*3.4. Hybrid Model*

The hybrid model shown in Figure 3 consists of the representative models of classification and regression combined together to increase the accuracy of the regression model. Model number 9 from the classification models (Table 2) is selected to be combined with the representative regression model (model number 8 from Table 2). In the resulting model, the output neurons of the classification model and original features are used as input features for the regression model. In this case, the eight aforementioned features were fed into the representative classification architecture, which resulted in seven categorical outputs. Then, these seven outputs with the eight original features served as the inputs of the candidate regression model. Finally, the regression model output is the DNA amount per bead.

The hybrid model is used to enhance the performance of regression. Figure 8 shows the results of the hybrid model on the train and test data, with an R\_Squared of around 97%, a slope of around 0.68, and a maximum standard error of 0.005. Similar to Figure 7, the average DNA amount per bead prediction of each output class is plotted versus its corresponding ground truth. Comparing the hybrid model (Figure 8) and regression model (Figure 7), it can be seen that the slope of the model is improved by around 21%, by knowing the fact that the ideal slope is 1. In addition, the R\_Squared value for the train and test data is improved.

**Figure 8.** Representative hybrid model on (**a**) train and (**b**) test data.

To date, many studies have shown the effectiveness of using a hybrid model to enhance the performance of various systems. For instance, Liaqat et al. [44] proposed a hybrid model approach that combines seven classification algorithms with deep learning models to identify posture detection. In this study, the outputs of the ML classifiers and deep learning models were used as inputs for a convolutional neural network (CNN) architecture. The experimental results demonstrated that the proposed hybrid approach resulted in a better performance compared to traditional machine learning methods [44]. Chieregato et al. [51] also proposed a hybrid model that integrates machine-learning with deep learning methods and is designed to be used as a tool to support clinical decisionmaking. The proposed hybrid model is capable of predicting COVID-19 outcomes from CT images and clinical data. The reason for combining several state-of-the-art algorithms to build hybrid models is to enhance the accuracy of the model and increase its capability to tolerate significant data incompleteness [52]. However, complexity arises when one or

more deep learning algorithms are combined, so careful consideration needs to be given to the selection of algorithms with different architectures to achieve better performance. Compared to conventional models, the hybrid model may take longer to train or tune.

By employing a hybrid regression model on data from impedance cytometry measurements of DNA, we have observed an 8% improvement in R\_Squared compared to the linear regression model reported by Sui et al. [5]. The results presented in this work demonstrate the ability of the proposed neural network to use the information embedded in raw impedance data to predict the amount of DNA concentration coupled to beads. Artificial intelligence (AI) approaches provide a promising new direction to efficiently extract the information embedded in the electrical signals. From an application point of view, machine learning algorithms enable the development of intelligent microfluidic platforms. These platforms are operated by data-driven models and characterized by increased automation [19]. The results presented in this work demonstrate the ability of neural networks to efficiently predict the amount of immobilized DNA that is fixed in 300 bp. In developing our methods, three network types were considered: classification, regression, and a hybrid model. After selecting the best features, we constructed classification and regression models with optimized numbers of hidden layers. In the next step, a hybrid model was presented to improve the R\_Squared of the model. The use of AI in analyzing impedance signals could present new challenges and opportunities for next-generation impedance cytometry systems.

#### **4. Conclusions**

In this study, we used a machine learning approach to predict the DNA amount per bead by leveraging electrical measurements from a Zurich Instruments tool. Multifrequency impedance cytometry was performed to measure the electrical impedance responses at 8 different frequencies, ranging from 100 kHz to 20 MHz. In this experiment 6 different DNA concentrations were coupled to paramagnetic beads and passed through the microfluidic channel. To account for device-to-device variation, the response of bare streptavidin-coated paramagnetic beads was studied.

In the next step, we employed data from impedance cytometry measurements of DNA immobilized on paramagnetic beads to develop deep learning methods that can predict the amount of immobilized DNA that is fixed in 300 bp. The dataset used in this study consists of around 105,000 pieces of data with five electrical features. As a first step, we performed feature selection to identify the best combination of features. It was shown that when the base and power for the real, imaginary, and absolute values of the peak intensity were separated, better performance was achieved. Therefore, we continued our analysis using eight features.

In the next step, three different machine learning methods were presented, namely, classification, regression, and a hybrid model, to predict the DNA amount per bead. For classification and regression, underfitting and overfitting were studied by investigating 10 different deep learning architectures. For both classification and regression problems, the architecture with the highest performance was selected as the representative model. We were able to achieve around 75% accuracy for classification and an R\_Squared of around 96% for regression. For the regression model, the average prediction values were plotted against ground truth, with a slope of 0.47 for the trend line.

To improve the performance of the regression model, a novel hybrid regression model was presented. In this approach, the best deep learning architectures for classification and regression were combined to predict the DNA amount per bead. The results showed that the proposed hybrid approach achieved a better performance as compared to the previous representative of regression models. In comparison to the regular regression model, the slope of the trend line improved by around 21%. The outcomes presented in this study demonstrate the ability of the proposed neural network to use the information embedded in raw impedance data to predict the DNA concentrations coupled to beads.

In future work, the focus will be on using automotive approaches to tune hyperparameters of deep learning methods, such as grid search, random search, and Bayesian search. The hybrid model has a longer training runtime than traditional machine learning algorithms, so further improvement and optimization are necessary to reduce the time cost. Additionally, testing different configurations of microfluid channels in terms of size and structure will be considered to assess the impact on the model's performance and create a more generalized model.

**Author Contributions:** Methodology, investigation, software, and writing—original draft preparation, M.K. and A.P.K.; formal analysis, experimental data, conceptualization, resources, and writing review and editing, J.S., N.G. and C.S.; supervision and project administration, M.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Science Foundation with Award Nos. 1711165, 1846740, and 2002511, and by a grant from the National Institute of Child Health and Human Development (R01HD102537).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to ethical constraints.

**Acknowledgments:** The authors are thankful to their respective institutions/universities for providing valuable support and funding to conduct this research work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
