People
Arkadz Kirshtein
Norbert Wiener Assistant Professor
Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
BromfieldPearson
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 subdomain structures
and interactions. These include multicomponent 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, electrorheological 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.
