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.

Functional transcriptional signatures for tumor-type-agnostic phenotype prediction

Cancer transcriptional patterns exhibit both shared and unique features across diverse cancer types, but whether these patterns are sufficient to characterize the full breadth of tumor phenotype heterogeneity remains an open question. We hypothesized that cancer transcriptional diversity mirrors patterns in normal tissues optimized for distinct functional tasks. Starting with normal tissue transcriptomic profiles, we use non-negative matrix factorization to derive six distinct transcriptomic phenotypes, called archetypes, which combine to describe both normal tissue patterns and variations across a broad spectrum of malignancies. We show that differential enrichment of these signatures correlates with key tumor characteristics, including overall patient survival and drug sensitivity, independent of clinically actionable DNA alterations. Additionally, we show that in HR+/HER2- breast cancers, metastatic tumors adopt transcriptomic signatures consistent with the invaded tissue. Broadly, our findings suggest that cancer often arrogates normal tissue transcriptomic characteristics as a component of both malignant progression and drug response. This quantitative framework provides a strategy for connecting the diversity of cancer phenotypes and could potentially help manage individual patients.

Unbalanced regularized optimal mass transport with applications to fluid flows in the brain

As a generalization of the optimal mass transport (OMT) approach of Benamou and Brenier's, the regularized optimal mass transport (rOMT) formulates a transport problem from an initial mass configuration to another with the optimality defined by the total kinetic energy, but subject to an advection-diffusion constraint equation. Both rOMT and the Benamou and Brenier's formulation require the total initial and final masses to be equal; mass is preserved during the entire transport process. However, for many applications, e.g., in dynamic image tracking, this constraint is rarely if ever satisfied. Therefore, we propose to employ an unbalanced version of rOMT to remove this constraint together with a detailed numerical solution procedure and applications to analyzing fluid flows in the brain.

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.

Abstract 6541: Geometry of gene expression network reveals potential novel indicator in Ewing sarcoma

Oncogenic driver mutations in different pediatric sarcoma subtypes have been identified but may not be druggable. In general, identifying novel therapeutic targets and biomarkers for response remains a major challenge. We hypothesize that considering the structure of the interaction network in which the genes operate as a system is crucial for understanding a gene's role. We propose to use the protein interaction network geometry to characterize the shape of network architecture and identify key aspects of direct and indirect cooperation pertaining to the cancer network and prognosis using geometrical methods.

We model gene networks as weighted graphs where edges indicate protein-level interactions and edge weights estimate the strength of the interaction. The Human Protein Reference Database was used to define the gene network topology. RNA-Seq data from pediatric sarcoma tissues extracted from patients treated at MSK (n=12 Ewing sarcoma; n=29 osteosarcoma; n=20 desmoplastic small round cell tumor) was employed to prescribe correlation-based weights to create pediatric sarcoma subtype-specific weighted graphs. The geometry of the weighted gene networks was computed via a discrete notion of Ricci curvature.

Intuitively, the curvature provides a measure of feedback (triangles) in the network. Positive curvature reflects robust communication and ease of information transfer, while negative curvature reflects bridge-like architecture or bottlenecks of information flow. We utilized a dynamic (multi-scale) notion of curvature to quantify the functional associations between genes, computed as a function of scale between diffusion processes initially localized on each node (i.e., gene). The curvature becomes more positive on edges between communal genes and more negative on bridge-like edges between communities, until reaching the critical scale. Curvature therefore, as we demonstrate, partitions the cancer networks into functionally associated communities.

Community detection by removing bridge-edges, determined as edges with negative curvature at the critical scale, revealed sarcoma subtype-specific preferential gene associations. In particular, we agnostically found the EWSR1-FLI1 association in a cluster that was unique to the Ewing sarcoma network. Interestingly, we found ETV6 in the same community as the characteristic Ewing sarcoma EWSR1-FLI1 feature, suggesting a novel implication of ETV6 in Ewing sarcoma. These results suggest that persisting communities found by leveraging the cancer network geometry may identify potential mechanisms of drug resistance and actionable therapeutic targets.

Citation Format: Rena Elkin, Jung Hun Oh, Filemon Dela Cruz, Larry Norton, Joseph O. Deasy, Andrew L. Kung, Allen R. Tannenbaum. Geometry of gene expression network reveals potential novel indicator in Ewing sarcoma [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 6541.

