Abstract
A novel method for four-dimensional superficial wall strain and stress (4D-SWS) is derived from the arterial motion as pictured by invasive coronary angiography. Compared with the conventional finite element analysis of cardiovascular biomechanics using the estimated pulsatile pressure, the 4D-SWS approach can calculate the dynamic mechanical state of the superficial wall in vivo, which could be directly linked with plaque rupture or stent fracture. The validation of this approach using in silico models showed that the distribution and maximum values of superficial wall stress were similar to those calculated by conventional finite element analysis. The in vivo deformation was validated on 16 coronary arteries, from the comparison of centerlines predicted by the 4D-SWS approach against the actual centerlines reconstructed from angiograms at a randomly selected time-point, which demonstrated a good agreement of the centerline morphology between both approaches (scaling: 0.995 ± 0.018 and dissimilarity: 0.007 ± 0.014). The in silico vessel models with softer plaque and larger plaque burden presented more variation in mean lumen diameter and resulted in higher superficial wall stress. In more than half of the patients (n = 16), the maximum superficial wall stress was found at the proximal lesion shoulder. Additionally, in three patients who later suffered from acute coronary syndrome, the culprit plaque rupture sites co-localized with the site of highest superficial wall stress on their baseline angiography. These representative cases suggest that angiography-based superficial wall dynamics have the potential to identify coronary segments at high-risk of plaque rupture and fracture sites of implanted stents. Ongoing studies are focusing on identifying weak spots in coronary bypass grafts, and on exploring the biomechanical mechanisms of coronary arterial remodeling and aneurysm formation. Future developments involve integration of fast computational techniques to allow online availability of superficial wall strain and stress in the catheterization laboratory.
Introduction
Coronary arteries are continuously subjected to biomechanical forces, including myocardial contraction and relaxation, intraluminal pulsatile blood pressure, flow drag forces, and constrained by surrounding tissues. These biomechanical forces generate dynamic strain and stress on the coronary arterial wall (Figure 1A). The dynamic wall stress induced by cyclic deformation, which is around 103~105 times greater than fluid-induced endothelial shear stress (ESS) (), can trigger the rupture of atherosclerotic fibrous cap and disruption of inflamed vulnerable plaque (). With increased severity and extent of coronary artery disease, the vascular dynamic deformation performance could be deteriorated due to the loss of elasticity (). Furthermore, the dynamic stress and deformation of atherosclerotic coronary arterial walls (Figure 1B) are particularly relevant to vascular remodeling acute clinical events, such as myocardial infarction or unstable angina (), as well as the biomechanical compatibility of implanted stents and scaffolds ().
Figure 1
The deformation of coronary arteries in vivo can be quantitatively measured by mechanical strain. The mechanical strain of arterial wall is defined as the stretching or compressing, and angular deformation relative to its predefined reference state. This wall strain caused by vessel deformation can be assessed from modern standard X-ray coronary angiography. Taking into account the maximum speed of 34.5–250.0 mm/s of the arterial motion in early systole (
An attractive feature of this approach is an inverse computation method that the cyclic motion of coronary arteries in vivo is used to calculate the dynamic strain and stress of arterial walls for intraprocedural on-line computation and analysis. The arterial motion and deformation represent the resultant of various complex biomechanical and physiological alterations, including pulsatile blood pressure, vessel stretching, bending and twisting, and acting on both normal and diseased vessel segments, each with different wall composition and mechanical properties. Another promising feature of this approach is that it focuses on the biomechanical state of the superficial layer of vessel wall (i.e., the interface between lumen and subendothelial layer), which could be directly linked with plaque rupture or stent fracture.
To further understand the biomechanical triggering mechanisms of acute coronary events and eventually improve the prediction of future events, it may be of paramount importance to take SWS into account. Indeed, the angiography-based SWS reflects the dynamic deformation of coronary arteries during the cardiac cycle and “hot spots” may identify coronary segments at higher risk of plaque rupture or dissection. This review highlights the concept and validation of this new method and its potential value in identifying vulnerable coronary plaque and therefore at high risk of acute disruption or rapid disease progression.
