# Machine Learning Driven Contouring of High-Frequency Four-Dimensional Cardiac Ultrasound Data
## 1 Introduction  
As heart disease remains the number one cause of death in the United States [1], echocardiography remains an integral tool to the proper diagnosis and prognosis of abnormal cardiac function. Furthermore, the development of murine models of cardiacdisease have provided researchers a strong foundation to further our understanding of pathological hallmarks and how specific genetic and/or environmental factors might drive progression [2; 3; 4; 5; 6]. To bridge the gap between imaging technology and murine disease models, high-frequency ultrasound uses MHz frequency ultrasonic waves to acquire images of small structures (e.g., mouse left ventricle with a thickness of \(\sim\)1 mm) that are rapidly moving (e.g., mouse heart rate is \(\sim\)500-600 bpm), thus too difficult to be adequately viewed using clinical ultrasound systems. Recent advancements in high-frequency ultrasound technologies have also introduced a collection of four-dimensional ultrasound (4 DUS) approaches, allowing for more thorough analyses of cardiac motion beyond global metrics based on idealized geometries (i.e., ejection fraction, stroke volume), similar to that commonly reported with clinical cine-magnetic resonance imaging (cine-MRI) [7; 8; 9].  
In tandem with the advancement of ultrasound imaging technology, integrations of machine learning and artificial intelligence algorithms--particularly deep neural nets--have shown promise in rapidly and robustly characterizing cardiac kinematics and ultrasound data in general [10; 11; 12; 13; 14; 15; 16; 17]. While machine learning has demonstrated notable successes in ventricle segmentation on 4D cardiac MRI data [18; 19; 20], epicardial fat segmentation in Computed Tomography (CT) data [21; 22], and even boundary detection in clinical 2 DUS echocardiography data [10], applications to murine 4 DUS data remain limited [12]. This is in part due to unique challenges presented by 4 DUS data. Most notably, cardiac US images in mice show lower image contrast in combination with large amounts of speckle noise. Furthermore, as the probe typically covers half of the entire ventral thorax, these artifacts can even renderer manual segmentation difficult. Finally, 4 DUS data in general suffer from high dimensionality; even 3 DUS segmentation is considered a difficult problem given current tools [10]. The high dimensionality in combination with the relatively small sample sizes commonly seen in medical applications, of which our dataset is no exception, presents even further challenges.  
Here, we develop a machine learning model to contour 4 DUS data acquired from healthy and diseased (i.e., hypertrophic cardiomyopathy) mice. To our knowledge, this is the first publication of machine learning applied to murine cardiac 4 DUS data. While our model is described in detail below, it contains three fundamental components: (1) a low dimensional representation of the raw US data, (2) a basis expansion of time to incorporate the regularity in epicardial movement throughout the cardiac cycle, and (3) the requirement that the model need only predict output values at preselected anchor points using interpolating cubic splines to form the final output structure.  
The following section \"Materials and Methods\" outlines the procedures followed to acquire the data used in training our models, details each model's composition, and describes how we test each model's predictive accuracy. The \"Results and Discussion\" section then demonstrates our quantitative model performance tests' results and provides context regarding broader applicability and limitations. Finally, we discuss other modelling approaches for future work and potential clinical translatability.