Fast Image-Based Model of Mitral Valve Closure for Surgical Planning

Surgical repair of the mitral valve results in better outcomes than valve replacement, yet diseased valves are often replaced due to the technical difficulty of the repair process. A surgical planning system based on patient-specific medical images that allows surgeons to simulate and compare potential repair strategies could greatly improve surgical outcomes. The system must simulate valve closure quickly and handle the complex boundary conditions imposed by the chords that tether the valve leaflets. We have developed a process for generating a triangulated mesh of the valve surface from volumetric image data of the opened valve. The closed position of the mesh is then computed using a mass-spring model of dynamics. In the mass-spring model, triangle sides are treated as linear springs supporting only tension. Chords are also treated as linear springs, and self-collisions are detected and handled inelastically. The equations of motion are solved using implicit numerical integration. The simulated closed state is compared with an image of the same valve taken in the closed state to assess accuracy of the model. The model exhibits rapid valve closure and is able to predict the closed state of the valve with reasonable accuracy.Engineering and Applied Science

NOVEL STRATEGIES FOR THE MORPHOLOGICAL AND BIOMECHANICAL ANALYSIS OF THE CARDIAC VALVES BASED ON VOLUMETRIC CLINICAL IMAGES

This work was focused on the morphological and biomechanical analysis of the heart valves exploiting the volumetric data. Novel methods were implemented to perform cardiac valve structure and sub-structure segmentation by defining long axis planes evenly rotated around the long axis of the valve. These methods were exploited to successfully reconstruct the 3D geometry of the mitral, tricuspid and aortic valve structures. Firstly, the reconstructed models were used for the morphological analysis providing a detailed description of the geometry of the valve structures, also computing novel indexes that could improve the description of the valvular apparatus and help their clinical assessment. Additionally, the models obtained for the mitral valve complex were adopted for the development of a novel biomechanical approach to simulate the systolic closure of the valve, relying on highly-efficient mass-spring models thus obtaining a good trade-off between the accuracy and the computational cost of the numerical simulations. In specific: \u2022 First, an innovative and semi-automated method was implemented to generate the 3D model of the aortic valve and of its calcifications, to quantitively describe its 3D morphology and to compute the anatomical aortic valve area (AVA) based on multi-detector computed tomography images. The comparison of the obtained results vs. effective AVA measurements showed a good correlation. Additionally, these methods accounted for asymmetries or anatomical derangements, which would be difficult to correctly capture through either effective AVA or planimetric AVA. \u2022 Second, a tool to quantitively assess the geometry of the tricuspid valve during the cardiac cycle using multidetector CT was developed, in particular focusing on the 3D spatial relationship between the tricuspid annulus and the right coronary artery. The morphological analysis of the annulus and leaflets confirmed data reported in literature. The qualitative and quantitative analysis of the spatial relationship could standardize the analysis protocol and be pivotal in the procedure planning of the percutaneous device implantation that interact with the tricuspid annulus. \u2022 Third, we simulated the systolic closure of three patient specific mitral valve models, derived from CMR datasets, by means of the mass spring model approach. The comparison of the obtained results vs. finite element analyses (considered as the gold-standard) was performed tuning the parameters of the mass spring model, so to obtain the best trade-off between computational expense and accuracy of the results. A configuration mismatch between the two models lower than two times the in-plane resolution of starting imaging data was yielded using a mass spring model set-up that requires, on average, only ten minutes to simulate the valve closure. \u2022 Finally, in the last chapter, we performed a comprehensive analysis which aimed at exploring the morphological and mechanical changes induced by the myxomatous pathologies in the mitral valve tissue. The analysis of mitral valve thickness confirmed the data and patterns reported in literature, while the mechanical test accurately described the behavior of the pathological tissue. A preliminary implementation of this data into finite element simulations suggested that the use of more reliable patient-specific and pathology-specific characterization of the model could improve the realism and the accuracy of the biomechanical simulations

