Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery

Summary

In vivo cine intravascular ultrasound images show the coronary cross-sectional movement corresponding to different pressure loading conditions. Based on a finite element model, an iterative scheme was employed to determine the patient-specific mechanical properties of coronary arteries in vivo by matching coronary motion from the computational model and medical images.

Abstract

Quantifying the mechanical properties of coronary arterial walls could provide meaningful information for the diagnosis, management, and treatment of coronary artery diseases. Since patient-specific coronary samples are not available for patients requiring continuous monitoring, direct experimental testing of vessel material properties becomes impossible. Current coronary models typically use material parameters from available literature, leading to significant mechanical stress/strain calculation errors. Here, we would introduce a finite element model-based updating approach (FEMBUA) to quantify patient-specific in vivo material properties of coronary arteries based on medical images. In vivo cine intravascular ultrasound (IVUS) and virtual histology (VH)-IVUS images of coronary arteries were acquired from a patient with coronary artery disease. Cine IVUS images showing the vascular movement over one cardiac cycle were segmented, and two IVUS frames with maximum and minimum lumen circumferences were selected to represent the coronary geometry under systolic and diastolic pressure conditions, respectively. VH-IVUS image was also segmented to obtain the vessel contours, and a layer thickness of 0.05 cm was added to the VH-IVUS contours to reconstruct the coronary geometry. A computational finite element model was created with an anisotropic Mooney-Rivlin material model used to describe the vessel's mechanical properties and pulsatile blood pressure conditions prescribed to the coronary luminal surface to make it contract and expand. Then, an iterative updating approach was employed to determine the material parameters of the anisotropic Mooney-Rivlin model by matching minimum and maximum lumen circumferences from the computational finite element model with those from cine IVUS images. This image-based finite element model-based updating approach could be successfully extended to determine the material properties of arterial walls in various vascular beds and holds the potential for risk assessment of cardiovascular diseases.

Introduction

Coronary artery disease (CAD) is one of the leading causes of mortality and morbidity, accounting for more than 9.14 million deaths in 2019 globally^1,2. The development of coronary artery diseases, such as atherosclerosis and stenosis, is often accompanied by alterations in mechanical forces and changes in vascular wall material properties³. The material properties of coronary arteries are not only the cornerstone to determine their mechanical response to the physiological loading but also the key elements to simulate the mechanical behavior of blood vessels, predict the development of atherosclerotic lesions, and evaluate the therapeutic effect of various medical devices^4,5. Consequently, a profound understanding and accurate quantification of coronary material properties hold paramount value for early disease diagnosis, precision medicine, and prognosis assessment⁶.

Mechanical experiments of isolated coronary tissues, such as planar biaxial testing, indentation testing, inflation-extension, and uniaxial extension testing, are common approaches to quantify the mechanical properties of coronary vessel walls ex vivo^7,8,9. From these approaches, coronary artery samples were obtained from patients or experimental animals. Mechanical testing was carried out to determine the strain responses of the vessel wall under different stress conditions, and then the material parameters were determined by fitting the experimental data¹⁰. Prior studies have shown that coronary properties are highly nonlinear and anisotropic¹¹. Although ex vivo experiments can provide accurate material properties data, significant limitations also exist, which are as follows: First, the mechanical behavior of the sample after taking out from the living subjects would be different from that under in vivo conditions, which may affect the accuracy of testing results. Second, due to ethical and practical constraints, it is difficult to obtain a large collection of normal or pathological tissues of coronary arteries to perform the mechanical testing.

To overcome these limitations, researchers have explored novel techniques for in vivo, real-time, and patient-specific quantification of coronary material properties. Among them, the finite element model based updating approach (FEMBUA) based on medical image holds the promise to address these challenging issues. This approach makes use of advanced imaging techniques like intravascular ultrasound (IVUS) and virtual histology (VH)-IVUS to capture detailed coronary geometry, tissue compositions, and its movement¹². By constructing 3D finite element (FE) models and incorporating patient-specific physiological blood pressure conditions, dynamic vascular behavior during cardiac cycles could be recovered by optimizing material parameters to match image data for rapid and accurate quantification of coronary material properties¹³. The advantages of the in vivo FE updating approach over ex vivo experiments include in vivo assessment without tissue excision, facilitating large-scale evaluations, and simulating vascular dynamics under complex conditions to aid the pathophysiology understanding of coronary diseases.

