ABSTRACT
We demonstrate the application of the Dynamic Mode Decomposition (DMD) for the diagnostic analysis of the nonlinear dynamics of a magnetized plasma in resistive magnetohydrodynamics. The DMD method is an ideal spatio-temporal matrix decomposition that correlates spatial features of computational or experimental data while simultaneously associating the spatial activity with periodic temporal behavior. DMD can produce low-rank, reduced order surrogate models that can be used to reconstruct the state of the system with high fidelity. This allows for a reduction in the computational cost and, at the same time, accurate approximations of the problem, even if the data are sparsely sampled. We demonstrate the use of the method on both numerical and experimental data, showing that it is a successful mathematical architecture for characterizing the helicity injected torus with steady inductive (HIT-SI) magnetohydrodynamics. Importantly, the DMD produces interpretable, dominant mode structures, including a stationary mode consistent with our understanding of a HIT-SI spheromak accompanied by a pair of injector-driven modes. In combination, the 3-mode DMD model produces excellent dynamic reconstructions across the domain of analyzed data.
ABSTRACT
OBJECTIVE: To evaluate endothelial cell density (ECD) of eye-bank-prepared tissue for use in Descemet's stripping automated endothelial keratoplasty (DSAEK). DESIGN: Prospective case series of consecutive corneal tissue prepared for DSAEK surgery. PARTICIPANTS: Sixty-seven sequential corneal-scleral tissue specimens representing 48 human donors processed for use in DSAEK surgery by the Regional Tissue Bank (Halifax, Nova Scotia). METHODS: Corneal-scleral donor tissue was obtained by in situ recovery. ECD was recorded using the EB-3000 XYZ (HAI Laboratories Inc, Lexington, MA) specular microscope within 24 hours of preservation. Before the tissue was dissected, the corneal thickness was measured using the DGH-550 PACHETTE 2 (DGH Technology, Exton, PA) ultrasound pachymeter. The dissection was performed using a 300-µm Moria ALTK model microkeratome (Moria Inc). The posterior bed thickness was measured, and the anterior flap was replaced. Endothelial cell count density was obtained after re-preservation. RESULTS: Complete measurements were obtained for 42 of 67 corneas. In 25 corneas it was not possible to obtain a postdissection ECD measurement. The mean ECD before dissection was 2806 ± 317 cells/mm(2). The mean ECD after dissection was 2772 ± 318 cells/mm(2). There was an average loss of 34 cells/mm(2) (95% CI -110 to 40 cells/mm(2), p = 0.3). CONCLUSIONS: This case series confirms that ECD is preserved when DSAEK tissue is prepared in advance of surgery by trained eye-bank technicians in a low-volume Canadian eye bank. It was difficult to obtain clear images of the endothelial cell layer postdissection, possibly because of tissue swelling or distortion. Sixty-six of 67 corneas included in the study were used for surgery.
