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 (\(\mu \)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 \(\mu \)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 \(\mu \)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.     

A novel approach to in vivo mitral valve stress analysis

Three-dimensional (3-D) echocardiography allows the generation of anatomically correct and time-resolved geometric mitral valve (MV) models. However, as imaged in vivo, the MV assumes its systolic geometric configuration only when loaded. Customarily, finite element analysis (FEA) is used to predict material stress and strain fields rendered by applying a load on an initially unloaded model. Therefore, this study endeavors to provide a framework for the application of in vivo MV geometry and FEA to MV physiology, pathophysiology, and surgical repair. We hypothesize that in vivo MV geometry can be reasonably used as a surrogate for the unloaded valve in computational (FEA) simulations, yielding reasonable and meaningful stress and strain magnitudes and distributions. Three experiments were undertaken to demonstrate that the MV leaflets are relatively nondeformed during systolic loading: 1) leaflet strain in vivo was measured using sonomicrometry in an ovine model, 2) hybrid models of normal human MVs as constructed using transesophageal real-time 3-D echocardiography (rt-3DE) were repeatedly loaded using FEA, and 3) serial rt-3DE images of normal human MVs were used to construct models at end diastole and end isovolumic contraction to detect any deformation during isovolumic contraction. The average linear strain associated with isovolumic contraction was 0.02 ± 0.01, measured in vivo with sonomicrometry. Repeated loading of the hybrid normal human MV demonstrated little change in stress or geometry: peak von Mises stress changed by <4% at all locations on the anterior and posterior leaflets. Finally, the in vivo human MV deformed minimally during isovolumic contraction, as measured by the mean absolute difference calculated over the surfaces of both leaflets between serial MV models: 0.53 ± 0.19 mm. FEA modeling of MV models derived from in vivo high-resolution truly 3-D imaging is reasonable and useful for stress prediction in MV pathologies and repairs.     

Personalized Computational Modeling of Mitral Valve Prolapse: Virtual Leaflet Resection

Posterior leaflet prolapse following chordal elongation or rupture is one of the primary valvular diseases in patients with degenerative mitral valves (MVs). Quadrangular resection followed by ring annuloplasty is a reliable and reproducible surgical repair technique for treatment of posterior leaflet prolapse. Virtual MV repair simulation of leaflet resection in association with patient-specific 3D echocardiographic data can provide quantitative biomechanical and physiologic characteristics of pre- and post-resection MV function. We have developed a solid personalized computational simulation protocol to perform virtual MV repair using standard clinical guidelines of posterior leaflet resection with annuloplasty ring implantation. A virtual MV model was created using 3D echocardiographic data of a patient with posterior chordal rupture and severe mitral regurgitation. A quadrangle-shaped leaflet portion in the prolapsed posterior leaflet was removed, and virtual plication and suturing were performed. An annuloplasty ring of proper size was reconstructed and virtual ring annuloplasty was performed by superimposing the ring and the mitral annulus. Following the quadrangular resection and ring annuloplasty simulations, patient-specific annular motion and physiologic transvalvular pressure gradient were implemented and dynamic finite element simulation of MV function was performed. The pre-resection MV demonstrated a substantial lack of leaflet coaptation which directly correlated with the severe mitral regurgitation. Excessive stress concentration was found along the free marginal edge of the posterior leaflet involving the chordal rupture. Following the virtual resection and ring annuloplasty, the severity of the posterior leaflet prolapse markedly decreased. Excessive stress concentration disappeared over both anterior and posterior leaflets, and complete leaflet coaptation was effectively restored. This novel personalized virtual MV repair strategy has great potential to help with preoperative selection of the patient-specific optimal MV repair techniques, allow innovative surgical planning to expect improved efficacy of MV repair with more predictable outcomes, and ultimately provide more effective medical care for the patient.     

