Seminars archive
Upcoming Seminars   Seminar: Algebra Title to be announced Renee Bell, University of Pennsylvania   Seminar: Combinatorics On the ErdosGyarfas distinct distances problem with local constraints Cosmin Pohoata, The California Institute of Technology   Seminar: Algebra Title to be announced Eva Bayer Fluckinger, EPFL   Seminar: Algebra Joint AthensAtlanta Number Theory Seminar Larry Rolen and Bianca Viray, Vanderbilt and University of Washington   Seminar: Algebra Title to be announced Anne Qu\'eguinerMathieu, Paris   Seminar: Algebra Title to be announced Natalie Paquette, Caltech  Past Seminars   Seminar: Numerical Analysis and Scientific Computing A computational model of drug delivery through microcirculation to compare different tumor treatment options Paolo Zunino, University of Pittsburgh Venue: MSC N304 Show abstract Starting from the fundamental laws of filtration and transport in biological tissues, we develop a mathematical model able to capture the interplay between blood perfusion, fluid exchange with the interstitial volume, mass transport in the capillary bed, through the capillary walls and into the surrounding tissue. These phenomena are accounted at the microscale level, where the capillary bed and the interstitial volume are viewed as two separate regions. The capillary bed is described as a network of vessels carrying blood flow.
We complement the model with a state of art numerical solver, based on the finite element method. The numerical scheme is based on the idea to represent the capillary bed as a network of onedimensional channels that acts as a concentrated source of flow immersed into the interstitial volume, because of the natural leakage of capillaries. As a result, it can be classified as an embedded multiscale method.
We apply the model to study drug delivery to tumors. Owing to its general foundations, the model can be adapted to describe and compare various treatment options. In particular, we consider drug delivery from bolus injection and from nanoparticles, which are in turn injected into the blood stream. The computational approach is prone to perform a systematic quantification of the treatment performance, enabling the analysis of interstitial drug concentration levels, drug metabolization rates, cell surviving fractions and the corresponding timecourses. Our study suggests that for the treatment based on bolus injection, the drug dose is not optimally delivered to the tumor interstitial volume. Using nanoparticles as intermediate drug carriers overrides the shortcomings of the previous delivery approach.
Being directly derived from the fundamental laws of flow and transport, the model relies on general foundations and it is prone to be extended in different directions. On one hand, we are planning to combine it with a poroelastic description of the interstitial tissue, in order to capture the interplay of mechanical deformations and transport phenomena. On the other hand, the model may be adapted in future to study different types of cancer, provided that suitable metrics are available to quantify the transport properties of a specific tumor mass.   Seminar: Algebra Algebraic cycles and degeneration Jaya Iyer, IMSC Chennai   Seminar: Algebra Forms of Toric Varieties Alex Duncan, University of Michigan   Seminar: General Colloquium Enabling Highly Accurate LargeScale Phylogenetic Estimation Shel Swenson, University of Southern California   Seminar: General Colloquium A Brief History of Ramsey Theory Steven La Fleur, Emory University   Seminar: Computer Science MultiStructured Inference in TexttoText Generation Kapil Thadani, Columbia University   Seminar: Computer Science Opinion Mining for the Internet: Models, Algorithms and Predictive Analytics Arjun Mukherjee, University of Illinois at Chicago   Seminar: Computer Science Secure and PrivacyAssured Outsourced Cloud Data Services Ming Li, Utah State University   Colloquium Optimization with sparse matrix cone constraints Martin Andersen, Technical University of Denmark   Seminar: Computational Mathematics Regularization in Tomography  Dealing with Ambiguity and Noisy Data Per Christian Hansen, Technical University of Denmark 
