Tissue-scale, personalized modeling and simulation of prostate cancer growth.

Recently, mathematical modeling and simulation of diseases and their treatments have enabled the prediction of clinical outcomes and the design of optimal therapies on a personalized (i.e., patient-specific) basis. This new trend in medical research has been termed "predictive medicine." Prostate cancer (PCa) is a major health problem and an ideal candidate to explore tissue-scale, personalized modeling of cancer growth for two main reasons: First, it is a small organ, and, second, tumor growth can be estimated by measuring serum prostate-specific antigen (PSA, a PCa biomarker in blood), which may enable in vivo validation. In this paper, we present a simple continuous model that reproduces the growth patterns of PCa. We use the phase-field method to account for the transformation of healthy cells to cancer cells and use diffusion-reaction equations to compute nutrient consumption and PSA production. To accurately and efficiently compute tumor growth, our simulations leverage isogeometric analysis (IGA). Our model is shown to reproduce a known shape instability from a spheroidal pattern to fingered growth. Results of our computations indicate that such shift is a tumor response to escape starvation, hypoxia, and, eventually, necrosis. Thus, branching enables the tumor to minimize the distance from inner cells to external nutrients, contributing to cancer survival and further development. We have also used our model to perform tissue-scale, personalized simulation of a PCa patient, based on prostatic anatomy extracted from computed tomography images. This simulation shows tumor progression similar to that seen in clinical practice.

Shape component analysis: structure-preserving dimension reduction on biological shape spaces.

MOTIVATION: Quantitative shape analysis is required by a wide range of biological studies across diverse scales, ranging from molecules to cells and organisms. In particular, high-throughput and systems-level studies of biological structures and functions have started to produce large volumes of complex high-dimensional shape data. Analysis and understanding of high-dimensional biological shape data require dimension-reduction techniques. RESULTS: We have developed a technique for non-linear dimension reduction of 2D and 3D biological shape representations on their Riemannian spaces. A key feature of this technique is that it preserves distances between different shapes in an embedded low-dimensional shape space. We demonstrate an application of this technique by combining it with non-linear mean-shift clustering on the Riemannian spaces for unsupervised clustering of shapes of cellular organelles and proteins. AVAILABILITY AND IMPLEMENTATION: Source code and data for reproducing results of this article are freely available at https://github.com/ccdlcmu/shape_component_analysis_Matlab The implementation was made in MATLAB and supported on MS Windows, Linux and Mac OS. CONTACT: geyang@andrew.cmu.edu.

Semi-Automated Quantitative Evaluation of Neuron Developmental Morphology In Vitro Using the Change-Point Test.

Neuron morphology gives rise to distinct axons and dendrites and plays an essential role in neuronal functionality and circuit dynamics. In rat hippocampal neurons, morphological development occurs over roughly one week in vitro. This development has been qualitatively described as occurring in 5 stages. Still, there is a need to quantify cell growth to monitor cell culture health, understand cell responses to sensory cues, and compare experimental results and computational growth model predictions. To address this need, embryonic rat hippocampal neurons were observed in vitro over six days, and their processes were quantified using both standard morphometrics (degree, number of neurites, total length, and tortuosity) and new metrics (distance between change points, relative turning angle, and the number of change points) based on the Change-Point Test to track changes in path trajectories. Of the standard morphometrics, the total length of neurites per cell and the number of endpoints were significantly different between 0.5, 1.5, and 4 days in vitro, which are typically associated with Stages 2-4. Using the Change-Point Test, the number of change points and the average distance between change points per cell were also significantly different between those key time points. This work highlights key quantitative characteristics, both among common and novel morphometrics, that can describe neuron development in vitro and provides a foundation for analyzing directional changes in neurite growth for future studies.

RibSeg v2: A Large-scale Benchmark for Rib Labeling and Anatomical Centerline Extraction.

Automatic rib labeling and anatomical centerline extraction are common prerequisites for various clinical applications. Prior studies either use in-house datasets that are inaccessible to communities, or focus on rib segmentation that neglects the clinical significance of rib labeling. To address these issues, we extend our prior dataset (RibSeg) on the binary rib segmentation task to a comprehensive benchmark, named RibSeg v2, with 660 CT scans (15,466 individual ribs in total) and annotations manually inspected by experts for rib labeling and anatomical centerline extraction. Based on the RibSeg v2, we develop a pipeline including deep learning-based methods for rib labeling, and a skeletonization-based method for centerline extraction. To improve computational efficiency, we propose a sparse point cloud representation of CT scans and compare it with standard dense voxel grids. Moreover, we design and analyze evaluation metrics to address the key challenges of each task. Our dataset, code, and model are available online to facilitate open research at https://github.com/M3DV/RibSeg.

