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Feiger B, Jensen CW, Bryner BS, Segars WP, Randles A. Modeling the effect of patient size on cerebral perfusion during veno-arterial extracorporeal membrane oxygenation. Perfusion 2023:2676591231187962. [PMID: 37395266 PMCID: PMC10786318 DOI: 10.1177/02676591231187962] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/04/2023]
Abstract
INTRODUCTION A well-known complication of veno-arterial extracorporeal membrane oxygenation (VA ECMO) is differential hypoxia, in which poorly-oxygenated blood ejected from the left ventricle mixes with and displaces well-oxygenated blood from the circuit, thereby causing cerebral hypoxia and ischemia. We sought to characterize the impact of patient size and anatomy on cerebral perfusion under a range of different VA ECMO flow conditions. METHODS We use one-dimensional (1D) flow simulations to investigate mixing zone location and cerebral perfusion across 10 different levels of VA ECMO support in eight semi-idealized patient geometries, for a total of 80 scenarios. Measured outcomes included mixing zone location and cerebral blood flow (CBF). RESULTS Depending on patient anatomy, we found that a VA ECMO support ranging between 67-97% of a patient's ideal cardiac output was needed to perfuse the brain. In some cases, VA ECMO flows exceeding 90% of the patient's ideal cardiac output are needed for adequate cerebral perfusion. CONCLUSIONS Individual patient anatomy markedly affects mixing zone location and cerebral perfusion in VA ECMO. Future fluid simulations of VA ECMO physiology should incorporate varied patient sizes and geometries in order to best provide insights toward reducing neurologic injury and improved outcomes in this patient population.
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Affiliation(s)
- Bradley Feiger
- Department of Bioengineering, School of Medicine, Duke University, Durham, NC, USA
| | - Christopher W Jensen
- Department of Bioengineering, School of Medicine, Duke University, Durham, NC, USA
- Division of Cardiovascular and Thoracic Surgery, Department of Surgery, Duke University, Durham, NC, USA
| | - Benjamin S Bryner
- Division of Cardiovascular and Thoracic Surgery, Department of Surgery, Duke University, Durham, NC, USA
| | - William P Segars
- Department of Radiology, School of Medicine, Duke Medicine, Chicago, IL, USA
| | - Amanda Randles
- Department of Bioengineering, School of Medicine, Duke University, Durham, NC, USA
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2
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Fritz M, Köppl T, Oden JT, Wagner A, Wohlmuth B, Wu C. A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3612. [PMID: 35522186 DOI: 10.1002/cnm.3612] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2022] [Revised: 03/30/2022] [Accepted: 04/27/2022] [Indexed: 06/14/2023]
Abstract
In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are considered, to start from the aortic inlet to the capillaries and tissue of the breast. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic partial differential equations (PDEs) is considered to simulate blood flow in larger arteries with highly elastic vessel walls. Second, we assign 1D linearized hyperbolic PDEs to model the smaller arteries with stiffer vessel walls. The third model type consists of ODE systems (0D models). It is used to model the arterioles and peripheral circulation. Finally, homogenized 3D porous media models are considered to simulate flow and transport in capillaries and tissue within the breast volume. Sink terms are used to account for the influence of the venous and lymphatic systems. Combining the four model types, we obtain two different 1D-0D-3D coupled models for simulating blood flow and transport processes: The first model results in a fully coupled 1D-0D-3D model covering the complete path from the aorta to the breast combining a generic arterial network with a patient specific breast network and geometry. The second model is a reduced one based on the separation of the generic and patient specific parts. The information from a calibrated fully coupled model is used as inflow condition for the patient specific sub-model allowing a significant computational cost reduction. Several numerical experiments are conducted to calibrate the generic model parameters and to demonstrate realistic flow simulations compared to existing data on blood flow in the human breast and vascular system. Moreover, we use two different breast vasculature and tissue data sets to illustrate the robustness of our reduced sub-model approach.
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Affiliation(s)
- Marvin Fritz
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - Tobias Köppl
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - John Tinsley Oden
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, USA
| | - Andreas Wagner
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - Barbara Wohlmuth
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - Chengyue Wu
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, USA
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3
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Krivovichev GV. Steady-state solutions of one-dimensional equations of non-Newtonian hemodynamics. INT J BIOMATH 2022. [DOI: 10.1142/s1793524522500334] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper is devoted to obtaining and analysis of steady-state solutions of one-dimensional equations for the simulation of blood flow when the non-Newtonian nature of blood is taken into account. The models, based on the rheological relations, widely used for the blood, are considered. The expressions for the nonlinear frictional term are presented. For the Power Law, Simplified Cross, and Quemada models, the exact integrals of the nonlinear ordinary differential equation, obtained from the averaged momentum equation, are obtained. It is demonstrated that several solutions exist for every rheological model, but the physically relevant solutions can be selected by the appropriate value of Mach number. The effects of the velocity profile and the value of hematocrit on the steady-state solutions are analyzed. It is demonstrated that the flattening of the velocity profile, which is typical for the blood, leads to the diminishing of the length of the interval, where the solution exists. The same effect is observed when the hematocrit value is increased.
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Affiliation(s)
- Gerasim V. Krivovichev
- Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034, Russian Federation
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4
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Abstract
The paper is devoted to the comparison of different one-dimensional models of blood flow. In such models, the non-Newtonian property of blood is considered. It is demonstrated that for the large arteries, the small parameter is observed in the models, and the perturbation method can be used for the analytical solution. In the paper, the simplified nonlinear problem for the semi-infinite vessel with constant properties is solved analytically, and the solutions for different models are compared. The effects of the flattening of the velocity profile and hematocrit value on the deviation from the Newtonian model are investigated.
