Goceri; Zarine K. Shah, Metin N. Gurcan
- Fluid–structure interaction and structural analyses using a
comprehensive mitral valve model with 3D chordal structure- Authors: Milan Toma; Daniel R. Einstein, Charles H. Bloodworth, Richard P. Cochran, Ajit P. Yoganathan, Karyn S. Kunzelman
Abstract: Over the years, three-dimensional models of the mitral valve have generally been organized around a simplified anatomy. Leaflets have been typically modeled as membranes, tethered to discrete chordae typically modeled as one-dimensional, non-linear cables. Yet, recent, high-resolution medical images have revealed that there is no clear boundary between the chordae and the leaflets. In fact, the mitral valve has been revealed to be more of a webbed structure whose architecture is continuous with the chordae and their extensions into the leaflets. Such detailed images can serve as the basis of anatomically accurate, subject-specific models, wherein the entire valve is modeled with solid elements that more faithfully represent the chordae, the leaflets, and the transition between the two. These models have the potential to enhance our understanding of mitral valve mechanics and to re-examine the role of the mitral valve chordae, which heretofore have been considered to be ‘invisible’ to the fluid and to be of secondary importance to the leaflets. However, these new models also require a rethinking of modeling assumptions. In this study, we examine the conventional practice of loading the leaflets only and not the chordae in order to study the structural response of the mitral valve apparatus. Specifically, we demonstrate that fully resolved 3D models of the mitral valve require a fluid–structure interaction analysis to correctly load the valve even in the case of quasi-static mechanics. While a fluid–structure interaction mode is still more computationally expensive than a structural-only model, we also show that advances in GPU computing have made such models tractable. Copyright © 2016 John Wiley & Sons, Ltd.Over the years, 3D models of the mitral valve have generally been organized around a simplified anatomy. In this study, we examine the conventional practice of loading the leaflets only and not the chordae in order to study the structural response of the mitral valve apparatus. Specifically, we demonstrate that fully resolved 3D models of the mitral valve require a fluid–structure interaction analysis to correctly load the valve even in the case of quasi-static mechanics.
PubDate: 2016-07-28T06:30:34.816973-05:
DOI: 10.1002/cnm.2815
- Authors: Milan Toma; Daniel R. Einstein, Charles H. Bloodworth, Richard P. Cochran, Ajit P. Yoganathan, Karyn S. Kunzelman
- Third-order harmonic expansion of the magnetoencephalography forward and
inverse problems in an ellipsoidal brain model- Authors: Mauricio Alcocer-Sosa; David Gutiérrez
Abstract: We present a forward modeling solution in the form of an array response kernel for magnetoencephalography. We consider the case when the brain's anatomy is approximated by an ellipsoid and an equivalent current dipole model is used to approximate brain sources. The proposed solution includes the contributions up to the third-order ellipsoidal harmonic terms; hence, we compare this new approximation against the previously available one that only considered up to second-order harmonics. We evaluated the proposed solution when used in the inverse problem of estimating physiologically feasible visual evoked responses from magnetoencephalography data. Our results showed that the contribution of the third-order harmonic terms provides a more realistic representation of the magnetic fields (closer to those generated with a numerical approximation based on the boundary element method) and, subsecuently, the estimated equivalent current dipoles are a better fit to those observed in practice (e.g., in visual evoked potentials). Copyright © 2016 John Wiley & Sons, Ltd.The solution of the forward problem in magnetoencephalography, for the case when the brain's geometry is approximated by an ellipsoid, previuosly considered only up to the second-order harmonics. However, we show that the forward solution is improved by adding the contribution of third-order ellipsoidal harmonics. Furthermore, such improvement in the generated magnetic fields also has a positive impact in the inverse problem of estimating evoked brain responses.
