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76


Commentary: Diameter and wall stress-Wrong Laplace, wrong time? [Editorial]

DeAnda, Abe; Rajagopal, Keshava; Griffith, Boyce E
PMID: 34217538
ISSN: 1097-685x
CID: 4932792

Models for plasma kinetics during simultaneous therapeutic plasma exchange and extracorporeal membrane oxygenation

Puelz, Charles; Danial, Zach; Raval, Jay S; Marinaro, Jonathan L; Griffith, Boyce E; Peskin, Charles S
This paper focuses on the derivation and simulation of mathematical models describing new plasma fraction in blood for patients undergoing simultaneous extracorporeal membrane oxygenation and therapeutic plasma exchange. Models for plasma exchange with either veno-arterial or veno-venous extracorporeal membrane oxygenation are considered. Two classes of models are derived for each case, one in the form of an algebraic delay equation and another in the form of a system of delay differential equations. In special cases, our models reduce to single compartment ones for plasma exchange that have been validated with experimental data (Randerson et al., 1982, Artif. Organs, 6, 43-49). We also show that the algebraic differential equations are forward Euler discretizations of the delay differential equations, with timesteps equal to transit times through model compartments. Numerical simulations are performed to compare different model types, to investigate the impact of plasma device port switching on the efficiency of the exchange process, and to study the sensitivity of the models to their parameters.
PMID: 33626571
ISSN: 1477-8602
CID: 4794752

Adherens junction engagement regulates functional patterning of the cardiac pacemaker cell lineage

Thomas, Kandace; Henley, Trevor; Rossi, Simone; Costello, M Joseph; Polacheck, William; Griffith, Boyce E; Bressan, Michael
Cardiac pacemaker cells (CPCs) rhythmically initiate the electrical impulses that drive heart contraction. CPCs display the highest rate of spontaneous depolarization in the heart despite being subjected to inhibitory electrochemical conditions that should theoretically suppress their activity. While several models have been proposed to explain this apparent paradox, the actual molecular mechanisms that allow CPCs to overcome electrogenic barriers to their function remain poorly understood. Here, we have traced CPC development at single-cell resolution and uncovered a series of cytoarchitectural patterning events that are critical for proper pacemaking. Specifically, our data reveal that CPCs dynamically modulate adherens junction (AJ) engagement to control characteristics including surface area, volume, and gap junctional coupling. This allows CPCs to adopt a structural configuration that supports their overall excitability. Thus, our data have identified a direct role for local cellular mechanics in patterning critical morphological features that are necessary for CPC electrical activity.
PMID: 33891897
ISSN: 1878-1551
CID: 4847602

A poroelastic immersed finite element framework for modelling cardiac perfusion and fluid-structure interaction

Richardson, Scott I Heath; Gao, Hao; Cox, Jennifer; Janiczek, Rob; Griffith, Boyce E; Berry, Colin; Luo, Xiaoyu
Modern approaches to modelling cardiac perfusion now commonly describe the myocardium using the framework of poroelasticity. Cardiac tissue can be described as a saturated porous medium composed of the pore fluid (blood) and the skeleton (myocytes and collagen scaffold). In previous studies fluid-structure interaction in the heart has been treated in a variety of ways, but in most cases, the myocardium is assumed to be a hyperelastic fibre-reinforced material. Conversely, models that treat the myocardium as a poroelastic material typically neglect interactions between the myocardium and intracardiac blood flow. This work presents a poroelastic immersed finite element framework to model left ventricular dynamics in a three-phase poroelastic system composed of the pore blood fluid, the skeleton, and the chamber fluid. We benchmark our approach by examining a pair of prototypical poroelastic formations using a simple cubic geometry considered in the prior work by Chapelle et al (2010). This cubic model also enables us to compare the differences between system behaviour when using isotropic and anisotropic material models for the skeleton. With this framework, we also simulate the poroelastic dynamics of a three-dimensional left ventricle, in which the myocardium is described by the Holzapfel-Ogden law. Results obtained using the poroelastic model are compared to those of a corresponding hyperelastic model studied previously. We find that the poroelastic LV behaves differently from the hyperelastic LV model. For example, accounting for perfusion results in a smaller diastolic chamber volume, agreeing well with the well-known wall-stiffening effect under perfusion reported previously. Meanwhile differences in systolic function, such as fibre strain in the basal and middle ventricle, are found to be comparatively minor.
PMID: 33559359
ISSN: 2040-7947
CID: 4800772

