Network-Based Approach for Modeling and Analyzing Coronary Angiography

N E T W O R K - B A S E D A P P R O A C H F O R M O D E L I N G A N D A N A L Y Z I N G C O R O N A RY A N G I O G R A P H Y A P R E P R I N T Babak Rav andi ∗ Department of Computer and Information T echnology Purdue Univ ersity W est Lafayette, Indiana 47906, USA bravandi@purdue.edu Arash Rav andi Devision of Orthopeadic Rheumatology Friedrich–Alexander Uni versity Erlangen-N ¨ urnberg W aldkrankenhaus Erlangen, 91054 Erlangen, Germany arash.ravandi@fau.de September 9, 2019 A B S T R AC T Significant intra-observ er and inter-observ er v ariability in the interpretation of coronary angiograms are reported. This v ariability is in part due to the common practices that rely on performing visual inspections by specialists (e.g., the thickness of coronaries). Quantitativ e Coronary Angiography (QCA) approaches are emer ging to minimize observ er’ s error and furthermore perform predictions and analysis on angiography images. Howe ver , QCA approaches suffer from the same problem as they mainly rely on performing visual inspections by utilizing image processing techniques. In this work, we propose an approach to model and analyze the entire cardio vascular tree as a com- plex network deri ved from coronary angiograph y images. This approach enables to analyze the graph structure of coronary arteries. W e conduct the assessments of network integration, degree distribution, and controllability on a healthy and a diseased coronary angiogram. Through our dis- cussion and assessments, we propose modeling the cardiov ascular system as a complex network is an essential phase to fully automate the interpretation of coronary angiographic images. W e sho w how netw ork science can provide a ne w perspective to look at coronary angiograms. 1 Introduction Coronary Heart Disease (CHD) is a major cause of disability and death in dev eloped countries. Although ov er the past four decades CHD mortality rates have declined worldwide, CHD remains responsible for one-third of all deaths in people over age of 35 [1]. In vasi ve coronary angiography is the current gold standard to determine the presence, location, and stage of coronary artery disease as well as to follow-up with the patients after therapeutic procedures [2]. Howe ver , potential observer error from performing visual analysis of Coronary Angiograms (CAs) has been estimated to be over 35% [3]. Quantitati ve Coronary Angiography (QCA) approaches are emerging to minimize the observer error and further perform predictions and analysis on angiography images [4]. Feyter et al. [5] classified the limitations of QCA approaches to three categories: patient related, technique related, and methodology related. Subsequently , immense technical improvements in the medical imaging techniques and adv ances in machine learning hav e been achieved [6, 7, 8]; notably , 3D Reconstruction of coronary angiography from 2D images [9, 10]. Howe ver , the main limitation of QCA approaches remains on capturing physiological characteristics such as side branches and bifurcations, hemodynamic assessment, and v asomotion that are technically difficult to measure [11, 12, 13]. Hence, sev eral angiography phenomena can lead QCA approaches toward over or underestimation of parameters such as extensi ve calcium deposits, acute or chronic thromb us, and slow flo w [14]. Due to these limitations, QCA approaches lack sufficient accuracy to be employed for clinical purposes [4]. W e believe the missing key is dynamization of QCA; that can be achie ved by utilizing the structural characteristics of the cardiov ascular coronary tree as a complex network. ∗ Corresponding Author – https://bravandi.net A P R E P R I N T - S E P T E M B E R 9 , 2 0 1 9 The adv antage of utilizing networks naturally arises from the way of thinking behind it, that is focusing on the relations among the entities rather than the entities themselves. For instance, consider the fact that humans and some plants hav e about 25,000 genes [15]. Having around the same number of genes does not reflect the biological complexity of humans compared to such plants. Many biologists believ e the complexity of an organism arises from the complexity of the interactions between its genes. The great genome project provided us with the book of life containing the description of all genes, and networks are providing the map of life that describes the dynamics in which genes interact with each other [16, 17]. 