A method for real-time mechanical characterisation of microcapsules

Abstract

Characterising the mechanical properties of flowing microcapsules is important from both fundamental and applied points of view. In the present study, we develop a novel multilayer perceptron (MLP)-based machine learning (ML) approach, for real-time simultaneous predictions of the membrane mechanical law type, shear and area-dilatation moduli of microcapsules, from their camera-recorded steady profiles in tube flow. By MLP, we mean a neural network where many perceptrons are organised into layers. A perceptron is a basic element that conducts input-output mapping operation. We test the performance of the present approach using both simulation and experimental data. We find that with a reasonably high prediction accuracy, our method can reach an unprecedented low prediction latency of less than 1 millisecond on a personal computer. That is the overall computational time, without using parallel computing, from a single experimental image to multiple capsule mechanical parameters. It is faster than a recently proposed convolutional neural network-based approach by two orders of magnitude, for it only deals with the one-dimensional capsule boundary instead of the entire two-dimensional capsule image. Our new approach may serve as the foundation of a promising tool for real-time mechanical characterisation and online active sorting of deformable microcapsules and biological cells in microfluidic devices.

Keywords: Machine learning; Microcapsules; Multilayer perceptron; Real-time characterisation.

Fig. 1

Illustration of an initially spherical capsule flowing in a capillary tube. The capsule reaches a steady shape after travelling a short distance. We use the footprint profile of the steady capsule to predict its membrane mechanical properties

Fig. 2

Illustration of the typical architecture of an MLP

Fig. 3

Illustration of the preparation of training samples of the MLP. The steady footprint profile of a capsule is discretised into equally spaced membrane nodes. The origin of the coordinate system is chosen as the mass centre of the capsule’s profile. Coordinates of the membrane nodes are built into a 1D vector, which serves as an input of the network

Fig. 4

Illustration of the present image processing procedure which converts the experimental image of a capsule in tube flow into a 1D footprint-boundary coordinates vector that can be processed by the MLP

Fig. 5

Comparison of the steady footprint profiles of capsules with different types of membranes (SK and Hooke’s, respectively) but the same $K_s$ and $G_s$. Capillary numbers are $C{a}^{K_s}=$ 0.055, $C{a}^{G_s}=0.165$

Fig. 6

Comparisons of the predicted a $C{a}^{K_s}$ and b $C{a}^{G_s}$ with the corresponding ground truth. The solid lines are used as guides for the eyes representing perfect agreement. The insets in (a) are steady footprint profiles of capsules with an NH membrane which show the extent of capsule deformation. The membrane elastic moduli $K_s$ and $G_s$ are related to the capillary numbers by $K_s=\mu U/C{a}^{K_s}$ and $G_s=\mu U/C{a}^{G_s}$, respectively

Fig. 7

Effect of the number of membrane nodes representing a capsule’s steady footprint profile on a prediction accuracy, indicated by the MAPE of the predicted $C{a}^{K_s}$ (the lower the MAPE, the higher the prediction accuracy), and b prediction time of the present MLP. The same training and testing data of Fig. 6 have been used

Fig. 8

a Comparison of the predicted capsule membrane area-dilatational modulus $K_s$, using the MLP and DCNN, with that reported in experiments (Risso et al. 2006). The capsule was flowed through a tube at two speeds, leading to different values of $C{a}^{K_s}$ and distinct levels of deformation. Photo insets are images of steady capsule profiles at the corresponding flow speed taken from Risso et al. (2006). b Predicted membrane shear modulus $G_s$ by the MLP and DCNN

Fig. 9

Effect of image resolution on prediction accuracy of the present MLP. a, b Capsules images with different resolutions. There are a 42 and b 138 pixels on the diameter of the undeformed capsule. c Comparison of predicted $K_s$, from images with different resolutions, with the experimental measurement (Risso et al. 2006)