Abstract 4657: Topological data analysis reveals pan-cancer immune phenotypes with immune-related survival differences

Cancer immune phenotypes present a wide range of heterogeneity across cases, with individual tumors displaying unique patterns of infiltrating immune cell types. Deconvolutional methods allow for scoring of various immune cell types in bulk tumor RNA as a quantification of immune phenotype. Understanding how immune phenotype relates to clinical outcome remains limited. Here, we demonstrate an approach applying topological data analysis to investigate differences of immune phenotype in a pan-cancer cohort (TCGA; n=11,373 tumors). We first define an Immune Activation Score based on relative abundance of activator and suppressor immune cell types and find this score depends on cancer type and distinguishes overall survival outcomes. We then implement a robust Mapper-based algorithm to delineate clusters of immune phenotypes of tumor samples across pan-cancer and within cancer types. Our method identifies immune-activated and immune-suppressed phenotypes with distinct survival outcomes and molecular features.

Citation Format: Kevin A. Murgas, Jung H. Oh, Joseph O. Deasy, Allen R. Tannenbaum. Topological data analysis reveals pan-cancer immune phenotypes with immune-related survival differences. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 4657.

Long-term p21 and p53 dynamics regulate the frequency of mitosis events and cell cycle arrest following radiation damage

Radiation exposure of healthy cells can halt cell cycle temporarily or permanently. In this work, we analyze the time evolution of p21 and p53 from two single cell datasets of retinal pigment epithelial cells exposed to several levels of radiation, and in particular, the effect of radiation on cell cycle arrest. Employing various quantification methods from signal processing, we show how p21 levels, and to a lesser extent p53 levels, dictate whether the cells are arrested in their cell cycle and how frequently these mitosis events are likely to occur. We observed that single cells exposed to the same dose of DNA damage exhibit heterogeneity in cellular outcomes and that the frequency of cell division is a more accurate monitor of cell damage rather than just radiation level. Finally, we show how heterogeneity in DNA damage signaling is manifested early in the response to radiation exposure level and has potential to predict long-term fate.

aWCluster: A Novel Integrative Network-Based Clustering of Multiomics for Subtype Analysis of Cancer Data

The remarkable growth of multi-platform genomic profiles has led to the challenge of multiomics data integration. In this study, we present a novel network-based multiomics clustering founded on the Wasserstein distance from optimal mass transport. This distance has many important geometric properties making it a suitable choice for application in machine learning and clustering. Our proposed method of aggregating multiomics and Wasserstein distance clustering (aWCluster) is applied to breast carcinoma as well as bladder carcinoma, colorectal adenocarcinoma, renal carcinoma, lung non-small cell adenocarcinoma, and endometrial carcinoma from The Cancer Genome Atlas project. Subtypes were characterized by the concordant effect of mRNA expression, DNA copy number alteration, and DNA methylation of genes and their neighbors in the interaction network. aWCluster successfully clusters all cancer types into classes with significantly different survival rates. Also, a gene ontology enrichment analysis of significant genes in the low survival subgroup of breast cancer leads to the well-known phenomenon of tumor hypoxia and the transcription factor ETS1 whose expression is induced by hypoxia. We believe aWCluster has the potential to discover novel subtypes and biomarkers by accentuating the genes that have concordant multiomics measurements in their interaction network, which are challenging to find without the network inference or with single omics analysis.

vWCluster: Vector-valued optimal transport for network based clustering using multi-omics data in breast cancer

In this paper, we present a network-based clustering method, called vector Wasserstein clustering (vWCluster), based on the vector-valued Wasserstein distance derived from optimal mass transport (OMT) theory. This approach allows for the natural integration of multi-layer representations of data in a given network from which one derives clusters via a hierarchical clustering approach. In this study, we applied the methodology to multi-omics data from the two largest breast cancer studies. The resultant clusters showed significantly different survival rates in Kaplan-Meier analysis in both datasets. CIBERSORT scores were compared among the identified clusters. Out of the 22 CIBERSORT immune cell types, 9 were commonly significantly different in both datasets, suggesting the difference of tumor immune microenvironment in the clusters. vWCluster can aggregate multi-omics data represented as a vectorial form in a network with multiple layers, taking into account the concordant effect of heterogeneous data, and further identify subgroups of tumors in terms of mortality.

