Collapsed cone convolution and analytical anisotropic algorithm dose calculations compared to VMC++ Monte Carlo simulations in clinical cases

The purpose of this work was to study and quantify the differences in dose distributions computed with some of the newest dose calculation algorithms available in commercial planning systems. The study was done for clinical cases originally calculated with pencil beam convolution (PBC) where large density inhomogeneities were present. Three other dose algorithms were used: a pencil beam like algorithm, the anisotropic analytic algorithm (AAA), a convolution superposition algorithm, collapsed cone convolution (CCC), and a Monte Carlo program, voxel Monte Carlo (VMC++). The dose calculation algorithms were compared under static field irradiations at 6 MV and 15 MV using multileaf collimators and hard wedges where necessary. Five clinical cases were studied: three lung and two breast cases. We found that, in terms of accuracy, the CCC algorithm performed better overall than AAA compared to VMC++, but AAA remains an attractive option for routine use in the clinic due to its short computation times. Dose differences between the different algorithms and VMC++ for the median value of the planning target volume (PTV) were typically 0.4% (range: 0.0 to 1.4%) in the lung and -1.3% (range: -2.1 to -0.6%) in the breast for the few cases we analysed. As expected, PTV coverage and dose homogeneity turned out to be more critical in the lung than in the breast cases with respect to the accuracy of the dose calculation. This was observed in the dose volume histograms obtained from the Monte Carlo simulations.

Convolution roots and differentiability of isotropic positive definite functions on spheres

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Diagnostic accuracy of coronary in-stent restenosis using 64-slice computed tomography: comparison with invasive coronary angiography

OBJECTIVES: This study sought to evaluate the diagnostic accuracy of coronary binary in-stent restenosis (ISR) with angiography using 64-slice multislice computed tomography coronary angiography (CTCA) compared with invasive coronary angiography (ICA). BACKGROUND: A noninvasive detection of ISR would result in an easier and safer way to conduct patient follow-up. METHODS: We performed CTCA in 81 patients after stent implantation, and 125 stented lesions were scanned. Two sets of images were reconstructed with different types of convolution kernels. On CTCA, neointimal proliferation was visually evaluated according to luminal contrast attenuation inside the stent. Lesions were graded as follows: grade 1, none or slight neointimal proliferation; grade 2, neointimal proliferation with no significant stenosis (<50%); grade 3, neointimal proliferation with moderate stenosis (> or =50%); and grade 4, neointimal proliferation with severe stenosis (> or =75%). Grades 3 and 4 were considered binary ISR. The diagnostic accuracy of CTCA compared with ICA was evaluated. RESULTS: By ICA, 24 ISRs were diagnosed. Sensitivity, specificity, positive predictive value, and negative predictive value were 92%, 81%, 54%, and 98% for the overall population, whereas values were 91%, 93%, 77%, and 98% when excluding unassessable segments (15 segments, 12%). For assessable segments, CTCA correctly diagnosed 20 of the 22 ISRs detected by ICA. Six lesions without ISR were overestimated as ISR by CTCA. As the grade of neointimal proliferation by CTCA increases, the median value of percent diameter stenosis increased linearly. CONCLUSIONS: Binary ISR can be excluded with high probability by CTCA, with a moderate rate of false-positive results.

Novel radiotherapy techniques for involved-field and involved-node treatment of mediastinal Hodgkin lymphoma: when should they be considered and which questions remain open?

PURPOSE Hodgkin lymphoma (HL) is a highly curable disease. Reducing late complications and second malignancies has become increasingly important. Radiotherapy target paradigms are currently changing and radiotherapy techniques are evolving rapidly. DESIGN This overview reports to what extent target volume reduction in involved-node (IN) and advanced radiotherapy techniques, such as intensity-modulated radiotherapy (IMRT) and proton therapy-compared with involved-field (IF) and 3D radiotherapy (3D-RT)- can reduce high doses to organs at risk (OAR) and examines the issues that still remain open. RESULTS Although no comparison of all available techniques on identical patient datasets exists, clear patterns emerge. Advanced dose-calculation algorithms (e.g., convolution-superposition/Monte Carlo) should be used in mediastinal HL. INRT consistently reduces treated volumes when compared with IFRT with the exact amount depending on the INRT definition. The number of patients that might significantly benefit from highly conformal techniques such as IMRT over 3D-RT regarding high-dose exposure to organs at risk (OAR) is smaller with INRT. The impact of larger volumes treated with low doses in advanced techniques is unclear. The type of IMRT used (static/rotational) is of minor importance. All advanced photon techniques result in similar potential benefits and disadvantages, therefore only the degree-of-modulation should be chosen based on individual treatment goals. Treatment in deep inspiration breath hold is being evaluated. Protons theoretically provide both excellent high-dose conformality and reduced integral dose. CONCLUSION Further reduction of treated volumes most effectively reduces OAR dose, most likely without disadvantages if the excellent control rates achieved currently are maintained. For both IFRT and INRT, the benefits of advanced radiotherapy techniques depend on the individual patient/target geometry. Their use should therefore be decided case by case with comparative treatment planning.

Streak detection algorithm for space debris detection on optical images.

Any image processing object detection algorithm somehow tries to integrate the object light (Recognition Step) and applies statistical criteria to distinguish objects of interest from other objects or from pure background (Decision Step). There are various possibilities how these two basic steps can be realized, as can be seen in the different proposed detection methods in the literature. An ideal detection algorithm should provide high recognition sensitiv ity with high decision accuracy and require a reasonable computation effort . In reality, a gain in sensitivity is usually only possible with a loss in decision accuracy and with a higher computational effort. So, automatic detection of faint streaks is still a challenge. This paper presents a detection algorithm using spatial filters simulating the geometrical form of possible streaks on a CCD image. This is realized by image convolution. The goal of this method is to generate a more or less perfect match between a streak and a filter by varying the length and orientation of the filters. The convolution answers are accepted or rejected according to an overall threshold given by the ackground statistics. This approach yields as a first result a huge amount of accepted answers due to filters partially covering streaks or remaining stars. To avoid this, a set of additional acceptance criteria has been included in the detection method. All criteria parameters are justified by background and streak statistics and they affect the detection sensitivity only marginally. Tests on images containing simulated streaks and on real images containing satellite streaks show a very promising sensitivity, reliability and running speed for this detection method. Since all method parameters are based on statistics, the true alarm, as well as the false alarm probability, are well controllable. Moreover, the proposed method does not pose any extraordinary demands on the computer hardware and on the image acquisition process.