PROPOSED RESEARCH PLAN:
Assessment of biomechanical environment in peripheral vascular lesions using computational modeling
Last edits made 8 December 2009
GREEN - action items
Yellow - new language as agreed to in 9/2/2009 conversation
Strikeout (black/red) - language that we agreed should be removed in 9/2/2009 call
Added by John Muskivitch
Deleted by John Muskivitch
Added by Tina Morrison
Deleted by Tina Morrison
Background
The peripheral vasculature remains a challenging biomechanical environment for cardiovascular implants, particularly bare metal stents. That the environment can be described as the combined loading of mechanical forces due to leg motion and fluid forces due to pulsatile blood flow is a simplification indeed. However, that assumption will enable investigators to characterize and assess the biomechanical environment of patients with peripheral arterial disease using two different computational methodologies but the same collected information from the clinical study. The use of quantitative image processing techniques, coupled with sophisticated computational modeling, will be used to quantify the biomechanical environment in the lower extremities before and after that underwent revascularization treatment using stenting.
Static quantities, such as anatomical parameters and plaque distributions, measured from medical imaging can be used to characterize the geometrical structure of the vasculature. Vessel deformations and blood flow velocity waveforms can be quantified using medical imaging data combined with reconstruction techniques to characterize the mechanical and fluid environment. Though in vivo the two act in concert, the mechanical and fluid environments may be examined separately to provide unique insights. Thus, two mechanics approaches are proposed to effectively evaluate the biomechanical environment of the SFA. Once these aspects are characterized, the two mechanisms can be combined to examine the coupled fluid-structure interactions.
Imaging and Modeling Objectives
This project will utilize medical imaging data from a variety of imaging modalities, new and developed reconstruction algorithms, and advanced solid and fluid mechanical simulations through finite element analysis and other mathematical algorithms. An overview of the imaging and modeling objectives are:
(i) employ image reconstruction algorithms to extract essential anatomical geometry information from the imaging database generated by the clinical study to create realistic computer models of the SFA lesions with and or without stents at the pre-operative, post-operative and follow-up stages;
(ii) predict the spatio-temporal biomechanical distribution and acute arterial deformation due to stenting and ballooning;
(iii) quantify changes in arterial vessel geometry for several postures of the leg - straight leg and flexure at several angles;
(iv) construct a solid model of a diseased vessel to replace the “rigid-cylinder” paradigm of device evaluation; and
(v) validate the computational predictions using the boundary condition data obtained from the prospective pilot study.
Possible Imaging Modalities
(7/8/2009 meeting) ADD: what other types of images will give what information e.g.,
§ CT: centerline of vessel and vessel curvature (ACTION: Paul will follow-up with Dr. Kashyap to see if he is willing to do straight and bent leg; but large xray doses)
§ Gated-CT: lumen cross-section, axial and circumferential changes in deformation due to pulsatile motion
§ IVUS and CT cross-section: detailed vessel cross-sections (areas, circumference, curvature), plaque composition and distribution
§ DUS: time sample from spectral doppler - velocity waveform in specific regions (proximal, within and distal to stent - depends on stent); some pts may be able to do both straight and bent (thinner pts) and might be able to get a cine loop
§ X-ray: post-stenting - how stent deforms with leg motion (stent bending); match with simulation (validation tool)
§ Angio: post-stenting (at time of implantation) - help with straight and bent leg curvatures if Dr. Kashyap is willing to do these types of images in the pts. Quantitative Vascular Analysis: nice lumen profiles, similar to IVUS (2D plane only, but quicker) - validation for IVUS
Flesh out this section once we've had the endpoint discussion.
Model Construction
We The numerical simulations will begin with simplified models of arterial vessels to quantify the mechanical environment of the femoro-popliteal vasculature during pre- and post stent implantation and also under when subjected to several loading conditions. We will quantify The non-linearities associated with the stent-arterial wall contact problem such as elasto-plasticity of the stent and geometric (large motions) and material non-linearities (deformations) of the stent and the arterial wall during knee flexure will be modeled.