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5
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Larson K, Bowman C, Papadimitriou C, Koumoutsakos P, Matzavinos A. Detection of arterial wall abnormalities via Bayesian model selection. ROYAL SOCIETY OPEN SCIENCE 2019; 6:182229. [PMID: 31824680 PMCID: PMC6837237 DOI: 10.1098/rsos.182229] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/13/2019] [Accepted: 09/17/2019] [Indexed: 06/10/2023]
Abstract
Patient-specific modelling of haemodynamics in arterial networks has so far relied on parameter estimation for inexpensive or small-scale models. We describe here a Bayesian uncertainty quantification framework which makes two major advances: an efficient parallel implementation, allowing parameter estimation for more complex forward models, and a system for practical model selection, allowing evidence-based comparison between distinct physical models. We demonstrate the proposed methodology by generating simulated noisy flow velocity data from a branching arterial tree model in which a structural defect is introduced at an unknown location; our approach is shown to accurately locate the abnormality and estimate its physical properties even in the presence of significant observational and systemic error. As the method readily admits real data, it shows great potential in patient-specific parameter fitting for haemodynamical flow models.
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Affiliation(s)
- Karen Larson
- Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
| | - Clark Bowman
- Department of Mathematics and Statistics, Hamilton College, Clinton, NY 13323, USA
| | - Costas Papadimitriou
- Department of Mechanical Engineering, University of Thessaly, 38334 Volos, Greece
| | - Petros Koumoutsakos
- Computational Science and Engineering Laboratory, ETH Zürich CH-8092, Switzerland
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6
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A novel, FFT-based one-dimensional blood flow solution method for arterial network. Biomech Model Mechanobiol 2019; 18:1311-1334. [PMID: 30955132 PMCID: PMC6748896 DOI: 10.1007/s10237-019-01146-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2018] [Accepted: 03/28/2019] [Indexed: 01/08/2023]
Abstract
In the present work, we propose an FFT-based method for solving blood flow equations in an arterial network with variable properties and geometrical changes. An essential advantage of this approach is in correctly accounting for the vessel skin friction through the use of Womersley solution. To incorporate nonlinear effects, a novel approximation method is proposed to enable calculation of nonlinear corrections. Unlike similar methods available in the literature, the set of algebraic equations required for every harmonic is constructed automatically. The result is a generalized, robust and fast method to accurately capture the increasing pulse wave velocity downstream as well as steepening of the pulse front. The proposed method is shown to be appropriate for incorporating correct convection and diffusion coefficients. We show that the proposed method is fast and accurate and it can be an effective tool for 1D modelling of blood flow in human arterial networks.
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7
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Koeppl T, Santin G, Haasdonk B, Helmig R. Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e3095. [PMID: 29732723 DOI: 10.1002/cnm.3095] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2017] [Revised: 02/22/2018] [Accepted: 04/15/2018] [Indexed: 06/08/2023]
Abstract
In this work, we consider 2 kinds of model reduction techniques to simulate blood flow through the largest systemic arteries, where a stenosis is located in a peripheral artery, i.e., in an artery that is located far away from the heart. For our simulations, we place the stenosis in one of the tibial arteries belonging to the right lower leg (right posterior tibial artery). The model reduction techniques that are used are on the one hand dimensionally reduced models (1-D and 0-D models, the so-called mixed-dimension model) and on the other hand surrogate models produced by kernel methods. Both methods are combined in such a way that the mixed-dimension models yield training data for the surrogate model, where the surrogate model is parametrised by the degree of narrowing of the peripheral stenosis. By means of a well-trained surrogate model, we show that simulation data can be reproduced with a satisfactory accuracy and that parameter optimisation or state estimation problems can be solved in a very efficient way. Furthermore, it is demonstrated that a surrogate model enables us to present after a very short simulation time the impact of a varying degree of stenosis on blood flow, obtaining a speedup of several orders over the full model.
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Affiliation(s)
- Tobias Koeppl
- Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart, Pfaffenwaldring 61, D-70569, Stuttgart, Germany
| | - Gabriele Santin
- Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany
| | - Bernard Haasdonk
- Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany
| | - Rainer Helmig
- Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart, Pfaffenwaldring 61, D-70569, Stuttgart, Germany
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8
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Ghigo A, Abou Taam S, Wang X, Lagrée PY, Fullana JM. A one-dimensional arterial network model for bypass graft assessment. Med Eng Phys 2017; 43:39-47. [DOI: 10.1016/j.medengphy.2017.02.002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2016] [Revised: 01/05/2017] [Accepted: 02/05/2017] [Indexed: 10/20/2022]
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9
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Puelz C, Čanić S, Rivière B, Rusin CG. Comparison of reduced models for blood flow using Runge-Kutta discontinuous Galerkin methods. APPLIED NUMERICAL MATHEMATICS : TRANSACTIONS OF IMACS 2017; 115:114-141. [PMID: 29081563 PMCID: PMC5654593 DOI: 10.1016/j.apnum.2017.01.005] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class describes mass and velocity. Further, the averaging process employed in the model derivation requires the specification of the axial velocity profile; this choice differentiates models within each class. Discrepancies among differing models have yet to be investigated. In this paper, we comment on some theoretical differences among models and systematically compare them for physiologically relevant vessel parameters, network topology, and boundary data. In particular, the effect of the velocity profile is investigated in the cases of both smooth and discontinuous solutions, and a recommendation for a physiological model is provided. The models are discretized by a class of Runge-Kutta discontinuous Galerkin methods.