PubDate: 2016-07-27T06:25:52.376519-05:
DOI: 10.1002/cnm.2810
- Authors: Mauricio Alcocer-Sosa; David Gutiérrez
- Transversally enriched pipe element method (TEPEM): An effective numerical
approach for blood flow modeling- Authors: Luis Mansilla Alvarez; Pablo Blanco, Carlos Bulant, Enzo Dari, Alessandro Veneziani, Raúl Feijóo
Abstract: In this work, we present a novel approach tailored to approximate the Navier–Stokes equations to simulate fluid flow in three-dimensional tubular domains of arbitrary cross-sectional shape. The proposed methodology is aimed at filling the gap between (cheap) one-dimensional and (expensive) three-dimensional models, featuring descriptive capabilities comparable with the full and accurate 3D description of the problem at a low computational cost. In addition, this methodology can easily be tuned or even adapted to address local features demanding more accuracy. The numerical strategy employs finite (pipe-type) elements that take advantage of the pipe structure of the spatial domain under analysis. While low order approximation is used for the longitudinal description of the physical fields, transverse approximation is enriched using high order polynomials. Although our application of interest is computational hemodynamics and its relevance to pathological dynamics like atherosclerosis, the approach is quite general and can be applied in any internal fluid dynamics problem in pipe-like domains. Numerical examples covering academic cases as well as patient-specific coronary arterial geometries demonstrate the potentialities of the developed methodology and its performance when compared against traditional finite element methods. Copyright © 2016 John Wiley & Sons, Ltd.We present a numerical strategy tailored to simulate fluid flow in 3D tubular domains. The methodology features descriptive capabilities comparable to 3D models, but at a low computational cost. The domain of analysis is split into pipe elements (slabs). While low order approximation for the longitudinal description of the physical fields is employed, transverse approximation is enriched using high order polynomials. Several numerical examples ranging from academic cases to patient-specific coronary arterial geometries demonstrate the potentialities proposed methodology.
PubDate: 2016-07-27T06:16:23.273082-05:
DOI: 10.1002/cnm.2808
- Authors: Luis Mansilla Alvarez; Pablo Blanco, Carlos Bulant, Enzo Dari, Alessandro Veneziani, Raúl Feijóo
- Finite element analysis of the effect of medullary contact on fracture
healing and remodeling in the intramedullary interlocking nail-fixed tibia
fracture- Authors: Haosen Wang; Zhixiu Hao, Shizhu Wen
Abstract: Intramedullary interlocking nail is an effective treatment for tibial diaphyseal fracture. The contact between medullary rod and diaphyseal cortex is able to enhance fracture stability. However, how and to what degree the contact affects fracture healing and subsequent bone remodeling is still unclear. To investigate this, fracture healing and remodeling algorithms were combined, improved, and used to simulate the healing and remodeling processes in a transverse tibial diaphyseal fracture fixed with an intramedullary interlocking nail device. Two different diaphyseal fracture statuses, three different initial loading levels, and two nail materials were considered. The results showed that the medullary contact could significantly enhance the fixation stability; the strain reduction was up to 80% in the initial granulation callus. However, low initial loading level was found to be a more potential risk factor for the insufficient loading-induced nonunion other than medullary contact and stiffer nail material. Furthermore, the stabilizing effect of medullary contact diminished when stiff bone tissue formed in the callus; thus, the remodeling in the long-term was not affected by medullary contact. Copyright © 2016 John Wiley & Sons, Ltd.A numerical model composed of fracture healing, and remodeling model was developed and used to simulate the effect of medullary contact between intramedullary rod and cortical bone. The contact was found to be beneficial for fracture stability. Although medullary contact increased the risk of insufficient stimulation-induced nonunion, the main cause to this complication was found to be the low initial loading. The medullary contact did not compromise the final remodeling of the fracture callus, as compared with non-contact group.
