English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The purpose of this paper is to model mathematically certain mechanicalaspects of defibrillation. The time deformation of the heart tissue is modeledwith the elastodynamics equations dealing with the displacement field as mainunknown. These equations are coupled with a pressure whose variationscharacterize the defibrillation process. The pressure variable corresponds to aLagrange multiplier associated with the so-called global injectivity condition.We develop a hybrid optimal control approach in a general framework that coversin particular the maximization of the variations of this pressure, and also thetime the maximum is reached. The control operator is distributed, and can bedescribed in a form that corresponds to geometric aspects of the modeling. Formathematical convenience a damping term is added, and mathematical analysisbased on the $\L^p$-parabolic maximal regularity is provided for the stateequations and the rigorous derivation of optimality conditions. Numericalsimulations for a toy-model exploit these optimality conditions and illustratethe capacity of the approach.

Modeling defibrillation as a hybrid optimal control problem constrained with hyperelasticity and the global injectivity condition