1.1 Innovation Heart is a comple x system consist of an interconnected network of coronary arteries as the heart’ s blood supplier . The innov ation of the proposed approach is its ability to create a collecti ve vie w of the heart’ s coronary circulation system by capturing the structure of coronary tree. Our approach enables analyzing netw ork structure-functions relationships, through which, we can identify hidden patterns in coronary networks. Such patterns relate to the formation or existence of conditions such as stenosis. The following summarizes contrib utions of this work: • W e propose a ne w perspective to analyze and understand coronary angiography images based on capturing the network structure of coronary tree. • W e treat the cardiov ascular system as a complex system and present a sho wcase of three network assessments on a healthy and a diseased coronary angiogram. • W e discuss how network science can provide insights from the graph structure of coronary arteries, and ultimately pav es the way to fully automate the interpretation of coronary angiography images. This article is organized as follows: Section 2 provides a brief ov erview of employing network science in modeling and understanding biological systems. In Section 3, we introduce our modeling approach by conducting three network- based assessments on two CA. Lastly , we discuss our vision in Section 4. 2 Complex Networks and Biological Systems In recent years, there has been growing interest in comple x, self-or ganizing networks often employed to model the dy- namics and structure of complex systems [18]. These are dynamical networks of dif fusely interconnected components. Their beha vior is a manifestation of the beha vior of the individual components and a reflection of the structural con- nections between these components. Examples of complex dynamic graphs abound in nature, from the microscopic cellular lev el where cells synchronize to perform their functions (heart beating [19] and neural graphs [20]) to large ecological graphs that respond to perturbations through very slo w ev olutionary behaviors [21]. Lusis and W eiss [22] provided a comprehensive revie w of the adv ances achie ved by employing network science to in vestigate the cardiov ascular system and diseases from the molecular lev el (genes and proteins). They showed system- based approaches are likely to play an important role in understanding the higher-order interactions that lead to forma- tion of diseases such as heart failure, atherosclerosis, cardiac hypertroph y , and arrhythmias. Moreover , Dashtbozorg et al. [6] proposed an automated graph-based approach to classify the retinal blood v essels. Their study was able to label retinal blood vessels with up to 89% accuracy . In another study , Estrada et al. [23] proposed a graph-theoretic framew ork to classify the retinal blood vessels. Their approach obtained an accuracy lev el up to 93.5%. Furthermore, W est et al. [24] introduced a general model of the circulatory systems as space-filling fractal networks. Their model deriv es the well known biological scaling relationship (i.e., metabolic-rate ∝ body-mass 3 / 4 ) shedding light on the ev olution of biological systems. The abov e studies demonstrate the practicality and adv antages of modeling blood vessels as a comple x network and utilizing network sciences to analyze the graph structure of the circulatory system. 3 Proposed A ppr oach and Case Study In this section, we propose our model by presenting a case study for both healthy and diseased CAs. The case study concentrates only on the Left Coronary Arteries (LCA). W e label an angiogram as diseased if a stenosis exists in the LCA. Howe ver , without loss of generality , the proposed model is naturally e xtendable to integrate all cardiac vessels and pro vide a complete map of heart coronary arteries. Figure 1 illustrates a CA and the process to deri ve a network of coronary v essels. A network consists of a set of nodes (representing a system entities) and a set of edges (capturing a relationship between those entities). In the proposed model, a node represents an intersection between v essels, and a weighted edge represents a vessel. The weight of an edge is calculated by multiplying the diameter of a vessel by its length. T wo steps were tak en to create the coronary networks in this work: 1) identify the intersections of vessels 2 A P R E P R I N T - S E P T E M B E R 9 , 2 0 1 9 ( a ) Coro n a ry A n g iog ram ( b ) Nod e s a n d E d g e s ( c ) Deri v e d Coro n a ry Net w o rk Figure 1: An example of network creation process (i.e., nodes), and 2) measure the length and diameter of each sub-vessel between the identified nodes and calculate the weights of edges. W e employed graphical filters to magnify the vessels as presented in Fig. 1 (b) and manually conducted these steps. Howe ver , without loss of generality , one can fully automate the network creation process by employing the variety of tools dev eloped for performing visual inspections on angiography images [25, 9, 26, 11]. Figure 1 (c) presents the created weighted coronary network. 