DEVELOPMENT AND IMPLEMENTATION OF NOVEL STRATEGIES TO EXPLOIT 3D ULTRASOUND IMAGING IN CARDIOVASCULAR COMPUTATIONAL BIOMECHANICS

Introduction In the past two decades, major advances have been made in cardiovascular diseases assessment and treatment owing to the advent of sophisticated and more accurate imaging techniques, allowing for better understanding the complexity of 3D anatomical cardiovascular structures1. Volumetric acquisition enables the visualization of cardiac districts from virtually any perspective, better appreciating patient-specific anatomical complexity, as well as an accurate quantitative functional evaluation of chamber volumes and mass avoiding geometric assumptions2. Additionally, this scenario also allowed the evolution from generic to patient-specific 3D cardiac models that, based on in vivo imaging, faithfully represent the anatomy and different cardiac features of a given alive subject, being pivotal either in diagnosis and in planning guidance3. Precise morphological and functional knowledge about either the heart valves\u2019 apparatus and the surrounding structures is crucial when dealing with diagnosis as well as preprocedural planning4. To date, computed tomography (CT) and real-time 3D echocardiography (rt3DE) are typically exploited in this scenario since they allow for encoding comprehensive structural and dynamic information even in the fourth dimension (i.e., time)5,6. However, owing to its cost-effectiveness and very low invasiveness, 3D echocardiography has become the method of choice in most situations for performing the evaluation of cardiac function, developing geometrical models which can provide quantitative anatomical assessment7. Complementing this scenario, computational models have been introduced as numerical engineering tools aiming at adding qualitative and quantitative information on the biomechanical behavior in terms of stress-strain response and other multifactorial parameters8. In particular, over the two last decades, their applications have been ranging from elucidating the heart biomechanics underlying different patho-physiological conditions9 to predicting the effects of either surgical or percutaneous procedures, even comparing several implantation techniques and devices10. At the early stage, most of the studies focused on FE modeling in cardiac environment were based on paradigmatic models11\u201315, being mainly exploited to explore and investigate biomechanical alterations following a specific pathological scenario or again to better understand whether a surgical treatment is better or worse than another one. Differently, nowadays the current generation of computational models heavily exploits the detailed anatomical information yielded by medical imaging to provide patient-specific analyses, paving the way toward the development of virtual surgical-planning tools16\u201319. In this direction, cardiac magnetic resonance (CMR) and CT/micro-CT are the mostly accomplished imaging modality, since they can provide well-defined images thanks to their spatial and temporal resolutions20\u201325. Nonetheless, they cannot be applied routinely in clinical practice, as it can be differently done with rt3DE, progressively became the modality of choice26 since it has no harmful effects on the patient and no radiopaque contrast agent is needed. Despite these advantages, 3D volumetric ultrasound imaging shows intrinsic limitations beyond its limited resolution: i) the deficiency of morphological detail owing to either not so easy achievable detection (e.g., tricuspid valve) or not proper acoustic window, ii) the challenge of tailoring computational models to the patient-specific scenario mimicking the morphology as well as the functionality of the investigated cardiac district (e.g., tethering effect exerted by chordal apparatus in mitral valve insufficiency associated to left ventricular dilation), and iii) the needing to systematically analyse devices performances when dealing with real-life cases where ultrasound imaging is the only performable technique but lacking of standardized acquisition protocol. Main findings In the just described scenario, the main aim of this work was focused on the implementation, development and testing of numerical strategies in order to overcome issues when dealing with 3D ultrasound imaging exploitation towards predictive patient-specific modelling approaches focused on both morphological and biomechanical analyses. Specifically, the first specific objective was the development of a novel approach integrating in vitro imaging and finite element (FE) modeling to evaluate tricuspid valve (TV) biomechanics, facing with the lack of information on anatomical features owing to the clinically evident demanding detection of this anatomical district through in vivo imaging. \u2022 An innovative and semi-automated framework was implemented to generate 3D model of TV, to quantitively describe its 3D morphology and to assess its biomechanical behaviour. At this aim, an image-based in vitro experimental approach was integrated with numerical models based on FE strategy. Experimental measurements directly performed on the benchmark (mock circulation loop) were compared with geometrical features computed on the 3D reconstructed model, pinpointing a global good consistency. Furthermore, obtained realistic reconstructions were used as the input of the FE models, even accounting for proper description of TV leaflets\u2019 anisotropic mechanical response. As done experimentally, simulations reproduced both \u201cincompetent\u201d (FTR) and \u201ccompetent-induced\u201d (PMA), proving the efficiency of such a treatment and suggesting translational potential to the clinic. The second specific aim was the implementation of a computational framework able to reproduce a functionally equivalent model of the mitral valve (MV) sub-valvular apparatus through chordae tendineae topology optimization, aiming at chordae rest length arrangement to be able to include their pre-stress state associated to specific ventricular conformation. \u2022 We sought to establish a framework to build geometrically tractable, functionally equivalent models of the MV chordae tendineae, addressing one of the main topics of the computational scientific literature towards the development of faithful patient-specific models from in vivo imaging. Exploiting the mass spring model (MSM) approach, an iterative tool was proposed aiming to the topology optimization of a paradigmatic chordal apparatus of MVs affected by functional regurgitation, in order to be able to equivalently account for tethering effect exerted by the chordae themselves. The results have shown that the algorithm actually lowered the error between the simulated valve and ground truth data, although the intensity of this improvement is strongly valve-dependent.Finally, the last specific aim was the creation of a numerical strategy able to allow for patient-specific geometrical reconstruction both pre- and post- LVAD implantation, in a specific high-risk clinical scenario being rt3DE the only available imaging technique to be used but without any acquisition protocol. \u2022 We proposed a numerical approach which allowed for a systematic and selective analysis of the mechanism associated to intraventricular thrombus formation and thrombogenic complications in a LVAD-treated dilated left ventricle (LV). Ad-hoc geometry reconstruction workflow was implemented to overcome limitations associated to imaging acquisition in this specific scenario, thus being able to generate computational model of the LV assisted with LVAD. In details, results suggested that blood stasis is influenced either by LVAD flow rate and, to a greater extent, by LV residual contractility, being the positioning of the inflow cannula insertion mandatory to be considered when dealing with LVAD thrombogenic potential assessment

