Developing clinical work suggests that vascular stiffening plays a role in the progression of pulmonary hypertension (PH), while recent studies in animal models of hypoxic PH have found significant proximal vascular stiffening in the diseased population. Here, we develop and validate a minimally invasive, clinically realizable method to estimate the local elastic modulus of the proximal pulmonary arteries from pressure-diameter (PD) data. PD measurements were made in the main pulmonary arteries of 16 calves; lumen diameter was assessed using color M-mode tissue Doppler imaging ultrasound, while pressure was measured via catheter. Two methods corresponding to thin-walled pressure vessel theory ("thin") and Lame's equation for a thick-walled cylinder ("thick") were used to approximate the artery elastic modulus from PD measurements. The harvested arteries were tested independently to determine their "true" ex vivo elastic modulus and stiffness. Both approximations displayed excellent correlation with ex vivo elastic modulus of the calf main pulmonary artery (thin r(2) = 0.811; thick r(2) = 0.844; both P < 0.01). Bland-Altman analysis indicated that the thick-walled approximation has better overall agreement with ex vivo modulus. The approximations displayed quantitatively distinct regression slopes that were statistically different (P = 0.02). The elastic modulus of the main pulmonary artery can be reasonably estimated from combined color M-mode tissue Doppler imaging ultrasound and catheter pressure measurements in calves. Such measurements may be a valuable tool in the diagnosis and treatment of human PH.
A new constitutive model for elastic, proximal pulmonary artery tissue is presented here, called the Total Crimped Fiber Model. This model is based on the material and micro-structural properties of the two main, passive, load-bearing components of the artery wall, elastin and collagen. Elastin matrix proteins are modeled with an orthotropic neo-Hookean material. High stretch behavior is governed by an orthotropic crimped fiber material, modeled as a planar sinusoidal linear elastic beam, which represents collagen fiber deformations. Collagen-dependent artery orthotropy is defined by a structure tensor representing the effective orientation distribution of collagen fiber bundles. Therefore, every parameter of the total crimped fiber model is correlated with either a physiologic structure or geometry or is a mechanically-measured material property of the composite tissue. Further, by incorporating elastin orthotropy, this model better represents the mechanics of arterial tissue deformation. These advancements result in a micro-structural total crimped fiber model of pulmonary artery tissue mechanics which demonstrates good quality of fit and flexibility for modeling varied mechanical behaviors encountered in disease states.
Understanding how arterial remodeling changes the mechanical behavior of pulmonary arteries (PAs) is important to the evaluation of pulmonary vascular function. Early and current efforts have focused on the arteries' histological changes, their mechanical properties under in vitro mechanical testing, and their zero-stress and no-load states. However, the linkage between the histology and mechanical behavior is still not well understood. To explore this linkage, we investigated the geometry, residual stretch, and histology of proximal PAs in both adult rat and neonatal calf hypoxic models of pulmonary hypertension (PH), compared their changes due to chronic hypoxia across species, and proposed a two-layer mechanical model of artery to relate the opening angle to the stiffness ratio of the PA outer to inner layer. We found that the proximal PA remodeling in calves was quite different from that in rats. In rats, the arterial wall thickness, inner diameter, and outer layer thickness fraction all increased dramatically in PH and the opening angle decreased significantly, whereas in calves, only the arterial wall thickness increased in PH. The proposed model predicted that the stiffness ratio of the calf proximal PAs changed very little from control to hypertensive group, while the decrease of opening angle in rat proximal PAs in response to chronic hypoxia was approximately linear to the increase of the stiffness ratio. We conclude that the arterial remodeling in rat and calf proximal PAs is different and the change of opening angle can be linked to the change of the arterial histological structure and mechanics.
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