A method of identifying cell suspension concentration based on bioimpedance spectroscopy

Liu Sheng-Long; Yang Lu; Zhu Cheng-Jun; Liu Kai; Han Wei; Yao Jia-Feng

doi:10.7498/aps.71.20211837

Abstract

Based on bioimpedance spectroscopy technology, a method of automatically identifying the cell suspension concentration is proposed. This method combines multiple linear regression algorithm and bioimpedance spectroscopy technology, which can identify the concentration of cell suspension quickly and accurately. Firstly, a strategy of random distribution of cell locations is proposed to simulate the true existence of cells. Secondly, 2400 groups of normal, cancerous and mixed cell models with different concentrations are generated by numerical simulation and their bioimpedance spectroscopy data are calculated.Thirdly, the multiple linear regression algorithm (MLR), support vector machine (SVM), and gradient boosting regression algorithm (GBR) are used to identify the concentration of cancerous cells. The simulation results show that the MLR is the best regression model for cell suspension concentration identification and its average goodness of fit and mean square error are 0.9997 and 0.0008respectively. Finally, the MLR is applied to the identification of red blood cell suspensions with different concentrations, the experimental results show that the average goodness of fit and mean square error are 0.9998 and 0.0079, respectively, indicating that this method has a greater ability to identify cell suspension concentrations.

Keywords:

Authors and contacts

1.
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2.
Department of Oncology, the First Affiliated Hospital with Nanjing Medical University, Nanjing 210029, China
3.
Nanjing Stomatological Hospital Medical School of Nanjing University, Nanjing 210008, China

Corresponding author: Yao Jia-Feng, jiaf.yao@nuaa.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 62071224), and the Open Fund Project of State Key Laboratory of Precision Measuring Technology and Instruments, China (Grant No. pilab2107)

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References

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Cited By

图 1 细胞仿真模型

Figure 1. Cell simulation model.

DownLoad: Full-Size Img PowerPoint

图 2 细胞位置随机分布策略示意图. 蓝色表示正常细胞, 绿色表示癌变细胞

Figure 2. Schematic diagram of random distribution strategy of cell location. Blue indicates normal cells, and green indicates cancerous cells.

DownLoad: Full-Size Img PowerPoint

图 3 部分浓度癌变细胞的Nyquist图　(a) 癌变细胞浓度为 1% 时的 5 次细胞随机分布的Nyquist图; (b) 不同癌变细胞浓度的Nyquist图

Figure 3. Nyquist plot of cancerous cells at partial concentrations: (a) Nyquist plots of randomly distributed cells at 5 times when the concentration of cancerous cells is 1%; (b) Nyquist plots of different cancerous cell concentrations.

DownLoad: Full-Size Img PowerPoint

图 4 三种回归模型对仿真数据集的训练结果　(a) 训练集的训练结果; (b) 测试集的预测结果

Figure 4. The training results of the three regression models on the simulation data set: (a) Training results of the training set; (b) predicted results on the test set.

DownLoad: Full-Size Img PowerPoint

图 5 三种回归模型对部分数据预测值与真实值的差异　(a) 训练集预测值与真实值的差异; (b) 测试集预测值与真实值的差异

Figure 5. The difference between the predicted value and the true value of partial data by three regression models: (a) The difference between the predicted value of the training set and the true value; (b) the difference between the predicted value of the test set and the true value.

DownLoad: Full-Size Img PowerPoint

图 6 生物阻抗谱检测实验设备　(a) 实验设备原理图; (b) 传感器结构图

Figure 6. Bioelectrical impedance spectroscopy instrument: (a) Schematic diagram of experimental equipment; (b) sensor structure diagram.

DownLoad: Full-Size Img PowerPoint

图 7 MLR对数据集预测值与真实值的差异, 内插图是MLR预测值与真实值的误差放大图像

Figure 7. The difference between the predicted value and the true value of the data set by MLR. The inset is an enlarged image of the error between the MLR predicted value and the true value.

