Noninvasive measurement of time-varying three-dimensional relative pressure fields within the human heart

Understanding cardiac blood flow patterns is important in the assessment of cardiovascular function. Three-dimensional flow and relative pressure fields within the human left ventricle are demonstrated by combining velocity measurements with computational fluid mechanics methods. The velocity field throughout the left atrium and ventricle of a normal human heart is measured using time-resolved three-dimensional phase-contrast MRI. Subsequently, the time-resolved three-dimensional relative pressure is calculated from this velocity field using the pressure Poisson equation. Noninvasive simultaneous assessment of cardiac pressure and flow phenomena is an important new tool for studying cardiac fluid dynamics.     

The presence of arachnoiditis affects the characteristics of CSF flow in the spinal subarachnoid space: a modelling study

Syringomyelia is a neurological disorder characterised by high pressure fluid-filled cysts within the spinal cord. As syringomyelia is associated with abnormalities of the central nervous system that obstruct cerebrospinal fluid (CSF) flow, it is thought that changes in CSF dynamics play an important role in its pathogenesis. Using three-dimensional computational models of the spinal subarachnoid space (SAS), this study aims to determine SAS obstructions, such as arachnoiditis, change in CSF dynamics in the SAS. The geometry of the SAS was reconstructed from a series of MRI images. CSF is modelled as an incompressible Newtonian fluid with a dynamic viscosity of 1 mPa s. Three computational models simulated CSF flow in either the unobstructed SAS, or with the SAS obstructed by a porous region simulating dorsal or circumferential arachnoiditis. The permeability of this porous obstruction was varied for the model with dorsal arachnoiditis. The results show that arachnoiditis increases flow resistance in the SAS and this is accompanied by a modest increase in magnitude and/or shift in timing (with respect to the cardiac cycle) of the CSF pressure drop across the region of arachnoiditis. This study suggests that syrinx formation may be related to a change in temporal CSF pulse pressure dynamics.     

An approach to the simulation of fluid-structure interaction in the aortic valve

A pair of finite element models has been employed to study the interaction of blood flow with the operation of the aortic valve. A three-dimensional model of the left ventricle with applied wall displacements has been used to generate data for the spatially and time-varying blood velocity profile across the aortic aperture. These data have been used as the inlet loading conditions in a three-dimensional model of the aortic valve and its surrounding structures. Both models involve fluid-structure interaction and simulate the cardiac cycle as a dynamic event. Confidence in the models was obtained by comparison with data obtained in a pulse duplicator. The results show a circulatory flow being generated in the ventricle which produces a substantially axial flow through the aortic aperture. The aortic valve behaves in an essentially symmetric way under the action of this flow, so that the pressure difference across the leaflets is approximately uniform. This work supports the use of spatially uniform but temporally variable pressure distributions across the leaflets in dry or structural models of aortic valves. The study is a major advance through its use of truly three-dimensional geometry, spatially non-uniform loading conditions for the valve leaflets and the successful modelling of progressive contact of the leaflets in a fluid environment.     

A coupled sharp-interface immersed boundary-finite-element method for flow-structure interaction with application to human phonation

A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to simulate flow-induced vibrations of the vocal folds during phonation. Both two- and three-dimensional models have been examined and qualitative, as well as quantitative comparisons, have been made with established results in order to validate the solver. The solver is used to study the onset of phonation in a two-dimensional laryngeal model and the dynamics of the glottal jet in a three-dimensional model and results from these studies are also presented.     

