Multi-scaled temporal modeling of cardiovascular disease progression: An illustration of proximal arteries in pulmonary hypertension.

The progression of cardiovascular disease is intricately influenced by a complex interplay between physiological pathways, biochemical processes, and physical mechanisms. This study aimed to develop an in-silico physics-based approach to comprehensively model the multifaceted vascular pathophysiological adaptations. This approach focused on capturing the progression of proximal pulmonary arterial hypertension, which is significantly associated with the irreversible degradation of arterial walls and compensatory stress-induced growth and remodeling. This study incorporated critical characteristics related to the distinct time scales for the deformation, thus reflecting the impact of mean pressure on artery growth and tissue damage. The in-silico simulation of the progression of pulmonary hypertension was realized based on computational code combined with the finite element method (FEM) for the simulation of disease progression. The parametric studies further explored the consequences of these irreversible processes. This computational modeling approach may advance our understanding of pulmonary hypertension and its progression.

Investigating the influence of collagen cross-linking on mechanical properties of thoracic aortic tissue.

Vascular diseases, such as abdominal aortic aneurysms, are associated with tissue degeneration of the aortic wall, resulting in variations in mechanical properties, such as tissue ultimate stress and a high slope. Variations in the mechanical properties of tissues may be associated with an increase in the number of collagen cross-links. Understanding the effect of collagen cross-linking on tissue mechanical properties can significantly aid in predicting diseased aortic tissue rupture and improve the clarity of decisions regarding surgical procedures. Therefore, this study focused on increasing the density of the aortic tissue through cross-linking and investigating the mechanical properties of the thoracic aortic tissue in relation to density. Uniaxial tensile tests were conducted on the porcine thoracic aorta in four test regions (anterior, posterior, distal, and proximal), two loading directions (circumferential and longitudinal), and density increase rates (0%-12%). As a result, the PPC (Posterior/Proximal/Circumferential) group experienced a higher ultimate stress than the PDC (Posterior/Distal/Circumferential) group. However, this relationship reversed when the specimen density exceeded 3%. In addition, the ultimate stress of the ADC (Anterior/Distal/Circumferential) and PPC group was greater than that of the APC (Anterior/Proximal/Circumferential) group, while these findings were reversed when the specimen density exceeded 6% and 9%, respectively. Finally, the high slope of the PDL (Posterior/Distal/Longitudinal) group was lower than that of the ADL (Anterior/Distal/Longitudinal) group, but the high slope of the PDL group appeared larger due to the stabilization treatment. This highlights the potential impact of density variations on the mechanical properties of specific specimen groups.

A biochemomechanical model of collagen turnover in arterial adaptations to hemodynamic loading.

The production, removal, and remodeling of fibrillar collagen is fundamental to mechanical homeostasis in arteries, including dynamic morphological and microstructural changes that occur in response to sustained changes in blood flow and pressure under physiological conditions. These dynamic processes involve complex, coupled biological, chemical, and mechanical mechanisms that are not completely understood. Nevertheless, recent simulations using constrained mixture models with phenomenologically motivated constitutive relations have proven able to predict salient features of the progression of certain vascular adaptations as well as disease processes. Collagen turnover is modeled, in part, via stress-dependent changes in collagen half-life, typically within the range of 10-70 days. By contrast, in this work we introduce a biochemomechanical approach to model the cellular synthesis of procollagen as well as its transition from an intermediate state of assembled microfibrils to mature cross-linked fibers, with mechano-regulated removal. The resulting model can simulate temporal changes in geometry, composition, and stress during early vascular adaptation (weeks to months) for modest changes in blood flow or pressure. It is shown that these simulations capture salient features from data presented in the literature from different animal models.

Mechanical characterization of human umbilical arteries by thick-walled models: Enhanced vascular compliance by removing an abluminal lining.

