Abstract
DEVELOPMENTAL BIOLOGY Animal Cells and Systems Vol. 16, No. 2, April 2012, 121126 Deformation prediction by a feed forward artiﬁcial neural network during mouse embryo micromanipulation a b b Ali A. Abbasi *, G.R. Vossoughi and M.T. Ahmadian a b School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran; Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran (Received 12 June 2011; received in revised form 13 September 2011; accepted 3 October 2011) In this study, a neural network (NN) modeling approach has been used to predict the mechanical and geometrical behaviors of mouse embryo cells. Two NN models have been implemented. In the first NN model dimple depth (w), dimple radius (a) and radius of the semi-circular curved surface of the cell (R) were used as inputs of the model while indentation force (f) was considered as output. In the second NN model, indentation force (f), dimple radius (a) and radius of the semi-circular curved surface of the cell (R) were considered as inputs of the model and dimple depth was predicted as the output of the model. In addition, sensitivity analysis has been carried out to investigate the influence of the significance of input parameters on the mechanical behavior of mouse embryos. Experimental data deduced by Fluckiger (2004) were collected to obtain training and test data for the NN. The results of these investigations show that the correlation values of the test and training data sets are between 0.9988 and 1.0000, and are in good agreement with the experimental observations. Keywords: artiﬁcial neural network; biological cells; error back propagation algorithm; sensitivity analysis 1. Introduction On one hand, although these experimental techni- ques have been a significant influence in biological cell Living cells are always exposed to mechanical stimu- studies, hey have problems such as difficult implemen- lation in the human body. Often, it is important for tation, poor controllability, high cost, etc. (Tan et al. us to investigate how cells react mechanically to 2010). On the other hand, in some cases it is reported physical loads and how the distribution and transmis- that using different mechanical models for the same sion of these mechanical signals are ultimately con- type of cells has led to differing mechanical properties. verted to chemical and biological responses in the For example in studying neutrophils, derived mechan- cells (Lim et al. 2006; Lee and Rhee 2009). Conse- ical properties using the Newtonian liquid drop model quently, to understand the cell functions and beha- and the Maxwell model are different (Lim et al. 2006). vior, the relationship between cellular deformations Other methods which are usually used in cell and mechanical forces in living cells is important. In indentation experiments are the contact mechanics order to study the biomechanical properties of models, including the Hertzian model and the Sneddon biological cells, recently there has been an extensive model. These models cannot be used where large interest in the literature. Because of the heterogeneous deformations are considered because large deforma- nature of biological cells, different experimental tions violate the small deformation assumption of the techniques are used and devised to probe the response contact mechanics models. Furthermore, in contact of cells such as atomic force microscopy (AFM) ( Sen mechanics models only a local dimple geometry change et al. 2005; Lulevich et al. 2006), laser/optical is taken into account and the global geometry of the tweezers (Dao et al. 2003), microplate stretcher deformed cell remains unchanged. Other limitations of (Thoumine and Ott 1997), micropipette aspiration the contact mechanics models in large deformations (Vaziri and Kaazempur Mofrad 2007) and tapered have been reported elsewhere (Sun et al. 2003; Kim micropipette (He et al. 2007). et al. 2008). These different experimental techniques have led to In previous investigations on biological cells (Sun a variety of different mechanical models developed by et al. 2003) a point-load model has been proposed to various researchers to interpret and explain the experi- predict the indentation force of biological membranes, mental data such as cortical shell liquid core models with its analytical solution given as follows: (or liquid drop models), solid models, fractional "# 3 2 4 2 derivative models, cytoskeletal models for adherent 2pEhw 3 4f þ f þ 2ln f F ¼ (1) cells, a spectrin-network model for erythrocytes, etc. 2 2 2 a ð1 nÞ ð1 f Þð1 f þ ln f Þ (Lim et al. 2006). *Corresponding author. Email: a_abbasi@mech.sharif.ir ISSN 1976-8354 print/ISSN 2151-2485 online # 2012 Korean Society for Integrative Biology http://dx.doi.org/10.1080/19768354.2011.629680 http://www.tandfonline.com 122 A.A. Abbasi et al. Where f ¼ c is the indenter