Research

A stabilized formulation for the solution of unsteady Stokes equation in the frequency domain

In our earlier study, we showed that simulating cardiorespiratory flows in the frequency domain presents a significant cost advantage over a traditional time formulation. That earlier study, however, relied on a crude Bubnov-Galerkin finite element method that posed some limitations on the applicability of a time-spectral method. In a more recent study, we systematically developed a more elegant stabilized finite element method that strictly uses real arithmetics and permits the use of similar interpolation functions for pressure and velocity for ease of implementation. This method, which is mass conservative up to the tolerance of the underlying linear solver, significantly outperforms its temporal counterparts in modeling cardiorespiratory flows. See this article for more details.

A cell-resolved Lagrangian solver for simulation of cells in macroscale flows

Direct simulation of red blood cells in macroscale vessels is computationally unaffordable as the two are separated by a large gap in length scale. To overcome this separation of scales, we introduced an affordable computational framework that accurately resolves the stress and deformation of individual cells in a spatially and temporally varying macroscale flow field such as those found in a typical medical device. The underlying idea of the present framework is to treat cells as one-way coupled tracers in the macroscale flow, extract flow dynamics in their vicinity, and then solve thin-shell structural equations to capture cells deformation. This work, which is featured in the Journal of Computational Physics, incorporates the use of the boundary integral method and spherical harmonics to shed light on the cell's dynamics in stage-one operation performed on single ventricles that historically experience a high rate of failure due to clot formation. See this article for more details.

A low-Reynolds ejector-pump design for single ventricles 

Our earlier proposal of the assisted bidirectional Glenn (ABG) procedure was proposed to address the drawbacks of the conventional surgery performed on neonates with single-ventricle physiology. Despite success in reducing heart workload and maintaining sufficient pulmonary flow, the ABG also raised the superior vena cava (SVC) pressure to a level that may not be tolerated by infants. In this study, we proposed a new ejector pump design to lower the SVC pressure. The idea behind this design was to move the nozzle insertion point upstream and utilize a slit shape outlet to promote mixing and pressure recovery. Our multidomain simulations showed a significant improvement achieved by this new design, lowering the SVC pressure by 4 mmHg below that of the original ABG and the bidirectional Glenn operation. See this and this article for more details.

A vacuum helmet for capturing pathogen-bearing droplets

With the rise of the pandemic, there has been a need for designing a device that protects dentists and otolaryngologists when they are practicing on patients. In this study, we proposed and simulated a helmet design that could be used by patients to minimize transmission risk by retaining droplets created through coughing. The helmet has a port for accessing the mouth and nose and another port connected to a vacuum source to prevent droplets from exiting through the access port and contaminating the environment or clinical practitioners. We used computational fluid dynamics (CFD) in conjunction with Lagrangian point-particle tracking to simulate droplet trajectories when a patient coughs while using this device. The results of this study show that 100% of the airborne droplets and 99.6% of all cough droplets are captured by this helmet. See this article for more details.

A scalable spectral Stokes solver for simulation of time-periodic flows

Simulation of unsteady creeping flow in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. In this study, we propose an alternative approach that is formulated based on the unsteady Stokes equation expressed in the spectral domain. The advantageous of the new formulation are: 1) by solving for a few modes rather than thousands of time steps, it significantly reduces the computational cost, 2) it exhibits a super convergence behavior versus the number of computed modes, and 3) it is embarrassingly parallelizable, thus enabling scalable calculations at a much larger number of processors. The proposed method produces more accurate results at 1\% to 11\% of the cost of the standard technique for a variety of studied cases. See this article for more details.

Optimal O(N) techniques for collision detection and particle localization

The cost of tracking Lagrangian particles in a domain discretized on an unstructured grid can become prohibitively expensive as the number of particles or elements grows. A major part of the cost in these calculations is spent on locating the element that hosts a particle and detecting binary collisions, with the latter traditionally requiring O(N^2) operations, N being the number of particles. This paper introduces an optimal search box strategy to significantly reduce the cost of these two operations, ensuring a nearly O(N) scaling of the cost of collision detection for large-scale simulations. The particle localization strategy is constructed by obtaining an a priori estimate for the optimal number of search boxes as a function of the number of elements, particles, and time steps. The introduced method is generic, as it must be tuned only once for a given implementation and element type. The optimal number of search boxes for collision detection, although complex in form, can be reasonably approximated as the number of particles. In this study, we show the optimality of our method using three drastically varying geometries. See this article for more details.