Dynamics of the benthic boundary layer in a strongly forced stratified lake

Field data and the three-dimensional (3D) Estuary and Lake Computer Model (ELCOM) were used to investigate the impact of periodic forcing on the structure and dynamics of the benthic boundary layer (BBL) in Lake Kinneret, Israel, a large lake that experiences strong thermal stratification and wind forcing events. Microstructure data were used to derive the thickness of the BBL and to describe the mean turbulent properties within the BBL. Time series temperature data from thermistor chains were used to characterize the thermal structure of the lake and the basin-scale internal wave field in the lake that was shown to force the turbulent field in the BBL. A clear connection between the dynamics of the BBL and the large-scale features of the flow is presented. The time history of the thickness of the BBL, the mixing in the BBL and the resulting cross-shore flux were shown to vary with the phase of the basin-scale internal wave field. Detailed comparison of simulation results with field data revealed that the model captured well the lake hydrodynamics and the spatial and temporal evolution of energetics of the BBL. Together, field data and numerical modelling provided a clear characterization of the dynamics of the turbulent BBL and its central role in setting up a boundary layer mass flux up the slope from the lake bottom to the height of the metalimnion. Both the turbulent environment in the BBL and the mass flux are of great importance for the ecological processessing of material in a lake.     

4D subject-specific inverse modeling of the chick embryonic heart outflow tract hemodynamics

Blood flow plays a critical role in regulating embryonic cardiac growth and development, with altered flow leading to congenital heart disease. Progress in the field, however, is hindered by a lack of quantification of hemodynamic conditions in the developing heart. In this study, we present a methodology to quantify blood flow dynamics in the embryonic heart using subject-specific computational fluid dynamics (CFD) models. While the methodology is general, we focused on a model of the chick embryonic heart outflow tract (OFT), which distally connects the heart to the arterial system, and is the region of origin of many congenital cardiac defects. Using structural and Doppler velocity data collected from optical coherence tomography, we generated 4D (\(\hbox {3D}\,+\,\hbox {time}\)) embryo-specific CFD models of the heart OFT. To replicate the blood flow dynamics over time during the cardiac cycle, we developed an iterative inverse-method optimization algorithm, which determines the CFD model boundary conditions such that differences between computed velocities and measured velocities at one point within the OFT lumen are minimized. Results from our developed CFD model agree with previously measured hemodynamics in the OFT. Further, computed velocities and measured velocities differ by \(<\)15 % at locations that were not used in the optimization, validating the model. The presented methodology can be used in quantifications of embryonic cardiac hemodynamics under normal and altered blood flow conditions, enabling an in-depth quantitative study of how blood flow influences cardiac development.     

The effects of the interthalamic adhesion position on cerebrospinal fluid dynamics in the cerebral ventricles

The interthalamic adhesion is a unique feature of the third ventricle in the brain. It differs in shape and size and its location varies between individuals. In this study, computational fluid dynamics was performed on 4 three-dimensional models of the cerebral ventricular system with the interthalamic adhesion modeled in different locations in the third ventricle. Cerebrospinal fluid (CSF) was modeled as incompressible Newtonian fluid and flow was assumed laminar. The periodic motion of CSF flow as a function of the cardiac cycle starting from diastole was prescribed as the inlet boundary condition at the foramen of Monroe. Results from this study show how the location of the interthalamic adhesion influences the pattern of pressure distribution in the cerebral ventricles. In addition, the highest CSF pressure in the third ventricle can vary by ～50% depending on the location of the interthalamic adhesion. We suggest that the interthalamic adhesion may have functional implications on the development of hydrocephalus and it is important to model this anatomical feature in future studies.     

Numerical modeling of simulated blood flow in idealized composite arterial coronary grafts: steady state simulations

