Overset meshing in combination with novel blended weak-strong fluid-structure interactions for simulations of a translating valve in series with a second valve

Mechanical circulatory support (MCS) devices can bridge the gap to transplant whilst awaiting a viable donor heart. The Realheart Total Artificial Heart is a novel positive-displacement MCS that generates pulsatile flow via bileaflet mechanical valves. This study developed a combined computational fluid dynamics and fluid-structure interaction (FSI) methodology for simulating positive displacement bileaflet valves. Overset meshing discretised the fluid domain, and a blended weak-strong coupling FSI algorithm was combined with variable time-stepping. Four operating conditions of relevant stroke lengths and rates were assessed. The results demonstrated this modelling strategy is stable and efficient for modelling positive-displacement artificial hearts.

Direct 0D-3D coupling of a lattice Boltzmann methodology for fluid-structure aortic flow simulations

This work introduces a numerical approach and implementation for the direct coupling of arbitrary complex ordinary differential equation- (ODE-)governed zero-dimensional (0D) boundary conditions to three-dimensional (3D) lattice Boltzmann-based fluid-structure systems for hemodynamics studies. In particular, a most complex configuration is treated by considering a dynamic left ventricle- (LV-)elastance heart model which is governed by (and applied as) a nonlinear, non-stationary hybrid ODE-Dirichlet system. Other ODE-based boundary conditions, such as lumped parameter Windkessel models for truncated vasculature, are also considered. Performance studies of the complete 0D-3D solver, including its treatment of the lattice Boltzmann fluid equations and elastodynamics equations as well as their interactions, is conducted through a variety of benchmark and convergence studies that demonstrate the ability of the coupled 0D-3D methodology in generating physiological pressure and flow waveforms-ultimately enabling the exploration of various physical and physiological parameters for hemodynamics studies of the coupled LV-arterial system. The methods proposed in this paper can be easily applied to other ODE-based boundary conditions as well as to other fluid problems that are modeled by 3D lattice Boltzmann equations and that require direct coupling of dynamic 0D boundary conditions.

Predicting critical closing pressure in children with obstructive sleep apnea using fluid-structure interaction

Surgical treatment of obstructive sleep apnea (OSA) in children requires knowledge of upper airway dynamics, including the closing pressure (Pcrit), a measure of airway collapsibility. We applied a flow-structure interaction (FSI) computational model to estimate Pcrit in patient-specific upper airway models obtained from magnetic resonance imaging (MRI) scans. We sought to examine the agreement between measured and estimated Pcrit from FSI models in children with Down syndrome. We hypothesized that the estimated Pcrit would accurately reflect measured Pcrit during sleep and therefore reflect the severity of OSA as measured by the obstructive apnea-hypopnea index (AHI). All participants (n = 41) underwent polysomnography and sedated sleep MRI scans. We used Bland-Altman plots to examine the agreement between measured and estimated Pcrit. We determined associations between estimated Pcrit and OSA severity, as measured by AHI, using regression models. The agreement between passive and estimated Pcrit showed a fixed bias of -1.31 [confidence interval (CI) = -2.78, 0.15] and a nonsignificant proportional bias. A weaker agreement with active Pcrit was observed. A model including AHI, gender, an interaction term for AHI, and gender and neck circumference explained the largest variation (R2 = 0.61) in the relationship between AHI and estimated Pcrit (P < 0.0001). Overlap between the areas of the airway with the lowest stiffness, and areas of collapse on dynamic MRI, was 77.4 ± 30% for the nasopharyngeal region and 78.6 ± 33% for the retroglossal region. The agreement between measured and estimated Pcrit and the significant association with AHI supports the validity of Pcrit estimates from the FSI model.NEW & NOTEWORTHY We present a noninvasive method for estimating critical closing pressure (Pcrit) using fluid-structure interaction (FSI) simulations and magnetic resonance imaging (MRI) scans in patients with obstructive sleep apnea (OSA). We used patient-specific stiffness measures in our FSI model to account for any individual variability in the elasticity of soft tissues surrounding the upper airway. We validated this model by measuring the degree of agreement between measured and estimated Pcrit.

Flow Interactions Between Low Aspect Ratio Hydrofoils in In-line and Staggered Arrangements

