Mathematical modelling of implant in an operated hernia for estimation of the repair persistence

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Abstract
This paper presents mathematical modelling of an implanted surgical mesh used in the repair process of the abdominal hernia. The synthetic implant is simulated by a membrane structure. The author provides a material modelling of the implant based on the dense net model appropriate for technical fabrics. The accuracy of the proposed solution is evaluated by comparing the simulations of the dynamic behaviour of the system with the experiments carried out on physical models of implanted mesh. The model can be used to estimate the repair persistence for different mesh materials, fixing systems and different numbers of tacks to be provided during the surgery in order to resist the cough pressure and required action to avoid hernia recurrence. The persistence of the repaired hernia is assessed on the basis of the values of the forces in the tissue-implant joints because the usual form of the repair failure is due to as the joint disconnection or tissue failure.