Calculation Mehtods of Angiography-Based 4D Coronary Artery Dynamics
The concept and application of this method are illustrated in Figure 2. Coronary angiograms with minimal vessel image overlap and foreshortening are selected (
Figure 2

Methods of angiography-based 4D coronary arterial wall dynamics assessment and calculation. Five frames corresponding to specific time-points during the cardiac cycle are identified from the electrocardiogram: (A) mid-diastole (diastasis), (B) end-diastole, (C) early-systole, (D) end-systole, and (E) early-diastole. Left coronary arteries present large deformations in vivo. The local displacements of the superficial wall are determined between these arterial geometries at two consecutive time instants. By using global point-wise displacement mapping relationship on the arteries at the current time-point, the wall strain is determined. Considering the material properties of normal and fibrous tissues, superficial wall stress is further calculated (a–e). Modified from Wu et al. (
The clinical feasibility of this approach was first confirmed in a selected case with large coronary artery deformation and motion during cardiac cycle (Figure 2). The calculated motion of the left anterior descending (LAD) and the diagonal artery (Supplementary Videos 1, 2) were consistent with the angiogram (Supplementary Video 3). The LAD moved longitudinally, while the tortuous diagonal artery exhibited remarkable curl motion (
Figure 3

Time-averaged maximum principal strain and displacement at several locations on the LAD and diagonal arteries. The time-averaged maximal principal strain and displacement at the numbered nodes of interest on the diagonal (A,B) and LAD (C,D) with stenostic segments (dark brown). These nodes at the stenotic segments have lower strain than those at the normal segments.
In Silico and In Vivo Validation Studies
The calculation of wall stress was first validated on in silico stenosis models (n = 32) (
Figure 4

Comparison of the stress distribution of lipid-rich plaque models calculated by the conventional structural mechanical force-based method and superficial wall displacement-based method. There is similar wall stress distribution along the longitudinal superficial wall of the lipid-rich plaque models calculated by the conventional structural mechanical force-based method (A–C) and by superficial wall displacement-based method (a–c), regardless of the presence of arterial remodeling. Prox: Proximal; Dist: distal. Six red arrows show the lesion segments of two structural models with three types of arterial remodeling. Modified from Wu et al. (
For in vivo validation, our SWS computation procedures were performed on angiographic images from 16 patients with intermediate coronary stenoses included in the Functional Assessment by Various flOw Reconstructions (FAVOR) pilot study (
Angiography-Based 4D Coronary Arterial Wall Dynamics: Future Directions and Limitations
Table 1 summarizes the value and limitations of this method and its potential clinical usefulness, which is reviewed in greater detail in the following sections.
Table 1
| Value and limitations | |
| Value | 1. Angiography-based solution and potential online availability in the catheterization laboratory. |
| 2. Realistic reflection of the cyclic motion of arterial wall in vivo. | |
| 3. Assessment of the global and local features of the arterial wall with the amplitude and rate of changes in multiple parameters. | |
| Limitations | 1. Sensitive to the accuracy of lumen segmentation, especially at location of severe stenosis. |
| 2. Heart rate-dependent coronary motion. | |
| 3. Further validation of clinical predictive potential needed. | |
| Potential clinical applications | |
| 1. Assessment of the native vessel dynamics | |
| a. Identification of weak spots in a diseased vessel along the longitudinal direction. | |
| b. Differentiation of high-risk vessel segments in patients with non-obstructive coronary artery or multivessel disease. | |
| c. Biomechanical assessment of arterial remodeling, aneurysm formation, and lumen patency. | |
| 2. Assessment of the implanted device dynamics | |
| a. Assessment of the fracture risk and fatigue life of coronary stents. | |
| b. Evaluation of the early discontinuity of bioresorbable scaffolds. | |
| c. Assessment of the effects of wall strain on the patency of (bioresorbable) bypass grafts | |
Value and limitations of angiography-based 4D coronary artery dynamic method and clinical usefulness.
