2009
Segmentation d’Images multi-canal de résonance magnétique T2 avec morphologie mathématique multidimensionnelle [Magnetic resonance T2 multi-channel image segmentation with multidimensional mathematical morphology]
Wuilian Torres, Miguel Martín-Landrove, Marco Paluszny, Gabriel Padilla, Giovanni Figueroa
XXIIe colloque GRETSI (traitement du signal et des images), Dijon (FRA), 8-11 septembre 2009 [article in french]
A method for T2-weighted tumor image segmentation based on vector mathematical morphology techniques is proposed for tissue classification towards a possible assessment of subclinical pathology. For image segmentation, vector morphological operators are defined that use as ordering criteria a reduced order followed by a lexicographic order. Using dilation and erosion operators so defined, a morphological gradient operator is determined and spatial image segmentation is performed by watershed operations. For each segment, a characteristic vector pixel is determined by a modified vector median allowing for tissue characterization, i.e., segments with similar vector pixels correspond to similar tissues. Finally, vector pixels coming from different segments are grouped by means of hierarchical grouping until a radiological relevant number of tissues is obtained.
Tumor segmentation of multi-echo MR T2-weighted images with morphological operators
W. Torres, M. Martín-Landrove, M. Paluszny, G. Figueroa, G. Padilla
Medical Imaging 2009: Image Processing, edited by Josien P. W. Pluim, Benoit M. Dawant, Proc. of SPIE Vol. 7259, 72594E
In the present work an automatic brain tumor segmentation procedure based on mathematical morphology is proposed. The approach considers sequences of eight multi-echo MR T2-weighted images. The relaxation time T2 characterizes the relaxation of water protons in the brain tissue: white matter, gray matter, cerebrospinal fluid (CSF) or pathological tissue. Image data is initially regularized by the application of a log-convex filter in order to adjust its geometrical properties to those of noiseless data, which exhibits monotonously decreasing convex behavior. Finally the regularized data is analyzed by means of an 8-dimensional morphological eccentricity filter. In a first stage, the filter was used for the spatial homogenization of the tissues in the image, replacing each pixel by the most representative pixel within its structuring element, i.e. the one which exhibits the minimum total distance to all members in the structuring element. On the filtered images, the relaxation time T2 is estimated by means of least square regression algorithm and the histogram of T2 is determined. The T2 histogram was partitioned using the watershed morphological operator; relaxation time classes were established and used for tissue classification and segmentation of the image. The method was validated on 15 sets of MRI data with excellent results.
Boosting the inverse interpolation problem by a sum of decaying exponentials using an algebraic approach
Marco Paluszny, Miguel Martín–Landrove, Giovanni Figueroa, Wuilian Torres
Electronic Transactions on Numerical Analysis. Volume 34, pp. 163-169, 2009.
An algebraic method is proposed to solve the inverse interpolation problem for data fitting by a linear combination of decaying exponentials. The method transforms the interpolation question into a problem of finding the roots of a single polynomial. The method is validated by numerical simulations using noiseless synthetic data with excellent results. The method is applied to medical data coming from magnetic resonance images of tumoral lesions in brain to obtain relaxation rate distribution functions, with results that are trustworthy and fast when compared with inverse Laplace methods.
A multi-strategy method for MRI segmentation
M. Martín-Landrove, M. Paluszny, G. Figueroa, W. Torres, G. Padilla
O. Dössel and W C. Schlegel (Eds.): WC 2009, IFMBE Proceedings 25/IV, pp. 1222–1225, 2009.
An accurate method for T2-weighted MRI segmentation according to tissue transversal magnetization decay rates is presented. By means of a sequence of geometric image filters a classification of the pixels’ intensity decay curves is provided. This can be done through a double strategy: First a log-convexity filter is applied in order to regularize image intensity decay by adjusting its geometrical properties to those that are expected from noiseless data, i.e., monotonous and convex behavior. In doing so, image noise is somewhat filtered and controlled. Data points are fitted by an over determined interpolation procedure. Decay rate distributions are obtained and tissue classification is performed by means of the determination of principal decay rates or decay modes using a suitable mathematical morphology operator, i.e., watershed or similar. Image segmentation is performed by linear regression analysis on a pixel by pixel basis assuming that the pixel intensity decay is composed by a linear superposition of the decay modes previously obtained from the decay rate distribution function. The main advantage of the proposed multi-strategy approach rests in the accuracy and speed of calculation with respect to other methods such as Inverse Laplace Transform algorithms. The method could be easily extended to any exponentially decaying set of images such as diffusion-weighted MRI.
