Webster equation

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

E_{s}(r_{eff})=E_{0,s}+\rho r_{eff}

where

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}}}

E_s = implant surface energy you want to adsorb the proteins you want

r_eff = implant surface roughness

E_0,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". news.brown.edu.
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". Biomaterials. pp. 4756–4768. doi:10.1016/j.biomaterials.2007.07.018.
"Webster's Equation and the Vocal Tract". ccrma.stanford.edu. Retrieved 2023-05-09.
van den Doel, K.; Ascher, U. M. "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.
Bednarik, M.; Cervenka, M. (2020-03-17). "A wide class of analytical solutions of the Webster equation". Journal of Sound and Vibration. 469: 115169. doi:10.1016/j.jsv.2019.115169. ISSN 0022-460X.

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[1] "Webster named AIMBE fellow". news.brown.edu.

[2] 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". Biomaterials. pp. 4756–4768. doi:10.1016/j.biomaterials.2007.07.018.

[3] "Webster's Equation and the Vocal Tract". ccrma.stanford.edu. Retrieved 2023-05-09.

[4] van den Doel, K.; Ascher, U. M. "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.

[5] Bednarik, M.; Cervenka, M. (2020-03-17). "A wide class of analytical solutions of the Webster equation". Journal of Sound and Vibration. 469: 115169. doi:10.1016/j.jsv.2019.115169. ISSN 0022-460X.