No abstract

Respiratory motion limits the potential of modern high-precision radiotherapy techniques such as IMRT and particle therapy. Due to the uncertainty of tumour localization, the ability of achieving dose conformation often cannot be exploited sufficiently, especially in the case of lung tumours. Various methods have been proposed to track the position of tumours using external signals, e.g. with the help of a respiratory belt or by observing external markers. Retrospectively gated time-resolved x-ray computed tomography (4D CT) studies prior to therapy can be used to register the external signals with the tumour motion. However, during treatment the actual motion of internal structures may be different. Direct control of tissue motion by online imaging during treatment promises more precise information. On the other hand, it is more complex, since a larger amount of data must be processed in order to determine the motion. Three major questions arise from this issue. Firstly, can the motion that has occurred be precisely determined in the images? Secondly, how large must, respectively how small can, the observed region be chosen to get a reliable signal? Finally, is it possible to predict the proximate tumour location within sufficiently short acquisition times to make this information available for gating irradiation? Based on multiple studies on a porcine lung phantom, we have tried to examine these questions carefully. We found a basic characteristic of the breathing cycle in images using the image similarity method normalized mutual information. Moreover, we examined the performance of the calculations and proposed an image-based gating technique. In this paper, we present the results and validation performed with a real patient data set. This allows for the conclusion that it is possible to build up a gating system based on image data, solely, or (at least in avoidance of an exceeding exposure dose) to verify gates proposed by the various external systems.

While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are intermittent between regular and chaotic, which makes them particularly interesting in physical studies. However, mathematical methods for the analysis of systems with slow mixing rates were developed just recently and are still difficult to apply to realistic models. Here we reduce those methods to a practical scheme that allows us to obtain a nearly optimal bound on mixing rates. We demonstrate how the method works by applying it to several classes of chaotic billiards with slow mixing as well as discuss a few examples where the method, in its present form, fails.

No abstract

We study the Lorentz gas in small external electric and magnetic fields, E and B, with the particle kinetic energy held fixed by a Gaussian "thermostat" (a modification of a model of Moran and Hoover.) Here we prove rigorously that : (1) Starting from any smooth initial density, a unique stationary, ergodic measure (whose support is fractal) is approached for times t → ∞. (2) The steady-state electric current, J(B, E), is given by a Kawasaki formula and the entropy production J • E/T, with T the "temperature," is equal to both the asymptotic decay rate of the Gibbs entropy and minus the sum of the Lyapunov exponents. (3) The Einstein relation and Kubo formulas hold, i.e. J(B, E) = σ(B) • E+ higher order terms, with the diffusion matrix D(B) at E = 0 given by k B T times the symmetric partσ(B) of the conductivity matrix. Pacs. Nos. 05.60, 05.45