We are working to develop a hybrid valve whose leaflets are composed of an extra-thin superelastic Nitinol mesh tightly enclosed by multiple layers of smooth muscle, fibroblast/myofibroblast, and endothelial cells of the patient who will receive the valve. Inspired by the limitations of the current approached in tissue engineering of heart valves, we approached the problem fundamentally different, by creating a valve based on a non-degradable scaffold that remains permanently and supports the leaflets. This approach to engineering heart valves holds promise for combining the mechanical valves' long-term durability advantages with biological valves' improved biocompatibility and hemodynamics.
Valve replacement with mechanical or bioprosthetic prostheses is the most common intervention for valvular disease, with almost 300.000 annual replacements worldwide. Although existing valve prostheses generally have resulted in enhanced survival and quality of life, prosthesis associated problems affect over a third of the patients within ten years post operatively. Prosthetic valves are non-viable structures and, therefore, do not have the ability to grow, repair or adjust to functional demand changes. Living, tissue engineered heart valves may overcome these limitations. Heart valve tissue engineering seeks to overcome these limitations.
One of the major complications observed with current tissue engineered heart valves (TEHV) is leaflet retraction. To enhance our understanding of this phenomenon a series of experiments is performed, and computational models are developed to quantitatively analyze cell mediated compaction and collagen remodeling in engineering cardiovascular substitutes.
Approximately 300,000 people worldwide suffer from severe aortic stenosis. Transcatheter Aortic Valve Implantation (TAVI) procedure is a minimally invasive procedure in which a patient's failing aortic valve is replaced with an artificial heart valve using a catheter-based approach. The TAVR technology consists of a balloon-expandable stent with an integrated (bovine pericardial) valve. The stents used in this procedure need to sustain higher radial forces than those typically used in the treatment of coronary artery disease. The current technologies are constantly improving, and this talk will present a computationlly efficient novel way to model optimal design of stents for these procedures. The mathematical model is based on dimension reduction and multiscale approaches. Instead of treating the entire stent as one 3D elastic body, the new approach models a stent as a net of curved stent struts. The new approach avoids the known computational issues associated with computer simulation of slender bodies, and is 100's of times computationally more efficient than the classical 3D-approaches. This makes computational testing of a large number of stent configurations for optimal stent design feasible, and the coupling between stent elastodynamics and fluid-structure interaction modeling blood flow though the stented aortic annulus or stented coronary artery within computational reach.
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.
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
The formation of an intravascular blood clot involves two intertwined processes: platelet deposition and coagulation. Vascular injury triggers two intertwined processes, platelet deposition and coagulation, and can lead to the formation of an intravascular clot (thrombus) that may grow to occlude the vessel. Formation of the thrombus involves complex biochemical, biophysical, and biomechanical interactions that are also dynamic and spatially-distributed, and occur on multiple spatial and temporal scales. We previously developed a spatial-temporal mathematical model of these interactions and looked at the interplay between physical factors (flow, transport to the clot, platelet distribution within the blood) and biochemical ones in determining the growth of the clot. Here we extend this model to include reduction of the advection and diffusion of the coagulation proteins in regions of the clot with high platelet number density.
The effect of this reduction, in conjunction with limitations on fluid and platelet transport through dense regions of the clot, can be profound. We found that hindered transport leads to the formation of smaller and denser clots compared to the case with no protein hindrance. The limitation on protein transport confines the important activating complexes to small regions in the interior of the thrombus and greatly reduces the supply of substrates to these complexes. Ultimately, this decreases the rate and amount of thrombin production and leads to greatly slowed growth and smaller thrombus size. Our results suggest a possible physical mechanism for limiting thrombus growth.
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.
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.
The heart is a coupled electro-fluid-mechanical system. In this talk, I will present mathematical models and adaptive numerical methods for describing cardiac mechanics and fluid dynamics, focusing on cardiac fluid-structure interaction (FSI). Our basic approach to simulating cardiac dynamics is the immersed boundary (IB) method, which is a mathematical formulation for fluid-structure systems in which an incompressible structure is immersed in a viscous incompressible fluid.
I will focus here on extensions of the IB method that enable the treatment of immersed structures that are described using finite-strain continuum mechanics models, including structure-based hyperelastic constitutive models that can be related to experimental data sets, and the application of these methods to simulating valvular dynamics. I will also describe new extensions of the IB method that enable the simulation of prosthetic heart valves with rigid components. Time permitting, I will also describe applications of these methods to detailed models of cardiac muscle mechanics.
