Vittoria Flamini

Fibre orientation of fresh and frozen porcine aorta determined non-invasively using diffusion tensor imaging.

Diffusion tensor imaging analysis was applied to fresh and frozen porcine aortas in order to determine fibre orientation. Fresh and stored frozen porcine aortas were imaged in a 7 T scanner with a diffusion weighted spin echo sequence (six gradient directions, matrix 128×128 pixels, 2.8 cm×2.8 cm field of view). The images were taken for different b values, ranging from 200 s/mm(2) to 1600 s/mm(2). For each dataset the diffusion tensor was evaluated, fractional anisotropy (FA) maps were calculated, and the fibres mapped. The arterial fibres resulting were postprocessed and their fibre angle evaluated. The FA maps, the dominant fibre angle, and the fibre pattern in the arterial wall thickness were compared in the fresh and in the stored frozen aortas. The technique was able to determine a fibre pattern in the fresh healthy aorta that is in accordance with the data available in literature and to identify an alteration in the fibre pattern caused by freezing. This study shows that this technique has potential for studying fibre orientation and fibre distribution in humans and could be further developed to diagnose fibre alterations due to cardiovascular diseases. In fact, our results suggest that DTI has the potential to determine the fibrous structure of arteries non-invasively. This capability could be further developed to study the natural remodelling of the aorta in vivo due to age and/or gender or to obtain information on aortic diseases at an early stage of their evolution.

Immersed boundary-finite element model of fluid–structure interaction in the aortic root

It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid–structure interaction model of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin’s immersed boundary (IB) method with a finite element description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configuration of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left-ventricular fluid dynamics.

Evaluation of a validation method for MR imaging-based motion tracking using image simulation

Magnetic Resonance (MR) imaging-based motion and deformation tracking techniques combined with finite element (FE) analysis are a powerful method for soft tissue constitutive model parameter identification. However, deriving deformation data from MR images is complex and generally requires validation. In this paper a validation method is presented based on a silicone gel phantom containing contrasting spherical markers. Tracking of these markers provides a direct measure of deformation. Validation of in vivo medical imaging techniques is often challenging due to the lack of appropriate reference data and the validation method may lack an appropriate reference. This paper evaluates a validation method using simulated MR image data. This provided an appropriate reference and allowed different error sources to be studied independently and allowed evaluation of the method for various signal-to-noise ratios (SNRs). The geometric bias error was between 0– voxels while the noisy magnitude MR image simulations demonstrated errors under 0.1161 voxels (SNR: 5–35).

Imaging Arterial Fibres Using Diffusion Tensor Imaging—Feasibility Study and Preliminary Results

MR diffusion tensor imaging (DTI) was used to analyze the fibrous structure of aortic tissue. A fresh porcine aorta was imaged at 7T using a spin echo sequence with the following parameters: matrix 128 128 pixel; slice thickness 0.5 mm; interslice spacing 0.1 mm; number of slices 16; echo time 20.3 s; field of view 28 mm 28 mm. Eigenvectors from the diffusion tensor images were calculated for the central image slice and the averaged tensors and the eigenvector corresponding to the largest eigenvalue showed two distinct angles corresponding to near and to the transverse plane of the aorta. Fibre tractography within the aortic volume imaged confirmed that fibre angles were oriented helically with lead angles of and . The findings correspond to current histological and microscopy data on the fibrous structure of aortic tissue, and therefore the eigenvector maps and fibre tractography appear to reflect the alignment of the fibers in the aorta. In view of current efforts to develop noninvasive diagnostic tools for cardiovascular diseases, DTI may offer a technique to assess the structural properties of arterial tissue and hence any changes or degradation in arterial tissue.

Imaging and finite element analysis: a methodology for non-invasive characterization of aortic tissue.

Characterization of the mechanical properties of arterial tissues usually involves an invasive procedure requiring tissue removal. In this work we propose a non-invasive method to perform a biomechanical analysis of cardiovascular aortic tissue. This method is based on combining medical imaging and finite element analysis (FEA). Magnetic resonance imaging (MRI) was chosen since it presents relatively low risks for human health. A finite element model was created from the MRI images and loaded with systolic physiological pressures. By means of an optimization routine, the structural material properties were changed until average strains matched those measured by MRI. The method outlined in this work produced an estimate of the in situ properties of cardiovascular tissue based on non-invasive image datasets and finite element analysis.

Simulating the Dynamics of an Aortic Valve Prosthesis in a Pulse Duplicator: Numerical Methods and Initial Experience.