The decellularized human umbilical artery (HUA) is considered as a promising option for small-diameter, tissue-engineered vascular grafts (TEVGs). Our previous study showed that the HUA bears a thin, watertight lining on its outermost abluminal surface. Removal of this abluminal lining layer improves efficacy of the perfusion-assisted decellularization of the HUA and increases its compliance. As stress across the wall is believed to affect growth and remodeling of the TEVG, it is imperative to mechanically characterize the HUA using thick-walled models. Combining inflation experiments and computational methods, we investigate the mechanical properties of the HUA before and after the abluminal lining removal to examine the HUA's wall mechanics. The inflation tests of five HUAs were performed to obtain the mechanical and geometrical response of the vessel wall before and after the lining layer removal. Using nonlinear hyperelastic models, the same responses are obtained computationally using the thick-walled models. The experimental data are incorporated into the computational models to estimate the mechanical and orientation parameters of the fibers and isotropic matrix of different layers in the HUAs. The parameter fitting of both thick-walled models (before and after the abluminal lining removal) results in most of the R-squared values for measuring the goodness of fitting to be over 0.90 for all samples. The compliance of the HUA increases from a mean value of 2.60% per 100 mmHg before the removal of the lining to a mean value of 4.21% per 100 mmHg after the removal. The results reveal that, although the abluminal lining is thin, it is stiff and capable of supporting majority of the high luminal pressure, and that the inner layer is far less stressed than the abluminal lining. Computational simulations also show that removal of the abluminal lining increases the circumferential wall stress by up to 280 kPa under the in vivo luminal pressure. The integrated computational and experimental approaches provide more accurate estimates of the material behaviors of HUAs employed in grafts and, in turn, the study enhances our understanding of interactions between the graft and the native vessel on vascular growth and remodeling.

A multiscale framework for defining homeostasis in distal vascular trees: applications to the pulmonary circulation.

Pulmonary arteries constitute a low-pressure network of vessels, often characterized as a bifurcating tree with heterogeneous vessel mechanics. Understanding the vascular complexity and establishing homeostasis is important to study diseases such as pulmonary arterial hypertension (PAH). The onset and early progression of PAH can be traced to changes in the morphometry and structure of the distal vasculature. Coupling hemodynamics with vessel wall growth and remodeling (G&R) is crucial for understanding pathology at distal vasculature. Accordingly, the goal of this study is to provide a multiscale modeling framework that embeds the essential features of arterial wall constituents coupled with the hemodynamics within an arterial network characterized by an extension of Murray's law. This framework will be used to establish the homeostatic baseline characteristics of a pulmonary arterial tree, including important parameters such as vessel radius, wall thickness and shear stress. To define the vascular homeostasis and hemodynamics in the tree, we consider two timescales: a cardiac cycle and a longer period of vascular adaptations. An iterative homeostatic optimization, which integrates a metabolic cost function minimization, the stress equilibrium, and hemodynamics, is performed at the slow timescale. In the fast timescale, the pulsatile blood flow dynamics is described by a Womersley's deformable wall analytical solution. Illustrative examples for symmetric and asymmetric trees are presented that provide baseline characteristics for the normal pulmonary arterial vasculature. The results are compared with diverse literature data on morphometry, structure, and mechanics of pulmonary arteries. The developed framework demonstrates a potential for advanced parametric studies and future G&R and hemodynamics modeling of PAH.

A Biochemomechanical Model of Collagen Turnover in Arterial Adaptations to Hemodynamic Loading.

The production, removal, and remodeling of fibrillar collagen is fundamental to arterial homeostasis, including dynamic morphological and microstructural changes that occur in response to sustained changes in blood flow and pressure under physiological conditions. These dynamic processes involve complex, coupled biological, chemical, and mechanical mechanisms that are not completely understood. Nevertheless, recent simulations using constrained mixture models with phenomenologically motivated constitutive relations have demonstrated a capability to predict salient features of the progression of certain vascular adaptations and disease processes. Collagen turnover is modeled, in part, via stress-dependent changes in collagen half-life, typically taken within the range of 10â€"70 days. By contrast, in this work we introduce a biochemomechanical approach to model the cellular synthesis of procollagen as well as its transition from an intermediate state of assembled microfibrils to mature cross-linked fibers, with mechano-regulated removal. The resulting model can simulate temporal changes in geometry, composition, and stress during early vascular adaptation (weeks to months) for modest changes in blood flow or pressure. It is shown that these simulations capture salient features from data presented in the literature from different animal models.

Deep Learning on Multiphysical Features and Hemodynamic Modeling for Abdominal Aortic Aneurysm Growth Prediction.

