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Predicting regression of a Ductus Arteriosus
Author(s) -
Hussain Juzar,
Ahmed Humza A.,
Grant William A.,
Hernandez Michelle D.,
Quick Christopher M.,
Stewart Randolph H.
Publication year - 2017
Publication title -
the faseb journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.709
H-Index - 277
eISSN - 1530-6860
pISSN - 0892-6638
DOI - 10.1096/fasebj.31.1_supplement.860.9
Subject(s) - ductus arteriosus , shear stress , shunt (medical) , cardiology , mechanics , hagen–poiseuille equation , pulmonary artery , medicine , blood flow , pulsatile flow , physics , flow (mathematics)
The ductus arteriosus (DA) is a shunt connecting the pulmonary artery to the aorta allowing blood to bypass the lungs in a fetus. Although radius is a key variable that is correlated with incidence of patency, the primary mechanical properties of the shunt and the cardiovascular system that impact the regression of the DA after birth remain unknown. However, similar instabilities have been identified in blood vessels using mathematical modeling. Because sustained decreases in endothelial shear stress causes vessels to grow narrower, under the right conditions, vessels in a vascular network can enter a positive feedback loop. Decreases in flow yield decreased radii, which in turn increases resistance to flow. We therefore hypothesized that the patency and spontaneous regression of the DA is a manifestation of adaptation to shear stress, leading to equilibrium radii that may be stable or unstable. We first assumed the standard minimal closed‐loop model, which consists of two ventricles, four vascular compartments, and pulmonary and systemic resistances. We then assumed a shunt where blood flow and endothelial shear stress were governed by Poiseuille's Law. This resulted in a prediction that endothelial shear stress is a complex function of radius, but has a similar form to shear stress in a vessel within a vascular network. Assuming that the shunt remodels so that radius increases linearly with endothelial shear stress yields two potential equilibrium radii, the smaller of which is inherently unstable. This model not only provides a mechanism to explain shunt patency, but also predicts which combinations of parameters would predispose regression when the shunt constricts below a critical, unstable radius. Furthermore, by performing a simple sensitivity analysis, critical parameters are identified that can predispose shunts to spontaneously regress. Taken together, the present work provides critical insights into risk factors and potential medical treatments for patent ductus arteriosus.