Mathematics Guiding Bioartificial Heart Valve Design

(October 28,2013 - October 31,2013 )

Organizers


Suncica (Sunny) Canic
Mathematics, University of Houston--Downtown
Boyce Griffith
Medicine, New York University School of Medicine
Arash Kheradvar
Biomedical Engineering, University of California Irvine
Stephen Little
Cardiovascular Imaging Section, Department of Cardiology, Houston Methodist Hospital

This Special Topics Workshop will address the development of mathematical and computational modeling techniques that can be used to facilitate the development and optimal design of cardiac valve prostheses and other cardiovascular devices. Workshop topics will include the design of tissue scaffolds and cardiovascular stents used in bioartificial heart valve design and replacement, and also fluid-structure interaction between blood and cardiovascular tissue. The speakers will include mathematicians, biomedical engineers, and medical specialists. Poster presentations by students and post-doctoral researchers will also be included.

Accepted Speakers

Hamed Alavi
Biomedical Engineering, University of California, Irvine
Frank Baaijens
Biomedical Engineering, Eindhoven University of Technology
Abe DeAnda
Cardiothoracic Surgery, New York University
Aaron Fogelson
Department of Mathematics, University of Utah
Liang Ge
Surgery, University of California San Francisco
Anvar Gilmanov
College of Science and Engineering, University of Minnesota
Jane Grande-Allen
Bioengineering, Rice University
Frédéric Heim
Research & Development, Universit'e de Haute Alsace
Matt Jackson
Cardiovascular Hemodynamics Imaging Laboratory, The Methodist DeBakey Heart and Vascular Center
Gerald Lawrie
Cardiovascular Surgery, Baylor College of Medicine
Xiaoyu Luo
School of Mathematics and Statistics, University of Glasgow
Alison Marsden
Mechanical and Aerospace Engineering, University of California, San Diego
Laura Miller
Mathematics , University of North Carolina, Chapel Hill
Mohammad Mofrad
Departments of Bioengineering and Mechanical Engineering, University of California Berkeley
Annalisa Quaini
Mathematics, University of Houston
Michael Sacks
Biomedical Engineering/ICES, University of Texas
Craig Simmons
Mechanical and Industrial Engineering, University of Toronto
Julia Swanson
Thoracic & Cardiovascular Surgery, University of Virginia
Robert Tranquillo
Biomedical Engineering, University of Minnesota
Raoul van Loon
College of Engineering, Swansea University
Alessandro Veneziani
Mathematics and Computer Science, Emory University
Ajit Yoganathan
Biomedical Engineering, Georgia Institute of Technology
Paolo Zunino
Department of Mechanical Engineering and Materials Science, University of Pittsburgh
Monday, October 28, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:25 AM
Gerald Lawrie - 100% Reparability in Mitral Valve Surgery

100% Reparability in Mitral Valve Surgery


Importance of Restoration of Normal Annular, Papillary Muscle and Outflow Tract Dynamics and Strain by an Engineered Approach

09:25 AM
09:35 AM

Question & Discussion

09:35 AM
10:00 AM
Raoul van Loon - Aortic valve modelling in 3D and 0D

Aortic valve modelling in 3D and 0D

10:00 AM
10:25 AM

Break

10:25 AM
11:25 AM
Michael Sacks - Multiscale models of the mitral valve

Multiscale models of the mitral valve

11:25 AM
11:35 AM

Question & Discussion

11:35 AM
12:00 PM
Frédéric Heim - Transcatheter Heart Valve Design: Textile as an Alternative to Biological Tissue?

Transcatheter surgery, has become today a technology of choice to relieve patients from vascular diseases like valve stenosis. Far less traumatic for the patient, this technique is also less expensive and less time consuming, which makes it very attractive for the medical world. One of the main limits of the devices used clinically is related to the fragility of the biological tissue (chemically treated bovine pericardium), which is used as valve material. Degradations can occur especially when the valve is crimped within the stent for catheter insertion purpose. Moreover, once implanted, the stent is generally deformed, which induces additional stress in the leaflets. Textile material could be a potential candidate to replace biological tissue. A heart valve undergoes a combination of flexural and tensile stress during operation. A fabric having lower flexural resistance can be expected to have longer working life. Among fibers available, one that has been used most extensively in implants (arterial and stent grafts for example) is polyester. It is biocompatible and resistant to degradation when in contact with body fluids. Today fabric prototypes have been designed and manufactured in order to reproduce the native valve design. Measured in vitro performances show results close to those obtained with other commercially available devices in terms of regurgitation. Moreover, the interaction of the textile material with the living tissues has been studied in vivo in sheep models and showed 2 months survival time, which is encouraging. Fatigue tests performed under physiological conditions have led to 200 Mio cycling duration with no significant degradation of the textile material. Basically, the first evaluation results confirm that textile is a serious candidate for non invasive valve replacement. Further tests are still running as a huge potential remains in varying the fabric construction parameters and the surface treatments to optimize the valve performances.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:25 PM
Anvar Gilmanov - Patient specific simulations of native and prosthetic heart valves

