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Optimization of Media Change Intervals through Hydrogels Using Mathematical Models.

ABSTRACT: Three-dimensional cell culture in engineered hydrogels is increasingly used in tissue engineering and regenerative medicine. The transfer of nutrients, gases, and waste materials through these hydrogels is of utmost importance for cell viability and response, yet the translation of diffusion coefficients into practical guidelines is not well established. Here, we combined mathematical modeling, fluorescent recovery after photobleaching, and hydrogel diffusion experiments on cell culture inserts to provide a multiscale practical approach for diffusion. We observed a dampening effect of the hydrogel that slowed the response to concentration changes and the creation of a diffusion gradient in the hydrogel by media refreshment. Our designed model combined with measurements provides a practical point of reference for diffusion coefficients in real-world culture conditions, enabling more informed choices on hydrogel culture conditions. This model can be improved in the future to simulate more complicated intrinsic hydrogel properties and study the effects of secondary interactions on the diffusion of analytes through the hydrogel.

SUBMITTER: Ruiter FAA

PROVIDER: S-EPMC9930106 | biostudies-literature | 2023 Feb

REPOSITORIES: biostudies-literature

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Optimization of Media Change Intervals through Hydrogels Using Mathematical Models.

Ruiter Floor A A FAA King Jasia J Swapnasrita Sangita S Giselbrecht Stefan S Truckenmüller Roman R LaPointe Vanessa L S VLS Baker Matthew B MB Carlier Aurélie A

Biomacromolecules 20230201 2

Three-dimensional cell culture in engineered hydrogels is increasingly used in tissue engineering and regenerative medicine. The transfer of nutrients, gases, and waste materials through these hydrogels is of utmost importance for cell viability and response, yet the translation of diffusion coefficients into practical guidelines is not well established. Here, we combined mathematical modeling, fluorescent recovery after photobleaching, and hydrogel diffusion experiments on cell culture inserts ...[more]

PMID: 36724373

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Project description:BackgroundThe advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging.ResultsTo address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions.ConclusionsThe inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

Dataset Information

Optimization of Media Change Intervals through Hydrogels Using Mathematical Models.

Publications

Optimization of Media Change Intervals through Hydrogels Using Mathematical Models.

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