Atherosclerosis is one of the leading causes of global death and morbidity, and it's multifactorial and complex nature makes a multidisciplinary approach to tackling it important. Now, imaging is a powerful tool to analyze black morphology but it can't yet give us an understanding of the underlying mechanisms of work. And this is where computational simulation comes in.
From a fluid dynamics point of view, we know that factors such as wall shear stress intobio blood flow can impact endothelial cell function and new transport processes involved in atherosclerosis formation. But to truly understand the patient's specific mechanics, fluid structure interaction techniques, or episodic short, can be used to simulate the interaction between blood flow, artery mechanics and general cardiac function. And this methodology presents an approach to do just this, by reconstructing and bio mechanically simulating a patient's coronary artery from optical coherence tomography, or OCT for short, and invasive angiography.
We then also discussed the clinical relevance results and the comparisons to follow up imaging. Now, the fundamentals behind the methodology are built on the finite element and finite volume methods. And while we demonstrate the simulation method here using the commercial software, ANSYS procedure can be adapted to any episodic capable software or codes.
Match baseline and follow up OCT images, using anatomical landmarks, such as bifurcations and using images starting immediately proximal to the most distal bifurcation and distal to the most proximal bifurcation. The images between these landmarks are to be analyzed Load the first image into the digitizer and mark the catheter center points and limits for the scale. Export these points to use later, mark the edge of the lumen, starting from the same location in every image and being sure to capture the curves of the lumen as accurately as possible.
Leave a gap over the artifacts as the reconstruction process will interpolate across these regions at a later stage. Export these files to a data format and repeat this for every image. In your dot-com software, extract the outer wall in high attenuation regions, by using visible parts of the outer elastic membrane to fit an ellipse, to estimate the outer wall location, Define the lipid arc, calculate it to the lumen centroid, and pluck cap thickness.
These will be used to analyze lesion progression along with lumen area. Then import these overlaid images into the image digitizer to select the outer wall points. Similarly for the lipids select, the lipid surface, starting from the same end of the lipid in every case, Load the first angiographic image in the image digitizer, select the edges of the catheter to scale the image in later steps.
And then mark the catheter central line beginning with the proximal marker and moving distally with evenly spaced points. Export the data to adapt format. Repeat these steps for every image before carrying out the cross section reconstruction process.
In a 3d modeling software import and generate the cross-sections, one file at a time, to create a solid component, select all the curves and lock them together, ensuring that add frozen is selected to generate a new solid. Now carry out these steps for the lumen, lipids and outer wall. To subtract the lumen and lipids from the artery wall, create a Boolean operation and choose the target body as the wall and the lipids and lumina as the tool body.
It's important to share typology between the wall and lipids to ensure that mesh nodes are shared in future steps. To do this, highlight the wall and their lipids, and right-click to create a part. To set the material properties for the artery and lipid enter engineering data and add a new material called artery Drag density and the five parameter Mooney Riverland model and set their parameters.
Repeat this for the lipid and to the motor component, suppress the lumen component and assign the previously defined materials to the artery and lipid solids. The geometry now needs to be meshed, set the physics preference to nonlinear mechanical and specify the mesh sizing. Here we have used adaptive meshing with the target size of 0.14 millimeters.
Adjust the mesh preferences as needed to obtain reasonable mask unit values. Here we aim for at least two to three mesh elements across gaps, such as the fibrous cap. Generating the mesh may take some time due to the complex geometry.
For FSI simulations, turn automatic time stepping off, and define a sub step as one and set the simulation end time. In this case 0.8 seconds, system coupling we control the time and sub steps, set the solver type to program control to use either the direct or iterative method. Direct methods are more robust, but use a significant amount more memory.
Set the Newton refs and method to full. Specify the system coupling domain as the inner wall of the artery by inserting a fluid solid interface. This will pass data between the structure and fluid at this location.
The displacement boundary conditions can be entered as a displacement function in the X, Y and Z direction, applied at the inlet and outlets. To assist in troubleshooting errors under the solution tab insert for Newton rafts residuals. These can be viewed if errors arise to find the troublesome geometry or mesh locations.
Enter the model tab, check the units and suppress the artery and lipid part. Leading the fluid domain. Specify the mesh metrics and generate the mesh, checking skewness and adjusting if necessary.
It is good practice to use a similar size mesh and shape as we did in the structural part on the regions where the fluid solid interaction is occurring. Create name selections for the inlet, outlet and wall, to be passed into fluent. Now enter the setup tab and ensure that double position is enabled.
Set the solver type to pressure based and ensure that time is set to transient. Enable the K-Omega viscous turbulence model and enable sheer stress transport and low-re corrections. To enable nonlinear viscosity models with turbulence.
