On the biomechanics of heart valve function

Abstract

Heart valves (HVs) are fluidic control components of the heart that ensure unidirectional blood flow during the cardiac cycle. However, this description does not adequately describe the biomechanical ramifications of their function in that their mechanics are multi-modal. Moreover, they must replicate their cyclic function over an entire lifetime, with an estimated total functional demand of least 3x10(9) cycles. The focus of the present review is on the functional biomechanics of heart valves. Thus, the focus of the present review is on functional biomechanics, referring primarily to biosolid as well as several key biofluid mechanical aspects underlying heart valve physiological function. Specifically, we refer to the mechanical behaviors of the extracellular matrix structural proteins, underlying cellular function, and their integrated relation to the major aspects of valvular hemodynamic function. While we focus on the work from the author's laboratories, relevant works of other investigators have been included whenever appropriate. We conclude with a summary of important future trends.

Figure 1

A schematic approach to the biomechanics of heart valve function. As in other physiological systems, valve function can be divided into multiple length scales. While the major drivers are organ-scale hemodynamic phenomena, key to this review are underlying tissue and cellular components that facilitate and regulate these remarkable functional processes of valve function. Moreover, while this system is hierarchical, there are interactions (horizontal arrows) that have not been well described and are likely paramount in valve physiology and function.

Figure 2

(a) A representative in-vivo LV pressure-MV areal strain curve, which is analogous to a stress-strain curve for the leaflet. Here we observed a response, analogous to the classic non-linear soft tissue response, where the valve tissue undergoes large strains (up to 30% change in area) with minimal pressures, followed by a linear response highly stiff response corresponding to valve closure. Inset - A schematic of the MV anterior leaflet showing the 9 sonomicrometry transducer array. (b) Representative time-areal strain traces, along with the corresponding areal strain rate data. Strain rates were quite high, on the order of 1000%/sec. (c,d) Using similar techniques for the MV annulus, annular strains were shown to be regionally and temporally variant with stretches of −15% to 6%. This confirms the highly dynamic nature of the MV annulus and may be related to the varied fibrous-muscle structure of the annulus. Taken from (Sacks et al. 2006).

Figure 3

(a) Stress computed during the opening phase of the cardiac cycle using experimentally determined leaflet material properties and physiologic pressure boundary conditions on the fluid. Leaflet motion computed using 2D FSI simulation (Vigmostad et al., 2008), 3D flow loop experiments (Iyengar et al., 2001), and 3D FEM computations (Kim et al., 2008). (b–e) Here, the same boundary conditions are employed for both simulations, but with different for material properties. Results showing a comparison of the pressure build-up (in Pa) with a high stiffness valve (b) and physiologic valve properties (c). In (d–e), axial velocity (in m/s) is shown for the two cases.

Figure 4

(a) The AV showing, where a 1 mm × 1 mm section was removed to illustrate in (b) the 3D the tri-layered leaflet structure (Courtesy Resolution Science Corporation, CA). (c,d) A magnified view of a partially separated AV leaflet showing the numerous connections found throughout the spongiosa. (e,f) Conventional circumferential histologic cross-sections from separated AV layers, showing that the remaining spongiosa displayed no visible damage induced during separation.

Figure 5

Representative loading and unloading curves for the (a) AV and the (b) MVAL depicting minimal energy loss. Mean (c) AV and (d) MVAL energy storage and dissipation for all stretch rates, with hysteresis defined as the area under tension-areal stretch curve. Both leaflets demonstrated very small hysteretic losses and neither leaflet demonstrated measureable change in hysteresis with strain rate.

Figure 6

Using both small angle X-ray and tissue level strain measurements of the porcine MVAL, we observed that (a) collagen fibril D-period strain (ε_D) and (b) tissue areal strain vs. time during creep tests demonstrated no detectable change with time. In contrast, biaxial stress relaxation experiments (c,d) demonstrated continued relaxation over the similar time scales. Data presented as mean±SEM

Figure 7

Schematic showing (a) the orientation of the AV leaflet specimen used for flexural testing, including the location of the transmural measurement region, which was flexed in two directions to alternately subject the tissue layers to tension/compression (b)? The resulting transmural strain distribution of Λ₁ with increasing curvature along the normalized thickness (V=ventricularis and F=fibrosa) for the (c) AC and (b) WC directions. Here, the intersection of the composite plots with Λ₁ of 1 determined the location of the neutral axis, which was near the center and not dependent of flexural direction.

Figure 8

(a) Representative stress-strain data in the circumferential and b) radial directions for a AV leaflet cusp demonstrating the effects of transverse loading (in-plane coupling). The underlying structural basis for this behavior is best shown by a schematic showing the fibrous structure of the cusp depicting the large collagen cords which undergo large rotations with loading (b). As the radial loads become larger with respect to the circumferential loads, the collagen fibers undergo large rotations causing contraction along the circumferential axis without buckling and allows for very large radial strains.

Figure 9

(a) A representative example of the effective fiber stress-strain curve of heart valve leaflets (MVAL), showing the characteristic long toe region, transitional region, and subsequent linear region. (b) Corresponding tangent modulus of the fiber stress-strain curve. Note the sharp rise of tangent modulus in the middle of transitional region and the followed plateau that shows a constant tensile modulus in linear region. (c) The standard exponential model fitted to the data predicts a continuous increase of stiffness beyond the used data range, whereas the fiber recruitment model correctly predicates a linear stress-strain relationship beyond the used data range.

Figure 10

Results of the 3D stress model of the AV along with the reconstructed layer stresses under physiological strains, based on biaxial experimental data taken from separated layers (Fig. 4). While the fibrosa layer clearly dominated the circumferential response, the ventricularis contributes ~2/3 of the total stress in the radial direction. Note, however, that the ventricularis only “kicks in” at radial stretches >1.4, suggesting a “over distention” protection role.

Figure 11

(a) Collagen alignment results for circumferential strips of AV tissue subjected to 0, 10, and 20% strain. (b) Corresponding TEM images of AVICs at 0, 10, and 20% strain, with the drawn arrows show orientation of circumferential strain. (c) Both the cellular and nuclear aspect ratios changed similarly with strain and collagen alignment, supporting the use of NAR as a measure of cellular strain. In the intact valve, at 0 mmHg transvalvular pressure AVIC NAR values were uniform across the leaflet thickness In contrast, for normalized thickness positions between 0.4–1 (i.e., within the fibrosa layer) the AVIC NAR exhibited a trend of increased value with increased thickness position, approaching an average value of ~4.8 at 90 mmHg. These data indicate that AVICs in the different leaflet layers are subjected to dramatically different external stresses.

Figure 12

(a) Using micropipette aspiration, the effective stiffness, E, of VICs from each valve demonstrated highly significant differences (p<0.001) in mechanical properties between the AVIC and MVIC populations and the PVIC and TVIC populations. N=hearts used and n=cells tested for each valve type. (b) Time dependent responses during the aspiration experiment for AVIC indicated that both the BSLS and SLS model fit well. Inset table shows determined parameters from both models for the representative AVIC (n=1) that was used.

Figure 13

(a) M vs. Δκ relations for both the AC and WC directions for specimens tested in 5 mM and 90 mM KCl, showing a highly linear response. To simulate the cellular responses in-situ a macro/micro model cellular level finite element model was developed (b). Here a bilayer model to simulate bending was utilized, the a 100 mm × 100 mm micro model utilized to estimate cellular contributions.