We present a novel computational framework to simulate fluid-structure interaction of implanted tri-leaflet valve at the aortic position of a left heart system with blood flows through this valve. The tri-leaflet tissue valve is implanted at the left ventricle outflow tract with anatomic orientation. The motion of the left ventricle is reconstructed directly from Magnetic Resonance Imaging (MRI) and is prescribed as boundary condition for the computational model. The structural model of the tissue valve is simulated as a thin body with rotation free shell element model of [Stolarski H, Gilmanov A, Sotiropoulos F. Non-linear rotation-free 3-node shell finite-element formulation: IJNME, 2013; 95 (9) , pp. 740-770]. Standard three-node linear finite-element is applied for the discretization of the structure. The multi-block flow solver [Borazjani, I., Ge, L., Le, T., and Sotiropoulos, F., A parallel overset-curvilinear-immersed boundary framework for simulating complex 3D incompressible flows. Computers and Fluids, 2013; 77, pp. 76-96], which is able to simulate complex geometries with multiple branches, is coupled with the finite-element model of the structure.

02:25 PM
03:00 PM

Question & Discussion

03:00 PM
03:25 PM
Ajit Yoganathan - Experimental platforms for validating computational approaches to heart valve mechanics

This talk will discuss the various versions of left heart simulators that have been developed at the Cardiovascular Fluid Mechanics Laboratory at the Georgia Institute of Technology, specifically designed to provide high fidelity experimental datasets necessary for rigorous validation of computational tools for simulating heart valve flows. These systems are capable of simulating physiological and pathological flow, pressure and geometric conditions, and can be investigated using a variety of experimental tools to measure relevant biomechanical quantities. Such robust multi-modality experimental platforms play a critical role in the development, validation and widespread acceptance of computational tools towards developing patient specific treatment and surgical interventions for heart valve applications.

03:25 PM
03:50 PM

Break

03:50 PM
04:15 PM
Jane Grande-Allen - Developing a mechanically biomimetic hydrogel scaffold for heart valve tissue engineering

The essential function of heart valves is made possible by the unique microstructural arrangement of fibrous extracellular matrix proteins within the valve leaflet tissue, but these valvular structure-function relationships have not been translated into the next generation of valve tissue engineering investigations and for in vitro analyses of valvular cell biology and disease. The primary microstructural attributes of aortic valves are their anisotropic nature and their interconnected, layered structure, which provide valvular interstitial cells (VICs) with heterogeneous pericellular environments. We are integrating these heterogeneous structure and material characteristics of heart valves into hydrogel biomaterials. Hydrogel biomaterials (particularly poly ethylene glycol diacrylate, PEGDA) are appealing for use as TEHV scaffolds because they have tunable structure and mechanics, can be readily bio-functionalized, and can easily encapsulate cells. Research concerning these materials, however, has generally been focused on their biological activities, as opposed to the development of advanced material behavior. This presentation will describe our experience with hydrogels and our efforts to apply novel patterning and layering methodologies to generate advanced 3D hydrogels that mimic the complex microstructure and material behavior of aortic valve tissue. Constitutive modeling of the patterned hydrogel scaffolds will also be described.

04:15 PM
04:25 PM

Question & Discussion

04:25 PM
05:30 PM

PANEL DISCUSSION - Functional Valve Imaging: From Bench to Bedside and back

05:30 PM
06:30 PM

Poster Session and Reception

06:45 PM

Shuttle pick-up from MBI

Tuesday, October 29, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:25 AM
Stephen Little - Time for AVR...Calculating Risk
Time for AVR...Calculating Risk
09:25 AM
09:35 AM

Questions & Discussion

09:35 AM
10:00 AM
Frank Baaijens - Cell-mediated retraction and remodeling in engineered cardiovascular tissues

Cell-mediated retraction and remodeling in engineered cardiovascular tissues

10:00 AM
10:25 AM

Break

10:25 AM
10:50 AM
David Paniagua - Percutaneous Heart Valve from bench to bedside

Percutaneous Heart Valve from bench to bedside

10:50 AM
11:00 AM

Questions & Discussion

11:00 AM
11:25 AM
Matt Jackson - A pulsatile in vitro heart valve model utilizing multi-modality imaging for assessment of transvalvular flow and velocity fields

This talk will describe the development of the multi-modality compatible (MRI, CT, ECHO) flow loop within the Cardiovascular Hemodynamics Imaging Laboratory at the Methodist DeBakey Heart and Vascular Center. We propose that clinical imaging techniques paired with a controlled, pulsatile flow simulator will establish a foundation of data needed for validation of computational techniques.