Geometry
We have been working with Computational models of single vessel lesions with or without stents and their stenting are currently being studied. We developed Physiologically realistic computational models of the single arterial vessels have been developed using SolidWorks (Dassault Systemes). Serial cross-sectional bitmap VH IVUS images (Volcano Therapeutics, Inc) of the patient’s vasculature extracted from the patient will be used to reconstruct the geometry of arterial cross-section. All bitmap images will be processed to eliminate any possible backgrounds and artifacts, and pixel values based on the 8-bit range will be extracted for all zones of interest. Our image processing algorithms have the ability to automatically crop and identify the luminal, medial and adventitial boundaries and exclusively characterize the plaque composition in the arterial wall that includes calcified, lipid-laded, and necrotic areas. Furthermore, the ability of the image reconstruction technique to automatically identify the stent geometry will also be demonstrated. All the IVUS cross-section images will be sequentially processed to identify the individual components of the arterial wall and the lumen. Subsequently, these cross-sectional models will be connected to generate a three-dimensional reconstructed geometry of the arterial vessel that will be further exported in the form of a Parasolid file to perform computational simulations.
Material Model
The mechanical behavior of the stent on the arterial wall will be studied by using a quasi-static mechanical analysis approach. At the outset, an appropriate constitutive model an isotropic elasticity will be assumed used for the stent material. However, large deflections and strains will occur during stent expansion and knee flexure. In order to incorporate this phenomenon, the geometric non-linearity requires inputting the material properties and outputting the results in terms of true stress and true strain. We will use Von Mises yield criterion and bi-linear isotropic hardening rule to describe the mechanical properties of the material under these conditions. The values for the Young's modulus, Poisson's ratio, yield stress and the tangent modulus for the plastic hardening phase of the stent will be extracted from the manufacturer's manual. The material model selected and used will have all of the necessary material constants and parameters to properly represent the stent behavior. The potential variation in the mechanical properties of the material due to such things as temperature, non-linear elasticity, superelasticity, etc., must be included. All material processing and its effect on residual stresses and strains must be evaluated and included as appropriate.
Fluid Mechanical Evaluation
àInsert already well proposed fluid components
As successful representations of the mechanical behavior are developed, We will then extend the methodology will be extended to more physiologic scenarios using higher fidelity models incorporating coupled time-dependent fluid-structure interactions. No slip boundary conditions will be assumed at the blood-tissue and blood-stent interfaces. Inlet luminal flow will be prescribed as a physiologic pulsatile profile obtained from the DUS measurements. A zero pressure boundary condition will be applied at the outlet. Variable material properties of different components of the arterial plaque will be incorporated using in-built user-defined functions. We will use the Arbitrary Lagrangian-Eulerian (ALE) finite-element method (COMSOL, Inc.) to solve the coupling of fluid flow and wall deformation. The ALE technique in Computational Fluid Dyanamics (CFD) requires the generation of computational meshes with associated Degrees of Freedom (DOF) that, would inturn, determine the fidelity of the numerical simulations.
Finite element meshes of the structural and fluid regions will be generated automatically from imported Parasolid files and post-processed to ensure regularity in regions of high curvature and proximal to the stented region. The volumes structure of the stent will be typically meshed with multi-node hexahedral elements which are suitable for the type of material model and character of the behavior being simulated (plasticity, creep, stress stiffening, large deflection and large strain analysis). Meshes created within the arterial wall also take into account the spatial distribution and material composition of fibrous, fibro-fatty, necrotic core, and dense calcium rich areas. Unstructured grid generation scheme will be used to discretize the luminal, medial and adventitial zones. Optimal selection of the type of mesh elements along with suitable size functions and adaptive local mesh refinements resolve discontinuities in a computationally efficient manner.
