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Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation


A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281–1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of ‘large’ arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the ‘smaller’ arteries and veins of radii \(\ge \)50 \(\upmu \)m. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment for circulatory diseases within the lung.

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    As is common for studies of cardiovascular dynamics, all pressures are given in mmHg. The conversion to SI units is 1 mmHg \(=\) 133.3 Pa.


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Olufsen was funded in part by the National Science Foundation, Award No. NSF-DMS-1122424 and by the National Institute of Health Virtual Physiological Rat Center under Award No. 5-P50-GM094503-02. Vaughan was funded by a studentship from the UK EPSRC. Qureshi was funded by a scholarship from IIU and HEC Pakistan and by PG mobility scholarship from the College of Science and Engineering, University of Glasgow, to visit Olufsen’s group.

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Correspondence to N. A. Hill.

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Qureshi, M.U., Vaughan, G.D.A., Sainsbury, C. et al. Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation. Biomech Model Mechanobiol 13, 1137–1154 (2014). https://doi.org/10.1007/s10237-014-0563-y

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  • Pulmonary circulation
  • Pulmonary hypertension
  • Resistance arteries
  • Structured tree
  • Multiscale mathematical model