2010
Recovery of relaxation rates in MRI T2 weighted brain images via exponential fitting
M.Paluszny, M.Lentini, M.Martín-Landrove, W.Torres, R.Martín
Exponential Data Fitting and Its Applications, V. Pereyra, G Scherer (Eds.) Chapter 2, 2010
We consider synthetic magnetic resonance images of a brain slice generated with the BrainWeb resource. They correspond to measurements taken at various times and record the intensity of the response signal of the probed tissue to a magnetic pulse. The specific property measured, which is considered in this chapter, is transverse magnetization. The transverse magnetization decay technique can be used to obtain several images for a given axial slice of tissue. Namely, for each pixel the time uniform sequence of transverse magnetization measurements yields information about the tissues at that pixel and for a given time the responses of all the pixels form an image of the slice. In clinical studies this data is acquired using the magnetic resonance procedure. Mathematically this decay is described as a linear combination of decaying exponentials and it strongly correlates to the tissue type at each pixel. We consider several approaches to extract the exponents and estimates of the fractions of each tissue type for every pixel in a region of interest. The main thrust is on separation of variables techniques, by looking at Prony’s method, some special Vandermonde systems and linear regression. We consider comparisons of a Prony technique and the classical separable nonlinear least squares method.
A technique of three-dimensional reconstruction of myocardial tissue damage after ischemic heart disease using image processing in cardiac magnetic resonance imaging
Giovana Gavidia, Eduardo Soudah, Jorge Pérez, Miguel Cerrolaza, Miguel Martín-Landrove, Eugenio Oñate
Modelos Computacionales en Ingeniería: Desarrollos Novedosos y Aplicaciones, R. Chacón, F. León, V. Duarte, O. Verastegui (Eds.) SVMNI 2010 [article in spanish]
Acute myocardial infarction (AMI) is a type of Ischemic Heart Disease (IHD) that usually occurring after a partial or complete obstruction of a coronary artery. This leads to tissue damage observed in the loss of a variable zone of functional myocardial known as left ventricular scar. Cardiac Magnetic Resonance (CMR) can be used to visualize the transmural extent of myocardial infarction with high spatial resolution and to identify of viable myocardium. The ventricular scar has specific characteristics that allow segmentation of IHD from no ischemic tissue. Moreover, CMR segmentation generates different zones within the lesion that may reflect heterogeneity of tissue damage. In this work a novel and comprehensive technique of 3D reconstruction to visualize the geometric model of left ventricle and the scar tissue is proposed. Firstly, the low quality of CMR is solved using enhancement algorithms to reduce image noise and increase the contrast of structures of interest. This step is very important because in CMR the distinction between normal and abnormal tissue is subtle and the accurate interpretation of scar is difficult if noise levels are high. Then, we use a hybrid segmentation approach in multi-stage to identify the scar tissue and obtain the left ventricular, the zone of infarction and necrosis. Finally, these data are used to generate discrete models using Computer-Aided Design (CAD) tools and verify its utility for analysis with the Finite Element Methods. The models generated can be applied in several clinical cases and get results fast and useful for understanding quantitative and qualitative information of ventricular function from the 3D structures obtained.
An application of mathematical morphology for brain tumor segmentation in multimodality MRI
Omar León, Miguel Martín-Landrove, Wuilian Torres
Modelos Computacionales en Ingeniería: Desarrollos Novedosos y Aplicaciones, R. Chacón, F. León, V. Duarte, O. Verastegui (Eds.) SVMNI 2010
In the present work an automatic brain tumor segmentation procedure based on mathematical morphology is proposed. The approach considers the use of multimodality MRI, i.e., use of different MRI acquisition routines applied on the patient sequentially, so that for each image plane, each pixel is described by a vector with dimensionality N depending on the number of MRI modalities employed in every case and components given by the gray level corresponding to each MRI modality. Patient movement in brain is not usually an issue so image data is frequently well registered. Image data were analyzed by means of an N-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, joint histograms, corresponding to different combinations of MRI modalities, where partitioned using morphological operators and methods in pattern recognition; classes were established according to medical criteria and used for tissue classification and segmentation of the image. The method was validated on several sets of MRI data with excellent results.