PubDate: 2016-07-26T05:40:31.884607-05:
DOI: 10.1002/cnm.2816
- Authors: Haosen Wang; Zhixiu Hao, Shizhu Wen
- Coupling schemes for the FSI forward prediction challenge: Comparative
study and validation- Authors: Mikel Landajuela; Marina Vidrascu, Dominique Chapelle, Miguel A. Fernández
Abstract: This paper presents a numerical study in which several partitioned solution procedures for incompressible fluid-structure interaction are compared and validated against the results of an experimental fluid-structure interaction benchmark. The numerical methods discussed cover the three main families of coupling schemes: strongly coupled, semi-implicit, and loosely coupled. Very good agreement is observed between the numerical and experimental results. The comparisons confirm that strong coupling can be efficiently avoided, via semi-implicit and loosely coupled schemes, without compromising stability and accuracy. Copyright © 2016 John Wiley & Sons, Ltd.Several state-of-the-art partitioned solution procedures for incompressible fluid-structure interaction are thoroughly compared and validated against experimental data. The considered methods are parameter free and cover the three main categories of coupling schemes: strongly coupled, semi-implicit and loosely coupled. Previous studies in this direction used synthetic data as reference or were limited to a single method. Very good agreement is observed between the numerical and experimental results.
PubDate: 2016-07-21T05:40:36.405277-05:
DOI: 10.1002/cnm.2813
- Authors: Mikel Landajuela; Marina Vidrascu, Dominique Chapelle, Miguel A. Fernández
- Cortical bone fracture analysis using XFEM – case study
- Authors: Ashraf Idkaidek; Iwona Jasiuk
Abstract: We aim to achieve an accurate simulation of human cortical bone fracture using the extended finite element method within a commercial finite element software abaqus. A two-dimensional unit cell model of cortical bone is built based on a microscopy image of the mid-diaphysis of tibia of a 70-year-old human male donor. Each phase of this model, an interstitial bone, a cement line, and an osteon, are considered linear elastic and isotropic with material properties obtained by nanoindentation, taken from literature.The effect of using fracture analysis methods (cohesive segment approach versus linear elastic fracture mechanics approach), finite element type, and boundary conditions (traction, displacement, and mixed) on cortical bone crack initiation and propagation are studied. In this study cohesive segment damage evolution for a traction separation law based on energy and displacement is used. In addition, effects of the increment size and mesh density on analysis results are investigated.We find that both cohesive segment and linear elastic fracture mechanics approaches within the extended finite element method can effectively simulate cortical bone fracture. Mesh density and simulation increment size can influence analysis results when employing either approach, and using finer mesh and/or smaller increment size does not always provide more accurate results. Both approaches provide close but not identical results, and crack propagation speed is found to be slower when using the cohesive segment approach. Also, using reduced integration elements along with the cohesive segment approach decreases crack propagation speed compared with using full integration elements. Copyright © 2016 John Wiley & Sons, Ltd.We find that cohesive segment and linear elastic fracture mechanics approaches within the extended finite element method can both effectively simulate cortical bone fracture. However, results obtained from both approaches are sensitive to finite element model mesh density and to analysis increment size, where using finer mesh and/or smaller analysis increment size does not always provide more accurate results. Also the linear elastic fracture mechanics approach showed faster cracks propagation with more realistic behavior compared with the cohesive segment approach.
PubDate: 2016-07-12T06:40:40.987749-05:
DOI: 10.1002/cnm.2809
- Authors: Ashraf Idkaidek; Iwona Jasiuk
- Fluid-structure interaction including volumetric coupling with homogenised
subdomains for modeling respiratory mechanics- Authors: Lena Yoshihara; Christian J. Roth, Wolfgang A. Wall
Abstract: In this article, a novel approach is presented for combining standard fluid-structure interaction with additional volumetric constraints to model fluid flow into and from homogenised solid domains. The proposed algorithm is particularly interesting for investigations in the field of respiratory mechanics as it enables the mutual coupling of airflow in the conducting part and local tissue deformation in the respiratory part of the lung by means of a volume constraint. In combination with a classical monolithic fluid-structure interaction approach, a comprehensive model of the human lung can be established that will be useful to gain new insights into respiratory mechanics in health and disease. To illustrate the validity and versatility of the novel approach, three numerical examples including a patient-specific lung model are presented. The proposed algorithm proves its capability of computing clinically relevant airflow distribution and tissue strain data at a level of detail that is not yet achievable, neither with current imaging techniques nor with existing computational models. Copyright © 2016 John Wiley & Sons, Ltd.In this work, a standard monolithic fluid–structure interaction approach is extended by an additional constraint that couples fluid flow and regional parenchymal inflation. Higher airway tree generations are homogenised within the solid domains and provide physiologically correct boundary conditions to airflow into the single regions of the lung. Monolithic treatment enables an efficient and stable coupling in real patient-specific models.
