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# Human coronary plaque wall thickness correlated positively with flow shear stress and negatively with plaque wall stress: an IVUS-based fluid-structure interaction multi-patient study

- Rui Fan
^{1}, - Dalin Tang
^{2, 3}Email author, - Chun Yang
^{3, 4}, - Jie Zheng
^{5}, - Richard Bach
^{6}, - Liang Wang
^{2}, - David Muccigrosso
^{5}, - Kristen Billiar
^{7}, - Jian Zhu
^{8}, - Genshan Ma
^{8}, - Akiko Maehara
^{9}and - Gary S Mintz
^{9}

**13**:32

https://doi.org/10.1186/1475-925X-13-32

© Fan et al.; licensee BioMed Central Ltd. 2014

**Received:**24 December 2013**Accepted:**7 March 2014**Published:**26 March 2014

## Abstract

### Background

Atherosclerotic plaque progression and rupture are believed to be associated with mechanical stress conditions. In this paper, patient-specific in vivo intravascular ultrasound (IVUS) coronary plaque image data were used to construct computational models with fluid-structure interaction (FSI) and cyclic bending to investigate correlations between plaque wall thickness and both flow shear stress and plaque wall stress conditions.

### Methods

IVUS data were acquired from 10 patients after voluntary informed consent. The X-ray angiogram was obtained prior to the pullback of the IVUS catheter to determine the location of the coronary artery stenosis, vessel curvature and cardiac motion. Cyclic bending was specified in the model representing the effect by heart contraction. 3D anisotropic FSI models were constructed and solved to obtain flow shear stress (FSS) and plaque wall stress (PWS) values. FSS and PWS values were obtained for statistical analysis. Correlations with p < 0.05 were deemed significant.

### Results

Nine out of the 10 patients showed positive correlation between wall thickness and flow shear stress. The mean Pearson correlation r-value was 0.278 ± 0.181. Similarly, 9 out of the 10 patients showed negative correlation between wall thickness and plaque wall stress. The mean Pearson correlation r-value was -0.530 ± 0.210.

### Conclusion

Our results showed that plaque vessel wall thickness correlated positively with FSS and negatively with PWS. The patient-specific IVUS-based modeling approach has the potential to be used to investigate and identify possible mechanisms governing plaque progression and rupture and assist in diagnosis and intervention procedures. This represents a new direction of research. Further investigations using more patient follow-up data are warranted.

## Keywords

- Coronary
- Fluid-structure interaction
- Plaque rupture
- Plaque progression
- IVUS

## Introduction

**Human coronary morphological plaque vulnerability index (MPVI) definition and AHA classifications**

MPVI | Plaque | Description | AHA classification |
---|---|---|---|

V = 0 | Very stable | Normal or slight intimal thickening | Type I, some atherogenic lipoprotein and intimal thickening |

V = 1 | Stable | Moderate intimal thickening, no extracellular lipid, calcification or significant inflammation | Type II (fatty streak), III (preatheroma) |

V = 2 | Slightly unstable | Small lipid core (<30% of plaque size); calcification may be present; thick fibrous cap (> 150 μm); little or no inflammation at plaque shoulders | Type IV, Vb, and Vc with less than 30% NC by area; or VII/VIII |

V = 3 | Moderately unstable | Moderate lipid core (30 – 40% of plaque size) and fibrous cap (65 – 150 μm); moderate intraplaque hemorrhage; moderate inflammation. | Type Va, IV/V with 30-40% NC by area |

V = 4 | Highly unstable | Large lipid core(>40%); thin fibrous cap (< 65 μm); large intraplaque hemorrhage; extensive inflammation; evidence of previous plaque rupture | Type VI; IV/V with > 40% NC by area |

In vivo image-based coronary plaque modeling papers are relatively rare because clinical recognition of vulnerable coronary plaques has remained challenging [9, 10, 23]. We have published results based on follow-up studies showing that advanced carotid plaque had positive correlation with flow shear stress and negative correlation with plaque wall stress (PWS) [15]. In this paper, patient-specific intravascular ultrasound (IVUS)-based coronary plaque models with fluid-structure interaction (FSI), on-site pressure and ex vivo biaxial mechanical testing of human coronary plaque material properties were constructed to obtain flow shear stress and plaque wall stress data from ten (10) patients to investigate possible associations between vessel wall thickness and both flow shear stress and plaque wall stress conditions. The information may be helpful in establishing mechanisms governing plaque progression and rupture and may eventually be useful in cardiovascular disease diagnosis, prevention, or necessary interventions.