Isolated effect of geometry on mitral valve function for in silico model development

Computational models for the heart's mitral valve (MV) exhibit several uncertainties that may be reduced by further developing these models using ground-truth data-sets. This study generated a ground-truth data-set by quantifying the effects of isolated mitral annular flattening, symmetric annular dilatation, symmetric papillary muscle (PM) displacement and asymmetric PM displacement on leaflet coaptation, mitral regurgitation (MR) and anterior leaflet strain. MVs were mounted in an in vitro left heart simulator and tested under pulsatile haemodynamics. Mitral leaflet coaptation length, coaptation depth, tenting area, MR volume, MR jet direction and anterior leaflet strain in the radial and circumferential directions were successfully quantified at increasing levels of geometric distortion. From these data, increase in the levels of isolated PM displacement resulted in the greatest mean change in coaptation depth (70% increase), tenting area (150% increase) and radial leaflet strain (37% increase) while annular dilatation resulted in the largest mean change in coaptation length (50% decrease) and regurgitation volume (134% increase). Regurgitant jets were centrally located for symmetric annular dilatation and symmetric PM displacement. Asymmetric PM displacement resulted in asymmetrically directed jets. Peak changes in anterior leaflet strain in the circumferential direction were smaller and exhibited non-significant differences across the tested conditions. When used together, this ground-truth data-set may be used to parametrically evaluate and develop modelling assumptions for both the MV leaflets and subvalvular apparatus. This novel data may improve MV computational models and provide a platform for the development of future surgical planning tools.     

Spatial and functional modeling of carnivore and insectivore molariform teeth

The interaction between the two main competing geometric determinants of teeth (the geometry of function and the geometry of occlusion) were investigated through the construction of three-dimensional spatial models of several mammalian tooth forms (carnassial, insectivore premolar, zalambdodont, dilambdodont, and tribosphenic). These models aim to emulate the shape and function of mammalian teeth. The geometric principles of occlusion relating to single- and double-crested teeth are reviewed. Function was considered using engineering principles that relate tooth shape to function. Substantial similarity between the models and mammalian teeth were achieved. Differences between the two indicate the influence of tooth strength, geometric relations between upper and lower teeth (including the presence of the protocone), and wear on tooth morphology. The concept of "autocclusion" is expanded to include any morphological features that ensure proper alignment of cusps on the same tooth and other teeth in the tooth row. It is concluded that the tooth forms examined are auto-aligning, and do not require additional morphological guides for correct alignment. The model of therian molars constructed by Crompton and Sita-Lumsden ([1970] Nature 227:197-199) is reconstructed in 3D space to show that their hypothesis of crest geometry is erroneous, and that their model is a special case of a more general class of models.     

Structural simulations of prosthetic tri-leaflet aortic heart valves

This study presents a combined computational and experimental approach for the nonlinear structural simulations of polymeric tri-leaflet aortic valves (PAVs). Nonlinear shell-based and quasi-static finite-element (FE) structural models are generated for a prosthetic valve geometry that includes the leaflets, stents and root materials, such as the bottom base and outside walls. The PAV structural model is subject to an ensemble averaged transvalvular pressure waveform measured from repeated in vitro tests conducted with a left heart simulator. High-resolution optical measurements are used to measure the in vitro kinematics of the leaflets and the stents. Qualitative and quantitative deformation measures are defined in order to compare the predicted kinematics from the PAV models with the in vitro measurements. Six new quantitative deformation metrics are introduced. They include three distances measuring the current PAV geometric center to the leaflet edges while additional three distances define the stent post-to-stent post (SPTSP) distances. The structural model is able to predict the kinematic deformation metrics with maximum errors around 10% especially in systole where the displacements are larger in magnitude. The combined structural modeling with experimental simulations along with the new proposed deformation metrics provide an effective way to study the PAV structural behavior and a path for improving the structural design of prosthetic valves.     

An inverse modeling approach for stress estimation in mitral valve anterior leaflet valvuloplasty for in-vivo valvular biomaterial assessment

