Supravalvular aortic stenosis (SVAS) is associated with decreased elastin and altered arterial mechanics. Mice with a single deletion in the elastin gene (ELN ϩ/Ϫ ) are models for SVAS. Previous studies have shown that elastin haploinsufficiency in these mice causes hypertension, decreased arterial compliance, and changes in arterial wall structure. Despite these differences, ELN ϩ/Ϫ mice have a normal life span, suggesting that the arteries remodel and adapt to the decreased amount of elastin. To test this hypothesis, we performed in vitro mechanical tests on abdominal aorta, ascending aorta, and left common carotid artery from ELN ϩ/Ϫ and wild-type (C57BL/6J) mice. We compared the circumferential and longitudinal stress-stretch relationships and residual strains. The circumferential stress-stretch relationship is similar between genotypes and changes Ͻ3% with longitudinal stretch at lengths within 10% of the in vivo value. At mean arterial pressure, the circumferential stress in the ascending aorta is higher in ELN ϩ/Ϫ than in wild type. Although arterial pressures are higher, the increased number of elastic lamellae in ELN ϩ/Ϫ arteries results in similar tension/lamellae compared with wild type. The longitudinal stress-stretch relationship is similar between genotypes for most arteries. Compared with wild type, the in vivo longitudinal stretch is lower in ELN ϩ/Ϫ abdominal and carotid arteries and the circumferential residual strain is higher in ELN ϩ/Ϫ ascending aorta. The increased circumferential residual strain brings the transmural strain distribution in ELN ϩ/Ϫ ascending aorta close to wild-type values. The mechanical behavior of ELN ϩ/Ϫ arteries is likely due to the reduced elastin content combined with adaptive remodeling during vascular development. stress; residual strain; opening angle; compliance; longitudinal ELASTIN AND COLLAGEN are the principal determinants of passive artery mechanics. Elastin provides reversible extensibility during cyclic loading of the cardiac cycle (22), whereas collagen provides strength and prevents failure at high pressure (11). It is believed that elastin bears load in both the circumferential and longitudinal directions, whereas collagen bears load mostly in the circumferential direction. Elastin is believed responsible for the in vivo longitudinal retraction force in arteries and consequent shortening upon excision. Decreased elastin content with aging, hypertension, and atherosclerosis is accompanied by a decrease in longitudinal retraction force and circumferential compliance (change in diameter for a specified change in pressure) (8). Decreased elastin content also is found in genetic diseases such as supravalvular aortic stenosis (SVAS). SVAS is a congenital narrowing of the large arteries caused by deletions within the elastin gene that lead to functional haploinsufficiency (10). SVAS patients often exhibit hypertension (1) and have thinner and more numerous elastic lamellae (19).Elastin is encoded by a single gene (ELN); hence, the contribution of elastin to pa...

In humans and many other mammals, the cortex (the outer layer of the brain) folds during development. The mechanics of folding are not well understood; leading explanations are either incomplete or at odds with physical measurements. We propose a mathematical model in which (i) folding is driven by tangential expansion of the cortex and (ii) deeper layers grow in response to the resulting stress. In this model the wavelength of cortical folds depends predictably on the rate of cortical growth relative to the rate of stress-induced growth. We show analytically and in simulations that faster cortical expansion leads to shorter gyral wavelengths; slower cortical expansion leads to long wavelengths or even smooth (lissencephalic) surfaces. No inner or outer (skull) constraint is needed to produce folding, but initial shape and mechanical heterogeneity influence the final shape. The proposed model predicts patterns of stress in the tissue that are consistent with experimental observations.

Dilation of the ascending aorta, associated with Marfan Syndrome, bicuspid aortic valve, or advanced age, may lead to aortic dissection and rupture. Mathematical models can be used to assess the relative importance of increased wall stresses and decreased strength in these mechanical failures. To obtain needed inputs for such models, mechanical properties of dilated human ascending aorta were measured in vitro. Specimens for opening angle, biaxial elastic, and uniaxial circumferential strength tests were cut from excised tissue obtained from 54 patients (age 18-81 years) undergoing elective aortic graft replacement surgery. Opening angle was significantly greater in patients older than 50 years (262 degrees + 76 degrees, n = 21) compared to younger patients (202 degrees +/- 70 degrees, n = 13). All biaxial elastic specimens (n = 40) exhibited nonlinear stress-strain behavior. Rapid increases in circumferential and axial stresses occurred at lower strains in the older patient group than in the younger. Mean strength was significantly lower in older patients (1.35 +/- 0.37 MPa, n= 14) than younger (2.04 +/- 0.46 MPa, n = 11, age <50 years). These changes in mechanical properties suggest that age may influence the risk of aortic dissection or rupture of dilated ascending aorta.

White matter in the brain is structurally anisotropic, consisting largely of bundles of aligned, myelin-sheathed axonal fibers. White matter is believed to be mechanically anisotropic as well. Specifically, transverse isotropy is expected locally, with the plane of isotropy normal to the local mean fiber direction. Suitable material models involve strain energy density functions that depend on the I4 and I5 pseudo-invariants of the Cauchy–Green strain tensor to account for the effects of relatively stiff fibers. The pseudo-invariant I4 is the square of the stretch ratio in the fiber direction; I5 contains contributions of shear strain in planes parallel to the fiber axis. Most, if not all, published models of white matter depend on I4 but not on I5. Here, we explore the small strain limits of these models in the context of experimental measurements that probe these dependencies. Models in which strain energy depends on I4 but not I5 can capture differences in Young’s (tensile) moduli, but will not exhibit differences in shear moduli for loading parallel and normal to the mean direction of axons. We show experimentally, using a combination of shear and asymmetric indentation tests, that white matter does exhibit such differences in both tensile and shear moduli. Indentation tests were interpreted through inverse fitting of finite element models in the limit of small strains. Results highlight that: (1) hyperelastic models of transversely isotropic tissues such as white matter should include contributions of both the I4 and I5 strain pseudo-invariants; and (2) behavior in the small strain regime can usefully guide the choice and initial parameterization of more general material models of white matter.

This study describes the measurement of fields of relative displacement between the brain and the skull in vivo by tagged magnetic resonance imaging and digital image analysis. Motion of the brain relative to the skull occurs during normal activity, but if the head undergoes high accelerations, the resulting large and rapid deformation of neuronal and axonal tissue can lead to long-term disability or death. Mathematical modelling and computer simulation of acceleration-induced traumatic brain injury promise to illuminate the mechanisms of axonal and neuronal pathology, but numerical studies require knowledge of boundary conditions at the brain -skull interface, material properties and experimental data for validation. The current study provides a dense set of displacement measurements in the human brain during mild frontal skull impact constrained to the sagittal plane. Although head motion is dominated by translation, these data show that the brain rotates relative to the skull. For these mild events, characterized by linear decelerations near 1.5g (g ¼ 9.81 m s 22) and angular accelerations of 120 -140 rad s 22 , relative brain -skull displacements of 2-3 mm are typical; regions of smaller displacements reflect the tethering effects of brain -skull connections. Strain fields exhibit significant areas with maximal principal strains of 5 per cent or greater. These displacement and strain fields illuminate the skull -brain boundary conditions, and can be used to validate simulations of brain biomechanics.