In addition, special care will be taken while meshing structural regions with high stress/strain gardients and fluid regions closer to all interfaces by employing suitable boundary layers [ACTION (John): clarify that this is specific to fluid and add some structural stuff]. Mesh density studies will be performed on a candidate patient’s geometry at the pre-operative stage for both the structural and fluid simulations. where the density of the mesh size will be doubled with successive simulations until convergence.
Solid (or Structural) Mechanical Evaluation
The following studies have utilized different imaging modalities to quantify changes due to non-pulsatile motion with MRI [Choi 2009] and deformation due to pulsatile flow with gated-CT [Morrison 2009] and ultrasound [Gorgeon 2008]. Thus, the vessel wall deformation in the superficial femoral artery can be quantified in similar manners. Furthermore, the anatomical parameters gathered from those measurements can be utilized to construct a three-dimensional model of a diseased artery to represent the vasculature of patients with PAD.
Currently, the FDA receives from sponsors finite element modeling test reports to support the approval of their device for market or for an investigational device exemption. For the SFA in particular, the modeling approach typically presented consists of crimping, deploying, and deforming the stent in a manner that is intended to mimic deformation in the leg. While the crimping aspect of the simulation is appropriate to model using a rigid cylinder, deployment and deforming the stent in a compliant cylinder is not. Unless the sponsor is making direct comparisons with the bench-top fatigue testing of the stent (which is usually not the case), deforming the stent deployed is a compliant mock artery is not representative of the anatomy or material properties of a diseased SFA. One of the objectives of the computational modeling portion of this proposal is to replace the rigid (or compliant) cylinder with a model of a vessel that represents the vessel typically observed clinically in patients with PAD.
For example, the anatomical parameters measured over the patient population could be incorporated to represent an average, or more extreme, version of a patient with PAD. Furthermore, the model could have plaque densities and distributions also mimicking that of the average or more extreme case of a patient. Much research has been done to quantify the material properties of blood vessel and plaque depositions (ref), and incorporating those to generate a realistic diseased vessel is not out of reach.
Once the model is complete, the stent under examination could be deployed and deformed in the diseased vessel rather than the rigid cylinder. Moreover, the deformations under which the stent would be deformed in the simulation could also be calculated from the reconstructed image data set. Employing techniques already developed for MRI, CT, etc, may result in accurate quantification of vessel wall deformation.
Fluid-Structure Coupling
Last Edits made 9 September 2009
GREEN - action items
Yellow - new language as agreed to in 9/2/2009 conversation
Strikeout (black/red) - language that we agreed should be removed in 9/2/2009 call
Added by John Muskivitch
Deleted by John Muskivitch
ACTION (Brian): Add a sentence about main goal - how artery changes with flexion. Biomechanical forces resulting from the movement of the leg create a complex set of forces that act on the walls of the arteries. These forces can combine with In addition, inertial and viscous forces generated due to fluid flow, pressure changes due to pulsatile nature of the cardiac cycle combine together to generate a nonlinear effect on the arterial wall. When these forces are acting either at a lesion site or within revascularized segment, the spatio-temporal force distribution becomes nonintuitive to realize. Only Computational modeling can provide a cost-effective means by which to generate quantitative maps of dynamically changing forces acting on the vessel wall.
We will use Quantitative image processing techniques coupled with sophisticated computational modeling will be used to quantify the mechanical environment in the lower extremities that underwent revascularization treatment using stenting.
(i) employ image reconstruction algorithms to extract essential geometry information from the imaging database to create realistic computer models of the SFA lesions with or without stents at the pre-operative, post-operative and follow-up stages,
(ii) predict the spatio-temporal biomechanical distribution and acute arterial deformation due to stenting and ballooning,
(iii) quantify changes in arterial vessel geometry for several postures of the leg - straight leg and flexure at several angles, and
(iv) validate the computational predictions using the boundary condition data obtained from the prospective pilot study.