Prediction of abdominal aortic aneurysm (AAA) growth is of essential importance for the early treatment and surgical intervention of AAA. Capturing key features of vascular growth, such as blood flow and intraluminal thrombus (ILT) accumulation play a crucial role in uncovering the intricated mechanism of vascular adaptation, which can ultimately enhance AAA growth prediction capabilities. However, local correlations between hemodynamic metrics, biological and morphological characteristics, and AAA growth rates present high inter-patient variability that results in that the temporal-spatial biochemical and mechanical processes are still not fully understood. Hence, this study aims to integrate the physics-based knowledge with deep learning with a patch-based convolutional neural network (CNN) approach by incorporating important multiphysical features relating to its pathogenesis for validating its impact on AAA growth prediction. For this task, we observe that the unstructured multiphysical features cannot be directly employed in the kernel-based CNN. To tackle this issue, we propose a parameterization of features to leverage the spatio-temporal relations between multiphysical features. The proposed architecture was tested on different combinations of four features including radius, intraluminal thrombus thickness, time-average wall shear stress, and growth rate from 54 patients with 5-fold cross-validation with two metrics, a root mean squared error (RMSE) and relative error (RE). We conduct extensive experiments on AAA patients, the results show the effect of leveraging multiphysical features and demonstrate the superiority of the presented architecture to previous state-of-the-art methods in AAA growth prediction.

Computational modelling of multi-temporal ventricular-vascular interactions during the progression of pulmonary arterial hypertension.

A computational framework is developed to consider the concurrent growth and remodelling (G&R) processes occurring in the large pulmonary artery (PA) and right ventricle (RV), as well as ventricular-vascular interactions during the progression of pulmonary arterial hypertension (PAH). This computational framework couples the RV and the proximal PA in a closed-loop circulatory system that operates in a short timescale of a cardiac cycle, and evolves over a long timescale due to G&R processes in the PA and RV. The framework predicts changes in haemodynamics (e.g. 68.2% increase in mean PA pressure), RV geometry (e.g. 38% increase in RV end-diastolic volume) and PA tissue microstructure (e.g. 90% increase in collagen mass) that are consistent with clinical and experimental measurements of PAH. The framework also predicts that a reduction in RV contractility is associated with long-term RV chamber dilation, a common biomarker observed in the late-stage PAH. Sensitivity analyses on the G&R rate constants show that large PA stiffening (both short and long term) is affected by RV remodelling more than the reverse. This framework can serve as a foundation for the future development of a more predictive and comprehensive cardiovascular G&R model with realistic heart and vascular geometries.

Region-dependent mechanical characterization of porcine thoracic aorta with a one-to-many correspondence method to create virtual datasets using uniaxial tensile tests.

The simulation of the cardiovascular system and in silico clinical trials have garnered attention in the biomedical engineering field. Physics-based modeling is essential to associate with physical and clinical features. In physics-based constitutive modeling, the identification of the parameters and estimation of their ranges based on appropriate experiments are required. Uniaxial tests are commonly used in the field of vascular mechanics, but they have limitations in fully characterizing the regional mechanical behavior of the aorta. Therefore, this study is aimed at identifying a method to integrate constitutive models with experimental data to elucidate regional aortic behavior. To create a virtual two-dimensional dataset, a pair of uniaxial experimental datasets in the longitudinal and circumferential directions was combined using a one-to-many correspondence method such as bootstrap aggregation. The proposed approach is subsequently applied to three constitutive models, i.e., the Fung model, Holzapfel model, and constrained mixture model, to estimate the material parameters based on the four test regions of the porcine thoracic aorta. Finally, the regional difference in the mechanical behavior of the aorta, the correlation between the experimental characteristics and model parameters, and the inter-correlation of the material parameters are confirmed. This integrative approach will enhance the prediction capability of the model with respect to the regions of the aorta.

Data-driven computational models of ventricular-arterial hemodynamics in pediatric pulmonary arterial hypertension.

Pulmonary arterial hypertension (PAH) is a complex disease involving increased resistance in the pulmonary arteries and subsequent right ventricular (RV) remodeling. Ventricular-arterial interactions are fundamental to PAH pathophysiology but are rarely captured in computational models. It is important to identify metrics that capture and quantify these interactions to inform our understanding of this disease as well as potentially facilitate patient stratification. Towards this end, we developed and calibrated two multi-scale high-resolution closed-loop computational models using open-source software: a high-resolution arterial model implemented using CRIMSON, and a high-resolution ventricular model implemented using FEniCS. Models were constructed with clinical data including non-invasive imaging and invasive hemodynamic measurements from a cohort of pediatric PAH patients. A contribution of this work is the discussion of inconsistencies in anatomical and hemodynamic data routinely acquired in PAH patients. We proposed and implemented strategies to mitigate these inconsistencies, and subsequently use this data to inform and calibrate computational models of the ventricles and large arteries. Computational models based on adjusted clinical data were calibrated until the simulated results for the high-resolution arterial models matched within 10% of adjusted data consisting of pressure and flow, whereas the high-resolution ventricular models were calibrated until simulation results matched adjusted data of volume and pressure waveforms within 10%. A statistical analysis was performed to correlate numerous data-derived and model-derived metrics with clinically assessed disease severity. Several model-derived metrics were strongly correlated with clinically assessed disease severity, suggesting that computational models may aid in assessing PAH severity.