A kinetic model for tumor survival curves: Its relation to the linear-quadratic model
R. Martín-Landrove, N. Guillén, M. Martín-Landrove
O. Dössel and W.C. Schlegel (Eds.): WC 2009, IFMBE Proceedings 25/III, pp. 508–511, 2009.
The linear-quadratic model has been widely used to describe tumor survival curves for doses under 10 Gy. The absence of a proposed mechanism behind the linearquadratic model is an important limitation for the proper interpretation of clinical results. Models based on a detailed mechanism have the unpleasant feature of a large number of parameters, which makes also the interpretation and use in quantitative radiobiology a very hard task. In this work a simple microscopic model based on reversible and irreversible DNA damage is proposed. The model is able to describe the survival curves at high and low LET for V-79 cells in late S phase of Chinese hamsters [7]. The new set of parameters can be related to the ones of the linear-quadratic model and in this way a connection with DNA damage and repair mechanisms is made. At the same time the evolution equations open the possibility for continuous and fractionated treatment plans.
Statistical mechanics and the evolution of polygenic quantitative traits
N. H. Barton, H. P. de Vladar
Genetics 181: 997–1011, 2009
The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified version of that approach, which makes the analogy more precise and applies quite generally to describe
the evolution of allele frequencies. We calculate explicitly how the macroscopic quantities (i.e., quantities that depend on the quantitative trait) depend on evolutionary forces, in a way that is independent of the microscopic details. We first show that the stationary distribution of allele frequencies under drift, selection, and mutation maximizes a certain measure of entropy, subject to constraints on the expectation of observable quantities. We then approximate the dynamical changes in these expectations, assuming that the distribution of allele frequencies always maximizes entropy, conditional on the expected values. When applied to directional selection on an additive trait, this gives a very good approximation to the evolution of the trait mean and the genetic variance, when the number of mutations per generation is sufficiently high (4Nm . 1). We show how the method can be modified for small mutation rates (4Nm/ 0). We outline how this method describes epistatic interactions as, for example, with stabilizing selection.
Characterization and clinical evaluation of a novel IMRT quality assurance system
Ramaswamy Sadagopan, Jose A. Bencomo, Rafael Martin L., Gorgen Nilsson, Thomas Matzen, Peter A. Balter
JOURNAL OF APPLIED CLINICAL MEDICAL PHYSICS, VOLUME 10, NUMBER 2, SPRING 2009
Intensity-modulated radiation therapy (IMRT) is a complex procedure that involves the delivery of complex intensity patterns from various gantry angles. Due to the complexity of the treatment plans, the standard care is to perform measurement-based, patient-specific quality assurance (QA). IMRT QA is traditionally done with film for relative dose in a plane and with an ion chamber for absolute dose. This is a laborious and time-consuming process. In this work, we characterized, commissioned, and evaluated the QA capabilities of a novel commercial IMRT device, Delta4, (ScandiDos, Uppsala, Sweden). This device consists of diode matrices in two orthogonal planes inserted in a cylindrical acrylic phantom that is 22 cm in diameter. Although the system has detectors in only two planes, it provides a novel interpolation algorithm that is capable of estimating doses at points where no detectors are present. Each diode is sampled per beam pulse so that the dose distribution can be evaluated on segment-by-segment, beam-by-beam, or as a composite plan from a single set of measurements. The end user can calibrate the system to perform absolute dosimetry, eliminating the need for additional ion chamber measurements. The patient’s IMRT plan is imported into the device over the hospital LAN and the results of the measurements can be displayed as gamma profiles, distance-to-agreement maps, dose difference maps, or the measured dose distribution can be superimposed on the patient’s anatomy to display an as-delivered plan. We evaluated the system’s reproducibility, stability, pulse-rate dependence, dose-rate dependence, angular dependence, linearity of dose response, and energy response using carefully planned measurements. We also validated the system’s interpolation algorithm by measuring a complex dose distribution from an IMRT treatment. Several simple and complex isodose distributions planned using a treatment planning system were delivered to the QA device; the planned and measured dose distributions were then compared and analyzed. In addition, the dose distributions measured by conventional IMRT QA, which uses an ion chamber and film, were compared. We found that the Delta4 device is accurate and reproducible and that its interpolation algorithm is valid. In addition, the supplied software and network interface allow a streamlined IMRT QA process.
