Fig. 1

Schematic diagram of the numerical simulation model (color online)"

Fig. 2

Procedure for characterizing deformed cell images through OpenCV. The binarization of the original 2D cell deformation image (a) obtained from the numerical calculations results in (b). Subsequently, the cell contour is extracted, and its centroid is computed, yielding (c). Shifting the centroid to the origin and starting from Point "A" (d), the contour points are systematically selected in a counterclockwise manner with an angular interval. All these contour points are connected to the origin, forming a vector. (e) The xi and yi coordinates of the contour points are connected in a serpentine fashion, serving as the input of the NN (color online)"

Fig. 3

Architecture of the MI-CNN model. The input of the MI-CNN model is the contour data obtained by processing the deformation images of cells at time steps obtained in the finite element simulation shown in Fig. 2 (Input 1). This model includes a series of 2D convolutional layers for feature extraction and a max-pooling layer. Then, a flat layer is used to place all extracted features into a single-column feature vector. Combined with time and position information, it forms the input for a fully connected layer (Input 2). According to different settings of the loss function, it can be used to predict the elastic modulus E of cells (regression problem) and the type of constitutive equation (classification problem) (color online)"

Table 1

Overview of network setups in the MI-CNN model (ns=11)"

Fig. 4

Prediction of the MI-CNN model on E when ns=21: (a) training and validation loss history plot after 50 000 training steps and (b) R2 plot assessing the model's fitting performance to the dataset. The horizontal axis represents the E used in numerical simulations, while the vertical axis represents the NN-predicted E. Points closer to the dashed line indicate better performance. Red, blue, and green dots correspond to training, validation, and test data, with average R2 of 0.999 4, 0.999 4, and 0.999 6, respectively (color online)"

Table 2

Comparison of model accuracy with literatures"

Fig. 5

Effects of ns on the MI-CNN, CNN, and FNN models: (a) R2, (b) RRMSE, (c) RMAPE, (d) the number of NN parameters nNN (color online)"

Fig. 6

(a) Three-class classification results of the MI-CNN model (ns=16) for the K-V, N-H, and M-R constitutive models with c2/c1=0.1. (b) Comparison of cell deformations obtained using the M-R and N-H constitutive equations at an elastic modulus of E=2 kPa in the microchannel at T=11 ms (color online)"

Fig. 7

Results of classification and regression using the K-V, N-H, and M-R constitutive model datasets with c2/c1=1.0: (a) classification results of the three constitutive models using the MI-CNN model (ns=16), (b) prediction results of E using the MI-CNN model (ns=21) (color online)"

Fig. 8

E regression analysis using the MI-CNN model with ns=26 on datasets with different levels of noise: (a) small noise, (b) medium noise, and (c) large noise (color online)"

Fig. 9

Influence of elastic modulus E on the deformation ability of cells: (a) the roundness DC of cells in the region of interest and (b) the deformed cell images in the region of interest for different E (color online)"

Fig. 10

Influence of ns on the performance of the MI-CNN model under three levels of noise: (a) R2 and RRMSE; (b) RMAPE (color online)"