Use of minimal invasive extracorporeal circulation in cardiac surgery: principles, definitions and potential benefits. A position paper from the Minimal invasive Extra-Corporeal Technologies international Society (MiECTiS).

Minimal invasive extracorporeal circulation (MiECC) systems have initiated important efforts within science and technology to further improve the biocompatibility of cardiopulmonary bypass components to minimize the adverse effects and improve end-organ protection. The Minimal invasive Extra-Corporeal Technologies international Society was founded to create an international forum for the exchange of ideas on clinical application and research of minimal invasive extracorporeal circulation technology. The present work is a consensus document developed to standardize the terminology and the definition of minimal invasive extracorporeal circulation technology as well as to provide recommendations for the clinical practice. The goal of this manuscript is to promote the use of MiECC systems into clinical practice as a multidisciplinary strategy involving cardiac surgeons, anaesthesiologists and perfusionists.

Steiner’s formula in the Heisenberg group

Steiner’s tube formula states that the volume of an ϵ-neighborhood of a smooth regular domain in Rn is a polynomial of degree n in the variable ϵ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ϵ-neighborhood with respect to the Heisenberg metric is an analytic function of ϵ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms.