Dispersion Particle Concentration Measurement via Stochastic Motion Modeling
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Solution Overview
Problem
Existing methods for determining particle concentration in dispersions, such as single particle tracking, face challenges in accurately calculating concentration without prior knowledge of the effective observation volume and are prone to sampling bias, especially for particles smaller than 500nm, due to variations in image processing settings and particle mobility.
Innovation Solution
A method and system that derive the effective observation volume from time-dependent observations, accounting for stochastic motion-related parameters to accurately determine particle concentration without calibration, and correct for sampling bias by modeling particle trajectories and mobility probabilities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If single particle tracking is used to determine particle concentration, then particle concentration can be measured without labels, but accurate concentration determination requires prior knowledge of effective observation volume which is difficult to obtain
Solution Approach 1:
The system performs self-calibration by using the particle trajectories themselves to determine the effective observation volume. The methodology extracts calibration information from the motion characteristics of particles within the observation volume, eliminating the need for external reference measurements or separate calibration procedures.
Solution Approach 2:
The invention changes the approach from using fixed geometric parameters to using dynamic motion parameters (trajectory length, diffusion coefficients) to characterize the observation volume. By relating particle motion statistics to the effective observation volume, the system achieves accurate concentration measurements without traditional calibration.
2Productivity
If particle concentration is determined by counting trajectories in a fixed time interval, then concentration can be calculated, but fast moving particles are overrepresented leading to sampling bias
Solution Approach 1:
The system uses feedback from trajectory length measurements to correct concentration calculations. By monitoring the distribution of trajectory lengths and using this information to weight or adjust particle counts, the methodology compensates for the overrepresentation of fast-moving particles and achieves unbiased concentration measurements.
Solution Approach 2:
The invention collects excessive trajectory data including short trajectories that would normally be discarded. By incorporating all trajectories regardless of length and using statistical methods to extract accurate concentration information, the system avoids bias from selective filtering while maintaining measurement efficiency.
3Ease of operation
If effective observation volume is assumed to be known a priori, then concentration calculations are simplified, but the assumption leads to inaccurate results when particles and medium differ from reference conditions
Solution Approach 1:
The system performs preliminary analysis of particle trajectories to determine the effective observation volume specific to each measurement condition. By extracting calibration parameters from the actual experimental data before concentration calculation, the methodology ensures accuracy while maintaining operational simplicity through automated procedures.
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
Enables accurate determination of particle concentration and size distributions for both monodisperse and polydisperse samples, including particles smaller than 500nm, by inherently accounting for observation volume and mobility-dependent probabilities, thereby improving measurement precision and reducing bias.
Implementation Method 1
particles undergoing at least partially stochastic motion in a dispersion
Data Source
AI summary
A method for determining a size or shape related parameter of an effective observation volume for an observation technique for particles undergoing at least partially stochastic motion in a dispersion is described. The method is based on a time-series of observations. The method comprises determining one or more time- dependent characteristics of the dispersion or its particles based on the time-series of observations, determining at least one stochastic motion-related parameter representative for the at least partially stochastic motion of at least one particle in the dispersion, and determining a size or shape related parameter of the effective observation volume by modeling of the at least partially stochastic motion of the particle movement in the dispersion, the modeling taking into account the at least one stochastic motion-related parameter and the determined one or more characteristics.