Webster equation
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Short description: Mathematical model
The Webster equation, proposed by Thomas J. Webster, is a mathematical model used to predict the adsorption of proteins onto biomaterial surfaces.[1]
It takes into account the chemical and physical properties of the biomaterial surface, as well as the characteristics of the protein being adsorbed.[2]
Equation
The equation is
- [math]\displaystyle{ E_s(r_{eff}) = E_{0,s} + \rho r_{eff} }[/math]
where
- [math]\displaystyle{ r_{eff} = \frac{S_{unit}}{S_{measured}} \cdot \sqrt{\frac{\sum\limits_{i=1}^{N} (Z_{i,\text{filtered}} - Z_{\text{ave,filtered}})^2}{N}} }[/math]
- Es = implant surface energy you want to adsorb the proteins you want
- reff = implant surface roughness
- E0,s = starting implant surface energy before nanoscale surface modification
- r = empirical factor
- S = surface area x, y, z = directions
- N = number of measurements[3]
Application
The Webster equation predicts the optimal nanofeatures an implant should have to promote tissue growth, reduce infection, limit inflammation, or control other biological functions. It can be used to design implants that are customized to meet specific biological requirements.[4][5]
References
- ↑ "Webster named AIMBE fellow" (in en). https://news.brown.edu/articles/2011/12/webster-named-aimbe-fellow.
- ↑ Khang, Dongwoo; Kim, Sung Yeol; Liu-Snyder, Peishan; Palmore, G. Tayhas R.; Durbin, Stephen M.; Webster, Thomas J. (1 November 2007). "Enhanced fibronectin adsorption on carbon nanotube/poly(carbonate) urethane: Independent role of surface nano-roughness and associated surface energy" (in en). Biomaterials 28 (32): 4756–4768. doi:10.1016/j.biomaterials.2007.07.018. PMID 17706277. https://www.sciencedirect.com/science/article/abs/pii/S0142961207005418.
- ↑ "Webster's Equation and the Vocal Tract". https://ccrma.stanford.edu/~bilbao/booktop/node153.html.
- ↑ van den Doel, K.; Ascher, U. M. (2008). "Real-Time Numerical Solution of Webster's Equation on A Nonuniform Grid". IEEE Transactions on Audio, Speech, and Language Processing 16 (6): 1163–1172. doi:10.1109/TASL.2008.2001107. ISSN 1558-7924. https://ieeexplore.ieee.org/document/4566086.
- ↑ Bednarik, M.; Cervenka, M. (2020-03-17). "A wide class of analytical solutions of the Webster equation" (in en). Journal of Sound and Vibration 469: 115169. doi:10.1016/j.jsv.2019.115169. ISSN 0022-460X. Bibcode: 2020JSV...46915169B. https://www.sciencedirect.com/science/article/pii/S0022460X19307321.
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