PCR Ct Value Determination via Rotational Transform
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for determining the cycle threshold (Ct) value in PCR amplification curves are sensitive to noisy data and have many poorly defined parameters, making them difficult to optimize, especially for data sets with high baselines.
Innovation Solution
A method involving a rotation transformation of the PCR data set to rotate the Ct value to a minimum or maximum along the intensity axis, combined with a Levenberg-Marquardt regression process to adjust the data and remove outliers, allowing for precise determination of the Ct value.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing methods (AFL value approach, second derivative method) are used to determine Ct value, then the Ct value can be identified, but the methods are sensitive to noisy data and have many poorly defined parameters making them difficult to optimize
Solution Approach 1:
The patent transforms the original fluorescence intensity data into a rotated coordinate system where the Ct value corresponds to a specific geometric feature (minimum or maximum point). This parameter transformation changes the problem from finding a threshold value in noisy data to identifying an extremum point in transformed data, which is more robust to noise and has clearly defined optimization criteria
Solution Approach 2:
The patent replaces the traditional mathematical approaches (derivative calculations, threshold setting) with a geometric transformation approach. By rotating the data coordinates and identifying extremum points, the method substitutes complex parameter optimization with a simpler geometric identification process that is less sensitive to data noise
2Measurement precision
If existing methods with many parameters (50 or more) are used, then Ct value determination is possible, but the parameters are poorly defined and very difficult to optimize
Solution Approach 1:
The patent extracts the essential feature for Ct determination by transforming the data into a coordinate system where the Ct value appears as a distinct geometric feature (extremum point). This extraction eliminates the need for multiple poorly defined parameters by focusing on a single, clearly identifiable geometric property in the transformed space
Solution Approach 2:
The patent changes the parameter space by applying a coordinate rotation transformation. This parameter change converts a problem with 50+ poorly defined parameters into a problem with a single, well-defined geometric feature (the extremum point in rotated coordinates), dramatically simplifying the determination process
3Measurement precision
If AFL value approach is used, then Ct value can be determined, but it does not work well for data sets with high baselines
Solution Approach 1:
The patent introduces a new dimension by rotating the data into a different coordinate system. This dimensional transformation allows the Ct value to be identified as a geometric feature (extremum) in the rotated space, which is independent of the baseline level in the original coordinate system, thereby improving adaptability to high baseline data
Data Source
AI summary
Systems and methods for determining the elbow or Ct value in a real-time, or kinetic, PCR amplification curve data set. A PCR data set may be visualized in a two-dimensional plot of fluorescence intensity vs. cycle number. The data set may be adjusted to have a zero slope. In one aspect, a data set is fit to a double sigmoid curve function with the function parameters determined using a Levenberg-Marquardt regression process. The determined parameters are used to subtract off the linear growth portion from the data set to provide a modified data set. For multiple data sets, all the data curves can be aligned in this manner to have a common baseline slope, e.g., a slope of zero. A rotation transform is applied to a modified data set to rotate the data about a defined coordinate such as the origin so that the data point representing the Ct value becomes a minimum or a maximum along the intensity axis. The data point representing the elbow or Ct value of the curve is identified, and this data point is then rotated back and the cycle number of the data point is returned or displayed.