A novel physiologically based algorithm (PBA) for the computation of fractional flow reserve (FFR) in coronary artery trees (CATs) using computational fluid dynamics (CFD) is proposed and developed. The PBA is based on the extension of Murray's law and additional inlet conditions prescribed iteratively, and is implemented in OpenFOAM for testing and validation. 3D models of CATs are created using CT scans and computational meshes, and the results are compared to in-vasive coronary angiographic (ICA) data to validate the accuracy and effectiveness of the PBA. The discrepancy between calculated and experimental FFR is within 2.33-5.26% in steady-state and transient simulations, respectively, when convergence is reached. The PBA is a reliable and physiologically sound technique compared to the current lumped parameter model (LPM), which is based on empirical scaling correlations and requires nonlinear iterative computing for conver-gence. The accuracy of the PBA method is further confirmed using the FDA nozzle, which demonstrates good alignment with CFD-validated values.