Methods
Data information and preparation
This work included eight male patients with A-fib in 52–61 age groups. Our work was based on delayed enhancement cardiac CT image datasets obtained by ten sets of time frames at the same position using different contrast mediums, each containing one complete cardiac cycle. Philips computerized tomography instrument was utilized to obtain the image dataset of. Each patient's data set included 392 images with 512 × 512 dimensions that covered the entire thoracic region.
All the 392 images were stacked up to get a 3D view of the thoracic region. Then we extracted only those images which included only the heart. These images were 204 in number. Since the thoracic region contains the heart, ribcage and spinal cord, which can make difficult the visualization of the heart, that is the rationale for our clearing out the surrounding structures by removing the pixels representing these structures. The 3D view was visualized through the Volume Viewer App of MATLAB R2018a. After that, a masking filter was applied to these images to highlight the required area by changing the color of the original images. An image display threshold setting of –190 to –30 Hounsfield Units (HU) was identified for epicardial fat on grayscale; other research also suggested a threshold of -200 to -50 HU [5, 7]. The images were sent to mask the pixel values which lie between -190 to -30 HU. The fat tissues on the atrium of the heart were identified using the pixel value range masked over the entire dataset. The above-mentioned methodology has already been described in our previously published study [8]. We extracted the desired dataset of 36 images from each patient’s data which contains the fat region of the atrium. We cropped these fat regions from all the images and made 36 patches of 32 × 32 dimensions. These 36 patches were concatenated to form one large patch. Additionally another 36 patches are extracted from the atrium containing non-fat tissues and preceded the same way as mentioned (Fig. 1).
Persistent homology filtration
Key objects in topological data analysis are filtered simplicial complexes, called filtrations. Homology is a method for in an accurate measuring the shape of a geometric object by counting holes or features of various dimensions. Its output is a vector space for each non-negative integer k whose dimension (called the k-th Betti number) is the feature count for holes of dimension k. This notion extends to filtered simplicial complex by producing a “persistence vector space”, the analogue of vector spaces, as well as the analogue of dimension, which is called a persistence barcode or persistence diagram. These PH diagrams can be thought of as finite collections (unordered) of intervals, and one uses various algebraic combinations of the lengths of the intervals as well as their midpoints [9].
Filtration is the first step of PH which produces a series of simplicial complexes for a scale proximity parameters (ε). We observe the filtration procedure for a point cloud data set where each point is surrounded by a sphere of radius ε. We draw an edge between two spots at each intersection of two spheres. Filtering data creates a simplicial complex space from which PH quantifies the presence of n-dimensional holes, which include 0-dimensional holes, 1-dimensional holes, circles/loops/tunnels, and 2-dimensional holes. Since the best value for the scale ε cannot be determined, the primary principle of PH is to move through all possible values (0) to see how the homology of these components changes [10]. We evaluate the times of birth (ε emerges) and death (ε vanishes) for each n-dimensional structure (Fig. 2).
Results and discussion
In left atrium epicardial fat tissue, we see the range of Betti numbers varies less (0–30), while in the non-fat tissue, the range of the Betti numbers is large (0–100). After Betti number, we plotted PH. Figure 3 shows the PH diagrams of left atrium epicardial fat and non-fat tissue. In the diagram of epicardial fat tissue, the points are closer towards the diagonal line, which means a topology with many small holes, but in non-fat tissue, the points are more scattered and concentrated away from diagonal that means topology is smoother on a small scale. This is the other way to calculate the pattern between two groups of tissues.
Fat tissues are the adipose tissue that helps in storing energy, and in distress, they provide support to the system for the proper execution of body functions. They insulate the body and act as an endocrine organ. The adipose tissue between the visceral pericardium and the myocardium is known as epicardial fat [11]. The increased epicardial fat on the left atrium wall hampers electrical conduction. Several studies have been reported that provide evidence of epicardial fat in the atrium causing A-fib [12, 13]. To measure cardiac fats, a couple of imaging modalities such as magnetic resonance imaging (MRI), echocardiography, and computed tomography (CT) are currently accessible in the market. However, detection of the fat can need either manual strategies which can be tedious or using some available strategies [14,15,16,17]. TDA combines algebraic topology and statistical learning techniques to provide a mathematical foundation for studying the shape of data. TDA also offers dimensionality reduction and noise stability. Here, we applied PH, an algebraic method of TDA that discover the topology of data to find new and distinctive features. The basic idea behind PH is to replace data points with a parametrized family of simplicial complexes, which can generally be depicted as a union of points, edges, triangles, tetrahedrons, and higher-dimensional polytopes, and encode the change of the simplicial complexes' topological features (such as the number of connected components, holes, and voids) across various parameters for data analysis [18,19,20]. Our PH diagrams represent the distinct comparison between fat tissue and non-fat tissues in our data. Our results have shown that this method may help in identifying the fat tissue from non-fat tissue for better stratification. In conclusion, by analyzing CT patches using a topological data analysis approach known as persistent homology, we have identified patterns in barcodes and persistence diagrams that discriminate cardiac patients whoexperience epicardial fat tissue versus those who do not have epicardial fat tissue. While promising, our results will need to be validated on a larger cohort.
Limitations of the study
We have used very small number of the patients with A-fib. The data was validated under the supervision of cardiologists.