## Methods

### IVUS data acquisition

### Biaxial testing and anisotropic model of human coronary material properties

_{1}and I

_{2}are the first and second invariants of right Cauchy-Green deformation tensor

**C**defined as C = [

*C*

_{ ij }] =

**X**

^{T}

**X**,

**X**= [X

_{ij}] = [∂x

_{i}/∂a

_{j}], (x

_{i}) is current position, (a

_{i}) is original position,

*I*

_{4}=

*C*

_{ ij }(

**n**

_{ c })

_{ i }(

**n**

_{ c })

_{ j }

*,*

**n**

_{ c }is the unit vector in the circumferential direction of the vessel, c

_{1}, D

_{1}, D

_{2}, and K

_{1}and K

_{2}are material constants. A least-squares method was used to determine the parameter values in Eq. (1) to fit our experimental circumferential and axial stress-stretch data [24]. Five human coronary plaque samples were tested and the one with median stiffness was used in this paper. The parameter values are: c

_{1}= -1312.9 kPa, c

_{2}= 114.7 kPa, D1 = 629.7 kPa, D

_{2}= 2.0, K

_{1}= 35.9 kPa, K

_{2}= 23.5. Figure 5c shows that our model with parameters selected with this procedure fits very well with the measured experimental data. Our measurements are also consistent with data available in the literature [25–27].

### Reconstruction of plaque 3D geometry and mesh generation

_{2}norms of solution differences of all components, including stress, strain, displacements, flow velocity, and pressure) were less than 2%. The mesh was then chosen for our simulations. The number of elements used for the 10 plaques is given in Table 2.

**Number of elements used in the 10 models**

Patient | Wall-element-tissue | Wall-element-lipid | Wall-element-Ca | Wall-all-element (sum) | Wall-node | Fluid-element | Fluid-node |
---|---|---|---|---|---|---|---|

P1 | 18570 | 1554 | 0 | 20124 | 22880 | 62283 | 12027 |

P2 | 48840 | 1470 | 0 | 50310 | 55680 | 160752 | 29715 |

P3 | 22620 | 1140 | 0 | 23760 | 26800 | 108221 | 20226 |

P4 | 24504 | 888 | 0 | 25392 | 29914 | 227508 | 42312 |

P5 | 23976 | 1368 | 0 | 25344 | 29904 | 346195 | 61821 |

P6 | 19800 | 3240 | 0 | 23040 | 27216 | 291137 | 52262 |

P7 | 28071 | 279 | 0 | 28350 | 32000 | 195501 | 35764 |

P8 | 28122 | 228 | 0 | 28350 | 32000 | 192915 | 36017 |

P9 | 27148 | 2808 | 2384 | 32340 | 38073 | 209326 | 38273 |

P10 | 30164 | 320 | 1856 | 32340 | 38073 | 199434 | 36664 |

### The FSI model with cyclic bending and boundary conditions

where **u** and p are fluid velocity and pressure, **u**
_{g} is mesh velocity, μ is the dynamic viscosity (μ = 0.04 P), ρ is density, Γ stands for vessel inner boundary, **x** is the current position of Γ, **σ** is stress tensor (superscripts indicate different materials), **ϵ** is strain tensor, **v** is solid displacement vector, superscript letters “r” and “s” were used to indicate different materials. For simplicity, all material densities were set to 1 g⋅cm^{-3} in this paper.

3D coronary plaque FSI models for the ten patients were constructed and solved by ADINA (Adina R &D, Watertown, MA) to calculate flow and stress/strain distributions. Each IVUS slice was divided into 4 quarters with each quarter containing 25 data points taken on the lumen. Average FSS and PWS values from each quarter were obtained from all slices of a plaque corresponding to maximum pressure condition for statistical analysis. Standard linear correlation analysis was performed to find possible correlations between wall thickness and the mechanical stressess (FSS and PWS). Correlations with p < 0.05 were deemed significant.

## Results

### Plaque wall thickness correlates positively with flow shear stress and negatively with plaque wall stress

**Plaque wall thickness correlates positively with flow shear stress and negatively with plaque wall stress**

Patient | P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 | P9 | P10 |
---|---|---|---|---|---|---|---|---|---|---|

Segment length (cm) | 2.15 | 5.16 | 3.30 | 6.60 | 4.40 | 2.80 | 3.15 | 3.15 | 27.5 | 27.5 |