Numerical simulations of the nonsymmetric growth and remodeling of arteries under axial twisting.

Blood vessels are often subjected to axial twisting during body movement or surgery. Sustained twisting may lead to blood vessel growth and remodeling, however, it remains unclear how the extracellular matrix in the blood vessels remodel under sustained axial twisting. This study aimed to develop a computational model to simulate stress-induced growth and remodeling (G&R) of thin-walled blood vessels under axial twisting. Cylindrical vessels were subjected to a step increase in axial torque while the axial stretch and lumen pressure remained constant. The vessel walls were modeled based on the constrained mixture theory given as microstructure-based discrete fiber families with isotropic matrix structure models. Simulation results demonstrated that in response to a constant twist angle loading, arterial wall thickness, mass, and twisting torque gradually increase towards a new steady state. However, the stress and mass decrease in one diagonal fiber family while increasing in the other diagonal fiber family before reaching plateaus. A novel finding was that the two helical collagen fiber families showed different growth rates and patterns during remodeling, driven by the different fiber stresses generated by the twisting, and led to non-symmetric material properties. This study sheds new light on arterial wall remodeling under axial twisting.

Association of vortical structures and hemodynamic parameters for regional thrombus accumulation in abdominal aortic aneurysms.

The intraluminal thrombus (ILT) has been shown to negatively impact the progression of the abdominal aortic aneurysms (AAAs). The formation of this thrombus layer has been connected to the local flow environment within AAAs, but the specific mechanisms leading to thrombus formation are still not fully understood. Our study investigated the association between vortical structures, near-wall hemodynamic metrics (e.g., time averaged wall shear stress (TAWSS) and oscillatory shear index (OSI)), and ILT accumulation in a longitudinal cohort of 14 AAAs (53 scans total). Vortices and hemodynamic parameters were estimated using hemodynamic simulations performed to each scan of each patient and compared to local 3D changes of ILT thickness between two consecutive scans (ΔILT). Results showed that vortices formed and remained strong and close to the lumen surface in AAAs without an ILT, while in AAAs with ILTs these detached from the lumen surface and dissipated nearby wall region where an increase in ILT thickness was observed. Although low TAWSS was observed in regions with and without ILT accumulation, an inverse correlation between ∆ILT and TAWSS was observed within the regions that experienced a thrombus growth. Our results support the idea that vortical structures might be playing a role modulating ILT accumulation into specific wall regions. Also, it submits the idea that the low TAWSS will be modulating the growth of thrombus within these preferred ILT accumulated regions.

Growth-profile configuration for specific deformations of tubular organs: A study of growth-induced thinning and dilation of the human cervix.

Growth is a significant factor that results in deformations of tubular organs, and particular deformations associated with growth enable tubular organs to perform certain physiological functions. Configuring growth profiles that achieve particular deformation patterns is critical for analyzing potential pathological conditions and for developing corresponding clinical treatments for tubular organ dysfunctions. However, deformation-targeted growth is rarely studied. In this article, the human cervix during pregnancy is studied as an example to show how cervical thinning and dilation are generated by growth. An advanced hyperelasticity theory called morphoelasticity is employed to model the deformations, and a growth tensor is used to represent growth in three principle directions. The computational results demonstrate that both negative radial growth and positive circumferential growth facilitate thinning and dilation. Modeling such mixed growth represents an advancement beyond commonly used uniform growth inside tissues to study tubular deformations. The results reveal that complex growth may occur inside tissues to achieve certain tubular deformations. Integration of further biochemical and cellular activities that initiate and mediate such complex growth remains to be explored.

Defining a master curve of abdominal aortic aneurysm growth and its potential utility of clinical management.

