Bio-Chemo-Mechanical Models of Vascular Mechanics

Abstract

Models of vascular mechanics are necessary to predict the response of an artery under a variety of loads, for complex geometries, and in pathological adaptation. Classic constitutive models for arteries are phenomenological and the fitted parameters are not associated with physical components of the wall. Recently, microstructurally-linked models have been developed that associate structural information about the wall components with tissue-level mechanics. Microstructurally-linked models are useful for correlating changes in specific components with pathological outcomes, so that targeted treatments may be developed to prevent or reverse the physical changes. However, most treatments, and many causes, of vascular disease have chemical components. Chemical signaling within cells, between cells, and between cells and matrix constituents affects the biology and mechanics of the arterial wall in the short- and long-term. Hence, bio-chemo-mechanical models that include chemical signaling are critical for robust models of vascular mechanics. This review summarizes bio-mechanical and bio-chemo-mechanical models with a focus on large elastic arteries. We provide applications of these models and challenges for future work.

Figure 1

Artistic rendering of the medial layer of the rat abdominal aorta based on images from serial block face scanning electron microscopy. Reproduced from O’Connell et al. with permission from Elsevier. EL = elastic lamellae; EP = elastin pores; ES = elastin struts; Cyt = SMC cytoplasm; N = SMC nucleus. Image is oriented with the arterial lumen at the top and is 80 μm x 60 μm x 45 μm [circumferential (θ) x axial (Z) x radial (r)].

Figure 2

Confocal image of collagen fibers in the adventitia of a rabbit carotid artery stained with CNA35-OG488, a fluorescently-labeled collagen specific binding protein. Reproduced from Rezakhaniha et al. under open access agreement. Collagen fiber parameters that can be measured include global angle (a), thickness (t), overall length (L_f), and length of a straight line connecting the ends (L_o).

Figure 3

Block diagram of the coupled electrochemical-chemomechanical SMC model presented in Yang et al.. A stimulus to the cell membrane causes a Ca²⁺ current to flow into the cell to the internal fluid compartments. This alters Ca²⁺ concentration, which controls actin-myosin contractile kinetics. The phosphorylation state of the myosin crossbridges controls the cell mechanical behavior and consequently the force generation.

Figure 4

Summary of considerations for bio-chemo-mechanical modeling of vascular mechanics. For this review, we focused on chemical signaling that affects SMC active properties, but SMC passive properties and chemical effects on matrix proteins, such as degradation by proteases, mechanical alteration by crosslinking molecules, and synthesis of new matrix by SMCs are also important considerations in coupled models.

Figure 5

Illustration of the reference configurations for a constrained mixture model of aortic growth and development. Reproduced from Wagenseil with permission from Springer. Arterial wall components (k = elastin, collagen, and SMCs) are turned over in response to changes in the hemodynamic forces on the arterial wall. They are produced at their natural or homeostatic stretch ratios in each direction (λ^k_θh, λ^k_zh) at some time in development when the mixture (composite arterial wall) is stretched λ_θu, λ_zu from its unloaded state. At the current time, the mixture is stretched λ_θ, λ_z from its unloaded state and the components are stretched λ^k_θ, λ^k_z from their homeostatic states. The stress in the mixture is the sum of the stresses in each component.