11:25 AM
11:35 AM

Break

11:35 AM
12:00 PM
Arash Kheradvar - Measure of Asymmetry of Transmitral Vortex Ring

Measure of Asymmetry of Transmitral Vortex Ring

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:25 PM
Robert Tranquillo - Completely-biological Tissue-engineered Heart Valves Based on Predictable Cell Induced Contraction and Alignment of Biopolymers

A first-generation tissue-engineered heart valve (TEHV) based on cell-contracted biopolymers to achieve both the geometry and gross alignment of the root and leaflets is summarized, including predictions of our Anisotropic Biphasic Theory (ABT) of Tissue-Equivalent Mechanics (Barocas and Tranquillo, J Biomech Eng, 1997) and a sheep implantation study. A recent second-generation tubular TEHV fabricated from a decellularized tissue tube mounted on a frame with three struts, which upon back-pressure cause the tube to collapse into three coapting "leaflets", is then discussed. The tissue is again completely biological, fabricated from fibroblasts dispersed within a fibrin gel, compacted into a circumferentially-aligned tube on a mandrel, and matured using a bioreactor system that applied cyclic distension. Following decellularization, the resulting tissue possesses tensile mechanical properties, mechanical anisotropy, and collagen content that are comparable to native pulmonary valve leaflets. When mounted on a custom frame and tested within a pulse duplicator system, the tubular TEHV displays excellent function under both aortic and pulmonary conditions, with minimal regurgitant fractions and transvalvular pressure gradients at peak systole, as well as well as effective orifice areas exceeding those of current commercially available valve replacements. A short-term fatigue test of one million cycles with pulmonary pressure gradients was conducted without significant change in mechanical properties and no observable macroscopic tissue deterioration. Ongoing efforts utilize FEA to optimize the frame design. The tubular TEHVpresents an attractive potential alternative to current tissue valve replacements due to its avoidance of chemical fixation and utilization of a tissue conducive to recellularization by host cell infiltration.

02:25 PM
03:00 PM

Questions & Discussion

03:00 PM
03:25 PM
Annalisa Quaini - A Fluid-Structure Interaction Model to Simulate Mitral Valve Regurgitant Flow

We discuss the numerical simulation of the hemodynamics conditions encountered in patients with mitral regurgitation (MR). Our computational model represents the interaction between blood and an elastic wall containing a geometric orifice which mimics a leaky mitral valve during ventricular systole. This fluid-structure interaction (FSI) model is validated against experiments performed in an in vitro mock heart chamber developed at the Methodist DeBakey Heart & Vascular Center. Numerical results are compared to experimental measurements for different flow scenarios, ranging from mild to severe MR, and the computational FSI model is used to to show strengths and limitations of echocardiographic methods to assess the severity of mitral regurgitation.

03:25 PM
04:00 PM

Break

04:00 PM
05:00 PM
05:15 PM

Shuttle pick-up from MBI

Wednesday, October 30, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:25 AM
Craig Simmons - Microenvironmental regulation of aortic valve (patho)biology: Implications for valve design

The cellular microenvironment in the aortic valve is defined by a variety of biomechanical-, biochemical-, and extracellular-mediated factors, the combination of which can maintain valve homeostasis or drive pathogenesis. We have studied the valve microenvironment in the context of aortic valve calcification and fibrosis, with particular focus on the contributions of hemodynamics and extracellular matrix properties to local regulation of side-specific valve cell phenotypes and focal pathological alterations. These studies not only provide novel insights into the complex cellular and molecular processes that integrate to regulate valve cell pathobiology, but also suggest strategies to direct aortic valve regeneration. In this presentation, I will describe what we have learned about the native aortic valve microenvironment and its regulation of valve cells, and how we are using that knowledge, in combination with microtechnologies and statistical modeling, to define engineered microenvironments that predictably and optimally guide heart valve tissue regeneration.

09:25 AM
09:35 AM

Questions & Discussion

09:35 AM
10:00 AM
Mohammad Mofrad - Multiscale Models of the Human Aortic Valve

Multiscale Models of the Human Aortic Valve


Linking the Organ Scale to Single Cells

10:00 AM
10:25 AM

Break

10:25 AM
10:50 AM
Alison Marsden - Patient specific multiscale modeling in pediatric cardiology

Single ventricle heart patients typically undergo a three-staged surgical repair to route the venous return directly to the pulmonary arteries, separating the systemic and pulmonary circulations. We will present our recent work combining shape optimization and multiscale modeling to compare existing designs and develop novel methods for the three stages of single ventricle repair. The optimization algorithm we present is an efficient surrogate pattern search method that is coupled to the finite element flow solver in an automated loop.Multiscale modeling couples the 3D Navier Stokes solution with a 0D lumped parameter network to model the heart, coronary arteries, and systemic and pulmonary circulations. Coupling is done with an efficient, modular, and stable implicit method. The use of a multiscale method allows us to capture changes in global circulatory response resulting from changes in local anatomy. We will present representative examples that illustrate the potential of multi scale modeling to impact single ventricle repair, including comparison of different surgical options for the stage two Glenn and stage three Fontan surgeries. Issues and potential for clinical translation will be discussed

10:50 AM
11:00 AM

Questions & Discussion

11:00 AM
11:25 AM
Suncica (Sunny) Canic - Mathematical Modeling of Endovascular Stents
Mathematical Modeling of Endovascular Stents
11:25 AM
11:35 AM

Questions & Discussion

11:35 AM
12:00 PM
Paolo Zunino - Computational modelling of drug eluting stents

Computational modelling of drug eluting cardiovascular stents

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:25 PM
Alessandro Veneziani - Inverse problems in Cardiovascular Design

The introduction of numerical procedures as a part of an established clinical routine and more in general of a consolidated support to the decision making process of physicians is more than a perspective, it is part of practice in several groups.


