Image-based Modeling of Blood Flow in Pulmonary Arteries Using a One-dimensional Finite Element Method Coupled to a Morphometry- Based Model of the Distal Vessels

Figure 1. Geometric model of proximal pulmonary arteries in a pig superimposed with volume rendered anatomic data obtained using CE-MRA The pulmonary circulation serves the important role of evenly distributing blood throughout the lungs so that gas exchange can occur over as large a surface area as possible. Individuals with unilateral pulmonary stenosis, a narrowing of either the right pulmonary artery (RPA) or left pulmonary artery (LPA), often experience greater blood flow to the contralateral than the ipsilateral lung. An understanding of the impact of the severity of the pulmonary stenosis on the resulting hemodynamic conditions may be gained from accurate modeling. Theoretical models of pulsatile flow in the pulmonary circulation have heretofore been based on lumped parameter or linear wave propagation approaches. The latter approach, based on solving partial differential equations arising from the principles of conservation of mass and momentum, requires a description of the structure of the vascular tree and the distensibility of its vessels. This morphometric and elasticity data has been assembled and used in the analysis of blood flow in the lung of a dog [1] and a cat [2]. The input impedances of these lung models compared favorably with experimentally measured input impedances. We have previously described a finite element method to solve the nonlinear, one-dimensional equations used for modeling blood flow in elastic vessels [3]. Prediction of flow with this method has been validated in vivo using the case of aortic stenosis in the presence of a bypass graft [4]. Impedance boundary conditions have recently been developed for this method [5]. We describe a new approach to simulate blood flow in subjectspecific models of the pulmonary arteries that consists of: (i) a onedimensional finite element model of the proximal pulmonary arteries created from three-dimensional medical imaging data and (ii) calculation of the terminal impedance of the branch vessels included in the one-dimensional finite element model using morphometry data. We describe the application of this approach to simulate pulsatile blood flow in a model of the pulmonary arteries of a pig imaged using magnetic resonance imaging (MRI). METHODS Anatomic data for the porcine pulmonary arteries were obtained using contrast-enhanced magnetic resonance angiography (CE-MRA) with a 1.5 T MRI system (Signa, GE Medical Systems, Waukesha, WI). A rapid, three-dimensional acquisition was performed with respiration suspended, a phased array receive coil, and the following parameters: TR=4.6 ms, TE=1.0 ms, flip angle=15°, FOV=28 cm, and NEX=1. Cine phase-contrast MRI (4D-Flow) was used to obtain velocity information throughout the cardiac cycle for a volume including the MPA, RPA, and LPA [6]. Planes in this volume were extracted from which flow through the MPA, RPA, and LPA were computed using Tecplot (Amtec Engineering, Inc.). A geometric model of the resolvable pulmonary arterial anatomy was created from each set of MRA data using custom image segmentation and geometric modeling procedures [7,8]. One such model is shown in figure 1. The termination points of the model are chosen at bifurcations of vessels whose diameters can be clearly discerned from the MRA data. While a porcine pulmonary morphometric data set is not available, Huang et al. [9] have published a set of human pulmonary morphometric data generated with the diameter-defined Strahler ordering system, including the connectivity, diameters, and lengths of 15 orders of pre-capillary vessels. An order is assigned to each outlet