This is joint work with Charles Peskin and David McQueen (New York University) and Xiaoyu Luo (University of Glasgow).
Background: Transcatheter aortic valve replacement has emerged as a promising therapy for treatment of severe aortic stenosis. While it has been shown that these valves can be safely delivered and implanted, studies of valve longevity are lacking due to the infancy of the technology. Particularly, the effects of stent crimping on the valve's leaflets has not yet been sufficiently investigated. In this study, we have characterized the effects of crimping on pericardial leaflets in time and through the depth of the tissue.
Methods: To test the structural changes at the surface and deep layers of bovine pericardial leaflets, Scanning-Electron-Microscopy and Second-Harmonic-Generation microscopy were used. An un-crimped tissue sample was imaged, followed by imaging a segment of tissue after crimping in a stented transcatheter valve, immediately following, at 20 minutes, and 60 minutes after crimping. The crimping experiment was performed for multiple crimping sizes (i.e., 14, 16, and 18 French-catheter). We defined a "damage index" that quantifies the level of leaflet structural changes due to crimping.
Results: Based on the calculated damage indices and analyses of the raw images, it was determined that crimping does measurable damage to the leaflet tissue that persists with time.
Conclusions: Significant tissue damage was observed at the surface layers of the leaflets. In the deeper tissue layers, damage was substantial for 14Fr crimping, however, it became less significant but still visible for larger collapse profiles. It can be concluded that the crimping may induce substantial structural damages to pericardial leaflets that does not improve in time.
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.
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.
Nature has chosen the mitral valve to be the only bileaflet valve inside the heart. Compared to the symmetric geometry of trileaflet valves, e.g., the aortic valve, the nonsymmetric geometry of the mitral valve forms a vortex ring in the left ventricle whose deviation from axisymmetry is more prominent. In addition, it has been visually observed — mainly through contrast echocardiography and echocardiographic particle image velocimetry — that the forming transmitral vortex ring possesses a non-axisymmetric shape as it propagates toward the left ventricular apex. The shape and formation of transmitral vortex rings have been shown to be associated with the diastolic function of the left ventricle. In this study, we quantitatively studied how the mitral valve leaflet affects the symmetry of transmitral vortex ring.
In this work, we utilized the axisymmetry index, which we have developed previously, and measured the deviation of a vortex ring from axisymmetry. Through this index, we studied the effect of the mitral valve's anterior leaflet on the axisymmetry of the generated vortex ring based on the three-dimensional data acquired using defocusing digital particle image velocimetry. Vortex rings were generated downstream of a D-shaped orifice with and without the anterior leaflet due to various stroke ratios within a range anticipated in the left ventricle. The piston expels the fluid toward the opening of the cylinder where two different orifices were investigated. One orifice mimicked the D-shaped mitral valve with a leaflet. Another orifice was the same D-shaped outlet but without the leaflet. The valve models were made of silicone rubber. The thickness of the leaflet was chosen to be equal to that of a natural mitral valve (i.e., 0.5 mm). We used a generalized linear model regression to quantify the effect of the leaflet, stroke ratio, and vortex evolution on the axisymmetry index, ξ, by using 36 observations. A p-value less than 0.05 was considered statistically significant. The results showed that the presence of the anterior leaflet significantly (p-value<0.05) affect the symmetry of the transmitral vortex ring. Results indicated that the presence of the anterior leaflet improved the axisymmetry of the ring.
Dysfunction of the mitral valve (MV) causes significant mortality and remains a major medical problem worldwide. Numerical simulation of mitral valve biomechanics can provide insight into valve function and dysfunction. Because of the difficulties associated with both the finite-strain deformational kinematics and fluid-structure interaction, most MV models that include realistic anatomical geometries and constitutive models consider only the structural mechanics of the valve.
In this study, we are developing an image-derived fibre-reinforced MV model with fluid-structure interactions.
