Andrew Drach

Mitral Valve Chordae Tendineae: Topological and Geometrical Characterization

Mitral valve (MV) closure depends upon the proper function of each component of the valve apparatus, which includes the annulus, leaflets, and chordae tendineae (CT). Geometry plays a major role in MV mechanics and thus highly impacts the accuracy of computational models simulating MV function and repair. While the physiological geometry of the leaflets and annulus have been previously investigated, little effort has been made to quantitatively and objectively describe CT geometry. The CT constitute a fibrous tendon-like structure projecting from the papillary muscles (PMs) to the leaflets, thereby evenly distributing the loads placed on the MV during closure. Because CT play a major role in determining the shape and stress state of the MV as a whole, their geometry must be well characterized. In the present work, a novel and comprehensive investigation of MV CT geometry was performed to more fully quantify CT anatomy. In vitro micro-tomography 3D images of ovine MVs were acquired, segmented, then analyzed using a curve-skeleton transform. The resulting data was used to construct B-spline geometric representations of the CT structures, enriched with a continuous field of cross-sectional area (CSA) data. Next, Reeb graph models were developed to analyze overall topological patterns, along with dimensional attributes such as segment lengths, 3D orientations, and CSA. Reeb graph results revealed that the topology of ovine MV CT followed a full binary tree structure. Moreover, individual chords are mostly planar geometries that together form a 3D load-bearing support for the MV leaflets. We further demonstrated that, unlike flow-based branching patterns, while individual CT branches became thinner as they propagated further away from the PM heads towards the leaflets, the total CSA almost doubled. Overall, our findings indicate a certain level of regularity in structure, and suggest that population-based MV CT geometric models can be generated to improve current MV repair procedures.

A Comprehensive Framework for the Characterization of the Complete Mitral Valve Geometry for the Development of a Population-Averaged Model

Simulations of the biomechanical behavior of the Mitral Valve (MV) based on simplified geometric models are difficult to interpret due to significant intra-patient variations and pathologies in the MV geometry. Thus, it is critical to use a systematic approach to characterization and population-averaging of the patient-specific models. We introduce a multi-scale modeling framework for characterizing the entire MV apparatus geometry via a relatively small set of parameters. The leaflets and annulus are analyzed using a superquadric surface model superimposed with fine-scale filtered level-set field. Filtering of fine-scale features is performed in a spectral space to allow control of resolution, resampling and robust averaging. Chordae tendineae structure is modeled using a medial axis representation with superimposed filtered pointwise cross-sectional area field. The chordae topology is characterized using orientation and spatial distribution functions. The methodology is illustrated with the analysis of an ovine MV microtomography imaging data.

Population-Averaged Geometric Model of Mitral Valve From Patient-Specific Imaging Data

The mitral valve (MV) is one of the atrioventricular heart valves and regulates the blood flow between the left atrium and ventricle during the cardiac cycle. Its anatomical structure is comprised of anterior and posterior leaflets, chordae tendineae, and papillary muscles. The main function of the MV is to prevent blood flow regurgitation back into the left atrium during systole. Abnormalities in geometry of MV can lead to mitral insufficiency disorder, which requires either valve replacement or surgical repair to restore proper MV coaptation. Annually, over 40,000 patients in the U.S. alone are treated for MV disorders [1]. In the past two decades, the emphasis in MV treatment has been shifting from replacement toward repair due to lower morbidity and mortality of the latter approach [2]. However, the natural anatomical variability of human MV geometry precludes the use of single or simplified geometries for the simulation of surgical repair. One of the ways to address this issue is by using patient-specific diagnosis and modeling [3], or population-averaged geometric models of MV. The existing approaches for characterization and reconstruction of the cardiovascular organ-level geometry include fitting of predefined sets of nonuniform rational B-splines (NURBS) to the imaging data [4], and using spheroidal harmonics representations [5]. Even though it is possible to construct average geometric models this way, the analysis of anatomical shape variations becomes difficult in this setting because of the confounding of dimensional and shape descriptors. At the same time, none of the existing methods allow integration of the high-fidelity in vitro data with lower-resolution in vivo imaging in a consistent manner. In this work, we formulate the framework for building the population-averaged geometric model of MV, which lends to straightforward analysis of dimensional and anatomical variations. In the sections to follow, we discuss the procedure and advantages of this method for the development of robust medical devices and treatment procedures.

