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

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 wer...

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