PubDate: 2016-07-08T03:16:00.048821-05:
DOI: 10.1002/cnm.2812
- Authors: Lena Yoshihara; Christian J. Roth, Wolfgang A. Wall
- Contributions of prestrains, hyperelasticity, and muscle fiber activation
on mitral valve systolic performance- Authors: Victorien Prot; Bjorn Skallerud
Abstract: The present study addresses the contributions of prestrains and muscle fiber activation to the global response of the mitral valve during systole. A finite element model of a porcine mitral valve is created using anatomical measurements and 3D echocardiographic recordings. The passive behavior of the leaflets is modeled using a transversely isotropic hyperelastic constitutive model, and we assume orthotropic muscle activations in the anterior leaflet. A simple approach to incorporate prestrains in the mitral valve apparatus is used by expanding the mitral annulus before applying the ventricular pressure to the mitral leaflets. Several finite element analyses are run with or without muscle activation and with or without prestrains. The analysis results are compared at peak systole with the echocardiograpic recordings. The case where prestrains and activation are accounted for simultaneously is the most efficient to approach the physiological flat shape of the closed valve observed in the echocardiograpic measurements. These results suggest that the active components present in the mitral leaflets and the presence of prestrains contribute to the physiological deformations of the mitral valve at peak systole and that material models based on in vitro mechanical testing are not sufficient for numerical studies of the mitral apparatus. Copyright © 2016 John Wiley & Sons, Ltd.The present study addresses the contributions of prestrains and muscle fiber activation to the global response of the mitral valve during systole using the finite element method. The analysis where prestrains and muscle activation are accounted for simultaneously is the most efficient to approach the physiological flat shape observed in the echocardiography. This study suggests that the active components present in the mitral leaflets and the presence of prestrains contribute to the physiological deformations of the valve.
PubDate: 2016-07-05T09:00:47.771441-05:
DOI: 10.1002/cnm.2806
- Authors: Victorien Prot; Bjorn Skallerud
- Boundary Value Problems for Second-Order Elliptic Operators Satisfying a
Carleson Condition- Authors: Martin Dindoš; Jill Pipher, David Rule
Abstract: Let Ω be a Lipschitz domain in ℝn, n ≥ 2, and L = div A∇· be a second-order elliptic operator in divergence form. We establish the solvability of the Dirichlet regularity problem with boundary data in H1,p(∂Ω) and of the Neumann problem with Lp(∂Ω) data for the operator L on Lipschitz domains with small Lipschitz constant. We allow the coefficients of the operator L to be rough, obeying a certain Carleson condition with small norm. These results complete the results of Dindoš, Petermichl, and Pipher (2007), where the Lp(∂Ω) Dirichlet problem was considered under the same assumptions, and Dindoš and Rule (2010), where the regularity and Neumann problems were considered on two-dimensional domains.© 2016 Wiley Periodicals, Inc.