OBJECTIVE: The maximum diameter measurement of an abdominal aortic aneurysm (AAA), which depends on orthogonal and axial cross-sections or maximally inscribed spheres within the AAA, plays a significant role in the clinical decision making process. This study aims to build a total of 21 morphological parameters from longitudinal CT scans and analyze their correlations. Furthermore, this work explores the existence of a "master curve" of AAA growth, and tests which parameters serve to enhance its predictability for clinical use. METHODS: 106 CT scan images from 25 Korean AAA patients were retrospectively obtained. We subsequently computed morphological parameters, growth rates, and pair-wise correlations, and attempted to enhance the predictability of the growth for high-risk aneurysms using non-linear curve fitting and least-square minimization. RESULTS: An exponential AAA growth model was fitted to the maximum spherical diameter, as the best representative of the growth among all parameters (r-square: 0.94) and correctly predicted to 15 of 16 validation scans based on a 95% confidence interval. AAA volume expansion rates were highly correlated (r=0.75) with thrombus accumulation rates. CONCLUSIONS: The exponential growth model using spherical diameter provides useful information about progression of aneurysm size and enables AAA growth rate extrapolation during a given surveillance period.

Plasticity and Enzymatic Degradation Coupled With Volumetric Growth in Pulmonary Hypertension Progression.

Pulmonary hypertension (PH) is one of the least understood and highly elusive cardiovascular conditions associated with elevated pulmonary arterial pressure. Although the disease mechanisms are not completely understood, evidence has accumulated from human and animal studies that irreversible processes of pulmonary arterial wall damage, compensated by stress-mediated growth, play critical roles in eliciting the mechanisms of disease progression. The aim of this study is to develop a thermodynamic modeling structure of the pulmonary artery to consider coupled plastic-degradation-growth irreversible processes to investigate the mechanical roles of the dissipative phenomena in the disease progression. The proposed model performs a model parameter study of plastic deformation and degradation processes coupled with dissipative growth subjected to elevated pulmonary arterial pressure and computationally generates in silico simulations of PH progression using the clinical features of PH, found in human morphological and mechanical data. The results show that considering plastic deformation can provide a much better fitting of the ex vivo inflation tests than a widely used pure hyperelastic model in higher pressure conditions. In addition, the parameter sensitivity study illustrates that arterial damage and growth cause the increased stiffness, and the full simulation (combining elastic-plastic-degradation-growth models) reveals a key postpathological recovery process of compensating vessel damage by vascular adaptation by reducing the rate of vessel dilation and mediating vascular wall stress. Finally, the simulation results of luminal enlargement, arterial thickening, and arterial stiffness for an anisotropic growth are found to be close to the values from the literature.

CRIMSON: An open-source software framework for cardiovascular integrated modelling and simulation.

In this work, we describe the CRIMSON (CardiovasculaR Integrated Modelling and SimulatiON) software environment. CRIMSON provides a powerful, customizable and user-friendly system for performing three-dimensional and reduced-order computational haemodynamics studies via a pipeline which involves: 1) segmenting vascular structures from medical images; 2) constructing analytic arterial and venous geometric models; 3) performing finite element mesh generation; 4) designing, and 5) applying boundary conditions; 6) running incompressible Navier-Stokes simulations of blood flow with fluid-structure interaction capabilities; and 7) post-processing and visualizing the results, including velocity, pressure and wall shear stress fields. A key aim of CRIMSON is to create a software environment that makes powerful computational haemodynamics tools accessible to a wide audience, including clinicians and students, both within our research laboratories and throughout the community. The overall philosophy is to leverage best-in-class open source standards for medical image processing, parallel flow computation, geometric solid modelling, data assimilation, and mesh generation. It is actively used by researchers in Europe, North and South America, Asia, and Australia. It has been applied to numerous clinical problems; we illustrate applications of CRIMSON to real-world problems using examples ranging from pre-operative surgical planning to medical device design optimization.

Machine learning approaches to surrogate multifidelity Growth and Remodeling models for efficient abdominal aortic aneurysmal applications.

Computational Growth and Remodeling (G&R) models have been widely used to capture the pathological development of arterial diseases and have shown promise for aiding clinical diagnosis, prognosis prediction, and staging classification. However, due to the high complexity of the arterial adaptation mechanism, high-fidelity arterial G&R simulation usually takes hours or even days, which hinders its application in clinical practice. To remedy this problem, we develop a computationally efficient arterial G&R simulation framework that comprehensively combines the physics-based G&R simulations and data-driven machine learning approaches. The proposed framework greatly enhances the computational efficiency of arterial G&R simulations, thereby enabling more time-consuming arterial applications, including personalized parameter estimation and arterial disease progression prediction. In particular, we achieve significant computational cost reduction mainly through two methods: (1) constructing a Multifidelity Surrogate (MFS) to approximate multifidelity G&R simulations by using a cokriging approach and (2) developing a novel iterative optimization algorithm for personalized parameter estimation. The proposed framework is demonstrated by estimating G&R model parameters and predicting individual aneurysm growth using follow-up CT images of Abdominal Aortic Aneurysms (AAAs) from 21 patients. Results show that the personalized parameters are satisfactorily estimated and the growth of AAAs is predicted within the clinically relevant time frame, i.e., less than 2 h, without a loss of accuracy.

