Effect of Edge-to-Edge Mitral Valve Repair on Chordal Strain: Fluid-Structure Interaction Simulations.

Edge-to-edge repair for mitral valve regurgitation is being increasingly performed in high-surgical risk patients using minimally invasive mitral clipping devices. Known procedural complications include chordal rupture and mitral leaflet perforation. Hence, it is important to quantitatively evaluate the effect of edge-to-edge repair on chordal integrity. in this study, we employ a computational mitral valve model to simulate functional mitral regurgitation (FMR) by creating papillary muscle displacement. Edge-to-edge repair is then modeled by simulated coaptation of the mid portion of the mitral leaflets. in the setting of simulated FMR, edge-to-edge repair was shown to sustain low regurgitant orifice area, until a two fold increase in the inter-papillary muscle distance as compared to the normal mitral valve. Strain in the chordae was evaluated near the papillary muscles and the leaflets. Following edge-to-edge repair, strain near the papillary muscles did not significantly change relative to the unrepaired valve, while strain near the leaflets increased significantly relative to the unrepaired valve. These data demonstrate the potential for computational simulations to aid in the pre-procedural evaluation of possible complications such as chordal rupture and leaflet perforation following percutaneous edge-to-edge repair.

Fluid-structure interaction and structural analyses using a comprehensive mitral valve model with 3D chordal structure.

Over the years, three-dimensional models of the mitral valve have generally been organized around a simplified anatomy. Leaflets have been typically modeled as membranes, tethered to discrete chordae typically modeled as one-dimensional, non-linear cables. Yet, recent, high-resolution medical images have revealed that there is no clear boundary between the chordae and the leaflets. In fact, the mitral valve has been revealed to be more of a webbed structure whose architecture is continuous with the chordae and their extensions into the leaflets. Such detailed images can serve as the basis of anatomically accurate, subject-specific models, wherein the entire valve is modeled with solid elements that more faithfully represent the chordae, the leaflets, and the transition between the two. These models have the potential to enhance our understanding of mitral valve mechanics and to re-examine the role of the mitral valve chordae, which heretofore have been considered to be 'invisible' to the fluid and to be of secondary importance to the leaflets. However, these new models also require a rethinking of modeling assumptions. In this study, we examine the conventional practice of loading the leaflets only and not the chordae in order to study the structural response of the mitral valve apparatus. Specifically, we demonstrate that fully resolved 3D models of the mitral valve require a fluid-structure interaction analysis to correctly load the valve even in the case of quasi-static mechanics. While a fluid-structure interaction mode is still more computationally expensive than a structural-only model, we also show that advances in GPU computing have made such models tractable. Copyright © 2016 John Wiley & Sons, Ltd.

Fluid-Structure Interaction Analysis of Ruptured Mitral Chordae Tendineae.

The chordal structure is a part of mitral valve geometry that has been commonly neglected or simplified in computational modeling due to its complexity. However, these simplifications cannot be used when investigating the roles of individual chordae tendineae in mitral valve closure. For the first time, advancements in imaging, computational techniques, and hardware technology make it possible to create models of the mitral valve without simplifications to its complex geometry, and to quickly run validated computer simulations that more realistically capture its function. Such simulations can then be used for a detailed analysis of chordae-related diseases. In this work, a comprehensive model of a subject-specific mitral valve with detailed chordal structure is used to analyze the distinct role played by individual chordae in closure of the mitral valve leaflets. Mitral closure was simulated for 51 possible chordal rupture points. Resultant regurgitant orifice area and strain change in the chordae at the papillary muscle tips were then calculated to examine the role of each ruptured chorda in the mitral valve closure. For certain subclassifications of chordae, regurgitant orifice area was found to trend positively with ruptured chordal diameter, and strain changes correlated negatively with regurgitant orifice area. Further advancements in clinical imaging modalities, coupled with the next generation of computational techniques will enable more physiologically realistic simulations.

High-resolution subject-specific mitral valve imaging and modeling: experimental and computational methods.

