Abstract
Dynamic mode decomposition (DMD) is a purely data-driven and equation-free technique for reduced-order modeling of dynamical systems and fluid flow. DMD finds a best fit linear reduced-order model that represents any given spatiotemporal data. In DMD, each mode evolves with a fixed frequency and therefore DMD modes represent physically meaningful structures that are ranked based on their dynamics. The application of DMD to patient-specific cardiovascular flow data is challenging. First, the input flow rate is unsteady and pulsatile. Second, the flow topology can change significantly in different phases of the cardiac cycle. Finally, blood flow in patient-specific diseased arteries is complex and often chaotic. The objective of this study was to overcome these challenges using our proposed multistage dynamic mode decomposition with control (mDMDc) method and use this technique to study patient-specific blood flow physics. The inlet flow rate was considered as the controller input to the systems. Blood flow data were divided into different stages based on the inlet flow waveform and DMD with control was applied to each stage. The system was augmented to consider both velocity and wall shear stress (WSS) vector data, and therefore study the interaction between the coherent structures in velocity and near-wall coherent structures in WSS. First, it was shown that DMD modes can exactly represent the analytical Womersley solution for incompressible pulsatile flow in tubes. Next, our method was applied to image-based coronary artery stenosis and cerebral aneurysm models where complex blood flow patterns are anticipated. The flow patterns were studied using the mDMDc modes and the reconstruction errors were reported. Our augmented mDMDc framework could capture coherent structures in velocity and WSS with a fewer number of modes compared to the traditional DMD approach and demonstrated a close connection between the velocity and WSS modes.
Highlights
Patient-specific computational fluid dynamics (CFD) has evolved over the past two decades to become a leading modality for obtaining 3D time-resolved blood flow data [1,2]
The goal of this study is to demonstrate that multistage dynamic mode decomposition with control (mDMDc) could reveal the hidden low dimensionality in patient-specific blood flow data and facilitate quantitative flow physics analysis
The application of Dynamic mode decomposition (DMD) to cardiovascular flow physics raises a major question: why is DMD an appropriate framework to represent velocity and wall shear stress (WSS) data from patient-specific cardiovascular flows?. To answer this question we demonstrated that the classical Womersley solution could be represented using DMD modes and DMD analysis precisely identifies the frequencies in the Womersley solution
Summary
Patient-specific computational fluid dynamics (CFD) has evolved over the past two decades to become a leading modality for obtaining 3D time-resolved blood flow data [1,2]. Advances in these simulations have recently led to the first ever food and drug administration (FDA) approval of computer simulations in evaluating the severity of coronary artery disease using CFD derived fractional flow reserve [3]. Thanks to today’s computational power and high-performance computing, we are capable of generating hemodynamic data with extraordinarily high spatiotemporal resolution consisting of meshes with tens of millions of degrees of freedom and spanning tens of thousands of intra-cardiac time steps [4,5]. The field of “hybrid analytics" is developed to approximate a nonlinear dynamical system with a system that can switch between different linear models [8,9]
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