Before revision:  We quantify the uncertainty in geometric features of the network using density estimation techniques to specify probability densities for vessel radius and length . We sample from these distributions , compute model parameters, and propagate uncertainties to pressure and flow predictions using a one-dimensional ( 1D ) fluid dynamics model.
After revision:  We quantify the uncertainty in geometric features of the network using density estimation techniques to specify probability densities for vessel radius and length , and then sample from these distributions , compute model parameters, and propagate uncertainties to pressure and flow predictions using a one-dimensional ( 1D ) fluid dynamics model.