A one-dimensional mixed porohyperelastic transport swelling finite element model with growth

A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth

The purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid/fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To illustrate the capabilities of this model, several example finite element test problems are considered using model geometry and material parameters based on experimental data from a porcine coronary artery. Multiple growth laws are considered, including time-driven, concentration-driven, and stress-driven growth. Time-driven growth is compared against an exact analytical solution to validate the model. For concentration-dependent growth, changing the diffusivity (representing a change in drug) fundamentally changes growth behavior. We further demonstrate that for stress-dependent, solid-only growth of an artery, growth of an MPHETS model results in a more uniform hoop stress than growth in a hyperelastic model for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To our knowledge, this manuscript provides the first full description of an MPHETS model with growth. The developed computational framework can be used in concert with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues.

A porohyperelastic finite element model of the eye: the influence of stiffness and permeability on intraocular pressure and optic nerve head biomechanics

Progressively deteriorating visual field is a characteristic feature of primary open-angle glaucoma (POAG), and the biomechanics of optic nerve head (ONH) is believed to be important in its onset. We used porohyperelasticity to model the complex porous behavior of ocular tissues to better understand the effect variations in ocular material properties can have on ONH biomechanics. An axisymmetric model of the human eye was constructed to parametrically study how changes in the permeabilities of retina-Bruch's-choroid complex (k(RBC)), sclera k(sclera), uveoscleral pathway (k(UVSC)) and trabecular meshwork k(TM) as well as how changes in the stiffness of the lamina cribrosa (LC) and sclera affect IOP, LC strains, and translaminar interstitial pressure gradients (TLIPG). Decreasing k(RBC) from 5 × 10(- 12) to 5 × 10(- 13) m/s increased IOP and LC strains by 17%, and TLIPG by 21%. LC strains increased by 13% and 9% when the scleral and LC moduli were decreased by 48% and 50%, respectively. In addition to the trabecular meshwork and uveoscleral pathway, the retina-Bruch's-choroid complex had an important effect on IOP, LC strains, and TLIPG. Changes in k(RBC) and scleral modulus resulted in nonlinear changes in the IOP, and LC strains especially at the lowest k(TM) and k(UVSC). This study demonstrates that porohyperelastic modeling provides a novel method for computationally studying the biomechanical environment of the ONH. Porohyperelastic simulations of ocular tissues may help provide further insight into the complex biomechanical environment of posterior ocular tissues in POAG.

Growing matter: a review of growth in living systems

Living systems can grow, develop, adapt, and evolve. These phenomena are non-intuitive to traditional engineers and often difficult to understand. Yet, classical engineering tools can provide valuable insight into the mechanisms of growth in health and disease. Within the past decade, the concept of incompatible configurations has evolved as a powerful tool to model growing systems within the framework of nonlinear continuum mechanics. However, there is still a substantial disconnect between the individual disciplines, which explore the phenomenon of growth from different angles. Here we show that the nonlinear field theories of mechanics provide a unified concept to model finite growth by means of a single tensorial internal variable, the second order growth tensor. We review the literature and categorize existing growth models by means of two criteria: the microstructural appearance of growth, either isotropic or anisotropic; and the microenvironmental cues that drive the growth process, either chemical or mechanical. We demonstrate that this generic concept is applicable to a broad range of phenomena such as growing arteries, growing tumors, growing skin, growing airway walls, growing heart valve leaflets, growing skeletal muscle, growing plant stems, growing heart valve annuli, and growing cardiac muscle. The proposed approach has important biological and clinical applications in atherosclerosis, in-stent restenosis, tumor invasion, tissue expansion, chronic bronchitis, mitral regurgitation, limb lengthening, tendon tear, plant physiology, dilated and hypertrophic cardiomyopathy, and heart failure. Understanding the mechanisms of growth in these chronic conditions may open new avenues in medical device design and personalized medicine to surgically or pharmacologically manipulate development and alter, control, or revert disease progression.