Modeling material transport regulation and traffic jam in neurons using PDE-constrained optimization.

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.

Modeling neuron growth using isogeometric collocation based phase field method.

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.

Surface Remeshing: A Systematic Literature Review of Methods and Research Directions.

Triangle meshes are used in many important shape-related applications including geometric modeling, animation production, system simulation, and visualization. However, these meshes are typically generated in raw form with several defects and poor-quality elements, obstructing them from practical application. Over the past decades, different surface remeshing techniques have been presented to improve these poor-quality meshes prior to the downstream utilization. A typical surface remeshing algorithm converts an input mesh into a higher quality mesh with consideration of given quality requirements as well as an acceptable approximation to the input mesh. In recent years, surface remeshing has gained significant attention from researchers and engineers, and several remeshing algorithms have been proposed. However, there has been no survey article on remeshing methods in general with a defined search strategy and article selection mechanism covering the recent approaches in surface remeshing domain with a good connection to classical approaches. In this article, we present a survey on surface remeshing techniques, classifying all collected articles in different categories and analyzing specific methods with their advantages, disadvantages, and possible future improvements. Following the systematic literature review methodology, we define step-by-step guidelines throughout the review process, including search strategy, literature inclusion/exclusion criteria, article quality assessment, and data extraction. With the aim of literature collection and classification based on data extraction, we summarized collected articles, considering the key remeshing objectives, the way the mesh quality is defined and improved, and the way their techniques are compared with other previous methods. Remeshing objectives are described by angle range control, feature preservation, error control, valence optimization, and remeshing compatibility. The metrics used in the literature for the evaluation of surface remeshing algorithms are discussed. Meshing techniques are compared with other related methods via a comprehensive table with indices of the method name, the remeshing challenge met and solved, the category the method belongs to, and the year of publication. We expect this survey to be a practical reference for surface remeshing in terms of literature classification, method analysis, and future prospects.

Deep learning of material transport in complex neurite networks.

Neurons exhibit complex geometry in their branched networks of neurites which is essential to the function of individual neuron but also brings challenges to transport a wide variety of essential materials throughout their neurite networks for their survival and function. While numerical methods like isogeometric analysis (IGA) have been used for modeling the material transport process via solving partial differential equations (PDEs), they require long computation time and huge computation resources to ensure accurate geometry representation and solution, thus limit their biomedical application. Here we present a graph neural network (GNN)-based deep learning model to learn the IGA-based material transport simulation and provide fast material concentration prediction within neurite networks of any topology. Given input boundary conditions and geometry configurations, the well-trained model can predict the dynamical concentration change during the transport process with an average error less than 10% and [Formula: see text] times faster compared to IGA simulations. The effectiveness of the proposed model is demonstrated within several complex neurite networks.

Reaction diffusion system prediction based on convolutional neural network.

The reaction-diffusion system is naturally used in chemistry to represent substances reacting and diffusing over the spatial domain. Its solution illustrates the underlying process of a chemical reaction and displays diverse spatial patterns of the substances. Numerical methods like finite element method (FEM) are widely used to derive the approximate solution for the reaction-diffusion system. However, these methods require long computation time and huge computation resources when the system becomes complex. In this paper, we study the physics of a two-dimensional one-component reaction-diffusion system by using machine learning. An encoder-decoder based convolutional neural network (CNN) is designed and trained to directly predict the concentration distribution, bypassing the expensive FEM calculation process. Different simulation parameters, boundary conditions, geometry configurations and time are considered as the input features of the proposed learning model. In particular, the trained CNN model manages to learn the time-dependent behaviour of the reaction-diffusion system through the input time feature. Thus, the model is capable of providing concentration prediction at certain time directly with high test accuracy (mean relative error <3.04%) and 300 times faster than the traditional FEM. Our CNN-based learning model provides a rapid and accurate tool for predicting the concentration distribution of the reaction-diffusion system.