The diversity of mitral valve (MV) geometries and multitude of surgical options for correction of MV diseases necessitates the use of computational modeling. Numerical simulations of the MV would allow surgeons and engineers to evaluate repairs, devices, procedures, and concepts before performing them and before moving on to more costly testing modalities. Constructing, tuning, and validating these models rely upon extensive in vitro characterization of valve structure, function, and response to change due to diseases. Micro-computed tomography ([Formula: see text]CT) allows for unmatched spatial resolution for soft tissue imaging. However, it is still technically challenging to obtain an accurate geometry of the diastolic MV. We discuss here the development of a novel technique for treating MV specimens with glutaraldehyde fixative in order to minimize geometric distortions in preparation for [Formula: see text]CT scanning. The technique provides a resulting MV geometry which is significantly more detailed in chordal structure, accurate in leaflet shape, and closer to its physiological diastolic geometry. In this paper, computational fluid-structure interaction (FSI) simulations are used to show the importance of more detailed subject-specific MV geometry with 3D chordal structure to simulate a proper closure validated against [Formula: see text]CT images of the closed valve. Two computational models, before and after use of the aforementioned technique, are used to simulate closure of the MV.

Comparison of realistic and idealized breathing patterns in computational models of airflow and vapor dosimetry in the rodent upper respiratory tract.

CONTEXT: Computational fluid dynamics (CFD) simulations of airflows coupled with physiologically based pharmacokinetic (PBPK) modeling of respiratory tissue doses of airborne materials have traditionally used either steady-state inhalation or a sinusoidal approximation of the breathing cycle for airflow simulations despite their differences from normal breathing patterns. OBJECTIVE: Evaluate the impact of realistic breathing patterns, including sniffing, on predicted nasal tissue concentrations of a reactive vapor that targets the nose in rats as a case study. MATERIALS AND METHODS: Whole-body plethysmography measurements from a free-breathing rat were used to produce profiles of normal breathing, sniffing and combinations of both as flow inputs to CFD/PBPK simulations of acetaldehyde exposure. RESULTS: For the normal measured ventilation profile, modest reductions in time- and tissue depth-dependent areas under the curve (AUC) acetaldehyde concentrations were predicted in the wet squamous, respiratory and transitional epithelium along the main airflow path, while corresponding increases were predicted in the olfactory epithelium, especially the most distal regions of the ethmoid turbinates, versus the idealized profile. The higher amplitude/frequency sniffing profile produced greater AUC increases over the idealized profile in the olfactory epithelium, especially in the posterior region. CONCLUSIONS: The differences in tissue AUCs at known lesion-forming regions for acetaldehyde between normal and idealized profiles were minimal, suggesting that sinusoidal profiles may be used for this chemical and exposure concentration. However, depending upon the chemical, exposure system and concentration and the time spent sniffing, the use of realistic breathing profiles, including sniffing, could become an important modulator for local tissue dose predictions.

Development of a Zealand white rabbit deposition model to study inhalation anthrax.

Despite using rabbits in several inhalation exposure experiments to study diseases such as anthrax, there is a lack of understanding regarding deposition characteristics and fate of inhaled particles (bio-aerosols and viruses) in the respiratory tracts of rabbits. Such information allows dosimetric extrapolation to humans to inform human outcomes. The lung geometry of the New Zealand white rabbit (referred to simply as rabbits throughout the article) was constructed using recently acquired scanned images of the conducting airways of rabbits and available information on its acinar region. In addition, functional relationships were developed for the lung and breathing parameters of rabbits as a function of body weight. The lung geometry and breathing parameters were used to extend the existing deposition model for humans and several other species to rabbits. Evaluation of the deposition model for rabbits was made by comparing predictions with available measurements in the literature. Deposition predictions in the lungs of rabbits indicated smaller deposition fractions compared to those found in humans across various particle diameter ranges. The application of the deposition model for rabbits was demonstrated by extrapolating deposition predictions in rabbits to find equivalent human exposure concentrations assuming the same dose-response relationship between the two species. Human equivalent exposure concentration levels were found to be much smaller than those for rabbits.

Fluid-Structure Interaction Analysis of Papillary Muscle Forces Using a Comprehensive Mitral Valve Model with 3D Chordal Structure.

