(382c) Rigorous Mathematic Approach for Chemotherapy Design In the Brain

The malignant glioblastoma is a devastating
disease of central nerve system of the brain often lethal in few months time. Combining
chemotherapy, radiation therapy, genetic therapy may extend significantly life
expectation of patients suffering from this disease, provided that the cancer
can be destroyed without harming excessively the patient's brain. Therefore, the
challenge for designing effective chemotherapy lies in distributing the chemotherapeutic
toxin so that it kills cancer cell while at the same time not causing excessive
damage to healthy brain tissue. This problem requires the optimal choice of catheter
injection position and design parameters like number of outlet ports and port
configuration to best discharge the toxins as well as and design parameters
like insertion pressure, flow and dilution rate. It is still the state-of-art
treatment of this process to rely on surgeon institution in term of catheter's
locations for design parameters and flow rates.

In this presentation, we propose
a rigorous mathematical optimization problem on a distributed two-dimensional
or three dimensional brain to determine the optimal catheter location,
injection pressure and other parameters such as number of hole or outlets. We
will use as the objective function the maximal coverage cancerous tissue as
well as adjacent white matter tracts where reoccurrence is likely, while at the
same time minimizing the concentration of toxins to cortical areas responsible
for critical brain function such as smell and sight. We formulate a rigorous distributed
optimization problem with partial differential equations constraints representing
momentum, specie transport phenomena. The finite volume discretization method using
unstructured grid is used to solve the resulting non-linear mathematical
program with stochastic mathematical programming techniques.

The methodology of the design of catheter
locations integrates interdisciplinary expertise from systems biology and
engineering optimization. The approach will allow physicians and scientists to
design and optimize chemotherapy in a systematic fashion, thus reducing the
need for trial-and-error animal experiments.