3.1 Healthy and Diseased Coronary Networks Figure 2 presents angiograms for both a healthy and a diseased heart alongside their corresponding coronary net- works. The healthy angiogram is collected from [27] and the source of diseased angiogram is in [28]. In the diseased angiogram, a stenosis is marked by the green arrow . The healthy-case and disease-case angiograms in Fig. 2 are not related to each other . Our goal is to utilize the CAs in Fig. 2 to introduce our modeling approach. The global network characteristics [18] of healthy-case and disease-case networks are summarized in T able 1, in the follo wing fiv e columns: 1) number of nodes represents the number of intersections between the v essels, 2) number of edges rep- resents the number of vessels, 3) averag e de gree presents the av erage number of connections of the nodes, 4) avera ge clustering coefficient captures the degree of connectedness among neighbors of nodes, and 5) diameter length of a network presents the length of the longest shortest path between all combinations of nodes. At the first glance, the av erage clustering coefficient of the disease-case network is relati vely smaller than the healthy-case by 36%. ( b ) Di se a se - Case A n g iog ram ( d ) Di se a se - Case Net w o rk ste n o sis ( a ) Hea lth y - Case A n g iog ram ( c ) Hea lth y - Case Net w o rk Figure 2: Healthy and disease-case coronary angiograms and their networks. 3 A P R E P R I N T - S E P T E M B E R 9 , 2 0 1 9 T able 1: Coronary network characteristics Network Number of nodes Number of edges A verage degree A verage clustering coefficient Diameter length Healthy-Case 115 140 2.4348 0.099 23 Disease-Case 109 138 2.5321 0.063 24 3.2 Network Visualization V isualizations of networks may provide insights on their structure and patterns of connections. Figure 3 illustrates the deriv ed coronary networks in a circular layout. The thickness of edges (i.e., weights) represents the diameter of vessels multiplied by their length (the unit of measurements is pixel). Also, the green boxes in Fig. 3 mark Λ -branches as illustrated by Fig. 4. A Λ -branch consists of a single parent node that only has two children (i.e., the coronary tree leav es) who are not connected to an y other nodes. Also, the parent node must only ha ve a single additional connection other than its children. The disease-case network has se veral more Λ -branches compared to the healthy-case netw ork. This indicates blood is not being properly supplied to the diseased heart. The ab undance of Λ -branches could reflect the Neov ascularization phenomenon [29], which happens when the blood is not being properly supplied and the heart starts creating new vessels. These vessels can be observed in Fig. 2 (b) where man y small vessels are emerged from the main arteries. In the ne xt section, we sho w ho w to systematically capture this behavior by analyzing the de gree distrib ution of coronary networks. ( a ) H ea lthy - Ca se Ne twork ( b ) D ise ase - Ca se Ne twork aa Figure 3: Coronary networks visualizations. Thickness of edges indicate the vessel’ s diameter times their length and the green boxes mark Λ -branches. 𝑝 𝐿 1 𝐿 2 Figure 4: Λ -branch structure. 4 A P R E P R I N T - S E P T E M B E R 9 , 2 0 1 9 3.3 Assessment of Degree Distribution The degree distribution of a network represents the distrib ution of connections among nodes. In the coronary networks, the degree distribution presents the extent, in which, vessels are connected to each other . Blood flows in a fixed direction in human’ s cardio vascular system. Hence, we employ directed edges to capture the direction of blood flo w . Figure 5 illustrates a directed Λ -branch with the degrees of its nodes. For a giv e node, the total-de gr ee indicates its number of connections, the in-de gree indicates the number of connections to the node, and the out-de gree indicates the number of connections