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. Analysis identified six distinct gene modules corresponding to sets of genes interacting in response to immunotherapy. One module alone, overlapping with the nuclear factor kappa-B pathway (NFkB), was associated with improved patient survival and a positive clinical response to immunotherapy. This analysis demonstrates the usefulness of dynamic Ollivier-Ricci curvature as a general method for identifying information-sharing gene modules in cancer.

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. We demonstrate that this approach yields the best concordance with histological subtypes, validated against three state-of-the-art methods. Second, to identify molecular targets that would be missed by more conventional methods of analysis, we applied a novel unsupervised method to cluster gene interactomes represented as networks in pediatric sarcoma. RNA-Seq data were mapped to protein-level interactomes to construct weighted networks that were then subjected to a non-Euclidean, multi-scale geometric approach centered on a discrete notion of curvature. This provides a measure of the functional association among genes in the context of their connectivity. In confirmation of the validity of this method, hierarchical clustering revealed the characteristic EWSR1-FLI1 fusion in Ewing sarcoma. Furthermore, assessing the effects of in silico edge perturbations and simulated gene knockouts as quantified by changes in curvature, we found non-trivial gene associations not previously identified.

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. Analysis identified six distinct gene modules corresponding to sets of genes interacting in response to immunotherapy. One module alone, overlapping with the nuclear factor kappa-B pathway (NFKB), was associated with improved patient survival and a positive clinical response to immunotherapy. This analysis demonstrates the usefulness of dynamic Ollivier-Ricci curvature as a general method for identifying information-sharing gene modules in cancer.

Gene interaction network analysis in multiple myeloma detects complex immune dysregulation associated with shorter survival.

The plasma cell cancer multiple myeloma (MM) varies significantly in genomic characteristics, response to therapy, and long-term prognosis. To investigate global interactions in MM, we combined a known protein interaction network with a large clinically annotated MM dataset. We hypothesized that an unbiased network analysis method based on large-scale similarities in gene expression, copy number aberration, and protein interactions may provide novel biological insights. Applying a novel measure of network robustness, Ollivier-Ricci Curvature, we examined patterns in the RNA-Seq gene expression and CNA data and how they relate to clinical outcomes. Hierarchical clustering using ORC differentiated high-risk subtypes with low progression free survival. Differential gene expression analysis defined 118 genes with significantly aberrant expression. These genes, while not previously associated with MM, were associated with DNA repair, apoptosis, and the immune system. Univariate analysis identified 8/118 to be prognostic genes; all associated with the immune system. A network topology analysis identified both hub and bridge genes which connect known genes of biological significance of MM. Taken together, gene interaction network analysis in MM uses a novel method of global assessment to demonstrate complex immune dysregulation associated with shorter survival.

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. To address this, our group has developed geometric network analysis techniques on multi-omics data in connection with prior biological knowledge derived from protein-protein interactions (PPIs) or pathways. Geometric features obtained from the genomic network, such as Ollivier-Ricci curvature and the invariant measure of the associated Markov chain, have been shown to be predictive of survival outcomes in various cancers. In this study, we propose a novel supervised deep learning method called geometric graph neural network (GGNN) that incorporates such geometric features into deep learning for enhanced predictive power and interpretability. More specifically, we utilize a state-of-the-art graph neural network with sparse connections between the hidden layers based on known biology of the PPI network and pathway information. Geometric features along with multi-omics data are then incorporated into the corresponding layers. The proposed approach utilizes a local-global principle in such a manner that highly predictive features are selected at the front layers and fed directly to the last layer for multivariable Cox proportional-hazards regression modeling. The method was applied to multi-omics data from the CoMMpass study of multiple myeloma and ten major cancers in The Cancer Genome Atlas (TCGA). In most experiments, our method showed superior predictive performance compared to other alternative methods.

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. Copy number alterations (CNAs) from targeted and whole-exome sequencing data were extracted for HGSOC patients (n = 45) treated with ICIs. CNAs at a gene level were represented on a protein-protein interaction network to define patient-specific networks with a fixed topology. A version of Ollivier-Ricci curvature was used to identify genes that play a potentially key role in response to immunotherapy and further to stratify patients at high risk of mortality. Overall survival (OS) was defined as the time from the start of ICI treatment to either death or last follow-up. Kaplan-Meier analysis with log-rank test was performed to assess OS between the high and low curvature classified groups. The network curvature analysis stratified patients at high risk of mortality with p = 0.00047 in Kaplan-Meier analysis in HGSOC patients receiving ICI. Genes with high curvature were in accordance with CNAs relevant to ovarian cancer. Network curvature using CNAs has the potential to be a novel predictor for OS in HGSOC patients treated with immunotherapy.