Localization of Coronary Plaque at Risk of Rupture and Prediction of Future Events in Patients With Mild or Non-obstructive Coronary Artery Disease (NOCA)
Histopathological post-mortem studies in victims of sudden coronary death demonstrated that acute thrombi are associated in 55–65% with the rupture of a thin fibrous cap atheroma (
Although, several attempts have been made to establish the criteria that define such rupture-prone plaques using cardiac imaging, the absolute event rates predicted by intravascular imaging remain low under the current best of medical treatment (
Figure 5

Angiography-based superficial wall stress on diagnostic angiography and late plaque rupture. Baseline angiography shows (yellow circle) an intermediate mid-LCx lesion (A–C). Superficial wall stress, calculated by the 4D approach at baseline angiography, reveals more local stress concentration in the stenotic segment (white arrow) or throat site (a–c). This location corresponds with the site of lumen irregularity, thrombus, and plaque rupture during late acute coronary syndrome, as shown by OCT on selected cross-sections (I-III), 3D rendering (D), and longitudinal OCT (E). The reconstructed throat segment and lesion shoulders are shown along with percent diameter stenosis (F). Modified from Wu et al. (
Figure 6 shows another example to suggest the association between superficial wall stress and newly developed stenosis at follow-up. After physiological assessment during index PCI (Figure 6A, baseline angiography), RCA showed preserved iFR value and the stent implantation in the proximal and distal lesions was deferred. On day 785, the patient was admitted for recurrent unstable angina. Repeat angiography (Figure 6B) showed that RCA had only a TIMI grade 2 flow, which was predominantly caused by the progression of the distal lesion. The initial diagnostic coronary angiogram was analyzed by both superficial wall stress (Figure 6C) and ESS (Figure 6D) to investigate their impacts on possible plaque progression. In contrast to superficial wall stress calculated based on the deformation of coronary artery during cardiac cycle, ESS is the friction between intravascular blood flow and endothelial layer, and was analyzed by computational fluid dynamics. In Figure 6C, the high level of time-averaged superficial wall stress was found at the site of distal stenosis with rapid progression (Figure 6B, yellow arrow). Figure 6D shows that the high time-averaged ESS is located at the stenotic segments RCA (lesions left untreated), while the mid-segment exhibits a very low ESS (<1 Pa). The expanded view shows that ESS is correlated with lumen diameter (Figure 6F). These observations illustrate the potential of angiography-based superficial wall stress for the identification of rupture-prone plaque. With further prospective validation, this technique can hopefully inform personalized patient care with optimized pharmacological therapy or local device-based plaque modification.
Figure 6

Effects of vessel deformation-induced superficial wall stress and fluid-induced endothelial shear stress on plaque progression and clinical adverse events. The moderate lesions in proximal and distal RCA remained untreated according to physiological guidance with iFR (A). On day 785, the patient was admitted to the hospital due to recurrent angina. Angiography demonstrated the progression of the distal RCA stenosis with impaired TIMI-2 coronary flow, suggesting plaque progression as well as potential atheroma rupture (B). The time-averaged superficial wall stress was relatively high at the distal RCA with 56 kPa (C) and co-located with the site of late plaque rupture (B). (D) Relatively high time-averaged endothelial shear stress (ESS) (6–7 Pa) was located at the stenotic segments of proximal and distal RCA (lesions left untreated), while the mid-segment exhibits a very low ESS (<1 Pa). (E,F) Expanded views of superficial wall stress and ESS distribution.