However, this process still requires some steps both in terms of infrastructures (to bring computational tools to the operating room or the bedside) and methods. In particular, the quality of the numerical results needs to be assessed and certified. The reliability of simulations calls for an accurate quantification and possibly reduction of uncertainty. In this scenario and in view of terrific advancements of measuring techniques, an important research line €“ quite established in other fields €“ is data assimilation, i.e. the integration of numerical simulations and measurements.


We may say that numerical models provide a background knowledge (based on physical principles and constitutive laws, not patient-specific) while measures give a foreground (individual) information; accuracy of in silico procedures relies on the correct integration of these two levels of knowledge of the problem.


Uncertainty of mathematical models, evident for instance in the limited knowledge we have of parameters featured by differential equations may be significantly reduced by the availability of data; quality of measures, on the other hand, can be strongly enhanced by comparison with mathematical models.


In this talk we will address some examples of variational data assimilation in cardiovascular mathematics, referring to two applications:


1) identification of cardiac conductivity from potential measures;



2) estimation of vascular compliance from images, by soilving inverse fluid-structure interaction problems.


A major concern in solving inverse problems for partial differential equations is the computational cost.


Appropriate model reduction techniques are required to contain computational costs and will be discussed in the talk.

02:25 PM
03:00 PM

Questions & Discussion

03:00 PM
03:25 PM
Julia Swanson - Shape and Stiffness of the Anterior Mitral Leaflet in the Beating Heart

Use of Reverse Finite Element Analysis to Determine Mitral Valve Stiffness in the Beating Heart

03:25 PM
03:35 PM

Questions & Discussion

03:35 PM
04:00 PM

Break

04:00 PM
04:25 PM
Elliott Groves - Immediate and Delayed Effects of Stent Crimping on Transcatheter Valves

Immediate and Delayed Effects of Stent Crimping on Transcatheter Valves

04:25 PM
04:35 PM

Questions & Discussion

04:50 PM

Shuttle pick-up from MBI

06:30 PM
07:00 PM

Cash Bar

07:00 PM
08:30 PM

Banquet in the Fusion Room (Crowne Plaza Hotel)

Thursday, October 31, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:25 AM

TBD

09:25 AM
09:35 AM

Questions & Discussion

09:35 AM
10:00 AM
Lakshmi Prasad Dasi - Sub-Kolmogorov Turbulence in Heart Valve Flows: Theory to Predict Distribution of Viscous Shear Stress on Blood Cells

Sub-Kolmogorov Turbulence in Heart Valve Flows: Theory to Predict Distribution of Viscous Shear Stress on Blood Cells.

10:00 AM
10:25 AM

Break

10:25 AM
10:50 AM
Laura Miller - Scaling effects during heart chamber and valve development

Vertebrate cardiogenesis is believed to be partially regulated by fluid forces imposed by blood flow in addition to myocardial activity and other epigenetic factors. To understand the flow field within the embryonic heart, numerical simulations using the immersed boundary method were performed on a series of models that represent simplified versions of some of the early morphological stages of heart development. The results of the numerical study were validated using flow visualization experiments conducted on equivalent dynamically scaled physical models. Striking changes in flow patterns are observed for Reynolds numbers between 1 and 100. Changes in chamber depth, cardiac cushion height, and the formation of trabeculae can also dramatically change the flow at these scales. These fluid dynamic changes could be important to induce shear sensing at the endothelial surface layer which is thought to be a part of regulating the proper morphological development and functionality of the valves, chambers, and trabeculae.

10:50 AM
11:00 AM

Questions & Discussion

11:00 AM
11:25 AM
Boyce Griffith - Modeling cardiac fluid-structure interaction

Modeling cardiac fluid-structure interaction.