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Affiliation(s)
- Charles Puelz
- Rice University, Department of Computational and Applied Mathematics
| | | | - Béatrice Rivière
- Rice University, Department of Computational and Applied Mathematics
| | - Craig G Rusin
- Baylor College of Medicine, Department of Pediatric Cardiology
- Texas Children's Hospital, Department of Pediatric Medicine-Cardiology
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10
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Lal R, Mohammadi B, Nicoud F. Data assimilation for identification of cardiovascular network characteristics. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2017; 33:e2824. [PMID: 27531694 DOI: 10.1002/cnm.2824] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2016] [Revised: 07/05/2016] [Accepted: 08/12/2016] [Indexed: 06/06/2023]
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.
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Affiliation(s)
- Rajnesh Lal
- IMAG, Universite de Montpellier, Montpellier, CC051, 34095, France
| | - Bijan Mohammadi
- IMAG, Universite de Montpellier, Montpellier, CC051, 34095, France
| | - Franck Nicoud
- IMAG, Universite de Montpellier, Montpellier, CC051, 34095, France
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11
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Chnafa C, Valen-Sendstad K, Brina O, Pereira V, Steinman D. Improved reduced-order modelling of cerebrovascular flow distribution by accounting for arterial bifurcation pressure drops. J Biomech 2017; 51:83-88. [DOI: 10.1016/j.jbiomech.2016.12.004] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Revised: 11/04/2016] [Accepted: 12/03/2016] [Indexed: 01/25/2023]
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12
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Keijsers JMT, Leguy CAD, Huberts W, Narracott AJ, Rittweger J, Vosse FNVD. Global sensitivity analysis of a model for venous valve dynamics. J Biomech 2016; 49:2845-2853. [PMID: 27457428 DOI: 10.1016/j.jbiomech.2016.06.029] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2016] [Revised: 06/22/2016] [Accepted: 06/23/2016] [Indexed: 10/21/2022]
Abstract
Chronic venous disease is defined as dysfunction of the venous system caused by incompetent venous valves with or without a proximal venous obstruction. Assessing the severity of the disease is challenging, since venous function is determined by various interacting hemodynamic factors. Mathematical models can relate these factors using physical laws and can thereby aid understanding of venous (patho-)physiology. To eventually use a mathematical model to support clinical decision making, first the model sensitivity needs to be determined. Therefore, the aim of this study is to assess the sensitivity of the venous valve model outputs to the relevant input parameters. Using a 1D pulse wave propagation model of the tibial vein including a venous valve, valve dynamics under head up tilt are simulated. A variance-based sensitivity analysis is performed based on generalized polynomial chaos expansion. Taking a global approach, individual parameter importance on the valve dynamics as well as importance of their interactions is determined. For the output related to opening state of the valve, the opening/closing pressure drop (dpvalve,0) is found to be the most important parameter. The venous radius (rvein,0) is related to venous filling volume and is consequently most important for the output describing venous filling time. Finally, it is concluded that improved assessment of rvein,0 and dpvalve,0 is most rewarding when simulating valve dynamics, as this results in the largest reduction in output uncertainty. In practice, this could be achieved using ultrasound imaging of the veins and fluid structure interaction simulations to characterize detailed valve dynamics, respectively.
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Affiliation(s)
- J M T Keijsers
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands; Institute of Aerospace Medicine, German Aerospace Center, Cologne, Germany.
| | - C A D Leguy
- Institute of Aerospace Medicine, German Aerospace Center, Cologne, Germany
| | - W Huberts
- Department of Biomedical Engineering, Maastricht University, Maastricht, The Netherlands
| | - A J Narracott
- Medical Physics Group, Department of Cardiovascular Science, University of Sheffield, Sheffield, United Kingdom; INSIGNEO Institute for in silico Medicine, University of Sheffield, Sheffield, United Kingdom
| | - J Rittweger
- Institute of Aerospace Medicine, German Aerospace Center, Cologne, Germany
| | - F N van de Vosse
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
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13
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Drzisga D, Köppl T, Pohl U, Helmig R, Wohlmuth B. Numerical modeling of compensation mechanisms for peripheral arterial stenoses. Comput Biol Med 2016; 70:190-201. [DOI: 10.1016/j.compbiomed.2016.01.015] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Revised: 12/14/2015] [Accepted: 01/14/2016] [Indexed: 11/26/2022]
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14
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Fluid friction and wall viscosity of the 1D blood flow model. J Biomech 2016; 49:565-71. [PMID: 26862041 DOI: 10.1016/j.jbiomech.2016.01.010] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2015] [Revised: 11/10/2015] [Accepted: 01/09/2016] [Indexed: 11/23/2022]
Abstract
We study the behavior of the pulse waves of water into a flexible tube for application to blood flow simulations. In pulse waves both fluid friction and wall viscosity are damping factors, and difficult to evaluate separately. In this paper, the coefficients of fluid friction and wall viscosity are estimated by fitting a nonlinear 1D flow model to experimental data. In the experimental setup, a distensible tube is connected to a piston pump at one end and closed at another end. The pressure and wall displacements are measured simultaneously. A good agreement between model predictions and experiments was achieved. For amplitude decrease, the effect of wall viscosity on the pulse wave has been shown as important as that of fluid viscosity.
