FE modeling has been used to simulate growth in the context of biological tissues for many applications including joint morphogenesis and bone growth, skeletal muscle sarcomere shortening, cortical folding in the brain, tumor growth, abdominal aortic aneurysms, and cardiac growth and remodeling. However, analytical models alone cannot provide information within the context of complex, anatomically realistic three-dimensional (3D) tissue shapes.įinite element (FE) models offer a way to simulate 3D tissue growth and study how growth is affected by biological and biomechanical conditions. These models have been adapted and enhanced to model various tissues such as cartilage, tissues with unidirectional fibers, and charged fluids in a solid matrix. The majority of this work has used analytical models based on the theoretical framework of finite elasticity, finite growth, and constrained mixtures, which models growth through deformations, stress-dependent growth, and in the context of various tissue constituents, respectively. The role of mechanics on biological growth and remodeling has been commonly studied via modeling (see a recent summary by Ambrosi et al. Modeling of these complex processes can lead to a deeper understanding of biological mechanisms while also providing predictive tools to study the impact of external stimuli. These processes may also be affected by changes in external stimuli that can result from conditions such as injury, disease, or therapeutic treatments. Growth and remodeling of tissues are critical biological processes that can be influenced by biological stimuli such as cell type and density, hormones and other growth factors, and mechanical stimuli. In summary, we illustrate here the importance of the choice of implementation approach for modeling growth, provide a framework for converting models between implementation approaches, and highlight important considerations for comparing results in prior work and developing new models of tissue growth. Node- and element-based approaches matched marginally better when the conversion coefficient to relate the approaches was optimized based on the results of initial simulations, rather than using the theoretically predicted conversion coefficient (median difference in node position 0.042 cm versus 0.052 cm, respectively). The node-based approach was unaffected by modulus. We found that material properties (modulus) affected growth in the element-based approach, with growth completely restricted for high modulus values relative to the growth stimulus, and no restriction for low modulus values. We used a previously reported node-based approach implemented via thermal expansion and an element-based approach implemented via osmotic swelling, and we derived a mathematical relationship to relate the growth resulting from these approaches.

This study directly compared node-based and element-based approaches to understand the isolated impact of implementation method on growth predictions by simulating growth of a bone rudiment geometry, and determined what conditions produce similar results between the approaches. Previous work has simulated growth using node-based or element-based approaches, and this implementation choice may influence predicted growth, irrespective of the applied growth model.

Finite element analysis is a useful tool to model growth of biological tissues and predict how growth can be impacted by stimuli.

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