# Simulation-Driven Machine Learning for Predicting Stent Expansion in Calcified Coronary Artery
## 1 Introduction  
Heavily calcified arteries are commonly associated with suboptimal stenting outcomes, including stent underexansion and malapposition [1; 2], which have been associated with chronic complications, such as restenosis and thrombosis [1; 3; 4; 5; 6]. The calcification characteristics (such as calcification angle, area, calcium scores, etc.) are associated with stenting outcomes in a clinical setting [1; 7; 8]. Calcium score, assessed by intravascular ultrasound (IVUS) or optical coherence tomography (OCT), has been commonly used as a biomarker for clinical classification and risk management [9; 10; 11]. A retrospective study showed that lesions with a higher calcium score often require post-dilation using a larger non-compliant balloon at a higher inflation pressure [7]. Another retrospective study has shown that stenting expansion is related to the calcification angle and area assessed with OCT images [1]. An OCT-based calcium scoring system was proposed to predict the possibility of stent underexansion [8]. The score depends on the maximum angle, thickness, and the length of thecalcification, with critical values of 180\({}^{\circ}\), 0.5 mm, and 5 mm, respectively. These retrospective studies provide a qualitative relationship between calcification characteristics and stent expansion.  
Mechanical tests and in vitro/silico studies have also been performed to quantitatively inspect the mechanism of the stent-artery interaction in a calcified artery. Nanoindentation tests of calcified arteries showed that the Young's modulus of calcification is 690 MPa, which is much larger than that of fibrotic tissue, which is in the range of 50 to 980 kPa [12; 13]. Uniaxial tensile tests of calcified artery segments along the circumferential direction showed that a larger calcification volume reduces the stretch capability of the artery [14; 15]. Our previous work has demonstrated that stenting induces larger stretch in the fibrotic tissue than that in calcification, which contributes to lumen gain [2; 16]. Specifically, the calcification angle determines the arterial stretch and thus lumen gain.  
Machine learning (ML) methods have been integrated with engineering approaches for mechanistic prediction. Combined with finite element (FE) or molecular dynamic simulation, ML methods have been used to predict the Young's modulus of composite materials [17; 18]. Simulation could provide enriched datasets in the computational domain, such as the stress/strain inside the artery, which is difficult to measure using experimental techniques. These datasets could enhance the training of the ML, which would then help to optimize virtual tests. On the other hand, ML has been used for image processing, pattern identification [19; 20], and predicting in-stent restenosis based on acute stenting outcomes (lumen area, shape, etc.), as well as demographic characteristics such as diabetes and other related diseases [21; 22]. However, ML has not been integrated with FE methods yet to predict stent expansion.  
In this work, we developed simulation-driven ML models to predict the post-stenting lumen area in a calcified coronary artery. An in-silico stenting procedure was performed in a patient-specific coronary artery model reconstructed from OCT images in our previous work [16]. The mechanistic understanding from FE simulation inspired us to select stretch features besides classical calcification features. Eight pre-stenting features and the post-stenting lumen area were used to train and test ML models. The accuracy of the ML models was evaluated in terms of the prediction error, i.e., the percentage difference between the predicted lumen area and the one obtained from FE simulation. Two subgroups, stretch features and calcification features, were compared to study the influence of feature selection on the prediction. In addition, the influence of neighboring cross sections on the prediction was also investigated by averaging each feature over eight neighboring cross sections.