Instruments known as biological field effect transistors (BioFETs) have potential to offer affordable and highly sensitive medical diagnostics that can be administered point of care. Signal is separated from noise in these instruments with stochastic regression, a technique that involves modeling the signal with a linear deterministic drift term and a white noise term that captures stochastic...
Mathematical models of tumor growth are essential for complementing experimental findings and furthering the understanding of cancer development and spread, as well as optimizing therapy. This talk presents a novel age-structured partial differential equation (PDE) model. The underlying process for tumor growth is similar to classical models, where growth is driven by pressure-limited cell...
Biological field effect transistors are portable and highly sensitive biosensors that show promise as medical diagnostic instruments. During a typical experiment, chemical reactants from solution diffuse onto a surface to bind with receptors that are confined to the surface. This produces a time series signal that may be used to analyze the reaction of interest. In experimentally relevant...
A novel chip-scale electrochemical biosensor is being developed to detect biomolecules with high sensitivity. Unlike traditional methods such as qPCR that require specialized equipment and trained personal, these cost-effective and portable chip-scale sensors are designed to administer tests at the point of care. Target molecules of interest are immobilized on the surface, and specific...
Stochastic methods have recently been used to solve important problems in mathematical biology, from modeling degradation of protective layers in biosensors to separating signal from noise in diagnostic instruments. Deterministic tools like integrodifferential and partial differential equations remain powerful for modeling phenomena like reaction-diffusion processes and tumor growth. In these...
