Solution Multiplicity of Inversion Problems in Distributed Systems

The treatment of certain diseases of the central nervous system (Alzheimer, Huntington disease, etc) require the insertion of therapeutic drug molecules directly into the porous tissue of target areas deep in the brain. The design of invasive drug delivery therapies [Nicholson, 1985] constitutes a challenging transport problem with complex metabolic drug-neural interaction. The efficiency of the treatments depends strongly on the drugs’ molecular properties and its metabolic uptake into the brain tissue. However, it is very difficult to experimentally measure transport and metabolic reaction properties of large drug molecules in the brain tissue with high accuracy. The discovery of those transport and metabolic properties constitutes large-scale transport and kinetic inversion problems (TKIP). However, the complexity of the underlying transport mechanism and the measurement noise in the advanced imaging data through magnetic resonance imaging (MRI), computer tomography (CT) or ultrasound render challenges for finding multiple solutions to this inversion problem. This presentation proposes to identify all the possible solutions to the inversion problem from the advanced imaging data.