The International Journal of Cardiovascular Imaging

, Volume 27, Issue 3, pp 397–402

Impact of plaque haemorrhage and its age on structural stresses in atherosclerotic plaques of patients with carotid artery disease: an MR imaging-based finite element simulation study


    • University Department of RadiologyUniversity of Cambridge, Addenbrooke’s Hospital
  • Zhongzhao Teng
    • University Department of RadiologyUniversity of Cambridge, Addenbrooke’s Hospital
  • Victoria E. Young
    • University Department of RadiologyUniversity of Cambridge, Addenbrooke’s Hospital
  • Chengcheng Zhu
    • University Department of RadiologyUniversity of Cambridge, Addenbrooke’s Hospital
  • Tjun Y. Tang
    • University Department of RadiologyUniversity of Cambridge, Addenbrooke’s Hospital
  • Martin J. Graves
    • University Department of RadiologyUniversity of Cambridge, Addenbrooke’s Hospital
  • Jonathan H. Gillard
    • University Department of RadiologyUniversity of Cambridge, Addenbrooke’s Hospital
Original Paper

DOI: 10.1007/s10554-010-9679-z

Cite this article as:
Sadat, U., Teng, Z., Young, V.E. et al. Int J Cardiovasc Imaging (2011) 27: 397. doi:10.1007/s10554-010-9679-z


Plaque haemorrhage (PH) in atherosclerotic plaques is associated with recurrent thromboembolic ischaemic events. The healing process predominantly involves the repair of the plaque rupture site and the replacement of fresh PH with chronic PH, which is either reabsorbed or replaced by fibrous tissue. The extent to which the presence of PH, and its type i.e. fresh or chronic, affects plaque stability remains unexplored. Finite element analysis (FEA)-based biomechanical stress simulations can provide quantification of the percentage contribution of PH and its types to the biomechanical stresses of plaques, thereby providing information about its role in plaque stability. Fifty-two patients with atherosclerotic carotid disease underwent high resolution magnetic resonance (MR) imaging of their carotid arteries in a 1.5 Tesla MR system. Twenty-three patients had MR-identifiable PH and were selected. Only those images of these patients were used for simulations, which had evidence of PH. Manual segmentation of plaque components, such as lipid pool, fibrous tissue, calcium and PH, was done using carotid MR images. Plaque components and vessel wall were modelled as isotropic, incompressible hyperelastic materials with non-linear properties undergoing deformation under patient-specific blood pressure loading. Two dimensional structure-only FEA was used for quantification of maximum critical stress (M-CStress) of plaques. The median M-CStress of symptomatic patients with fresh PH was 159 kPa (IQR: 114–253). Because PH usually occurs within the lipid pool, when the simulation was repeated with lipid pool replacing fresh PH to simulate the pre-rupture plaque state, M-CStress was reduced by 26% [118 kPa (IQR: 79–189) (P = 0.001)]. When fresh PH was replaced with chronic PH it resulted in a 30% reduction in the M-CStress [118 kP (IQR: 79–189), (P = 0.001)]. PH affects stresses within atheroma to various degrees depending on its type, thereby influencing plaque stability to a different extent, with fresh PH significantly increasing the biomechanical stresses. Plaque component-dependent stress analysis has the potential of identifying the critical nature of various plaque components.


Magnetic resonance imagingStrokeTransient Ischaemic attacksAtherosclerosisFinite element analysisBiomechanical stressPlaque Haemorrhage


Patients suffering from a transient ischaemic attack (TIA) are at high risk of a stroke or recurrent TIAs, with more than half of them occurring within the first 24 h [1]. Two important characteristics of a carotid plaque associated with recurrent TIAs, are a thin fibrous cap (FC) with or without erosion or disruption and plaque haemorrhage (PH). In biomechanical terms, thromboembolic events occur when the plaque stress exceeds the material strength of FC. The risk of recurrent thromboembolic events gradually decreases, presumably resulting from changes in the carotid plaque components: repair of the FC and gradual reabsorption or organization of the PH.

