Significant progress has been made in computational modeling aimed at understanding and predicting cardiovascular diseases; these advances encompass various aspects, such as growth and remodeling (G&R) (Braeu et al., 2017, Caulk et al., 2018, Humphrey, 2021, Zeinali-Davarani and Baek, 2012), fluid–structure interaction (Lan et al., 2022, Rostam-Alilou et al., 2022), and multi-scale spatial and temporal modeling (Corti et al., 2022, Gharahi et al., 2023). Disease progression is influenced by a complex interplay between physiological pathways, biochemical processes, and physical mechanisms (Hassoun et al., 2009, Pan et al., 2021). Continuum mechanics-based approaches can be used in computational modeling to capture the multifaceted vascular pathophysiological adaptations.

Pulmonary arterial hypertension (PAH) is characterized by the persistent elevation of arterial blood pressure in the pulmonary circulation (Zambrano et al., 2018). Its key features include elevated arterial pressure, arteriosclerosis, arterial wall thickening, and increased arterial diameter (Chazova et al., 1995, Mahammedi et al., 2013). Despite the progress made in modern clinical treatments, the prognosis for patients with PAH remains poor, with a survival rate of 68 % and at 1 year a rapid decline to 39 % after 3 years (Mandras et al., 2020). Consequently, prognostic risk assessment methods for PAH patients have become a pivotal research area in the medical and biological communities. Although the underlying mechanisms related to disease progression are complex and have not yet been comprehensively elucidated, excessive elastolytic enzyme activity has been recognized as a significant contributor to PAH progression (Thenappan et al., 2018). Using an ex-vivo animal model, Tan et al. (2014) demonstrated that high pressure elevated the expression of pro-inflammatory molecules in pulmonary artery, which shows the necessity of introducing the dissipative processes into models to comprehend disease progression. Lee and Baek (2021) proposed a model in which mechanical deterioration was linked to stress-mediated growth and remodeling, thereby capturing features across multiple temporal scales through the vascular growth and tissue damage caused by pulsatility during the cardiac cycle. Nevertheless, their modeling efforts primarily focused on theoretical thermodynamic formulations, which were limited to an idealized geometry. The model was constrained by a strong assumption of an idealized thin-walled tube, unable to accurately reflect the actual structure of arteries.

The goal of this study is to build a three-dimensional (3D) model that enables in silico study of the progression of pulmonary hypertension for realistic simulations. The 3D model considered the non-stress-free nature of the artery and accounted for the impact of arterial pressure. Additionally, dissipative formulations (Lee, 2021a) considering a coupled growth–degradation model were implemented into a finite element method (FEM) for the simulation. This implemented formulation was based on the Lagrangian formulation (Lee, 2023). Disease progression simulations were conducted using a multi-scaled temporal approach. Arterial thickness, diameter, and soft tissue material stiffness were compared under different growth and degradation parameters. Compared with the follow-up statistics of PAH patients, the growth–degradation model shows good flexibility and adaptability.