Stress-Swelling Finite Element Modeling of Cervical Response With Homeostatic Collagen Fiber Distributions.

During pregnancy, the cervix experiences significant mechanical property change due to tissue swelling, and to ongoing changes in the collagen content. In this paper, we model how these two effects contribute to cervical deformation as the pressure load on top of the cervix increases. The cervix and its surrounding supporting ligaments are taken into consideration in the resulting mechanical analysis. The cervix itself is treated as a multilayered tube-like structure, with layer-specific collagen orientation. The cervical tissue in each layer is treated in terms of a collagen constituent that remodels with time within a ground substance matrix that experiences swelling. The load and swelling are taken to change sufficiently slowly so that the collagen properties at any instant can be regarded as being in a state of homeostasis. Among other things, the simulations show how the luminal cross-sectional area varies along its length as a function of pressure and swelling. In general, an increase in pressure causes an overall shortening of the lumen while an increase in swelling has the opposite effect.

A structured continuum modelling framework for martensitic transformation and reorientation in shape memory materials.

Models for shape memory material behaviour can be posed in the framework of a structured continuum theory. We study such a framework in which a scalar phase fraction field and a tensor field of martensite reorientation describe the material microstructure, in the context of finite strains. Gradients of the microstructural descriptors naturally enter the formulation and offer the possibility to describe and resolve phase transformation localizations. The constitutive theory is thoroughly described by a single free energy function in conjunction with a path-dependent dissipation function. Balance laws in the form of differential equations are obtained and contain both bulk and surface terms, the latter in terms of microstreses. A natural constraint on the tensor field for martensite reorientation gives rise to reactive fields in these balance laws. Conditions ensuring objectivity as well as the relation of this framework to that provided by currently used models for shape memory alloy behaviour are discussed.

Hyperelastic modeling of swelling in fibrous soft tissue with application to tracheal angioedema.

Angioedema, the rapid swelling of under-skin tissue, is typically triggered by complex biochemical processes that disrupt an original steady state filtration of liquid through the tissue. Swelling stabilizes once a new steady state is achieved in which the tissue has significantly increased liquid content. These processes are controlled by events at the molecular to the cellular length scale. For describing consequences at organ level length scales it is useful to invoke consolidated continuum mechanics treatments within a generalized hyperelastic framework. We describe the challenges associated with such modeling and demonstrate their use in the context of tracheal angioedema. The trachea is modeled as a two layered cylindrical tube. The inner layer and outer layer represent the soft mucosal tissue and the stiffer cartilaginous tissue respectively. Axially oriented fibers contribute anisotropy to the inner layer, and the swelling is largely confined to this layer. A boundary value problem is formulated; existence and uniqueness is verified. Numerical solutions track airway constriction as a function of mucosal swelling.

Sulcal Cavitation in Linear Head Acceleration: Possible Correlation With Chronic Traumatic Encephalopathy.

Traumatic Brain Injury (TBI) is a significant public health and financial concern that is affecting tens of thousands of people in the United States annually. There were over a million hospital visits related to TBI in 2017. Along with immediate and short-term morbidity from TBI, chronic traumatic encephalopathy (CTE) can have life-altering, chronic morbidity, yet the direct linkage of how head impacts lead to this pathology remains unknown. A possible clue is that chronic traumatic encephalopathy appears to initiate in the depths of the sulci. The purpose of this study was to isolate the injury mechanism/s associated with blunt force impact events. To this end, drop tower experiments were performed on a human head phantom. Our phantom was fabricated into a three-dimensional extruded ellipsoid geometry made out of Polyacrylamide gelatin that incorporated gyri-sulci interaction. The phantom was assembled into a polylactic acid 3D-printed skull, surrounded with deionized water, and enclosed between two optical windows. The phantom received repetitive low-force impacts on the order of magnitude of an average boxing punch. Intracranial pressure profiles were recorded in conjunction with high-speed imaging, 25 k frames-per-second. Cavitation was observed in all trials. Cavitation is the spontaneous formation of vapor bubbles in the liquid phase resulting from a pressure drop that reaches the vapor pressure of the liquid. The observed cavitation was predominately located in the contrecoup during negative pressure phases of local intracranial pressure. To further investigate the cavitation interaction with the brain tissue phantom, a 2D plane strain computational model was built to simulate the deformation of gyrated tissue as a result from the initiation of cavitation bubbles seen in the phantom experiments. These computational experiments demonstrated a focusing of strain at the depths of the sulci from bubble expansion. Our results add further evidence that mechanical interactions could contribute to the development of chronic traumatic encephalopathy and also that fluid cavitation may play a role in this interaction.

On collagen fiber morphoelasticity and homeostatic remodeling tone.

A variety of biochemical and physical processes participate in the creation and maintenance of collagen in biological tissue. Under mechanical stimuli these collagen fibers undergo continuous processes of morphoelastic change. The model presented here is motivated by experimental reports of stretch-stabilization of the collagen fibers to enzymatic degradation. The fiber structure is modeled in terms of a fiber density evolution that is regulated by means of a fixed creation rate and a mechano-sensitive dissolution rate. The theory accounts for the possibly different natural configurations of the fiber unit constituents and the ground substance matrix. It also generalizes previous theoretical descriptions so as to account for finite survival times of the individual fiber units. Special consideration is given to steady state fiber-remodeling processes in which fiber creation and dissolution are in balance. Fiber assembly processes that involve prestretching the fiber constituents yield a homeostatic stress response with a characteristic fiber tone. Fiber density returns to homeostasis after mechanical disruption when sufficient time has passed.