High resolution magnetic resonance (MR) imaging can assist us in identifying vulnerable plaques and assess their morphological changes [2]. It can also be used to assess the plaque component-dependent biomechanical stresses using computational simulations [37]. This can highlight the extent to which a plaque component can influence the stresses within a plaque which make it high-risk. To our knowledge, no previous biomechanical study has investigated the impact of PH and its types i.e. fresh or chronic, on structural plaque stresses. The aim of this study was to assess the effect of PH and age of PH on plaque stresses by performing patient-specific MR-based computational simulations.


Fifty-two patients with carotid atherosclerotic disease underwent high resolution MRI of their carotid arteries in a 1.5Tesla MRI system (Signa HDx GE Healthcare, Waukesha, WI) with a 4-channel phased-array neck coil (PACC, Machnet BV, Elde, The Netherlands). They were acutely symptomatic i.e. they had had ischaemic cerebrovascular symptoms within the 72 h before undergoing MR imaging. The study protocol was reviewed and approved by the regional research ethics committee and all patients gave written informed consent.

Movement artefact was minimized using a dedicated vacuum-based head restraint system (VAC-LOK Cushion, Oncology Systems Limited, UK) to fix the head and neck in a comfortable position and allow close apposition of the surface coils. Two-dimensional time-of-flight (TOF) MR angiography was performed to identify the location of the carotid bifurcation and the region of maximum stenosis on each side. 3 mm thickness axial images were acquired through the common carotid artery 12 mm below the carotid bifurcation to a point 12 mm distal to the extent of the stenosis identified on the TOF sequence. This method ensured that the entire carotid plaque was imaged [8]. The following MRI protocol, previously used by our group [9, 10], was used to delineate various plaque components such as fibrous cap (FC), lipid-rich necrotic core (LR/NC) and PH: T1 weighted (repetition time/echo time: 1 × RR/7.8 ms) with fat saturation, T2 weighted (repetition time/echo time: 2 × RR/100 ms) with fat saturation; and short tau inversion recovery (STIR) (repetition time/echo time/inversion time: 2 × RR/46 ms/150 ms). The field of view was 10 × 10 cm and matrix size 256 × 256. The in-plane spatial resolution achieved was of the order of 0.39 × 0.39 mm [8].

Plaques of those patients (n = 23) were selected only who had MR evidence of plaque haemorrhage. Only those slices of these plaques were used for this simulation study which showed presence of plaque haemorrhage. Plaque components were manually delineated by an experienced MR reader (US) and confirmed by consultant neuroradiologist (JHG) using CMR Tools (London, UK), using previously published criteria [10, 11]. The age of PH was established using previously published criteria [12] as fresh (<1 week), recent (1–6 weeks) and old haemorrhage (>6 weeks). The latter two were categorized as chronic for the sake of simplicity for biomechanical simulations. Following the plaque segmentation, a closed B-spline technique was used to smooth the geometry for mesh generation.

Biomechanical modelling

The investigators responsible for the entire computational analysis were not involved in the acquisition of MR data and image segmentation and had no knowledge of timing of symptoms in any of the subjects. A pre shrink process was used as before to obtain the zero-pressure geometry, which was used as the numerical starting geometry, and to recover the in vivo geometry when pressure was imposed in the lumen [13]. The shrinkage of the contours of lumen and outer wall was numerically determined following an iterative procedure so that: (1) the vessel cross-sectional area was conserved (conservation of mass); and (2) the pressurized morphology with diastolic blood pressure and the original in vivo morphology had the best agreement. The determined shrinkage was applied to all the slices of this. The average inner circumference shrinkage rate was 9.81% (standard deviation ±1.94%).