radius and a is dimple activation function that has been used between the radius of the cell. Here, n, E, h and F are the Poisson processing elements is a hyperbolic sigmoid transfer ratio, Young’s modulus, thickness of membrane and function as follows: measured force, respectively. Some limitations of point-load models are as 1 e f ðxÞ¼ (2) follows: this model assumes that membrane stress 1 þ e within the dimple is uniform. Also, residual stress of Since the normalizing operation depends on the the membrane is assumed to be zero, which is not the selected activation function, the data were normalized case in reality (Sun et al. 2003). On the other hand, it within the range of91 (Bahrami et al. 2005): has been assumed that the interaction of the cytoplasm and membrane is uniform, which it is not in reality. X X Furthermore, as can be seen, Eqn. (1) is somewhat min X ¼ (3) complicated, and it may be subject to variations due to X X max min parametric uncertainties. Where X and X are the minimum and maximum min max Hence, the need is felt for simpler, cheaper and values of X; X is the normalized value and n is the more precise models that can relate the deformed cell number of the data set. The output y produced by the configuration to external applied force and do not neuron iin the layer l is given by the following include incorrect assumptions. relationship (Jajarmi and Eivani 2009): One engineering approach for prediction of the indentation force or dimple depth is based on the utilization of artificial neural networks (ANNs). y ¼ f ð w þ bÞ (4) i ij A neural network consists of many processing elements j¼1 which operate in parallel and are connected by several Here f is the activation function, n is the number of links with variable weights and biases, which are elements in the layer l 1, w is the weight associated typically adjusted during the training process (Bahrami ij with the connection between the neuron i in the layer et al. 2005). land the neuron j in the layer l 1, whose output is Our approach includes the following aspects: first, w , and bis the offset or bias which shifts the an ANN model proposed previously (Ahmadian et al. activation function along the basic axes. An iterative 2010) is reviewed and further extended. Second; some algorithm adjusts the weights of connections while the untrained samples are preserved for testing proposes to y response of the output neurons can be close to the present the prediction capability of the ANN model. Third, sensitivity analysis is performed to investigate the desired response t, which can be tested by minimizing parameters influencing indentation force and dimple the learning error in each training (i.e. epoch), defined depth. Fourth, the results of thesensitivity analysis are by mean square error (MSE) (Dashtbayazi et al. compared with previous analytical analysis to further 2007): verify the results of the ANN modeling approach. MSE ¼ ðt y Þ (5) i i 2. Artificial neural network technique i¼1 Artificial neural networks (ANNs), also called ‘neural Where N is the total number of training patterns, t the networks’, are collections of small individual intercon- target (i.e. desired) output value, and y is the network nected processing units with weights and biases asso- output value. The performance of the developed net- ciated with each connection. Learning is the first step work was evaluated with the help of Bahrami et al. necessary in including intelligence in neural networks. 2005; Jajarmi and Eivani 2009; Yazdanmehr et al. 2009: During the learning process, the network autono- mously adjusts the connection weighs and biases 1. Drawing a scatter diagram of estimated versus among the processing units according to imposed experimental values. learning rules and, thereby, obtains unique knowledge 2. Computing mean absolute error (MAE) using: from the data. In the second step, the learned neural network generates accurate output from the input data jj x y MAE ¼ (6) and, thereby, the network model is prepared for subsequent applications (Bahrami et al. 2005). 0 0 In these investigations, the feed-forward multilayer Where x ¼ X X , X is the target output and X is the perceptron has been used and trained with the error mean of X and y ¼ Y Y , Y is the network output back propagation algorithm (Nguyen et al. 1944). The and Y is the mean of Y. Animal Cells and Systems 123 3. Sensitivity analysis 3.2. Relative importance (RI) Sensitivity analysis is used to determine the relative This index which is referred to as relative importance, importance of each of the input parameters on the RI, evaluates the contribution of each input variable to model outputs. In other words, this analysis can help to the output by interpreting the interconnection weights identify input parameters influencing the model beha- of the neural