A cardiac magnetic resonance (MR) imaging study was performed on a healthy volunteer, Images from twelve slices along the left ventricular outflow tract (LVOT) were acquired to cover the entire mitral valve, and used for MV reconstruction. Simulations were performed using an immersed boundary method that incorporates a finite element description of the structural mechanics (IB/FE), which enables us to model fluid-structure interaction while accounting for the nonlinear, anisotropic material response of the mitral valve leaflets. The leaflets were modelled as an incompressible fibre-reinforced material with an invariant-based strain energy function. Our numerical scheme employs an unstructured FE discretization of structural domain while retaining a Cartesian grid finite difference scheme for the incompressible Navier-Stokes equations for the fluid. Fluid patterns as well as fibre strain and stress distribution in the MV leaflets will be presented. We also discuss the effects of chordae on the dynamics of the MV.
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
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.
The aortic valve (AV) controls the flow of oxygen-rich blood from the left ventricle to the aorta and thereby the rest of the body. Normally, the aortic valve functions very efficiently, providing negligible resistance to forward flow and allowing minimal backflow. The mechanical function of aortic valve can, however, be affected by pathological conditions. The most common valvular disease is calcific aortic stenosis (CAS). In CAS, the aortic valve undergoes changes very similar to those seen in atherosclerosis. First, inflammatory cells migrate to the site. Monocytes adhere to the endothelial layer, infiltrate it, and differentiate into macrophages. The macrophages send intracellular signals to nearby fibroblasts, causing the fibroblasts to promote cellular proliferation and matrix remodeling. Macrophages add calcium deposits to the matrix. Eventually, the remodeled matrix and calcium deposits build up to yield a thickened, stiffened leaflet. These changes can affect mechanical function, a result known as stenosis. To understand the mechanisms of calcific aortic stenosis, and to evaluate methods of prevention and treatment for this disease, we have developed a set of multiscale models to examine the dynamic behavior of the human aortic valve at the cell, tissue, and organ length scales. Each model is fully three-dimensional and includes appropriate nonlinear, anisotropic material models. The organ-scale model incorporates a dynamic fluid-structure interaction that predicts the motion of the blood, cusps, and aortic root throughout the full cycle of opening and closing. The tissue-scale model simulates the behavior of the aortic valve cusp tissue including the sub-millimeter features of multiple layers and undulated geometry. The cell-scale model predicts cellular deformations of individual cells within the cusps. Each simulation has been verified against experimental data. The three simulations are linked: deformations from the organ-scale model are applied as boundary conditions to the tissue-scale model, and the same is done between the tissue and cell scales. The complete set of simulations has enabled the analysis of the AV mechanical behavior across the range of length scales needed to examine biological processes in the valve.
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.
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.
Anterior mitral leaflet stiffness was determined in vivo using an ovine model. A reverse finite element analysis was used to calculate leaflet stiffness during systole in the beating heart. Multiple observations were made over a series of experiments. The anterior mitral leaflet owes its systolic stiffness to both its shape and highly active material properties. In the closed valve, its saddle shape provides radial leaflet compression and circumferential leaflet tension that offset to minimize deformation with pressure loading. In response to A-wave excitation, cardiac myocytes in the annular half of the leaflet provide a stiffening twitch at the beginning of each ventricular systole. This stiffness-twitch is abolished by beta-blockade, but insensitive to neural stimulation. The bulk of steady-state leaflet stiffness is provided by contractile cells (likely VICs, cross-linking collagen throughout the leaflet), insensitive to beta-blockade, but responding to neural stimulation with rapid increases or decreases of overall leaflet stiffness. The stiffness of this leaflet may be under reflex and/or central control, providing leaflet stiffness changes to maintain appropriate outflow-tract geometry under widely-varying hemodynamic conditions.
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.
This presentation will consist of 2 parts.
The first part will focus on the fictitious domain method for modeling the aortic valve with and without adaptivity of the mesh in the vicinity of the valve. This method will then be used for simulations with parameterised valve geometries in order to easily investigate the main geometric characteristics of the valve. This is illustrated through the dynamic variations of the geometric orifice area during the opening of different valves.
In the second part of the presentation a framework will be introduced that is aimed at an investigation of the interactions of valvular lesions with the heart and arterial system. A parameter estimation is performed on a lumped model of heart, valve and arterial system with synthetic data currently being generated through a 1D network model.
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.
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 analysis of the cardiovascular system is a challenging
application for fluid dynamics and mass transport modeling, involving
various flow regimes, fluid / structure interaction, transport through
porous media and multiscale phenomena, giving rise to several issues
at the level of mathematical modeling and numerical analysis.
