Webster equation

The Webster equation, proposed by Thomas J. Webster, is a mathematical model used to predict the adsorption of proteins onto biomaterial surfaces.

It takes into account the chemical and physical properties of the biomaterial surface, as well as the characteristics of the protein being adsorbed.

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

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.