In this paper, key steps of the finite element model-based updating approach are introduced, which include a detailed segmentation and processing of cine IVUS and VH-IVUS image, reconstruction of computational thin-layer structure-only model, execution of the iterative scheme to search optimal material parameters for coronary arterial tissues. The aim of this protocol is to quantify the material properties of the coronary artery from a sample patient with CAD using the FEMBUA method as a demonstration, especially the illustration of step-by-step methods. We concluded by discussing the significance and other aspects of this in vivo method.

The selected participant is a 64-year-old female with no previous clinical history of coronary artery disease. This patient was diagnosed with coronary artery disease after having symptoms of chest pain. The coronary angiogram and IVUS scan were performed to confirm the diagnosis. A plaque lesion with 60% stenosis was found in the middle of the left anterior descending artery. After assessment, optimal medical therapy was adopted to treat the patient.

Protocol

De-identified clinical data, including in vivo IVUS images and blood pressure data, were acquired from a patient with CAD at Zhongda Hospital, Southeast University, with informed consent obtained. The sample patient was selected from the patient pool of a clinical study on intermediate coronary atherosclerotic lesions to demonstrate the method for quantifying the material properties of patient-specific coronary vessels¹⁴. The study was conducted following the protocol approved by the Clinical Research Ethics Committee of Zhongda Hospital, Southeast University (approval number: 2017ZDSYLL023-p01).

1. Data acquisition and processing

1. Cine IVUS and VH-IVUS image acquisition
   1. Place the IVUS catheter distal to the atherosclerotic lesion with the guidance of a coronary angiogram and pull it back to the proximal side. Generate grayscale IVUS images along the way to visualize the cross-section of the coronary vessel.
   2. Use the IVUS imaging system equipped with a high-performance 20 MHz, 2.9F platinum catheter to acquire IVUS images of the coronary arterial segment with atherosclerotic plaque from the patient with CAD (Figure 1).
   3. During the IVUS image acquisition, pause the catheter at the pre-selected lesion site for approximately 2 s to obtain a sequence of IVUS images called cine IVUS. The cine IVUS images clearly showed the dynamic cross-sectional changes at the given plaque site over the cardiac cycle.
   4. Generate VH-IVUS images based on IVUS frames acquired at the instant of R peak on electrocardiograms to visualize plaque components in color-coded form using the imaging system.
      NOTE: VH-IVUS images provide an intuitive color map for four key plaque components in the atherosclerotic plaque: lipid-rich necrotic core (lipid) in red, calcification in white, fibrous tissue in dark green, and fibrous adipose tissue in light green.
   5. Save VH-IVUS and cine IVUS images in DICOM format for offline analysis.
2. Image segmentation and processing
   1. Open DICOM files using the viewer, double-click the Corresponding Sequence Name to open the image and click Export > Export Images to save each cine IVUS frame or VH-IVUS frame as an individual image in BMP format. Each BMP image contains 500 x 500 pixels, as indicated by the original DICOM file.
   2. Examine the cine IVUS image frame by frame to find the consecutive frames obtained at the pre-selected plaque site during one cardiac cycle. There were 26 cine IVUS frames generated during one cardiac cycle for this sample plaque site.
   3. Examine all the generated VH-IVUS images to find the VH-IVUS image obtained at the given plaque site. The VH-IVUS images used here were created using one IVUS frame from the cine IVUS frames in one cardiac cycle.
   4. Segment VH-IVUS and cine IVUS images using ImageJ software to obtain the contours of vessel boundaries and plaque component boundaries (See Figure 1C).
      1. Select Straight > Segmented Line tab and manually delineate the contours of the lumen, outer boundary of the coronary vessel, and plaque components on cine IVUS and VH-IVUS images. For the cine IVUS image, only segment the contours of the lumen and outer vessel boundary, while for the VH-IVUS image, segment the contours of the lumen, outer vessel boundary, and plaque component boundaries.
      2. For simplicity, keep only large lipid components for generating a finite element model and ignore small, isolated lipid components. Only one lipid was present in this plaque sample. Overlay the delineated contours onto the original images using Image > Overlay > Add Selection tab.
      3. Navigate to the To ROI Manager menu to manage contours, adjust properties, and set colors and line width to proper values for better visualization. Select the Properties tab, set the stroke color to a different color, and fill in the line width at width. Here, set the line colors as green, blue, and red for lumen, outer-boundary, and lipid contours, respectively, and the line width as 3.
      4. Smooth contours using Edit > Selection > Fit Spline from the command bar after selecting a specific contour to get a smooth contour. This operation utilizes spline curve fitting techniques to automatically smooth the contours.
      5. Click File > Save As > XY Coordinates tab to save point coordinates of each contour like lumen, outer-boundary, and plaque component in a separate txt file. This file contains the x and y coordinate values of the points constituting the contour, with pixels as the unit.
   5. Record the real physical size of each pixel in cine IVUS and VH-IVUS images (denoted as pixel size) from the DICOM file. The real distance for one pixel in the IVUS data used here is 0.002 cm. This information would be used to convert the point coordinates with the pixel as the unit to real distance with cm as the unit.
3. Contour data processing
   1. Cine IVUS contour data processing
      1. Read txt files of lumen contours from all cine IVUS images in one cardiac cycle with MATLAB.
      2. Multiply all lumen contours by pixel size to get the actual size of the lumen contours.
      3. Calculate lumen circumferences for all lumen contours and identify the IVUS frames with maximum (Cmax) and minimum (Cmin) lumen circumferences, representing diastolic and systolic conditions, respectively.
   2. VH-IVUS contour data processing
      1. Read txt files of the contours of the lumen, outer-boundary, and plaque components from the VH-IVUS image with MATLAB.
      2. Multiply all contours by pixel size to get the actual size of all contours.
      3. Re-divide each contour into 100 equally spaced points and perform 2D smoothing to get new VH-IVUS contour data to replace the old ones.

