**1. Introduction**

DNA, the carrier of genetic information, is highly important in the biology and molecular electronics fields [1]. In addition to its biological role, DNA is a topic of significant interest with applications in nanotechnology, self-assembly, and structural flexibility, making it a subject of great interest [2–4]. Moreover, the DNA molecule is a source of rich electrical properties and has the potential to be used as a conducting material in electronic circuits [1]. Due to its electrical properties, we can utilize a multi-frequency lock-in amplifier (Zurich Instruments HF2A, Zurich, Switzerland) to measure the impedance response of beads coupled with different DNA amounts [1]. In this instrument, when a paramagnetic bead or particle passes through the sensing region, it interferes with the AC electric field between two electrodes, and consequently, a momentary increase in impedance can be observed [5]. Nowadays, an impedance-based cytometer can be implemented for the detection of bacteria, DNA amount per bead, cancer cells, and many other biological cells [5–9]. Many studies have shown the importance and application of microfluidic biosensors as a fast, reliable, and rapid platform for early-stage disease detection, as well as many other applications. For example, Mok et al. studied the development of a microfluidic platform to detect proteins [10]. Mahmoodi et al. developed a biosensor platform to detect cortisol in in small volumes of human serum [11]. The goal of this study was to create a cost-effective point-of-care and self-testing platform. Furniturewalla et al. developed a platform to count

**Citation:** Kokabi, M.; Sui, J.; Gandotra, N.; Pournadali Khamseh, A.; Scharfe, C.; Javanmard, M. Nucleic Acid Quantification by Multi-Frequency Impedance Cytometry and Machine Learning. *Biosensors* **2023**, *13*, 316. https:// doi.org/10.3390/bios13030316

Received: 11 January 2023 Revised: 15 February 2023 Accepted: 20 February 2023 Published: 24 February 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the number of blood cells from a pin-prick blood sample pipetted into a standard microfluidic PDMS chip [12]. Xie et al. developed a biomolecular sensing method that utilizes an array of nanoscale wells functionalized with antibodies. The method monitors changes in ionic resistance as the target protein binds inside the wells [13]. On the other hand, the development of microfluidic chips and experimental design often involves extensive investment and time effort, and it is prone to user bias. In this paper, we propose a machine learning (ML)-based model to address this difficulty.

Artificial intelligence (AI) has grown rapidly over the past decade and can be widely used in many aspects of biological information, ranging from drug discovery prediction to cancer prognosis [14–18]. Artificial intelligence employs a variety of statistical methods to detect and extract key features from complex datasets. In addition, AI provides a robust framework for creating feature representations from high-dimensional inputs and generalizing knowledge to new scenarios [19]. In recent years, the integration of machine learning methods with microfluidics has become a popular area of research. The combination of microfluidics, which generates large amounts of data, with machine learning for the analysis of these complex data sets represents a promising development in biotechnology [19–24]. To date, many studies have shown the application of machine learning to impedance cytometry. For example, Caselli et al. demonstrated the ability of neural networks to decipher impedance cytometer signals. They utilized an experimental dataset to predict single cell features, which were then used as inputs for classifier models [25]. Patel et al. applied a designed biosensor for detecting hemoglobin biomolecules with high sensitivity using polynomial regression models [26]. Schütt et al. applied a k-means algorithm for subpopulation clustering of peripheral blood mononuclear cells, based on peak voltage and phase [27]. As another example, Honrado et al. developed an ML-based method of classification of impedance data to distinguish and quantify cellular subpopulations at the early apoptotic versus late apoptotic and necrotic states [28]. Ahuja et al. used a support vector machine (SVM) classifier to discriminate between live and dead breast cancer cells by using the peak impedance magnitude and phase [29]. Feng et al. used fully connected networks to estimate three biophysical parameters based on the peak impedance amplitude at four frequencies, allowing them to classify five cell types [30]. Meanwhile, Sui et al. used a combination of multi-frequency impedance cytometry and supervised machine learning to classify particle barcodes [31].

Given the clinical significance of DNA, here we examine if a machine learning approach could facilitate and expedite the process of identifying the DNA amount per bead. In this analysis, six different concentrations of DNA, with a fixed length of 300 bp (base pairs), are coupled with 2.8 μm paramagnetic beads and passed through a custom-made microfluidic channel. Then, electrical measurements within the microfluidic chip are obtained to construct a machine learning model. The machine learning algorithm learns the relationship between the electrical measurements as an input and the DNA concentration per bead as an output. As a result, the machine learning approach could learn from historical data obtained from experiments to predict new output values [32]. With this technique, a trained model can be generalized to predict the DNA amount per bead for beads with an unknown DNA concentration. The objective of this study is to leverage the electrical measurements obtained from the Zurich Instruments tool, such as the frequency, peak intensity, and phase change of the peak intensity, to predict the DNA concentration. In this work, we proposed a novel regression approach to predict the amount of DNA by using electrical measurement features. To quantify the performance of the specified model, three types of machine learning approaches were constructed: classification, regression, and a hybrid model. In our analysis, we benchmarked 10 different deep learning architectures from simple to complex on four figures of merit (FOMs), namely, accuracy and error for the classification method, R\_Squared, and the mean square error (MSE) of the regression model. Furthermore, we combined the best architectures from classification and regression to propose a novel hybrid regression model with an R\_Squared value of 97%. The trained

hybrid regression model may provide a general platform to predict the DNA amount per bead from electrical measurements obtained from the Zurich Instruments tool.