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15
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Donders WP, Huberts W, van de Vosse FN, Delhaas T. Personalization of models with many model parameters: an efficient sensitivity analysis approach. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2015; 31:n/a-n/a. [PMID: 26017545 DOI: 10.1002/cnm.2727] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2015] [Revised: 05/22/2015] [Accepted: 05/25/2015] [Indexed: 05/25/2023]
Abstract
Uncertainty quantification and global sensitivity analysis are indispensable for patient-specific applications of models that enhance diagnosis or aid decision-making. Variance-based sensitivity analysis methods, which apportion each fraction of the output uncertainty (variance) to the effects of individual input parameters or their interactions, are considered the gold standard. The variance portions are called the Sobol sensitivity indices and can be estimated by a Monte Carlo (MC) approach (e.g., Saltelli's method [1]) or by employing a metamodel (e.g., the (generalized) polynomial chaos expansion (gPCE) [2, 3]). All these methods require a large number of model evaluations when estimating the Sobol sensitivity indices for models with many parameters [4]. To reduce the computational cost, we introduce a two-step approach. In the first step, a subset of important parameters is identified for each output of interest using the screening method of Morris [5]. In the second step, a quantitative variance-based sensitivity analysis is performed using gPCE. Efficient sampling strategies are introduced to minimize the number of model runs required to obtain the sensitivity indices for models considering multiple outputs. The approach is tested using a model that was developed for predicting post-operative flows after creation of a vascular access for renal failure patients. We compare the sensitivity indices obtained with the novel two-step approach with those obtained from a reference analysis that applies Saltelli's MC method. The two-step approach was found to yield accurate estimates of the sensitivity indices at two orders of magnitude lower computational cost.
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Affiliation(s)
- W P Donders
- Department of Biomedical Engineering, School for Mental Health and Neuroscience (MHENS), Maastricht University, Maastricht, The Netherlands
| | - W Huberts
- Department of Biomedical Engineering, School for Cardiovascular Diseases (CARIM), Maastricht University, Maastricht, The Netherlands
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - F N van de Vosse
- Department of Biomedical Engineering, School for Cardiovascular Diseases (CARIM), Maastricht University, Maastricht, The Netherlands
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - T Delhaas
- Department of Biomedical Engineering, School for Cardiovascular Diseases (CARIM), Maastricht University, Maastricht, The Netherlands
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16
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Acosta S, Puelz C, Riviére B, Penny DJ, Rusin CG. Numerical Method of Characteristics for One-Dimensional Blood Flow. JOURNAL OF COMPUTATIONAL PHYSICS 2015; 294:96-109. [PMID: 25931614 PMCID: PMC4410450 DOI: 10.1016/j.jcp.2015.03.045] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.
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Affiliation(s)
- Sebastian Acosta
- Department of Pediatric Cardiology, Baylor College of Medicine, Texas
| | - Charles Puelz
- Department of Computational and Applied Mathematics, Rice University, Texas
| | - Béatrice Riviére
- Department of Computational and Applied Mathematics, Rice University, Texas
| | - Daniel J. Penny
- Department of Pediatric Cardiology, Baylor College of Medicine, Texas
- Department of Pediatric Medicine – Cardiology, Texas Children’s Hospital
| | - Craig G. Rusin
- Department of Pediatric Cardiology, Baylor College of Medicine, Texas
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17
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Mynard JP, Valen-Sendstad K. A unified method for estimating pressure losses at vascular junctions. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2015; 31:e02717. [PMID: 25833463 DOI: 10.1002/cnm.2717] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2015] [Revised: 03/18/2015] [Accepted: 03/20/2015] [Indexed: 06/04/2023]
Abstract
In reduced-order (0D/1D) blood or respiratory flow models, pressure losses at junctions are usually neglected. However, these may become important where velocities are high and significant flow redirection occurs. Current methods for estimating losses rely on relatively complex empirical equations that are only valid for specific junction geometries and flow regimes. In pulsatile multi-directional flows, switching between empirical equations upon reversing flow may introduce unrealistic discontinuities in simulated haemodynamic waveforms. Drawing from work by Bassett et al. (SAE Trans 112:565-583, 2003), we therefore developed a unified method (Unified0D) for estimating loss coefficients that can be applied to any junction (i.e. any number of branches at any angle) and any flow regime. Discontinuities in simulated waveforms were avoided by extending Bassett et al.'s control volume-based method to incorporate a 'pseudodatum' supplier branch, an imaginary effective vessel containing all inflow to the junction. Energy exchange between diverging flow streams was also accounted for empirically. The formulation was validated using high resolution computational fluid dynamics in a wide range flow conditions and junction configurations. In a pulsatile 1D simulation exhibiting transitions between four different flow regimes, the new formulation produced smooth transitions in calculated pressure losses.
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Affiliation(s)
- Jonathan P Mynard
- Biomedical Simulation Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada
- Heart Research, Clinical Sciences, Murdoch Childrens Research Institute, Parkville, VIC, Australia
- Department of Paediatrics, University of Melbourne, Parkville, VIC, Australia
| | - Kristian Valen-Sendstad
- Biomedical Simulation Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada
- Center for Biomedical Computing, Simula Research Laboratory, Lysaker, Norway
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18
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Manini S, Antiga L, Botti L, Remuzzi A. pyNS: an open-source framework for 0D haemodynamic modelling. Ann Biomed Eng 2014; 43:1461-73. [PMID: 25549775 DOI: 10.1007/s10439-014-1234-y] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2014] [Accepted: 12/19/2014] [Indexed: 10/24/2022]
Abstract
A number of computational approaches have been proposed for the simulation of haemodynamics and vascular wall dynamics in complex vascular networks. Among them, 0D pulse wave propagation methods allow to efficiently model flow and pressure distributions and wall displacements throughout vascular networks at low computational costs. Although several techniques are documented in literature, the availability of open-source computational tools is still limited. We here present python Network Solver, a modular solver framework for 0D problems released under a BSD license as part of the archToolkit ( http://archtk.github.com ). As an application, we describe patient-specific models of the systemic circulation and detailed upper extremity for use in the prediction of maturation after surgical creation of vascular access for haemodialysis.
