Neuron Growth and Neurodevelopmental Disorders Modeling with Isogeometric Analysis, Biophysics, and Machine Learning

<p dir="ltr">Neurons are the fundamental component of the brain, consisting of the cell body, dendrites, and an axon. Multiple neurons form neurite networks to perform complex tasks. Neurological disorders exist when neurons are damaged or lose connections. Studying the neurodevelopmental process and associated neuron growth factors (NGF) could significantly strengthen our understanding and potentially lead to effective treatment strategies. Neuron growth is a complex, multi-stage process in which neurons develop sophisticated morphologies and interwoven neurite networks. This makes conventional computational neuron growth modeling challenging and necessitates sophisticated modeling techniques to accurately represent the diverse morphologies and growth patterns. A computational model that can simulate these diverse and dynamic growth processes is essential for advancing our understanding of neurodevelopmental processes and function. These models could substantially benefit neuron culturing experiments by offering researchers a platform to test hypotheses and protocols in silico before progressing to in vitro or clinical studies. By studying disruptions in these processes through the models, researchers can gain insights into how such disturbances might lead to neurological disorders. This approach enhances our understanding of neuronal dynamics and aids in developing interventions for neurological disorders, necessitating a robust computational framework that emphasize the importance of integrating advanced mathematical and computational techniques to capture the intricacies of neuron growth accurately and efficiently. </p><p dir="ltr">Recent advances in experimental research have allowed us to examine the effects of various neuron growth factors, such as NGF and neurotrophin concentrations, that play crucial roles in neurite outgrowth, survival, and differentiation. Additionally, these studies have provided insights into the potential causes of neurological diseases, such as Alzheimer's, Parkinson's, and amyotrophic lateral sclerosis. Despite these advances, there is a need for computational tools that can accurately simulate the neuron growth process. Existing bio-phenomenon-based models often overlook NGFs. On the other hand, biophysics-based models require extensive and computationally expensive governing equations, limiting the practicality of large-scale simulations. Moreover, these models often struggle to capture the dynamic transitions between different stages of neuron growth. These transitions are critical for understanding how neurons develop their complex morphologies and how disruptions in these processes may lead to neurodevelopmental disorders (NDDs). NDDs are among the most prevalent chronic diseases in the U.S., severely impacting the formation of central and peripheral nervous systems. Consisting of a wide array of disorders, such as autism spectrum disorder, attention deficit hyperactivity disorder, and epilepsy, NDDs are characterized by progressive impairments in cognitive, speech, memory, motor, and other neurological functions. The heterogeneous nature of NDDs makes it significantly challenging to identify the exact cause, impeding accurate diagnosis and the development of targeted treatments. A computational model for NDDs could enhance our understanding of the various factors involved and assist in identifying root causes to expedite treatment development. </p><p dir="ltr">Despite significant advances in experimental neuroscience that have identified factors influencing neuron growth and mechanisms underlying neurological disorders, computational tools are still needed to simulate neuron growth and NDDs biomimetically and efficiently. This thesis introduces a novel computational framework to enhance the understanding of neuron growth processes and associated NDDs. The framework leverages the convergence of spline modeling, computational mechanics, neurophysiology, and data-driven modeling techniques. The computational framework includes: (1) The development of an IGA-collocationbased phase field model that simulates neuron growth behaviors; (2) Integration of experimental data for biomimetic simulation of neurite morphological evolution to capture dynamic transitions in growth stages and accurately reflect complex neuronal behaviors, along with a customized convolutional neural network (CNN) based on an autoencoder to enhance computational efficiency and reduce simulation time; (3) The implementation of the IGA neuron growth model in C++ using truncated T-spline with local refinements for computational efficiency and accuracy by reducing necessary degrees of freedom (DOFs) with a thorough investigation of factors contributing to abnormal morphological transformation, including retraction and atrophy associated with NDDs, as well as a MetaFormer-based ML model that offers fast and accurate predictions of NDDs based on healthy neurite growth; and (4) Extension of the neuron growth model to 3D using truncated hierarchical B-splines (THB-splines) with multiple levels of local refinements. This computational framework seeks to bridge the gap in high-fidelity mathematical modeling and efficient simulation tools. These tools are crucial for elucidating the complex biophysics of NDDs and for shaping future targeted therapeutic strategies and treatments. </p>