Mesh generation, computational models and solution methods

The two-dimensional computational mesh was made and the model was solved using ADINA8.5 (ADINA Inc., MA, USA). All plaque components including fibrous tissue, haemorrhage, lipid core, calcification and healthy arterial wall were assumed to be non-linear, isotropic and hyper-elastic [3]. The modified Mooney-Rivlin strain energy density function was used to describe the material [14]. The material parameters were used from previously published studies: vessel material: c1 = 36.8 kPa, D1 = 14.4 kPa, D2 = 2; fibrous cap: c1 = 73.6 kPa, D1 = 28.8 kPa, D2 = 2.5; lipid core: c1 = 2 kPa, D1 = 2 kPa, D2 = 1.5: calcification, c1 = 368 kPa, D1 = 144 kPa, D2 = 2.0; fresh PH: c1 = 1 kPa, D1 = 1 kPa, D2 = 0.25 and for chronic PH: c1 = 9 kPa, D1 = 9 kPa, D2 = 0.25 [15]. A pulsating pressure was imposed in the lumen using the systolic/diastolic arm pressure data for each patient at the time of the MRI. Pressure at the out-boundary of each vessel slice was set to zero.

Definition and calculation of maximum critical stress (M-CStress)

M-CStress was defined as the maximum principal stress over the vulnerable site i.e. minimum FC thickness or plaque shoulder [16]. Healthy regions where no plaque components were present and rupture was unlikely were excluded from the analysis, even if a high stress concentration occurred there. To assess the stress change due to the presence of PH, PH was replaced by lipid pool to indicate a baseline state, and a stress calculation was done. This is in accordance with Kolodgie et al’s assessment that the extent of intraplaque haemorrhage corresponds positively to the size of the necrotic core [17]. To assess the effect of PH by varying its age, the simulations were repeated by using material properties of chronic haemorrhage.

Statistical analysis

The analysis of variance was validated using the Shapiro–Wilk test. The continuous variables were assessed using Mann–Whitney test. A P-value of less than 0.05 was deemed significant. All statistical analysis was performed in GraphPad Instat (Version: 3.06).


23 carotid plaques with MR evidence of plaque haemorrhage were observed to have fresh haemorrhage. Seventy MR slices with PH were identified within these plaques and used for 2-dimensional computational simulations (210 simulations in total were performed). The degree of carotid luminal stenosis was moderate (50–69%). The median M-CStress of symptomatic patients with fresh PH was 159 kPa (IQR: 114–253). Because PH usually occurs within lipid rich necrotic core, when the simulation was repeated with fresh PH replaced by lipid pool to simulate a pre-rupture state, the median M-CStress was 118 kPa (IQR: 79–189) (P = 0.001), showing that fresh PH caused a 26% median (IQR: 13–50) increase in the M-CStress from baseline. The simulation performed with chronic haemorrhage replacing fresh PH gave a median M-CStress of 118 kP (IQR: 79–189), (P = 0.001). This indicated a 30% (IQR: 19–44) median reduction in the M-CStress. A diagrammatic representation of these simulations has been presented in Fig. 1.
Fig. 1

Panel A, B, C, D showing T1, proton density (PD), T2 and STIR weighted black-blood MR images- red asterisk indicating lumen, green asterisk indicating fresh PH which is hyperintense on T1 weighted image and isointense on PD, T2 and STIR weighted images, yellow asterisk indicates lipid content. Panel E showing contours of plaque components used for stress simulations (green: fresh PH, yellow: lipid content), Panel F: Band plot when simulation is done with fresh PH, followed by simulation performed with fresh PH replaced by chronic PH (Panel G) and lipid content (Panel H). It shows that maximum critical stress changes with change of material properties with maximum stress in the presence of fresh PH with lower stresses if simulation is performed with fresh PH replaced by chronic PH and lipid core