Multi-resolution geometric modeling of the mitral heart valve leaflets

An essential element of cardiac function, the mitral valve (MV) ensures proper directional blood flow between the left heart chambers. Over the past two decades, computational simulations have made marked advancements toward providing powerful predictive tools to better understand valvular function and improve treatments for MV disease. However, challenges remain in the development of robust means for the quantification and representation of MV leaflet geometry. In this study, we present a novel modeling pipeline to quantitatively characterize and represent MV leaflet surface geometry. Our methodology utilized a two-part additive decomposition of the MV geometric features to decouple the macro-level general leaflet shape descriptors from the leaflet fine-scale features. First, the general shapes of five ovine MV leaflets were modeled using superquadric surfaces. Second, the finer-scale geometric details were captured, quantified, and reconstructed via a 2D Fourier analysis with an additional sparsity constraint. This spectral approach allowed us to easily control the level of geometric details in the reconstructed geometry. The results revealed that our methodology provided a robust and accurate approach to develop MV-specific models with an adjustable level of spatial resolution and geometric detail. Such fully customizable models provide the necessary means to perform computational simulations of the MV at a range of geometric accuracies in order to identify the level of complexity required to achieve predictive MV simulations.

A non-invasive method for the determination of in vivo mitral valve leaflet strains: Determination of in vivo mitral valve leaflet strains

Assessment of mitral valve (MV) function is important in many diagnostic, prognostic, and surgical planning applications for treatment of MV disease. Yet, to date, there are no accepted noninvasive methods for determination of MV leaflet deformation, which is a critical metric of MV function. In this study, we present a novel, completely noninvasive computational method to estimate MV leaflet in-plane strains from clinical-quality real-time three-dimensional echocardiography (rt-3DE) images. The images were first segmented to produce meshed medial-surface leaflet geometries of the open and closed states. To establish material point correspondence between the two states, an image-based morphing pipeline was implemented within a finite element (FE) modeling framework in which MV closure was simulated by pressurizing the open-state geometry, and local corrective loads were applied to enforce the actual MV closed shape. This resulted in a complete map of local systolic leaflet membrane strains, obtained from the final FE mesh configuration. To validate the method, we utilized an extant in vitro database of fiducially labeled MVs, imaged in conditions mimicking both the healthy and diseased states. Our method estimated local anisotropic in vivo strains with less than 10% error and proved to be robust to changes in boundary conditions similar to those observed in ischemic MV disease. Next, we applied our methodology to ovine MVs imaged in vivo with rt-3DE and compared our results to previously published findings of in vivo MV strains in the same type of animal as measured using surgically sutured fiducial marker arrays. In regions encompassed by fiducial markers, we found no significant differences in circumferential(P = 0.240) or radial (P = 0.808) strain estimates between the marker-based measurements and our novel noninvasive method. This method can thus be used for model validation as well as for studies of MV disease and repair.

Corrosion Rates and Changes in Mechanical Properties of Copper Alloys due to Seawater Exposure

A field study on corrosion was conducted on several copper alloys subjected to prolonged exposure in seawater. Rectangular plates made of nine alloys were deployed for a year in the North Atlantic Ocean. Material loss rates were quantified by measuring the difference in weight between the initial virgin specimens and the cleaned specimens after recovery. Changes in mechanical properties due to the seawater exposure were quantified by performing standard uniaxial tension tests. Stress-strain dependence was obtained for each of the tested materials using the digital image correlation technique. Some degradation of tensile strength was observed in all alloys, but for most of them it was not substantial.© 2012 ASME

Credibility, Replicability, and Reproducibility in Simulation for Biomedicine and Clinical Applications in Neuroscience

Modeling and simulation in computational neuroscience is currently a research enterprise to better understand neural systems. It is not yet directly applicable to the problems of patients with brain disease. To be used for clinical applications, there must not only be considerable progress in the field but also a concerted effort to use best practices in order to demonstrate model credibility to regulatory bodies, to clinics and hospitals, to doctors, and to patients. In doing this for neuroscience, we can learn lessons from long-standing practices in other areas of simulation (aircraft, computer chips), from software engineering, and from other biomedical disciplines. In this manuscript, we introduce some basic concepts that will be important in the development of credible clinical neuroscience models: reproducibility and replicability; verification and validation; model configuration; and procedures and processes for credible mechanistic multiscale modeling. We also discuss how garnering strong community involvement can promote model credibility. Finally, in addition to direct usage with patients, we note the potential for simulation usage in the area of Simulation-Based Medical Education, an area which to date has been primarily reliant on physical models (mannequins) and scenario-based simulations rather than on numerical simulations.