11:25 AM
11:35 AM

Questions & Discussion

11:35 AM
12:00 PM
Aaron Fogelson - Modeling Platelet Deposition and Coagulation under Flow: Transport of Platelets and Proteins to and within the Thrombus

Modeling Platelet Deposition and Coagulation under Flow: Transport of Platelets and Proteins to and within the Thrombus

12:00 PM
12:10 PM

Questions & Discussion

12:10 PM
12:35 PM

TBD

12:35 PM

Shuttle pick-up from MBI

Name Affiliation
Alavi, Hamed salavi@uci.edu Biomedical Engineering, University of California, Irvine
Baaijens, Frank f.p.t.baaijens@tue.nl Biomedical Engineering, Eindhoven University of Technology
Buchanan, Rachel rachelbuchanan@utexas.edu Biomedical Engineering, The University of Texas at Austin
Bukac, Martina martina@math.uh.edu Mathematics, University of Pittsburgh
Canic, Suncica (Sunny) canic@math.uh.edu Mathematics, University of Houston--Downtown
Dasi, Lakshmi Prasad lakshmi.dasi@colostate.edu Department of Mechanical Engineering, Colorado State University
DeAnda, Abe abe.deanda@nyumc.org Cardiothoracic Surgery, New York University
Falahatpisheh, Ahmad afalahat@uci.edu Mechanical and Aerospace Engineering, University of California, Irvine
Flamini, Vittoria vflamini@poly.edu Mechanical and Manufacturing Engineering, Polytechnic Institute of New York University
Fogelson, Aaron fogelson@math.utah.edu Department of Mathematics, University of Utah
Ge, Liang Liang.Ge@va.gov Surgery, University of California San Francisco
Gilmanov, Anvar gilmanov.anvar@gmail.com College of Science and Engineering, University of Minnesota
Goergen, Craig cgoergen@purdue.edu Biomedical Engineering, Purdue University
Grande-Allen, Jane grande@rice.edu Bioengineering, Rice University
Griffith, Boyce griffith@cims.nyu.edu Medicine, New York University School of Medicine
Grosberg, Anna grosberg@uci.edu Biomedical Engineering, University of California, Irvine
Groves, Elliott egroves@uci.edu Cardiology, University of California, Irvine
Heim, Frederic Frederic.Heim@uha.fr Research & Development, Universit'e de Haute Alsace
Jackson, Matt msjackson@tmhs.org Cardiovascular Hemodynamics Imaging Laboratory, The Methodist DeBakey Heart and Vascular Center
Joshi, Sunnie Sjoshi@temple.edu Mathematics, Temple University
Kheradvar, Arash arashkh@uci.edu Biomedical Engineering, University of California Irvine
Lawrie, Gerald gmlawrie@att.net Cardiovascular Surgery, Baylor College of Medicine
Little, Stephen shlittle@tmhs.org Cardiovascular Imaging Section, Department of Cardiology, Houston Methodist Hospital
Luo, Xiaoyu Xiaoyu.Luo@glasgow.ac.uk School of Mathematics and Statistics, University of Glasgow
Marsden, Alison amarsden@ucsd.edu Mechanical and Aerospace Engineering, University of California, San Diego
Miller, Laura lam9@email.unc.edu Mathematics , University of North Carolina, Chapel Hill
Mofrad, Mohammad mofrad@berkeley.edu Departments of Bioengineering and Mechanical Engineering, University of California Berkeley
Mohammadi, Hadi hadi.mohammadi@ubc.ca Engineering, University of British Columbia
Pahlevan, Niema pahlevan@caltech.edu Bioengineering, California Institute of Technology
Quaini, Annalisa quaini@math.uh.edu Mathematics, University of Houston
Reimer, Jay jay.m.reimer@gmail.com Biomedical Engineering, University of Minnesota
Sacks, Michael msacks@ices.utexas.edu Biomedical Engineering/ICES, University of Texas
Schmidt, Jillian schm1546@umn.edu Department of Chemical Engineering and Materials Science, University of Minnesota
Simmons, Craig c.simmons@utoronto.ca Mechanical and Industrial Engineering, University of Toronto
Singer, Mike msinger2006@gmail.com Stenomics, LLC, Stenomics, LLC
Swanson, Julia juliaswan@me.com Thoracic & Cardiovascular Surgery, University of Virginia
Toma, Milan tomamil@tomamil.eu Biomedical Engineering, Georgia Institute of Technology
Tranquillo, Robert tranquillo@umn.edu Biomedical Engineering, University of Minnesota
van Loon, Raoul r.vanloon@swansea.ac.uk College of Engineering, Swansea University
Veneziani, Alessandro aleveneziani@gmail.com Mathematics and Computer Science, Emory University
Yoganathan, Ajit ajit.yoganathan@bme.gatech.edu Biomedical Engineering, Georgia Institute of Technology
Zakerzadeh, Rana raz25@pitt.edu Mechanical Engineering, University of Pittsburgh
Zunino, Paolo paz13@pitt.edu Department of Mechanical Engineering and Materials Science, University of Pittsburgh
Cell-mediated retraction and remodeling in engineered cardiovascular tissues

Cell-mediated retraction and remodeling in engineered cardiovascular tissues

Mathematical Modeling of Endovascular Stents
Mathematical Modeling of Endovascular Stents
Sub-Kolmogorov Turbulence in Heart Valve Flows: Theory to Predict Distribution of Viscous Shear Stress on Blood Cells

Sub-Kolmogorov Turbulence in Heart Valve Flows: Theory to Predict Distribution of Viscous Shear Stress on Blood Cells.

