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PurposeNetwork analysis methods can potentially quantify cancer disturbances 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.MethodsCopy 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.ResultsThe network curvature analysis stratified patients at high risk of mortality with p=0.00047 in Kaplan-Meier analysis. Genes with high curvature were in accordance with CNAs relevant to ovarian cancer.ConclusionNetwork curvature using CNAs has the potential to be a novel predictor for OS in HGSOC patients treated with immunotherapy.

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. Ten patients with head and neck squamous cell carcinoma (HNSCC) were enrolled in the study between June 2014 and October 2015 and under-went 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). 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 8.67–18.76% and 12.76–30.36%, respectively. The OMT model accounts for intervoxel CA movement and results show that the forward flux (ΦF) is comparable with the ETM-derived Ktrans. This is a novel data-driven study based on optimal mass transport principles applied to patient DCE imaging to analyze CA flow in HNSCC.

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.

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.

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.

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 4 min over ∼3 hrs 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.