Percutaneous treatment of patients with heart diseases: selection, guidance and follow-up. A review

Aortic stenosis and mitral regurgitation, patent foramen ovale, interatrial septal defect, atrial fibrillation and perivalvular leak, are now amenable to percutaneous treatment. These percutaneous procedures require the use of Transthoracic (TTE), Transesophageal (TEE) and/or Intracardiac echocardiography (ICE). This paper provides an overview of the different percutaneous interventions, trying to provide a systematic and comprehensive approach for selection, guidance and follow-up of patients undergoing these procedures, illustrating the key role of 2D echocardiography

Geometry of J.D'Alembert equation

This is the last chapter of a book devoted to a very interesting and actual problem in Mathematical Analysis. Here the geometric theory of PDE's is considered and applied to the d'Alembert equation in its connection with the problem of representation of functions by (partial) separation of variables

Ulam stability in geometry of PDE's

The unstability of characteristic flows of solutions of PDE's is related to the Ulam stability of functional equations. In particular, we consider, as master equation, the Navier-Stokes equation. The integral (co)bordism groups, that have recently been introduced by A. Pr\'astaro to solve the problem of existence of global solutions of the Navier-Stokes equation, lead to a new application of the Ulam stability for functional equations. This allowed us here to prove that the characteristic flows associated to perturbed solutions of global laminar solutions of the Navier-Stokes equation, can be characterized by means of a stable (as well superstable) functional equation (\textit{functional Navier-stokes equation}). In such a framework a natural criterion to recognize stable laminar solutions is given also

On the Ulam stability in geometry of PDE's

The article is concerned with the problem of unstability of flows corresponding to solutions of the Navier-Stokes equation in relation with the stability of a new functional equation that is stable as well as superstable in an extended Ulam sense. In such a framework a natural characterization of global stable laminar flow is given also

On the geometric approach to an equation of J.D'Alembert.

Here we announce some firt results on the J. D'Alembert equation $({{\partial^2}\over{\partial x\partial y}}\log f)=0$. More precisely, by using a geometric framework we prove that the set of smooth functions of two variables $f(x,y)$, solutions of the J. D'Alembert equation, is larger than the set of functions of the form $f(x,y)=h(x).g(y)$

Latent left ventricular ouflow tract obstruction induced by abnormal hypertrophic papillary muscle caused myocardial ischemia.

Left ventricular outflow tract (LVOT) obstruction is a typical recognized feature in hypertrophic cardiomyopathy. However, it has been shown in other clinical scenarios such as acute ischemia. In some patients, LVOT obstruction may only be detectable with provocation testing such as exercise stress. Accurate and timely diagnosis, therefore, relies on recognizing an echocardiographic substrate in which LVOT obstruction may occur, such as ventricular hypertrophy. This report describes the case of a patient presenting with effort ECG and signs of myocardial ischemia, with no significant narrowing of coronary arteries but with latent LVOT obstruction due to the presence of an abnormal hypertrophic papillary muscle instead of a typical ventricle hypertrophy

Results on the J.d'Alembert equation

A new $m$-d'Alembert equation, $m\ge 2$, is introduced in the category of quantum manifolds (in the sense introduced by A.Prastaro), that extends the commutative generalized d'Alembert equation previously considered by the same authors. For such a new equation we give theorems of existence of local and global solutions

Percutaneousvapproach to treatment of coronary disease in a patient with uremic cardiomyopathy

Uremic cardiomyopathy is chronic ischemic left ventricular dysfunction characterized by heart failure, myocardial ischemia, hypotension in dialysis and arrhythmia. This nosologic entity represents a leading cause of morbidity and mortality among patients with end-stage renal disease receiving long-term hemodialysis. It is intuitive that revascularization in the presence of coronary artery disease in these patients represents an effective option for improving their prognosis. Although the surgical option seems to be followed by the best clinical outcome, some patients refuse this option and others are not good candidates for surgery. The present report describes the case of a patient affected by uremic cardiomyopathy and severe coronary artery disease in whom revascularization with percutaneous coronary angioplasty was followed by a significant improvement in quality of lif