Estimation of regional tissue stresses in the functioning heart valve remains an important goal in our understanding of normal valve function and in developing novel engineered tissue strategies for valvular repair and replacement. Methods to accurately estimate regional tissue stresses are thus needed for this purpose, and in particular to develop accurate, statistically informed means to validate computational models of valve function. Moreover, there exists no currently accepted method to evaluate engineered heart valve tissues and replacement heart valve biomaterials undergoing valvular stresses in blood contact. While we have utilized mitral valve anterior leaflet valvuloplasty as an experimental approach to address this limitation, robust computational techniques to estimate implant stresses are required. In the present study, we developed a novel numerical analysis approach for estimation of the in-vivo stresses of the central region of the mitral valve anterior leaflet (MVAL) delimited by a sonocrystal transducer array. The in-vivo material properties of the MVAL were simulated using an inverse FE modeling approach based on three pseudo-hyperelastic constitutive models: the neo-Hookean, exponential-type isotropic, and full collagen–fiber mapped transversely isotropic models. A series of numerical replications with varying structural configurations were developed by incorporating measured statistical variations in MVAL local preferred fiber directions and fiber splay. These model replications were then used to investigate how known variations in the valve tissue microstructure influence the estimated ROI stresses and its variation at each time point during a cardiac cycle. Simulations were also able to include estimates of the variation in tissue stresses for an individual specimen dataset over the cardiac cycle. Of the three material models, the transversely anisotropic model produced the most accurate results, with ROI averaged stresses at the fully-loaded state of  432.6±46.5 kPa and 241.4±40.5 kPa in the radial and circumferential directions, respectively. We conclude that the present approach can provide robust instantaneous mean and variation estimates of tissue stresses of the central regions of the MVAL.     

In vitro and in silico approaches to quantify the effects of the Mitraclip® system on mitral valve function

Mitraclip^® implantation is widely used as a valid alternative to conventional open-chest surgery in high-risk patients with severe mitral valve (MV) regurgitation. Although effective in reducing mitral regurgitation (MR) in the majority of cases, the clip implantation produces a double-orifice area that can result in altered MV biomechanics, particularly in term of hemodynamics and mechanical stress distribution on the leaflets.In this scenario, we combined the consistency of in vitro experimental platforms with the versatility of numerical simulations to investigate clip impact on MV functioning. The fluid dynamic determinants of the procedure were experimentally investigated under different working conditions (from 40 bpm to 100 bpm of simulated heart rate) on six swine hearts; subsequently, fluid dynamic data served as realistic boundary conditions in a computational framework able to quantitatively assess the post-procedural MV biomechanics. The finite element model of a human mitral valve featuring an isolated posterior leaflet prolapse was reconstructed from cardiac magnetic resonance. A complete as well as a marginal, sub-optimal grasping of the leaflets were finally simulated.The clipping procedure resulted in a properly coapting valve from the geometrical perspective in all the simulated configurations. Symmetrical complete grasping resulted in symmetrical distribution of the mechanical stress, while uncomplete asymmetrical grasping resulted in higher stress distribution, particularly on the prolapsing leaflet.This work pinpointed that the mechanical stress distribution following the clipping procedure is dependent on the cardiac hemodynamics and has a correlation with the proper execution of the grasping procedure, requiring accurate evaluation prior to clip delivery.     

An inverse modeling approach for semilunar heart valve leaflet mechanics: exploitation of tissue structure

Determining the biomechanical behavior of heart valve leaflet tissues in a noninvasive manner remains an important clinical goal. While advances in 3D imaging modalities have made in vivo valve geometric data available, optimal methods to exploit such information in order to obtain functional information remain to be established. Herein we present and evaluate a novel leaflet shape-based framework to estimate the biomechanical behavior of heart valves from surface deformations by exploiting tissue structure. We determined accuracy levels using an “ideal” in vitro dataset, in which the leaflet geometry, strains, mechanical behavior, and fibrous structure were known to a high level of precision. By utilizing a simplified structural model for the leaflet mechanical behavior, we were able to limit the number of parameters to be determined per leaflet to only two. This approach allowed us to dramatically reduce the computational time and easily visualize the cost function to guide the minimization process. We determined that the image resolution and the number of available imaging frames were important components in the accuracy of our framework. Furthermore, our results suggest that it is possible to detect differences in fiber structure using our framework, thus allowing an opportunity to diagnose asymptomatic valve diseases and begin treatment at their early stages. Lastly, we observed good agreement of the final resulting stress–strain response when an averaged fiber architecture was used. This suggests that population-averaged fiber structural data may be sufficient for the application of the present framework to in vivo studies, although clearly much work remains to extend the present approach to in vivo problems.     