Inverse modeling framework for characterizing patient-specific microstructural changes in the pulmonary arteries.

Microstructural changes in the pulmonary arteries associated with pulmonary arterial hypertension (PAH) is not well understood and characterized in humans. To address this issue, we developed and applied a patient-specific inverse finite element (FE) modeling framework to characterize mechanical and structural changes of the micro-constituents in the proximal pulmonary arteries using in-vivo pressure measurements and magnetic resonance images. The framework was applied using data acquired from a pediatric PAH patient and a heart transplant patient with normal pulmonary arterial pressure, which serves as control. Parameters of a constrained mixture model that are associated with the structure and mechanical properties of elastin, collagen fibers and smooth muscle cells were optimized to fit the patient-specific pressure-diameter responses of the main pulmonary artery. Based on the optimized parameters, individual stress and linearized stiffness resultants of the three tissue constituents, as well as their aggregated values, were estimated in the pulmonary artery. Aggregated stress resultant and stiffness are, respectively, 4.6 and 3.4 times higher in the PAH patient than the control subject. Stress and stiffness resultants of each tissue constituent are also higher in the PAH patient. Specifically, the mean stress resultant is highest in elastin (PAH: 69.96, control: 14.42 kPa-mm), followed by those in smooth muscle cell (PAH: 13.95, control: 4.016 kPa-mm) and collagen fibers (PAH: 13.19, control: 2.908 kPa-mm) in both the PAH patient and the control subject. This result implies that elastin may be the key load-bearing constituent in the pulmonary arteries of the PAH patient and the control subject.

Potential damage in pulmonary arterial hypertension: An experimental study of pressure-induced damage of pulmonary artery.

Pulmonary arterial hypertension (PAH) is associated with elevated pulmonary arterial pressure. PAH prognosis remains poor with a 15% mortality rate within 1 year, even with modern clinical management. Previous clinical studies proposed wall shear stress (WSS) to be an important hemodynamic factor affecting cell mechanotransduction, growth and remodeling, and disease progress in PAH. However, WSS in vivo is typically at most 2.5 Pa and a doubt has been cast whether WSS alone can drive disease progress. Furthermore, our current understanding of PAH pathology largely comes from small animals' studies in which caliber enlargement, a hallmark of PAH in humans, is rarely reported. Therefore, a large-animal experiment on pulmonary arteries (PAs) is needed to validate whether increased pressure can induce enlargement of PAs caliber. In this study, we use an inflation testing device to characterize the mechanical behavior, both nonlinear elastic behavior and irreversible damage of porcine arteries. The parameters of elastic behavior are estimated from the inflation test at a low-pressure range before and after over-pressurization. Then, histological images are qualitatively examined for medial and adventitial layers. This study sheds light on the relevance of pressure-induced damage mechanism in human PAH.

Intraluminal thrombus effect on the progression of abdominal aortic aneurysms by using a multistate continuous-time Markov chain model.

OBJECTIVE: To investigate the relationship between the characteristics of intraluminal thrombus (ILT) with abdominal aortic aneurysm (AAA) expansion. METHODS: This retrospective clinical study applied homogeneous multistate continuous-time Markov chain models to longitudinal computed tomography (CT) data from Korean patients with AAA. Four AAA states were considered (early, mild, severe, fatal) and the maximal thickness of the ILT (maxILT), the fraction of the wall area covered by the ILT (areafrac) and the fraction of ILT volume (volfrac) were used as covariates. RESULTS: The analysis reviewed longitudinal CT images from 26 patients. Based on likelihood-ratio statistics, the areafrac was the most significant biomarker and maxILT was the second most significant. In addition, within AAAs that developed an ILT layer, the analysis found that the AAA expands relatively quickly during the early stage but the rate of expansion reduces once the AAA has reached a larger size. CONCLUSION: The results recommend surgical intervention when a patient has an areafrac more than 60%. Although this recommendation should be considered with caution given the limited sample size, physicians can use the proposed model as a tool to find such recommendations with their own data.