A Direct Comparison of Node and Element-Based Finite Element Modeling Approaches to Study Tissue Growth

Finite element analysis is a useful tool to model growth of biological tissues and predict how growth can be impacted by stimuli. 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. 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. 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. 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. The node-based approach was unaffected by modulus. 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). 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.