Model geometry construction
We have been working with Computational models of single vessel lesions with or without stents and their stenting are currently being studied. We developed Physiologically realistic computational models of the single arterial vessels have been developed using SolidWorks (Dassault Systemes). Serial cross-sectional bitmap VH IVUS images (Volcano Therapeutics, Inc) extracted from the patient will be used to reconstruct the geometry of arterial cross-section. All bitmap images will be processed to eliminate any possible backgrounds and artifacts, and pixel values based on the 8-bit range will be extracted for all zones of interest. Our image processing algorithms have the ability to automatically crop and identify the luminal, medial and adventitial boundaries and exclusively characterize the plaque composition in the arterial wall that includes calcified, lipid-laded, and necrotic areas. Further, the ability of the image reconstruction technique to automatically identify the stent geometry will also be demonstrated. All the IVUS cross-section images will be sequentially processed to identify the individual components of the arterial wall and the lumen. Subsequently, these cross-sectional models will be connected to generate a three-dimensional reconstructed geometry of the arterial vessel that will be further exported in the form of a Parasolid file to perform computational simulations.
(7/8/2009 meeting) ADD: what other types of images will give what information
e.g.,
-
CT: centerline of vessel and vessel curvature (ACTION: Paul will follow-up with Dr. Kashyap to see if he is willing to do straight and bent leg; but large xray doses)
-
IVUS and CT cross-section: detailed vessel cross-sections (areas & curvature), plaque composition
-
DUS: time sample from spectral doppler - velocity waveform in specific regions (proximal, within and distal to stent - depends on stent); some pts may be able to do both straight and bent (thinner pts) and might be able to get a cine loop
-
X-ray: post-stenting - how stent deforms with leg motion (stent bending); match with simulation (validation tool)
-
Angio: post-stenting (at time of implantation) - help with straight and bent leg curvatures if Dr. Kashyap is willing to do these types of images in the pts. Quantitative Vascular Analysis: nice lumen profiles, similar to IVUS (2D plane only, but quicker) - validation for IVUS
flesh out this section once we've had the endpoint discussion
Numerical simulations
We The numerical simulations will begin with simplified models of arterial vessels to quantify the mechanical environment of the femoro-popliteal vasculature during pre- and post stent implantation and also under when subjected to several loading conditions. We will quantify The non-linearities associated with the stent-arterial wall contact problem such as elasto-plasticity of the stent and geometric (large motions) and material non-linearities (deformations) of the stent and the arterial wall during knee flexure will be modeled.
The mechanical behavior of the stent on the arterial wall will be studied by using a quasi-static mechanical analysis approach. At the outset, an appropriate constitutive model an isotropic elasticity will be assumed used for the stent material. However, large deflections and strains will occur during stent expansion and knee flexure. In order to incorporate this phenomenon, the geometric non-linearity requires inputting the material properties and outputting the results in terms of true stress and true strain. We will use Von Mises yield criterion and bi-linear isotropic hardening rule to describe the mechanical properties of the material under these conditions. The values for the Young's modulus, Poisson's ratio, yield stress and the tangent modulus for the plastic hardening phase of the stent will be extracted from the manufacturer's manual. The material model selected and used will have all of the necessary material constants and parameters to properly represent the stent behavior. The potential variation in the mechanical properties of the material due to such things as temperature, non-linear elasticity, superelasticity, etc., must be included. All material processing and its effect on residual stresses and strains must be evaluated and included as appropriate.
As successful representations of the mechanical behavior are developed, We will then extend the methodology will be extended to more physiologic scenarios using higher fidelity models incorporating coupled time-dependent fluid-structure interactions. No slip boundary conditions will be assumed at the blood-tissue and blood-stent interfaces. Inlet luminal flow will be prescribed as a physiologic pulsatile profile obtained from the DUS measurements. A zero pressure boundary condition will be applied at the outlet. Variable material properties of different components of the arterial plaque will be incorporated using in-built user-defined functions. We will use the Arbitrary Lagrangian-Eulerian (ALE) finite-element method (COMSOL, Inc.) to solve the coupling of fluid flow and wall deformation. The ALE technique in Computational Fluid Dyanamics (CFD) requires the generation of computational meshes with associated Degrees of Freedom (DOF) that, would inturn, determine the fidelity of the numerical simulations.
