Modeling and Optimization of Nonlinear Viscoelastic Behavior for Tissue-Engineered Blood Vessels

Abstract

Vascular tissue engineering technology uses tubular viscoelastic materials as intermediaries to transmit the mechanical stimuli required for the construction of vascular grafts. However, most existing studies rely on elastic models, which fail to capture the time-dependent nature of viscoelastic materials. Moreover, the long fabrication cycles, high costs, and complex parameter measurements in tissue engineering pose significant challenges to experimental approaches. There is thus an urgent need to develop a viscoelastic mechanical model that combines physical interpretability, computational efficiency, and predictive accuracy, enabling precise characterization of material responses and unified quantification across experimental platforms. Here, we propose an error-corrected linear solid (ECLS) model with an embedded correction term to address the predictive deviations of conventional models in nonlinear viscoelastic scenarios. Instead of expanding the traditional model structure, the ECLS incorporates an error correction method that improves predictive performance while maintaining structural simplicity. Experiments were conducted on three representative viscoelastic materials—silicone rubber, polyurethane, and polytetrafluoroethylene—to acquire time-resolved response data through stress relaxation and creep tests. The fitting performance was quantitatively evaluated using the Euclidean norm and the Akaike information criterion, enabling a systematic comparison between the ECLS model and three classical models (Kelvin–Voigt, Maxwell, and standard linear solid [SLS]). The results show that the ECLS model exhibits higher predictive accuracy over a wide time range, with an average goodness of fit (R²) of 0.99, representing an improvement of ∼6% compared to the SLS model. Furthermore, the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) of the ECLS model are at least one order of magnitude lower than those of the traditional models, significantly improving the description of nonlinear viscoelastic behavior and providing more accurate predictions of material viscoelastic mechanical behavior. Therefore, the ECLS model not only improves the modeling accuracy of viscoelastic behavior but also establishes a unified and scalable framework for predicting and optimizing the mechanical performance of tissue-engineered vessels, expanding the application potential of mechanical modeling in bioreactor design and biomaterials development.

Impact Statement

This study presents an improved ECLS model, demonstrating its capability in accurately predicting the complex viscoelastic behavior of materials used in vascular tissue engineering. By improving the fitting accuracy of traditional models and expanding the applicability of the model across different timescales and mechanical environments, the ECLS model provides a more reliable framework for optimizing the mechanical performance of tissue-engineered blood vessels. This research contributes to the design of vascular grafts and the development of bioreactor systems and holds broader application potential in tissue engineering and biomaterials science.