Numerical models of native heart valves are being used to study valve biomechanics to aid design and development of repair procedures and replacement devices. These models have evolved from simple two-dimensional approximations to complex three-dimensional, fully coupled fluid-structure interaction (FSI) systems. Such simulations are useful for predicting the mechanical and hemodynamic loading on implanted valve devices. A current challenge for improving the accuracy of these predictions is choosing and implementing modeling boundary conditions. In order to address this challenge, we are utilizing an advanced in vitro system to validate FSI conditions for the mitral valve system. Explanted ovine mitral valves were mounted in an in vitro setup, and structural data for the mitral valve was acquired with [Formula: see text]CT. Experimental data from the in vitro ovine mitral valve system were used to validate the computational model. As the valve closes, the hemodynamic data, high speed leaflet dynamics, and force vectors from the in vitro system were compared to the results of the FSI simulation computational model. The total force of 2.6 N per papillary muscle is matched by the computational model. In vitro and in vivo force measurements enable validating and adjusting material parameters to improve the accuracy of computational models. The simulations can then be used to answer questions that are otherwise not possible to investigate experimentally. This work is important to maximize the validity of computational models of not just the mitral valve, but any biomechanical aspect using computational simulation in designing medical devices.

Comparative Risks of Aldehyde Constituents in Cigarette Smoke Using Transient Computational Fluid Dynamics/Physiologically Based Pharmacokinetic Models of the Rat and Human Respiratory Tracts.

Computational fluid dynamics (CFD) modeling is well suited for addressing species-specific anatomy and physiology in calculating respiratory tissue exposures to inhaled materials. In this study, we overcame prior CFD model limitations to demonstrate the importance of realistic, transient breathing patterns for predicting site-specific tissue dose. Specifically, extended airway CFD models of the rat and human were coupled with airway region-specific physiologically based pharmacokinetic (PBPK) tissue models to describe the kinetics of 3 reactive constituents of cigarette smoke: acrolein, acetaldehyde and formaldehyde. Simulations of aldehyde no-observed-adverse-effect levels for nasal toxicity in the rat were conducted until breath-by-breath tissue concentration profiles reached steady state. Human oral breathing simulations were conducted using representative aldehyde yields from cigarette smoke, measured puff ventilation profiles and numbers of cigarettes smoked per day. As with prior steady-state CFD/PBPK simulations, the anterior respiratory nasal epithelial tissues received the greatest initial uptake rates for each aldehyde in the rat. However, integrated time- and tissue depth-dependent area under the curve (AUC) concentrations were typically greater in the anterior dorsal olfactory epithelium using the more realistic transient breathing profiles. For human simulations, oral and laryngeal tissues received the highest local tissue dose with greater penetration to pulmonary tissues than predicted in the rat. Based upon lifetime average daily dose comparisons of tissue hot-spot AUCs (top 2.5% of surface area-normalized AUCs in each region) and numbers of cigarettes smoked/day, the order of concern for human exposures was acrolein > formaldehyde > acetaldehyde even though acetaldehyde yields were 10-fold greater than formaldehyde and acrolein.

Comparison of CT-derived ventilation maps with deposition patterns of inhaled microspheres in rats.

PURPOSE: Computer models for inhalation toxicology and drug-aerosol delivery studies rely on ventilation pattern inputs for predictions of particle deposition and vapor uptake. However, changes in lung mechanics due to disease can impact airflow dynamics and model results. It has been demonstrated that non-invasive, in vivo, 4DCT imaging (3D imaging at multiple time points in the breathing cycle) can be used to map heterogeneities in ventilation patterns under healthy and disease conditions. The purpose of this study was to validate ventilation patterns measured from CT imaging by exposing the same rats to an aerosol of fluorescent microspheres (FMS) and examining particle deposition patterns using cryomicrotome imaging. MATERIALS AND METHODS: Six male Sprague-Dawley rats were intratracheally instilled with elastase to a single lobe to induce a heterogeneous disease. After four weeks, rats were imaged over the breathing cycle by CT then immediately exposed to an aerosol of ∼ 1 µm FMS for ∼ 5 minutes. After the exposure, the lungs were excised and prepared for cryomicrotome imaging, where a 3D image of FMS deposition was acquired using serial sectioning. Cryomicrotome images were spatially registered to match the live CT images to facilitate direct quantitative comparisons of FMS signal intensity with the CT-based ventilation maps. RESULTS: Comparisons of fractional ventilation in contiguous, non-overlapping, 3D regions between CT-based ventilation maps and FMS images showed strong correlations in fractional ventilation (r = 0.888, p < 0.0001). CONCLUSION: We conclude that ventilation maps derived from CT imaging are predictive of the 1 µm aerosol deposition used in ventilation-perfusion heterogeneity inhalation studies.

