## Complex Flow Modeling & Simulation Lab - Research

**Methodology**

Immersed boundary method (IBM) is gaining increasing attentions on its unique capability to deal with complex stationary/moving boundaries, which makes it ideally suitable to complex flow modeling, such as those encountered in the biological, physiological, and bio-inspired systems. A three-dimensional sharp interface IBM based incompressible flow solver been developed for complex flow simulations. The key features of this solver are:

- The ability to perform direct-numerical simulation (DNS) of flows with complex moving boundaries with 2
^{nd}order accuracy in both space and time domains; - Full parallelization using message passing interface (MPI) which allows for rapid simulation on O(10
^{3}) processors; - A hierarchical nested grid approach based grid refinement technology which allows a high level of flexibility in local refinement to further improve the accuracy and efficiency of the solver;
- A continuum based FEM model coupled to flow solver for modeling flow-induced deformation and dynamics of inhomogeneous viscoelastic structures.

**Complex Flow Analysis**

A series of computer tools based on novel model reduction and decomposition techniques as well as the new Lagrangian definition of vortex were developed for studying the dynamic behavior of complex nonlinear flows, such as those routinely encountered in biological and physiological systems. Techniques include:

- POD (Principle Orthogonal Decomposition)
- DMD (Dynamic Mode Decomposition)
- LCS (Lagrangian Coherent Structure)

Computed LCS of (a) airflow in larynx during phonation and (b) blood flow in left ventricle during diastole. |

**Numerical modeling of Flow-structure interaction during phonation**

Phonation is a complex biological phenomenon which results from a highly coupled biomechanical interaction between glottal aerodynamics and vocal fold tissue vibrations. We have conducted high-fidelity FSI simulations on three-dimensional larynx models to gain insights into the biophysics of phonation. Self-sustained vocal fold vibrations with vibratory modes that correspond to physiological observations have been successfully captured. Dynamic behaviors of both phonatory flow and vocal fold deformation and their implications in voice production were investigated. A detailed analysis of the velocity and vorticity fields showed that the downstream vortex asymmetric structures induce a flow at the glottal exit which is the primary driver for glottal jet deflection. We also examined the effect of false vocal folds on phonation, and found that false-vocal folds tend to aid phonation by reducing the effort required to phonate and by increasing the sound intensity for a given effort.

**Cardiac Flow Modeling**

The key features of cardiac flows: highly complex three-dimensional geometries, relatively high (~4000) Reynolds numbers which result in transition to turbulence, and finally, large-scale boundary motion induced by active (muscle contraction) as well as passive (flow-induced such as in valve leaflets) mechanisms, represent a significant challenge for modeling of cardiac hemodynamics. Consequently, modelers resort to gross simplifications in the geometry, kinematics or the flow physics. The human heart is, however, a finely tuned instrument where all the components/features work in concert to produce high levels of performance and ad-hoc simplifications of any of these features can have unknown implications for model fidelity. In the current effort, we develop an integrated computational framework to perform patient-specific simulations of the whole heart system in all their complexity, which includes hemodynamics, tissue mechanics as well as electrophysiology. Special interests are given to the hemodynamic aspect of cardiac functions. Results will provide a comprehensive picture of the biomechanical aspects that contribute to a variety of flow-related heart diseases, such as diastolic heart dysfunction, hypertrophic cardiomyopathy, etc.

Cardiac Flow simulation on a patient specific model |

**Vascular flow Modeling**

Coronary artery stenosis, a partial narrowing of the coronary vessel, restricts the blood flow and may lead to ischemia and subsequent myocardial infarction. The anatomical assessment of lesion severity by invasive Quantitative Coronary Angiography (QCA) has been shown to be inadequate for identification of ischemic lesions, as opposed to hemodynamic assessment based on trans-stenotic pressure-drop measurement. Fractional Flow Reserve (FFR), defined as the ratio of the distal and proximal pressures across the lesion during hyperemia, is considered as the gold-standard for identification of significant lesions. Recently, several methods have been proposed for non-invasive estimation of trans-stenotic pressure drop, ranging from simple Poiseuille based estimates on QCA-derived simple geometries to unsteady 3-D computational fluid dynamics (CFD) based methods. The objective of this project is to estimate the non-invasive FFR values using combined QCA and CFD approach. Multi-scale modeling is employed to compute the coronary flow, which couples 3D Navier-Stoke equations for aorta and main coronary arteries with the 0D lumped element model for the coronary bed and heart. The simulated FFR values are validated through clinical pressure catheter measurements.