Due to advances in medical imaging, computational fluid dynamics algorithms and high performance computing, computer simulation is developing into an important tool for understanding the relationship ...between cardiovascular diseases and intraventricular blood flow. The field of cardiac flow simulation is challenging and highly interdisciplinary. We apply a computational framework for automated solutions of partial differential equations using Finite Element Methods where any mathematical description directly can be translated to code. This allows us to develop a cardiac model where specific properties of the heart such as fluid-structure interaction of the aortic valve can be added in a modular way without extensive efforts. In previous work, we simulated the blood flow in the left ventricle of the heart. In this paper, we extend this model by placing prototypes of both a native and a mechanical aortic valve in the outflow region of the left ventricle. Numerical simulation of the blood flow in the vicinity of the valve offers the possibility to improve the treatment of aortic valve diseases as aortic stenosis (narrowing of the valve opening) or regurgitation (leaking) and to optimize the design of prosthetic heart valves in a controlled and specific way. The fluid-structure interaction and contact problem are formulated in a unified continuum model using the conservation laws for mass and momentum and a phase function. The discretization is based on an Arbitrary Lagrangian-Eulerian space-time finite element method with streamline diffusion stabilization, and it is implemented in the open source software Unicorn which shows near optimal scaling up to thousands of cores. Computational results are presented to demonstrate the capability of our framework.
Cardiac disease and clinical intervention may both lead to an increased risk for thrombosis events due to a modified blood flow in the heart, and thereby a change in the mechanical stimuli of blood ...cells passing through the chambers of the heart. Specifically, the degree of platelet activation is influenced by the level and type of mechanical stresses in the blood flow. In this article we analyze the blood flow in the left ventricle of the heart through a computational model constructed from patient-specific data. The blood flow in the ventricle is modelled by the Navier-Stokes equations, and the flow through the mitral valve by a parameterized model which represents the projected opening of the valve. A finite element method is used to solve the equations, from which a simulation of the velocity and pressure of the blood flow is constructed. The intraventricular blood flow is complex, in particular in diastole when the inflow jet from the atrium breaks down into turbulent flow on a range of scales. A triple decomposition of the velocity gradient tensor is then used to distinguish between rigid body rotational flow, irrotational straining flow, and shear flow. The triple decomposition enables the separation of three fundamentally different flow structures, that each generates a distinct type of mechanical stimulus on the blood cells in the flow. We compare the results in a simulation where a mitral valve clip intervention is modelled, which leads to a significant modification of the intraventricular flow. Further, we perform a sensitivity study of the results with respect to the positioning of the clip. It was found that the shear in the simulation cases treated with clips increased more compared to the untreated case than the rotation and strain did. A decrease in valve opening area of 64% in one of the cases led to a 90% increase in rotation and strain, but a 150% increase in shear. The computational analysis opens up for improvements in models of shear-induced platelet activation, by offering an algorithm to distinguish shear from other modalities in intraventricular blood flow.
Aortic stiffness plays a critical role in the evolution of cardiovascular diseases, but the assessment requires specialized equipment. Photoplethysmography (PPG) and single-lead electrocardiogram ...(ECG) are readily available in healthcare and wearable devices. We studied whether a brief PPG registration, alone or in combination with single-lead ECG, could be used to reliably estimate aortic stiffness.
A proof-of-concept study with simultaneous high-resolution index finger recordings of infrared PPG, single-lead ECG, and finger blood pressure (Finapres) was performed in 33 participants median age 44 (range 21-66) years, 19 men and repeated within 2 weeks. Carotid-femoral pulse wave velocity (cfPWV; two-site tonometry with SphygmoCor) was used as a reference. A brachial single-cuff oscillometric device assessed aortic pulse wave velocity (aoPWV; Arteriograph) for further comparisons. We extracted 136 established PPG waveform features and engineered 13 new with improved coupling to the finger blood pressure curve. Height-normalized pulse arrival time (NPAT) was derived using ECG. Machine learning methods were used to develop prediction models.
The best PPG-based models predicted cfPWV and aoPWV well (root-mean-square errors of 0.70 and 0.52 m/s, respectively), with minor improvements by adding NPAT. Repeatability and agreement were on par with the reference equipment. A new PPG feature, an amplitude ratio from the early phase of the waveform, was most important in modelling, showing strong correlations with cfPWV and aoPWV (
= -0.81 and -0.75, respectively, both
< 0.001).
Using new features and machine learning methods, a brief finger PPG registration can estimate aortic stiffness without requiring additional information on age, anthropometry, or blood pressure. Repeatability and agreement were comparable to those obtained using non-invasive reference equipment. Provided further validation, this readily available simple method could improve cardiovascular risk evaluation, treatment, and prognosis.
This is Volume 4 of the book series of the Body and Soul mathematics education reform program. It presents a unified new approach to computational simulation of turbulent flow starting from the ...general basis of calculus and linear algebra of Vol 1-3.