PubDate: 2016-06-13T09:40:25.675676-05:
DOI: 10.1002/cpa.21649
- Authors: Martin Dindoš; Jill Pipher, David Rule
- On the Global Solution of a 3-D MHD System with Initial Data near
Equilibrium- Authors: Hammadi Abidi; Ping Zhang
Abstract: In this paper, we prove the global existence of smooth solutions to the three-dimensional incompressible magnetohydrodynamical system with initial data close enough to the equilibrium state, (e3,0). Compared with previous works by Lin, Xu, and Zhang and by Xu and Zhang, here we present a new Lagrangian formulation of the system, which is a damped wave equation and which is nondegenerate only in the direction of the initial magnetic field. Furthermore, we remove the admissible condition on the initial magnetic field, which was required in the earlier works. By using the Frobenius theorem and anisotropic Littlewood-Paley theory for the Lagrangian formulation of the system, we achieve the global L1-in-time Lipschitz estimate of the velocity field, which allows us to conclude the global existence of solutions to this system. In the case when the initial magnetic field is a constant vector, the large-time decay rate of the solution is also obtained.© 2016 Wiley Periodicals, Inc.
PubDate: 2016-05-10T03:20:22.857425-05:
DOI: 10.1002/cpa.21645
- Authors: Hammadi Abidi; Ping Zhang
- Long-Time Behavior, Invariant Measures, and Regularizing Effects for
Stochastic Scalar Conservation Laws- Authors: Benjamin Gess; Panagiotis E. Souganidis
Abstract: We study the long-time behavior and regularity of the pathwise entropy solutions to stochastic scalar conservation laws with random-in-time spatially homogeneous fluxes and periodic initial data. We prove that the solutions converge to their spatial average, which is the unique invariant measure of the associated random dynamical system, and provide a rate of convergence, the latt3er being new even in the deterministic case for dimensions higher than 2. The main tool is a new regularization result in the spirit of averaging lemmata for scalar conservation laws, which, in particular, implies a regularization by noise-type result for pathwise quasi-solutions.© 2016 Wiley Periodicals, Inc.
PubDate: 2016-05-10T03:20:22.063664-05:
DOI: 10.1002/cpa.21646
- Authors: Benjamin Gess; Panagiotis E. Souganidis
- Singularities of Solutions to Quadratic Vector Equations on the Complex
Upper Half-Plane- Authors: O. Ajanki; L. Erdős, T. Krüger
Abstract: Let S be a positivity-preserving symmetric linear operator acting on bounded functions. The nonlinear equation −1m=z+Sm with a parameter z in the complex upper half-plane ℍ has a unique solution m with values in ℍ. We show that the z-dependence of this solution can be represented as the Stieltjes transforms of a family of probability measures v on ℝ. Under suitable conditions on S, we show that v has a real analytic density apart from finitely many algebraic singularities of degree at most 3.Our motivation comes from large random matrices. The solution m determines the density of eigenvalues of two prominent matrix ensembles: (i) matrices with centered independent entries whose variances are given by S and (ii) matrices with correlated entries with a translation-invariant correlation structure. Our analysis shows that the limiting eigenvalue density has only square root singularities or cubic root cusps; no other singularities occur.© 2016 Wiley Periodicals, Inc.
PubDate: 2016-04-09T05:31:04.786506-05:
DOI: 10.1002/cpa.21639
- Authors: O. Ajanki; L. Erdős, T. Krüger
- Well-Posed Treatment of Space-Charge Layers in the Electroneutral Limit of
Electrodiffusion- Authors: Adam R. Stinchcombe; Yoichiro Mori, Charles S. Peskin
Abstract: The electroneutral model describes cellular electrical activity, accounting for ionic concentration dynamics without resolution of the fine spatial scales of the space-charge layer. This is done by asserting that the ionic solution is electrically neutral at each point in space. However, electroneutrality is inconsistent with the original boundary conditions at cell membranes. We consider three separate methods of resolving this inconsistency that result in well-posed models that are accurate approximations to a detailed model in which the space-charge layer is fully resolved. A particular electrodiffusion problem is utilized to make the discussion specific. © 2016 Wiley Periodicals, Inc.
PubDate: 2016-02-29T05:36:40.978415-05:
DOI: 10.1002/cpa.21630
- Authors: Adam R. Stinchcombe; Yoichiro Mori, Charles S. Peskin