Experimental Studies and Numerical Modeling of Copper Nets in Marine Environment

Copper alloy netting is increasingly used for offshore aquaculture, harbor protection and other marine applications. Its advantageous characteristics include high resistance to biofouling and increased strength compared to polymer nets. However, the hydrodynamic properties of copper nets are not well studied. In this paper, the results of experimental studies of drag forces on copper alloy net panels are reported. Based on these studies, empirical values for drag coefficients are proposed for various types of copper nets, and compared to the corresponding data for polymer netting. It is shown that copper nets exhibit significantly lower resistance to the current flow which corresponds to lower values of drag coefficient. Coefficients obtained from the experiments are incorporated into the finite element program Aqua-FE, developed at the University of New Hampshire for analysis of flexible structures subjected to waves and currents in marine environment. The results of the numerical simulations for a small volume fish cage, subjected to two different sets of environmental conditions, are analyzed to compare how introduction of copper netting instead of traditional nylon nets affects the dynamic response of the system.Copyright

Design approach of an aquaculture cage system for deployment in the constructed channel flow environments of a power plant

This study provides an engineering approach for designing an aquaculture cage system for use in constructed channel flow environments. As sustainable aquaculture has grown globally, many novel techniques have been introduced such as those implemented in the global Atlantic salmon industry. The advent of several highly sophisticated analysis software systems enables the development of such novel engineering techniques. These software systems commonly include three-dimensional (3D) drafting, computational fluid dynamics, and finite element analysis. In this study, a combination of these analysis tools is applied to evaluate a conceptual aquaculture system for potential deployment in a power plant effluent channel. The channel is supposedly clean; however, it includes elevated water temperatures and strong currents. The first portion of the analysis includes the design of a fish cage system with specific net solidities using 3D drafting techniques. Computational fluid dynamics is then applied to evaluate the flow reduction through the system from the previously generated solid models. Implementing the same solid models, a finite element analysis is performed on the critical components to assess the material stresses produced by the drag force loads that are calculated from the fluid velocities.

Development of a Functionally Equivalent Model of the Mitral Valve Chordae Tendineae Through Topology Optimization

Ischemic mitral regurgitation (IMR) is a currently prevalent disease in the US that is projected to become increasingly common as the aging population grows. In recent years, image-based simulations of mitral valve (MV) function have improved significantly, providing new tools to refine IMR treatment. However, clinical implementation of MV simulations has long been hindered as the in vivo MV chordae tendineae (MVCT) geometry cannot be captured with sufficient fidelity for computational modeling. In the current study, we addressed this challenge by developing a method to produce functionally equivalent MVCT models that can be built from the image-based MV leaflet geometry alone. We began our analysis using extant micron-resolution 3D imaging datasets to first build anatomically accurate MV models. We then systematically simplified the native MVCT structure to generate a series of synthetic models by consecutively removing key anatomic features, such as the thickness variations, branching patterns, and chordal origin distributions. In addition, through topology optimization, we identified the minimal structural complexity required to capture the native MVCT behavior. To assess the performance and predictive power of each synthetic model, we analyzed their performance by comparing the mismatch in simulated MV closed shape, as well as the strain and stress tensors, to ground-truth MV models. Interestingly, our results revealed a substantial redundancy in the anatomic structure of native chordal anatomy. We showed that the closing behavior of complete MV apparatus under normal, diseased, and surgically repaired scenarios can be faithfully replicated by a functionally equivalent MVCT model comprised of two representative papillary muscle heads, single strand chords, and a uniform insertion distribution with a density of 15 insertions/cm2. Hence, even though the complete sub-valvular structure is mostly missing in in vivo MV images, we believe our approach will allow for the development of patient-specific complete MV models for surgical repair planning.