Effects of organelle shape on fluorescence recovery after photobleaching

The determination of diffusion coefficients from fluorescence recovery data is often complicated by geometric constraints imposed by the complex shapes of intracellular compartments. To address this issue, diffusion of proteins in the lumen of the endoplasmic reticulum (ER) is studied using cell biological and computational methods. Fluorescence recovery after photobleaching (FRAP) experiments are performed in tissue culture cells expressing GFP-KDEL, a soluble, fluorescent protein, in the ER lumen. The three-dimensional (3D) shape of the ER is determined by confocal microscopy and computationally reconstructed. Within these ER geometries diffusion of solutes is simulated using the method of particle strength exchange. The simulations are compared to experimental FRAP curves of GFP-KDEL in the same ER region. Comparisons of simulations in the 3D ER shapes to simulations in open 3D space show that the constraints imposed by the spatial confinement result in two- to fourfold underestimation of the molecular diffusion constant in the ER if the geometry is not taken into account. Using the same molecular diffusion constant in different simulations, the observed speed of fluorescence recovery varies by a factor of 2.5, depending on the particular ER geometry and the location of the bleached area. Organelle shape considerably influences diffusive transport and must be taken into account when relating experimental photobleaching data to molecular diffusion coefficients. This novel methodology combines experimental FRAP curves with high accuracy computer simulations of diffusion in the same ER geometry to determine the molecular diffusion constant of the solute in the particular ER lumen.     

On the relative importance of rheology for image-based CFD models of the carotid bifurcation

BACKGROUND: Patient-specific computational fluid dynamics (CFD) models derived from medical images often require simplifying assumptions to render the simulations conceptually or computationally tractable. In this study, we investigated the sensitivity of image-based CFD models of the carotid bifurcation to assumptions regarding the blood rheology. METHOD OF APPROACH: CFD simulations of three different patient-specific models were carried out assuming: a reference high-shear Newtonian viscosity, two different non-Newtonian (shear-thinning) rheology models, and Newtonian viscosities based on characteristic shear rates or, equivalently, assumed hematocrits. Sensitivity of wall shear stress (WSS) and oscillatory shear index (OSI) were contextualized with respect to the reproducibility of the reconstructed geometry, and to assumptions regarding the inlet boundary conditions. RESULTS: Sensitivity of WSS to the various rheological assumptions was roughly 1.0 dyn/cm(2) or 8%, nearly seven times less than that due to geometric uncertainty (6.7 dyn/cm(2) or 47%), and on the order of that due to inlet boundary condition assumptions. Similar trends were observed regarding OSI sensitivity. Rescaling the Newtonian viscosity based on time-averaged inlet shear rate served to approximate reasonably, if overestimate slightly, non-Newtonian behavior. CONCLUSIONS: For image-based CFD simulations of the normal carotid bifurcation, the assumption of constant viscosity at a nominal hematocrit is reasonable in light of currently available levels of geometric precision, thus serving to obviate the need to acquire patient-specific rheological data.     

Validation of CFD simulations of cerebral aneurysms with implication of geometric variations

BACKGROUND: Computational fluid dynamics (CFD) simulations using medical-image-based anatomical vascular geometry are now gaining clinical relevance. This study aimed at validating the CFD methodology for studying cerebral aneurysms by using particle image velocimetry (PIV) measurements, with a focus on the effects of small geometric variations in aneurysm models on the flow dynamics obtained with CFD. METHOD OF APPROACH: An experimental phantom was fabricated out of silicone elastomer to best mimic a spherical aneurysm model. PIV measurements were obtained from the phantom and compared with the CFD results from an ideal spherical aneurysm model (S1). These measurements were also compared with CFD results, based on the geometry reconstructed from three-dimensional images of the experimental phantom. We further performed CFD analysis on two geometric variations, S2 and S3, of the phantom to investigate the effects of small geometric variations on the aneurysmal flow field. Results. We found poor agreement between the CFD results from the ideal spherical aneurysm model and the PIV measurements from the phantom, including inconsistent secondary flow patterns. The CFD results based on the actual phantom geometry, however, matched well with the PIV measurements. CFD of models S2 and S3 produced qualitatively similar flow fields to that of the phantom but quantitatively significant changes in key hemodynamic parameters such as vorticity, positive circulation, and wall shear stress. CONCLUSION: CFD simulation results can closely match experimental measurements as long as both are performed on the same model geometry. Small geometric variations on the aneurysm model can significantly alter the flow-field and key hemodynamic parameters. Since medical images are subjected to geometric uncertainties, image-based patient-specific CFD results must be carefully scrutinized before providing clinical feedback.     

