Mathematical modeling of plaque progression and associated microenvironment: How far from predicting the fate of atherosclerosis?

Blood Lipoproteins Shape the Phenotype and Lipid Content of Early Atherosclerotic Lesion Macrophages: A Dual-Structured Mathematical Model

Macrophages in atherosclerotic lesions exhibit a spectrum of behaviours or phenotypes. The phenotypic distribution of monocyte-derived macrophages (MDMs), its correlation with MDM lipid content, and relation to blood lipoprotein densities are not well understood. Of particular interest is the balance between low density lipoproteins (LDL) and high density lipoproteins (HDL), which carry bad and good cholesterol respectively. To address these issues, we have developed a mathematical model for early atherosclerosis in which the MDM population is structured by phenotype and lipid content. The model admits a simpler, closed subsystem whose analysis shows how lesion composition becomes more pathological as the blood density of LDL increases relative to the HDL capacity. We use asymptotic analysis to derive a power-law relationship between MDM phenotype and lipid content at steady-state. This relationship enables us to understand why, for example, lipid-laden MDMs have a more inflammatory phenotype than lipid-poor MDMs when blood LDL lipid density greatly exceeds HDL capacity. We show further that the MDM phenotype distribution always attains a local maximum, while the lipid content distribution may be unimodal, adopt a quasi-uniform profile or decrease monotonically. Pathological lesions exhibit a local maximum in both the phenotype and lipid content MDM distributions, with the maximum at an inflammatory phenotype and near the lipid content capacity respectively. These results illustrate how macrophage heterogeneity arises in early atherosclerosis and provide a framework for future model validation through comparison with single-cell RNA sequencing data.

Plaque Ruptures Are Related to High Plaque Stress and Strain Conditions: Direct Verification by Using In Vivo OCT Rupture Data and FSI Models

BACKGROUND

While it has been hypothesized that high plaque stress and strain may be related to plaque rupture, its direct verification using in vivo coronary plaque rupture data and full 3-dimensional fluid-structure interaction models is lacking in the current literature due to difficulty in obtaining in vivo plaque rupture imaging data from patients with acute coronary syndrome. This case-control study aims to use high-resolution optical coherence tomography-verified in vivo plaque rupture data and 3-dimensional fluid-structure interaction models to seek direct evidence for the high plaque stress/strain hypothesis.

METHODS

In vivo coronary plaque optical coherence tomography data (5 ruptured plaques, 5 no-rupture plaques) were acquired from patients using a protocol approved by the local institutional review board with informed consent obtained. The ruptured caps were reconstructed to their prerupture morphology using neighboring plaque cap and vessel geometries. Optical coherence tomography-based 3-dimensional fluid-structure interaction models were constructed to obtain plaque stress, strain, and flow shear stress data for comparative analysis. The rank-sum test in the nonparametric test was used for statistical analysis.

RESULTS

Our results showed that the average maximum cap stress and strain values of ruptured plaques were 142% (457.70 versus 189.22 kPa; P=0.0278) and 48% (0.2267 versus 0.1527 kPa; P=0.0476) higher than that for no-rupture plaques, respectively. The mean values of maximum flow shear stresses for ruptured and no-rupture plaques were 145.02 dyn/cm2 and 81.92 dyn/cm2 (P=0.1111), respectively. However, the flow shear stress difference was not statistically significant.

CONCLUSIONS

This preliminary case-control study showed that the ruptured plaque group had higher mean maximum stress and strain values. Due to our small study size, larger scale studies are needed to further validate our findings.

Exploring the Effects of Local Air Pollution on Popliteal Artery Aneurysms

Objectives: A growing body of evidence highlights the effects of air pollution on chronic and acute cardiovascular diseases, such as associations between PM10 and several cardiovascular events. However, evidence of the impact of fine air pollutants on the development and progression of peripheral arterial aneurysms is not available. Methods: Data were obtained from the multicenter PAA outcome registry POPART and the German Environment Agency. Means of the mean daily concentration of PM10, PM2.5, NO2, and O3 concentrations were calculated for 2, 10, and 3650 days prior to surgery for each patient. Additionally, weighted ten-year averages were analyzed. Correlation was assessed by calculating Pearson correlation coefficients, and regression analyses were conducted as multiple linear or multiple logistic regression, depending on the dependent variable. Results: For 1193 patients from the POPART registry, paired air pollution data were available. Most patients were male (95.6%) and received open surgical repair (89.9%). On a regional level, the arithmetic means of the daily means of PM10 between 2000 and 2022 were neither associated with average diameters nor runoff vessels. Negative correlations for mean PAA diameter and mean NO2, as well as a positive correlation with mean O3, were found; however, they were not statistically significant. On patient level, no evidence for an association of mean PM10 exposure over ten years prior to inclusion in the registry and PAA diameter or the number of runoff vessels was found. Weighted PM10, NO2, and O3 exposure over ten years also did not result in significant associations with aneurysm diameter or runoff vessels. Short-term air pollutant concentrations were not associated with symptomatic PAAs or with perioperative complications. Conclusions: We found no indication that long-term air pollutant concentrations are associated with PAA size or severity, neither on a regional nor individual level. Additionally, short-term air pollution showed no association with clinical presentation or treatment outcomes.