2. Finite element model

1. Coronary vessel geometry reconstruction
   1. Create one layer of contours in three-dimensional space by adding z coordinate value for all points of VH-IVUS contours, including lumen, outer-boundary, and lipid, and set z = 0 for all points (Figure 2).
   2. Create another layer of contours by adding z coordinate value for all points of VH-IVUS contours and reset z = 0.05 cm for all points.
      NOTE: These two layers of contours reconstruct the 3D coronary vessel geometry for the thin-layer structure-only model by adding a fixed 0.05 cm layer thickness to VH-IVUS contours (Figure 2).
2. Finite element mesh generation
   1. Create two auxiliary contours by linearly interpolating lumen and outer-boundary contours with weights 1/3 and 2/3 (Figure 3A) for each layer.
   2. Divide vessel area into 8 circumferential parts and 3 radial parts (see Figure 3B) by connecting the lumen/outer boundary to the closest point on the lipid contour (e.g., points A and B in Figure 3B) or two auxiliary contours with radial lines.
   3. Connect all points between layers with straight lines, forming a 3D structure with 3 x 8 volumes (Figure 3B). Divide each volume using hexahedral elements to generate the finite element mesh (Figure 3C) and different material groups (Figure 3D).
   4. Perform a mesh analysis by refining mesh density by 10% until changes in solutions < 5%.
3. Material property definition
   1. Use a modified anisotropic Mooney-Rivlin material model to describe the material properties of the coronary vessel wall. Coronary vessels and plaque components were assumed to be hyperelastic, anisotropic, nearly incompressible, and homogeneous materials, and the strain energy density function of the modified anisotropic Mooney-Rivlin material model is:
           (1)
         (2)
          (3)
      where I₁ and I₂ are the first and second invariants of the right Cauchy-Green deformation tensor C defined as c = [c_ij] = X^TX, X = [X_ij] = [], (X_i) was the current position (a_j) was the original position, I₄ = c_ij(n_c)_i(n_c)_j, n_c was the unit vector in the circumferential direction of the vessel. c₁, c₂, D₁, D₂, K₁ and K₂ were patient-specific material parameters.
   2. Assign the initial values of material parameters for a patient-specific coronary vessel according to the ex vivo biaxial testing results, that is, c₁ = −1,312.9 kPa, c₂ = 114.7 kPa, D₁ = 629.7 kPa, D₂ = 2.0, K₁ = 35.9 kPa and K₂ = 23.5 (Figure 4A-B)^13,15.
   3. Assign the material parameters for the plaque component if present. More specifically, for lipids, c₁=0.5 kPa, c₂=0, D₁=0.5 kPa, and D2=1.5; for calcification, we used c1=920 kPa, c2=0, D1=360 kPa, and D₂=2.0 (Figure 4B)¹⁶.
      NOTE: Plaque components (lipid and calcification) were assumed to be hyperelastic, isotropic, and nearly incompressible, and their mechanical properties were described by isotropic Mooney-Rivlin material model with the strain energy density functions given in formula (2).
4. Governing equations and boundary conditions setting
   1. Define governing equations for the thin-layer structure-only model, which includes motion equation, nonlinear Cauchy-Green strain-displacement relation, and coronary vessel material model¹¹.
   2. Prescribe patient-specific blood pressure waveforms on the lumen surface to simulate real physiological conditions (Figure 4C). To obtain patient-specific blood pressure waveforms, scale a typical aortic pressure waveform with systolic and diastolic pressure values measured by arm cuff (Figure 4D).

