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.

Coronary blood flows through a complex vasculature that is regulated by a number of physiological mechanisms, including myogenic, shear regulation, and metabolic control. Namani et al. describe a fully integrative and anatomically correct model that accurately predicts experimental observations.

The anisotropic mechanical properties of magnetically aligned fibrin gels were measured by magnetic resonance elastography (MRE) and by a standard mechanical test: unconfined compression. Soft anisotropic biomaterials are notoriously difficult to characterize, especially in vivo. MRE is wellsuited for efficient, non-invasive, and nondestructive assessment of shear modulus. Directiondependent differences in shear modulus were found to be statistically significant for gels polymerized at magnetic fields of 11.7T and 4.7T compared to control gels. Mechanical anisotropy was greater in the gels polymerized at the higher magnetic field. These observations were consistent with results from unconfined compression tests. Analysis of confocal microscopy images of gels showed measurable alignment of fibrils in gels polymerized at 11.7T. This study provides direct, quantitative measurements of the anisotropy in mechanical properties that accompanies fibril alignment in fibrin gels.

The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isotropic soft material. A soft gel with controlled anisotropy was obtained by polymerizing a mixture of fibrinogen and thrombin solutions in a high field magnet (B ¼ 11.7 T); fibrils in the resulting gel were predominantly aligned parallel to the magnetic field. Aligned fibrin gels were subject to dynamic (20-40 Hz) shear deformation in two orthogonal directions. The shear storage modulus was 1.08 6 0. 42 kPa (mean 6 std. dev.) for shear in a plane parallel to the dominant fiber direction, and 0.58 6 0.21 kPa for shear in the plane of isotropy. Gels were indented by a rectangular tip of a large aspect ratio, aligned either parallel or perpendicular to the normal to the plane of transverse isotropy. Aligned fibrin gels appeared stiffer when indented with the long axis of a rectangular tip perpendicular to the dominant fiber direction. Three-dimensional numerical simulations of asymmetric indentation were used to determine the relationship between direction-dependent differences in indentation stiffness and material parameters. This approach enables the estimation of a complete set of parameters for an incompressible, transversely isotropic, linear elastic material.

Mechanical dyssynchrony (MD) affects left ventricular (LV) mechanics and coronary perfusion. To understand the multifactorial effects of MD, we developed a computational model that bi-directionally couples the systemic circulation with the LV and coronary perfusion with flow regulation. In the model, coronary flow in the left anterior descending (LAD) and left circumflex (LCX) arteries affects the corresponding regional contractility based on a prescribed linear LV contractility-coronary flow relationship. The model is calibrated with experimental measurements of LV pressure and volume, as well as LAD and LCX flow rate waveforms acquired under regulated and fully dilated conditions from a swine under right atrial (RA) pacing. The calibrated model is applied to simulate MD. The model can simultaneously reproduce the reduction in mean LV pressure (39.3%), regulated flow (LAD: 7.9%; LCX 1.9%), LAD passive flow (21.6%) and increase in LCX passive flow (15.9%). These changes are associated with right ventricular pacing compared to RA pacing measured in the same swine only when LV contractility is affected by flow alterations with a slope of 1.4 mmHg/ml2 in a contractility-flow relationship. In sensitivity analyses, the model predicts that coronary flow reserve (CFR) decreases and increases in the LAD and LCX with increasing delay in LV free wall contraction. These findings suggest that asynchronous activation associated with MD impacts (1) the loading conditions that further affect the coronary flow, which may explain some of the changes in , and (2) the coronary flow that reduces global contractility, which contributes to the reduction in LV pressure.