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19
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Huberts W, Donders WP, Delhaas T, van de Vosse FN. Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2014; 30:1679-1704. [PMID: 25377937 DOI: 10.1002/cnm.2695] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2014] [Revised: 09/11/2014] [Accepted: 10/29/2014] [Indexed: 05/28/2023]
Abstract
Patient-specific modeling requires model personalization, which can be achieved in an efficient manner by parameter fixing and parameter prioritization. An efficient variance-based method is using generalized polynomial chaos expansion (gPCE), but it has not been applied in the context of model personalization, nor has it ever been compared with standard variance-based methods for models with many parameters. In this work, we apply the gPCE method to a previously reported pulse wave propagation model and compare the conclusions for model personalization with that of a reference analysis performed with Saltelli's efficient Monte Carlo method. We furthermore differentiate two approaches for obtaining the expansion coefficients: one based on spectral projection (gPCE-P) and one based on least squares regression (gPCE-R). It was found that in general the gPCE yields similar conclusions as the reference analysis but at much lower cost, as long as the polynomial metamodel does not contain unnecessary high order terms. Furthermore, the gPCE-R approach generally yielded better results than gPCE-P. The weak performance of the gPCE-P can be attributed to the assessment of the expansion coefficients using the Smolyak algorithm, which might be hampered by the high number of model parameters and/or by possible non-smoothness in the output space.
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Affiliation(s)
- W Huberts
- Department of Biomedical Engineering, School of Cardiovascular Diseases (CARIM), Faculty of Health, Medicine and Life Sciences, Maastricht University; Department of Biomedical Engineering, Eindhoven University of Technology
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Wang X, Fullana JM, Lagrée PY. Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model. Comput Methods Biomech Biomed Engin 2014; 18:1704-25. [DOI: 10.1080/10255842.2014.948428] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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21
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Arterial pressure and flow wave analysis using time-domain 1-D hemodynamics. Ann Biomed Eng 2014; 43:190-206. [PMID: 25138163 PMCID: PMC4286649 DOI: 10.1007/s10439-014-1087-4] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2014] [Accepted: 08/01/2014] [Indexed: 11/29/2022]
Abstract
We reviewed existing methods for analyzing, in the time domain, physical mechanisms underlying the patterns of blood pressure and flow waveforms in the arterial system. These are wave intensity analysis and separations into several types of waveforms: (i) forward- and backward-traveling, (ii) peripheral and conduit, or (iii) reservoir and excess. We assessed the physical information provided by each method and showed how to combine existing methods in order to quantify contributions to numerically generated waveforms from previous cardiac cycles and from specific regions and properties of the numerical domain: the aortic root, arterial bifurcations and tapered vessels, peripheral reflection sites, and the Windkessel function of the aorta. We illustrated our results with numerical examples involving generalized arterial stiffening in a distributed one-dimensional model or localized changes in the model parameters due to a femoral stenosis, carotid stent or abdominal aortic aneurysm.
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22
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The influence of an unilateral carotid artery stenosis on brain oxygenation. Med Eng Phys 2014; 36:905-14. [DOI: 10.1016/j.medengphy.2014.03.020] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2013] [Revised: 03/24/2014] [Accepted: 03/31/2014] [Indexed: 11/23/2022]
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Netřebská H, Matěcha J, Schmirler M, Manoch L, Adamec J. Method for the evaluation of minor losses in pulsatile laminar fluid flow. EPJ WEB OF CONFERENCES 2014. [DOI: 10.1051/epjconf/20146702081] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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24
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Willemet M, Lacroix V, Marchandise E. Validation of a 1D patient-specific model of the arterial hemodynamics in bypassed lower-limbs: Simulations against in vivo measurements. Med Eng Phys 2013; 35:1573-83. [DOI: 10.1016/j.medengphy.2013.04.012] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2012] [Revised: 04/11/2013] [Accepted: 04/26/2013] [Indexed: 11/28/2022]
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Bokov P, Flaud P, Bensalah A, Fullana JM, Rossi M. Implementing boundary conditions in simulations of arterial flows. J Biomech Eng 2013; 135:111004. [PMID: 23896643 DOI: 10.1115/1.4025111] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2013] [Accepted: 07/29/2013] [Indexed: 11/08/2022]
Abstract
Computational hemodynamic models of the cardiovascular system are often limited to finite segments of the system and therefore need well-controlled inlet and outlet boundary conditions. Classical boundary conditions are measured total pressure or flow rate imposed at the inlet and impedances of RLR, RLC, or LR filters at the outlet. We present a new approach based on an unidirectional propagative approach (UPA) to model the inlet/outlet boundary conditions on the axisymmetric Navier-Stokes equations. This condition is equivalent to a nonreflecting boundary condition in a fluid-structure interaction model of an axisymmetric artery. First we compare the UPA to the best impedance filter (RLC). Second, we apply this approach to a physiological situation, i.e., the presence of a stented segment into a coronary artery. In that case a reflection index is defined which quantifies the amount of pressure waves reflected upon the singularity.
