ORCO: Ollivier-Ricci Curvature-Omics-an unsupervised method for analyzing robustness in biological systems.

Motivation: Although recent advanced sequencing technologies have improved the resolution of genomic and proteomic data to better characterize molecular phenotypes, efficient computational tools to analyze and interpret large-scale omic data are still needed.

Results: To address this, we have developed a network-based bioinformatic tool called Ollivier-Ricci curvature for omics (ORCO). ORCO incorporates omics data and a network describing biological relationships between the genes or proteins and computes Ollivier-Ricci curvature (ORC) values for individual interactions.

Biological correlates associated with high-risk breast cancer patients identified using a computational method.

Using a novel unsupervised method to integrate multi-omic data, we previously identified a breast cancer group with a poor prognosis. In the current study, we characterize the biological features of this subgroup, defined as the high-risk group, using various data sources. Assessment of three published hypoxia signatures showed that the high-risk group exhibited higher hypoxia scores (p < 0.

Divergent brain solute clearance in rat models of cerebral amyloid angiopathy and Alzheimer's disease.

Brain waste clearance from the interstitial fluid environment is challenging to measure, which has contributed to controversy regarding the significance of glymphatic transport impairment for neurodegenerative processes. Dynamic contrast enhanced MRI (DCE-MRI) with cerebrospinal fluid administration of Gd-tagged tracers is often used to assess glymphatic system function. We previously quantified glymphatic transport from DCE-MRI data utilizing regularized optimal mass transport (rOMT) analysis, however, information specific to glymphatic clearance was not directly derived.

Multi-scale geometric network analysis identifies melanoma immunotherapy response gene modules.

Melanoma response to immune-modulating therapy remains incompletely characterized at the molecular level. In this study, we assess melanoma immunotherapy response using a multi-scale network approach to identify gene modules with coordinated gene expression in response to treatment. Using gene expression data of melanoma before and after treatment with nivolumab, we modeled gene expression changes in a correlation network and measured a key network geometric property, dynamic Ollivier-Ricci curvature, to distinguish critical edges within the network and reveal multi-scale treatment-response gene communities.

Dynamic network curvature analysis of gene expression reveals novel potential therapeutic targets in sarcoma.

Network properties account for the complex relationship between genes, making it easier to identify complex patterns in their interactions. In this work, we leveraged these network properties for dual purposes. First, we clustered pediatric sarcoma tumors using network information flow as a similarity metric, computed by the Wasserstein distance.

Multi-Scale Geometric Network Analysis Identifies Melanoma Immunotherapy Response Gene Modules.

Melanoma response to immune-modulating therapy remains incompletely characterized at the molecular level. In this study, we assess melanoma immunotherapy response using a multi-scale network approach to identify gene modules with coordinated gene expression in response to treatment. Using gene expression data of melanoma before and after treatment with nivolumab, we modeled gene expression changes in a correlation network and measured a key network geometric property, dynamic Ollivier-Ricci curvature, to distinguish critical edges within the network and reveal multi-scale treatment-response gene communities.

Geometric graph neural networks on multi-omics data to predict cancer survival outcomes.

The advance of sequencing technologies has enabled a thorough molecular characterization of the genome in human cancers. To improve patient prognosis predictions and subsequent treatment strategies, it is imperative to develop advanced computational methods to analyze large-scale, high-dimensional genomic data. However, traditional machine learning methods face a challenge in handling the high-dimensional, low-sample size problem that is shown in most genomic data sets.

Visualizing Fluid Flows via Regularized Optimal Mass Transport with Applications to Neuroscience.

The regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the optimal mass transport (OMT) problem proposed by Benamou and Brenier. We show that the rOMT model serves as a powerful tool in computational fluid dynamics for visualizing fluid flows in the glymphatic system. In the present work, we describe how to modify the previous numerical method for efficient implementation, resulting in a significant reduction in computational runtime.

Geometric network analysis provides prognostic information in patients with high grade serous carcinoma of the ovary treated with immune checkpoint inhibitors.