A novel surgical design: The Assisted Bidirectional Glenn

In systemic-to-pulmonary shunt (SPS) circulatory arrangement, parallel blood flow occurs between the systemic and pulmonary circulations exposing the single ventricle in a state of volume and pressure overload. While treatment strategies for single ventricle patients have improved significantly over the past 20 years, there remain a number of serious deficiencies associated with the initial SPS physiology, leading to mortality rates as high as 21% and making this procedure much higher risk than the subsequent Glenn and Fontan procedures. In this study, we proposed a radically different surgical approach, called Assisted Bidirectional Glenn (ABG), that could avoid the dangerous SPS physiology of the stage one surgery, remove the volume and pressure loads on the single ventricle, and potentially reduce the number of surgeries from three to two, thereby significantly reducing patient risk. See this article for more details.

Surgical design optimization

Single ventricle defect is a pediatric condition that occurs in approximately 2.4 out of 10,000 live births and is uniformly fatal without surgical treatment, typically requiring a series of three palliative surgeries that start immediately after birth by inserting a systemic-to-pulmonary shunt (SPS). The SPS physiology is known to carry the highest mortality and morbidity in the life of a single ventricle patient. This is partly attributed to a delicate balance between pulmonary and systemic perfusion that must be maintained by the SPS. Since this balance highly depends on the SPS geometry, we performed a systematic geometrical optimization with respect to the SPS diameter, anastomosis location and angles. We developed a multiscale framework for these simulations which allows capturing global changes in circulation from changes in the SPS geometry. See this article for more details.

A multiscale approach for modeling circulatory system

Implementation of boundary conditions in cardiovascular simulations poses numerical challenges due to the complex dynamic behavior of the circulatory system. The use of elaborate closed-loop lumped parameter network (LPN) models of the heart and the circulatory system as boundary conditions for computational fluid dynamics (CFD) simulations can provide valuable global dynamic information, particularly for patient-specific simulations. In this work, we introduced a modular framework with excellent stability and convergence properties for coupling an arbitrary LPN to a finite element Navier-Stokes solver. See this article for more details.

Prevention of instability caused by backflow

Simulation divergence due to backflow is a common, but not fully addressed, problem in three-dimensional simulations of blood flow in the large vessels. Because backflow is a naturally occurring physiologic phenomenon, careful treatment is necessary to realistically model backflow without artificially altering the local flow dynamics. In this study, we introduced a stabilization formulation to improve robustness and stability characteristics of the simulation. This method offers reduced effect on both local and global hemodynamics, little-to-no increase in computational cost, negligible implementation effort, and elimination of the need for tunable parameters. See this article for more details.

An Eulerian framework for calculation of residence time

Cardiovascular simulations provide a promising means to predict the risk of thrombosis in grafts, devices, and surgical anatomies in adult and pediatric patients. Recent findings suggest that thrombosis risk is increased in regions of flow recirculation and high residence time (RT). Current approaches for calculating RT are typically based on releasing a finite number of Lagrangian particles into the flow field and calculating RT by tracking their positions. Special care must be taken in Lagrangian simulations to achieve temporal and spatial convergence, often requiring repeated calculations. In this work, we introduce a non-discrete method in which RT is calculated in an Eulerian framework using the solution of the advection-diffusion-reaction equation. See this article for more details.

An analytical description of particle clustering

Inertial particles in turbulent flow tend to accumulate in straining regions of the flow, forming preferentially-concentrated clusters. This phenomenon is primarily observed when the particles relaxation time is comparable to the time scale of the flow, viz. the Stokes number of order unity. Almost not clustering is observed when Stokes number is very large or very small. Although this nonlinear behavior has been established through several previous experiments and numerical simulations, no quantitatively-verified analytical model exists to describe this behavior. In this work, we proposed an asymptotic solution that captures this nonlinear behavior by expressing the Lyapunov exponents of inertial particle pairs in terms of the spectrum of the norm of the rotation- and strain-rates tensors. Comparing the results of this analysis to the reference results shows an excellent agreement.

One of the practical outcomes o f this study is discovery of a particular flow regime that leads to strong separation of inertial particles. As shown in the following animation, when inertial particles that differ in diameter by only 1% are placed in a specific oscillatory shear flow, they exhibit an interesting  behavior: one group of particles (colored in red) collapse toward a point whereas the other group (colored in black) disperse. Our hope is to construct precise particle separator by exploiting this behavior in the future.