Pan-Cancer Prediction of Cell-Line Drug Sensitivity Using Network-Based Methods

The development of reliable predictive models for individual cancer cell lines to identify an optimal cancer drug is a crucial step to accelerate personalized medicine, but vast differences in cancer cell lines and drug characteristics make it quite challenging to develop predictive models that result in high predictive power and explain the similarity of cell lines or drugs. Our study proposes a novel network-based methodology that breaks the problem into smaller, more interpretable problems to improve the predictive power of anti-cancer drug responses in cell lines. For the drug-sensitivity study, we used the GDSC database for 915 cell lines and 200 drugs. The theory of optimal mass transport was first used to separately cluster cell lines and drugs, using gene-expression profiles and extensive cheminformatic drug features, represented in a form of data networks. To predict cell-line specific drug responses, random forest regression modeling was separately performed for each cell-line drug cluster pair. Post-modeling biological analysis was further performed to identify potential biological correlates associated with drug responses. The network-based clustering method resulted in 30 distinct cell-line drug cluster pairs. Predictive modeling on each cell-line-drug cluster outperformed alternative computational methods in predicting drug responses. We found that among the four drugs top-ranked with respect to prediction performance, three targeted the PI3K/mTOR signaling pathway. Predictive modeling on clustered subsets of cell lines and drugs improved the prediction accuracy of cell-line specific drug responses. Post-modeling analysis identified plausible biological processes associated with drug responses.

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.

Supervised Image Classification Algorithm Using Representative Spatial Texture Features: Application to COVID-19 Diagnosis Using CT Images

Although there is no universal definition for texture, the concept in various forms is nevertheless widely used and a key element of visual perception to analyze images in different fields. The present work's main idea relies on the assumption that there exist representative samples, which we refer to as references as well, i.e., "good or bad" samples that represent a given dataset investigated in a particular data analysis problem. These representative samples need to be accounted for when designing predictive models with the aim of improving their performance. In particular, based on a selected subset of texture gray-level co-occurrence matrices (GLCMs) from the training cohort, we propose new representative spatial texture features, which we incorporate into a supervised image classification pipeline. The pipeline relies on the support vector machine (SVM) algorithm along with Bayesian optimization and the Wasserstein metric from optimal mass transport (OMT) theory. The selection of the best, "good and bad," GLCM references is considered for each classification label and performed during the training phase of the SVM classifier using a Bayesian optimizer. We assume that sample fitness is defined based on closeness (in the sense of the Wasserstein metric) and high correlation (Spearman's rank sense) with other samples in the same class. Moreover, the newly defined spatial texture features consist of the Wasserstein distance between the optimally selected references and the remaining samples. We assessed the performance of the proposed classification pipeline in diagnosing the corona virus disease 2019 (COVID-19) from computed tomographic (CT) images.

New Algorithms for 3-D Imaging and Analysis of Open-Celled Foams

Open-celled foams are three-dimensional networks of polymeric cells. The mechanical properties of a foam depend on the size and geometry of its cells. Since foams have a three-dimensional polyhedral structure, the two-dimensional characterization techniques currently used provide limited accuracy.

Nuclear magnetic resonance and x-ray tomography methods offeropportunities for three-dimensional imaging of these polyhedral structures. Software, which can use digital three-dimensional images to determine structural parameters such as strut length distribution, connectivity, and cell size, is being developed.

The image processing approach uses conformal curvature flow (CCF)segmentation to find the surfaces of foam struts in the 3-D images. Once these surfaces have been found, volume thinning is used to find the structural skeleton of the foam. The resulting data set can then be used to determine many statistical characteristics of the foam, including strut length distributions, window size and shape distributions, and cell size information.

Analysis of a reticulated polyurethane foam sample using these methods yielded a reasonable approximation of the structural skeleton of the sample.

