Search

Objective: Severe congenital aortic valve pathology in the growing patient remains a challenging clinical scenario. Bicuspidization of the diseased aortic valve has proven to be a promising repair technique with acceptable durability. However, most understanding of the procedure is empirical and retrospective. This work seeks to design the optimal gross morphology associated with surgical bicuspidization with simulations, based on the hypothesis that modifications to the free edge length cause or relieve stenosis. Methods: Model bicuspid valves were constructed with varying free edge lengths and gross morphology. Fluid-structure interaction simulations were conducted in a single patient-specific model geometry. The models were evaluated for primary targets of stenosis and regurgitation. Secondary targets were assessed and included qualitative hemodynamics, geometric height, effective height, orifice area and prolapse. Results: Stenosis decreased with increasing free edge length and was pronounced with free edge length less than or equal to 1.3 times the annular diameter d. With free edge length 1.5d or greater, no stenosis occurred. All models were free of regurgitation. Substantial prolapse occurred with free edge length greater than or equal to 1.7d. Conclusions: Free edge length greater than or equal to 1.5d was required to avoid aortic stenosis in simulations. Cases with free edge length greater than or equal to 1.7d showed excessive prolapse and other changes in gross morphology. Cases with free edge length 1.5-1.6d have a total free edge length approximately equal to the annular circumference and appeared optimal. These effects should be studied in vitro and in animal studies.

This thesis is concerned with modeling and simulation of the mitral valve, one of the four valves in the human heart. The valve is composed of leaflets attached to a ring, the free edges of which are supported by a system of chordae, which themselves are anchored to muscles inside the heart. First, we examine valve anatomy and show the results of original dissections. These display the gross anatomy and information on fiber structure of the mitral valve. Next, we build a model valve following a design-based approach to elasticity. We incorporate information from the dissections to specify the fiber topology of this model. We assume the valve achieves mechanical equilibrium while supporting a static pressure load. The solution to the resulting differential equations determines the pressurized configuration of the valve model. To complete the model we then specify a constitutive law based on experimental stress-strain relations from the literature. Finally, using the immersed boundary method, we simulate the model valve in fluid in a computer test chamber. The aim of this work is to determine the basic principles and mechanisms underlying the anatomy and function of the mitral valve., Comment: PhD Thesis, 2017, Department of Mathematics, Courant Institute of Mathematical Sciences, New York University. Condensed version: arXiv:1902.00018, https://doi.org/10.1002/cnm.3240

The immersed boundary (IB) method is a mathematical framework for fluid-structure interaction problems (FSI) that was originally developed to simulate flows around heart valves. Direct comparison of FSI simulations around heart valves against experimental data is challenging, however, due to the difficulty of performing robust and effective simulations, the complications of modeling a specific physical experiment, and the need to acquire experimental data that is directly comparable to simulation data. Such comparators are a necessary precursor for further formal validation studies of FSI simulations involving heart valves. In this work, we performed physical experiments of flow through a pulmonary valve in an in vitro pulse duplicator, and measured the corresponding velocity field using 4D flow MRI (4-dimensional flow magnetic resonance imaging). We constructed a computer model of this pulmonary artery setup, including modeling valve geometry and material properties via a technique called design-based elasticity, and simulated flow through it with the IB method. The simulated flow fields showed excellent qualitative agreement with experiments, excellent agreement on integral metrics, and reasonable relative error in the entire flow domain and on slices of interest. These results illustrate how to construct a computational model of a physical experiment for use as a comparator., Comment: Ann Biomed Eng (2023)

Bicuspid aortic valve is the most common congenital heart defect, affecting 1-2% of the global population. Patients with bicuspid valves frequently develop dilation and aneurysms of the ascending aorta. Both hemodynamic and genetic factors are believed to contribute to dilation, yet the precise mechanism underlying this progression remains under debate. Controlled comparisons of hemodynamics in patients with different forms of bicuspid valve disease are challenging because of confounding factors, and simulations offer the opportunity for direct and systematic comparisons. Using fluid-structure interaction simulations, we simulate flows through multiple aortic valve models in a patient-specific geometry. The aortic geometry is based on a healthy patient with no known aortic or valvular disease, which allows us to isolate the hemodynamic consequences of changes to the valve alone. Four fully-passive, elastic model valves are studied: a tricuspid valve and bicuspid valves with fusion of the left- and right-, right- and non-, and non- and left-coronary cusps. The resulting tricuspid flow is relatively uniform, with little secondary or reverse flow, and little to no pressure gradient across the valve. The bicuspid cases show localized jets of forward flow, excess streamwise momentum, elevated secondary and reverse flow, and clinically significant levels of stenosis. Localized high flow rates correspond to locations of dilation observed in patients, with the location related to which valve cusps are fused. Thus, the simulations support the hypothesis that chronic exposure to high local flow contributes to localized dilation and aneurysm formation.