Network analysis methods can potentially quantify cancer aberrations in gene networks without introducing fitted parameters or variable selection. A new network curvature-based method is introduced to provide an integrated measure of variability within cancer gene networks. The method is applied to high-grade serous ovarian cancers (HGSOCs) to predict response to immune checkpoint inhibitors (ICIs) and to rank key genes associated with prognosis.

Fisher-Rao Regularized Transport Analysis of the Glymphatic System and Waste Drainage.

In this work, a unified representation of all the time-varying dynamics is accomplished with a Lagrangian framework for analyzing Fisher-Rao regularized dynamical optimal mass transport (OMT) derived flows. While formally equivalent to the Eulerian based Schrödinger bridge OMT regularization scheme, the Fisher-Rao approach allows a simple and interpretable methodology for studying the flows of interest in the present work. The advantage of the proposed Lagrangian technique is that the time-varying particle trajectories and attributes are displayed in a single visualization.

A Vectorial Approach to Unbalanced Optimal Mass Transport.

Unbalanced optimal mass transport (OMT) seeks to remove the conservation of mass constraint by adding a source term to the standard continuity equation in the Benamou-Brenier formulation of OMT. In this study, we show how the unbalanced case fits into the vector-valued OMT framework simply by adding an auxiliary source layer and taking the flow between the source layer and the original layer(s) as the source term. This allows for unbalanced models both in the scalar and vector-valued density settings.

The glymphatic system and its role in cerebral homeostasis.

The brain's high bioenergetic state is paralleled by high metabolic waste production. Authentic lymphatic vasculature is lacking in brain parenchyma. Cerebrospinal fluid (CSF) flow has long been thought to facilitate central nervous system detoxification in place of lymphatics, but the exact processes involved in toxic waste clearance from the brain remain incompletely understood.

Publisher Correction: Optimal Mass Transport with Lagrangian Workflow Reveals Advective and Diffusion Driven Solute Transport in the Glymphatic System.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Optimal Mass Transport with Lagrangian Workflow Reveals Advective and Diffusion Driven Solute Transport in the Glymphatic System.

The glymphatic system (GS) hypothesis states that advective driven cerebrospinal fluid (CSF) influx from the perivascular spaces into the interstitial fluid space rapidly transport solutes and clear waste from brain. However, the presence of advection in neuropil is contested and solutes are claimed to be transported by diffusion only. To address this controversy, we implemented a regularized version of the optimal mass transport (rOMT) problem, wherein the advection/diffusion equation is the only a priori assumption required.

Optimal mass transport kinetic modeling for head and neck DCE-MRI: Initial analysis.

Purpose: Current state-of-the-art models for estimating the pharmacokinetic parameters do not account for intervoxel movement of the contrast agent (CA). We introduce an optimal mass transport (OMT) formulation that naturally handles intervoxel CA movement and distinguishes between advective and diffusive flows.

Method: Ten patients with head and neck squamous cell carcinoma (HNSCC) were enrolled in the study between June 2014 and October 2015 and underwent DCE MRI imaging prior to beginning treatment.

GlymphVIS: Visualizing Glymphatic Transport Pathways Using Regularized Optimal Transport.

The glymphatic system (GS) is a transit passage that facil-itates brain metabolic waste removal and its dysfunction has been asso-ciated with neurodegenerative diseases such as Alzheimer's disease. The GS has been studied by acquiring temporal contrast enhanced magnetic resonance imaging (MRI) sequences of a rodent brain, and tracking the cerebrospinal fluid injected contrast agent as it flows through the GS. We present here a novel visualization framework, GlymphVIS, which uses regularized optimal transport (OT) to study the flow behavior between time points at which the images are taken.

Cerebrospinal and interstitial fluid transport via the glymphatic pathway modeled by optimal mass transport.

The glymphatic pathway is a system which facilitates continuous cerebrospinal fluid (CSF) and interstitial fluid (ISF) exchange and plays a key role in removing waste products from the rodent brain. Dysfunction of the glymphatic pathway may be implicated in the pathophysiology of Alzheimer's disease. Intriguingly, the glymphatic system is most active during deep wave sleep general anesthesia.