3. Finite element model-based updating approach for patient-specific coronary artery material properties

NOTE: The iterative process to determine patient-specific coronary material properties is illustrated in Figure 5.

1. Determine the no-load geometry corresponding to the zero-pressure condition as the initial geometry for the computational model by shrinking the coronary geometry reconstructed from the VH-IVUS image axially with a fixed shrinkage rate of 95% and circumferentially with circumferential shrinkage (denoted as S) initially set as 98%.
   NOTE: Since the coronary geometry reconstructed from the VH-IVUS image was under in vivo conditions with blood pressure prescribed on the lumen and axial stretch from tethered distal and proximal coronary arterial segments, the in vivo coronary geometry should shrink circumferentially and axially to obtain the zero-pressure geometry.
2. Fix the axial shrinkage rate at 95% and update the circumferential shrinkage during the following steps.
3. Define the material ratio (denoted as k) to assign the patient-specific material properties of the coronary vessel as: that is, c₁ = k*(−1,312.9) kPa, c₂ = k*114.7 kPa, D₁ = k*629.7 kPa, K₁ = k*35.9 kPa, and fix D₂ = 2.0 and K₂ = 23.5.
   NOTE: Since only two data points (minimum and maximum lumen circumferences corresponding to diastolic and systolic pressures) were obtained to determine the unknown parameters (circumferential shrinkage rate S and material parameters of Mooney-Rivlin model), we reduced the number of unknown parameters by assuming that the in vivo patient-specific material properties of coronary vessel were proportional to the initial guess with material ratio denoted as k: that is, c₁ = k*(−1,312.9) kPa, c₂ = k*114.7 kPa, D₁ = k*629.7 kPa, K₁ = k*35.9 kPa, while D₂ = 2.0 and K₂ = 23.5 were fixed.
4. Update the k value set to an initial value k of 1 along with circumferential shrinkage rate S during the following iterative procedure.
5. Run software to solve the computational model to obtain the numerical results.
   1. Write all commands for creating the thin-layer structure-only model into a batch file (Supplementary File 1) using MATLAB.
   2. Load this batch file using the advanced user interface (AUI) to generate the model (Figure 6A). Solve the thin-layer structure-only model by clicking Data File/Solution and save it as a .dat file (Figure 6C). Simulate three cardiac cycles and adopt the solution in the last cycle to present numerical results.
   3. Export results of node coordinates to a txt file by navigating List > Value List > Zone and selecting X-POSITION, Y-POSITION, and Z-POSITION in Variables to List under Coordinate. Click Apply and Export to export the coordinate results.
   4. Save lumen contour data corresponding to diastolic and systolic pressure conditions to .txt files for lumen circumference calculations.
6. Compare lumen circumferences calculated by the FE model (thin-slice layer structure-only model) at diastolic pressure condition with in vivo cine IVUS data (Cmin) and check if the relative error was <1%. If the condition was met, then go to the next step, or otherwise update the material ratio k using the secant method and go to step 3.3 to re-run again^17,18.
   NOTE: In the first iterative, the Newton method was used to update the material ratio instead of the secant method.
7. Compare lumen circumferences calculated by the FE model at systolic pressure condition with in vivo cine IVUS data (Cmax) and check if the relative error was <1%. If yes, then stop the iterative procedure, or otherwise update the circumferential shrinkage rate S and redirect to step 3.4 to re-run again.
   NOTE: In the first iterative, the Newton method was used to update the circumferential shrinkage rate instead of the secant method.
8. Record optimal S and k values and calculate the corresponding material parameters of the Mooney-Rivlin material model.
9. Plot the circumferential and axial stress-stretch ratio curves of the coronary vessel (Figure 7), which can be derived as follows:
       (4)
   where σ represents Cauchy stress, λ represents stretch ratio, i = c, a represents the circumferential and axial directions.
   1. To draw a material curve in a particular direction, fix the stretch ratio in the other direction to 1. Calculate effective Young's modulus in the circumferential and axial (labeled YMc and YMa, respectively) as the slope of the scale function of the material curve at the stretch ratio interval [1.0, 1.1] to reflect the general material stiffness of the coronary artery¹³:
          (5)
10. Extract plaque stress/strain distributions at any time and record node distribution and maximum stress values during systolic and diastolic phases (Figure 8).

