Modified Sneddon Model for Cell Elastic Modulus Measurement
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Solution Overview
Problem
The Sneddon model used for measuring cell elastic modulus with AFM probes is inaccurate due to assumptions of small deformations and zero curvature radius, leading to significant errors in experimental data fitting.
Innovation Solution
ABAQUS is used to simulate the compression process of conical AFM probes into cells, considering curvature radius and half angle, to calculate and correct fitting errors, resulting in a modified formula for more accurate elastic modulus measurement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Sneddon model is used to fit the force-depth curve, then the elastic modulus can be obtained through standard least square method, but significant errors occur due to assumption of small deformation and zero curvature radius
Solution Approach 1:
The patent modifies the Sneddon model by changing key parameters: replacing the assumption of zero curvature radius with actual probe curvature radius (20-60 nm), and replacing small deformation assumption with large deformation analysis through ABAQUS simulation. The force-depth relationship is re-expressed as P=f(d,α,r,E,ν) to account for these parameter changes, significantly improving measurement accuracy.
Solution Approach 2:
The patent replaces the analytical Sneddon model with a numerical simulation approach using ABAQUS finite element software. This substitution allows the system to handle complex nonlinear contact problems and large deformations that the analytical model cannot accommodate, while still providing closed-form solutions through numerical fitting.
2Measurement precision
If AFM probe is compressed into cells at depths of tens to hundreds of nanometers, then sufficient contact area is achieved for measurement, but the deformation cannot be considered small compared to cell thickness
Solution Approach 1:
The patent transitions from static small deformation analysis to dynamic large deformation analysis by using ABAQUS simulation to model the progressive compression process. The simulation captures the evolving contact area and deformation state throughout the compression, allowing accurate characterization of the force-depth relationship under large deformation conditions.
3Device complexity
If the curvature radius of AFM probe tip is assumed to be 0 in Sneddon model, then the model remains simple, but machining accuracy limitations make the actual curvature radius 20-60 nm causing fitting errors
Solution Approach 1:
The patent applies local quality by considering the specific curvature radius of the probe tip (20-60 nm) rather than assuming a uniform zero value. The modified model incorporates the actual local geometry of the probe tip into the force-depth relationship, allowing accurate fitting that accounts for the non-zero curvature radius while maintaining model tractability through numerical methods.
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
The modified method provides a more accurate characterization of cell elastic modulus by accounting for nonlinear contact and large deformations, reducing errors associated with the Sneddon model, and aligning with macroscopic tests.
Implementation Method 1
the elastic modulus of the elastic half space, and ν is the Poisson's ratio of the elastic half space. When AFM was used to measure the elastic modulus of cells, the relationship curve between normal force P and compression depth d was obtained
Data Source
AI summary
This invention belongs to the technical field of cell mechanics and provides a modified method to fit cell elastic modulus based on Sneddon model. The process of the conical atomic force microscope probe compressing into the cell was simulated by ABAQUS. The simulation results are compared with the Sneddon model to get the error caused by Sneddon model. The fitting errors of Sneddon model under different circumstances were obtained by using the method of function fitting, so as to realize the modification of Sneddon model to fit cell elastic modulus. As a modified method to fit cell elastic modulus based on Sneddon model, it can be used to measure the elastic modulus of cells more accurately. The design process is convenient and fast. The design method is easy to master, and the process of use is convenient and simple.