Single-step stereolithography of complex anatomical models for optical flow measurements

Transparent stereolithographic rapid prototyping (RP) technology has already demonstrated in literature to be a practical model construction tool for optical flow measurements such as digital particle image velocimetry (DPIV), laser doppler velocimetry (LDV), and flow visualization. Here, we employ recently available transparent RP resins and eliminate time-consuming casting and chemical curing steps from the traditional approach. This note details our methodology with relevant material properties and highlights its advantages. Stereolithographic model printing with our procedure is now a direct single-step process, enabling faster geometric replication of complex computational fluid dynamics (CFD) models for exact experimental validation studies. This methodology is specifically applied to the in vitro flow modeling of patient-specific total cavopulmonary connection (TCPC) morphologies. The effect of RP machining grooves, surface quality, and hydrodynamic performance measurements as compared with the smooth glass models are also quantified.     

Geometric effects in gas vesicle buckling under ultrasound

Acoustic reporter genes based on gas vesicles (GVs) have enabled the use of ultrasound to noninvasively visualize cellular function in vivo. The specific detection of GV signals relative to background acoustic scattering in tissues is facilitated by nonlinear ultrasound imaging techniques taking advantage of the sonomechanical buckling of GVs. However, the effect of geometry on the buckling behavior of GVs under exposure to ultrasound has not been studied. To understand such geometric effects, we developed computational models of GVs of various lengths and diameters and used finite element simulations to predict their threshold buckling pressures and postbuckling deformations. We demonstrated that the GV diameter has an inverse cubic relation to the threshold buckling pressure, whereas length has no substantial effect. To complement these simulations, we experimentally probed the effect of geometry on the mechanical properties of GVs and the corresponding nonlinear ultrasound signals. The results of these experiments corroborate our computational predictions. This study provides fundamental insights into how geometry affects the sonomechanical properties of GVs, which, in turn, can inform further engineering of these nanostructures for high-contrast, nonlinear ultrasound imaging.     

Accuracy and reproducibility of CFD predicted wall shear stress using 3D ultrasound images

Computational fluid dynamics (CFD) flow simulation techniques have the potential to enhance our understanding of how haemodynamic factors are involved in atherosclerosis. Recently, 3D ultrasound has emerged as an alternative to other 3D imaging techniques, such as magnetic resonance angiography (MRA). The method can be used to generate realistic vascular geometry suitable for CFD simulations. In order to assess accuracy and reproducibility of the procedure from image acquisition to reconstruction to CFD simulation, a human carotid artery bifurcation phantom was scanned three times using 3D ultrasound. The geometry was reconstructed and flow simulations were carried out on the three sets as well as on a model generated using computer aided design (CAD) from the geometric information given by the manufacturer. It was found that the three reconstructed sets showed good reproducibility as well as satisfactory quantitative agreement with the CAD model. Analyzing two selected locations probably representing the 'worst cases,' accuracy comparing ultrasound and CAD reconstructed models was estimated to be between 7.2% and 7.7% of the maximum instantaneous WSS and reproducibility comparing the three scans to be between 8.2% and 10.7% of their average maximum.     

Can isolated annular dilatation cause significant ischemic mitral regurgitation? Another look at the causative mechanisms

This study was to investigate the mechanisms of ischemic mitral regurgitation (IMR) by using a finite element (FE) approach. IMR is a common complication of coronary artery disease; and it usually occurs due to myocardial infarction. The pathophysiological mechanisms of IMR have not been fully understood, much debate remains about the exact contribution of each mechanism to IMR. Two patient-specific FE models of normal mitral valves (MV) were reconstructed from multi-slice computed tomography scans. Different grades of IMR during its pathogenesis were created by perturbation of the normal MV geometry. Effects of annular dilatation and papillary muscle (PM) displacement (both isolated and combined) on the severity of IMR were examined. We observed greater increase in IMR (in terms of regurgitant area and coaptation length) in response to isolated annular dilatation than that caused by isolated PM displacement, while a larger PM displacement resulted in higher PM forces. Annular dilation, combined with PM displacement, was able to significantly increase the severity of IMR and PM forces. Our simulations demonstrated that isolated annular dilatation might be a more important determinant of IMR than isolated PM displacement, which could help explain the clinical observation that annular size reduction by restrictive annuloplasty is generally effective in treating IMR.     