Respiratory tract lung geometry and dosimetry model for male Sprague-Dawley rats.

While inhalation toxicological studies of various compounds have been conducted using a number of different strains of rats, mechanistic dosimetry models have only had tracheobronchial (TB) structural data for Long-Evans rats, detailed morphometric data on the alveolar region of Sprague-Dawley rats and limited alveolar data on other strains. Based upon CT imaging data for two male Sprague-Dawley rats, a 15-generation, symmetric typical path model was developed for the TB region. Literature data for the alveolar region of Sprague-Dawley rats were analyzed to develop an eight-generation model, and the two regions were joined to provide a complete lower respiratory tract model for Sprague-Dawley rats. The resulting lung model was used to examine particle deposition in Sprague-Dawley rats and to compare these results with predicted deposition in Long-Evans rats. Relationships of various physiologic variables and lung volumes were either developed in this study or extracted from the literature to provide the necessary input data for examining particle deposition. While the lengths, diameters and branching angles of the TB airways differed between the two Sprague-Dawley rats, the predicted deposition patterns in the three major respiratory tract regions were very similar. Between Sprague-Dawley and Long-Evans rats, significant differences in TB and alveolar predicted deposition fractions were observed over a wide range of particle sizes, with TB deposition fractions being up to 3- to 4-fold greater in Sprague-Dawley rats and alveolar deposition being significantly greater in Long-Evans rats. Thus, strain-specific lung geometry models should be used for particle deposition calculations and interspecies dose comparisons.

In situ casting and imaging of the rat airway tree for accurate 3D reconstruction.

The use of anatomically accurate, animal-specific airway geometries is important for understanding and modeling the physiology of the respiratory system. One approach for acquiring detailed airway architecture is to create a bronchial cast of the conducting airways. However, typical casting procedures either do not faithfully preserve the in vivo branching angles or produce rigid casts that when removed for imaging are fragile and thus easily damaged. We address these problems by creating an in situ bronchial cast of the conducting airways in rats that can be subsequently imaged in situ using three-dimensional micro-CT imaging. We also demonstrate that deformations in airway branch angles resulting from the casting procedure are small, and that these angle deformations can be reversed through an interactive adjustment of the segmented cast geometry. Animal work was approved by the Institutional Animal Care and Use Committee of Pacific Northwest National Laboratory.

Dynamic multiscale boundary conditions for 4D CT of healthy and emphysematous rats.

Changes in the shape of the lung during breathing determine the movement of airways and alveoli, and thus impact airflow dynamics. Modeling airflow dynamics in health and disease is a key goal for predictive multiscale models of respiration. Past efforts to model changes in lung shape during breathing have measured shape at multiple breath-holds. However, breath-holds do not capture hysteretic differences between inspiration and expiration resulting from the additional energy required for inspiration. Alternatively, imaging dynamically--without breath-holds--allows measurement of hysteretic differences. In this study, we acquire multiple micro-CT images per breath (4DCT) in live rats, and from these images we develop, for the first time, dynamic volume maps. These maps show changes in local volume across the entire lung throughout the breathing cycle and accurately predict the global pressure-volume (PV) hysteresis. Male Sprague-Dawley rats were given either a full- or partial-lung dose of elastase or saline as a control. After three weeks, 4DCT images of the mechanically ventilated rats under anesthesia were acquired dynamically over the breathing cycle (11 time points, ≤100 ms temporal resolution, 8 cmH2O peak pressure). Non-rigid image registration was applied to determine the deformation gradient--a numerical description of changes to lung shape--at each time point. The registration accuracy was evaluated by landmark identification. Of 67 landmarks, one was determined misregistered by all three observers, and 11 were determined misregistered by two observers. Volume change maps were calculated on a voxel-by-voxel basis at all time points using both the Jacobian of the deformation gradient and the inhaled air fraction. The calculated lung PV hysteresis agrees with pressure-volume curves measured by the ventilator. Volume maps in diseased rats show increased compliance and ventilation heterogeneity. Future predictive multiscale models of rodent respiration may leverage such volume maps as boundary conditions.