Quasi-analytical determination of nosologic maps and diffusion tensor anisotropy distribution functions in diffusion-weighted MRI
Miguel Martín-Landrove, Marco Paluszny, Giovanni Figueroa, Gabriel Padilla, Wuilian Torres
Modelos Computacionales en Ingeniería: Desarrollos Novedosos y Aplicaciones, R. Chacón, F. León, V. Duarte, O. Verastegui (Eds.) SVMNI 2010
An accurate method for diffusion-weighted MRI segmentation based on the image intensity exponential decay is presented. Diffusion coded images were obtained for three orthogonal gradient directions, allowing for image data parameterized by the Apparent Diffusion Coefficient (ADC) or independently by each orthogonal gradient component. 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. Diffusion coefficient distributions are obtained and tissue classification is performed by means of the determination of principal diffusion coefficients or diffusion 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 diffusion modes previously obtained from the diffusion coefficient distribution function. The main advantage of the proposed multi-strategy approach rests in its accuracy and speed of calculation with respect to other methods such as Inverse Laplace Transform algorithms, making it suitable for on line application on diffusion tensor imaging data. Nosologic maps were determined for the ADC image set and for each independent gradient direction. Since the number of gradient directions was not enough for a full description of the diffusion tensor, a particular definition was proposed allowing for determination of anisotropy distribution functions. Finally, ADC and anisotropy nosologic maps were combined to further assess tumor activity.
Fractionation Scheme Analysis with a Simple kinetic Model for Tumor Growth
Rafael Martín-Landrove, Miguel Martín-Landrove, Nilo Rafael Guillén-Rodríguez
Modelos Computacionales en Ingeniería: Desarrollos Novedosos y Aplicaciones, R. Chacón, F. León, V. Duarte, O. Verastegui (Eds.) SVMNI 2010
The linear-quadratic model has been widely used to describe tumor survival curves for doses under 10-15 Gy. The absence of a proposed mechanism behind the linear-quadratic 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 kinetic model based on reversible and irreversible DNA damage is used in order to analyze fractionated as well as continuous treatment plans. For cellular death the effect to be considered is the irreversibility of DNA damage and it could happen in a single direct step or in a two-step process where the generation of an intermediate reversible DNA damage could take place and it does not interfere with the tumor proliferation process. This model is able to describe the survival curves at high and low LET and its fundamental parameters are related in a simple way to the ones of the linear-quadratic model. From the clinical point of view it is important to have a model that allows the study of the system evolution and at the same time is able to provide its relation to the absorbed dose for treatment planning
Brain Tumor Staging and Classification by Analysis of Contour Critical Exponents
Miguel Yánez, Belkis López, Miguel Martín-Landrove
Modelos Computacionales en Ingeniería: Desarrollos Novedosos y Aplicaciones, R. Chacón, F. León, V. Duarte, O. Verastegui (Eds.) SVMNI 2010
In general, tumors exhibit irregular borders with geometrical properties which are expected to depend upon their degree of malignancy [1, 2]. To appropriately evaluate these irregularities, it is necessary to apply segmentation procedures on the image to clearly define the active region of the tumor and its contour. In the present work, 3D imaging data sets coming from a radiotherapy service database and including contrast CT and contrast T1-weighted MRI of brain tumors were used to evaluate contour parameters that can be correlated to biopsy for tissue classification and reference tumor staging. Data sets were previously classified according to histopathological studies in order to establish a timeline somewhat related to staging. Contours were obtained for different image planes to test for variations depending on plane direction. To determine these contours, several segmentation procedures were performed on the images, including gray level threshold, mathematical morphology operators and deformable contours (snakes). Critical exponents [3] coming from contour roughness were calculated. The results obtained showed a good correlation between these critical exponents and the degree of malignancy of the tumor.
