Chromatogram Peak Area Bounds Under Constrained Model Fitting
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for fitting model functions to chromatograms in chromatography struggle to accurately evaluate the upper and lower bounds of peak areas, particularly for impurities in pharmaceutical products, which are crucial for quality management.
Innovation Solution
A method and device that utilize optimization calculations to fit model functions to chromatograms, allowing for the evaluation of maximum or minimum peak areas by constraining the residual error within a predetermined range, thereby enabling the estimation of upper and lower bounds of peak areas.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a model function is fitted to a plausible shape representing the actually measured waveform, then the fitting accuracy is improved, but the evaluation of peak area bounds becomes insufficient for impurity management
Solution Approach 1:
The patent changes the optimization objective from minimizing fitting error to maximizing/minimizing peak area under constrained fitting error. This parameter change allows the system to evaluate peak area bounds while maintaining adequate model function fitting, thereby improving impurity management reliability without sacrificing fitting accuracy
Solution Approach 2:
Instead of fitting the model function to match the measured waveform shape (conventional approach), the patent inverts the approach by using the measured waveform to constrain the model function fitting and optimize for peak area bounds. This inversion enables reliable impurity evaluation even when the fitted shape differs from the measured waveform
2Measurement precision
If optimization calculation is performed to maximize or minimize peak area while constraining loss function, then peak area bound evaluation is improved, but calculation complexity increases
Solution Approach 1:
The patent performs preliminary action by first calculating the loss function value that represents the residual between the measured chromatogram and model function, then using this pre-calculated value as a constraint in the optimization calculation. This approach simplifies the overall calculation process while maintaining peak area bound evaluation accuracy
Solution Approach 2:
The patent creates a multi-functional optimization system that can simultaneously evaluate both upper and lower bounds of peak area using the same constrained optimization framework. This universal approach handles different impurity management scenarios (maximization and minimization) with a single calculation methodology, reducing overall system complexity
Data Source
AI summary
A peak area display device includes an acquirer, a peak area calculator and a display device. The acquirer acquires measurement data measured by a chromatograph. A peak area calculator fits a model function to a chromatogram by performing optimization calculation to maximize or minimize a peak area while keeping a value to be taken by a loss function representing a residual between the chromatogram obtained from the measurement data MD and the model function in a predetermined range. The peak area calculator obtains a maximum value or a minimum value of the peak area. A display device (display) displays the maximum value or the minimum value of the peak area obtained by the peak area calculator, or information obtained by a process of the maximum value or the minimum value of the peak area.