Mechanical Properties and Active Remodeling of Blood Vessels Gross anatomy of systemic and pulmonary circulation Microscopic structure Mechanical properties and testing Residual stress Remodeling Blood Vessels Blood vessels form arterial and venous networks in the systemic and pulmonary circulations Vessel walls have an intima, media and adventitia Composite tissue structure affects vessel properties Vessel mechanics can be affected by surrounding tissue Vessels are nonlinear, anisotropic, viscoelastic and exhibit preconditioning behavior Biaxial testing is used to measure anisotropic properties Blood vessels propagate pulse waves along their walls Blood vessels have residual stress in the no-load state Blood vessel structure, mechanics and residual stress can change (remodel) with changes in blood pressure Structure 1
Systemic Arterial Tree Schema of the canine systemic arterial tree (from Nichols WW and O Rourke MF, 1990) Elastic Artery Structure Muscular Artery Structure Elastic artery has thicker intimal layer commensurate with their elastic behavior Smooth muscle cells are organized differently As shown later, elastic artery has more elastin Schematic cross-section showing the three layers intima, media and adventitia and their primary constituents (from Rhodin JAG, 1979) Musculo-Elastic Fascicle F Schema of the musculo-elastic fascicle that was proposed by Clark & Glagov. E denotes elastin, Ce denotes smooth muscle cells, and F denotes collagen bundles which exist between the elastin sheets (from Clark & Glagov, 1985) 2
Vasa Vasorum Figure 8.2:5 in textbook. Photograph of the pulmonary artery of a rabbit, showing the vasa vasorum in the wall. Vessel Remodeling during Hypertension Figure 8.13:2 in textbook. Response of the pulmonary arterial structure to a step increase of pulmonary blood pressure. Wall composition: Canine arteries ARTERY % H2O % COLLAGEN % ELASTIN C:E RATIO a. aorta 70.4 ± 0.4 45.5 ± 1.7 30.1 ± 1.7 1.58 ± 0.15 Carotid 71.1 ± 0.1 50.7 ± 2.1 20.1 ± 1.0 2.55 ± 0.13 Coronary 63.2 ± 1.0 47.9 ± 2.6 15.6 ± 0.7 3.12 ± 0.12 Femoral 68.0 ± 0.3 44.5 ± 1.4 24.5 ± 1.6 1.89 ± 0.14 Mesentary 70.8 ± 0.5 38.1 ± 1.7 26.5 ± 1.7 1.51 ± 0.15 Renal 70.4 ± 0.7 42.6 ± 1.6 18.7 ± 1.8 2.46 ± 0.27 From Fischer GM & Llaurado JG, 1966. % H20 is per wet weight, whereas protein is per unit dry weight; c:e denotes collagen to elastin ratio 3
Study of mechanical properties Assumptions for the determination of the mechanical properties of blood vessels The wall is non-homogeneous, anelastic, and anisotropic; The stress-strain relationship is nonlinear; Mechanical properties depend on vessel type, location, condition, and environment Simplifying Assumptions: Wall is homogeneous, pseudoelastic, incompressible Shape of the vessels is thick-walled cylindrical tube Possible testing approaches: Uniaxial test: stretch vessel strip in one direction. Biaxial test: Cut open vessel longitudinally and stretched in longitudinal and hoop directions Inflate intact vessel Bend vessel wall strips Vessel Test Apparatus Typical experimental set-up from which a majority of the data on arterial wall behavior has been obtained. Cyclic inflation tests at a fixed axial extension are easily performed with this set-up (from Takamizawa K & Hayashi K, 1987). 4
Bending Test System Figure 8.8:1 in text. A sketch of Fung s apparatus for measuring the strains in an arterial specimen subjected to bending. Example: Two-Dimensional Inflation Test Average 2 nd Piola-Kirchhoff Stress: where p is blood pressure, r I and r o are internal and external radii, h is vessel wall thickness, and λ θ and λ z are stretch ratios in the circumferential and longitudinal directions. P!! = pr i h! " 2 pr i 2 P zz = h! z2 r i + r o ( ) Lagrangian Strain: E θθ and E zz are Green strains in the circumferential and longitudinal directions: E!! = 1 " 2 ( 2!1! ) where! " = r d! R d" E zz = 1 2 2!1 (! z ) Tangent Modulus Elastic arteries (i.e. the aorta) behave more linearly due to their high elastin content The mechanical properties of arteries become more nonlinear further away from the heart Text figure 8.3:1. Plot of the Young s modulus (tangent modulus, dt/dλ) vs. the tensile stress (T) in a specimen of thoracic aorta of the dog in a loading process. Part (a) shows a power law for small T and an approximate straight line for T greater than 20 kpa. Part (b) shows the straight-line representation for various segments of the aorta. 5
Inelastic properties Preconditioning Behavior First Piola-Kirchhoff stress P 11 versus stretch λ 1 of passive bovine coronary artery: Cyclic responses during uniaxial testing note preconditioned behavior after 15 cycles and the diminishing hysteresis (data from Humphrey JD, et al, 1996). Stress Relaxation Uniaxial stress relaxation (first Piola-Kirchhoff stress P 11 ) of a passive bovine coronary artery: (data from Humphrey JD, Salunke N, Tippett B, 1996). 6
Structure-function relationship of residual stress Nonhomogeneous Residual Stress Opening angle in the rat aorta as a function of location from the aortic root (0%) to the aorto-iliac bifurcation (100%) (from Liu SQ & Fung YC, 1988) Residual Stress Distributions Calculated distributions of the transmural residual Cauchy stress (t rr, t θθ and t zz ) through the wall of an unloaded, intact elastic rabbit artery (see text for numerical values of the vessel geometry and properties) 7
Effects of Residual Stress Calculated distributions of the transmural Cauchy stress, with and without residual stress: - pressure is 120 mmhg and axial stretch is 1.691 - Note reductions in the gradients of the stresses when residual stress is included. - (Chuong CJ & Fung YC, 1986). Residual Strain The opening-up (right) of originally unloaded intact arterial ring (left) following a radial cut (from Fung, 1984) Opening Angles A B C Adventitia is the origin of the residual stress Opening-up of inner (panel B) and outer (panel C) unloaded arterial rings taken from a single (panel A) arterial cross-section the dashed line in panel A shows where the original cut was made to separate the ring into concentric rings (from Vossoughi J et al, 1993). 8
Referring Strain to the Stress-Free State Schema of the mappings from a cut, stress-free configuration, to an unloaded intact configuration, to a loaded configuration Blood Vessels: Summary of Key Points Blood vessels form arterial and venous networks in the systemic and pulmonary circulations Vessel walls have an intima, media and adventitia Composite tissue structure affects vessel properties Vessel mechanics can be affected by surrounding tissue Vessels are nonlinear, anisotropic, viscoelastic and exhibit preconditioning behavior Biaxial testing is used to measure anisotropic properties Blood vessels propagate pulse waves along their walls Blood vessels have residual stress in the no-load state Blood vessel structure, mechanics and residual stress can change (remodel) with changes in blood pressure 9