This paper presents a comparative study of simulated blood flow in different configurations of simplified composite arterial coronary grafts (CACGs). Even though the composite arterial grafting is increasingly used in cardiac surgery, it is still questionable whether or not the blood flow in such grafts can adequately meet the demands of the native myocardial circulation. A computational fluid dynamics (CFD) model was developed to conduct computer-based studies of simulated blood flow in four different geometric configurations of CACGs, corresponding to routinely used networks in cardiac surgery coronary grafts (T, Y, Pi and sequential). The flow was assumed three-dimensional, laminar and steady and the fluid as Newtonian, while the vessel walls were considered as inelastic and impermeable. It was concluded that local haemodynamics, practically described by velocity, pressure drop, wall shear stress (WSS) and flow rates, may be strongly influenced by the local geometry, especially at the anastomotic sites. The computations were made at mean flow rates of 37.5, 75 and 150ml/min. The side-branch outflow rates, computed for each bypass graft, showed noticeable differences. The results, which were found both qualitatively and quantitatively consistent with other studies, indicate that the Pi-graft exhibits significantly less uniform distribution of outflow rates than the other geometric configurations. Moreover, prominent variations in WSS and velocity distribution among the assessed CACGs were predicted, showing remarkable flow interactions among the arterial branches. The lowest shear stress regions were found on the lateral walls of bifurcations, which are predominantly susceptible to the occurrence of coronary artery disease (CAD). In contrast, the highest WSS were observed at the turn of the arterial branches.     

The active and passive ciliary motion in the embryo node: A computational fluid dynamics model

The breaking of left–right symmetry in the mammalian embryo is believed to occur in a transient embryonic structure, the node, when cilia create a leftward flow of liquid. The two-cilia hypothesis proposes that the node contains two kinds of primary cilia: motile cilia that rotate autonomously to generate the leftward fluid flow and passive cilia that act as mechano-sensors, responding to flow. While studies support this hypothesis, the mechanism by which the sensory cilia respond to the fluid flow is still unclear. In this paper, we present a computational model of two cilia, one active and one passive. By employing computational fluid dynamics, deformable mesh computational techniques and fluid–structure interaction analysis, and solving the three-dimensional unsteady transport equations, we study the flow pattern produced by the movement of the active cilium and the response of the passive cilium to this flow. Our results reveal that clockwise rotation of the active cilium can generate a counter-clockwise elliptical rotation and overall lateral displacement for its neighboring passive one, of measurable magnitude and consistent pattern. This supports the plausibility of the two-cilia hypothesis and helps quantify the motion pattern for the passive cilium induced by this regional flow.     

Conformational Particularities of the Tachykinin-Like Decapeptide Sialokinin I

This paper reports the study of the three-dimensional structure of the tachykinin-like decapeptide sialokinin I molecule using molecular mechanics and molecular dynamics. Fragment analysis was used to identify the stable spatial structures of sialokinin I, which may be present as a set of conformations that are characterized by the relatively labile N-terminal tripeptide and the conformationally rigid C-terminal heptapeptide. It has been demonstrated that the sialokinin I molecule tends to adopt nearly isoenergetic conformations with different structural types at the N-end of the peptide chain, which change into the alpha-helix turn at its C-end. Molecular dynamics was employed to model the sialokinin I molecule mobility in its stable conformations both in a vacuum and when surrounded by water molecules.

     

Torsional motion of the left ventricle does not affect ventricular fluid dynamics of both foetal and adult hearts

Left ventricular torsion is caused by shortening and relaxation of the helical fibres in the myocardium, and is thought to be an optimal configuration for minimizing myocardial tissue strains. Characteristics of torsional motion has also been proposed to be markers for cardiac dysfunction. However, its effects on fluid and energy dynamics in the left ventricle have not been comprehensively investigated. To investigate this, we performed image-based flow simulations on five healthy adult porcine and two healthy human foetal left ventricles (representing two different length scales) at different degrees of torsional motions. In the adult porcine ventricles, cardiac features such as papillary muscles and mitral valves, and cardiac conditions such as myocardial infarctions, were also included to investigate the effect of twist. The results showed that, for all conditions investigated, ventricular torsional motion caused minimal changes to flow patterns, and consistently accounted for less than 2% of the energy losses, wall shear stresses, and ejection momentum energy. In contrast, physiological characteristics such as chamber size, stroke volume and heart rate had a much greater influence on flow patterns and energy dynamics. The results thus suggested that it might not be necessary to model the torsional motion to study the flow and energy dynamics in left ventricles.     

