Towards improving the accuracy of aortic transvalvular pressure gradients: rethinking Bernoulli

The transvalvular pressure gradient (TPG) is commonly estimated using the Bernoulli equation. However, the method is known to be inaccurate. Therefore, an adjusted Bernoulli model for accurate TPG assessment was developed and evaluated. Numerical simulations were used to calculate TPG_CFD in patient-specific geometries of aortic stenosis as ground truth. Geometries, aortic valve areas (AVA), and flow rates were derived from computed tomography scans. Simulations were divided in a training data set (135 cases) and a test data set (36 cases). The training data was used to fit an adjusted Bernoulli model as a function of AVA and flow rate. The model-predicted TPG_Model was evaluated using the test data set and also compared against the common Bernoulli equation (TPG_B). TPG_B and TPG_Model both correlated well with TPG_CFD (r > 0.94), but significantly overestimated it. The average difference between TPG_Model and TPG_CFD was much lower: 3.3 mmHg vs. 17.3 mmHg between TPG_B and TPG_CFD. Also, the standard error of estimate was lower for the adjusted model: SEE_Model = 5.3 mmHg vs. SEE_B = 22.3 mmHg. The adjusted model's performance was more accurate than that of the conventional Bernoulli equation. The model might help to improve non-invasive assessment of TPG. Graphical abstract Processing pipeline for the definition of an adjusted Bernoulli model for the assessment of transvalvular pressure gradient. Using CT image data, the patient specific geometry of the stenosed AVs were reconstructed. Using this segmentation, the AVA as well as the volume flow rate was calculated and used for model definition. This novel model was compared against classical approaches on a test data set, which was not used for the model definition.