DownLoad: Full-Size Img PowerPoint

表 1 仿真参数汇总^[23]

Table 1. Summary of simulation parameters.

	参数	正常B细胞	癌变B细胞
电导率 σ/(S·m^–1)	背景溶液	0.6	0.6
	细胞膜	5.6 × 10^–5	9.1 × 10^–6
	细胞质	1.31	0.48
	核膜	1.11 × 10^–2	4.4 × 10^–3
	核质	2.04	1.07
相对介电常数 ε	背景溶液	80	80
	细胞膜	12.8	9.8
	细胞质	60	60
	核膜	106	60.3
	核质	120	120
几何参数/μm	仿真区域 L × L	20 × 20	20 × 20
	电极长度 l	4	4
	细胞半径 R₁	3.3	5.2
	细胞核半径 R₂	2.8	4.4
	细胞膜厚 d₁	0.007	0.007
	核膜厚度 d₂	0.04	0.04

DownLoad: CSV

表 2 仿真数据的三种回归算法五折验证结果

Table 2. Validation results of three regression algorithms for simulation data.

	MLR		SVR		GBR
	R²	MSE	R²	MSE	R²	MSE
1	0.9999	0.0006	0.0006	0.0257	0.9994	0.0066
2	0.9995	0.0009	0.0009	0.0313	0.9985	0.0171
3	0.9998	0.0006	0.0006	0.0336	0.9986	0.0179
4	0.9999	0.0012	0.0012	0.0267	0.9986	0.0156
5	0.9996	0.0008	0.0008	0.0335	0.9987	0.0176
平均数	0.9997	0.0008	0.0008	0.0302	0.9988	0.0150

DownLoad: CSV

表 3 每种红细胞悬浮液浓度下的平均绝对误差

Table 3. The average absolute error of each red blood cell suspension concentration.

浓度/%	0	10	15	20	25	30	40	50
平均绝对误差	0.0104	0.0124	0.0113	0.0134	0.0129	0.0165	0.0158	0.0161

DownLoad: CSV

表 4 MLR回归算法的五折交叉验证结果

Table 4. Cross validation results of MLR regression algorithm.

	1	2	3	4	5	平均数
R²	1.0000	0.9998	0.9999	0.9996	0.9999	0.9998
MSE	0.0015	0.0021	0.0152	0.0035	0.0173	0.0079