This paper presents a new method for modeling the mechanics of the aortic valve, and simulates its interaction with blood. As much as possible, the model construction is based on first principles, but such that the model is consistent with experimental observations. We require that tension in the leaflets must support a pressure, then derive a system of partial differential equations governing its mechanical equilibrium. The solution to these differential equations is referred to as the predicted loaded configuration; it includes the loaded leaflet geometry, fiber orientations and tensions needed to support the prescribed load. From this configuration, we derive a reference configuration and constitutive law. In fluid-structure interaction simulations with the immersed boundary method, the model seals reliably under physiological pressures, and opens freely over multiple cardiac cycles. Further, model closure is robust to extreme hypo- and hypertensive pressures. Then, exploiting the unique features of this model construction, we conduct experiments on reference configurations, constitutive laws, and gross morphology. These experiments suggest the following conclusions, which are directly applicable to the design of prosthetic aortic valves. (i) The loaded geometry, tensions and tangent moduli primarily determine model function. (ii) Alterations to the reference configuration have little effect if the predicted loaded configuration is identical. (iii) The leaflets must have sufficiently nonlinear material response to function over a variety of pressures. (iv) Valve performance is highly sensitive to free edge length and leaflet height. For future use, our aortic valve modeling framework offers flexibility in patient-specific models of cardiac flow.

This work is concerned with modeling and simulation of the mitral valve, one of the four valves in the human heart. The valve is composed of leaflets, the free edges of which are supported by a system of chordae, which themselves are anchored to the papillary muscles inside the left ventricle. First, we examine valve anatomy and present the results of original dissections. These display the gross anatomy and information on fiber structure of the mitral valve. Next, we build a model valve following a design-based methodology, meaning that we derive the model geometry and the forces that are needed to support a given load, and construct the model accordingly. We incorporate information from the dissections to specify the fiber topology of this model. We assume the valve achieves mechanical equilibrium while supporting a static pressure load. The solution to the resulting differential equations determines the pressurized configuration of the valve model. To complete the model we then specify a constitutive law based on a stress-strain relation consistent with experimental data that achieves the necessary forces computed in previous steps. Finally, using the immersed boundary method, we simulate the model valve in fluid in a computer test chamber. The model opens easily and closes without leak when driven by physiological pressures over multiple beats. Further, its closure is robust to driving pressures that lack atrial systole or are much lower or higher than normal.

Helium nanodroplets are doped with cesium and molecular hydrogen and subsequently ionized by electrons. Mass spectra reveal H$_x$Cs$^{+}$ ions that contain as many as 130 hydrogen atoms. Two features in the spectra are striking: First, the abundance of ions with an odd number of hydrogen atoms is very low; the abundance of HCs$^+$ is only 1 % that of H$_2$Cs$^+$. The dominance of even-numbered species is in stark contrast to previous studies of pure or doped hydrogen cluster ions. Second, the abundance of (H$_2$)$_n$Cs$^+$ features anomalies at n = 8, 12, 32, 44, and 52. Guided by previous work on ions solvated in hydrogen and helium we assign the anomalies at n = 12, 32, 44 to the formation of three concentric, solid-like solvation shells of icosahedral symmetry around Cs$^+$. Preliminary density functional theory calculations for n $\le$ 14 are reported as well., Comment: 14 pages, 5 figures

The spin filter capability of a (0,8) armchair graphene nanoribbon with Fe atoms at substitutional sites is investigated by density functional theory in combination with the non-equilibrium Greens function technique. For specific arrangements, a high degree of spin polarization is achieved. These include a single substitution at an edge position or double substitution in the central sector of the transmission element. The possibility of switching between majority and minority spin polarization by changing the double substitution geometry is predicted. Including the bias dependence of the transmission function proves to be essential for correct representation of the spin-resolved current-voltage profiles.

