Abdallah El Hamidi

A Direct PCA-Based Approach for Real-Time Description of Physiological Organ Deformations

Dynamic magnetic resonance (MR)-imaging can provide functional and positional information in real-time, which can be conveniently used online to control a cancer therapy, e.g., using high intensity focused ultrasound or radio therapy. However, a precise real-time correction for motion is fundamental in abdominal organs to ensure an optimal treatment dose associated with a limited toxicity in nearby organs at risk. This paper proposes a real-time direct principal component analysis (PCA)-based technique which offers a robust approach for motion estimation of abdominal organs and allows correcting motion related artifacts. The PCA was used to detect spatio-temporal coherences of the periodic organ motion in a learning step. During the interventional procedure, physiological contributions were characterized quantitatively using a small set of parameters. A coarse-to-fine resolution scheme is proposed to improve the stability of the algorithm and afford a predictable constant latency of 80 ms. The technique was evaluated on 12 free-breathing volunteers and provided an improved real-time description of motion related to both breathing and cardiac cycles. A reduced learning step of 10 s was sufficient without any need for patient-specific control parameters, rendering the method suitable for clinical use.

Necessary Conditions for Local and Global Solvability of Non-Diagonal Degenerate Systems

Cross-diffusion has been widely considered either in the mechanical description of diffusion or in the stochastic point process description of interacting populations, in the mathematical modelling of spatially structured epidemic or ecological systems and for the geographical diffusion of innovation. In this paper, specific attention is devoted to blowingup solutions of some systems which may reflect either failures in the modelling or genuine phenomena like aggregation of populations. Furthemore, necessary conditions for local and global existence of solutions to the considered systems are presented.

Existence and nonexistence results for reaction-diffusion equations in product of cones

Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.