Dependence of leukocyte capture on instantaneous pulsatile flow

Atherosclerosis, an artery disease, is currently the leading cause of death in the United States in both men and women. The first step in the development of atherosclerosis involves leukocyte adhesion to the arterial endothelium. It is broadly accepted that blood flow, more specifically wall shear stress (WSS), plays an important role in leukocyte capture and subsequent development of an atherosclerotic plaque. What is less known is how instantaneous WSS, which can vary by up to 5 Pa over one cardiac cycle, influences leukocyte capture. In this paper we use direct numerical simulations (DNS), performed using an in-house code, to illustrate that leukocyte capture is different whether as a function of instantaneous or time-averaged blood flow. Specifically, a stenotic plaque is modeled using a computational fluid dynamics (CFD) solver through fully three-dimensional Navier-Stokes equations and the immersed boundary method. Pulsatile triphasic inflow is used to simulate the cardiac cycle. The CFD is coupled with an agent-based leukocyte capture model to assess the impact of instantaneous hemodynamics on stenosis growth. The computed wall shear stress agrees well with the results obtained with a commercial software, as well as with theoretical results in the healthy region of the artery. The analysis emphasizes the importance of the instantaneous flow conditions in evaluating the leukocyte rate of capture. That is, the capture rate computed from mean flow field is generally underpredicted compared to the actual rate of capture. Thus, in order to obtain a reliable estimate, the flow unsteadiness during a cardiac cycle should be taken into account.     

A fully coupled fluid-structure interaction model of the secondary lymphatic valve

Abstract

The secondary lymphatic valve is a bi-leaflet structure frequent throughout collecting vessels that serves to prevent retrograde flow of lymph. Despite its vital function in lymph flow and apparent importance in disease development, the lymphatic valve and its associated fluid dynamics have been largely understudied. The goal of this work was to construct a physiologically relevant computational model of an idealized rat mesenteric lymphatic valve using fully coupled fluid-structure interactions to investigate the relationship between three-dimensional flow patterns and stress/deformation within the valve leaflets. The minimum valve resistance to flow, which has been shown to be an important parameter in effective lymphatic pumping, was computed as 268?g/mm⁴?s. Hysteretic behavior of the lymphatic valve was confirmed by comparing resistance values for a given transvalvular pressure drop during opening and closing. Furthermore, eddy structures were present within the sinus adjacent to the valve leaflets in what appear to be areas of vortical flow; the eddy structures were characterized by non-zero velocity values (up to ～4?mm/s) in response to an applied unsteady transvalvular pressure. These modeling capabilities present a useful platform for investigating the complex interplay between soft tissue motion and fluid dynamics of lymphatic valves and contribute to the breadth of knowledge regarding the importance of biomechanics in lymphatic system function.     

A model of calcium activation of the cardiac thin filament

The cardiac thin filament regulates actomyosin interactions through calcium-dependent alterations in the dynamics of cardiac troponin and tropomyosin. Over the past several decades, many details of the structure and function of the cardiac thin filament and its components have been elucidated. We propose a dynamic, complete model of the thin filament that encompasses known structures of cardiac troponin, tropomyosin, and actin and show that it is able to capture key experimental findings. By performing molecular dynamics simulations under two conditions, one with calcium bound and the other without calcium bound to site II of cardiac troponin C (cTnC), we found that subtle changes in structure and protein contacts within cardiac troponin resulted in sweeping changes throughout the complex that alter tropomyosin (Tm) dynamics and cardiac troponin--actin interactions. Significant calcium-dependent changes in dynamics occur throughout the cardiac troponin complex, resulting from the combination of the following: structural changes in the N-lobe of cTnC at and adjacent to sites I and II and the link between them; secondary structural changes of the cardiac troponin I (cTnI) switch peptide, of the mobile domain, and in the vicinity of residue 25 of the N-terminus; secondary structural changes in the cardiac troponin T (cTnT) linker and Tm-binding regions; and small changes in cTnC-cTnI and cTnT-Tm contacts. As a result of these changes, we observe large changes in the dynamics of the following regions: the N-lobe of cTnC, the mobile domain of cTnI, the I-T arm, the cTnT linker, and overlapping Tm. Our model demonstrates a comprehensive mechanism for calcium activation of the cardiac thin filament consistent with previous, independent experimental findings. This model provides a valuable tool for research into the normal physiology of cardiac myofilaments and a template for studying cardiac thin filament mutations that cause human cardiomyopathies.     