Results

We describe in detail the FEMBUA method, which enables rapid plaque material and stress analysis of coronary plaques after real-time IVUS imaging and can determine the in vivo material properties and biomechanical results of plaques. The in vivo material parameters of the Mooney-Rivlin material model for this coronary vessel are provided in Table 1. The simulation results of the finite element model, including the stress/strain distributions in the coronary vessel, are plotted in Figure 8. A detailed analysis of the results is as follows.

It takes about 2 h to finish the entire process and to obtain in vivo material parameters for this coronary vessel, including cine IVUS and VH-IVUS image segmentation, construction of the computational FE model, and execution of the iterative procedure to quantify the material properties. This method can meet the requirements of rapid clinical examination with high timeliness.

For this coronary vessel, the two quantities were determined following the FEMBUA method as k = 1.125 and S = 98%. Other in vivo material parameters of the Mooney-Rivlin material model for this coronary vessel are provided in Table 1. Its material curves in both circumferential and axial directions are plotted in Figure 7. Both directions exhibited a J-shape material curve, indicating the nonlinear stress-stretch relationship with increased tissue stiffness when the stretch ratio was elevated. The straight lines were the scale functions to fit these nonlinear material curves, and their slopes were the effective Young's moduli. The YMc and YMa for this coronary vessel are 1055.41 and 1835.77 kPa, respectively.

The simulation results of the finite element model, including the stress/strain distributions in the coronary vessel, are plotted in Figure 8. The stress distribution corresponding to systolic pressure conditions is higher than that of diastolic pressure conditions. Also, local stress concentration could be observed in regions with thin vessel thickness or fibrous cap regions. Given that plaque rupture often occurs at the fibrous cap and the shoulder regions, the peak stress and strain values over these critical regions are reported in Table 2.

We performed the mesh analysis by gradually increasing the mesh density, and the mesh refinement would stop if a finer mesh could yield insignificant changes in solutions. The element/grid distribution and stress results for this model are shown in Supplementary Table 1. The table gives more comparative and detailed results, showing insignificant differences between models with different element numbers. The results show that, after refining the mesh density four times, the relative errors of maximum and minimum stress are within 5%. Since the FEMBUA method involves an iterative process, a relatively low mesh density was adopted to save computational costs. According to the results, it can be seen that the current mesh quantity (element number = 900) meets the requirements and has little influence on the stress results.

Figure 1: Acquisition and contour extraction of Cine IVUS and VH-IVUS. (A) IVUS catheter withdrawal direction and catheter paused site (marked with a star) to obtain Cine IVUS images. (B) Cine IVUS with lumen circumferences of Cmin and Cmax and corresponding VH-IVUS image. (C) IVUS contours extraction. Please click here to view a larger version of this figure.

Figure 2: Reconstructed 3D coronary vessel geometry with a 0.05 cm thickness. Please click here to view a larger version of this figure.

Figure 3: Finite element mesh generation process for thin-slice structure-only model. (A) Contour points on 2D plane. (B) Geometric lines for mesh generation. (C) Finite element mesh. (D) Generated different material groups. Please click here to view a larger version of this figure.