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LIANG FUYOU, TAKAGI SHU, LIU HAO. THE INFLUENCES OF CARDIOVASCULAR PROPERTIES ON SUPRASYSTOLIC BRACHIAL CUFF WAVE STUDIED BY A SIMPLE ARTERIAL-TREE MODEL. J MECH MED BIOL 2012. [DOI: 10.1142/s0219519411004605] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
It has been found that a pronounced secondary systolic peak appears on the oscillometric wave recorded by a brachial oscillometric cuff as cuff pressure is raised to a suprasystolic level. This finding has accordingly motivated some studies aimed to explore the potential value carried by the cuff wave for assessing arterial stiffness. However, so far, there remain considerable controversies in the literature regarding the cardiovascular properties that dominate the characteristics of the cuff wave. In this context, we developed a simple arterial-tree model and applied it to investigate the respective influence on the cuff wave of various cardiovascular properties and the associated wave interaction phenomena. It was found that (1) neither aortic stiffness nor brachial arterial stiffness can uniquely determine the time lag (Δt) between the first and secondary peaks of the cuff wave, although both of them significantly influence Δt; and (2) the BAIx (an index that characterize the height of the secondary peak relative to the first) is sensitive to most of the investigated cardiovascular properties and physiological conditions, such as arterial stiffness, intensity of wave reflection in the lower body and heart rate, etc. These findings suggest that the reliability of assessing aortic stiffness based solely on the timings and heights of the two peaks is limited. Moreover, we argued that the controversial findings presented in previous model-based studies are likely to be caused by limitations related to the research objectives or computation conditions of the studies.
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Affiliation(s)
- FUYOU LIANG
- Computational Science Research Program, RIKEN, Wako, Saitama, Japan
| | - SHU TAKAGI
- Computational Science Research Program, RIKEN, Wako, Saitama, Japan
- Department of Mechanical Engineering, The University of Tokyo, Tokyo, Japan
| | - HAO LIU
- Graduate School of Engineering, Chiba University, Chiba-Shi, Chiba, Japan
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Abstract
An improved one-dimensional mathematical model based on the Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation whose coefficients are smoothly varying functions of the spatial variable. The resulting momentum equation along with the continuity equation and pressure-area relation form our reduced-order model for physiological fluid flows in one dimension and are aimed at providing accurate and fast-to-compute global models for physiological systems represented as networks of quasi one-dimensional fluid flows. The consequent nonlinear coupled system of equations is solved by the Lax-Wendroff scheme and is then applied to an open model arterial network of the human vascular system containing the largest 55 arteries. The proposed model with functional coefficients is compared with current classical one-dimensional theories which assume steady state Hagen-Poiseuille velocity profiles, either parabolic or plug-like, throughout the whole arterial tree. The effects of the nonlinear term in the momentum equation and different strategies for bifurcation points in the network, as well as the various lumped parameter outflow boundary conditions for distal terminal points are also analyzed. The results show that the proposed model can be used as an efficient tool for investigating the dynamics of reduced-order models of flows in physiological systems and would, in particular, be a good candidate for the one-dimensional, system-level component of geometric multiscale models of physiological systems.
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Affiliation(s)
- OMER SAN
- Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, VA 24061, USA
| | - ANNE E. STAPLES
- Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, VA 24061, USA
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Saito M, Ikenaga Y, Matsukawa M, Watanabe Y, Asada T, Lagrée PY. One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results. J Biomech Eng 2012; 133:121005. [PMID: 22206422 DOI: 10.1115/1.4005472] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Pulse wave evaluation is an effective method for arteriosclerosis screening. In a previous study, we verified that pulse waveforms change markedly due to arterial stiffness. However, a pulse wave consists of two components, the incident wave and multireflected waves. Clarification of the complicated propagation of these waves is necessary to gain an understanding of the nature of pulse waves in vivo. In this study, we built a one-dimensional theoretical model of a pressure wave propagating in a flexible tube. To evaluate the applicability of the model, we compared theoretical estimations with measured data obtained from basic tube models and a simple arterial model. We constructed different viscoelastic tube set-ups: two straight tubes; one tube connected to two tubes of different elasticity; a single bifurcation tube; and a simple arterial network with four bifurcations. Soft polyurethane tubes were used and the configuration was based on a realistic human arterial network. The tensile modulus of the material was similar to the elasticity of arteries. A pulsatile flow with ejection time 0.3 s was applied using a controlled pump. Inner pressure waves and flow velocity were then measured using a pressure sensor and an ultrasonic diagnostic system. We formulated a 1D model derived from the Navier-Stokes equations and a continuity equation to characterize pressure propagation in flexible tubes. The theoretical model includes nonlinearity and attenuation terms due to the tube wall, and flow viscosity derived from a steady Hagen-Poiseuille profile. Under the same configuration as for experiments, the governing equations were computed using the MacCormack scheme. The theoretical pressure waves for each case showed a good fit to the experimental waves. The square sum of residuals (difference between theoretical and experimental wave-forms) for each case was <10.0%. A possible explanation for the increase in the square sum of residuals is the approximation error for flow viscosity. However, the comparatively small values prove the validity of the approach and indicate the usefulness of the model for understanding pressure propagation in the human arterial network.