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 results are demonstrated on a number of synthetic and real vector-valued data sets.

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. Over the past 8 yr, novel data in animals and humans have begun to shed new light on these processes in the form of the "glymphatic system," a brain-wide perivascular transit passageway dedicated to CSF transport and interstitial fluid exchange that facilitates metabolic waste drainage from the brain. Here we will discuss glymphatic system anatomy and methods to visualize and quantify glymphatic system (GS) transport in the brain and also discuss physiological drivers of its function in normal brain and in neurodegeneration.

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. rOMT analysis with a Lagrangian perspective of GS transport revealed that solute speed was faster in CSF compared to grey and white matter. Further, rOMT analysis also demonstrated 2-fold differences in regional solute speed within the brain. Collectively, these results imply that advective transport dominates in CSF while diffusion and advection both contribute to GS transport in parenchyma. In a rat model of cerebral small vessel disease (cSVD), solute transport in the perivascular spaces (PVS) and PVS-to-tissue transfer was slower compared to normal rats. Thus, the analytical framework of rOMT provides novel insights in the local dynamics of GS transport that may have implications for neurodegenerative diseases. Future studies should apply the rOMT analysis approach to confirm GS transport reductions in humans with cSVD.

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. This provides a natural capability to identify and distinguish flows under different conditions. The Lagrangian analysis applied to the glymphatic system (brain waste removal pathway associated with Alzheimer's Disease) successfully captures known flows and distinguishes between flow patterns under two different anesthetics, providing deeper insights into altered states of waste drainage.

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. The CA tissue concentration information was taken as the input in the data-driven OMT model. The OMT approach was tested on HNSCC DCE data that provides quantitative information for forward flux ( ΦF ) and backward flux ( ΦB ). OMT-derived ΦF was compared with the volume transfer constant for CA, Ktrans , derived from the Extended Tofts Model (ETM). RESULTS: The OMT-derived flows showed a consistent jump in the CA diffusive behavior across the images in accordance with the known CA dynamics. The mean forward flux was 0.0082 ± 0.0091 ( min-1 ) whereas the mean advective component was 0.0052 ± 0.0086 ( min-1 ) in the HNSCC patients. The diffusive percentages in forward and backward flux ranged from 8.67% to 18.76% and 12.76% to 30.36%, respectively. The OMT model accounts for intervoxel CA movement and results show that the forward flux ( ΦF ) is comparable with the ETM-derived Ktrans . CONCLUSIONS: This is a novel data-driven study based on optimal mass transport principles applied to patient DCE imaging to analyze CA flow in HNSCC.

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. Using this regularized OT app-roach, we can incorporate diffusion, handle noise, and accurately capture and visualize the time varying dynamics in GS transport. Moreover, we are able to reduce the registration mean-squared and infinity-norm error across time points by up to a factor of 5 as compared to the current state-of-the-art method. Our visualization pipeline yields flow patterns that align well with experts' current findings of the glymphatic system.

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. By using paramagnetic tracers administered into CSF of rodents, we previously showed the utility of MRI in characterizing a macroscopic whole brain view of glymphatic transport but we have yet to define and visualize the specific flow patterns. Here we have applied an alternative mathematical analysis approach to a dynamic time series of MRI images acquired every 4min over ∼3h in anesthetized rats, following administration of a small molecular weight paramagnetic tracer into the CSF reservoir of the cisterna magna. We use Optimal Mass Transport (OMT) to model the glymphatic flow vector field, and then analyze the flow to find the network of CSF-ISF flow channels. We use 3D visualization computational tools to visualize the OMT defined network of CSF-ISF flow channels in relation to anatomical and vascular key landmarks from the live rodent brain. The resulting OMT model of the glymphatic transport network agrees largely with the current understanding of the glymphatic transport patterns defined by dynamic contrast-enhanced MRI revealing key CSF transport pathways along the ventral surface of the brain with a trajectory towards the pineal gland, cerebellum, hypothalamus and olfactory bulb. In addition, the OMT analysis also revealed some interesting previously unnoticed behaviors regarding CSF transport involving parenchymal streamlines moving from ventral reservoirs towards the surface of the brain, olfactory bulb and large central veins.