from the node. Figure 6 presents the in-degree, out-degree, and total-degree distributions of the healthy-case and disease-case net- works. At the first glance, there is no significant dif ference between the de gree distributions of the coronary networks. Howe ver , a significant difference is observ ed by comparing the quartile-de gree distributions of the healthy-case and disease-case networks, which is presented in Fig. 7. In the healthy-case network, most nodes are concentrated in the fourth quartile for all three de gree distributions. Howe ver , in the disease-case netw ork, the concentration of in-de gree distribution is shifted to the third quartile. This shift is due to the abundance of directed Λ -branches in the disease-case network. T o conclude, the patterns of connections in coronary networks could provide insights on the condition of the cardio v ascular system. For example, the analysis of degree-distribution could be used to determine the e xtent, in which, a heart is trying to create new v essels to overcome inef ficient blood circulation. in - degree: 1 out - deg ree : 0 total - degree: 1 in - degree: 1 out - deg ree : 2 total - degree: 3 𝑝 𝐿 1 𝐿 2 Figure 5: Directed Λ -branch structure. ( b ) Dise ase - Ca se Ne tw ork 0.0 0.2 0.4 0.6 0 1 2 3 4 5 ( a ) He al thy - Ca se Ne tw ork 0.0 0.2 0.4 0.6 Proportio n 0 1 2 3 4 5 6 In - degr ee O ut - degr ee T otal - degree Figure 6: Degree distributions of coronary networks. ( b ) Di se a se - Ca se Ne tw o rk in - degree di s tributi on i s c oncentrated i n the 3 rd quartil e ( a ) He a lth y - Ca se Ne tw o rk Proportio n in - degree di s tributi on i s c onc entrated i n the 4 th quartil e In - degree O ut - degree T otal - degree Figure 7: Quartile degree distributions of coronary networks. 5 A P R E P R I N T - S E P T E M B E R 9 , 2 0 1 9 3.4 Assessment of Network Integration The efficienc y of a network is the measurement of how efficiently it exchanges information. In transportation networks, this measurement corresponds to the ef ficiency of patrons commuting in terms of time and distance. W e can utilize the patterns of connections in structure of systems to infer their functional efficienc y [30]. The assessment of integration in the coronary networks corresponds to quantifying the ef ficiency of blood circulation in the cardiov ascular system. Figure 8 provides three measures of network integration: shortest-paths length , routing-ef ficiency , and searc h- information . The shortest-paths length provides the least number of hops (i.e., edges) that needs to be taken to navigate from any source node to any destination node [18]. Figure 8 (a) and (d) present the lengths of shortest-paths between all pairs of nodes. The r outing efficiency , also kno wn as global efficienc y enables to quantify ho w cost-ef ficient a particular network is, where the cost depends on the weight of edges [31]. Hence, this assessment enables to include the vessel’ s diameter and length (i.e., weight of edges) in quantifying the ef ficiency of blood circulation. For all pairs of nodes, we present this measurement in Fig. 8 (b) and (e). Lastly , the searc h-information quantifies the amount of information needed for a walker to perform an ef ficient routing (i.e., quantify accessibility or hiddenness). That is, ho w much information is needed for a walker to w alk on a shortest path when the walk er randomly travels between the nodes [32, 33]. Figure 8 (c) and (f) present this measurement between all pairs of nodes in the healthy-case and disease-case coronary networks. Through the assessment of network integration, we observe that the healthy-case network requires less information to find ef ficient routes. In other words, shortest paths are less hidden in the healthy-case network compared to the disease-case (i.e., smaller sear ch-information ). This observ ation indicates the measurement of searc h-information could be used as a feature to classify healthy and diseased coronary networks. 2 4 6 8 10 12 14 16 Blood V es se l Int er se ct ion 0.0 5 0.1 0.1 5 0.2 0.2 5 4 6 8 10 12 14 16 Blood V es se l Int er se ct ion Blood V es se l Int er se ct ion Blood V es se l Int er se ct ion 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 0.0 4 0.0 6 0.1 2 0.1 8 0.2 2 0.0 8 0.1 0 .14 0.1 6 0 .20 0.2 4 Blood V es se l Int er se ct ion Blood V es se l Int er se ct ion Blood V es se l Int er se ct ion Blood V es se l Int er se ct ion 𝐴𝑣 𝑔𝑇𝑜 𝑝10 % = 18 . 29 𝐴𝑣 𝑔𝑇𝑜 𝑝10 % = 16 . 74 𝐴𝑣 𝑔𝑇𝑜 𝑝10 % = 0 . 