Crack formation during solid pyrolysis: evolution, pattern formation and statistical behaviour.

As solids pyrolyse during combustion, they lose chemical and structural integrity by gradually degrading into residual char and forming defects such as voids, fissures and cracks. The material degradation process, which is coupled to the crack formation process, is described using a theoretical model and is numerically simulated using the finite-element method for a generic, charring, rubber-like material. In this model, a slab of material is subjected to an external, localized heat flux and, as the material degrades, cracks form when the local principal stress exceeds a defined cracking threshold. The magnitude of the cracking threshold σ c is systematically varied in order to examine its influences on crack initiation, evolution, distribution and behaviour over time. When σ c exceeds the maximum principal stress for the entire process, σ m , then no cracks are generated. We quantify how the average crack spacing, total crack length and crack initiation time depend upon the ratio σ c /σ m . Two characteristic domains of crack formation behaviour are identified from the crack initiation behaviour. Correlations are produced for the crack length evolution and final crack length values as functions of σ c /σ m . Crack intersection patterns and behaviour are described and characterized.

Hyperelastic modeling of the combined effects of tissue swelling and deformation-related collagen renewal in fibrous soft tissue.

A continuum mechanics constitutive model is presented for the interaction between swelling and collagen remodeling in biological soft tissue. The model is inherently two-way: swelling stretches the collagen fibers which affects their rate of degradation-the remodeled fibrous microarchitecture provides selective directional stiffening that causes the swollen tissue to expand more in the unreinforced directions. The constitutive model specifically treats stretch-stabilization wherein the rate of enzymatic-induced degradation of collagen is a decreasing function of fiber stretch. New collagen replacement takes place in a generally swollen environment, and this synthesis is tracked as a function of time by means of a time integration scheme that accounts for the historical sequence of collagen recreation. The model allows for the specification of the collagen pre-stretch at the time of first synthesis, thus allowing for the consideration of either initially limp replacement fiber or initially pre-tensioned replacement fiber. Loading and swelling that occurs on time scales that are commensurate with the natural time scales for fiber degradation and replacement lead to the consideration of time-integral constitutive equations. Loading and swelling that take place on time scales that are very different from that of the remodeling time scales provide a simplified treatment in which there are definite notions of a short-time instantaneous response and also a large-time approach to a steady-state condition of homeostasis.

Computational modeling of tracheal angioedema due to swelling of the submucous tissue layer.

Angioedema is a tissue-swelling pathology due to rapid change in soft tissue fluid content. Its occurrence in the trachea is predominantly localized to the soft mucous tissue that forms the innermost tracheal layer. The biomechanical consequences, such as airway constriction, are dependent upon the ensuing mechanical interactions between all of the various tissues that comprise the tracheal tube. We model the stress interactions by treating the trachea organ as a three-tissue system consisting of swellable mucous in conjunction with nonswelling cartilage and nonswelling trachealis musculature. Hyperelastic constitutive modeling is used by generalizing the standard anisotropic, incompressible soft tissue framework to incorporate the swelling effect. Finite element stress analysis then proceeds with swelling of the mucous layer providing the driving factor for the mechanical analysis. The amount of airway constriction is governed by the mechanical interaction between the three predominant tissue types. The detailed stress analysis indicates the presence of stress concentrations near the various tissue junctions. Because of the tissue's nonlinear mechanical behavior, this can lead to material stiffness fluctuations as a function of location on the trachea. Patient specific modeling is presented. The role of the modeling in the interpretation of diagnostic procedures and the assessment of therapies is discussed.

On the computation of stress in affine versus nonaffine fibril kinematics within planar collagen network models.

Some recent analyses modeled the response of collagenous tissues, such as epicardium, using a hypothetical network consisting of interconnected springlike fibers. The fibers in the network were organized such that internal nodes served as the connection point between three such collagen springs. The results for assumed affine and nonaffine deformations are contrasted after a homogeneous deformation at the boundary. Affine deformation provides a stiffer mechanical response than nonaffine deformation. In contrast to nonaffine deformation, affine deformation determines the displacement of internal nodes without imposing detailed force balance, thereby complicating the simplest intuitive notion of stress, one based on free body cuts, at the single node scale. The standard notion of stress may then be recovered via average field theory computations based on large micromesh realizations. An alternative and by all indications complementary viewpoint for the determination of stress in these collagen fiber networks is discussed here, one in which stress is defined using elastic energy storage, a notion which is intuitive at the single node scale. It replaces the average field theory computations by an averaging technique over randomly oriented isolated simple elements. The analytical operations do not require large micromesh realizations, but the tedious nature of the mathematical manipulation is clearly aided by symbolic algebra calculation. For the example case of linear elastic deformation, this results in material stiffnesses that relate the infinitesimal strain and stress. The result that the affine case is stiffer than the nonaffine case is recovered, as would be expected. The energy framework also lends itself to the natural inclusion of changes in mechanical response due to the chemical, electrical, or thermal environment.