Chromophore Concentration Estimation via Mixed Beer-Lambert KWW Model
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current spectroscopic methods for estimating chromophore concentrations in samples, based on the Beer-Lambert Law and multiple linear regression, result in errors of several percent, necessitating a more accurate approach for processing spectrographic data.
Innovation Solution
The implementation of a photon scattering and absorption model based on the mixed Beer-Lambert/Kohlrausch-Williams-Watts Model, combined with Kernel Partial Least Squares Regression, to improve the estimation of underlying concentrations of chromophores in samples by analyzing optical signals transmitted through and received from a sample.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a photon scattering and absorption model based on the mixed Beer-Lambert/Kohlrausch-Williams-Watts Model is applied, then measurement precision of chromophore concentrations is improved, but device complexity increases
Solution Approach 1:
The patent transforms the complex nonlinear spectroscopic data analysis problem into a linear regression problem by changing the parameter space. Specifically, it applies a Kohlrausch-Williams-Watts (KWW) function to model the photon scattering and absorption characteristics, then uses linear regression on the transformed parameters rather than attempting direct nonlinear fitting of raw spectroscopic data. This parameter transformation maintains high measurement precision while significantly reducing computational complexity.
Solution Approach 2:
The patent replaces complex iterative nonlinear optimization mechanisms with a simpler linear regression mechanism. Instead of using computationally intensive nonlinear least squares fitting to determine chromophore concentrations from spectroscopic data, the invention substitutes this with a linear regression approach applied to transformed data, achieving comparable or superior precision with reduced computational burden.
2Device complexity
If traditional Beer-Lambert Law and multiple linear regression techniques are used, then device complexity is kept simple, but measurement precision of chromophore concentrations deteriorates with errors on the order of several percent
Solution Approach 1:
The patent creates a composite analytical approach by combining the Beer-Lambert Law framework with the Kohlrausch-Williams-Watts (KWW) function model. This composite model integrates the physical principles of light absorption (Beer-Lambert) with a mathematical function that accounts for photon scattering effects (KWW), producing a more accurate representation of spectroscopic data than either model alone, thereby improving measurement precision while maintaining relative simplicity.
Solution Approach 2:
The patent performs preliminary transformation of the spectroscopic data using the KWW function before applying regression analysis. By pre-processing the raw spectroscopic observations through this mathematical transformation, the data is prepared in a form that is more amenable to accurate and efficient analysis, improving measurement precision before the actual concentration calculation step.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This method provides a closer approximation of chromophore concentrations, reducing errors and enhancing the accuracy of spectroscopic data processing, particularly in both high and low absorption sample areas.
Implementation Method 1
applying a photon scattering and absorption model based on a mixed Beer-Lambert/Kohlrausch-Williams-Watts Model (KWW) for photon diffusion
Implementation Method 2
applying a photon scattering and absorption model based on a mixed Beer-Lambert/Kohlrausch-Williams-Watts Model (KWW) for photon diffusion
Data Source
AI summary
Embodiments disclosed herein may include methods and systems capable of estimating the underlying concentrations of chromophores in a sample. The photon scattering and absorption model may be based on Laplace and stable distributions, which may reveal that measurements in diffuse reflectance may follow a Beer-Lambert and Kohlrausch-Williams-Watts (KWW) product. This Beer-Lambert portion of the product may dominate in high absorption sample areas, while the KWW portion of the product may dominate in low absorption sample areas.