Mathematical modeling of the impact of recirculation on exchange kinetics in tandem extracorporeal membrane oxygenation and therapeutic plasma exchange

Puelz, Charles; Marinaro, Jonathan L; Park, Yara A; Griffith, Boyce E; Peskin, Charles S; Raval, Jay S
Vascular access connection configurations during tandem extracorporeal membrane oxygenation (ECMO) and therapeutic plasma exchange (TPE) may impact exchange kinetics. In these tandem procedures, typically the TPE inlet line is proximal to the TPE return line with respect to blood flow in the ECMO device, maximizing the opportunity for replacement fluid homogenization within the ECMO circuit. However, if TPE inlet and return line connections are switched, recirculation-a phenomenon in which replacement fluid leaving the TPE return line is prematurely drawn into the TPE inlet line prior to satisfactory homogenization within the ECMO circuit-will occur. Such recirculation could diminish TPE efficacy in patients on ECMO and mitigate therapeutic benefits. Using a mathematical model of recirculation in tandem ECMO and TPE, we demonstrate that the predicted impact of recirculation is negligible and vascular access connection positioning does not appear to be a point of clinical concern with regard to TPE kinetics.
PMID: 33030779
ISSN: 1098-1101
CID: 4627072

Stabilization approaches for the hyperelastic immersed boundary method for problems of large-deformation incompressible elasticity

Vadala-Roth, Ben; Acharya, Shashank; Patankar, Neelesh A; Rossi, Simone; Griffith, Boyce E
The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses Lagrangian coordinates to describe the structural deformations, stresses, and resultant forces. Integral transforms with Dirac delta function kernels connect the Eulerian and Lagrangian frames. The fluid and the structure are both typically treated as incompressible materials. Upon discretization, however, the incompressibility of the structure is only maintained approximately. To obtain an immersed method for incompressible hyperelastic structures that is robust under large structural deformations, we introduce a volumetric energy in the solid region that stabilizes the formulation and improves the accuracy of the numerical scheme. This formulation augments the discrete Lagrange multiplier for the incompressibility constraint, thereby improving the original method's accuracy. This volumetric energy is incorporated by decomposing the strain energy into isochoric and dilatational components, as in standard solid mechanics formulations of nearly incompressible elasticity. We study the performance of the stabilized method using several quasi-static solid mechanics benchmarks, a dynamic fluid-structure interaction benchmark, and a detailed three-dimensional model of esophageal transport. The accuracy achieved by the stabilized immersed formulation is comparable to that of a stabilized finite element method for incompressible elasticity using similar numbers of structural degrees of freedom.
PMCID:7263477
PMID: 32483394
ISSN: 0045-7825
CID: 4468862

Fluid-Structure Interaction Models of Bioprosthetic Heart Valve Dynamics in an Experimental Pulse Duplicator

Lee, Jae H; Rygg, Alex D; Kolahdouz, Ebrahim M; Rossi, Simone; Retta, Stephen M; Duraiswamy, Nandini; Scotten, Lawrence N; Craven, Brent A; Griffith, Boyce E
Computer modeling and simulation is a powerful tool for assessing the performance of medical devices such as bioprosthetic heart valves (BHVs) that promises to accelerate device design and regulation. This study describes work to develop dynamic computer models of BHVs in the aortic test section of an experimental pulse-duplicator platform that is used in academia, industry, and regulatory agencies to assess BHV performance. These computational models are based on a hyperelastic finite element extension of the immersed boundary method for fluid-structure interaction (FSI). We focus on porcine tissue and bovine pericardial BHVs, which are commonly used in surgical valve replacement. We compare our numerical simulations to experimental data from two similar pulse duplicators, including a commercial ViVitro system and a custom platform related to the ViVitro pulse duplicator. Excellent agreement is demonstrated between the computational and experimental results for bulk flow rates, pressures, valve open areas, and the timing of valve opening and closure in conditions commonly used to assess BHV performance. In addition, reasonable agreement is demonstrated for quantitative measures of leaflet kinematics under these same conditions. This work represents a step towards the experimental validation of this FSI modeling platform for evaluating BHVs.
PMID: 32034607
ISSN: 1573-9686
CID: 4311262