Each year, approximately 250,000 surgical procedures are performed to repair or to replace cardiac valves [1], and of these, approximately 50,000 are aortic valve replacement operations. Despite decades of development, many of the limitations of cardiac valve prostheses remain consequences of the fluid dynamics generated by the replacement valve [1]. To enable cross-validation studies that allow for detailed comparisons of experimental and computational results, we are developing fluid-structure interaction (FSI) models of the dynamics of aortic valve prostheses mounted in a ViVitro Systems, Inc. pulse duplicator apparatus. Such an experimentally validated computational model promises both to facilitate the design of novel valve prostheses, and also to assist in the regulatory process, by providing access to detailed spatially- and temporally-resolved flow data that are challenging to obtain via experimental approaches. Our numerical approach to FSI is based on the immersed boundary (IB) method [2]. The structural dynamics are described in Lagrangian form using a material coordinate system, whereas the momentum of the fluid-solid system and the viscosity and incompressibility of the fluid are described in Eulerian form using fixed Cartesian physical coordinates. Lagrangian and Eulerian variables are coupled by integral transforms with Dirac delta function kernels. When the equations are discretized, the singular delta function is replaced by a regularized version of the delta function. See Peskin [2] for details. To treat rigid body dynamics within the framework of the IB method, we adopt an approach similar to that recently developed by Kim and Peskin [3], in which the continuous equations are: ρ(∂u∂t(x,t)+u(x,t)·∇u(x,t))   =-∇p(x,t)+μ∇2u(x,t)+f(x,t) (1) ∇·u(x,t)=0 (2) f(x,t)=∫UF(s,t)δ(x-X(s,t))ds (3) ∂X∂t(s,t)=∫Ωu(x,t)δ(x-X(s,t))dx (4) ∂Y∂t(s,t)=V(t)+W(t)×R(s,t) (5) F(s,t)=κ(Y(s,t)-X(s,t)) (6) in which x∈Ω are physical coordinates, s∈U are material coordinates, X(s,t) and Y(s,t) are time-dependent mappings from material coordinates to current coordinates, u(x,t) is the Eulerian velocity field, p(x,t) is the Eulerian pressure field, f(x,t) and F(s,t) are equivalent Eulerian and Lagrangian force densities, ρ is the fluid density, μ is the fluid viscosity, and δ(x)=δ(x)δ(y)δ(z) is the three-dimensional Dirac delta function. The force field F(s,t) acts to impose the rigidity constraint ∂X∂t(s,t)=U(s,t)=V(t)+W(t)×R(s,t) in which V(t) and W(t) are respectively the linear and angular velocity of the structure and R(s,t) is the radius vector. In the limit κ→∞, the constraint is imposed exactly; for finite κ>0, the constraint is only approximately satisfied. The dynamics of V(t) and W(t) are determined from the requirement that the time rate of change of the “excess” linear and angular momentum (i.e., in excess of the momentum accounted for by the momentum equation (1)) be proportional to the net force ∫Ω-F(s,t)ds and net torque ∫Ω-F(s,t)×R(s,t)ds acting on the body. Geometrical models of the aortic section of the ViVitro pulse duplicator and of a St. Jude Regent valve were created using SolidWorks (Dassault Systemes SolidWorks Corp., Waltham, MA). These geometrical models were meshed using CUBIT (Sandia National Laboratory, Albuquerque, NM). To drive flow through the valve, we impose a physiological left ventricular pressure waveform, and characteristic downstream compliance and resistance to mimic the response of the systemic circulation. Simulations used the IBAMR software [4]. Initial simulation results are shown in Fig. ​Fig.1,1, demonstrating that realistic flow rates can be obtained using this model under realistic driving and loading conditions. We are presently fine tuning this model in preparation for validation studies. Fig. 1 (a) Opening dynamics, (b) imposed driving pressure and computed loading pressure, and (c) computed flow rate

Mechanical behavior of peripheral stents and stent-vessel interaction: A computational study

ABSTRACT In this paper stents employed to treat peripheral artery disease are analyzed through a three-dimensional finite-element approach, based on a large-strain and large-displacement formulation. Aiming to evaluate the influence of some stent design parameters on stent mechanics and on the biomechanical interaction between stent and arterial wall, quasi-static and dynamic numerical analyses are carried out by referring to computational models of commercially and noncommercially available versions of both braided self-expandable stents and balloon-expandable stents. Addressing isolated device models, opening mechanisms and flexibility of both opened and closed stent configurations are numerically experienced. Moreover, stent deployment into a stenotic peripheral artery and possible postdilatation angioplasty (the latter for the self-expandable device only) are simulated by considering different idealized vessel geometries and accounting for the presence of a stenotic plaque. Proposed results highlight important differences in the mechanical response of the two types of stents, as well as a significant influence of the vessel shape on the stress distributions arising upon the artery-plaque system. Finally, computational results are used to assess both the stent mechanical performance and the effectiveness of the stenting treatment, allowing also to identify possible critical conditions affecting the risk of stent fracture, tissue damage, and/or pathological tissue response.

A numerical framework for the mechanical analysis of dual-layer stents in intracranial aneurysm treatment.

