People

Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
Bromfield-Pearson
Medford, MA 02155

Email @tufts.edu:
arkadz.kirshtein
Personal site

Expertise:
PDE analysis and computations, complex fluids, numerical analysis, mathematical modeling in physics and engineering, mathematical modeling in biology and medicine, bioinformatics, fluid dynamics, finite difference schemes.

Research:
My research is broadly in applied mathematical modeling and specific interests can be divided into two main areas: mathematical modeling and simulation of anisotropic complex fluids; and mathematical modeling and simulation of cancer development and treatment.

The main direction of my research is mathematical modeling and numerical simulation of anisotropic complex fluids whose motion is complicated by the existence of mesoscales or sub-domain structures and interactions. These include multi-component mixtures of immiscible fluids, viscoelastic and polymeric fluids. Such complex fluids are ubiquitous in daily life, e.g., they arise in a wide variety of mixtures, polymeric solutions, colloidal dispersions, biofluids, electro-rheological fluids, ionic fluids, liquid crystals, and liquid crystalline polymers. Indeed, materials modeled as complex fluids often have great practical utility since the microstructure can be manipulated by external fields or forces in order to produce useful mechanical, optical or thermal properties.

Another research area I joined recently is modeling of cancer development and treatment. A major clinical challenge is to obtain an effective treatment strategy for each patient or at least identify a subset of patients who could benefit from a particular treatment. Since each cancer has its own unique features, it is very important to obtain personalized cancer treatments and find a way to tailor treatment strategies for each patient based on each individual's characteristics, including race, gender, genetic factors, immune response variations. Recently, Quantitative and Systems Pharmacology (QSP) has been commonly used to discover, validate, and test drugs. QSP models are a system of differential equations that model the dynamic interactions between drug(s) and a biological system. These mathematical models provide an integrated “systems level” approach to determining mechanisms of action of drugs and finding new ways to alter complex cellular networks with mono or combination therapy to obtain effective treatments.