Our activity in this area is motivated by the design of biomedical devices, in particular drug eluting cardiovascular stents (DES). A stent is a small mesh tube that is inserted permanently into a partially occluded artery, with the aim to restore the original diameter of the arterial section and ensure the physiological flow rate. Also referred as medicated stents, DES are coated with a pharmacologic agent (drug), to be locally released with a controlled rate.
For the computational analysis of these devices (see for instance ), we first overview computational models applied to stent deployment, aiming to characterize the configuration of a vascular district after stenting. Then, fluid dynamics and intramural plasma filtration are addressed . The analysis of drug release requires merging mass transport models with materials science, in order to determine the release rate of the system at hand . We also discuss model reduction strategies in the framework of the immersed finite element method, aiming to efficiently couple the drug release models with the analysis of fluid dynamics . The combination of all these models gives rise to a virtual test bench, which has been applied to simulate the implantation of stents in complex realistic configurations.
Since DES can be seen as a particular type of vascular repair grafts, this activity is prone to several ramifications. As an instance for many other examples we mention bioresorbable stents (also known as bioresorbable vascular scaffolds). Although successful, issues about their short term mechanical integrity and the corresponding luminal loss are still open. Furthermore, the arterial wall has been considered so far as a static material, but it is well known that vascular remodeling takes place as a consequence of (i) the arterial damage induced during the device implantation, (ii) the subsequent altered flow conditions. Significant insight about the causes and the remedies for post-treatment complications could be gained if the current computational models were complemented by predictive models for arterial remodeling.
Mechanical forces that act on the aortic valve (AV) are thought to modulate aortic valve interstitial cell (AVIC) biosynthetic activity, and play an important role on AV pathophysiology. While advances have been made toward understanding extracellular matrix (ECM) mechanical behavior, AVIC-ECM coupling and its relation to phenotypic state remains poorly understood. A computational model was thus developed to derive AVIC contractile state in situ from tissue level measurements, and to gain insight into AVIC-ECM coupling. First, a macro-scale (tissue) model was used to predict the moment-curvature relationship of the AV leaflets under flexure deformations . Briefly, a three point bending approach was used to characterize the flexural stiffness of porcine AV leaflet specimens in the normal, hypertensive, and inactivated state. Moreover, by testing in both directions the influence of different layer properties could be directly examined. From the resulting moment-curvature data, the macro-scale model was utilized to estimate layer specific tissue properties at varying states of cellular contraction. As an extension of our previous work, a multi-layer/Ogden hyperelastic bimodular material model was used to capture the nonlinearity and unique bi-directional moment-curvature relation of the inactivated, normal, and activated states. The derived tissue-level properties were then used to develop a micro-scale (cell) model to probe specific influence of cell-ECM stiffness on the overall macrolevel mechanical properties. Transmural variation of ECM constituents and AVIC nuclear orientation were integrated into the micro-scale model. A first-order homogenization procedure was used to estimate the effects of varying cell stiffness on tissue mechanical properties. Results to date indicate that AVIC contraction induces ECM stiffening that is unique to each leaflet tissue layer. Moreover, when applied to new experimental data wherein statins were applied, AVICs exhibited a pronounced activated state in response to these pharmaceutical agents. This modeling approach provides a highly sensitive experimental/computat ional method to estimate AVIC/ECM behavior in situ directly from tissue level measurements.
Determining in vivo valve dynamics is an important step when designing artificial heart valves. A major goal of our laboratory is utilize high frequency, small animal ultrasound to quantify cardiac and vascular dynamics in mice and rats. Here we show that both aortic and mitral valve motion can be visualized in rodents in vivo. We can also use 3D ultrasound imaging to create volumetric computer models of the left ventricle, suprarenal abdominal aorta, and infrarenal abdominal aorta. By utilizing appropriate flow boundary conditions (determined by pulsed-wave Doppler), these geometric models can be used to run computational fluid dynamics simulations of blood flow in the left ventricle and large elastic arteries. Finally, we can also collect cardiac and respiratory gated 3D ultrasound data sets that can be combined to create 4D volumes of pulsing tissue. This is especially useful when studying cardiac motion, aortic pulsation, or even the position of valve leaflets. In summary, we believe in vivo imaging efforts can be used for a wide variety of cardiovascular research applications and will be helpful when evaluating the design of artificial heart valves.
