Bo Liao

Sheng Zhang, Bo Liao, Fei Liao

Enlightened from the inverse consideration of the stable continuous-time dynamics evolution, the Variation Evolving Method (VEM) analogizes the optimal solution to the equilibrium point of an infinite-dimensional dynamic system and solves it in an asymptotically evolving way. In this paper, the compact version of the VEM is further developed for the computation of Optimal Control Problems (OCPs) with terminal constraint. The corresponding Evolution Partial Differential Equation (EPDE), which describes the variation motion towards the optimal solution, is derived, and the costate-free optimality conditions are established. The explicit analytic expressions of the costates and the Lagrange multipliers adjoining the terminal constraint, related to the states and the control variables, are presented. With the semi-discrete method in the field of PDE numerical calculation, the EPDE is discretized as finite-dimensional Initial-value Problems (IVPs) to be solved, with common Ordinary Differential Equation (ODE) numerical integration methods.

Pengxu Wen, Tingting Yu, Ziwei Nie et al.

Intracranial pressure (ICP) elevation poses severe threats to cerebral function, thus necessitating monitoring for timely intervention. While lumbar puncture is the gold standard for ICP measurement, its invasiveness and associated risks drive the need for non-invasive alternatives. Optic nerve sheath diameter (ONSD) has emerged as a promising biomarker, as elevated ICP directly correlates with increased ONSD. However, current clinical practices for ONSD measurement suffer from inconsistency in manual operation, subjectivity in optimal view selection, and variability in thresholding, limiting their reliability. To address these challenges, we introduce a fully automatic two-stage framework for ICP grading, integrating keyframe identification, ONSD measurement and clinical data. Specifically, the fundus ultrasound video processing stage performs frame-level anatomical segmentation, rule-based keyframe identification guided by an international consensus statement, and precise ONSD measurement. The intracranial pressure grading stage then fuses ONSD metrics with clinical features to enable the prediction of ICP grades, thereby demonstrating an innovative blend of interpretable ultrasound analysis and multi-source data integration for objective clinical evaluation. Experimental results demonstrate that our method achieves a validation accuracy of $0.845 \pm 0.071$ (with standard deviation from five-fold cross-validation) and an independent test accuracy of 0.786, significantly outperforming conventional threshold-based method ($0.637 \pm 0.111$ validation accuracy, $0.429$ test accuracy). Through effectively reducing operator variability and integrating multi-source information, our framework establishes a reliable non-invasive approach for clinical ICP evaluation, holding promise for improving patient management in acute neurological conditions.