A non-local model for cancer stem cells and the tumour growth paradox.

The tumour growth paradox refers to the observation that incomplete treatment of cancers can enhance their growth. As shown here and elsewhere, the existence of cancer stem cells (CSCs) can explain this effect. CSC are less sensitive to treatments, hence any stress applied to the tumour selects for CSC, thereby increasing the fitness of the tumour. In this paper, we use a mathematical model to understand the role of CSC in the progression of cancer. Our model is a rather general system of integro-differential equations for tumour growth and tumour spread. Such a model has never been analysed, and we prove results on local and global existence of solutions, their uniqueness and their boundedness. We show numerically that this model exhibits the tumour growth paradox for all parameters tested. This effect becomes more relevant for small renewal rate of the CSC.

Tumours with cancer stem cells: A PDE model.

The role of cancer stem cells (CSC) in tumour growth has received increasing attention in the recent literature. Here we stem from an integro-differential system describing the evolution of a population of CSC and of ordinary (non-stem) tumour cells formulated and studied in a previous paper, and we investigate an approximation in which the system reduces to a pair of nonlinear coupled parabolic equation. We prove that the new system is well posed and we examine some general properties. Numerical simulations show more on the qualitative behaviour of the solutions, concerning in particular the so-called tumour paradox, according to which an increase of the mortality rate of ordinary (non-stem) tumour cells results asymptotically in a faster growth.

[Use of the TUT (Tension-free Vaginal Tape) in the treatment of female urinary stress incontinence. Preliminary results]. / Utilizzazione del TVT (Tension-free Vaginal Tape) nel trattamento dell'incontinenza urinaria femminile da sforzo. Risultati preliminari.

BACKGROUND: The Tension-free Vaginal Tape (TVT) represents the most recent technique for the treatment of genuine stress urinary incontinence (GSUI). The various number of surgical procedures proposed for the treatment of GSI very often do not lead to a complete remission of this pathology. The data from the literature show how TVT is a effective procedure for the treatment of female urinary incontinence. METHODS: Twenty-nine women with diagnosis of urinary incontinence underwent application of polypropilene band (TVT: tension-free vaginal tape) underneath the uretra, in order to treat this disorder. The procedure has been carried out in peripheral anesthesia. RESULTS: A complete remission of the urinary incontinence was obtained in 24 patients. In the remaining cases there was an improvement of the symptoms in two patients, whereas in two patients remained a secondary detrusor instability. In one case the external iliac vein was perforated thus requiring a surgical repair. CONCLUSION: The short surgical time, the feasibility of the procedure and the following short hospitalization made this technique well accepted either by the surgeons ang the patients. Moreover the possibility to carry out the procedure in peripheral anesthesia allows to have the collaboration of the patient. However this technique is not free of risks, how the serious complication we had can demonstrate.