Sub-Kolmogorov Turbulence in Heart Valve Flows: Theory to Predict Distribution of Viscous Shear Stress on Blood Cells

Prosthetic Heart valve flows are complex due to turbulence primarily generated in the high shear regions adjacent to leaflets, stent posts, and other stent structures. Estimating shear stress acting on blood elements is therefore critical towards developing design strategies to reduce shear induced platelet activation and hemolysis. In this talk, we present the complete description of dissipative length scales (eddies) and introduce theory to predict viscous shear stress acting on blood elements in a model prosthetic heart valve. High resolution particle image velocimetry (PIV) measurements reveal that the instantaneous dissipative eddies include sub-Kolmogorov length scales due to the highly intermittent nature of the instantaneous energy dissipation field. Nevertheless, the distribution of dissipative eddies appears universal in agreement with modern turbulence theory. Energy balance of instantaneous energy dissipation to the viscous shearing of plasma between blood elements reveals the distribution of viscous shear stress acting on blood cells. This distribution of shear stress peaks corresponding to eddies twice the Kolmogorov scale and sharply decays for eddies smaller than Kolmogorov scale in a universal manner. These results indicate that shear stress derived from energy dissipation is most representative for blood damage evaluation. Blood damage measurements in Reynolds number ranging from laminar through transitionally turbulent in pipe flows confirms that the energy balance approach indeed yields a single unified model to predict shear stress on blood elements applicable for both laminar and turbulent flow. The universality of small scale turbulence, and the unified approach to shear stress provides opportunity for next generation turbulence models for blood flow through heart valves and other cardiovascular devices.

The Aortic Root - Challenges in Re-Creating Nature

Traditional approaches to valve replacement surgery have focused on providing a mechanism for unidirectional flow and optimal mechanics i.e. maximizing the effective orifice area and minimizing the gradient across the valve. Surgery for the aortic root presents unique challenges as experimental and clinical research has demonstrated that the entire root apparatus is intimately connected in both valve and ventricular function. We discuss the anatomic features of the aortic root and the impact of traditional surgical approaches, and then present the challenges for the next generation of composite valve replacement

Modeling Platelet Deposition and Coagulation under Flow: Transport of Platelets and Proteins to and within the Thrombus

Modeling Platelet Deposition and Coagulation under Flow: Transport of Platelets and Proteins to and within the Thrombus

Patient specific simulations of native and prosthetic heart valves

We present a novel computational framework to simulate fluid-structure interaction of implanted tri-leaflet valve at the aortic position of a left heart system with blood flows through this valve. The tri-leaflet tissue valve is implanted at the left ventricle outflow tract with anatomic orientation. The motion of the left ventricle is reconstructed directly from Magnetic Resonance Imaging (MRI) and is prescribed as boundary condition for the computational model. The structural model of the tissue valve is simulated as a thin body with rotation free shell element model of [Stolarski H, Gilmanov A, Sotiropoulos F. Non-linear rotation-free 3-node shell finite-element formulation: IJNME, 2013; 95 (9) , pp. 740-770]. Standard three-node linear finite-element is applied for the discretization of the structure. The multi-block flow solver [Borazjani, I., Ge, L., Le, T., and Sotiropoulos, F., A parallel overset-curvilinear-immersed boundary framework for simulating complex 3D incompressible flows. Computers and Fluids, 2013; 77, pp. 76-96], which is able to simulate complex geometries with multiple branches, is coupled with the finite-element model of the structure.

Developing a mechanically biomimetic hydrogel scaffold for heart valve tissue engineering

The essential function of heart valves is made possible by the unique microstructural arrangement of fibrous extracellular matrix proteins within the valve leaflet tissue, but these valvular structure-function relationships have not been translated into the next generation of valve tissue engineering investigations and for in vitro analyses of valvular cell biology and disease. The primary microstructural attributes of aortic valves are their anisotropic nature and their interconnected, layered structure, which provide valvular interstitial cells (VICs) with heterogeneous pericellular environments. We are integrating these heterogeneous structure and material characteristics of heart valves into hydrogel biomaterials. Hydrogel biomaterials (particularly poly ethylene glycol diacrylate, PEGDA) are appealing for use as TEHV scaffolds because they have tunable structure and mechanics, can be readily bio-functionalized, and can easily encapsulate cells. Research concerning these materials, however, has generally been focused on their biological activities, as opposed to the development of advanced material behavior. This presentation will describe our experience with hydrogels and our efforts to apply novel patterning and layering methodologies to generate advanced 3D hydrogels that mimic the complex microstructure and material behavior of aortic valve tissue. Constitutive modeling of the patterned hydrogel scaffolds will also be described.

Modeling cardiac fluid-structure interaction

Modeling cardiac fluid-structure interaction.

Immediate and Delayed Effects of Stent Crimping on Transcatheter Valves

Immediate and Delayed Effects of Stent Crimping on Transcatheter Valves

Transcatheter Heart Valve Design: Textile as an Alternative to Biological Tissue?

