A Novel Estimation Approach of Pressure Gradient and Haemodynamic Stresses as Indicators of Pathological Aortic Flow Using Subvoxel Modelling

Objective: The flow downstream from aortic stenoses is characterised by the onset of shear-induced turbulence that leads to irreversible pressure losses. These extra losses represent an increased resistance that impacts cardiac efficiency. A novel approach is suggested in this study to accurately evaluate the pressure gradient profile along the aorta centreline using modelling of haemodynamic stress at scales that are smaller than the typical resolution achieved in experiments. Methods: We use benchmark data obtained from direct numerical simulation (DNS) along with results from in silico and in vitro three-dimensional particle tracking velocimetry (3D-PTV) at three voxel sizes, namely 750 $\mu$ m, 1 mm and 1.5 mm. A differential equation is derived for the pressure gradient, and the subvoxel-scale (SVS) stresses are closed using the Smagorinsky and a new refined model. Model constants are optimised using DNS and in silico PTV data and validated based on pulsatile in vitro 3D-PTV data and pressure catheter measurements. Results: The Smagorinsky-based model was found to be more accurate for SVS stress estimation but also more sensitive to errors especially at lower resolution, whereas the new model was found to more accurately estimate the projected pressure gradient even for larger voxel size of 1.5 mm albeit at the cost of increased sensitivity at this voxel size. A comparison with other methods in the literature shows that the new approach applied to in vitro PTV measurements estimates the irreversible pressure drop by decreasing the errors by at least 20%. Conclusion: Our novel approach based on the modelling of subvoxel stress offers a validated and more accurate way to estimate pressure gradient, irreversible pressure loss and SVS stress. Significance: We anticipate that the approach may potentially be applied to image-based in vivo , in vitro 4D flow data or in silico data with limited spatial resolution to assess pressure loss and SVS stresses in disturbed aortic blood flow.