Reply: The stresses of cardiovascular mechanics [Letter]

Rajagopal, Keshava; Griffith, Boyce E; DeAnda, Abe
PMID: 31757452
ISSN: 1097-685x
CID: 4237252

Analysis of multi-electron, multi-step homogeneous catalysis by rotating disc electrode voltammetry: theory, application, and obstacles

Lee, Katherine J; Gruninger, Cole T; Lodaya, Kunal M; Qadeer, Saad; Griffith, Boyce E; Dempsey, Jillian L
Rotating disc electrode (RDE) voltammetry has been widely adopted for the study of heterogenized molecular electrocatalysts for multi-step fuel-forming reactions but this tool has never been comprehensively applied to their homogeneous analogues. Here, the utility and limitations of RDE techniques for mechanistic and kinetic analysis of homogeneous molecular catalysts that mediate multi-electron, multi-substrate redox transformations are explored. Using the ECEC' reaction mechanism as a case study, two theoretical models are derived based on the Nernst diffusion layer model and the Hale transformation. Current-potential curves generated by these computational strategies are compared under a variety of limiting conditions to identify conditions under which the more minimalist Nernst Diffusion Layer approach can be applied. Based on this theoretical treatment, strategies for extracting kinetic information from the plateau current and the foot of the catalytic wave are derived. RDEV is applied to a cobaloxime hydrogen evolution reaction (HER) catalyst under non-aqueous conditions in order to experimentally validate this theoretical framework and explore the feasibility of RDE as a tool for studying homogeneous catalysts. Crucially, analysis of the foot-of-the-wave via this theoretical framework provides rate constants for elementary reaction steps that agree with those extracted from stationary voltammetric methods, supporting the application of RDE to study homogeneous fuel-forming catalysts. Finally, obstacles encountered during the kinetic analysis of cobaloxime, along with the voltammetric signatures used to diagnose this reactivity, are discussed with the goal of guiding groups working to improve RDE set-ups and help researchers avoid misinterpretation of RDE data.
PMID: 31984999
ISSN: 1364-5528
CID: 4298812

An Immersed Interface Method for Discrete Surfaces

Kolahdouz, Ebrahim M; Bhalla, Amneet Pal Singh; Craven, Brent A; Griffith, Boyce E
Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary (IB) method is a widely recognized and effective modeling paradigm for simulating fluid-structure interaction (FSI) in such systems, but a difficulty of the IB formulation of these problems is that the pressure and viscous stress are generally discontinuous at fluid-solid interfaces. The conventional IB method regularizes these discontinuities, which typically yields low-order accuracy at these interfaces. The immersed interface method (IIM) is an IB-like approach to FSI that sharply imposes stress jump conditions, enabling higher-order accuracy, but prior applications of the IIM have been largely restricted to numerical methods that rely on smooth representations of the interface geometry. This paper introduces an immersed interface formulation that uses only a C0 representation of the immersed interface, such as those provided by standard nodal Lagrangian finite element methods. Verification examples for models with prescribed interface motion demonstrate that the method sharply resolves stress discontinuities along immersed boundaries while avoiding the need for analytic information about the interface geometry. Our results also demonstrate that only the lowest-order jump conditions for the pressure and velocity gradient are required to realize global second-order accuracy. Specifically, we demonstrate second-order global convergence rates along with nearly second-order local convergence in the Eulerian velocity field, and between first- and second-order global convergence rates along with approximately first-order local convergence for the Eulerian pressure field. We also demonstrate approximately second-order local convergence in the interfacial displacement and velocity along with first-order local convergence in the fluid traction along the interface. As a demonstration of the method's ability to tackle more complex geometries, the present approach is also used to simulate flow in a patient-averaged anatomical model of the inferior vena cava, which is the large vein that carries deoxygenated blood from the lower extremities back to the heart. Comparisons of the general hemodynamics and wall shear stress obtained by the present IIM and a body-fitted discretization approach show that the present method yields results that are in good agreement with those obtained by the body-fitted approach.
PMCID:6892596
PMID: 31802781
ISSN: 0021-9991
CID: 4218742