network model (Mandal et al. 2009). If a vior. In the case of cell properties the available NN well-trained multilayer neural network model with an models have been used to identify more important m n 1architecture (i.e. m input nodes, n hidden input parameters for predicting deformation of the nodes and 1 output node) is considered, the following mouse embryo. In this study two techniques are used to procedure can be used to calculate the relative im- identify the most sensitive factors influencing predicted portance of input variables as follows: deformation: relative strength of effect (RSE) and relative importance (RI) methods. Step 1: a row vector, M (1 n), for the interconnection weights between the hidden layer nodes (n nodes) and the output layer nodes is constructed. Step 2: a m n matrix, W , for the interconnection 3.1. Relative strength of effect (RSE) weights between the input layer nodes (m) and the hidden layer nodes (n) is constructed. This technique was proposed by Yang and Zhang Step 3: the row vector, R ¼ MW , in which (1997). According to this technique, if there is a trained R ¼½ r r r ::: r , is calculated. 1 2 3 m neural network with a given sample data set, this Step 4: the relative importance, RI, of an input node is method can be used to recognize the most important calculated as follows: parameters in the model, hierarchically. Based on this criterion, inputs with higher RSE have a stronger effect jj r RI ¼ 100 ð%Þ; i ¼ 1 m: (10) on the model outputs. i m jj r According to Yang and Zhang (1997), the RSE can i¼1 be defined as follows: XX X RSE ¼ C ::: W Gðe ÞW Gðe Þ 4. The data base j k k j j j n n1 n n jn jn1 j1 The data used for this investigation were captured from experimental observations by Fluckiger (2004). These experimental data were generated by Yu Sun and his W Gðe ÞW Gðe Þ:::W Gðe Þ j j j j j j ij j n2 n1 n1 n3 n2 n2 1 1 co-workers (Sun et al. 2003) and come from multiple (7) indentation tests which have been done on a single embryo. The detailed experimental observations of the mouse embryo cell are presented in Table 1. To Where C is the normalized constant which controls the become further familiar with the method of sample maximum absolute value of RSE as unit, G denotes preparation, the readers can refer to Sun et al. (2003). the differentiation of the activation function, W is the Among these experiments, 70% of the data set (eight connected weight and e is the input signal which samples) was randomly selected for training the ANN comes into layer k. models while 30% percent of the remaining data sets Table 1. Experimental data sets fom mouse embryo (Fluckiger 2004). Data Dimple Radius of the Semi-circular Curved surface of the Measured Force Number Radius(um) Dimple Depth(um) cell(um) (uN) 1 18.375 11.754 12.76 1.052 2 18.7S5 13.887 12.54 2.379 3 19.572 15.039 12.24 3.418 4 19.866 16.425 11.76 4.511 5 20.412 17.289 11.52 5.655 6 20.748 17.496 11.14 6.013 7 22.113 19.017 10.68 6.762 a 22.512 21.006 10.13 8.148 9 22.879 22.905 10.10 9.664 10 22.932 24.399 9.860 11.96 11 23.079 25.155 9.650 13.39 124 A.A. Abbasi et al. (three samples) were used to validate the ability of the Table 2b. Key neural network model parameters for dimple depth prediction. ANN models to predict the indentation force and dimple depth of the mouse embryos. In the first NN Key parameter Value model used for indentation force prediction samples 2, 5 and 10 were randomly selected while in the second Layers 3 Hidden layer 1 NN model samples 3, 6 and 9 were randomly selected Neurons in hidden layer 5 to predict cell deformation. Neurons in input layer 2 Neurons in output layer 1 Learn rule Delta rule 5. Results and discussion Transfer function Hyperbolic sigmoid 5.1. Neural network results Learning momentum 0 Learning rate 0.15 Two ANN models with one hidden layer have been used and trained using the error back propagation algorithm (Nguyen et al. 1944). The inputs of the first samples 3, 6 and 9 were randomly selected for testing ANN model are dimple depth, dimple radius and and the remaining data were used for training the radius of the semi-circular curved surface of the cell model. The correlation values between experimental and indentation force is considered as an output, while and trained data are calculated as 1.0000 and 0.9999 in the second ANN model indentation force, dimple for the models that have been used for prediction of radius and radius of the semi circular curved surface of indentation force and dimple depth, respectively. More- the cell are used as inputs and dimple depth is predicted over, the corresponding MAEs of the indentation force in the output. The network’s state of knowledge can be and dimple depth are 1.60% and 6.01%, respectively. As determined by the weight and bias values when MAE can be seen, the NN models are successful in