Aortic parameters identification for boundary conditions in one-dimensional coronary blood flow model

Fractional flow reserve (FFR) allows determining the need for surgical intervention in the presence of stenosis in the coronary arteries. FFR is based on the ratio of mean blood pressure after stenosis and pressure in the aorta. Non-invasive assessment of FFR remains a relevant task in the diagnosis of vascular diseases. It allows FFR to be assessed without the use of expensive intravascular pressure detector and without excessive risk to the patient. Existing models often face limitations that prevent their widespread usage in clinical practice. Common limitations include the need for model personalisation and specific requirements for the input data. We propose a one-dimensional mathematical model of coronary blood flow for FFR evaluation. A distinctive feature of the model is modified boundary condition at the junction of the coronary arteries and the aorta. This boundary condition involves Windkessel model. Newton's method is used to solve the system of equations at the junction of the aorta, heart, and coronary arteries. An adaptive mechanism for automatically selecting parameters for a specific patient is also proposed. The new parameter selection mechanism allows the systolic and diastolic pressures measured in a patient to be reproduced over several computed cardiac cycles. Modified model decreases the duration of calculations by 40%. It also removes non-physiological reflections from blood pressure profile. The presence of non-physiological reflections does not affect the model's ability to reproduce the average pressure, but it can interfere with the calculation of various non-hyperemic indices based on the pressure profile in the diastolic phase. Validation of the model in a clinical case showed high accuracy: with an invasively measured FFR value of 0.89, the proposed model showed a value of 0.91, while the calculation using the original model gave a value of 0.85. In addition to computed tomography images, the proposed approach requires a limited set of data: stroke volume, heart rate, systolic and diastolic pressure. This allows for broader applicability of the model and simplifies its use. The results obtained show potential for the use clinical practice.