Dual-layer stents and multi-layer stents represent a new paradigm in endovascular interventions. Multi-layer stents match different stent designs in order to offer auxiliary functions. For example, dual-layer stents used in the endovascular treatment of intracranial aneurysms, like the FRED(TM) (MicroVention, CA) stent, combine a densely braided inner metallic mesh with a loosely braided outer mesh. The inner layer is designed to divert blood flow, whereas the outer one ensures microvessels branching out of the main artery remain patent. In this work, the implemented finite element (FE) analysis identifies the key aspects of dual-stent mechanics. In particular, dual-layer stents used in the treatment of intracranial aneurysms require the ability to conform to very narrow passages in their closed configuration, while at the same time they have to provide support and stability once deployed. This study developed a numerical framework for the analysis of dual-layer stents for endovascular intracranial aneurysm treatment. Our results were validated against analytical methods. For the designs considered, we observed that foreshortening was in average 37.5%±2.5%, and that doubling the number of wires in the outer stent increased bending moment by 23%, while halving the number of wires of the inner stent reduced von Mises stress by 2.3%. This framework can be extended to the design optimization of multi-layer stents used in other endovascular treatments.

Effects of mechanical loading on cortical defect repair using a novel mechanobiological model of bone healing

Mechanical loading is an important aspect of post-surgical fracture care. The timing of load application relative to the injury event may differentially regulate repair depending on the stage of healing. Here, we used a novel mechanobiological model of cortical defect repair that offers several advantages including its technical simplicity and spatially confined repair program, making effects of both physical and biological interventions more easily assessed. Using this model, we showed that daily loading (5N peak load, 2Hz, 60 cycles, 4 consecutive days) during hematoma consolidation and inflammation disrupted the injury site and activated cartilage formation on the periosteal surface adjacent to the defect. We also showed that daily loading during the matrix deposition phase enhanced both bone and cartilage formation at the defect site, while loading during the remodeling phase resulted in an enlarged woven bone regenerate. All loading regimens resulted in abundant cellular proliferation throughout the regenerate and fibrous tissue formation directly above the defect demonstrating that all phases of cortical defect healing are sensitive to physical stimulation. Stress was concentrated at the edges of the defect during exogenous loading, and finite element (FE)-modeled longitudinal strain (εzz) values along the anterior and posterior borders of the defect (~2200με) was an order of magnitude larger than strain values on the proximal and distal borders (~50-100με). It is concluded that loading during the early stages of repair may impede stabilization of the injury site important for early bone matrix deposition, whereas loading while matrix deposition and remodeling are ongoing may enhance stabilization through the formation of additional cartilage and bone.

Quantifying the ultrastructure of carotid artery using high-resolution micro-diffusion tensor imaging – comparison of intact vs. open cut tissue

Diffusion magnetic resonance imaging (dMRI) can provide insights into the microstructure of intact arterial tissue. The current study employed high magnetic field MRI to obtain ultra-high resolution dMRI at an isotropic voxel resolution of 117 µm3 in less than 2 hours of scan time. A parameter selective single shell (128 directions) diffusion-encoding scheme based on Stejskel-Tanner sequence with echo-planar imaging (EPI) readout was used. EPI segmentation was used to reduce the echo time (TE) and to minimise the susceptibility-induced artefacts. The study utilised the dMRI analysis with diffusion tensor imaging (DTI) framework to investigate structural heterogeneity in intact arterial tissue and to quantify variations in tissue composition when the tissue is cut open and flattened. For intact arterial samples, the region of interest (ROI) base comparison showed that the differences in fractional anisotropy (FA) and differences in mean diffusivity (MD) across the media layer were significantly higher (p < 0.05). For open cut flat samples, DTI based directionally invariant indices did not show significant differences across the media layer. For intact samples, fibre tractography based indices such as calculated helical angle and fibre dispersion showed near circumferential alignment and a high degree of fibre dispersion, respectively. This study demonstrates the feasibility of fast dMRI acquisition with ultra-high spatial and angular resolution at 7T. Using the optimised sequence parameters, this study shows that DTI based markers are sensitive to local structural changes in intact arterial tissue samples and these markers may have clinical relevance in the diagnosis of atherosclerosis and aneurysm.Diffusion magnetic resonance imaging (dMRI) can provide insights into the microstructure of intact arterial tissue. The current study employed high magnetic field MRI to obtain ultra-high resolution dMRI at an isotropic voxel resolution of 117 µm3 in less than 2 h of scan time. A parameter selective single shell (128 directions) diffusion-encoding scheme based on Stejskel-Tanner sequence with echo-planar imaging (EPI) readout was used. EPI segmentation was used to reduce the echo time (TE) and to minimise the susceptibility-induced artefacts. The study utilised the dMRI analysis with diffusion tensor imaging (DTI) framework to investigate structural heterogeneity in intact arterial tissue and to quantify variations in tissue composition when the tissue is cut open and flattened. For intact arterial samples, the region of interest base comparison showed significant differences in fractional anisotropy and mean diffusivity across the media layer (p  <  0.05). For open cut flat samples, DTI based directionally invariant indices did not show significant differences across the media layer. For intact samples, fibre tractography based indices such as calculated helical angle and fibre dispersion showed near circumferential alignment and a high degree of fibre dispersion, respectively. This study demonstrates the feasibility of fast dMRI acquisition with ultra-high spatial and angular resolution at 7 T. Using the optimised sequence parameters, this study shows that DTI based markers are sensitive to local structural changes in intact arterial tissue samples and these markers may have clinical relevance in the diagnosis of atherosclerosis and aneurysm.