Insights into regional adaptations in the growing pulmonary artery using a meso-scale structural model: effects of ascending aorta impingement.

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.

Pulmonary artery conduit in vivo dimensional requirements in a growing ovine model: comparisons with the ascending aorta.

BACKGROUND AND AIM OF THE STUDY: The pulmonary trunk (PT) structure and function are abnormal in multiple congenital cardiovascular diseases. Existing surgical treatments of congenital malformations of the right ventricular outflow tract and PT do not provide a long-term replacement that can adapt to normal growth. Although there is strong interest in developing tissue-engineered approaches for PT conduit replacement, there remains an absence of any complete investigation of the native geometric growth patterns of the PT to serve as a necessary benchmark. METHODS: Eleven Dorset sheep (aged 4-12 months) underwent a single cardiac magnetic resonance imaging study, from which luminal arterial surface points were obtained using a novel semi-automated segmentation technique. The three-dimensional shapes of the PT and ascending aorta (AA) were measured over the same time period to gain insight into differences in the geometric changes between these two great vessels. RESULTS: The volumetric growth of the PT appeared to be a linear function of age, whereas its surface geometry demonstrated non-uniform growth patterns. While tortuosity was maintained with age, the cross-sectional shape of the main pulmonary artery (MPA) evolved from circular in young animals to elliptical at 12 months. In addition, the distal MPA near the pulmonary artery bifurcation tapered with age. CONCLUSION: It can be concluded that postnatal growth of the PT is not a simple proportionate (i.e. isotropic) size increase, but rather exhibits complex three-dimensional geometric features during somatic growth.

Estimated in vivo postnatal surface growth patterns of the ovine main pulmonary artery and ascending aorta.

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.

Regional structural and biomechanical alterations of the ovine main pulmonary artery during postnatal growth.

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.

Characterization of the highly nonlinear and anisotropic vascular tissues from experimental inflation data: a validation study toward the use of clinical data for in-vivo modeling and analysis.

We study whether an inverse modeling approach is applicable for characterizing vascular tissue subjected to various levels of internal pressure and axial stretch that approximate in-vivo conditions. To compensate for the limitation of axial-displacement/pressure/diameter data typical of clinical data, which does not provide information about axial force, we propose to constrain the ratio of axial to circumferential elastic moduli to a typical range. Vessel wall constitutive behavior is modeled with a transversely isotropic hyperelastic equation that accounts for dispersed collagen fibers. A single-layer and a bi-layer approximation to vessel ultrastructure are examined, as is the possibility of obtaining the fiber orientation as part of the optimization. Characterization is validated against independent pipette-aspiration biaxial data on the same samples. It was found that the single-layer model based on homogeneous wall assumption could not reproduce the validation data. In contrast, the constrained bi-layer model was in excellent agreement with both types of experimental data. Due to covariance, estimations of fiber angle were slightly outside of the normal range, which can be resolved by predefining the angles to normal values. Our approach is relatively invariant to a constant or a variable axial response. We believe that it is suitable for in-vivo characterization.

MRI-based finite-element analysis of left ventricular aneurysm.

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.

Inverse parameter fitting of biological tissues: a response surface approach.

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.