Adaptive DNS/LES (direct numerical simulation/large-eddy simulation) is used to compute the drag coefficient $c_D$ for the flow past a sphere at Reynolds number $\hbox{\it Re}\,{=}\,10^4$. Using less ...than $10^5$ mesh points, $c_D$ is computed to an accuracy of a few percent, corresponding to experimental precision, which is at least an order of magnitude cheaper than standard non-adaptive LES computations in the literature. Adaptive DNS/LES is a General Galerkin G2 method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate solutions to the Navier–Stokes equations, with the mesh being adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, in this paper $c_D$. Both the stopping criterion and the mesh refinement strategy are based on a posteriori error estimates, in the form of a space–time integral of residuals multiplied by derivatives of the solution of an associated dual problem, linearized at the approximate solution, and with data coupling to the output of interest. There is no filtering of the equations, and thus no Reynolds stresses are introduced that need modelling. The stabilization in the numerical method is acting as a simple turbulence model.
To date, it is unclear how fluid dynamics stimulate mechanosensory cells to induce an osteoprotective or osteodestructive response. We investigated how murine hematopoietic progenitor cells respond ...to 2 minutes of dynamic fluid flow stimulation with a precisely controlled sequence of fluid shear stresses. The response was quantified by measuring extracellular adenosine triphosphate (ATP), immunocytochemistry of Piezo1, and sarcoplasmic/endoplasmic Ca2+ reticulum ATPase 2 (SERCA2), and by the ability of soluble factors produced by mechanically stimulated cells to modulate osteoclast differentiation. We rejected our initial hypothesis that peak wall shear stress rate determines the response of hematopoietic progenitor cells to dynamic fluid shear stress, as it had only a minor correlation with the abovementioned parameters. Low stimulus amplitudes corresponded to activation of Piezo1, SERCA2, low concentrations of extracellular ATP, and inhibition of osteoclastogenesis and resorption area, while high amplitudes generally corresponded to osteodestructive responses. At a given amplitude (3 Pa) and waveform (square), the duration of individual stimuli (duty cycle) showed a strong correlation with the release of ATP and osteoclast number and resorption area. Collectively, our data suggest that hematopoietic progenitor cells respond in a viscoelastic manner to loading, since a combination of high shear stress amplitude and prolonged duty cycle is needed to trigger an osteodestructive response.
Plain Language Summary
In case of painful joints or missing teeth, the current intervention is to replace them with an implant to keep a high‐quality lifestyle. When exercising or chewing, the cells in the bone around the implant experience mechanical loading. This loading generally supports bone formation to strengthen the bone and prevent breaking, but can also stimulate bone loss when the mechanical loading becomes too high around orthopedic and dental implants. We still do not fully understand how cells in the bone can distinguish between mechanical loading that strengthens or weakens the bone. We cultured cells derived from the bone marrow in the laboratory to test whether the bone loss response depends on (i) how fast a mechanical load is applied (rate), (ii) how intense the mechanical load is (amplitude), or (iii) how long each individual loading stimulus is applied (duration). We mimicked mechanical loading as it occurs in the body, by applying very precisely controlled flow of fluid over the cells. We found that a mechanosensitive receptor Piezo1 was activated by a low amplitude stimulus, which usually strengthens the bone. The potential inhibitor of Piezo1, namely SERCA2, was only activated by a low amplitude stimulus. This happened regardless of the rate of application. At a constant high amplitude, a longer duration of the stimulus enhanced the bone‐weakening response. Based on these results we deduce that a high loading amplitude tends to be bone weakening, and the longer this high amplitude persists, the worse it is for the bone.
Summary
An interface tracking finite element methodology is presented for 3D turbulent flow fluid‐structure interaction, including full‐friction contact and topology changes, with specific focus on ...heart valve simulations. The methodology is based on a unified continuum fluid‐structure interaction model, which is a monolithic approach, where the fundamental conservation laws are formulated for the combined fluid‐structure continuum. Contact is modeled by local phase changes in the unified continuum, and computational results show the promise of the approach. The core algorithms are all based on the solution of partial differential equations with standard finite element methods, and hence any general purpose finite element library which can leverage state of the art hardware platforms can be used for the implementation of the methodology.
In this work we propose a new stabilized approach for solving the incompressible Navier–Stokes equations on fixed overlapping grids. This new approach is based on the partition of unity finite ...element method, which defines the solution fields as weighted sums of local fields, supported by the different grids. Here, the discrete weak formulation of the problem is re-set in cG(1)cG(1) stabilized form, which has the dual benefit of lowering grid resolution requirements for convection dominated flows and allowing for the use of velocity and pressure discretizations which do not satisfy the inf–sup condition. Additionally, we provide an outline of our implementation within an existing distributed parallel application and identify four key options to improve the code efficiency namely: the use of cache to store mapped quadrature points and basis function gradients, the intersection volume splitting algorithm, the use of lower order quadrature schemes, and tuning the partition weight associated with the interface elements. The new method is shown to have comparable accuracy to the single mesh boundary-fitted version of the same stabilized solver based on three transient flow tests including both 2D and 3D settings, as well as low and moderate Reynolds number flow conditions. Moreover, we demonstrate how the four implementation options have a synergistic effect lowering the residual assembly time by an order of magnitude compared to a naive implementation, and showing good load balancing properties.
•A stabilized multidomain approach for solving incompressible fluid flow is proposed.•Problem is discretized using a partition of unity finite element approach (PUFEM).•A set of PUFEM implementation strategies are proposed and investigated.•The approach shown have comparable accuracy to boundary-fitted alternative.•Implementation choices are shown to significantly improve code efficiency.
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