On the design of an interactive, patient-specific surgical simulator for mitral valve repair

Surgical repair of the mitral valve is a difficult procedure that is often avoided in favor of less effective valve replacement because of the associated technical challenges facing non-expert surgeons. In the interest of increasing the rate of valve repair, an accurate, interactive surgical simulator for mitral valve repair was developed. With a haptic interface, users can interact with a mechanical model during simulation to aid in the development of a surgical plan and then virtually implement the procedure to assess its efficacy. Sub-millimeter accuracy was achieved in a validation study, and the system was successfully used by a cardiac surgeon to repair three virtual pathological valves.Engineering and Applied Science

Fast Interactive Simulations of Mitral Valve Repair

Engineering and Applied Science

Mathematical Modeling of Mitral Valve Dynamics: Nonlinear vs Linear Models

A tractable mathematical model of the valve dynamics is developed for the real time computations and in silico planning of the biomechanically consistent surgery on the ruptured chordae of the mitral valve. The geometry and dynamics of the heart contraction and valve closure are restored by digitization of the 2d echocardiography data measured on a patient. The chordae are modeled as branched systems of viscoelastic strings with zero bending rigidity. Both linear and nonlinear rheology of the heart tissues are considered. The corresponding numerical procedure is worked out. The developed model can be used for comparative study of different existing strategy of surgical restoration for individual patients as well as for fast real time computations of optimal location of the neochordae directly during the surgery

