On a stochastic nonclassical diffusion equation with standard and fractional Brownian motion

This paper is concerned with the mathematical analysis of terminal value problems (TVP) for a stochastic nonclassical diffusion equation, where the source is assumed to be driven by classical and fractional Brownian motions (fBms). Our two problems are to study in the sense of well-posedness and ill-posedness meanings. Here, a TVP is a problem of determining the statistical properties of the initial data from the final time data. In the case [Formula: see text], where [Formula: see text] is the fractional order of a Laplace operator, we show that these are well-posed under certain assumptions. We state a definition of ill-posedness and obtain the ill-posedness results for the problems when [Formula: see text]. The major analysis tools in this paper are based on properties of stochastic integrals with respect to the fBm.

Rotating Gamma System Irradiation: A Promising Treatment for Low-grade Brainstem Gliomas

AIM

To evaluate the role of rotating gamma system (RGS) radiosurgery for low-grade brainstem gliomas.

PATIENTS AND METHODS

Thirty-seven patients undergoing RGS radiosurgery at the Bach Mai Hospital Hanoi for low-grade brainstem glioma were included in this prospective interventional study. The median RGS dose was 12 Gy (range=8-16 Gy). Endpoints included response to RGS radiosurgery given as change in glioma size (maximum diameter), survival and adverse events. Follow-up was performed for 36 months. Three dose-groups (<13, 13-14 and >14 Gy) were compared for survival.

RESULTS

Mean glioma size decreased from 1.87 cm before RGS irradiation to 1.15 cm at 36 months. Mean survival was 39.5 months. Mean survival after <13, 13-14 and >14 Gy were 22.7, 66.7 and 49 months, respectively (p<0.05). Adverse events, mainly reduced appetite, sleep disturbances, headache and edema, were not associated with RGS dose and were easily managed.

CONCLUSION

RGS radiosurgery led to promising results with acceptable toxicity in patients with low-grade brainstem gliomas.