The augmented multistage dynamic mode decomposition with control (mDMDc) framework captured coherent structures in velocity and wall shear stress with fewer modes than the traditional DMD approach.
The proposed mDMDc method improves the modeling of complex, pulsatile patient-specific cardiovascular blood flow by capturing velocity and wall shear stress structures more efficiently than traditional methods.
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.
Habibi et al. (Tue,) conducted a other in Coronary artery stenosis and cerebral aneurysm. Multistage dynamic mode decomposition with control (mDMDc) vs. Traditional DMD approach was evaluated on Reconstruction errors and capture of coherent structures in velocity and wall shear stress. The augmented multistage dynamic mode decomposition with control (mDMDc) framework captured coherent structures in velocity and wall shear stress with fewer modes than the traditional DMD approach.
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