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Affiliation(s)
- Masashi Saito
- Laboratory of Ultrasonic Electronics, Doshisha University, 1-3 Tatara-Miyakodani, Kyotanabeshi, Kyoto, 610-0321, Japan
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Bode AS, Huberts W, Bosboom EMH, Kroon W, van der Linden WPM, Planken RN, van de Vosse FN, Tordoir JHM. Patient-specific computational modeling of upper extremity arteriovenous fistula creation: its feasibility to support clinical decision-making. PLoS One 2012; 7:e34491. [PMID: 22496816 PMCID: PMC3319586 DOI: 10.1371/journal.pone.0034491] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2011] [Accepted: 03/01/2012] [Indexed: 01/14/2023] Open
Abstract
Introduction Inadequate flow enhancement on the one hand, and excessive flow enhancement on the other hand, remain frequent complications of arteriovenous fistula (AVF) creation, and hamper hemodialysis therapy in patients with end-stage renal disease. In an effort to reduce these, a patient-specific computational model, capable of predicting postoperative flow, has been developed. The purpose of this study was to determine the accuracy of the patient-specific model and to investigate its feasibility to support decision-making in AVF surgery. Methods Patient-specific pulse wave propagation models were created for 25 patients awaiting AVF creation. Model input parameters were obtained from clinical measurements and literature. For every patient, a radiocephalic AVF, a brachiocephalic AVF, and a brachiobasilic AVF configuration were simulated and analyzed for their postoperative flow. The most distal configuration with a predicted flow between 400 and 1500 ml/min was considered the preferred location for AVF surgery. The suggestion of the model was compared to the choice of an experienced vascular surgeon. Furthermore, predicted flows were compared to measured postoperative flows. Results Taken into account the confidence interval (25th and 75th percentile interval), overlap between predicted and measured postoperative flows was observed in 70% of the patients. Differentiation between upper and lower arm configuration was similar in 76% of the patients, whereas discrimination between two upper arm AVF configurations was more difficult. In 3 patients the surgeon created an upper arm AVF, while model based predictions allowed for lower arm AVF creation, thereby preserving proximal vessels. In one patient early thrombosis in a radiocephalic AVF was observed which might have been indicated by the low predicted postoperative flow. Conclusions Postoperative flow can be predicted relatively accurately for multiple AVF configurations by using computational modeling. This model may therefore be considered a valuable additional tool in the preoperative work-up of patients awaiting AVF creation.
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Affiliation(s)
- Aron S Bode
- Department of Surgery, Maastricht University Medical Center, Maastricht, The Netherlands.
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A pulse wave propagation model to support decision-making in vascular access planning in the clinic. Med Eng Phys 2012; 34:233-48. [PMID: 21840239 DOI: 10.1016/j.medengphy.2011.07.015] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2010] [Revised: 05/05/2011] [Accepted: 07/18/2011] [Indexed: 11/23/2022]
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31
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Bode AS, Planken RN, Merkx MAG, van der Sande FM, Geerts L, Tordoir JHM, Leiner T. Feasibility of non-contrast-enhanced magnetic resonance angiography for imaging upper extremity vasculature prior to vascular access creation. Eur J Vasc Endovasc Surg 2011; 43:88-94. [PMID: 22070856 DOI: 10.1016/j.ejvs.2011.09.012] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2011] [Accepted: 09/12/2011] [Indexed: 11/28/2022]
Abstract
OBJECTIVES Preoperative mapping of arterial and venous anatomy helps to prevent postoperative complications after vascular access creation. The use of gadolinium in contrast-enhanced (CE) magnetic resonance angiography (MRA) has been linked to nephrogenic systemic fibrosis in patients with end-stage renal disease (ESRD). The purpose of this study was to evaluate non-contrast-enhanced (NCE) MRA for assessment of upper extremity and central vasculature and to compare it with CE-MRA. METHODS NCE and CE-MRA images were acquired in 10 healthy volunteers and 15 patients with ESRD. In each data set, two observers analysed 11 arterial and 16 venous segments with regard to image quality (0-4), presence of artefacts (0-2) and vessel-to-background ratio. RESULTS More arterial segments were depicted using CE-MRA compared to NCE-MRA (99% vs. 96%, p = 0.001) with mean image quality of 3.80 vs. 2.68, (p < 0.001) and mean vessel-to-background ratio of 6.47 vs. 4.14 (p < 0.001). Ninety-one percent of the venous segments were portrayed using NCE-MRA vs. 80% using CE-MRA (p < 0.001). Mean image quality and vessel-to-background ratio were 2.41 vs. 2.21 (p = 0.140) and 5.13 vs. 3.88 (p < 0.001), respectively. CONCLUSIONS Although arterial image quality and vessel-to-background ratios were lower, NCE-MRA is considered a feasible alternative to CE-MRA in patients with ESRD who need imaging of the upper extremity and central vasculature prior to dialysis access creation.
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Affiliation(s)
- A S Bode
- Department of Surgery, Maastricht University Medical Center, P. Debyelaan 25, 6202 AZ Maastricht, The Netherlands
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32
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Ho H, McGhee C, Hunter P. Numerical analysis for the blood flow in a patient-specific ophthalmic artery. Med Eng Phys 2011; 34:123-7. [PMID: 21764622 DOI: 10.1016/j.medengphy.2011.06.015] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2010] [Revised: 05/04/2011] [Accepted: 06/22/2011] [Indexed: 11/28/2022]
Abstract
In this paper we investigate blood flow in the ophthalmic artery (OA) which is the major artery supplying blood to the eyes. An OA and several other cerebral arteries are digitized from a computed tomography angiography (CTA) image of an aneurysm patient. Utilizing a reduced version (1D) of the governing Navier-Stokes equations we solve the transient flow in these arteries. The flow waveform of the patient-OA is compared with that in a healthy vascular tree, and also with published ultrasonic measurements. We found that hyperemia rather than ischemia occurred in the OA, and we suggest that this was unlikely to be the cause of impaired vision in the patient. A more likely explanation is the compression of the optic nerves caused by the mass of the aneurysm.
