Machine learning and fractal-based analysis for the automated diagnosis of cardiovascular diseases using magnetic resonance

Treballs Finals de Grau d'Enginyeria Informàtica, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Polyxeni Gkontra i Joan Carles Tatjer i Montaña[en] Cardiac magnetic resonance (CMR) is the reference imaging modality for the diagnose of cardiovascular diseases. Traditionally, simple CMR parameters related to the volume and shape of the cardiac structures are calculated by the medical professionals by means of manual or semi-automated approaches. This process is time-consuming and prone to human errors. Moreover, despite the importance of these traditional CMR indexes, they often fail to fully capture the complexity of the cardiac tissue. In this work, we propose a novel approach for automated cardiovascular disease diagnosis, using ischemic heart disease as an example use case. Towards this aim, we will use a state-of-the-art technology, supervised machine learning, and a promising mathematical tool, fractal-based analysis. In order to undertand the potential information that can be derived from fractal-based features, we introduce and explore the concepts of Haussdorff dimension, box-counting dimension and lacunarity. We describe the interrelationships among these concepts and present computational algorithms for calculating box-counting dimension and lacunarity. The study is based on data from a large-cohort study, UK Biobank, to extract box-counting dimension and lacunarity from CMR textures focusing on three cardiac structures of medical interest: the left ventricle, the right ventricle and the myocardium. The extraction of these features allows us to obtain quantitative parameters regarding the complexity and heterogeneity of the tissue. These fractal features, both individually and in conjunction with other vascular risk factors and CMR traditional indexes, are employed as inputs to state-of-the-art machine learning models, including SVM, XGBoost, and random forests. The objective is to determine if the inclusion of fractal features enhances the performance of currently employed parameters. The performance evaluation of our models is based on metrics such as balanced accuracy, F1 score, precision, and recall. The results obtained demonstrate the potential of fractal-based features in improving the accuracy and reliability of cardiovascular diseases diagnosis

Computing Local Fractal Dimension Using Geographical Weighting Scheme

The fractal dimension (D) of a surface can be viewed as a summary or average statistic for characterizing the geometric complexity of that surface. The D values are useful for measuring the geometric complexity of various land cover types. Existing fractal methods only calculate a single D value for representing the whole surface. However, the geometric complexity of a surface varies across patches and a single D value is insufficient to capture these detailed variations. Previous studies have calculated local D values using a moving window technique. The main purpose of this study is to compute local D values using an alternative way by incorporating the geographical weighting scheme within the original global fractal methods. Three original fractal methods are selected in this study: the Triangular Prism method, the Differential Box Counting method and the Fourier Power Spectral Density method. A Gaussian density kernel function is used for the local adaption purpose and various bandwidths are tested. The first part of this dissertation research explores and compares both of the global and local D values of these three methods using test images. The D value is computed for every single pixel across the image to show the surface complexity variation. In the second part of the dissertation, the main goal is to study two major U.S. cities located in two regions. New York City and Houston are compared using D values for both of spatial and temporal comparison. The results show that the geographical weighting scheme is suitable for calculating local D values but very sensitive to small bandwidths. New York City and Houston show similar global D results for both year of 2000 and 2016 indicating there were not much land cover changes during the study period