Assessment of the Mechanical Failure Risk of Coronary Stents
Histopathological studies have demonstrated that stent fracture is one of the potential causes of drug-eluting stent failure (
Although, it is recognized that repetitive and fluctuating stress, induced by the dynamic deformation of coronary arteries, is an important mechanism of stent fracture, quantitative analysis on in vivo mechanical stress in association with a stent fracture using FEA is still limited (
Figure 7

Prediction of late stent fracture by the pulse stress on the implanted stent using angiography-based 4D coronary artery dynamic method. (A) Angiography prior to implantation shows a total occlusion of the mid-segment of the RCA and a smooth curve of the implanted stent. (B) Visible contours of the inflated balloon delineate the proximal and distal ends of the implanted stent (Xience V). (C) Straightening of the proximal segment occurs following stent implantation. (D) The highest pulse stress (313.90 MPa), derived from the difference between the stress state at end-systole and end-diastole, is found at the site of 30.2 mm from the ostium. [(D'), red arrow] The zoomed view shows the pulse stress distribution of the implanted stent. Angiograms 20 months later show stent fracture (E) located at 30.8 mm from the ostium, resulting in luminal irregularity (F). The site of the highest pulse stress calculated by the angiography-based 4D dynamic method co-localizes with the stent fracture site [(F'), red arrow] documented 20 months later.
Relationship Between Dynamic Parameters, Vascular Remodeling, and Lumen Patency
Vascular remodeling can be considered as a dynamic functional and morphometric adaptive process of a vessel in response to biomechanical stimuli that lead to changes in vascular structure and properties (
It has been suggested that cyclic motion of coronary bypass grafts plays an important role in lumen patency (
Many approaches have been evaluated for the prediction of events and the estimation of plaque propensity for rupture, thrombosis, or progression, including intracoronary imaging and image-based computational modeling. Table 2 summarizes the strengths and limitations of relevant imaging modalities and imaging-based computational modeling techniques and application scenarios. From a biomechanical viewpoint, ESS (
Table 2
| Categories | Techniques | Theoretical strengths | Limitations | Application scenarios |
|---|---|---|---|---|
| Cardiac imaging | Angiography | • High spatial resolution (150~250 μm) • High temporal resolution (33~80 ms) • Dynamic blood flow • Dynamic motion and deformation of coronary tree | • Lacking 3D information | • Diagnosis of coronary artery anomalies and guide interventional therapy • 3D reconstruction of artery and centerline • 4D reconstruction of arterial dynamics |
| IVUS | • High penetration depths for assessing plaque burden and detecting lumen size | • Low spatial resolution (axial: 100~150 μm; lateral: 150~300 μm) • Limited for assessing strut malapposition and detecting thrombus | • Measurement of lumen and vessel dimensions, lesion characterizations • Guide interventional therapy | |
| OCT | • High spatial resolution (axial: 10~20 μm; lateral: 20~90 μm) for accurately detecting lumen, thrombus, or stent-related morphologies | • Low tissue penetration depths (~2 mm) • Limited for assessing plaque burden and detecting vessel size | • Measurement of lumen dimensions, lesion characterizations, evaluation of strut-level • Guide interventional therapy | |
| NIRS | • Quantitative assessment of lipid core burden index | • Limited for plaque structure and cap thickness | • Detection of lipid-rich plaque | |
| Image reconstruction | ANGUS | • More accurate for 3D reconstruction model of vessels | • Need angiography and IVUS • 3D reconstruction only at end-diastole | • For endothelial shear stress analysis |
| Image-based computational modeling | ESS | • Assessing the hemodynamics of near-wall with a profound influence on vascular biology based on angiography or combined with intravascular images | • Static assessment at end-diastole | • Assessing plaque progression and thrombogenesis |
| SWS | • Measuring the dynamics of the superficial wall base on angiography • Dynamic mechanical behavior of coronary arteries during a cardiac cycle | • Sensitive to arterial geometry • Heart rate-dependent coronary motion | • Assessment of the native vessel dynamics • Assessment of the implanted device dynamics (Detail see Table 1) | |
| PSS | • Assessing the stress state of the plaque structure based on IVUS | • Segmentation of detail plaque components • Require blood pressure and mechanical properties of plaque components | • Assessment of plaque rupture risk | |
| Elastography/palpography | • Measuring plaque strain in vivo based on IVUS | • Sensitive to heart beating and the location of imaging sensor | • Detection of the vulnerable plaques with a high strain region at the surface in the close vicinity of low strain regions |
Summary of cardiac imaging and computational modeling techniques.