One of the centre problems in personalized left ventricle (LV) modelling is to identify the patient-specific material parameters of the constitutive laws. These are developed to describe the mechanical behaviour of the myocardium, which is inhomogeneous, non-linear, incompressible, active, and with fibre-reinforced micro-structures. In this work, we develop a method for identifying the modelling parameters of a LV model, developed using the structure-based material (H-O) model (1) that takes into account of the complex 3D myo bre architecture of passive LV myocardium, and the myo lament model by Niederer et al. (2006) for the active contraction (2). The method is fi rst validated using a passive synthetic model that was initially developed by Wang et al. (3). The synthetic LV model is inflated with end-diastolic pressure. The eight passive parameters in the H-O model are divided into two subsets that are optimised through a multi-step optimisation procedure by matching the results to the known LV volume and strains. This method is then applied to a human subject, for which both passive and active modelling are required. The eight passive parameters are again tuned to match the measured LV volume and the estimated strains from the in-vivo cine-MRI (4). The 22 active parameters from the Niederer model are also tuned by adjusting a scaling parameter so as to match the measured LV volumes at both the end of systole and end of diastole. The results show that the simulated regional LV systolic strains agree well with the strains estimated from the cine-MRI. Work is ongoing on improving the accuracy and towards a more general approach for personalised material models with minimum in-vivo inputs.
A significant challenge in creating fibrin-based engineered cardiovascular tissues is obtaining sufficient mechanical properties for in vivo function by stimulating an increase in cellular collagen production during culture. The application of cyclic stretching has been shown to increase collagen deposition by cells entrapped within a fibrin gel; however, over time the cells adapt to constant amplitude cyclic stretching, suggesting that some perturbation to the constant amplitude regimen is required to maximize the beneficial effects. In this study, intermittent cyclic stretching is investigated as a method to increase the collagen content of fibrin-based engineered tissues, thus improving their mechanical properties.
A tissue-engineered heart valve (TEHV) was fabricated by mounting a decellularized tissue tube on a custom, 3-strutted frame that collapses into three coapting "leaflets" under back pressure. The entrapped ovine fibroblasts remodeled the fibrin gel during in vitro culture prior to decellularization. This tissue possessed tensile mechanical properties, mechanical anisotropy, and collagen content comparable to native pulmonary valve leaflets. The TEHV displayed excellent function in a custom pulse duplicator system under aortic and pulmonary conditions. This study presents an attractive potential alternative to current tissue valve replacements due its absence of chemical fixation and potential for host cell infiltration.
The performance of completely biological, decellularized engineered allografts in a sheep model was evaluated to establish clinical potential of these unique arterial allografts. The 4-mm diameter, 2-3 cm long grafts were fabricated from fibrin gel remodeled into an aligned tissue tube in vitro by ovine dermal fibroblasts. Decellularization and subsequent storage had little effect on graft properties, with burst pressure exceeding 4000 mmHg and the same compliance as the ovine femoral artery. Grafts were implanted interpositionally in the femoral artery of 6 sheep(n=9), with contralateral sham controls(n=3). At 8(n=5) and 24(n=4) weeks, all grafts were patent and showed no evidence of dilatation or mineralization. Mid-graft lumen diameter was unchanged. Extensive recellularization occurred, with most cells expressing ?SMA. Endothelialization was complete by 24 weeks with elastin deposition evident. Grafts pre-seeded with blood outgrowth endothelial cells(n=3) had greater endothelial coverage, smaller wall thickness, and more basement membrane after 9 weeks implantation, including a final week without anticoagulation therapy, compared to contralateral un-seeded controls. These completely biological grafts possessed circumferential alignment/mechanical anisotropy characteristic of native arteries and were cultured only two months prior to decellularization and storage as "off-the-shelf" grafts.
In the context of hemodynamics, we model blood flow in arteries as an incompressible Newtonian fluid confined by a multilayered poroelastic wall. We consider a two layer model for the arterial wall, where the inner layers behave as a thin structure modeled as a linearly elastic membrane, while the outer part of the artery is described by the Biot model. We propose and analyze a splitting strategy, which allows solving the Navier-Stokes and Biot equations separately. In this way, we uncouple the original problem into two parts defined on separate subregions, leading to a more efficient calculation of the numerical solution. The theoretical results will be complemented by numerical simulations. We numerically investigate the effects of porosity on the structure displacement and on the pressure wave propagation.