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

The fluid-structure energy exchange process for normal speech has been studied extensively, but it is not well understood for pathological conditions. Polyps and nodules, which are geometric abnormalities that form on the medial surface of the vocal folds, can disrupt vocal fold dynamics and thus can have devastating consequences on a patient''s ability to communicate. Our laboratory has reported particle image velocimetry (PIV) measurements, within an investigation of a model polyp located on the medial surface of an in vitro driven vocal fold model, which show that such a geometric abnormality considerably disrupts the glottal jet behavior. This flow field adjustment is a likely reason for the severe degradation of the vocal quality in patients with polyps. A more complete understanding of the formation and propagation of vortical structures from a geometric protuberance, such as a vocal fold polyp, and the resulting influence on the aerodynamic loadings that drive the vocal fold dynamics, is necessary for advancing the treatment of this pathological condition. The present investigation concerns the three-dimensional flow separation induced by a wall-mounted prolate hemispheroid with a 2:1 aspect ratio in cross flow, i.e. a model vocal fold polyp, using an oil-film visualization technique. Unsteady, three-dimensional flow separation and its impact of the wall pressure loading are examined using skin friction line visualization and wall pressure measurements.     

A mathematical description of blood spiral flow in vessels: application to a numerical study of flow in arterial bending

Local arterial haemodynamics has been associated with the pathophysiology of several cardiovascular diseases. The stable spiral blood-flows that were observed in vivo in several vessels, may play a dual role in vascular haemodynamics, beneficial since it induces stability, reducing turbulence in the arterial tree, and accounts for normal organ perfusion, but detrimental in view of the imparted tangential velocities that are involved in plaque formation and development. Being a spiral flow considered representative of the local blood dynamics in certain vessels, a method is proposed to quantify the spiral structure of blood flow. The proposed function, computed along a cluster of particle trajectories, has been tested for the quantitative determination of the spiral blood flow in a three-dimensional, s-shaped femoral artery numerical model in which three degrees of stenosis were simulated in a site prone to atherosclerotic development. Our results confirm the efficacy of the Lagrangian analysis as a tool for vascular blood dynamics investigation. The proposed method quantified spiral motion, and revealed the progression in the degree of stenosis, in the presented case study. In the future, it could be used as a synthetic tool to approach specific clinical complications.     

Characterization of the internal motions of a chimeric protein by 13C NMR highlights the important dynamic consequences of the engineering on a millisecond time scale.

By transferring the central curaremimetic beta hairpin of the snake toxin alpha into the scaffold of the scorpion charybdotoxin, a chimeric protein was constructed that reproduced the three-dimensional structure and partially reproduced the function of the parent beta hairpin, without perturbing the three-dimensional structure of the scaffold [1]. Picosecond to hour time scale motions of charybdotoxin and the engineered protein were observed, in order to evaluate the dynamic consequences of the six deletions and eight mutations differentiating the two molecules. The chimeric protein dynamics were also compared to that of toxin alpha, in order to examine the beta hairpin motions in both structural contexts. Thus, 13C R1, R1rho and 1H-->13C nOe were measured for all the CalphaHalpha and threonine CbetaHbeta vectors. As the proteins were not labeled, accordion techniques combined to coherence selection by pulsed field gradients and preservation of magnetization following equivalent pathways were used to considerably reduce the spectrometer time needed. On one hand, we observed that the chimeric protein and charybdotoxin are subjected to similar picosecond to nanosecond time scale motions except around the modified beta sheet region. The chimeric protein also exhibits an additional millisecond time scale motion on its whole sequence, and its beta structure is less stable on a minute to hour time scale. On the other hand, when the beta hairpin dynamics is compared in two different structural contexts, i.e. in the chimeric protein and the curaremimetic toxin alpha, the picosecond to nanosecond time scale motions are fairly conserved. However, the microsecond to millisecond time scale motions are different on most of the beta hairpin sequence, and the beta sheet seems more stable in toxin alpha than in the chimera. The slower microsecond to hour time scale motions seem to be extremely sensitive to the structural context, and thus poorly transferred from one protein to another.     