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Affiliation(s)
- Harvey Ho
- Bioengineering Institute, University of Auckland, Auckland, New Zealand.
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Marchandise E, Flaud P. Accurate modelling of unsteady flows in collapsible tubes. Comput Methods Biomech Biomed Engin 2011; 13:279-90. [PMID: 20373183 DOI: 10.1080/10255840903190726] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.
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Affiliation(s)
- Emilie Marchandise
- Department of Mechanical Engineering, Université Catholique de Louvain, Louvain-La-Neuve, Belgium.
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Leguy CAD, Bosboom EMH, Belloum ASZ, Hoeks APG, van de Vosse FN. Global sensitivity analysis of a wave propagation model for arm arteries. Med Eng Phys 2011; 33:1008-16. [PMID: 21600829 DOI: 10.1016/j.medengphy.2011.04.003] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2010] [Revised: 04/05/2011] [Accepted: 04/06/2011] [Indexed: 11/24/2022]
Abstract
Wave propagation models of blood flow and blood pressure in arteries play an important role in cardiovascular research. For application of these models in patient-specific simulations a number of model parameters, that are inherently subject to uncertainties, are required. The goal of this study is to identify with a global sensitivity analysis the model parameters that influence the output the most. The improvement of the measurement accuracy of these parameters has largest consequences for the output statistics. A patient specific model is set up for the major arteries of the arm. In a Monte-Carlo study, 10 model parameters and the input blood volume flow (BVF) waveform are varied randomly within their uncertainty ranges over 3000 runs. The sensitivity in the output for each system parameter was evaluated with the linear Pearson and ranked Spearman correlation coefficients. The results show that model parameter and input BVF uncertainties induce large variations in output variables and that most output variables are significantly influenced by more than one system parameter. Overall, the Young's modulus appears to have the largest influence and arterial length the smallest. Only small differences were obtained between Spearman's and Pearson's tests, suggesting that a high monotonic association given by Spearman's test is associated with a high linear corelation between the inputs and output parameters given by Pearson's test.
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Affiliation(s)
- C A D Leguy
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
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35
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Willemet M, Lacroix V, Marchandise E. Inlet boundary conditions for blood flow simulations in truncated arterial networks. J Biomech 2011; 44:897-903. [DOI: 10.1016/j.jbiomech.2010.11.036] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2010] [Revised: 10/28/2010] [Accepted: 11/30/2010] [Indexed: 10/18/2022]
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Leguy CAD, Bosboom EMH, Gelderblom H, Hoeks APG, van de Vosse FN. Estimation of distributed arterial mechanical properties using a wave propagation model in a reverse way. Med Eng Phys 2010; 32:957-67. [PMID: 20675178 DOI: 10.1016/j.medengphy.2010.06.010] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2009] [Revised: 02/12/2010] [Accepted: 06/27/2010] [Indexed: 11/28/2022]
Abstract
To estimate arterial stiffness, different methods based either on distensibility, pulse wave velocity or a pressure-velocity loop, have been proposed. These methods can be employed to determine the arterial mechanical properties either locally or globally, e.g. averaged over an entire arterial segment. The aim of this study was to investigate the feasibility of a new method that estimates distributed arterial mechanical properties non-invasively. This new method is based on a wave propagation model and several independent ultrasound and pressure measurements. Model parameters (including arterial mechanical properties) are obtained from a reverse method in which differences between modeling results and measurements are minimized using a fitting procedure based on local sensitivity indices. This study evaluates the differences between in vivo measured and simulated blood pressure and volume flow waveforms at the brachial, radial and ulnar arteries of 6 volunteers. The estimated arterial Young's modulus range from 1.0 to 6.0MPa with an average of (3.8±1.7)MPa at the brachial artery and from 1.2 to 7.8MPa with an average of (4.8±2.2)MPa at the radial artery. A good match between measured and simulated waveforms and the realistic stiffness parameters indicate a good in vivo suitability.
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Affiliation(s)
- C A D Leguy
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
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Neal ML, Kerckhoffs R. Current progress in patient-specific modeling. Brief Bioinform 2010; 11:111-26. [PMID: 19955236 PMCID: PMC2810113 DOI: 10.1093/bib/bbp049] [Citation(s) in RCA: 99] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2009] [Revised: 09/20/2009] [Indexed: 11/13/2022] Open
Abstract
We present a survey of recent advancements in the emerging field of patient-specific modeling (PSM). Researchers in this field are currently simulating a wide variety of tissue and organ dynamics to address challenges in various clinical domains. The majority of this research employs three-dimensional, image-based modeling techniques. Recent PSM publications mostly represent feasibility or preliminary validation studies on modeling technologies, and these systems will require further clinical validation and usability testing before they can become a standard of care. We anticipate that with further testing and research, PSM-derived technologies will eventually become valuable, versatile clinical tools.
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Affiliation(s)
- Maxwell Lewis Neal
- Division of Biomedical and Health Informatics, University of Washington, USA
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