Ricci curvature: An economic indicator for market fragility and systemic risk

Quantifying the systemic risk and fragility of financial systems is of vital importance in analyzing market efficiency, deciding on portfolio allocation, and containing financial contagions. At a high level, financial systems may be represented as weighted graphs that characterize the complex web of interacting agents and information flow (for example, debt, stock returns, and shareholder ownership). Such a representation often turns out to provide keen insights. We show that fragility is a system-level characteristic of "business-as-usual" market behavior and that financial crashes are invariably preceded by system-level changes in robustness. This was done by leveraging previous work, which suggests that Ricci curvature, a key geometric feature of a given network, is negatively correlated to increases in network fragility. To illustrate this insight, we examine daily returns from a set of stocks comprising the Standard and Poor's 500 (S&P 500) over a 15-year span to highlight the fact that corresponding changes in Ricci curvature constitute a financial "crash hallmark." This work lays the foundation of understanding how to design (banking) systems and policy regulations in a manner that can combat financial instabilities exposed during the 2007-2008 crisis.

Multimodal deformable registration of traumatic brain injury MR volumes via the Bhattacharyya distance

An important problem of neuroimaging data analysis for traumatic brain injury (TBI) is the task of coregistering MR volumes acquired using distinct sequences in the presence of widely variable pixel movements which are due to the presence and evolution of pathology. We are motivated by this problem to design a numerically stable registration algorithm which handles large deformations. To this end, we propose a new measure of probability distributions based on the Bhattacharyya distance, which is more stable than the widely used mutual information due to better behavior of the square root function than the logarithm at zero. Robustness is illustrated on two TBI patient datasets, each containing 12 MR modalities. We implement our method on graphics processing units (GPU) so as to meet the clinical requirement of time-efficient processing of TBI data. We find that 6 sare required to register a pair of volumes with matrix sizes of 256 × 256 × 60 on the GPU. In addition to exceptional time efficiency via its GPU implementation, this methodology provides a clinically informative method for the mapping and evaluation of anatomical changes in TBI.

Recursive feature elimination for brain tumor classification using desorption electrospray ionization mass spectrometry imaging

The metabolism and composition of lipids is of increasing interest for understanding and detecting disease processes. Lipid signatures of tumor type and grade have been demonstrated using magnetic resonance spectroscopy. Clinical management and ultimate prognosis of brain tumors depend largely on the tumor type, subtype, and grade. Mass spectrometry, a well-known analytical technique used to identify molecules in a given sample based on their mass, can significantly improve the problem of tumor type classification. This work focuses on the problem of identifying lipid features to use as input for classification. Feature selection could result in improvements in classifier performance, discovery of biomarkers, improved data interpretation, and patient treatment.

Joint CT/CBCT deformable registration and CBCT enhancement for cancer radiotherapy

This paper details an algorithm to simultaneously perform registration of computed tomography (CT) and cone-beam computed (CBCT) images, and image enhancement of CBCT. The algorithm employs a viscous fluid model which naturally incorporates two components: a similarity measure for registration and an intensity correction term for image enhancement. Incorporating an intensity correction term improves the registration results. Furthermore, applying the image enhancement term to CBCT imagery leads to an intensity corrected CBCT with better image quality. To achieve minimal processing time, the algorithm is implemented on a graphic processing unit (GPU) platform. The advantage of the simultaneous optimization strategy is quantitatively validated and discussed using a synthetic example. The effectiveness of the proposed algorithm is then illustrated using six patient datasets, three head-and-neck datasets and three prostate datasets.

Clinical Decision Support and Closed-Loop Control for Cardiopulmonary Management and Intensive Care Unit Sedation Using Expert Systems

Patients in the intensive care unit (ICU) who require mechanical ventilation due to acute respiratory failure also frequently require the administration of sedative agents. The need for sedation arises both from patient anxiety due to the loss of personal control and the unfamiliar and intrusive environment of the ICU, and also due to pain or other variants of noxious stimuli. While physicians select the agent(s) used for sedation and cardiovascular function, the actual administration of these agents is the responsibility of the nursing staff. If clinical decision support systems and closed-loop control systems could be developed for critical care monitoring and lifesaving interventions as well as the administration of sedation and cardiopulmonary management, the ICU nurse could be released from the intense monitoring of sedation, allowing her/him to focus on other critical tasks. One particularly attractive strategy is to utilize the knowledge and experience of skilled clinicians, capturing explicitly the rules expert clinicians use to decide on how to titrate drug doses depending on the level of sedation. In this paper, we extend the deterministic rule-based expert system for cardiopulmonary management and ICU sedation framework presented in [1] to a stochastic setting by using probability theory to quantify uncertainty and hence deal with more realistic clinical situations.