Many species of fish gather in dense collectives or schools where there are significant flow interactions from their shed wakes. Commonly, these swimmers shed a classic reverse von Kármán wake, however, schooling eels produce a bifurcated wake topology with two vortex rings shed per oscillation cycle. To examine the schooling interactions of a hydrofoil with a bifurcated wake topology, we present tomographic particle image velocimetry (tomo PIV) measurements of the flow interactions and direct force measurements of the performance of two low-aspect-ratio hydrofoils (AR=0.5) in an in-line and a staggered arrangement. Surprisingly, when the leader and follower are interacting in either arrangement there are only minor alterations to the flowfields beyond the superposition of the flowfields produced by the isolated leader and follower. Motivated by this finding, Garrick’s linear theory, a linear unsteady hydrofoil theory based on a potential flow assumption, was adapted to predict the lift and thrust performance of the follower. Here, the follower hydrofoil interacting with the leader’s wake is considered as the superposition of an isolated pitching foil with a time-varying cross-stream velocity derived from the wake flow measurements of the isolated leader. Linear theory predictions accurately capture the time-averaged lift force and some of the major peaks in thrust derived from the follower interacting with the leader’s wake in a staggered arrangement. The thrust peaks that are not predicted by linear theory are likely driven by spatial variations in the flowfield acting on the follower or nonlinear flow interactions; neither of which are accounted for in the simple theory. This suggests that unsteady potential flow theory that does account for spatial variations in the flowfield acting on a hydrofoil can provide a relatively simple framework to understand and model the flow interactions that occur in schooling fish. Additionally, schooling eels can derive thrust and efficiency increases of 63-80% in either a in-line or a staggered arrangement where the follower is between two branched momentum jets or with one momentum jet branch directly impinging on it, respectively.

Purely Elastic Fluid-Structure Interactions in Microfluidics: Implications for Mucociliary Flows

Fluid-structure interactions lie at the heart of the complex, and often highly coordinated, motions of actively driven microscale biological systems (e.g., translating cilia, flagella, and motile cells). Due to the highly viscoelastic nature of most relevant biological fluids and the small length scales involved, the viscous and inertial forces in such flows are dominated by elasticity. However, elastic effects are often overlooked in studies seeking to address phenomena like the synchronization of beating cilia. In this study, unique microfluidic experiments are presented to demonstrate that inertia-free viscoelastic flows can lead to highly regular beating of an immersed (passive) flexible structure, herein named "purely-elastic" fluid-structure interaction. It is also shown how two such flexible structures can achieve an extraordinary degree of synchronization, with a correlation coefficient approaching unity. The synchronization is a result of the generation of localized elastic stresses in the fluid that effectively link the two objects. These purely elastic interactions may be important to consider toward developing a complete understanding of the motions of microscale biological systems.

Mechanics of the Tricuspid Valve-From Clinical Diagnosis/Treatment, In-Vivo and In-Vitro Investigations, to Patient-Specific Biomechanical Modeling

Proper tricuspid valve (TV) function is essential to unidirectional blood flow through the right side of the heart. Alterations to the tricuspid valvular components, such as the TV annulus, may lead to functional tricuspid regurgitation (FTR), where the valve is unable to prevent undesired backflow of blood from the right ventricle into the right atrium during systole. Various treatment options are currently available for FTR; however, research for the tricuspid heart valve, functional tricuspid regurgitation, and the relevant treatment methodologies are limited due to the pervasive expectation among cardiac surgeons and cardiologists that FTR will naturally regress after repair of left-sided heart valve lesions. Recent studies have focused on (i) understanding the function of the TV and the initiation or progression of FTR using both in-vivo and in-vitro methods, (ii) quantifying the biomechanical properties of the tricuspid valve apparatus as well as its surrounding heart tissue, and (iii) performing computational modeling of the TV to provide new insight into its biomechanical and physiological function. This review paper focuses on these advances and summarizes recent research relevant to the TV within the scope of FTR. Moreover, this review also provides future perspectives and extensions critical to enhancing the current understanding of the functioning and remodeling tricuspid valve in both the healthy and pathophysiological states.

Patient-specific CT-based 3D passive FSI model for left ventricle in hypertrophic obstructive cardiomyopathy

Left ventricular outflow tract obstruction is observed in 70% of patients with hypertrophic cardiomyopathy, which occurs in about 1 of every 500 adults in the general population. It has been widely believed that the motion of the mitral valve, in particular, its systolic anterior motion (SAM), attributes significantly to such obstruction. For a better understanding of the mitral valve motion, a 3D patient-specific fluid-structure interaction model of the left ventricle from a patient with hypertrophic obstructive cardiomyopathy based on computed tomography (CT) scan images was proposed in this study. Displacement, structural stress, pressure, flow velocity and shear stress within the left ventricle and mitral valve were extracted to characterize their behavior. The maximum shear stress on mitral valve was 9.68 [Formula: see text]. The pressure on its posterior leaflet was higher than that on the anterior leaflet and the peak pressure on the mitral valve was 93.5 mm Hg which occurred at pre-SAM time. High angles of attack (54.3 ± 22.4°) were found in this patient. The methodology established in this study may have the potential to clarify the mechanisms of SAM and ultimately optimize surgical planning by comparing the mechanical results obtained from preoperative and postoperative models.

