log(gaussian) nonlinear regression curve  (GraphPad Software Inc)

Journal: Scientific Reports

Article Title: Decorin expression is associated with predictive diffusion MR phenotypes of anti-VEGF efficacy in glioblastoma

doi: 10.1038/s41598-020-71799-w

Figure Lengend Snippet: ADC histogram analysis and targeted biopsy acquisition. Pre and post contrast T1 MR images were acquired ( A ) to evaluate ADC levels of each voxel of enhancing tumor ( B ) to yield an ADC histogram ( C ). A double gaussian model (black line) was applied to this histogram (light blue line) to identify the higher (ADC H , red line) and lower (ADC L , blue line) distributions. A probability map ( D ), representing probability of a voxel occurring in the ADC L distribution was used to prospectively identify biopsy targets ( E ). These targets were loaded onto T1 with contrast images on intraoperative neuronavigation software ( F ) to facilitate tissue collection during tumor resection ( G ).

Article Snippet: Then, nonlinear regression using a double Gaussian model was performed (MATLAB, Release 2018b Version 9.5.0; The MathWorks Inc., Natick, Massachusetts) via the following equation (Fig. C): \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p(ADC)=f\cdot N\left({\mu }_{AD{C}_{L}}{\sigma }_{AD{C}_{L}}\right)+\left(1-f\right)N({\mu }_{AD{C}_{H}}{\sigma }_{AD{C}_{H}}),$$\end{document} p ( A D C ) = f · N μ A D C L σ A D C L + - f N ( μ A D C H σ A D C H ) , p(ADC) = probability of a specific ADC value, f = proportion of voxels in the histogram, N (μ,σ) = normal Gaussian distribution (mean μ; standard deviation σ), ADC L = lower Gaussian distribution, ADC H = higher Gaussian distribution.

Techniques: Software