prediction reaches the minimum value. Therefore, the optimum of indentation force and dimple depth. number of hidden units can be learned. The predicted indentation force and dimple depth The architectures of the ANN models that have by ANN models versus experimental values for testing been used for prediction of indentation force and sets are shown in Figures 1 and 2, respectively. The test dimple depth are presented in Table 2a and 2b, data sets were only used for testing purposes and are respectively. not involved in the model training process. MAE values for various hidden units in the models Consequently, the precision of the ANN models in that have been used for prediction of indentation force prediction is obviously confirmed by their performance and dimple depth were calculated. According to these on the testing data sets. The correlation value and MAE calculations, for the model used for prediction of for the testing data set in prediction of indentation force indentation force, the ANN with one hidden layer are 0.9999 and 4.65%, respectively, and the correspond- and 13 hidden units yields the smallest MAE (8.3556%) ing values in prediction of dimple depth are 0.9988 and while in the corresponding model used for prediction of 16.52%, respectively. These results validate that a good dimple depth, the smallest MAE is yielded when the model has one hidden layer and five hidden units (6.2965%). In the first neural network model, samples 2, 5 and 10 were randomly selected for testing Data points purposes, and the remaining samples were used for Best linear fit (y=x) training the network, while in the second investigation, Table 2a. Key neural network model parameters for indenta- tion force prediction. 8 Key parameter Value Layers 3 Hidden layer 1 Neurons in hidden layer 13 Neurons in input layer 2 Neurons in output layer 1 0 2 4 6 8 10 12 14 Learn rule Delta rule Experimental force (uN) Transfer function Hyperbolic sigmoid Learning momentum 0 Figure 1. Comparison of the predicted and experimental Learning rate 0.15 indentation force values using testing data. Predicted force (uN) Animal Cells and Systems 125 1.2 Data points Best linear fit (y=x) 0.8 0.6 0.4 0.2 -0.2 Dimple radius Indentation force Radius of the 0 semi-circular curve Network input 0 5 10 15 20 25 Experimental dimple depth (um) Figure 3. Signiﬁcance of the input parameters on deforma- tion using the RSE method. Figure 2. Comparison of the predicted and experimental dimple depth values using testing data. force-deformation diagram of mouse embryo according to the analysis of Flu ¨ ckiger (2004) in comparison with correlation occurred between experimental and pre- the experimental data is presented in Figure 5. dicted observations. As can be seen from this figure, the force-deforma- As can be seen from these results, for a given cell tion curve of the analysis which includs the effect of deformed by an indenter this simple ANN model semi-circular curved surface (R) is the same as that together with the experimental data is capable of which ignores this effect. accurately predicting the external applied force in an These results are another validation of the correct online process without needing a force sensor or, vice implementation of ANN models. versa, can be used to predict the deformed cell shape without needing a visual or displacement sensor and can reduce experimental cost. However, the price that must be paid for this simplicity and low-cost imple- 6. Conclusion mentation is that we cannot measure the mechanical In the present paper, ANN modeling has been applied to properties of biological cells such as Young’s modulus predict the geometrical and mechanical behavior of by this modeling approach. mouse embryos in a cell injection experiment. The predicted values obtained using the ANN approach are in good agreement with the experimental observa- 5.2. Sensitivity analysis results tions. Moreover, in order to ascertain the importance of each input parameter on the predicted deformation, The results of sensitivity analysis using the trained sensitivity analysis has been also done. Results of the ANN for deformation prediction are presented in sensitivity analysis show that indentation force is the Figures 3 and 4. Figure 3 shows the significance of most important parameter in prediction of deformation the input parameters on predicted deformation using the RSE method while the corresponding results using the RI method are shown in Figure 4. According to these figures, indentation force is the most effective parameter for predicted deformation, whereas the radius of the semi-circular curve (R) has not so much effect on output. In this figure, the radius of the semi-circular curve has negative RSE and RI 20 values, which means that with increasing values of R the predicted deformations are decreased