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, concentrationdriven, 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.

The development of small diameter tissue engineered blood vessels (TEBVs) with low thrombogenicity, low immunogenicity, suitable mechanical properties, and a capacity to remodel to their environment could significantly advance the treatment of coronary and peripheral artery disease. Despite significant advances in the field of tissue engineering, autologous vessels are still primarily utilized as grafts during bypass surgeries. However, undamaged autologous tissue may not always be available due to disease or prior surgery. TEBVs lack long-term efficacy due to a variety of types of failures including aneurysmal dilations, thrombosis, and rupture; the mechanisms of these failures are not well understood. In vitro mechanical testing may help the understanding of these failure mechanisms. The typical mechanical tests lack standardized methodologies; thus, results vary widely. The overall goal of this study is to develop novel experimental and mathematical models to study the mechanical properties and failure mechanisms of TEBVs. Our results suggest that burst pressure tests, the current standard, are not sufficient to assess a TEBVs’ suitability as a coronary substitute; creep and/or cyclic loading tests are also required. Results from this model can help identify the most insightful experiments and quantities to be measured – ultimately reducing the overall number of experimental iterations. Improving the testing and characterization of TEBVs is critically important in decreasing the time necessary to validate the mechanical and functional responses of TEBVs over time, thus quickly moving TEBVs from the benchtop to the patient.