Hybrid discrete-continuum multiscale model of tissue growth and remodeling.

Tissue growth and remodeling (G&R) is often central to disease etiology and progression, so understanding G&R is essential for understanding disease and developing effective therapies. While the state-of-the-art in this regard is animal and cellular models, recent advances in computational tools offer another avenue to investigate G&R. A major challenge for computational models is bridging from the cellular scale (at which changes are actually occurring) to the macroscopic, geometric-scale (at which physiological consequences arise). Thus, many computational models simplify one scale or another in the name of computational tractability. In this work, we develop a discrete-continuum modeling scheme for analyzing G&R, in which we apply changes directly to the discrete cell and extracellular matrix (ECM) architecture and pass those changes up to a finite-element macroscale geometry. We demonstrate the use of the model in three case-study scenarios: the media of a thick-walled artery, and the media and adventitia of a thick-walled artery, and chronic dissection of an arterial wall. We analyze each case in terms of the new and insightful data that can be gathered from this technique, and we compare our results from this model to several others. STATEMENT OF SIGNIFICANCE: This work is significant in that it provides a framework for combining discrete, microstructural- and cellular-scale models to the growth and remodeling of large tissue structures (such as the aorta). It is a significant advance in that it couples the microscopic remodeling with an existing macroscopic finite element model, making it relatively easy to use for a wide range of conceptual models. It has the potential to improve understanding of many growth and remodeling processes, such as organ formation during development and aneurysm formation, growth, and rupture.

In Situ Lumbar Facet Capsular Ligament Strains Due to Joint Pressure and Residual Strain.

The lumbar facet capsular ligament, which surrounds and limits the motion of each facet joint in the lumbar spine, has been recognized as being mechanically significant and has been the subject of multiple mechanical characterization studies in the past. Those studies, however, were performed on isolated tissue samples and thus could not assess the mechanical state of the ligament in vivo, where the constraints of attachment to rigid bone and the force of the joint pressure lead to nonzero strain even when the spine is not loaded. In this work, we quantified these two effects using cadaveric lumbar spines (five spines, 20 total facet joints harvested from L2 to L5). The effect of joint pressure was measured by injecting saline into the joint space and tracking the 3D capsule surface motion via digital image correlation, and the prestrain due to attachment was measured by dissecting a large section of the tissue from the bone and by tracking the motion between the on-bone and free states. We measured joint pressures of roughly 15-40 kPa and local first principal strains of up to 25-50% when 0.3 mL of saline was injected into the joint space; the subsequent increase in pressure and strain were more modest for further increases in injection volume, possibly due to leakage of fluid from the joint. The largest stretches were in the bone-to-bone direction in the portions of the ligament spanning the joint space. When the ligament was released from the vertebrae, it shrank by an average of 4-5%, with local maximum (negative) principal strain values of up to 30%, on average. Based on these measurements and previous tests on isolated lumbar facet capsular ligaments, we conclude that the normal in vivo state of the facet capsular ligament is in tension, and that the collagen in the ligament is likely uncrimped even when the spine is not loaded.

Through-thickness regional variation in the mechanical characteristics of the lumbar facet capsular ligament.

The human lumbar facet capsule, with the facet capsular ligament (FCL) that forms its primary constituent, is a common source of lower back pain. Prior studies on the FCL were limited to in-plane tissue behavior, but due to the presence of two distinct yet mechanically different regions, a novel out-of-plane study was conducted to further characterize the roles of the collagen and elastin regions. An experimental technique, called stretch-and-bend, was developed to study the tension-compression asymmetry of the FCL due to varying collagen fiber density throughout the thickness of the tissue. Each healthy excised cadaveric FCL sample was tested in four conditions depending on primary collagen fiber alignment and regional loading. Our results indicate that the FCL is stiffest when the collagen fibers (1) are aligned in the direction of loading, (2) are in tension, and (3) are stretched - 16% from its off-the-bone, undeformed state. An optimization routine was used to fit a four-parameter anisotropic, hyperplastic model to the experimental data. The average elastin modulus, E, and the average collagen fiber modulus, ξ, were 13.15 ± 3.59 kPa and 18.68 ± 13.71 MPa (95% CI), respectively.

A Hybrid Microstructural-Continuum Multiscale Approach for Modeling Hyperelastic Fibrous Soft Tissue.

The heterogeneous, nonlinear, anisotropic material behavior of biological tissues makes precise definition of an accurate constitutive model difficult. One possible solution to this issue would be to define microstructural elements and perform fully coupled multiscale simulation. However, for complex geometries and loading scenarios, the computational costs of such simulations can be prohibitive. Ideally then, we should seek a method that contains microstructural detail, but leverages the speed of classical continuum-based finite-element (FE) modeling. In this work, we demonstrate the use of the Holzapfel-Gasser-Ogden (HGO) model [1, 2] to fit the behavior of microstructural network models. We show that Delaunay microstructural networks can be fit to the HGO strain energy function by calculating fiber network strain energy and average fiber stretch ratio. We then use the HGO constitutive model in a FE framework to improve the speed of our hybrid model, and demonstrate that this method, combined with a material property update scheme, can match a full multiscale simulation. This method gives us flexibility in defining complex FE simulations that would be impossible, or at least prohibitively time consuming, in multiscale simulation, while still accounting for microstructural heterogeneity.