Enter the following command into the command console and enter yes when prompted. Under material, now define the blood properties, by entering density and selecting the non-Newtonian power law from the viscosity dropdown list. Compile, I use a defined function, containing the transient blood velocity and pressure checking the command line for any errors.
Now load the UVF. These can be applied to the inlet and outlet. Enable the dynamic mesh, including smoothing, re meshing, and the six degrees of freedom solver, setting the diffusion parameter 1.5 and the appropriate maximum and minimum scales for your mesh.
Create a new dynamic mesh zone, specify the wall of the lumen and select system coupling. This is the interface to pass data to the artery component of the simulation. Create the forming mesh zones for the inlet, outlet and interior lumen with appropriate values for the mesh scale.
Often negative cell volume errors are associated with this dynamic mesh. So check carefully and adjust the mesh scales if needed, for each region, ensure the pressure velocity coupling is set to couple and set the transient formulation and spatial discretization schemes to second order. In controls enter a current number of two and set the residual convergence criteria in the monitors tab.
Here, we've used the value of 1 here to the 5 five for continuity and one eight of the minus six for the remainder. To define a custom function for results such as local normalized helicity, select custom functions, under the parameters and customization tab, and insert a new function. Use the pop-up window to define as necessary.
In the run calculation tab, set the number of times steps to 160 with a time step size of five milliseconds and a number of iterations to 300. Check that the data sampling for time statistics is enabled and ensure that wall statistics and flow shear stresses are selected as well as our previously defined custom function. Create a data export in calculation activities, selecting the CFD post compatible option for post-processing.
If you wish to process results in a separate software, adjust the export type as necessary. Select all the regions and the results that you wish to export. Finally, initialize the simulation with the hybrid scheme.
Make sure both the structural influence setups are connected to system coupling and updated. In system coupling, set the end time to 0.8 seconds and the timestamp to 5 milliseconds, generally between 10 and 15 iterations as sufficient provided the both the structural and the fluid components are converging well. Select the wall and solid interface from the fluid and structural components, respectively and edit out a transfer, Adjust the under relaxation or ramping of the force being transferred from fluid to structure to assist in convergence.
When ready to run, click update, simulation data such as structural and fluid convergence and their respective data transfer convergence is printed in the console. Note that FSI simulations are computationally expensive, with this simulation taking roughly 11 days on a 16 core machine. Here we have focused on three important biomechanical results, namely wall shear stresses, intraluminal flow characteristics through the local normalized helicity, and structural stress in the form of the Von Mises effective stress.
Sheer stress is greatly driven by blood velocity. As we can see here, however, more detailed analysis of the time average sheer stress, the a solitary shear index, which is a measure of flow reversal and underlying sheer stress vector fields, could be more clinically informative, particularly by looking for attraction regions, which could draw in monocytes and lead to plaque growth. We can further visualize the heliacal flow patterns throughout the lumen with local normalized helicity to help conceptualize the link between helical flow structures and plaque growth.
Finally, higher Von Mises stress in the artery wall could suggest areas of cellular dysfunction or damage due to increase loading or suggest likely sites of plaque rupture, particularly due to thinner fibrous caps or stress intensifies at the pluck shoulder regions. We also see that stress is driven by artery bending and contraction in the proximal fibrous cap. Whereas the distillation stress is driven by blood pressure Our result, FSI simulations are uniquely placed to capture.
Through comparison with follow-up imaging. We see a decrease in lumen area in the distal region of the artery, which is also associated with an increase in the total liquid arc, suggesting lesion progression. By comparison, the proximal region sees a small decreased in lumen area, but a large decrease in the fibrous cap thickness suggesting a move to a more vulnerable phenotype.
These regions or progression or regression can then be compared to the baseline FSI simulation by analyzing patterns in war shear stress, intraluminal flow and structural stresses. Well, this methodology is presented for a single case. Analysis on larger data sets are acquired to determine the statistical significance of any correlations.
Something we hope this methodology can assist with. in this method, we've described the steps to reconstruct and bio mechanically simulate the patient's coronary artery, using fluid structure interaction techniques. We described the process of extracting the lumen, the lipid and the outer walls from OCT and recreating the three-dimensional shape, before describing the process of meshing, setting boundary conditions and system coupling domains.
And finally, running the simulation and post-processing results. The translation of our sheer stress intraluminal flow characteristics, and the structural response in the artery to clinical mean, was also discussed in terms of lesion progression with FSI based biomechanics, showing the potential to present a more complete picture, of a patient's current condition and prognosis. Now, while FSI is still very much developing and computationally expensive method, we believe that the process describing this methodology can be further built upon and used to assist clinical decision-making surrounding atherosclerosis progression.
