Neurodevelopmental disorders modeling using isogeometric analysis, dynamic domain expansion and local refinement

TL;DR

This work introduces a PETSc-backed, 2D isogeometric analysis phase-field model for neurodevelopmental disorders (NDDs) that couples neurite growth with neurotrophin dynamics. It integrates dynamic domain expansion and localized refinement using truncated T-splines to efficiently resolve evolving neurite interfaces, while solving a set of five coupled equations including phase-field evolution, tubulin transport, tubulin consumption, synaptogenesis, and a driving force that incorporates an optimal neurotrophin concentration $c_{opti}$. Parameter studies show how $c_{opti}$, diffusion $D_c$, and degradation rates $k_{p75}$ and $k_2$ influence retraction, atrophy, branching, and thickness, with qualitative validation against healthy human iPSC-derived neurons and damaged rat hippocampal cultures via external-cue guided simulations. The model provides mechanistic insights into NDDs and a scalable computational framework potentially useful for studying disease mechanisms and guiding therapeutic strategies. Future work aims to extend to 3D using truncated hierarchical B-splines, broaden experimental validation, and explore machine learning integrations for predictive time-series analysis.

Abstract

Neurodevelopmental disorders (NDDs) have arisen as one of the most prevailing chronic diseases within the US. Often associated with severe adverse impacts on the formation of vital central and peripheral nervous systems during the neurodevelopmental process, NDDs are comprised of a broad spectrum of disorders, such as autism spectrum disorder, attention deficit hyperactivity disorder, and epilepsy, characterized by progressive and pervasive detriments to cognitive, speech, memory, motor, and other neurological functions in patients. However, the heterogeneous nature of NDDs poses a significant roadblock to identifying the exact pathogenesis, impeding accurate diagnosis and the development of targeted treatment planning. A computational NDDs model holds immense potential in enhancing our understanding of the multifaceted factors involved and could assist in identifying the root causes to expedite treatment development. To tackle this challenge, we introduce optimal neurotrophin concentration to the driving force and degradation of neurotrophin to the synaptogenesis process of a 2D phase field neuron growth model using isogeometric analysis to simulate neurite retraction and atrophy. The optimal neurotrophin concentration effectively captures the inverse relationship between neurotrophin levels and neurite survival, while its degradation regulates concentration levels. Leveraging dynamic domain expansion, the model efficiently expands the domain based on outgrowth patterns to minimize degrees of freedom. Based on truncated T-splines, our model simulates the evolving process of complex neurite structures by applying local refinement adaptively to the cell/neurite boundary. Furthermore, a thorough parameter investigation is conducted with detailed comparisons against neuron cell cultures in experiments, enhancing our fundamental understanding of the mechanisms underlying NDDs.

Figures (10)

• Figure 1: Flow chart of the NDDs modeling pipeline. (A) The overall pipeline that conducts NDDs modeling. (B) Adaptive mesh refinement module that locally refines the mesh based on neuron outgrowth. (C) The IGA NDDs model simulates disorders using the phase field method, PETSc, and truncated T-splines. Parameters in red dashed boxes are selected to study their effects on NDDs. (D) Dynamic domain expansion module that directionally expands domain based on neurites near the domain boundary.
• Figure 2: Local refinements using truncated T-splines. (A) Phase field variable $\phi$ initialization on a coarse mesh. (B) Identifying elements at the $\phi$ interface. (C) Interface elements are locally refined with subdivision. (D) Detecting face-face intersections created by face extension from subdivisions. (E) Applying 1-ring of bisections to resolve these face-face intersections and maintaining the integrity of the mesh for truncated T-splines. (F) Generating locally refined T-mesh for truncated T-splines with enhanced accuracy in regions of interest. (G) Interpolating $\phi$ initialization from the coarse control mesh to the locally-refined mesh. (H) The locally refined $\phi$ initialization.
• Figure 3: Sequential representation of directional domain expansion in neuron outgrowth simulation. (A) The initial soma $\phi$ and checking for neurites near the domain boundary. (B) Detected neurite near the bottom boundary and subsequent bottom directional domain expansion. (C) As growth continues, neurites approach the top and left boundaries, and the domain is expanded along these directions. (D) Neurites detected near the top, left, and right boundaries, and domain expansions follow. (E) The expanded computational domain for neurite development. The process showcasing the model can adapt to the evolving morphology of the neuron and minimize unnecessary computational costs.
• Figure 4: Healthy neuron growth simulations. (A) Single neuron growth with many neurite morphologies. (B) Multiple-neuron growth simulations with neurite interactions. For multi-neuron cases, the initial soma placements are randomized in the domain.
• Figure 5: Impact of $c_{opti}$ variations on neurite morphology and development. (A) Variations of neurite growth behaviors as influenced by $c_{opti}$ values ranging from 0.5 to 3.0 with zoomed-in views of the intricate neurite structures at around 40,000 iterations, illustrating the progressive neurite density and branching complexity changes. (B) Demonstration of the dynamic retraction behaviors in the simulated neuron growth process with an initial $c_{opti}$ value of 1, which is subsequently reduced to 0 at 150,000 iterations during the simulation to mimic the effect of increasing $c_{neur}$ magnitude and its inverse relationship on neuron survival. Atrophies are marked with cyan dashed circles, and retractions are traced with magenta dashed lines. The $c_{opti}$ reduction simulates neurite retraction, showcasing the potential impacts of decreasing neurotrophic support on neurite morphology and structural integrity over time.