Mathematical Modeling of Mitral Valve Dynamics: Nonlinear vs Linear Models

A tractable mathematical model of the valve dynamics is developed for the real time computations and in silico planning of the biomechanically consistent surgery on the ruptured chordae of the mitral valve. The geometry and dynamics of the heart contraction and valve closure are restored by digitization of the 2d echocardiography data measured on a patient. The chordae are modeled as branched systems of viscoelastic strings with zero bending rigidity. Both linear and nonlinear rheology of the heart tissues are considered. The corresponding numerical procedure is worked out. The developed model can be used for comparative study of different existing strategy of surgical restoration for individual patients as well as for fast real time computations of optimal location of the neochordae directly during the surgery

Fast Surgical Simulation to Improve Mitral Valve Repair

Mitral valve repair, the preferred method of treating mitral regurgitation, is a demanding surgical procedure consisting of the resection and approximation of valve tissue. Operating on an arrested heart, the clinician is forced to predict closed valve shape and the effect of surgical modifications. The valve's complex morphology makes this a difficult task, and as a result, the procedure is underperformed by less experienced surgeons in lieu of the simpler, less effective valve replacement.Engineering and Applied Science

Fast Image-Based Mitral Valve Simulation from Individualized Geometry

International audienceBackground: Common surgical procedures on the mitral valve of the heart include modifications to the chordae tendineae. Such interventions are used when there is extensive leaflet prolapse caused by chordae rupture or elongation. Understanding the role of individual chordae tendineae before operating could be helpful to predict if the mitral valve will be competent at peak systole. Biomechanical modeling and simulation can achieve this goal.Methods: We present a method to semi-automatically build a mitral valve computational model from micro CT (computed tomography) scans: after manually picking chordae fiducial points, the leaflets are segmented and the boundary conditions as well as the loading conditions are automatically defined. Fast Finite Element Method (FEM) simulation is carried out using Simulation Open Framework Architecture (SOFA) to reproduce leaflet closure at peak systole. We develop three metrics to evaluate simulation results: i) point-to-surface error with the ground truth reference extracted from the CT image, ii) coaptation surface area of the leaflets and iii) an indication if the simulated closed leaflets leak.Results: We validate our method on three explanted porcine hearts and show that our model predicts the closed valve surface with point-to-surface error of appoximately 1mm, a reasonable coaptation surface area, and absence of leak at peak systole (maximum closed pressure). We also evaluate the sensitivity of our model to changes in various parameters (tissue elasticity, mesh accuracy, and the transformation matrix used for CT scan registration). We also measure the influence of the chordae tendineae positions on simulation results and show that marginal chordae have a greater influence on the final shape than intermediate chordae.Conclusions: The mitral valve simulation can help the surgeon understand valve behaviour and anticipate the outcome of a procedure

Mass-Spring Model for Simulation of Heart Valve Tissue Mechanical Behavior

Heart valves are functionally complex, making surgical repair difficult. Simulation-based surgical planning could facilitate repair, but current finite element (FE) studies are prohibitively slow for rapid, clinically oriented simulations. Mass-spring (M-S) models are fast but can be inaccurate. We quantify speed and accuracy differences between an anisotropic, nonlinear M-S and an efficient FE membrane model for simulating both biaxial and pressure loading of aortic valve (AV) leaflets. The FE model incurs approximately 10 times the computational cost of the M-S model. For simulated biaxial loading, mean error in normal strains is <1% for both FE and M-S models for equibiaxial loading but increases for non-equibiaxial states for the M-S model (7%). The M-S model was less able to simulate shear behavior, with mean strain error of approximately 80%. For pressurized AV leaflets, the M-S model predicts similar leaflet dimensions to the FE model (within 2.6%), and the coaptation zone is similar between models. The M-S model simulates in-plane behavior of AV leaflets considerably faster than the FE model and with only minor differences in the deformed mesh. While the M-S model does not allow explicit control of shear response, shear does not strongly influence shape of the simulated AV under pressure.Engineering and Applied Science