Current and Future Applications of Computational Fluid Dynamics in Coronary Artery Disease

Abstract

Hemodynamics interacts with the cellular components of human vessels, influencing function and healthy status. Locally acting hemodynamic forces have been associated-by a steadily increasing amount of scientific evidence-with nucleation and evolution of atherosclerotic plaques in several vascular regions, resulting in the formulation of the 'hemodynamic risk hypothesis' of the atherogenesis. At the level of coronary arteries, however, the complexity of both anatomy and physiology made the study of this vascular region particularly difficult for researchers. Developments in computational fluid dynamics (CFD) have recently allowed an accurate modelling of the intracoronary hemodynamics, thus offering physicians a unique tool for the investigation of this crucial human system by means of advanced mathematical simulations. The present review of CFD applications in coronary artery disease was set to concisely offer the medical reader the theoretical foundations of quantitative intravascular hemodynamics-reasoned schematically in the text in its basic (i.e., pressure and velocity) and derived quantities (e.g., fractional flow reserve, wall shear stress and helicity)-along with its current implications in clinical research. Moreover, attention was paid in classifying computational modelling derived from invasive and non-invasive imaging modalities with unbiased remarks on the advantages and limitations of each procedure. Finally, an extensive description-aided by explanatory figures and cross references to recent clinical findings-was presented on the role of near-wall hemodynamics, in terms of shear stress, and of intravascular flow complexity, in terms of helical flow.

Keywords: atherosclerosis; computational hemodynamics; computer model; computer simulation; coronary artery disease; helicity; virtual FFR; wall shear stress.

Fig. 1.

Workflow of patient-specific computational fluid dynamics simulations for an explanatory case of diseased right coronary artery. The artery model belongs to a patient recruited during the clinical trial RELATE (ClinicalTrials.gov Identifier: NCT04048005). ICA, invasive coronary angiography; CTCA, computed tomography coronary angiography; IVUS, intravascular ultrasound; OCT, optical coherence tomography; $\rho$, blood density; $\mu$, blood dynamic viscosity; TAWSS, time-average wall shear stress.

Fig. 2.

Explanatory strategies of computational fluid dynamics (CFD) boundary conditions (BCs) that can be prescribed to a diseased right coronary artery model. (A) In/out flow direction panel: the dark blue arrows display the direction of blood flow at each inlet/outlet boundary cross-section of the vessel model. (B) Measured flow rates panel: blood flow rate waveforms extracted from imaging or in vivo measurement techniques are prescribed at each model inlet/outlet cross-section of the vessel model. The measured blood flow rates applied as BCs are shown. (C) Measured inflow + lumped models panel: BCs are defined by coupling measured clinical data, available at the inflow section, with lumped parameter circuit models describing the peripheral vascular resistance and compliance. The diseased right coronary artery belongs to a patient recruited during the RELATE clinical trial (ClinicalTrials.gov Identifier: NCT04048005).

Fig. 3.

Explanatory case showing the typical output obtained through the ${\mathrm{VIRTUheart}}^{\text{𝐓𝐌}}$ system for the computation of the vFFR. (A) A 66-year-old man presented with chronic stable angina. The left anterior descending (LAD) coronary artery had a severe mid vessel stenosis (arrow). The measured FFR between the proximal and distal points (dashed line) was 0.77. (B) Angiograms were used to model the vFFR by using the ${\mathrm{VIRTUheart}}^{\text{TM}}$ system, which was calculated to be 0.75 over the same vessel segment. This is displayed in false color yellow, the straight yellow line connecting the same 2 points between which the vFFR was calculated, exactly matching the 2 spots marked by the dashed line in (A). (C) After implantation of a 2.75 $\times$ 18 mm stent at the stenosis, the measured FFR was 0.88 over the same segment. (D) Virtual coronary intervention using the VIRTUheart system was then used to implant a virtual 2.75 $\times$18 mm stent, and the recalculated vFFR was 0.88, corresponding to the green line connecting the 2 points. Reprinted with permission from Gosling RC, Morris PD, Silva Soto DA, Lawford PV, Hose DR, Gunn JP. Virtual Coronary Intervention: A Treatment Planning Tool Based Upon the Angiogram. JACC Cardiovasc Imaging. 2019; 12(5): 865–872. doi: 10.1016/j.jcmg.2018.01.019 [49] (http://creativecommons.org/licenses/by/4.0/).

