  The intracellular transport process plays an important role in delivering
essential materials throughout branched geometries of neurons for their
survival and function. Many neurodegenerative diseases have been associated
with the disruption of transport. Therefore, it is essential to study how
neurons control the transport process to localize materials to necessary
locations. Here, we develop a novel optimization model to simulate the traffic
regulation mechanism of material transport in complex geometries of neurons.
The transport is controlled to avoid traffic jam of materials by minimizing a
pre-defined objective function. The optimization subjects to a set of partial
differential equation (PDE) constraints that describe the material transport
process based on a macroscopic molecular-motor-assisted transport model of
intracellular particles. The proposed PDE-constrained optimization model is
solved in complex tree structures by using isogeometric analysis (IGA).
Different simulation parameters are used to introduce traffic jams and study
how neurons handle the transport issue. Specifically, we successfully model and
explain the traffic jam caused by reduced number of microtubules (MTs) and MT
swirls. In summary, our model effectively simulates the material transport
process in healthy neurons and also explains the formation of a traffic jam in
abnormal neurons. Our results demonstrate that both geometry and MT structure
play important roles in achieving an optimal transport process in neuron.
