Model Assumptions and Limitations
The main purpose of this paper is to communicate our views and preliminary evidence that the “local maximal stress hypothesis” should be used to replace the “maximal stress hypothesis” so that research effort could lead to better results and findings. The CPVI results were from 2D models based on 34 2D MRI slices from 14 patients while the corresponding histopathological data (HPVI) were used as the benchmark to quantify CPVI grades. Our findings will be further improved when more 3D data and results become available. When using 3D MRI data and 3D models, HPVI will be determined for each slice and the highest HPVI value from all the slices will be picked as the HPVI grade for the plaque under consideration. The 3D stress/strain solutions will be searched numerically to identify local maxima and their locations. Those sites will be examined and critical sites and the associated stress/strain values will be selected to be used for statistical analysis and CPVI assignment. We are currently accumulating more 3D plaque samples and results will be reported in a future paper.
Another limitation of the current investigation is that it is based on ex vivo MRI images. The plaques are no longer under in vivo conditions and there are normally considerable differences between their ex vivo and in vivo morphologies. As much as it is desired, in vivo 3D MRI data is not currently available. However, our preliminary results indicate that critical sites are related to local morphologies which are less affected by the differences between ex vivo and in vivo morphologies. The CSS process also helps to eliminate some artifacts caused by fixation procedures and deformation of plaque samples.
In a way, our current research can be viewed as a necessary preparation for future in vivo investigations. With all the above model limitations, our local maximal stress hypothesis and CSS method will remain applicable and will be used in our future investigations to improve the accuracy of our CPVI-based predictions.
CPVI Validation, Gold Standard, and Clinical Relevance
Histopathological analysis is currently regarded as the “gold standard” for validation of MRI tissue identification and is used in this paper as the gold standard for computational plaque assessment. HPVI is used as the benchmark to introduce and establish our stress-based CPVI. While postmortem histological sections do have deformations from their in vivo shape, their critical features such as cap thickness, lipid pool size can be determined, with the help of MRI images taken before sectioning. Long-term patient tracking data with the actual plaque progression and rupture rate can serve as a better in vivo “gold standard” for predictive research. However, collection of 3D in vivo data with detailed plaque component information and development of an in vivo plaque assessment scheme require better resolutions and long-term effort (5–10 years or longer). A gold standard for in vivo plaque assessment has yet to be established. Lack of an in vivo gold standard makes it difficult to assess plaques with ultimate confidence and accuracy. Our results provide initial evidence that computational plaque stress/strain analysis may lead to better quantitative predictions if it can be further validated by large-scale long-term patient studies.
Model Validation; Models Based on Histological, Ex Vivo and In Vivo Data
Computational model validations have been performed based on in vitro
experimental data in our previous studies and good agreement was found.33–36
It is well known that models based on histological sections are less accurate due to deformations from the fixation procedures.37
Our current models are based on ex vivo
MRI images and axial stretch (for 3D models) and pressurization (for 2D and 3D models) are added to recover the in vivo
shape of the plaque as much as computationally possible. For in vivo
image-based models, we actually need to shrink the plaque geometry to an estimated zero-stretch/zero pressure shape, then stretch and pressurize it to get the correct initial stress/strain distributions in the plaque. This step can affect the computational stress predictions by as much as 400–600%.38
Cardiac motion has considerable effect on stress/strain distributions in coronary arteries and will be added in our future models. Validation using in vivo
data is tied to the same resolution issues and is difficult at present time.
Selection of Indices and Multidimensional Nature of Rupture Risk Assessment
While the CS Stress-P1 values obtained by CSS method were used in this paper to quantify CPVI, it should be understood that the results are preliminary and are only from 2D models. All stress/strain components, together with their variations under pulsating pressure used in the simulation (, Pin = 90–150 mmHg) were examined. Stress/strain values at peak pressure (Pin = 150 mmHg), their variations between the maximum (150 mmHg) and minimum pressures (90 mmHg), shear stress/strain components were obtained by CSS method for statistical analysis. It was found from the 34 cases that CS Stress-P1 values have the best correlation with HPVI. Stress-P1 variations did not give better correlation, as we originally hoped to see.
We are searching for the right index or indices for plaque assessment. It is commonly believed that plaque rupture risk assessment should be multidimensional. Factors from plaque morphology, material strength, lumen surface erosion and inflammation, mechanical stress/strain conditions, blood pressure, cell activities, and chemical environment in the blood should all be taken into consideration. It must be noted that vulnerability is material dependent and the absolute value of stress compared to material strength is an important factor. Results from our 3D models, together with extensive statistical analysis, will give more complete and accurate mechanical analysis. Predictions from mechanical side can be compared with predictions from other channels for comparisons and mutual enhancement.
MRI Resolution Limitation and MRI Image-Based Modeling
For ex vivo 2D MRI images, we actually have 0.1 × 0.1 mm2 resolution for the first 18 cases, and 0.055 × 0.055 mm2 (FOV = 28 mm × 28 mm, Matrix = 512 × 512) for the last 16 cases (see ). Resolution limitation becomes a real problem mainly when in vivo 3D MRI data are used.
In computational models, contours (or surfaces if 3D method is used) for plaque components are generated based on segmentation data, with interpolations so that computational geometry can be generated. Once the computational geometry is generated, lumen area, lipid pool size, and cap thickness can be calculated numerically. While the actual image resolution does not change in this process, computational analyses are performed based on the computational geometries with high “numerical accuracies.” This is commonly done in MRI imaged-based research. Researchers who use MRI to conduct their research try their best to move forward with the limited resolution available, hoping future technology could bring better resolution (the “sit here and wait” strategy would not be helpful to our research). Because of that, computational predictions based on limited resolution can be regarded as “hypothetical” predictions, i.e., they are true if the original data can provide the resolution needed. There are other model assumptions (such as material properties and blood pressure conditions) which also make computational predictions hypothetical. As such, computational predictions are subject to further validations, and should be taken with precaution. One calming argument is that these limitations related to computational modeling can be viewed as “system errors.” When the same imaging technology and modeling procedure are applied to patients, all results come with the same system errors and comparative studies can still provide reliable predictions.
In summary, the 2D MRI data used in this paper have reasonable resolutions. However, 3D MRI-based models will have to carry that limitation in the near future while the MRI technology improves itself to deliver higher resolution.