Fig. 4.

Two case examples showing the results of the HeartFlow CFD based tool for the computation of the virtual fractional flow reserve from CTCA (i.e., the ${\mathrm{FFR}}_{\text{𝐂𝐓}}$). The examples highlight the benefit of ${\mathrm{FFR}}_{\text{CT}}$ in differentiating functional significance in coronary vessels with anatomically obstructive stenoses. (A) CCTA demonstrated significant coronary artery disease with stenosis $>$50% in the left anterior descending (LAD) artery. This was confirmed by quantitative angiography with a stenosis of 57%. The CFD model based on the CTCA revealed a hemodynamically significant lesion with ${\mathrm{FFR}}_{\text{CT}}$ in the distal LAD of 0.62. The measured FFR during invasive angiography was 0.65. (B) CCTA demonstrated a stenosis $>$50% in the mid right coronary artery (RCA). This was confirmed by quantitative angiography with a stenosis of 62%. Computed ${\mathrm{FFR}}_{\text{CT}}$ was 0.87, indicating a nonfunctionally significant stenosis. This was confirmed by a measured FFR of 0.86. Reprinted with permission from Zarins CK, Taylor CA, Min JK. Computed fractional flow reserve (${\mathrm{FFT}}_{\text{CT}}$) derived from coronary CT angiography. Journal of Cardiovascular Translational Research. 2013; 6(5): 708–714. doi: 10.1007/s12265-013-9498-4 [71]. (http://creativecommons.org/licenses/by/4.0/).

Fig. 5.

Luminal maps of (A) time-average wall shear stress (TAWSS), (B) topological shear variability index (TSVI) and (C) cycle-average local normalized helicity (LNH) for an explanatory diseased right coronary artery model. As expected, high TAWSS values characterize the stenotic region of the coronary artery, while low TAWSS are present downstream of the stenosis (panel A). As for the TSVI, a high variability in WSS contraction/expansion action at the endothelium during the cardiac cycle clearly emerges downstream of the stenosis, at the bifurcation region and at the side branch (panel B). Counter-rotating helical flow structures develop in the intravascular region of the coronary model here reported (panel C). Right-/left- handed helical blood patterns are identified by positive/negative LNH values and displayed in red/blue, respectively. The diseased right coronary artery belongs to a patient recruited during the RELATE clinical trial (ClinicalTrials.gov Identifier: NCT04048005).

Fig. 6.

Near-wall hemodynamic descriptors. (A) Example of WSS vector acting on a generic point at the luminal surface (black arrow) of a diseased right coronary artery. At the same point, the unit vector n normal to the vessel wall is reported (orange arrow). (B) Explanatory maps of WSS vector field (black arrows) with identified contraction/action regions at the luminal surface of the same artery coloured by blue/red, respectively. The diseased right coronary artery belongs to a patient recruited during the RELATE clinical trial (ClinicalTrials.gov Identifier: NCT04048005). The table at the bottom reports the WSS-based descriptors of disturbed flow. For each descriptor, a short caption together with the mathematical formulation is reported. T is the cardiac cycle; ${\mathrm{WSS}}_{\text{𝐮}}$ is the normalized WSS vector field.

Fig. 7.

Intravascular hemodynamic descriptors. Figure: example of the helical-shaped trajectory described by an element of blood moving within an explanatory model of right coronary artery. This diseased artery belongs to a patient recruited during the RELATE clinical trial (ClinicalTrials.gov Identifier: NCT04048005). $\gamma$ is the angle between local velocity (v) and vorticity ($𝝎$) vectors (black arrows). The table at the bottom reports the helical flow-based descriptors commonly used to characterize intracoronary hemodynamics. For each descriptor, a short caption together with the mathematical formulation is reported. T is the cardiac cycle; V is the whole arterial volume.