2.1. Medical Data
This is a case study of a 68 year old female who was diagnosed and treated due to a critical stenosis of the left internal carotid artery (stenosis of about 90% of lumen). She presented with a Transient Ischemic Attack (TIA) and due to her symptoms, she underwent AngioCT of the head and neck (GE Light-Speed 64 VCT; GE Healthcare, Fairfield, CT, USA).
Stenosis of the left internal carotid artery and concomitant disturbances in the left hemisphere perfusion were recognized. Patient was referred to the Doppler Ultrasound (US-Doppler) study (GE Vivid 7, GE Healthcare, Fairfield, CT, USA) to assess hemodynamics in the stenotic region. Critical stenosis (Figure 1
a) was diagnosed and due to persisting symptoms, the patient had a balloon angioplasty of the narrowed part of the vessel (Figure 1
For the better evaluation of ischemic area, CT-perfusion study was performed (Figure 2
). This is a fine method that evaluates the temporal changes in brain tissue density following contrast administration. The chronological changes in tissue density reflects the nature of tissue vascularity. In ischemic stroke, this technique enables differentiation of irrevocably damaged infarcted brain (the infarct core) from salvageable ischemic brain tissue (the penumbra). This is vital when qualifying for treatment (thrombolysis or clot retrieval). From the CT-perfusion study, the following parameters were analyzed before (Figure 2
a–c) and after (Figure 2
d–f) surgical intervention: blood flow, blood volume, mean transient time.
To control the surgery effect, another AngioCT with CT-perfusion study and US-Doppler examination were performed after the intervention. US-Doppler records were analyzed to extract velocity profiles as a function of time including one whole cardiac cycle for the purpose of computer simulations. After that, nine velocity profiles were prepared, one as an inlet boundary condition and eight for the verification of outlet conditions, as previously described [21
]. The study protocol was approved by the local ethics committee on the Medical University of Lodz (approval no.: RNN/126/07/KE).
2.2. Mathematical Model
In the first step, we made 3D reconstructions of carotid and vertebral arteries before (Figure 3
a) and after (Figure 3
b) surgical intervention with the use of the self-made semiautomatic algorithm for the image processing and 3DDoctror software (Able Software Corp., Lexington, MA, USA). AngioCT data encompassed vessel from the aortic arch up to the top of the skull. The resolution of the medical images was 512 × 512 and approximately 400 (slices with voxel size of 0.44 × 0.44 × 0.63 mm3
) were considered. First, AngioCT data had to be manually adjusted for brightness to achieve the highest contrast between blood vessels and surrounding tissues. The region growing technique to extract vessels from the background had to be applied. The self-made semiautomatic algorithm reconstructed small gaps in the blood vessels due to large brightness intensity variation inside the vessel. These gaps were eliminated manually using the ImageJ software and its tool for morphological holes filling. Finally, 3DDoctor software was applied to build 3D virtual models of analyzed vessels.
In the second step, to mimic clinical conditions at the inlet of analyzed mathematical domains, velocity profiles as a function of time including one whole cardiac cycle from US-Dopplers were applied. In the CFD technique first, the pre-processor ANSYS ICEM CFD (ANSYS, Canonsburg, PA, USA) to generate and discretize 3D geometries (Figure 3
c) was used. The numerical grids were composed of approximately 2,000,000 tetrahedral elements. Moreover, a boundary layer next to the wall was applied. To neglect the influence of the size and/or number of numerical grid elements on the results of computer simulation, a mesh independent test was performed. Finally, ANSYS FLUENT 18.2 software (ANSYS, Canonsburg, PA, USA), using Euler method for solving Navier-Stokes equations, was applied for blood hemodynamics reconstruction in the analyzed domains as previously described [22
]. We assumed that the blood flow was incompressible and laminar and used Dirichlet conditions for the description of the mathematical domain. According to it, the following boundary conditions were applied: domain inlet was described with the use of velocity-inlet (v(x,y,z)), outlets from the domain were described with the pressure conditions, and wall was treated as a rigid structure. Moreover, for the boundary conditions we used the following initial values: as blood velocity profile at the inlet US-Doppler traces before and after balloon angioplasty of the narrowed part of vessel, and at the outlets routine blood pressure value for the certain vessel type. Rheological properties of a blood were described with the use of modified Quemada’s model, as previously described [23
]. Application of this model allowed to treat blood viscosity not as a constant value, which means that when shear rate is increasing the value of blood viscosity is decreasing. Moreover, Quemada’s model includes initial parameters such as hematocrit (Hct), which was around 40% in the described patient. Therefore, blood hematocrit included in CFD model for the analyzed patients was 40%.
Into the analysis, we included not just the left internal carotid artery (LICA) that was stenotic but also the remaining vessels branching from the aortic arch. Since they create a system of interconnected vessels supplying the brain, pressures depend on each other. Moreover, as the two vertebral arteries join together into the basilar artery, we analyzed them together.
As the paper is focused on the prediction of the hemodynamics after restoration of the blood flow through the critically stenotic artery, we used the initial model (before the surgery) to compute probable models of blood flow through the dilated vessel (after the surgery). Nevertheless, balloon angioplasty of the narrowed artery does not guarantee restoration of the full patency. In this procedure, balloon is introduced through the endovascular catheter and when placed in the narrowed segment it is inflated, extending the vessel’s wall. Atherosclerotic plaque is compressed against the wall and the lumen of the artery increases. In this case it was 80% of the normal diameter. Thus, we used our model to predict three hemodynamic conditions associated with restoration of (1) partially improved (80% of lumen diameter—result actually obtained after the surgery); (2) impaired (60% of lumen diameter) and (3) fully improved blood hemodynamics (100% of lumen diameter). This was translated into changes of pressure. Firstly, based on the medical data from the analyzed patient we reconstructed blood flow for several clinical conditions (one before and three after surgical intervention). Therefore, in postsurgical status routine, blood pressure was set as an average value at the outlets of analyzed mathematical domains (marked as 0% pressure—Table 1
). Next, by increasing of blood pressure in the cranial part, impaired blood hemodynamics was simulated (marked as +20% pressure—Table 1
). Finally, by decreasing of blood pressure in the cranial part, improved blood hemodynamics was simulated (marked as −20% pressure—Table 1
). This approach allowed for analysis of stroke appearance, while higher and lower blood pressure values in the cranial part were calculated.