Figure 4: Computational thin-slice structure-only model of the coronary vessel. The model includes material property definition and boundary condition setting. (A) Set different material groups within the coronary artery. (B) Ex vivo coronary vessel materials curve. (C) Boundary condition loading. (D) Pressure curve. Please click here to view a larger version of this figure.

Figure 5: Iterative scheme. The iterative scheme to quantify in vivo plaque material properties of coronary vessels based on IVUS images. Please click here to view a larger version of this figure.

Figure 6: Use interface. The advanced user interface of ADINA software and relevant operations. Please click here to view a larger version of this figure.

Figure 7: Material curves. The material curves in circumferential and axial directions of the coronary vessel and their effective Young's moduli estimation. Please click here to view a larger version of this figure.

Figure 8: Thin-slice structure-only model of the coronary vessel geometry and simulated results. The figure includes stress distribution cloud map at diastolic and systolic pressure conditions. (A) Nodes Displayed. (B) Diastolic Stress. (C) Systolic Stress. The color bar indicates stress value. Please click here to view a larger version of this figure.

Material parameters	S(%)	C1(kPa)	C2(kPa)	D1(kPa)	K1(kPa)	YMa(kPa)	YMc(kPa)
	98%	-147.76	12.91	708.67	40.4	1055.41	1835.77

Table 1: Reference values for material parameters of the sample model.

Time at Diastolic Pressure		Time at Systolic Pressure
PWS (kPa)	PWSn	PWS (kPa)	PWSn
56.53	0.05402	64.51	0.05402

Table 2: Peak stress/strain values over the critical regions from the computational model. Abbreviations: Peak wall stress = PWS; Peak wall strain = PWSn. Stress unit: kPa.

Supplementary Table 1: The comparison stress results of different grid quantities in the same model.> Please click here to download this File.

Supplementary File 1: MATLAB codes. Please click here to download this File.

Discussion

Critical steps in the protocol
The most critical step in the finite element model-based updating approach lies in the iterative procedure. In the approach, the finite element model should accurately recover the coronary vessel motion on the vascular cross-section from in vivo cine IVUS images. To this purpose, minimizing the lumen circumference difference between the finite element model and in vivo images was adopted in this study to find the proper material properties. There were other key steps in the protocols, including image segmentation and processing, finite element model construction, and iterative schemes to quantify coronary vessel material properties. An improvement was to implement the automatic delineation of coronary plaque components to save time.

Significance of finite element modeling-based updating approach
Classically, mechanical experiments such as uniaxial/biaxial tensile testing, indentation testing, and pressure inflation testing were conducted to quantify the mechanical behavior of the cardiovascular tissues ex vivo^8,16. The clinical application of these approaches was limited due to the following reasons: 1) Ex vivo coronary arterial tissue samples are often not available. It is almost impossible to harvest the normal coronary samples in the clinical setting; 2) Material properties of arterial tissues might alter when taken out of living subjects; 3) it is not suitable for continuous monitoring in a patient-specific setting for personal management and precision medicine. Fortunately, FEMBUA provides another way to determine patient-specific tissue properties in vivo. The in vivo method could be easily modified to successfully apply to other biological tissues, such as aortic tissues¹⁹ and cardiac tissue²⁰, and even non-biological materials like metal²¹. Prior studies have demonstrated that patient-specific in vivo tissue material properties had a significant influence on cardiovascular biomechanics, especially in strain calculation, compared to ex vivo material properties¹¹. Therefore, patient-specific in vivo material properties are desirable for personalized treatment.

Even though in vivo and ex vivo methods are different, they could be integrated to inspire other approaches to quantify the mechanical properties of cardiovascular tissues. A hybrid approach that combines FEMBUA to match stress-strain data from biaxial/uniaxial experiments has been proposed for the aortic aneurysmal tissue²².

Potential clinical applications of Finite Element Modeling Based Updating Approach
FEMBUA based on IVUS image is of great importance in cardiovascular materials science, medical image analysis, and personalized medical device design. This proposed method does not need to cause dramatic damage to the investigated coronary vessel wall as in a situation like taking the tissue out of the living human body, so it is suitable for continuous patient monitoring, such as investigating the effect of in vivo mechanical properties on patient prognosis, which cannot be done by a classical mechanical experimental approach. In addition, the proposed FEMBUA method plays a key role in the treatment optimization of coronary stents and the diagnosis of cardiovascular diseases. Finely analyzing the structure and lesion characteristics of blood vessel walls could guide the selection of stent size and location, thus maintaining the structural and mechanical stability within tissues to a higher degree, reducing complications, and improving patient prognosis²³. In summary, the FEMBUA method has extensive and far-reaching application potential in the cardiovascular field.