MPVI | 2 | 2 | 3 | 3 | 3 | 3 | 3 | 2 | 4 | 4 |

Qts | 176 | 176 | 136 | 180 | 180 | 164 | 256 | 256 | 224 | 224 |

Correlation between vessel thickness and flow shear stress under maximum pressure | ||||||||||

r | 0.3963 | 0.2842 | 0.2982 | 0.1501 | -0.1305 | 0.377 | 0.443 | 0.456 | 0.1364 | 0.3687 |

p | 0 | 0.0001 | 0.0004 | 0.0443 | 0.0808 | 0 | 0 | 0 | 0.0414 | 0 |

Correlation between vessel thickness and plaque wall stress under maximum pressure | ||||||||||

r | 0.0019 | -0.444 | -0.614 | -0.620 | -0.477 | -0.687 | -0.714 | -0.543 | -0.502 | -0.699 |

p | 0.9799 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Correlation between vessel thickness and flow shear stress under minimum pressure | ||||||||||

r | 0.376 | 0.313 | 0.302 | 0.119 | -0.151 | 0.378 | 0.459 | 0.436 | 0.124 | 0.368 |

p | 0.000 | 0.000 | 0.000 | 0.113 | 0.042 | 0.000 | 0.000 | 0.000 | 0.063 | 0.000 |

Correlation between vessel thickness and plaque wall stress under minimum pressure | ||||||||||

r | 0.007 | -0.630 | -0.712 | -0.655 | -0.487 | -0.648 | -0.811 | -0.680 | -0.379 | -0.372 |

p | 0.932 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

Corresponding to minimum pressure condition (this is also when minimum curvature occurs), 7 out of the 10 patients showed positive correlation between plaque wall thickness and flow shear stress, 1 showed negative correlation, 2 showed no significance. The mean Pearson correlation r-value was 0.272 ± 0.189. For plaque wall stress, 9 out of the 10 patients showed negative correlation between wall thickness and plaque wall stress, about the same as the maximum pressure case. The mean Pearson correlation r-value was -0.537 ± 0.238.

### Effect of cyclic bending on plaque wall stress and strain behaviors

### Effects of cyclic bending on flow behaviors

## Discussion

Our results show that IVUS data could be used to construct computational models to calculate flow shear stress and plaque stress/strain conditions which may be used to identify possible mechanisms governing plaque progression and rupture. This adds mechanical stress conditions into the list of risk factors and represents a new direction of research. While many factors are involved in plaque progression and rupture process, it is natural to think that final plaque rupture happens when critical plaque stress/strain exceed the plaque cap ultimate material strength. IVUS-based computational models can provide accurate stress/strain calculations and can serve as a useful tool for physicians in their diagnosis and intervention surgical decision making process.

It should be made clear that our current data is wall thickness, which is not progression by itself. We are currently working on patient follow-up data and will report our findings when available. Plaque progression and rupture are closely related to each other. A better understanding of plaque progression may lead to better understanding of plaque rupture process and more accurate plaque assessment schemes.

Some limitations of this study include: a) patient-specific and tissue-specific material properties were not available for our study; b) while the angiographic movie provided information for the position of the myocardium and partial information for curvature variations, two movies with different (preferably orthogonal) view angles are needed to re-construct the 3D motion of the coronary and provide accurate curvature variation information; c) some data such as zero-stress conditions (opening angle), multi-layer vessel morphology and material properties are not possible to measure non-invasively in vivo; d) tethering and interaction between the heart and vessel could not be included because those measurements are not currently available. A model coupling heart motion and coronary bending would be desirable when required data become available.

## Conclusion

Image-based computational models with cyclic bending and fluid-structure interactions could be used to provide more accurate flow and mechanical stress/strain calculations which may be useful for plaque assessment and identification of mechanisms governing plaque progression and rupture. Our results indicated that plaque wall thickness had positive correlation with flow shear stress and negative correlation with plaque wall stress. More patient follow-up data are needed to continue our investigations.

## Authors’ information

Tang’s group has been publishing image-based modeling work in recent years. For more information, please visit Tang’s website: http://users.wpi.edu/~dtang/.

The Washington University group (Jie Zheng and Richard Bach) has been publishing in medical imaging for vulnerable plaques extensively, see website:

http://www.mir.wustl.edu/research/physician2.asp?PhysNum=78, and

http://wuphysicians.wustl.edu/physician2.aspx?PhysNum=2687

Ma and Zhu are clinicians and have been doing research in interventional medicine for coronary diseases: http://www.njzdyy.com/s/21/t/2/00/d2/info210.htm;

The Columbia group (Cardiovascular Research Foundation, Mintz and Maehara) has been playing a leading role in the cardiovascular research. Web: http://www.crf.org/

## Declarations

### Acknowledgement

This research was supported by US NIH/NIBIB R01 EB004759. Yang's research was supported in part by National Sciences Foundation of China 11171030.

## Authors’ Affiliations

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