Signal propagation of the MAPK cascade in Xenopus oocytes: role of bistability and ultrasensitivity for a mixed problem.

The MAPK signaling cascade is nowadays understood as a network module highly conserved across species. Its main function is to transfer a signal arriving at the plasma membrane to the cellular interior. Current understanding of 'how' this is achieved involves the notions of ultrasensitivity and bistability which relate to the nonlinear dynamics of the biochemical network, ignoring spatial aspects. Much less, indeed, is so far known about the propagation of the signal through the cytoplasm. In this work we formulate, starting from a Michaelis-Menten model for the MAPK cascade in Xenopus oocytes, a reaction-diffusion model of the cascade. We study this model in one space dimension. Basing ourselves on previous general results on reaction diffusion models, we particularly study for our model the conditions for signal propagation. We show that the existence of a propagating front depends sensitively on the initial and boundary conditions at the plasma membrane. Possible biological consequences of this finding are discussed.

Simulation of high-intensity focused ultrasound lesions in presence of boiling.

BACKGROUND: The lesions induced by high-intensity focused ultrasound (HIFU) thermal ablations are particularly difficult to simulate due to the complexity of the involved phenomena. In particular, boiling has a strong influence on the lesion shape. Thus, it must be accounted for if it happens during the pulses to be modeled. However, no acoustic model enables the simulation of the resulting wave scattering. Therefore, we propose an equivalent model for the heat deposition pattern in the presence of boiling. METHODS: Firstly, the acoustic field is simulated with k-Wave and the heat source term is calculated. Then, a thermal model is designed, including the equivalent model for boiling. It is rigorously calibrated and validated through the use of diversified ex vivo and in vivo data, including usually unexploited data types related to the bubble clouds. RESULTS: The proposed model enabled to efficiently simulate unitary pulses properties, including the sizes of the lesions, their morphology, the boiling onset time, and the influence of the boiling onset time on the lesions sizes. CONCLUSIONS: In this article, the whole procedure of model design, calibration, and validation is discussed. In addition to depicting the creative use of data, our modeling approach focuses on the understanding of the mechanisms influencing the shape of the lesion. Further work is required to study the influence of the remaining bubble clouds in the context of pulse groups.

Influence of Skin and Subcutaneous Tissue on High-Intensity Focused Ultrasound Beam: Experimental Quantification and Numerical Modeling.

High-intensity focused ultrasound (HIFU) enables the non-invasive thermal ablation of tumors. However, numerical simulations of the treatment remain complex and difficult to validate in clinically relevant situations. In this context, needle hydrophone measurements of the acoustic field downstream of seven rabbit tissue layers comprising skin, subcutaneous fat and muscle were performed in different geometrical configurations. Increasing curvature and thickness of the sample were found to decrease the focusing of the beam: typically, a curvature of 0.05 mm(-1) decreased the maximum pressure by 45% and doubled the focal area. A numerical model based on k-Wave Toolbox was found to be in very good agreement with the reported measurements. It was used to extrapolate the effect of the superficial tissues on peak positive and peak negative pressure at focus, which affects both cavitation and target heating. The shape of the interface was found to have a strong influence on the values, and it is therefore an important parameter to monitor or to control in the clinical practice. This also highlights the importance of modeling realistic configurations when designing treatment procedures.