Data-driven models for the prediction of coronary atherosclerotic plaque progression/regression

Coronary artery disease is defined by the existence of atherosclerotic plaque on the arterial wall, which can cause blood flow impairment, or plaque rupture, and ultimately lead to myocardial ischemia. Intravascular ultrasound (IVUS) imaging can provide a detailed characterization of lumen and vessel features, and so plaque burden, in coronary vessels. Prediction of the regions in a vascular segment where plaque burden can either increase (progression) or decrease (regression) following a certain therapy, has remained an elusive major milestone in cardiology. Studies like IBIS-4 showed an association between plaque burden regression and high-intensity rosuvastatin therapy over 13 months. Nevertheless, it has not been possible to predict if a patient would respond in a favorable/adverse fashion to such a treatment. This work aims to (i) Develop a framework that processes lumen and vessel cross-sectional contours and extracts geometric descriptors from baseline and follow-up IVUS pullbacks; and to (ii) Develop, train, and validate a machine learning model based on baseline/follow-up IVUS datasets that predicts future percent of atheroma volume changes in coronary vascular segments using only baseline information, i.e. geometric features and clinical data. This is a post hoc analysis, revisiting the IBIS-4 study. We employed 140 arteries, from 81 patients, for which expert delineation of lumen and vessel contours were available at baseline and 13-month follow-up. Contour data from baseline and follow-up pullbacks were co-registered and then processed to extract several frame-wise features, e.g. areas, plaque burden, eccentricity, etc. Each pullback was divided into regions of interest (ROIs), following different criteria. Frame-wise features were condensed into region-wise markers using tools from statistics, signal processing, and information theory. Finally, a stratified 5-fold cross-validation strategy (20 repetitions) was used to train/validate an XGBoost regression models. A feature selection method before the model training was also applied. When the models were trained/validated on ROI defined by the difference between follow-up and baseline plaque burden, the average accuracy and Mathews correlation coefficient were 0.70 and 0.41 respectively. Using a ROI partition criterion based only on the baseline's plaque burden resulted in averages of 0.60 accuracy and 0.23 Mathews correlation coefficient. An XGBoost model was capable of predicting plaque progression/regression changes in coronary vascular segments of patients treated with rosuvastatin therapy in 13 months. The proposed method, first of its kind, successfully managed to address the problem of stratification of patients at risk of coronary plaque progression, using IVUS images and standard patient clinical data.

On the nonlinear relationship between wall shear stress topology and multi-directionality in coronary atherosclerosis

BACKGROUND AND OBJECTIVE

In this paper we investigate twelve multi-directional/topological wall shear stress (WSS) derived metrics and their relationships with the formation of coronary plaques in both computational fluid dynamics (CFD) and dynamic fluid-structure interaction (FSI) frameworks. While low WSS is one of the most established biomechanical markers associated with coronary atherosclerosis progression, alone it is limited. Multi-directional and topological WSS derived metrics have been shown to be important in atherosclerosis related mechanotransduction and near-wall transport processes. However, the relationships between these twelve WSS metrics and the influence of both FSI simulations and coronary dynamics is understudied.

METHODS

We first investigate the relationships between these twelve WSS derived metrics, stenosis percentage and lesion length through a parametric, transient CFD study. Secondly, we extend the parametric study to FSI, both with and without the addition of coronary dynamics, and assess their correlations. Finally, we present the case of a patient who underwent invasive coronary angiography and optical coherence tomography imaging at two time points 18 months apart. Associations between each of the twelve WSS derived metrics in CFD, static FSI and dynamic FSI simulations were assessed against areas of positive/negative vessel remodelling, and changes in plaque morphology.

RESULTS

22-32% stenosis was the threshold beyond which adverse multi-directional/topological WSS results. Each metric produced a different relationship with changing stenoses and lesion length. Transient haemodynamics was impacted by coronary dynamics, with the topological shear variation index suppressed by up to 94%. These changes appear more critical at smaller stenosis levels, suggesting coronary dynamics could play a role in the earlier stages of atherosclerosis development. In the patient case, both dynamics and FSI vs CFD changes altered associations with measured changes in plaque morphology. An appendix of the linear fits between the various FSI- and CFD-based simulations is provided to assist in scaling CFD-based results to resemble the compliant walled characteristics of FSI more accurately.

CONCLUSIONS

These results highlight the potential for coronary dynamics to alter multi-directional/topological WSS metrics which could impact associations with changes in coronary atherosclerosis over time. These results warrant further investigation in a wider range of morphological settings and longitudinal cohort studies in the future.