3 𝐴𝑣 𝑔𝑇𝑜 𝑝10 % = 21 . 48 𝐴𝑣 𝑔𝑇𝑜𝑝1 0% = 0 . 34 𝐴𝑣 𝑔𝑇𝑜 𝑝10 % = 18 . 98 ( b ) He althy - Ca se – Ro uting Ef ficienc y ( c ) He althy - Ca se – Searc h Inf or mation ( a ) He althy - Ca se – Shortes t Pat hs Leng th ( e ) Dis eas e - Ca se – Ro uting Ef ficienc y ( f ) Dis eas e - Ca se – Searc h Inf or mation ( d ) Dis eas e - Ca se – Shortes t Pat hs Leng th Figure 8: Analysis of network integration between all pairs of nodes. 6 A P R E P R I N T - S E P T E M B E R 9 , 2 0 1 9 ( a ) Heal thy - Cas e – 42% Driv er Nodes ( b ) Di s eas e - Cas e – 37% Driv er Nodes Figure 9: The controllability assessment (driver nodes are mark ed with red color). 3.5 Assessment of Controllability The controllability of complex networks is the study of controlling the state of networks from any initial value to a desired value in finite time via stimulating a set of k ey nodes called driver nodes . Efficient algorithms are developed to identify dri ver nodes in comple x networks [34, 35]. Most control scenarios are interested in identifying a minimum number of dri ver nodes needed to control a system. In coronary networks, this is analogous with controlling the flo w of blood by modifying the flow that can pass through each node (arteries’ intersections). Figure 9 presents the driv er nodes (marked red) for both coronary networks. Intuitiv ely , being easy to control (for cardiov ascular systems) might be taken as a sign for healthiness. Howe ver , having a small percentage of dri ver nodes in a coronary netw ork indicates a small number of malfunctions can perturb the whole system. Hence, a health y netw ork with a high percentage of dri ver nodes is more resilient to malfunctions. Figure 9 shows the disease-case netw ork has less driv er nodes (37%) compared to the healthy-case network (42%). 4 Discussion and Conclusion The predominant methods to identify cardiov ascular conditions primarily focus on analyzing the visual properties of coronary arteries (e.g., the diameter of arteries). For instance, Soroushmehr et al. [26] proposed a QCA approach to assist the diagnosis of CAs. Their approach is primarily based on the visual properties of coronary arteries (e.g., thickness of the arteries) and it can be e xtended by employing network science. In addition to employing the visual properties of CAs, our proposed approach enables to analyze the dynamics of cardiovascular system. Moreover , Andrikos et al. [9] introduced a nov el approach for 3D reconstruction of CAs as illustrated in Fig. 10. Their approach can be naturally utilized to automate the process of network construction from CAs. The proposed modeling approach provides the basis for de velopment of a ne w systematic methodology to study the cardiov ascular system and automate the diagnosis of coronary network pathology . An advantage of such a method- ology is introducing new features based on network measurements such as the routing efficienc y and controllability . For instance, these features could be used for the early detection of cardiovascular pathology by training machine learning classifiers and dev eloping network-based diagnostic methods. Similarly , the proposed approach can improv e the accurac y of procedure follow-ups such as the early detection of re vascularization after stent implantation. Another important adv antage of developing a systematic methodology is minimizing human error that accounts for a significant observer error [3]. 7 A P R E P R I N T - S E P T E M B E R 9 , 2 0 1 9 Figure 10: 3D reconstruction of coronary angiograms (courtesy Andrikos et al. [9]). Furthermore, non-in v asiv e coronary angiograph y such as Computed T omography Angiography (CT A) are already of significant v alue in the diagnostic procedure of patients. Our modeling approach can enhance the current literature on computer-based approaches for the interpretation of CT A images [8, 7]. The proposed network-based approach pa ves the way to apply the whole arsenal of network science tools on analyzing and classifying the CAs. Howe ver , the authors acknowledge that a rigorous study with more than two CAs should be done to further formalize and validate this approach. 5 Acknowledgements The authors acknowledge Professor Joaqu ´ ın Go ˜ ni, School of Industrial Engineering at Purdue Univ ersity , W est Lafayette, USA and Dr . Sophoclis Sophocleous, Pulmonology Resident in Bethanien Hospital, Solingen, Germany for their help and guidance on this paper . W e like to thank Mr . 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