Three-dimensional visualization and morphometry of small airways from microfocal X-ray computed tomography

Physiological morphometry is a critical factor in the flow dynamics in small airways. In this study, we visualized and analyzed the three-dimensional structure of the small airways without dehydration and fixation. We developed a two-step method to visualize small airways in detail by staining the lung tissue with a radiopaque solution and then visualizing the tissue with a cone-beam microfocal X-ray computed tomographic (CT) system. To verify the applicability of this staining and CT imaging (SCT) method, we used the method to visualize small airways in excised rat lungs. By using the SCT method to obtain continuous CT images, three-dimensional branching and merging bronchi ranging from 500 to 150 microm (the airway generation=8-16) were successfully reconstructed. The morphometry of the small airways (diameter, length, branching angle and gravity angle between the gravity direction and airway vector) was analyzed using the three-dimensional thinning algorithm. The diameter and length exponentially decreased with the airway generation. The asymmetry of the bifurcation decreased with generation and one branching angle decided the other pair branching angle. The SCT method is the first reported method that yields faithful high-resolution images of soft tissue geometry without fixation and the three-dimensional morphometry of small airways is useful for studying the biomechanical dynamics in small airways.     

Fluid Dynamics of Ventricular Filling in the Embryonic Heart

The vertebrate embryonic heart first forms as a valveless tube that pumps blood using waves of contraction. As the heart develops, the atrium and ventricle bulge out from the heart tube, and valves begin to form through the expansion of the endocardial cushions. As a result of changes in geometry, conduction velocities, and material properties of the heart wall, the fluid dynamics and resulting spatial patterns of shear stress and transmural pressure change dramatically. Recent work suggests that these transitions are significant because fluid forces acting on the cardiac walls, as well as the activity of myocardial cells that drive the flow, are necessary for correct chamber and valve morphogenesis. In this article, computational fluid dynamics was used to explore how spatial distributions of the normal forces acting on the heart wall change as the endocardial cushions grow and as the cardiac wall increases in stiffness. The immersed boundary method was used to simulate the fluid-moving boundary problem of the cardiac wall driving the motion of the blood in a simplified model of a two-dimensional heart. The normal forces acting on the heart walls increased during the period of one atrial contraction because inertial forces are negligible and the ventricular walls must be stretched during filling. Furthermore, the force required to fill the ventricle increased as the stiffness of the ventricular wall was increased. Increased endocardial cushion height also drastically increased the force necessary to contract the ventricle. Finally, flow in the moving boundary model was compared to flow through immobile rigid chambers, and the forces acting normal to the walls were substantially different.     

Protein dynamics: Rotational diffusion of rigid and fluctuating three dimensional structures

The optimized Rouse-Zimm approximation to the local dynamics (ORZLD theory) is extended to treat three-dimensional structures. Rigid model chains of different dimensionality are considered. The local dynamics of random peptides are compared to the rotational correlation times of rigid three-dimensional protein structures. The treatment of these rigid limits is a necessary step in a more advanced ORZLD theory of the dynamics of proteins including fluctuations relative to the three-dimensional structure. © 1995 John Wiley & Sons, Inc.