FSI simulation of asymmetric mitral valve dynamics during diastolic filling

In this article, we present a fluid-structure interaction algorithm accounting for the mutual interaction between two rigid bodies. The algorithm was used to perform a numerical simulation of mitral valve (MV) dynamics during diastolic filling. In numerical simulations of intraventricular flow and MV motion, the asymmetry of the leaflets is often neglected. In this study the MV was rendered as two rigid, asymmetric leaflets. The 2D simulations incorporated the dynamic interaction of blood flow and leaflet motion and an imposed subject-specific, transient left ventricular wall movement obtained from ultrasound recordings. By including the full Jacobian matrix in the algorithm, the speed of the simulation was enhanced by more than 20% compared to using a diagonal Jacobian matrix. Furthermore, our results indicate that important features of the flow field may not be predicted by the use of symmetric leaflets or in the absence of an adequate model for the left atrium.     

Multi-Formalism Modelling and Simulation: Application to Cardiac Modelling

Cardiovascular modelling has been a major research subject for the last decade. Different cardiac models have been developed at a cellular level as well as at the whole organ level. Most of these models are defined by a comprehensive cellular modelling using continuous formalisms or by a tissue-level modelling often based on discrete formalisms. Nevertheless, both views still suffer from difficulties that reduce their clinical applications: the first approach requires heavy computational resources while the second one is not able to reproduce certain pathologies. This paper presents an original methodology trying to gather advantages from both approaches, by means of a hybrid model mixing discrete and continuous formalisms. This method has been applied to define a hybrid model of cardiac action potential propagation on a 2D grid of endocardial cells, combining cellular automata and a set of cells defined by the Beeler-Reuter model. For simulations under physiological and ischemic conditions, results show that the action potential propagation as well as electrogram reconstructions are consistent with clinical diagnosis. Finally, the advantage of the proposed approach is discussed within the frame of cardiac modelling and simulation.     

On the effect of parent-aneurysm angle on flow patterns in basilar tip aneurysms: towards a surrogate geometric marker of intra-aneurismal hemodynamics

As a part of previous computational fluid dynamic (CFD) validation studies, particle image velocimetry (PIV) of two anatomically realistic basilar artery tip aneurysm models revealed two distinct types of flow (one of which has yet to be reported in the literature), characterized by the location and strength of the intra-aneurismal vortex. We hypothesized that these distinct "hemodynamic phenotypes" could be anticipated by a simple geometric parameter: the angle of the aneurysm bulb relative to the parent artery. An idealized basilar tip aneurysm model was constructed to allow independent control of this angle, and CFD simulations were carried out for angles ranging from 2 degrees to 30 degrees , these extremes corresponding to the angles measured from the two anatomically realistic models. The gross hemodynamics predicted by the idealized model for 2 degrees and 30 degrees were consistent with those seen in the corresponding anatomically realistic models. For the idealized model, the flow type switched at an angle between 8 degrees and 12 degrees . Sensitivity studies suggested that, near these angles, the hemodynamic phenotype was sensitive to inflow momentum. Outside this range, however, the parent-bulb angle appeared to be a robust predictor of hemodynamic phenotype. Our findings suggest that blood flow dynamics in basilar artery tip aneurysms fall into one of the two broad phenotypes, each subject to distinct hemodynamic forces. That the general features of these flow types may be anticipated by a relatively simple-to-measure geometric parameter could help ease the introduction of hemodynamic information into routine clinical decision-making.     

A patient-specific aortic valve model based on moving resistive immersed implicit surfaces

In this paper, we propose a full computational framework to simulate the hemodynamics in the aorta including the valve. Closed and open valve surfaces, as well as the lumen aorta, are reconstructed directly from medical images using new ad hoc algorithms, allowing a patient-specific simulation. The fluid dynamics problem that accounts from the movement of the valve is solved by a new 3D–0D fluid–structure interaction model in which the valve surface is implicitly represented through level set functions, yielding, in the Navier–Stokes equations, a resistive penalization term enforcing the blood to adhere to the valve leaflets. The dynamics of the valve between its closed and open position is modeled using a reduced geometric 0D model. At the discrete level, a finite element formulation is used and the SUPG stabilization is extended to include the resistive term in the Navier–Stokes equations. Then, after time discretization, the 3D fluid and 0D valve models are coupled through a staggered approach. This computational framework, applied to a patient-specific geometry and data, allows to simulate the movement of the valve, the sharp pressure jump occurring across the leaflets, and the blood flow pattern inside the aorta.