Hydrogen storage by physisorption in carbon based materials is hindered by low adsorption energies. In the last decade doping of carbon materials with alkali, earth alkali or other metal atoms was proposed as a means to enhance adsorption energies, and some experiments have shown promising results. We investigate the upper bounds of hydrogen storage capacities of $C_{60}Cs$ clusters grown in ultracold helium nanodroplets by analyzing anomalies in the ion abundance that indicate shell closure of hydrogen adsorption shells. On bare $C_{60}^{+}$, a commensurate phase with 32 $H_2$ molecules was identified in previous experiments. Doping $C_{60}$ with a single cesium atom leads to an increase in relative ion abundance for the first 10 $H_2$ molecules, and the closure of the commensurate phase is shifted from 32 to 42 $H_2$ molecules. Density functional theory calculations indicate that thirteen energetically enhanced adsorption sites exist, where six of them fill the groove between Cs and $C_{60}$ and 7 are located at the cesium atom. We emphasize the large effect of the quantum nature of the hydrogen molecule on the adsorption energies, i.e. the adsorption energies are decreased by around 50% for $(H_2)C_{60}Cs$ and up to 80% for $(H_2)C_{60}$ by harmonic zero-point corrections, which represent an upper bound to corrections for dissociation energies ($D_e$ to $D_0$) by the vibrational ground states. Five normal modes of libration and vibration of $H_2$ physisorbed on the substrate contribute primarily to this large decrease in adsorption energies. A similar effect can be found for H2 physisorbed on benzene and is expected to be found for any other weakly $H_2$-binding substrate.

We show, with both experiment and theory, that adsorption of $CO_2$ is sensitive to charge on a capturing model carbonaceous surface. In the experiment we dope superfluid helium droplets with $C_{60}$ and $CO_2$ and expose them to ionising free electrons. Both positively and negatively charged $C_{60}(CO_2)_n^{+/-}$ cluster ion distributions are observed with a high-resolution mass spectrometer and these show remarkable and reproducible anomalies in intensities that are strongly dependent on the charge. The highest adsorption capacity is seen with $C_{60}^+$. Complementary density functional theory calculations and molecular dynamics simulations provided insight into the nature of the interaction of charged $C_{60}$ with $CO_2$ as well as trends in the packing of $C_{60}^+$ and $C_{60}^-$. The quadrupole moment of $CO_2$ itself was seen to be decisive in determining the charge dependence of the observed adsorption features. Our findings are expected to apply to adsorption of $CO_2$ by charged surfaces in general.

The immersed boundary (IB) method is a general mathematical framework for studying problems involving fluid-structure interactions in which an elastic structure is immersed in a viscous incompressible fluid. In the IB formulation, the fluid described by Eulerian variables is coupled with the immersed structure described by Lagrangian variables via the use of the Dirac delta function. From a numerical standpoint, the Lagrangian force spreading and the Eulerian velocity interpolation are carried out by a regularized, compactly supported discrete delta function, which is assumed to be a tensor product of a single-variable immersed-boundary kernel. IB kernels are derived from a set of postulates designed to achieve approximate grid translational invariance, interpolation accuracy and computational efficiency. In this note, we present new 5-point and 6-point immersed-boundary kernels that are $\mathscr{C}^3$ and yield a substantially improved translational invariance compared to other common IB kernels., Comment: 10 pages, 4 figures. This is an updated manuscript to the published version with a new 5-point kernel

Monotonicity in concurrent systems stipulates that, in any global state, extant system actions remain executable when new processes are added to the state. This concept is not only natural and common in multi-threaded software, but also useful: if every thread's memory is finite, monotonicity often guarantees the decidability of safety property verification even when the number of running threads is unknown. In this paper, we show that the act of obtaining finite-data thread abstractions for model checking can be at odds with monotonicity: Predicate-abstracting certain widely used monotone software results in non-monotone multi-threaded Boolean programs - the monotonicity is lost in the abstraction. As a result, well-established sound and complete safety checking algorithms become inapplicable; in fact, safety checking turns out to be undecidable for the obtained class of unbounded-thread Boolean programs. We demonstrate how the abstract programs can be modified into monotone ones, without affecting safety properties of the non-monotone abstraction. This significantly improves earlier approaches of enforcing monotonicity via overapproximations.

Predicate abstraction is a key enabling technology for applying finite-state model checkers to programs written in mainstream languages. It has been used very successfully for debugging sequential system-level C code. Although model checking was originally designed for analyzing concurrent systems, there is little evidence of fruitful applications of predicate abstraction to shared-variable concurrent software. The goal of this paper is to close this gap. We have developed a symmetry-aware predicate abstraction strategy: it takes into account the replicated structure of C programs that consist of many threads executing the same procedure, and generates a Boolean program template whose multi-threaded execution soundly overapproximates the concurrent C program. State explosion during model checking parallel instantiations of this template can now be absorbed by exploiting symmetry. We have implemented our method in the SATABS predicate abstraction framework, and demonstrate its superior performance over alternative approaches on a large range of synchronization programs.

Using time-resolved photoemission electron microscopy the excitation of uniform precession modes in individual domains of a weakly coupled spin-valve system has been studied. A coupling dependence of the precession frequencies has been found that can be reasonably well understood on the basis of a macrospin model. By tuning the frequency of the excitation source the uniform precession modes are excited in a resonant way., Comment: This article has been accepted by Journal of Applied Physics. After it is published, it will be found at http://jap.aip.org