ESS, endothelial shear stress; IVUS, intravascular ultrasound; NIRS, near-infrared spectroscopy; OCT, optical coherence tomography; PSS, plaque structural stress; SWS: superficial wall strain/stress.
Conclusions
In silico and in vivo studies have revealed that angiography-based assessment of dynamic coronary artery deformation allows computation of superficial wall strain and stress, as reported by Wu et al. (
Statements
Author contributions
XW, WW, PS, and YO conceived the idea and wrote the first draft. All authors contributed substantially to the discussion of content and reviewed/edited the manuscript before submission.
Funding
This work is supported by the Natural Science Foundation of Zhejiang Province, China (LQ20H180004) and Science Foundation Ireland (15/RP/2765). XW, CG, RW, and WW are supported by SFI Grant 15/RP/2765. ST has a research Grant from National Natural Science Foundation of China (81871460). EP and PB are supported by Australia Research Council (LP150100233).
Conflict of interest
CB reports institutional research grants (Thoraxcentrum Twente) from Abbott Vascular, Biotronik, Boston Scientific, and Medtronic, outside the submitted work. ST reports institutional research grants from Pulse medical imaging technology, Shanghai, China. WW reports institutional research grant and honoraria from MicroPort. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Supplementary material
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fcvm.2021.667310/full#supplementary-material
Supplementary Video 1Superficial wall dynamics of the left anterior descending. The LAD moved longitudinally, and the peak superficial wall stress was mainly located at the proximal and distal shoulders of the stenotic segments during the cardiac cycle.
Supplementary Video 2Superficial wall dynamics of the diagonal artery. The tortuous diagonal artery exhibited remarkable curl motion, and the peak superficial wall stress was located at the proximal and distal shoulders of the stenotic segments or on the inner and outer walls in segments with large curvature during the cardiac cycle.
Supplementary Video 3Coronary angiogram of a selected case with large deformation and motion. The angiogram shows the LAD with diffuse lesion and the diagonal artery with narrowing at ostium.
- ACS
acute coronary syndrome
- BA
bifurcation angle
- ESS
endothelial shear stress
- FEA
finite element analysis
- IVUS
intravascular ultrasound
- LAD
left anterior descending
- MACE
major adverse cardiovascular events
- NIRS
near-infrared spectroscopy
- OCT
optical coherence tomography
- PCI
percutaneous coronary intervention
- PSS
plaque structural stress
- RCA
right coronary artery
- SWS
superficial wall strain/stress
- 4D
four-dimensional.
Abbreviations
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Summary
Keywords
invasive coronary angiography, coronary artery dynamics, superficial wall strain, quantitative assessment method, computational coronary pathophysiology
Citation
Wu X, Ono M, Kawashima H, Poon EKW, Torii R, Shahzad A, Gao C, Wang R, Barlis P, von Birgelen C, Reiber JHC, Bourantas CV, Tu S, Wijns W, Serruys PW and Onuma Y (2021) Angiography-Based 4-Dimensional Superficial Wall Strain and Stress: A New Diagnostic Tool in the Catheterization Laboratory. Front. Cardiovasc. Med. 8:667310. doi: 10.3389/fcvm.2021.667310
Received
12 February 2021
Accepted
21 May 2021
Published
18 June 2021
Volume
8 - 2021
Edited by
Antonios Karanasos, Hippokration General Hospital, Greece
Reviewed by
Ankush Gupta, Military Hospital Jaipur, India; Philipp Stawowy, Deutsches Herzzentrum Berlin, Germany; Italo Porto, University of Genoa, Italy
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Copyright
© 2021 Wu, Ono, Kawashima, Poon, Torii, Shahzad, Gao, Wang, Barlis, von Birgelen, Reiber, Bourantas, Tu, Wijns, Serruys and Onuma.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: William Wijns william.wyns@gmail.com
This article was submitted to Cardiovascular Imaging, a section of the journal Frontiers in Cardiovascular Medicine
†These authors have contributed equally to this work
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