Research

Mathematics Interdisciplinary Applications

Mathematics, Interdisciplinary Applications includes resources concerned with mathematical methods whose primary focus is on a specific non-mathematics discipline (except biology) such as psychology, history, economics, etc. Resources that deal with mathematical biology are covered in the MATHEMATICAL AND COMPUTATIONAL BIOLOGY category. Resources that focus on specific mathematical topics such as differential equations, numerical analysis, nonlinearity, etc., are covered in the MATHEMATICS, APPLIED category.

Mathematics

Mathematics covers resources having a broad, general approach to the field. The category also includes resources focusing on specific fields of basic research in Mathematics such as topology, algebra, functional analysis, combinatorial theory, differential geometry and number theory.

Engineering

Computer Science

Engineering Computing & Technology (Eng)

At BioSFM Lab (Biosensors and Functional Materials Laboratory), our research program is devoted to advancing biosensing technologies through the combined use of impedance spectroscopy, functional materials engineering, and data-driven modeling approaches. Our work lies at the interface of materials science, electrical engineering, and computational biology, with the overarching aim of developing biosensing systems that are more sensitive, selective, and predictive than traditional methods.

Quartz Crystal Microbalance and Impedance-Based Sensing

Quartz Crystal Microbalance (QCM) sensors form a central axis of our research. While classical QCM applications focus primarily on the Sauerbrey relation—linking resonance frequency shifts to adsorbed mass—such approaches fail in complex liquid environments where viscous loading, viscoelasticity, and interfacial dynamics dominate the response. To address these limitations, our lab investigates the full impedance spectrum of QCM devices, encompassing motional resistance (Rₘ), inductance (Lₘ), motional capacitance (Cₘ), and static capacitance (C₀), as well as derived parameters such as conductance, susceptance, and phase angle. This holistic approach allows us to capture subtle biophysical signatures of molecular interactions, yielding richer datasets for downstream analysis.

Beyond Single-Parameter Analysis: Multivariate and AI-Assisted Models

Most impedance-based QCM studies monitor only peak frequency shifts or dissipation broadening. We depart from this paradigm by employing multivariate impedance descriptors, coupled with dimension reduction, feature ranking, and regression modeling. By applying kernel-based methods (e.g., HSIC, MI-based rankings) and ensemble regressors (RF, XGBoost, CatBoost), we quantify the relative informativeness of impedance parameters and construct predictive models that significantly enhance the limit of detection (LOD). This methodological framework allows us to systematically interrogate which impedance features are most critical for analyte quantification, ultimately leading to more robust biosensor calibration strategies.

Functional Materials and Biointerfaces

Our experimental work is underpinned by the design of functional material layers to engineer the sensor–analyte interface. Hydrogels, nanostructured coatings, and chemically functionalized thin films are employed to tune surface wettability, mechanical stiffness, and bio-recognition capabilities. By coupling these engineered surfaces with impedance spectroscopy, we aim to disentangle the relative contributions of mass adsorption, viscoelastic coupling, and hydration dynamics, thereby providing mechanistic insight into sensor responses. These studies directly inform the development of organ-on-chip systems, such as hydrogel-integrated heart-on-a-chip models, for investigating disease markers under physiologically relevant conditions.

Microfluidics and Robotic Automation

Recognizing the importance of reproducibility in biosensing experiments, we integrate QCM sensors with microfluidic flow cells for controlled delivery of analytes and temporal resolution of binding kinetics. In parallel, our team develops dual-axis robotic systems to automate procedures such as contact angle measurement and droplet deposition. These engineering advances reduce operator variability, enhance throughput, and enable standardized sensor characterization protocols, which are essential for translational research and clinical adaptation.

Computational and Theoretical Contributions

In addition to experimental investigations, our group actively contributes to the mathematical modeling of biosensor signals. By extending equivalent circuit models (e.g., Butterworth–Van Dyke formalism) to incorporate parallel admittance pathways and liquid-loading effects, we develop frameworks capable of reconciling experimental impedance spectra with theoretical predictions. These models provide the foundation for physics-informed machine learning approaches, where empirical QCM datasets are augmented with regularization informed by physical laws, leading to predictive models that generalize across experimental conditions.

Long-Term Vision

The ultimate goal of BioSFM Lab is to create next-generation, AI-assisted biosensing platforms that seamlessly integrate impedance spectroscopy, advanced material interfaces, and automated fluidic control. By doing so, we aim to move beyond endpoint detection towards real-time, high-resolution monitoring of molecular and cellular processes. Such systems hold transformative potential for applications ranging from early disease diagnostics to personalized drug screening and point-of-care testing.