An efficient algorithm for mapping imaging data to 3D unstructured grids in computational biomechanics.

Geometries for organ scale and multiscale simulations of organ function are now routinely derived from imaging data. However, medical images may also contain spatially heterogeneous information other than geometry that are relevant to such simulations either as initial conditions or in the form of model parameters. In this manuscript, we present an algorithm for the efficient and robust mapping of such data to imaging-based unstructured polyhedral grids in parallel. We then illustrate the application of our mapping algorithm to three different mapping problems: (i) the mapping of MRI diffusion tensor data to an unstructured ventricular grid; (ii) the mapping of serial cyrosection histology data to an unstructured mouse brain grid; and (iii) the mapping of computed tomography-derived volumetric strain data to an unstructured multiscale lung grid. Execution times and parallel performance are reported for each case.

An Implicit Elastic Theory for Lung Parenchyma.

The airways and parenchyma of lung experience large deformations during normal respiration. Spatially accurate predictions of airflow patterns and aerosol transport therefore require respiration to be modeled as a fluid-structure interaction problem. Such computational models in turn require constitutive models for the parencyhma that are both accurate and efficient. Herein, an implicit theory of elasticity is derived from thermodynamics to meet this need, leading to a generic template for strain-energy that is shown to be an exact analogue for the well-known Fung model that is the root of modern constitutive theory of tissues. To support this theory, we also propose a novel definition of Lagrangian strain rate. Unlike the classic definition of Lagrangian strain rate, this new definition is separable into volumetric and deviatoric terms, a separation that is both mathematically and physically justified. Within this framework, a novel material model capable of describing the elastic contribution of the nonlinear response of parenchyma is constructed and characterized against published data.

Development of a rhesus monkey lung geometry model and application to particle deposition in comparison to humans.

The exposure-dose-response characterization of an inhalation hazard established in an animal species needs to be translated to an equivalent characterization in humans relative to comparable doses or exposure scenarios. Here, the first geometry model of the conducting airways for rhesus monkeys is developed based upon CT images of the conducting airways of a 6-month-old male, rhesus monkey. An algorithm was developed for adding the alveolar region airways using published rhesus morphometric data. The resultant lung geometry model can be used in mechanistic particle or gaseous dosimetry models. Such dosimetry models require estimates of the upper respiratory tract volume of the animal and the functional residual capacity, as well as of the tidal volume and breathing frequency of the animal. The relationship of these variables to rhesus monkeys of differing body weights was established by synthesizing and modeling published data as well as modeling pulmonary function measurements on 121 rhesus control animals. Deposition patterns of particles up to 10 µm in size were examined for endotracheal and and up to 5 µm for spontaneous breathing in infant and young adult monkeys and compared to those for humans. Deposition fraction of respirable size particles was found to be higher in the conducting airways of infant and young adult rhesus monkeys compared to humans. Due to the filtering effect of the conducting airways, pulmonary deposition in rhesus monkeys was lower than that in humans. Future research areas are identified that would either allow replacing assumptions or improving the newly developed lung model.

Phase-contrast MRI and CFD modeling of apparent ³He gas flow in rat pulmonary airways.

Phase-contrast (PC) magnetic resonance imaging (MRI) with hyperpolarized ³He is potentially useful for developing and testing patient-specific models of pulmonary airflow. One challenge, however, is that PC-MRI provides apparent values of local ³He velocity that not only depend on actual airflow but also on gas diffusion. This not only blurs laminar flow patterns in narrow airways but also introduces anomalous airflow structure that reflects gas-wall interactions. Here, both effects are predicted in a live rat using computational fluid dynamics (CFD), and for the first time, simulated patterns of apparent ³He gas velocity are compared with in vivo PC-MRI. Results show (1) that correlations (R²) between measured and simulated airflow patterns increase from 0.23 to 0.79 simply by accounting for apparent ³He transport, and (2) that remaining differences are mainly due to uncertain airway segmentation and partial volume effects stemming from relatively coarse MRI resolution. Higher-fidelity testing of pulmonary airflow predictions should therefore be possible with future imaging improvements.

