Temporal Registration of Cardiac Multimodal Images Using Locally Linear Embedding Algorithm

Purpose: Multimodal Cardiac Image (MCI) registration is one of the evolving fields in the diagnostic methods of Cardiovascular Diseases (CVDs). Since the heart has nonlinear and dynamic behavior, Temporal Registration (TR) is the fundamental step for the spatial registration and fusion of MCIs to integrate the heart's anatomical and functional information into a single and more informative display. Therefore, in this study, a TR framework is proposed to align MCIs in the same cardiac phase. Materials and Methods: A manifold learning-based method is proposed for the TR of MCIs. The Euclidean distance among consecutive samples lying on the Locally Linear Embedding (LLE) of MCIs is computed. By considering cardiac volume pattern concepts from distance plots of LLEs, six cardiac phases (end-diastole, rapid-ejection, end-systole, rapid-filling, reduced-filling, and atrial-contraction) are temporally registered. Results: The validation of the proposed method proceeds by collecting the data of Computed Tomography Coronary Angiography (CTCA) and Transthoracic Echocardiography (TTE) from ten patients in four acquisition views. The Correlation Coefficient (CC) between the frame number resulted from the proposed method and manually selected by an expert is analyzed. Results show that the average CC between two resulted frame numbers is about 0.82±0.08 for six cardiac phases. Moreover, the maximum Mean Absolute Error (MAE) value of two slice extraction methods is about 0.17 for four acquisition views. Conclusion: By extracting the intrinsic parameters of MCIs, and finding the relationship among them in a lower-dimensional space, a fast, fully automatic, and user-independent framework for TR of MCIs is presented. The proposed method is more accurate compared to Electrocardiogram (ECG) signal labeling or time-series processing methods which can be helpful in different MCI fusion methods.

A Linear Dynamical Perspective on Epidemiology: Interplay Between Early COVID-19 Outbreak and Human Mobility

This paper investigates the impact of human activity and mobility (HAM) in the spreading dynamics of an epidemic. Specifically, it explores the interconnections between HAM and its effect on the early spread of the COVID-19 virus. During the early stages of the pandemic, effective reproduction numbers exhibited a high correlation with human mobility patterns, leading to a hypothesis that the HAM system can be studied as a coupled system with disease spread dynamics. This study applies the generalized Koopman framework with control inputs to determine the nonlinear disease spread dynamics and the input-output characteristics as a locally linear controlled dynamical system. The approach solely relies on the snapshots of spatiotemporal data and does not require any knowledge of the system’s physical laws. We exploit the Koopman operator framework by utilizing the Hankel Dynamic Mode Decomposition with Control (HDMDc) algorithm to obtain a linear disease spread model incorporating human mobility as a control input. The study demonstrated that the proposed methodology could capture the impact of local mobility on the early dynamics of the ongoing global pandemic. The obtained locally linear model can accurately forecast the number of new infections for various prediction windows ranging from two to four weeks. The study corroborates a leader-follower relationship between mobility and disease spread dynam-