Numerical simulation of the fluid structure interactions in a compliant patient-specific arteriovenous fistula

The objective of the study is to investigate numerically the fluid-structure interactions (FSI) in a patient-specific arteriovenous fistula (AVF) and analyze the degree of complexity that such a numerical simulation requires to provide clinically relevant information. The reference FSI simulation takes into account the non-Newtonian behavior of blood, as well as the variation in mechanical properties of the vascular walls along the AVF. We have explored whether less comprehensive versions of the simulation could still provide relevant results. The non-Newtonian blood model is necessary to predict the hemodynamics in the AVF because of the predominance of low shear rates in the vein. An uncoupled fluid simulation provides informative qualitative maps of the hemodynamic conditions in the AVF; quantitatively, the hemodynamic parameters are accurate within 20% maximum. Conversely, an uncoupled structural simulation with non-uniform wall properties along the vasculature provides the accurate distribution of internal wall stresses, but only at one instant of time within the cardiac cycle. The FSI simulation advantageously provides the time-evolution of both the hemodynamic and structural stresses. However, the higher computational cost renders a clinical use still difficult in routine.

Signal transduction in a compliant short loop of Henle

To study the transformation of fluctuations in filtration rate into tubular fluid chloride concentration oscillations alongside the macula densa, we have developed a mathematical model for tubuloglomerular feedback (TGF) signal transduction along the pars recta, the descending limb, and the thick ascending limb (TAL) of a short-looped nephron. The model tubules are assumed to have compliant walls and, thus, a tubular radius that depends on the transmural pressure difference. Previously, it has been predicted that TGF transduction by the TAL is a generator of nonlinearities: if a sinusoidal oscillation is added to a constant TAL flow rate, then the time required for a fluid element to traverse the TAL is oscillatory in time but nonsinusoidal. The results from the new model simulations presented here predict that TGF transduction by the loop of Henle is also, in the same sense, a generator of nonlinearities. Thus, this model predicts that oscillations in tubular fluid alongside the macula densa will be nonsinusoidal and will exhibit harmonics of sinusoidal perturbations of pars recta flow. Model results also indicate that the loop acts as a low-pass filter in the transduction of the TGF signal.

A model of cytoplasmically driven microtubule-based motion in the single-celled Caenorhabditis elegans embryo

We present a model of cytoplasmically driven microtubule-based pronuclear motion in the single-celled Caenorhabditis elegans embryo. In this model, a centrosome pair at the male pronucleus initiates stochastic microtubule (MT) growth. These MTs encounter motor proteins, distributed throughout the cytoplasm, that attach and exert a pulling force. The consequent MT-length-dependent pulling forces drag the pronucleus through the cytoplasm. On physical grounds, we assume that the motor proteins also exert equal and opposite forces on the surrounding viscous cytoplasm, here modeled as an incompressible Newtonian fluid constrained within an ellipsoidal eggshell. This naturally leads to streaming flows along the MTs. Our computational method is based on an immersed boundary formulation that allows for the simultaneous treatment of fluid flow and the dynamics of structures immersed within. Our simulations demonstrate that the balance of MT pulling forces and viscous nuclear drag is sufficient to move the pronucleus, while simultaneously generating minus-end directed flows along MTs that are similar to the observed movement of yolk granules toward the center of asters. Our simulations show pronuclear migration, and moreover, a robust pronuclear centration and rotation very similar to that observed in vivo. We find also that the confinement provided by the eggshell significantly affects the internal dynamics of the cytoplasm, increasing by an order of magnitude the forces necessary to translocate and center the pronucleus.

Patient-specific artery shrinkage and 3D zero-stress state in multi-component 3D FSI models for carotid atherosclerotic plaques based on in vivo MRI data

Image-based computational models for atherosclerotic plaques have been developed to perform mechanical analysis to quantify critical flow and stress/strain conditions related to plaque rupture which often leads directly to heart attack or stroke. An important modeling issue is how to determine zero stress state from in vivo plaque geometries. This paper presents a method to quantify human carotid artery axial and inner circumferential shrinkages by using patient-specific ex vivo and in vivo MRI images. A shrink-stretch process based on patient-specific in vivo plaque morphology and shrinkage data was introduced to shrink the in vivo geometry first to find the zero-stress state (opening angle was ignored to reduce the complexity), and then stretch and pressurize to recover the in vivo plaque geometry with computed initial stress, strain, flow pressure and velocity conditions. Effects of the shrink-stretch process on plaque stress/strain distributions were demonstrated based on patient-specific data using 3D models with fluid-structure interactions (FSI). The average artery axial and inner circumferential shrinkages were 25% and 7.9%, respectively, based on a data set obtained from 10 patients. Maximum values of maximum principal stress and strain increased 349.8% and 249% respectively with 33% axial stretch. Influence of inner circumferential shrinkage (7.9%) was not very noticeable under 33% axial stretch, but became more noticeable under smaller axial stretch. Our results indicated that accurate knowledge of artery shrinkages and the shrink-stretch process will considerably improve the accuracy of computational predictions made based on results from those in vivo MRI-based FSI models.