Transcatheter surgery, has become today a technology of choice to relieve patients from vascular diseases like valve stenosis. Far less traumatic for the patient, this technique is also less expensive and less time consuming, which makes it very attractive for the medical world. One of the main limits of the devices used clinically is related to the fragility of the biological tissue (chemically treated bovine pericardium), which is used as valve material. Degradations can occur especially when the valve is crimped within the stent for catheter insertion purpose. Moreover, once implanted, the stent is generally deformed, which induces additional stress in the leaflets. Textile material could be a potential candidate to replace biological tissue. A heart valve undergoes a combination of flexural and tensile stress during operation. A fabric having lower flexural resistance can be expected to have longer working life. Among fibers available, one that has been used most extensively in implants (arterial and stent grafts for example) is polyester. It is biocompatible and resistant to degradation when in contact with body fluids. Today fabric prototypes have been designed and manufactured in order to reproduce the native valve design. Measured in vitro performances show results close to those obtained with other commercially available devices in terms of regurgitation. Moreover, the interaction of the textile material with the living tissues has been studied in vivo in sheep models and showed 2 months survival time, which is encouraging. Fatigue tests performed under physiological conditions have led to 200 Mio cycling duration with no significant degradation of the textile material. Basically, the first evaluation results confirm that textile is a serious candidate for non invasive valve replacement. Further tests are still running as a huge potential remains in varying the fabric construction parameters and the surface treatments to optimize the valve performances.

A pulsatile in vitro heart valve model utilizing multi-modality imaging for assessment of transvalvular flow and velocity fields

This talk will describe the development of the multi-modality compatible (MRI, CT, ECHO) flow loop within the Cardiovascular Hemodynamics Imaging Laboratory at the Methodist DeBakey Heart and Vascular Center. We propose that clinical imaging techniques paired with a controlled, pulsatile flow simulator will establish a foundation of data needed for validation of computational techniques.

Measure of Asymmetry of Transmitral Vortex Ring

Measure of Asymmetry of Transmitral Vortex Ring

100% Reparability in Mitral Valve Surgery

100% Reparability in Mitral Valve Surgery


Importance of Restoration of Normal Annular, Papillary Muscle and Outflow Tract Dynamics and Strain by an Engineered Approach

Time for AVR...Calculating Risk
Time for AVR...Calculating Risk
Patient specific multiscale modeling in pediatric cardiology

Single ventricle heart patients typically undergo a three-staged surgical repair to route the venous return directly to the pulmonary arteries, separating the systemic and pulmonary circulations. We will present our recent work combining shape optimization and multiscale modeling to compare existing designs and develop novel methods for the three stages of single ventricle repair. The optimization algorithm we present is an efficient surrogate pattern search method that is coupled to the finite element flow solver in an automated loop.Multiscale modeling couples the 3D Navier Stokes solution with a 0D lumped parameter network to model the heart, coronary arteries, and systemic and pulmonary circulations. Coupling is done with an efficient, modular, and stable implicit method. The use of a multiscale method allows us to capture changes in global circulatory response resulting from changes in local anatomy. We will present representative examples that illustrate the potential of multi scale modeling to impact single ventricle repair, including comparison of different surgical options for the stage two Glenn and stage three Fontan surgeries. Issues and potential for clinical translation will be discussed

Scaling effects during heart chamber and valve development

Vertebrate cardiogenesis is believed to be partially regulated by fluid forces imposed by blood flow in addition to myocardial activity and other epigenetic factors. To understand the flow field within the embryonic heart, numerical simulations using the immersed boundary method were performed on a series of models that represent simplified versions of some of the early morphological stages of heart development. The results of the numerical study were validated using flow visualization experiments conducted on equivalent dynamically scaled physical models. Striking changes in flow patterns are observed for Reynolds numbers between 1 and 100. Changes in chamber depth, cardiac cushion height, and the formation of trabeculae can also dramatically change the flow at these scales. These fluid dynamic changes could be important to induce shear sensing at the endothelial surface layer which is thought to be a part of regulating the proper morphological development and functionality of the valves, chambers, and trabeculae.

Multiscale Models of the Human Aortic Valve

Multiscale Models of the Human Aortic Valve


Linking the Organ Scale to Single Cells

A Fluid-Structure Interaction Model to Simulate Mitral Valve Regurgitant Flow

We discuss the numerical simulation of the hemodynamics conditions encountered in patients with mitral regurgitation (MR). Our computational model represents the interaction between blood and an elastic wall containing a geometric orifice which mimics a leaky mitral valve during ventricular systole. This fluid-structure interaction (FSI) model is validated against experiments performed in an in vitro mock heart chamber developed at the Methodist DeBakey Heart & Vascular Center. Numerical results are compared to experimental measurements for different flow scenarios, ranging from mild to severe MR, and the computational FSI model is used to to show strengths and limitations of echocardiographic methods to assess the severity of mitral regurgitation.