To our knowledge, this is the first simulation study that attempts to quantify the percentage contribution of plaque haemorrhage to the simulated stresses within plaques. We were also successful in quantifying the impact of age of haemorrhage on the plaque stresses. It was observed that the presence of fresh haemorrhage caused a 26% increase in the maximum critical stress if the simulation was done by replacing the lipid pool with fresh PH. If the fresh PH was simulated to be replaced by chronic PH, a 30% decrease was observed. This clearly indicates that plaque stresses are high at the early stages of plaque haemorrhage development, when the haemorrhage is fresh, than later on as the haemorrhage tends to stabilize. The pathomechanical explanation is that due to its soft consistency, under blood pressure loading, it undergoes massive deformation which increases the stresses. Cyclic loading leads to material fatigue of the atherosclerotic tissue over a period of time [18], leading to recurrent plaque disruptions and recurrent thromboembolic events. A mural thrombus may form, when arterial blood comes into contact with the subendothelial tissue [19, 20]. Identification of such high-risk plaques is therefore crucial so that they can be managed urgently. The current UK National Stroke Strategy, also strongly recommends immediate aggressive management of patients with atherosclerotic carotid disease within 2 weeks of TIA/stroke, to get maximum benefit [21, 22]. Although to a clinician these findings may seem quite expected, the quantification of the percentage contributions of PH to plaque stresses offers evidence for the first time about how PH may affect plaque stability.

Keeping in mind the aetiology of PH, the presence of intraplaque haemorrhage can be considered as a warning sign of the occurrence of intraluminal thrombus (IT) and an indicator of the severity of plaque vulnerability, as shown by various investigators [10, 23, 24]. In this scenario a detailed biomechanical assessment of interaction between the PH and intrinsic plaque stresses is crucial to the understanding of the extent to which PH weakens the mechanical structure of the plaque by increasing the mechanical stresses within. Highlighting the gravity of this situation may assist clinicians to tailor optimal treatment strategies for managing IT, which remain controversial at the moment [25] i.e. urgent surgery (due to the potential risk that the IT might migrate or embolise to occlude a distal artery, or in situ thrombotic occlusion may occur [26, 27]) or medical treatment (because clinical deterioration is not observed during follow-up under medical treatment [2729]). As finite element analysis (FEA)-based computational simulations integrate information about plaque morphology, material properties of the plaque components and local haemodynamic factors; it provides a comprehensive assessment of plaque vulnerability compared to plaque morphology alone. MR imaging-based FEA has also been used to assess the stress profiles of different clinical groups such as differentiating between symptomatic and asymptomatic patients [30], acute and recently symptomatic patients [9]. The association between biomechanical stresses and subsequent cerebrovascular ischaemic events has also been recently reported, using FEA [31]. Biomechnical stress analysis may therefore help us refine our risk-stratification criteria for management of patients with carotid artery disease.

However, there were some study limitations: (1) Because this was not a 3D flow- interaction-coupled model, it was not possible to simulate the effect of turbulent flow and a pressure drop across a stenosis, which of course will affect the applied load. Local pressure distribution cannot currently be directly determined from non-invasive imaging. (2) Although the relative material properties of various plaque components are probably only an approximate representation of the actual material properties, they are the best available choice for the biomechanical simulations today. This limitation is difficult to overcome at present. (3) Histological co registration of MR images was not done in this study because our patients had moderate carotid stenosis and did not go for surgery. Moreover, we have already validated this technique [32].


PH affects stresses within atheroma to various degrees depending on its type, thereby influencing plaque stability to different extents, with fresh PH significantly increasing the biomechanical stresses. Plaque component-dependent stress analysis has the potential of identifying the critical nature of various plaque components and therefore may help us refine our risk-stratification criteria for management of patients with carotid artery disease.


Dr. Umar Sadat is supported by a Medical Research Council UK & Royal College of Surgeons of England Joint Clinical Research Training Fellowship. This research has also been supported by a Biomedical Research Centre National Institute of Health Research (BRC NIHR) grant.

Competing interests



Umar Sadat and Zhongzhao Teng have equal contribution in writing this manuscript.

Copyright information

© Springer Science+Business Media, B.V. 2010