Finite element meshes of the structural and fluid regions will be generated automatically from imported Parasolid files and post-processed to ensure regularity in regions of high curvature and proximal to the stented region. The volumes structure of the stent will be typically meshed with multi-node hexahedral elements which are suitable for the type of material model and character of the behavior being simulated (plasticity, creep, stress stiffening, large deflection and large strain analysis). Meshes created within the arterial wall also take into account the spatial distribution and material composition of fibrous, fibro-fatty, necrotic core, and dense calcium rich areas. Unstructured grid generation scheme will be used to discretize the luminal, medial and adventitial zones. Optimal selection of the type of mesh elements along with suitable size functions and adaptive local mesh refinements resolve discontinuities in a computationally efficient manner.
In addition, special care will be taken while meshing structural regions with high stress/strain gardients and fluid regions closer to all interfaces by employing suitable boundary layers [ACTION (John): clarify that this is specific to fluid and add some structural stuff]. Mesh density studies will be performed on a candidate patient’s geometry at the pre-operative stage for both the structural and fluid simulations. where the density of the mesh size will be doubled with successive simulations until convergence.
Post-processing of simulation results will be performed within the context of the simulation. For structural simulations, the rsults will be in the form of tables, contour maps stress and/or strain and deformed shape plots of key portions of the device. The fluid analysis will result in maps of flow streamlines, wall shear stress and pressure distributions ACTION (John): clarify that this is specific to fluid and add some structural stuff]. . The flow field will further be processed to identify near wall flow separation caused due to stenting using metrics that are based on the average mural values of the shear stress tensor. The maps and patterns we obtain can be overlaid against the localization of intimal hyperplasia and specific cell response. Similarly, computer models simulating different postures of knee flexion and their corresponding patient-specific spatio-temporal mechanical environment can be quantified from the imaging and initial boundary condition data obtained from each case.
The analysis should predict 1) the acute deformation of the artery lesion due to stenting and ballooning; 2) the acute deformation of the artery and stent during leg flexure; 3) the follow-up geometry of the artery and lesion with a straight leg; and 4) the follow-up deformation of the artery and stent during flexure.
Detailed fluid mechanic analysis is not of interest unless it helps predict the follow-up. Simply, if the lesion is less than 75%diameter occluded, then the reduction in flow across the lesion is not likely to be producing a significant reduction in flow.
John Muskivitch's comments - in BLUE BOLD - deletions are green box around character strike out.
I'm working to reorganize the protocol into two paths, really three. One that includes the solid/structural mechanics portion, outlining goal to create a the solid model of a diseased vessel; one that includes the fluid mechanics portion (already well posed); and third, the vision of combiningg those two into fluid-structure interaction type simulation. My goal is to add my final edits before the conf call on 9 Dec. I hurt my right elbow so typing is difficult this evening. I hope these edits will generate fruit discussions for the grant writing process. ~ Tina
I am in full agreement to Brian's first comment from August and also to Tina's edits. Although it would be great to have a complete detailed model including fluid-structure interaction, it is very important not to have too many parameters in the analysis. The consideration of the most relevant parameters regarding vessel geometry and deformation in conjunction with a good structural analysis (including well understood material bahavior and model)should be the first goal. The influence of the diseased vessel versus a healthy vessel onto the vessel deformation is another important aspect. With this knowledge, an improved loading regime and more realistic boundary conditions can be chosen and properly tested, as described by Tina. However, a detailed modelling of an artery for testing raises the question about which anatomy is appropiate and, it has to be decided which are the most relevant parameters and which are relevant at all. It is a tightrope walk, on one hand to consider all important details, and on the other hand to perform a robust and high quality numerical analysis with enough detail. I think this is a very interesting discussion and would be worth to talk about when all people are sitting in one room without time constraints... In a nutshell, it is good to aim for the complete sophisticated all-in-one model, but the steps towards this have to be well understood and the overview on the important things not lost.