DownLoad: CSV

[1]	付小芬, 熊小波 2017 检验医学与临床 14 274 Google Scholar Fu X F, Xiong X B 2017 Lab. Med. Clin. 14 274 Google Scholar
[2]	张瑛, 范卫民, 陈哲峰 2005 江苏医药 10 762 Google Scholar Zhang Y, Fang W M, Chen Z F 2005 Jiangsu. Med. J 10 762 Google Scholar
[3]	任丽蓉, 何蔺, 刘涛, 王浩宇 2020 西部医学 32 1132 Google Scholar Ren L R, He L, Liu T, Wang H Y 2020 Med. J. West Chin. 32 1132 Google Scholar
[4]	韩莎莎, 郭忠慧, 朱自严 2015 中国输血杂志 28 1463 Google Scholar Han S S, Guo Z H, Zhu Z Y 2015 Chin. J. Blood Transfusion 28 1463 Google Scholar
[5]	傅怡, 王洋, 白帆, 吴洁, 孙仁, 丁祖蓉, 董澄 2015 医用生物力学 30 392 Google Scholar Fu Y, Wang Y, Bai F, Wu J, Sun R, Ding Z R, Dong C 2015 J. Med. Biomech. 30 392 Google Scholar
[6]	孔雁, 姜达 2006 中国肿瘤 15 172 Google Scholar Kong Y, Jiang D 2006 Chin. Cancer 15 172 Google Scholar
[7]	冯也倩 2009 硕士学位论文 (长沙: 中南大学) Feng Y Q 2009 M. S. Thesis (Changsha: Central South University) (in Chinese)
[8]	杨蕊, 邹明强 2004 分析测试学报 06 124 Google Scholar Yang R, Zou M Q 2004 J. Instrumental. Anal. 06 124 Google Scholar
[9]	Nilsson G E, Zhai H, Chan H P, Farahmand S, Maibach H I 2009 Skin Res. Technol. 15 6 Google Scholar
[10]	Guo T, Liu F, Liu Y, Chen N K, Guan B O, Albert J 2014 Biosens. Bioelectron. 55 452 Google Scholar
[11]	杨宇祥, 乔洋 2013 仪器仪表学报 34 908 Google Scholar Yang Y X, Qiao Y 2013 Chin. J. Sci. Instrum. 34 908 Google Scholar
[12]	姚佳烽, 万建芬, 杨璐, 刘凯, 陈柏, 吴洪涛 2020 物理学报 69 163301 Google Scholar Yao J F, Wan J F, Yang L, Liu K, Chen B, Wu H T 2020 Acta Phys. Sin. 69 163301 Google Scholar
[13]	姚佳烽, 姜祝鹏, 徐梓菲, 刘夏移, 陈柏, 吴洪涛 2018 生物化工 4 4 Google Scholar Yao J F, Jiang Z P, Xu Z F, Liu X Y, Chen B, Wu H T 2018 Biol. Chem. Eng. 4 4 Google Scholar
[14]	Sun T P, Ching T S, Cheng C S, Huang S H, Chen Y J, Hsiao C S, Chang C H, Huang S Y, Shieh H L, Liu W H 2010 Cancer Epidemiol. 34 207 Google Scholar
[15]	Mellert F, Kai W, Schneider C, Dudykevych T, Preusse C J 2011 IEEE Trans. Biomed. Eng. 58 1511 Google Scholar
[16]	Czerniec S A, Ward L C, Lee M J, Refshauge K M, Beith J, Kilbreath S L 2011 Support. Care Cancer 19 703 Google Scholar
[17]	沈继云 2020 信息技术与信息化 5 228 Google Scholar Shen J Y 2020 Inf. Technol. Informatization 5 228 Google Scholar
[18]	柯鹏飞, 蔡茂国, 吴涛 2020 计算机工程 46 262 Google Scholar Ke P F, Cai M G, Wu T 2020 Comput. Eng. 46 262 Google Scholar
[19]	Kimberly S, Yiqiang S, Lisa G, Heather J, Maureen S, Mendonca E A 2020 Health Inform. J. 26 388 Google Scholar
[20]	刘泉声, 王栋, 朱元广, 杨战标, 伯音 2020 岩土力学 41 319 Google Scholar Liu Q S, Wang D, Zhu Y G, Yang Z B, Bo Y 2020 Rock Soil Mech. 41 319 Google Scholar
[21]	Keprate A, Ratnayake R M C 2017 2017 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM) Singapore, December 10-13, 2017 p1331
[22]	王征征, 张卫钢, 孙道斌, 张鑫, 王培丞 2020 计算机与数字工程 48 546 Google Scholar Wang Z Z, Zhang W G, Sun D B, Zhang Xin 2020 Comput. Digital Eng. 48 546 Google Scholar
[23]	Joshi R P, Qin H, Schoenbach K H 2004 3 rd International Symposium on Nonthermal Medical/Biological Treatments Using Electromagnetic Fields and Ionized Gases San Antonio, TX, the United States of Ameica, June 11–13, 2003 p1677
[24]	Jiang Z, Yao J, Wang L, Wu H, Huang J, Zhao T, Takei M 2019 IEEE Sens. J. 19 5979 Google Scholar
[25]	Li C, Xu P 2021 Neural Comput. Appl. 33 613 Google Scholar
[26]	Smola A J, Schölkopf B 2004 Stat. Comput. 14 199 Google Scholar
[27]	Zhang J G, Li Y Y, Cao J 2011 Proceedings of 2011 IEEE International Conference on Computer Science and Automation Engineering Shanghai China, June 10–12, 2011 p47

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