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We present a new computational framework of neuron growth based on the phase field method and develop an open-source software package called “NeuronGrowth_IGAcollocation”. Neurons consist of a cell body, dendrites, and axons. Axons and dendrites are long processes extending from the cell body and enabling information transfer to and from other neurons. There is high variation in neuron morphology based on their location and function, thus increasing the complexity in mathematical modeling of neuron growth. In this paper, we propose a novel phase field model with isogeometric collocation to simulate different stages of neuron growth by considering the effect of tubulin. The stages modeled include lamellipodia formation, initial neurite outgrowth, axon differentiation, and dendrite formation considering the effect of intracellular transport of tubulin on neurite outgrowth. Through comparison with experimental observations, we can demonstrate qualitatively and quantitatively similar reproduction of neuron morphologies at different stages of growth and allow extension towards the formation of neurite networks.

 

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 three-dimensional complex geometries of neurons. The transport is controlled to avoid traffic jams of materials by minimizing a predefined 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 the isogeometric analysis. 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 the 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 neurons.

 

Abstract 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. 

Abstract Aging-related periventricular white matter hyperintensities (pvWMHs) are a common observation in medical images of the aging brain. The underlying tissue damage is part of the complex pathophysiology associated with age-related microstructural changes and cognitive decline. PvWMH formation is linked to blood–brain barrier dysfunction from cerebral small vessel disease as well as the accumulation of cerebrospinal fluid in periventricular tissue due to progressive denudation of the ventricular wall. In need of a unifying theory for pvWMH etiology, image-based finite-element modeling is used to demonstrate that ventricular expansion from age-related cerebral atrophy and hemodynamic loading leads to maximum mechanical loading of the ventricular wall in the same locations that show pvWMHs. Ventricular inflation, induced via pressurization of the ventricular wall, creates significant ventricular wall stretch and stress on the ependymal cells lining the wall, that are linked to cerebrospinal fluid leaking from the lateral ventricles into periventricular white matter tissue. Eight anatomically accurate 3D brain models of cognitively healthy subjects with a wide range of ventricular shapes are created. For all models, our simulations show that mechanomarkers of mechanical wall loading are consistently highest in pvWMHs locations ( p < 0.05). Maximum principal strain, the ependymal cell thinning ratio, and wall curvature are on average 14%, 8%, and 24% higher in pvWMH regions compared to the remaining ventricular wall, respectively. Computational modeling provides a powerful framework to systematically study pvWMH formation and growth with the goal to develop pharmacological interventions in the future.