Mechanics-driven mechanobiological mechanisms of arterial tortuosity

Figures

• 

  Fig. 1. pDIC data collection and analysis. (A) Representative in situ image (photo credit: Dar Weiss, Yale University) of a tortuous descending thoracic aorta at zero blood pressure (arrow) in a 20-week-old Fbln5−/− mouse, which was excised and (B) mounted on a custom triple-needle assembly for placement in the panoramic digital image correlation (pDIC) system (fig. S2). Centerlines were computed for each (C) 3D reconstructed configuration at the sample-specific in vivo axial stretch and (D) used to calculate a tortuosity index (TI) at each pressure applied in vitro. Using the virtual field-based inverse method, spatial distributions of (E) circumferential and (F) axial material stiffness, (G) elastic stored energy, and other metrics (fig. S3) were identified and superimposed on the reconstructed reference configuration geometry (at in vivo axial stretch and 80 mmHg) and then unwrapped and plotted in θ − Z planes around the vessel circumference (θ ∈ [− 180,180]) and along its (Z) axial extent. The rightmost edge of each 3D rendering is at about 0°, whereas the leftmost edge is at about ±180°; see the middle panel of Fig. 3 for further clarification of the mapping from 3D to 2D. Edges of…

• 

  Fig. 2. Tortuosity correlates with reduced distensibility and deformability. (A) In vitro pressure versus loaded outer diameter curves for the four study groups reveal structural stiffening in the Fbln5−/− groups. (B) A TI was calculated at each pressure (10 to 140 mmHg) at the specimen-specific in vivo axial stretch. Data are shown as means ± SEM for each group. Note the marked differences in TI between Fbln5+/+ and Fbln5−/− aortas, with pressure-dependent changes in geometry exemplified above one TI versus pressure curve. The in vitro measured TI was plotted against the (C) stored energy and (D) circumferential stretch at 120 mmHg and against the (E) in vivo axial stretch and (F) structural distensibility, defined as (d2 − d1)/d1(P2 − P1), where d denotes diameter and P denotes pressure, with P2 > P1. Each point represents the mean of the distribution of one sample. Note the significant (P < 0.05) negative correlation between TI and all four metrics. Correlations were evaluated using the Pearson correlation coefficient, r.

• 

  Fig. 3. pDIC reveals regional differences in structure and properties in tortuosity. Inflection points, defined on the aortic centerline (Fig. 1), were used to divide all Fbln5−/− samples into four local regions along the long axis of the vessel: proximal (green and yellow), distal (blue and orange), convex (green and orange), and concave (yellow and blue), each consisting of ~100 elements. Box plots (average denoted by *) compare biaxial material stiffness and stretch at 120 mmHg between convex and concave regions at proximal and distal ends. Note the markedly higher circumferential (Circ.) stiffness and axial stretch and lower circumferential stretch in convex regions. The far-right column within each panel (separated by a dotted line and denoted Comp.) shows results from the computational G&R simulations (see below), confirming the same trends between convex and concave regions. The computational results for the proximal and distal ends are identical and are shown on all panels for clarity. An overbar denotes statistical significance between regions, with *P < 0.05, **P < 0.01, and ***P < 0.001. Effect sizes are shown in table S3. Last, note that the intercostal branches are…

• 

  Fig. 4. Multiphoton microscopy. (A) 3D images for convex and concave regions of 20- and 52-week-old Fbln5−/− aortas, shown here for selected axial-circumferential slices at specimen-specific in vivo axial stretch and 80 mmHg. Collagen appeared as undulated bundles with a preferential orientation in the adventitia; elastin-based structures were irregular and scattered in all regions, as expected with the absence of fibulin-5. (B) Mean thickness of the wall and adventitia obtained from multiple 3D images (age groups merged) at three physiologic pressures and the sample-specific axial in vivo axial stretch (see fig. S5, age effects). Adventitial thicknesses were normalized by, and thus independent of, overall wall thickness, which was lower in convex than in concave regions, with a higher fraction of adventitia in convex compared to concave regions and, consequently, the opposite for the medial fraction. (C) Orientation dispersion of collagen fibers determined for concave and convex regions at three different physiologic pressures and the sample-specific axial in vivo stretch. Higher dispersion manifested in the convex region compared to the concave regions in 20-week Fbln5−/−, while…

• 

  Fig. 5. Computational modeling reveals mechanisms of arterial tortuosity. Fully resolved, mechano-adapted, G&R responses (central column)—predicted for an initially straight cylindrical aortic segment having normal uniform geometric and material properties (ϑ = ϑWT) subjected to in vivo homeostatic conditions of blood pressure, flow rate, and axial stretch (representing an idealized Fbln5+/+ sample, not shown)—to local insults (two sites reflecting that observed via pDIC in a representative Fbln5−/− sample) in material properties (representing a modest local loss of elastic fiber integrity and remodeling of diagonal families of collagen toward the circumferential direction, top row), a change in perivascular tethering (mild local push and pull, middle row), or a change in local geometry (prescribed slight overall undulations, bottom row). Next, for all three types of insults considered here, a marked degeneration in elastin and collagen parameters toward those of the fibulin-5–null aorta (ϑWT → ϑKO) induces a severe axial growth response under in vivo blood pressure and flow, which leads to a nearly straight lengthening of the aorta for a constant axial tension prescribed at the ends…

• 

  Fig. 6. Abnormal axial elaboration of tissue off-loads the vessel and gives rise to tortuosity. Progressive initiation and development of persistent tortuosity (i.e., remaining in the absence of loading) for a normal aortic segment (left column; ϑ = ϑWT, including a modest change in local properties at two sites) induced by an increasingly greater loss of elastic fiber integrity ∆ϑ=∆ce=ce−cWTe combined with a gradual increase in orientation of diagonal fibers of collagen ∆ϑ = ∆α0 = α0 − α0WT (left to right) up to ϑ = ϑKO (right column); see table S2. Shown superimposed on the tortuous vessel are the regional values of biaxial wall stress (first and second rows), material stiffness (third and four rows), and change in wall volume (fifth row), the last revealing a gradual increase in mass by deposition along the axial direction (with luminal radius and wall thickness nearly preserved throughout). The G&R model predicted both an initial axial off-loading (second row) of the nearly straight artery until the loss of its structural stability (pre-buckling response, ∆ϑ ≲ 0.8 ∙ ∆ϑKO) and a tortuous remodeling that follows the instability (post-buckling response due to matrix turnover in evolving…