while with decreasing the values of R the predicted deformations are increased. These figures show that radius of the semi-circular curve has a negligible effect on output -10 Dimple radius Indentation force Radius of the and it can be removed from the model inputs. Network input semi-circular curve These results have a good agreement with previous analysis reported by Flu ¨ ckiger (2004). For a better Figure 4. Signiﬁcance of the input parameters on deforma- understanding of the results of sensitivity analysis, the tion using the RI method. Predicted dimple depth (um) Relative importance (%) RSE 126 A.A. Abbasi et al. –5 He JH, Xu W, Zhu L. 2007. Analytical model for extracting x 10 1.4 mechanical properties of a single cell in a tapered Without the effects of semi-circular curved surface(R) With the effects of semi-circular curved surface(R) micropipette. Appl Phys Lett. 90:023901023903. Experimental observations 1.2 Jajarmi P, Eivani AR. 2009. Modeling the electrical resistivity of ZnMnS nanocrystalline semiconductors. Comput Mater Sci. 46:124127. Kim Y, Shin JH, Kim J. 2008. Atomic force microscopy 0.8 probing for biomechanical characterization of living cells. Paper presented at: Proceedings of the 2nd Biennial 0.6 IEEE/RAS-EMBS International Conference on Biome- dical Robotics and Biomechatronics, Scottsdale, AZ, 0.4 USA. Lee A, Rhee M. 2009. Identiﬁcation and expression patterns 0.2 of kif3bz during the zebraﬁsh embryonic development. Anim Cells Syst. 13:411418. 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 Lim CT, Zhou EH, Quek ST. 2006. Mechanical models for –5 x 10 living cells a review. J Biomechan. 39:195216. Dimple depth (m) Lulevich V, Zink T, Chen HY, Liu FT, Liu GY. 2006. Cell mechanics using atomic force microscopy-based single- Figure 5. Investigation of effects of the semi-circular curved cell compression. Langmuir. 22:81518155. surface (R) using the force-deformation curve from previous Mandal S, Sivaprasad PV, Venugopal S, Murthy KPN. 2009. analysis (Fluckiger 2004). Arti?cial neural network modeling to evaluate and predict the deformation behavior of stainless steel type of the mouse embryo and the semi-circular curved AISI 304L during hot torsion. Appl Soft Comput. 9:237 surface of the cell has negligible effect on the predicted Nguyen HT, Prasad NR, Walker CR, Walker AE. 1944. A deformation. The developed models are suitable for ﬁrst course in fuzzy and neural control. Boca Raton: computing accurate reaction force on tools (for example Chapman & Hall/CRC. p. 237241. in cell manipulation tasks) and for computing deforma- Sen S, Subramanian S, Discher DE. 2005. Indentation and tion of biological cells for the virtual reality-based adhesive probing of a cell membrane with AFM: medical simulations. theoretical model and experiments. Biophys J. 89:3203 Sun Y, Wan KT, Roberts KP, Bischof JC, Nelson BJ. 2003. References Mechanical property characterization of mouse zona pellucida. IEEE Trans Nanobiosci. 2:279286. Ahmadian MT, Vossoughi GR, Abbasi AA, Raeissi P. 2010. Tan Y, Sun D, Huang W, Cheng SH. 2010. Characterizing Cell deformation modeling under external force using mechanical properties of biological cells by microinjec- artiﬁcial neural network. J Solid Mech. 2:190198. tion. IEEE Trans Nanobiosci. 9:171180. Bahrami A, Mousavi Anijdan SH, Madaah Hosseini HR, Thoumine O, Ott A. 1997. Time scale dependent viscoelastic Shafyei A, Narimani R. 2005. Effective parameters and contractile regimes in ﬁbroblasts probed by micro- modeling in compression of an austenitic stainless steel plate manipulation. J Cell Sci. 110:21092116. using artiﬁcial neural network. Comput Mater Sci. Vaziri A, Kaazempur Mofrad MR. 2007. Mechanics and 34:335341. deformation of the nucleus in micropipette aspiration Dao M, Lim CT, Suresh S. 2003. Mechanics of the human experiment. J Biomechan. 40:20532062. red blood cell deformed by optical tweezers. J Mech Phys Yang Y, Zhang Q. 1997. A hierarchical analysis for rock Solids. 51:22592280. engineering using artiﬁcial neural networks. Rock Mech Dashtbayazi MR, Shokuhfar A, Simchi A. 2007. Artiﬁcial Rock Engg. 30:207222. neural network modeling of mechanical alloying process Yazdanmehr M, Mousavi Anijdan SH, Samadi A, Bahrami for synthesizing of metal matrix nanocomposite powders. A. 2009. Mechanical behavior modeling of nanocrystal- Mater Sci Eng A. 466:274283. Fluckiger M. 2004. Cell membrane mechanical modeling for line nial compound by a feed-forward back propagation microrobotic cell manipulation [diploma thesis]. Zurich: multi-layer perceptron ANN. Comput Mater Sci. ETHZ Swiss Federal Institute of Technology, WS03/04. 44:12311235. Force (N)
Journal
Animal Cells and Systems
– Taylor & Francis
Published: Apr 1, 2012
Keywords: artificial neural network; biological cells; error back propagation algorithm; sensitivity analysis