Comparison of results from FEMBUA and ex vivo experimental approaches
Comparison analysis between FEMBUA and classical ex vivo experimental approaches has been conducted to assess the accuracy and efficacy of the novel in vivo approach. For simplification, coronary tissue stiffness from the mechanical approach was compared to those from in vivo studies using FEMBUA, and tissue stiffness from both methods was generally in the same magnitude range¹¹. The consistency was also confirmed in other vascular beds like aorta and carotid artery²⁴. Of note that the limited number of ex vivo studies could influence the conclusions abovementioned, since the tissue stiffness variability across different individuals is also pronounced. Nevertheless, these conclusions suggested that FEMBUA is an accurate and effective approach to quantifying the material properties of arterial walls.

Validation and robustness of FEMBUA method were also investigated by performing both the in vivo FEMBUA method and ex vivo experiment on the same arterial tissue for validation purposes^25,26,27. Liu et al. conducted in vivo and ex vivo experimental approaches on aortic tissues. Their findings revealed a close correlation between the material behavior curves generated by both methods, with an average mean absolute percentage error smaller than 5%²⁵. Further, Cosentino et al. performed a similar comparative analysis based on a larger sample cohort (n=10), with similar conclusions obtained²⁷. These findings collectively showed that FEMBUA could yield minimal discrepancies in biomechanical outcomes for identical samples. A further study also showed that the proposed method is reproducible and robust, as the study demonstrated that variations in mechanical properties had minimal impact on the simulated biomechanical outcomes in coronary artery models through finite element analysis²⁷.

Modeling assumptions and limitations
There are some assumptions involved in FEM for in vivo identification of the material properties of coronary arterial walls, which would impact the results from FEMBUA as described here. The axial shrinkage rate was assumed to be 95% since the actual axial shrinkage could not be obtained under in vivo conditions. The impact of axial stretch on material properties was investigated in prior studies, and the results indicated that smaller axial stretch led to greater slice shrinkage and softer material stiffness estimation^11,28,29,30. Therefore, patient-specific axial stretch data should be used when available. The quality evaluation of finite element mesh involves several key indicators, among which the shape of the mesh element is the main evaluation criterion in this paper, which is directly related to the stability of the numerical solution and iterative convergence. In practical applications, due to the complexity of the problem, it is necessary to weigh the indicators to meet the analysis needs, and if necessary, the mesh quality can be optimized by designing new segmentation methods and selecting suitable mesh types³¹. Special attention should be paid to small lipids at key sites during actual segmentation^32,33,34. In this implementation, small lipids in key sites (fibrous cap and shoulder) are retained, while lipids in other sites which have little influence on the stress/strain conditions. Blood pressure measured by arm cuff was used as a surrogate for on-site intracoronary pressure since invasive intracoronary pressure was not available for the patient. Active stress in the coronary artery was not considered since early evidence suggested that its contribution to the elastic properties of the living blood vessel was very small³⁵. Residual stress information was not available and thus was not included in this model^36,37. Structure-only models rather than more complex fluid-structure interaction models were used in the FEMBUA method, given it is more computationally efficient as iterative procedures typically need to solve the computational models several times to find the material properties constant.

In summary, image-based FEMBUA, different from other classical ex vivo experimental approaches, could be used to effectively determine the patient-specific material properties of coronary vessels in vivo. Since arterial tissue stiffness has already been employed in clinical settings as a risk factor for cardiovascular diseases, FEMBUA makes it possible to continuously monitor the coronary arterial mechanical properties under in vivo conditions and thus holds the potential in clinical applications for personalized treatment and precision medicine.

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Bee DICOM Viewer	SinoUnion Healthcare Inc.	Version 3.5.1	A DICOM image reader software
ADINA	Adina R & D	Version 9.0	Finite element solver
ImageJ	National Institutes of Health		Segmented IVUS contours
MATLAB	MathWorks	Version R2018a	Commercial programming platform
Volcano s5 imaging system	Volcano Company		Intravascular ultrasound imaging system