Vascular Compromise and Hemodynamics in Pulmonary Arterial Hypertension: Model Predictions

Abstract

A computer model of the normal pulmonary circulation based on animal (dog) data obtained in the literature was previously developed by Bshouty and Younes (for details see references [S1, S2]). The model is described briefly and only details not included in the original model development will be included here. The original model is a multibranch model that bifurcates sequentially starting from the pulmonary artery (PA) up to eight (four generations) precapillary and capillary channels. The model was later modified to include five generations ending in sixteen precapillary and capillary channels (Figure S1). On the venous side, the vessels converge and reunite sequentially to end in the left atrium (LA). The resistance of a given vessel in the model is dependent on vessel dimensions (length and cross-sectional area). Changes in vessel dimensions occur in response to changes in lung volume and intravascular pressure (P v ). The original multibranch model was developed between 1987 and 1989, when microprocessors operated at 4.77 MHz. At the time, each extra-alveolar vessel was divided into twenty-five segments. This was done in order to shorten the time needed to go through the thousands of calculations and iterations needed to produce a stable solution (which at the time, took several minutes per one set of data). With the development of faster microprocessors, the number of segments of each extra-alveolar vessel was gradually increased initially to one hundred segments and is currently set at a thousand segments. Results obtained with twenty-five segments differed from results obtained with one hundred segments at the second decimal level and results obtained with a thousand segments differed from results obtained with one hundred segments mostly at the third decimal level and are therefore, not clinically significant. Similarly, results obtained with the four-generation model when compared with the five-generation model differed only at the second decimal level and are therefore, also not clinically significant. All simulations presented in this paper were generated with the five-generation model and 1000 segment vessels (See footnote). Cross-sectional area of each arterial (A a ) and venous (A v ) segment is calculated based on the transmural pressure (P tm ) across that segment, P tm being intravascular minus perivascular pressure (P x ). The characteristic behaviour of A a as a function of P tm was derived from data obtained by Smith and Mitzner (S3) and Maloney et al (S4) and described in detail by Bshouty and Younes (S1). It is expressed by the following linear relationship,