Exponential convergence for Markov systems

Markov operators arising from graph directed constructions of iterated function systems are considered. Exponential convergence to an invariant measure is proved

Law of large numbers for random dynamical systems

We consider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We prove the existence of an exponentially attractive invariant measure and the strong law of large numbers

On a unique ergodicity of some Markov processes

It is proved that the sufficient condition for the uniqueness of an invariant measure for Markov processes with the strong asymptotic Feller property formulated by Hairer and Mattingly (Ann Math 164(3):993–1032, 2006) entails the existence of at most one invariant measure for e-processes as well. Some application to timehomogeneous Markov processes associated with a nonlinear heat equation driven by an impulsive noise is also given

Interstitial high-dose-rate brachytherapy in locally advanced and recurrent vulvar cancer

Purpose: The aim of the study was to report our experience with high-dose-rate interstitial brachytherapy (HDR-ISBT) in locally advanced and recurrent vulvar cancer. Material and methods: Between 2004 and 2014, fourteen women with locally advanced or recurrent vulvar cancer were treated using HDR-ISBT in our Centre. High-dose-rate interstitial brachytherapy was performed as a separate treatment or in combination with external beam radiotherapy (EBRT) (given prior to brachytherapy). Results: Patients were divided into: group I (n = 6) with locally advanced tumors, stages III-IVA after an incisional biopsy only, and group II (n = 8) with recurrent vulvar cancer after previous radical surgery. In group I, median follow up was 12 months (range 7-18 months); 1-year overall survival (OS) was 83%. Transient arrest of cancer growth or tumor regression was noticed in all patients but 4/6 developed relapse. Median time to failure was 6.3 months (range 3-11 months). The 1-year progression-free survival (PFS) was 33%. In group II, median follow up was 28 months (range 13-90 months). The 1-year and 3-year OS was 100% and 80%, respectively. The arrest of cancer growth or tumor regression was achieved in all patients. In 4/8 patients neither clinical nor histological symptoms of relapse were observed but 4/8 women experienced relapse. Median time to failure was 31 months (range 13-76 months). The 1-year and 3-year PFS was 100% and 62.5%, respectively. Two patients (14.3%) in group II had severe late toxicity (G3). Conclusions: High-dose-rate interstitial brachytherapy is a well-tolerated treatment option in selected patients with advanced or recurrent vulvar cancer. It is a safe and effective treatment modality for advanced and recurrent vulvar cancer, yielding good local control with acceptable late treatment related side effects. In our study, patients with recurrent vulvar cancer had better results in HDR-ISBT treatment, probably because of the smaller tumor volume. This hypothesis should be verified in a larger group of patients

Pre-operative high-dose-rate brachytherapy in early-stage cervical cancer: long-term single-center results

Purpose: The aim of the study was to report the outcomes of pre-operative high-dose-rate brachytherapy (pHDRBT), followed by hysterectomy in patients with early cervical cancer. Material and methods: From January, 1998 to December, 2003, 113 women with IB1, IB2, and IIA1 cervical cancer (according to International Federation of Gynecology and Obstetrics [FIGO] 2018) were treated with pHDR-BT, and 6 to 8 weeks later followed by radical hysterectomy. Patients found to have positive lymph nodes, residual cervical cancer, involved parametria, or lymphovascular space invasion (LVSI) received post-operative adjuvant therapy. Results: Post-operatively, 81.4% of patients had a complete response to pHDR-BT in the cervix, and 18.6% had residual cervical cancer. Failures occurred in 11/113 (9.7%) patients (all were stage IIA1), with pelvic recurrences in 5/113 (4.4%) and distant metastasis (DM) in 6/113 (5.3%). The 5- and 10-year disease-free survival (DFS) rates were 100% for IB1 and IB2, and 86.4% and 81.3% for IIA1, respectively. Lymph node involvement and/or residual cervical cancer correlated with worse DFS. Two vesicovaginal fistulas were observed (one in a patient treated only with pHDRBT and one in a woman, who underwent adjuvant external-beam radiotherapy [EBRT]). Two rectovaginal fistulas and one case of proctitis were observed in patients treated with adjuvant EBRT. Conclusions: pHDR-BT in early cervical cancer is well-tolerated and effective in sterilizing tumor cells in the cervix. The growing number of publications in this area may help define an optimal therapeutic scheme, but randomized trials are required to determine the best candidates for this treatment modality. In our opinion, cervical cancer patients with FIGO stage IIA1 are not good candidates for pHDR-BT, and could be given this treatment only after rigorous selection, including assessment with state-of-the-art imaging, due to higher probability of treatment failure