Multiscale models of the mitral valve

Multiscale models of the mitral valve

Microenvironmental regulation of aortic valve (patho)biology: Implications for valve design

The cellular microenvironment in the aortic valve is defined by a variety of biomechanical-, biochemical-, and extracellular-mediated factors, the combination of which can maintain valve homeostasis or drive pathogenesis. We have studied the valve microenvironment in the context of aortic valve calcification and fibrosis, with particular focus on the contributions of hemodynamics and extracellular matrix properties to local regulation of side-specific valve cell phenotypes and focal pathological alterations. These studies not only provide novel insights into the complex cellular and molecular processes that integrate to regulate valve cell pathobiology, but also suggest strategies to direct aortic valve regeneration. In this presentation, I will describe what we have learned about the native aortic valve microenvironment and its regulation of valve cells, and how we are using that knowledge, in combination with microtechnologies and statistical modeling, to define engineered microenvironments that predictably and optimally guide heart valve tissue regeneration.

Shape and Stiffness of the Anterior Mitral Leaflet in the Beating Heart

Use of Reverse Finite Element Analysis to Determine Mitral Valve Stiffness in the Beating Heart

Completely-biological Tissue-engineered Heart Valves Based on Predictable Cell Induced Contraction and Alignment of Biopolymers

A first-generation tissue-engineered heart valve (TEHV) based on cell-contracted biopolymers to achieve both the geometry and gross alignment of the root and leaflets is summarized, including predictions of our Anisotropic Biphasic Theory (ABT) of Tissue-Equivalent Mechanics (Barocas and Tranquillo, J Biomech Eng, 1997) and a sheep implantation study. A recent second-generation tubular TEHV fabricated from a decellularized tissue tube mounted on a frame with three struts, which upon back-pressure cause the tube to collapse into three coapting "leaflets", is then discussed. The tissue is again completely biological, fabricated from fibroblasts dispersed within a fibrin gel, compacted into a circumferentially-aligned tube on a mandrel, and matured using a bioreactor system that applied cyclic distension. Following decellularization, the resulting tissue possesses tensile mechanical properties, mechanical anisotropy, and collagen content that are comparable to native pulmonary valve leaflets. When mounted on a custom frame and tested within a pulse duplicator system, the tubular TEHV displays excellent function under both aortic and pulmonary conditions, with minimal regurgitant fractions and transvalvular pressure gradients at peak systole, as well as well as effective orifice areas exceeding those of current commercially available valve replacements. A short-term fatigue test of one million cycles with pulmonary pressure gradients was conducted without significant change in mechanical properties and no observable macroscopic tissue deterioration. Ongoing efforts utilize FEA to optimize the frame design. The tubular TEHVpresents an attractive potential alternative to current tissue valve replacements due to its avoidance of chemical fixation and utilization of a tissue conducive to recellularization by host cell infiltration.

Aortic valve modelling in 3D and 0D

Aortic valve modelling in 3D and 0D

Inverse problems in Cardiovascular Design

The introduction of numerical procedures as a part of an established clinical routine and more in general of a consolidated support to the decision making process of physicians is more than a perspective, it is part of practice in several groups.


However, this process still requires some steps both in terms of infrastructures (to bring computational tools to the operating room or the bedside) and methods. In particular, the quality of the numerical results needs to be assessed and certified. The reliability of simulations calls for an accurate quantification and possibly reduction of uncertainty. In this scenario and in view of terrific advancements of measuring techniques, an important research line – quite established in other fields – is data assimilation, i.e. the integration of numerical simulations and measurements.


We may say that numerical models provide a background knowledge (based on physical principles and constitutive laws, not patient-specific) while measures give a foreground (individual) information; accuracy of in silico procedures relies on the correct integration of these two levels of knowledge of the problem.


Uncertainty of mathematical models, evident for instance in the limited knowledge we have of parameters featured by differential equations may be significantly reduced by the availability of data; quality of measures, on the other hand, can be strongly enhanced by comparison with mathematical models.


In this talk we will address some examples of variational data assimilation in cardiovascular mathematics, referring to two applications:


1) identification of cardiac conductivity from potential measures;



2) estimation of vascular compliance from images, by soilving inverse fluid-structure interaction problems.


A major concern in solving inverse problems for partial differential equations is the computational cost.


Appropriate model reduction techniques are required to contain computational costs and will be discussed in the talk.

Experimental platforms for validating computational approaches to heart valve mechanics

This talk will discuss the various versions of left heart simulators that have been developed at the Cardiovascular Fluid Mechanics Laboratory at the Georgia Institute of Technology, specifically designed to provide high fidelity experimental datasets necessary for rigorous validation of computational tools for simulating heart valve flows. These systems are capable of simulating physiological and pathological flow, pressure and geometric conditions, and can be investigated using a variety of experimental tools to measure relevant biomechanical quantities. Such robust multi-modality experimental platforms play a critical role in the development, validation and widespread acceptance of computational tools towards developing patient specific treatment and surgical interventions for heart valve applications.

Computational modelling of drug eluting stents

Computational modelling of drug eluting cardiovascular stents