Comparative computational modeling of airflows and vapor dosimetry in the respiratory tracts of rat, monkey, and human.

Computational fluid dynamics (CFD) models are useful for predicting site-specific dosimetry of airborne materials in the respiratory tract and elucidating the importance of species differences in anatomy, physiology, and breathing patterns. We improved the imaging and model development methods to the point where CFD models for the rat, monkey, and human now encompass airways from the nose or mouth to the lung. A total of 1272, 2172, and 135 pulmonary airways representing 17±7, 19±9, or 9±2 airway generations were included in the rat, monkey and human models, respectively. A CFD/physiologically based pharmacokinetic model previously developed for acrolein was adapted for these anatomically correct extended airway models. Model parameters were obtained from the literature or measured directly. Airflow and acrolein uptake patterns were determined under steady-state inhalation conditions to provide direct comparisons with prior data and nasal-only simulations. Results confirmed that regional uptake was sensitive to airway geometry, airflow rates, acrolein concentrations, air:tissue partition coefficients, tissue thickness, and the maximum rate of metabolism. Nasal extraction efficiencies were predicted to be greatest in the rat, followed by the monkey, and then the human. For both nasal and oral breathing modes in humans, higher uptake rates were predicted for lower tracheobronchial tissues than either the rat or monkey. These extended airway models provide a unique foundation for comparing material transport and site-specific tissue uptake across a significantly greater range of conducting airways in the rat, monkey, and human than prior CFD models.

Branch-based model for the diameters of the pulmonary airways: accounting for departures from self-consistency and registration errors.

We examine a previously published branch-based approach for modeling airway diameters that is predicated on the assumption of self-consistency across all levels of the tree. We mathematically formulate this assumption, propose a method to test it and develop a more general model to be used when the assumption is violated. We discuss the effect of measurement error on the estimated models and propose methods that take account of error. The methods are illustrated on data from MRI and CT images of silicone casts of two rats, two normal monkeys, and one ozone-exposed monkey. Our results showed substantial departures from self-consistency in all five subjects. When departures from self-consistency exist, we do not recommend using the self-consistency model, even as an approximation, as we have shown that it may likely lead to an incorrect representation of the diameter geometry. The new variance model can be used instead. Measurement error has an important impact on the estimated morphometry models and needs to be addressed in the analysis.

Hypo-elastic model for lung parenchyma.

A simple, isotropic, elastic constitutive model for the spongy tissue in lung is formulated from the theory of hypo-elasticity. The model is shown to exhibit a pressure dependent behavior that has been interpreted in the literature as indicating extensional anisotropy. In contrast, we show that this behavior arises naturally from an analysis of isotropic hypo-elastic invariants and is a result of non-linearity, not anisotropy. The response of the model is determined analytically for several boundary value problems used for material characterization. These responses give insight into both the material behavior as well as admissible bounds on parameters. The model predictions are compared with published experimental data for dog lung.

A multiscale bidirectional coupling framework.

The lung is geometrically articulated across multiple scales from the trachea to the alveoli. A major computational challenge is to tightly link ODEs that describe lower scales to 3D finite element or finite volume models of airway mechanics using iterative communication between scales. In this study, we developed a novel multiscale computational framework for bidirectionally coupling 3D CFD models and systems of lower order ODEs. To validate the coupling framework, a four and eight generation Weibel lung model was constructed. For the coupled CFD-ODE simulations, the lung models were truncated at different generations and a RL circuit represented the truncated portion. The flow characteristics from the coupled models were compared to untruncated full 3D CFD models at peak inhalation and peak exhalation. Results showed that at no time or simulation was the difference in mass flux and/or pressure at a given location between uncoupled and coupled models was greater than 2.43%. The flow characteristics at prime locations for the coupled models showed good agreement to uncoupled models. Remarkably, due to reuse of the Krylov subspace, the cost of the ODE coupling is not much greater than uncoupled full 3D-CFD computations with simple prescribed pressure values at the outlets.