Konrad Engel

A new algorithm for optimal multileaf collimator field segmentation

We present a new efficient leaf sequencing algorithm for the generation of intensity maps by a nonnegative combination of segments. Intensity maps describe the intensity modulation of beams in radiotherapy. We only study the static case (step and shoot). We exactly optimize the total number of monitor units and heuristically optimize the number of segments. We present a short exact proof for a formula giving the smallest total number of monitor units and describe a class of algorithms yielding this minimal value. A special member of this class provides a solution with a very small number of segments.

Comparison of electron IMRT to helical photon IMRT and conventional photon irradiation for treatment of breast and chest wall tumours

BACKGROUND AND PURPOSE Conventional irradiation of breast and chest wall tumours may cause high doses in underlying organs. Intensity-modulated radiation therapy (IMRT) with photons achieves high conformity between treated and tumour volume but is associated with considerable low-dose effects which may induce secondary malignancies. We compare treatment plans of electron IMRT to helical photon IMRT and conventional irradiation. MATERIAL AND METHODS Treatment planning for three patients (breast, chest wall plus lymph nodes, sarcoma of medial chest wall/sternum) was performed using XiO 4.3.3 (CMS) for conventional photon irradiation, Hi-Art 2.2.2.05 (TomoTherapy) for helical photon IMRT, and a self-designed programme for electron IMRT. RESULTS The techniques resulted in similar mean and maximum target doses. Target coverage by the 95%-isodose was best with tomotherapy. Mean ipsilateral lung doses were similar with all techniques. Electron IMRT achieved best sparing of heart, and contralateral breast. Compared with photon IMRT, electron IMRT allowed better sparing of contralateral lung and total healthy tissue. CONCLUSIONS Electron IMRT is superior to conventional irradiation, as it allows satisfying target coverage and avoids high doses in underlying organs. Its advantage over photon IMRT is better sparing of most organs at risk (low-dose effects) which reduces the risk of radiation-induced malignancies.

Automatic Actin Filament Quantification of Osteoblasts and Their Morphometric Analysis on Microtextured Silicon-Titanium Arrays

Microtexturing of implant surfaces is of major relevance in the endeavor to improve biorelevant implant designs. In order to elucidate the role of biomaterial’s topography on cell physiology, obtaining quantitative correlations between cellular behavior and distinct microarchitectural properties is in great demand. Until now, the microscopically observed reorganization of the cytoskeleton on structured biomaterials has been difficult to convert into data. We used geometrically microtextured silicon-titanium arrays as a model system. Samples were prepared by deep reactive-ion etching of silicon wafers, resulting in rectangular grooves (width and height: 2 µm) and cubic pillars (pillar dimensions: 2 × 2 × 5 and 5 × 5 × 5 µm); finally sputter-coated with 100 nm titanium. We focused on the morphometric analysis of MG-63 osteoblasts, including a quantification of the actin cytoskeleton. By means of our novel software FilaQuant, especially developed for automatic actin filament recognition, we were first able to quantify the alterations of the actin network dependent on the microtexture of a material surface. The cells’ actin fibers were significantly reduced in length on the pillared surfaces versus the grooved array (4–5 fold) and completely reorganized on the micropillars, but without altering the orientation of cells. Our morpho-functional approach opens new possibilities for the data correlation of cell-material interactions.

Old and New Results for the Weighted t-Intersection Problem via AK-Methods

Let [n]: = {1, ..., n}, 2[n] be the power set of [n] and s ∈ [n]. A family F ⊆ 2[n] is called t-intersecting in [s] if

An Erdo¨s-Ko-Rado theorem for integer sequences of given rank

\left| {{X_1} \cap {X_2} \cap \left[ s \right]} \right| \geqslant t\,for\,all\,{X_1},{X_2}\, \in \,F.

Approximated matrix decomposition for IMRT planning with multileaf collimators

Let ω: 2[n] → ℝ+ be a given weight function and

A New Algorithm for a Field Splitting Problem in Intensity-Modulated Radiation Therapy

{M_s}\left( {n,t;\omega } \right):\, = \max \left\{ {\omega \left( F \right)} \right.:F\,is\,t - \operatorname{int} er\sec ting\,in\left. {\,\left[ s \right]} \right\}.