Tagged MRI and finite-element (FE) analysis are valuable tools in analyzing cardiac mechanics. To determine systolic material parameters in three-dimensional stress-strain relationships, we used tagged MRI to validate FE models of left ventricular (LV) aneurysm. Five sheep underwent anteroapical myocardial infarction (25% of LV mass) and 22 wk later underwent tagged MRI. Asymmetric FE models of the LV were formed to in vivo geometry from MRI and included aneurysm material properties measured with biaxial stretching, LV pressure measurements, and myofiber helix angles measured with diffusion tensor MRI. Systolic material parameters were determined that enabled FE models to reproduce midwall, systolic myocardial strains from tagged MRI (630 +/- 187 strain comparisons/animal). When contractile stress equal to 40% of the myofiber stress was added transverse to the muscle fiber, myocardial strain agreement improved by 27% between FE model predictions and experimental measurements (RMS error decreased from 0.074 +/- 0.016 to 0.054 +/- 0.011, P < 0.05). In infarct border zone (BZ), end-systolic midwall stress was elevated in both fiber (24.2 +/- 2.7 to 29.9 +/- 2.4 kPa, P < 0.01) and cross-fiber (5.5 +/- 0.7 to 11.7 +/- 1.3 kPa, P = 0.02) directions relative to noninfarct regions. Contrary to previous hypotheses but consistent with biaxial stretching experiments, active cross-fiber stress development is an integral part of LV systole; FE analysis with only uniaxial contracting stress is insufficient. Stress calculations from these validated models show 24% increase in fiber stress and 115% increase in cross-fiber stress at the BZ relative to remote regions, which may contribute to LV remodeling.

As the next step in our investigations into the structural adaptations of the main pulmonary artery (PA) during postnatal growth, we utilized the extensive experimental measurements of the growing ovine PA from our previous study (Fata et al., 2013, "Estimated in vivo Postnatal Surface Growth Patterns of the Ovine Main Pulmonary Artery and Ascending Aorta," J. Biomech. Eng., 135(7), pp. 71010-71012). to develop a structural constitutive model for the PA wall tissue. Novel to the present approach was the treatment of the elastin network as a distributed fiber network rather than a continuum phase. We then utilized this model to delineate structure-function differences in the PA wall at the juvenile and adult stages. Overall, the predicted elastin moduli exhibited minor differences remained largely unchanged with age and region (in the range of 150 to 200 kPa). Similarly, the predicted collagen moduli ranged from ∼1,600 to 2700 kPa in the four regions studied in the juvenile state. Interestingly, we found for the medial region that the elastin and collagen fiber splay underwent opposite changes (collagen standard deviation juvenile = 17 deg to adult = 28 deg, elastin standard deviation juvenile = 35 deg to adult = 27 deg), along with a trend towards more rapid collagen fiber strain recruitment with age, along with a drop in collagen fiber moduli, which went from 2700 kPa for the juvenile stage to 746 kPa in the adult. These changes were likely due to the previously observed impingement of the relatively stiff ascending aorta on the growing PA medial region. Intuitively, the effects of the local impingement would be to lower the local wall stress, consistent with the observed parallel decrease in collagen modulus. These results suggest that during the postnatal somatic growth period local stresses can substantially modulate regional tissue microstructure and mechanical behaviors in the PA. We further underscore that our previous studies indicated an increase in effective PA wall stress with postnatal maturation. When taken together with the fact that the observed changes in mechanical behavior and structure in the growing PA wall were modest in the other three regions studied, our collective results suggest that the majority of the growing PA wall is subjected to increasing stress levels with age without undergoing major structural adaptations. This observation is contrary to the accepted theory of maintenance of homeostatic stress levels in the regulation of vascular function, and suggests alternative mechanisms might regulate postnatal somatic growth. Understanding the underlying mechanisms will help to improve our understanding of congenital defects of the PA and lay the basis for functional duplication in their repair and replacement.

The engineering foundation for novel approaches for the repair of congenital defects that involve the main pulmonary artery (PA) must rest on an understanding of changes in the structure-function relationship that occur during postnatal maturation. In the present study, we quantified the postnatal growth patterns in structural and biomechanical behavior in the ovine PA in the juvenile and adult stages. The biaxial mechanical properties and collagen and elastin fiber architecture were studied in four regions of the PA wall, with the collagen recruitment of the medial region analyzed using a custom biaxial mechanical-multiphoton microscopy system. Circumferential residual strain was also quantified at the sinotubular junction and bifurcation locations, which delimit the PA. The PA wall demonstrated significant mechanical anisotropy, except in the posterior region where it was nearly isotropic. Overall, we observed only moderate changes in regional mechanical properties with growth. We did observe that the medial and lateral locations experience a moderate increase in anisotropy. There was an average of about 24% circumferential residual stain present at the luminal surface in the juvenile stage that decreased to 16% in the adult stage with a significant decrease at the bifurcation, implying that the PA wall remodels toward the bifurcation with growth. There were no measurable changes in collagen and elastin content of the tunica media with growth. On average, the collagen fiber recruited more rapidly with strain in the adult compared to the juvenile. Interestingly, the PA thickness remained constant with growth. When this fact is combined with the observed stable overall mechanical behavior and increase in vessel diameter with growth, a simple Laplace Law wall stress estimate suggests an increase in effective PA wall stress with postnatal maturation. This observation is contrary to the accepted theory of maintenance of homeostatic stress levels in the regulation of vascular function and suggests alternative mechanisms regulate postnatal somatic growth. Understanding the underlying mechanisms, incorporating important structural features during growth, will help to improve our understanding of congenital defects of the PA and lay the basis for functional duplication in their repair and replacement.

