Pulmonary vascular stiffness: measurement, modeling, and implications in normal and hypertensive pulmonary circulations

Abstract

This article introduces the concept of pulmonary vascular stiffness, discusses its increasingly recognized importance as a diagnostic marker in the evaluation of pulmonary vascular disease, and describes methods to measure and model it clinically, experimentally, and computationally. It begins with a description of systems-level methods to evaluate pulmonary vascular compliance and recent clinical efforts in applying such techniques to better predict patient outcomes in pulmonary arterial hypertension. It then progresses from the systems-level to the local level, discusses proposed methods by which upstream pulmonary vessels increase in stiffness, introduces concepts around vascular mechanics, and concludes by describing recent work incorporating advanced numerical methods to more thoroughly evaluate changes in local mechanical properties of pulmonary arteries.

Figure 1

Typical pressure-diameter curve for elastic tissues.

Figure 2

Typical conduit artery pressure-diameter (PD) response in acute and chronic models of hypertension. Left figure (149), diameter on abscissa: phenylephrine injection (active PH, APH), left PA occlusion (passive PH, PPH), or both (APPH) in an acute sheep model. Note that injection of a vasoconstrictor (phenylephrine) yields “active PH” along with reduced conduit artery diameter, while “passive PH” does not display conduit artery vasoconstriction. All the curves display roughly the same slope, suggesting that SMCs change the operating diameter but do not strongly affect the stiffness and that no strain-induced stiffening has occurred. Right figure (217), pressure on abscissa: (A) minimum diastolic pressure; (B) peak systolic pressure; (C) beginning of diastole; (D) later part of diastole, in a chronic hypobaric hypoxia calf model. In the calf, pressures are substantially higher which cause the diameter-pressure response to have a J-shape typically associated with collagen engagement. There also appears to be little to no acute SMC contribution to the mechanics of the proximal vasculature in the calf; such contributions would cause the PD curve to move downward and rightward from the low pressure condition without a significant change in slope. [Figures used with permission]

Figure 3

Idealized representations of the pulmonary circuit and their corresponding Windkessel models. C = (pulmonary artery) compliance, PAC; R = (total pulmonary) resistance, TPR; Z_c = characteristic impedance; L = inertance. [From (198); used with permission]

Figure 4

Tube geometry for the derivation of simple mechanics equations. P_i, P_o = pressures acting on inner and outer walls; T, tension within the artery; r_i, r_o = inner, outer arterial radii; h = wall thickness, I = tube length.

Figure 5

Deformation of a rectangular plate. (A) Un-deformed rectangular plate. (B) Deformed rectangular plate. Loads (F) are applied along the edges of the plate in the principle directions [circumferential (1) and longitudinal (2)].

Figure 6

Schematic diagram of artery wall in the zero-stress state used in the formulation of several arterial models. Arterial wall as modeled by (A) Fung (54), (B) Holzapfel (75), (C) Zulliger (218). Figures used with permission.