In this paper, we present the application of a semi-global inverse method for determining material parameters of biological tissues. The approach is based on the successive response surface method, and is illustrated by fitting constitutive parameters to two nonlinear anisotropic constitutive equations, one for aortic sinus and aortic wall, the other for aortic valve tissue. Material test data for the aortic sinus consisted of two independent orthogonal uniaxial tests. Material test data for the aortic valve was obtained from a dynamic inflation test. In each case, a numerical simulation of the experiment was performed and predictions were compared to the real data. For the uniaxial test simulation, the experimental targets were force at a measured displacement. For the inflation test, the experimental targets were the three-dimensional coordinates of material markers at a given pressure. For both sets of tissues, predictions with converged parameters showed excellent agreement with the data, and we found that the method was able to consistently identify model parameters. We believe the method will find wide application in biomedical material characterization and in diagnostic imaging.

In this study, we investigate whether an inverse modeling approach can be used to characterize vascular tissue behavior from experimental data of blood vessels subjected at various levels of internal pressure and axial stretch that mimics clinical data. In-vivo condition of blood vessel with either constant or variable axial response is considered. To compensate for the limitation of this data that does not provide axial force information, a new concept to constrain the ratio of axial to circumferential elastic moduli to a typical range is proposed. Vessel wall constitutive behavior was modeled with a transversely isotropic hyperelastic equation that accounts for dispersed collagen fibers, and both single-layer and bi-layer models were implemented for examination. The possibility of obtaining the fiber orientation in this approach was also evaluated. The characterized behavior was validated with an independent pipette-aspiration biaxial data on the same samples. It was found that homogenous assumption is an over-simplification. The constrained bi-layer model was in excellent agreement with both types of experimental data. Fiber angle is needed to be pre-defined to avoid covariance problem. Finally, our approach is relatively invariant to any particular axial response. Therefore, we believe that inverse modeling approach is suitable for in-vivo characterization.

Delineating the normal postnatal development of the pulmonary artery (PA) and ascending aorta (AA) can inform our understanding of congenital abnormalities, as well as pulmonary and systolic hypertension. We thus conducted the following study to delineate the PA and AA postnatal growth deformation characteristics in an ovine model. MR images were obtained from endoluminal surfaces of 11 animals whose ages ranged from 1.5 months/15.3 kg mass (very young) to 12 months/56.6 kg mass (adult). A bicubic Hermite finite element surface representation was developed for the each artery from each animal. Under the assumption that the relative locations of surface points were retained during growth, the individual animal surface fits were subsequently used to develop a method to estimate the time-evolving local effective surface growth (relative to the youngest measured animal) in the end-diastolic state. Results indicated that the spatial and temporal surface growth deformation patterns of both arteries, especially in the circumferential direction, were heterogeneous, leading to an increase in taper and increase in cross-sectional ellipticity of the PA. The longitudinal PA growth stretch of a large segment on the posterior wall reached 2.57 ± 0.078 (mean ± SD) at the adult stage. In contrast, the longitudinal growth of the AA was smaller and more uniform (1.80 ± 0.047). Interestingly, a region of the medial wall of both arteries where both arteries are in contact showed smaller circumferential growth stretches-specifically 1.12 ± 0.012 in the PA and 1.43 ± 0.071 in the AA at the adult stage. Overall, our results indicated that contact between the PA and AA resulted in increasing spatial heterogeneity in postnatal growth, with the PA demonstrating the greatest changes. Parametric studies using simplified geometric models of curved arteries during growth suggest that heterogeneous effective surface growth deformations must occur to account for the changes in measured arterial shapes during the postnatal growth period. This result suggests that these first results are a reasonable first-approximation to the actual effective growth patterns. Moreover, this study clearly underscores how functional growth of the PA and AA during postnatal maturation involves complex, local adaptations in tissue formation. Moreover, the present results will help to lay the basis for functional replacement by defining critical geometric metrics.

It has been estimated that worldwide 600,000 babies are born annually with significant congenital heart disease (1). Congenital heart and related vascular defects cause increased flow and pulmonary pressure leading to unfavorable vascular remodeling that results in pulmonary arterial hypertension (1). Developing tissue engineered replacements that mimic the growth and remodeling behavior of native tissue is the optimal approach in treatment of congenital arterial anomalies. The understanding of the underlying mechanisms leading to pulmonary arterial hypertension as well as replicating native pulmonary artery functionality in engineered replacements requires knowledge of native tissue mechanics and growth behavior. In the present study, we report novel information on the changes in the structure-mechanics behavior of the growing pulmonary artery.

The goal of this study is to develop a structurally based constitutive model to characterize the structure-function relationship of the vocal folds. Compared to phenomenological models, structurally based constitutive models allow direct prediction of changes in the mechanical behavior of the vocal folds as a result of aging or pathological conditions. The first significant step in developing such a mathematical model is to characterize the structural arrangement and load-bearing behavior of the collagen and elastin fibers, the two most mechanically significant structural proteins in the vocal fold. A micro horizontal uniaxial tensile system has been designed and coupled with the non-invasive multi-photon microscopy method. The load-bearing or recruitment behavior of collagen was characterized by simultaneously measuring the waviness of the collagen fibers and stress of the cover layer at different strain conditions. The structural arrangement of the collagen and elastin fibers in the different layers of the lamina propria were also quantified. The results of this study will directly elucidate the specific contributions of the elastin and collagen fibers to the vocal fold mechanical behavior under uniaxial tension. [Work supported by NIH.]