Classification of astrocytomas and oligodendrogliomas from mass spectrometry data using sparse kernel machines

Glioma histologies are the primary factor in prognostic estimates and are used in determining the proper course of treatment. Furthermore, due to the sensitivity of cranial environments, real-time tumor-cell classification and boundary detection can aid in the precision and completeness of tumor resection. A recent improvement to mass spectrometry known as desorption electrospray ionization operates in an ambient environment without the application of a preparation compound. This allows for a real-time acquisition of mass spectra during surgeries and other live operations. In this paper, we present a framework using sparse kernel machines to determine a glioma sample's histopathological subtype by analyzing its chemical composition acquired by desorption electrospray ionization mass spectrometry.

A compressive sensing approach for glioma margin delineation using mass spectrometry

Surgery, and specifically, tumor resection, is the primary treatment for most patients suffering from brain tumors. Medical imaging techniques, and in particular, magnetic resonance imaging are currently used in diagnosis as well as image-guided surgery procedures. However, studies show that computed tomography and magnetic resonance imaging fail to accurately identify the full extent of malignant brain tumors and their microscopic infiltration. Mass spectrometry is a well-known analytical technique used to identify molecules in a given sample based on their mass. In a recent study, it is proposed to use mass spectrometry as an intraoperative tool for discriminating tumor and non-tumor tissue. Integration of mass spectrometry with the resection module allows for tumor resection and immediate molecular analysis. In this paper, we propose a framework for tumor margin delineation using compressive sensing. Specifically, we show that the spatial distribution of tumor cell concentration can be efficiently reconstructed and updated using mass spectrometry information from the resected tissue. In addition, our proposed framework is model-free, and hence, requires no prior information of spatial distribution of the tumor cell concentration.

Agitation and pain assessment using digital imaging

Pain assessment in patients who are unable to verbally communicate with medical staff is a challenging problem in patient critical care. The fundamental limitations in sedation and pain assessment in the intensive care unit (ICU) stem from subjective assessment criteria, rather than quantifiable, measurable data for ICU sedation and analgesia. This often results in poor quality and inconsistent treatment of patient agitation and pain from nurse to nurse. Recent advancements in pattern recognition techniques using a relevance vector machine algorithm can assist medical staff in assessing sedation and pain by constantly monitoring the patient and providing the clinician with quantifiable data for ICU sedation. In this paper, we show that the pain intensity assessment given by a computer classifier has a strong correlation with the pain intensity assessed by expert and non-expert human examiners.

Relevance vector machine learning for neonate pain intensity assessment using digital imaging

Pain assessment in patients who are unable to verbally communicate is a challenging problem. The fundamental limitations in pain assessment in neonates stem from subjective assessment criteria, rather than quantifiable and measurable data. This often results in poor quality and inconsistent treatment of patient pain management. Recent advancements in pattern recognition techniques using relevance vector machine (RVM) learning techniques can assist medical staff in assessing pain by constantly monitoring the patient and providing the clinician with quantifiable data for pain management. The RVM classification technique is a Bayesian extension of the support vector machine (SVM) algorithm, which achieves comparable performance to SVM while providing posterior probabilities for class memberships and a sparser model. If classes represent "pure" facial expressions (i.e., extreme expressions that an observer can identify with a high degree of confidence), then the posterior probability of the membership of some intermediate facial expression to a class can provide an estimate of the intensity of such an expression. In this paper, we use the RVM classification technique to distinguish pain from nonpain in neonates as well as assess their pain intensity levels. We also correlate our results with the pain intensity assessed by expert and nonexpert human examiners.

Choice of in vivo versus idealized velocity boundary conditions influences physiologically relevant flow patterns in a subject-specific simulation of flow in the human carotid bifurcation

Accurate fluid mechanics models are important tools for predicting the flow field in the carotid artery bifurcation and for understanding the relationship between hemodynamics and the initiation and progression of atherosclerosis. Clinical imaging modalities can be used to obtain geometry and blood flow data for developing subject-specific human carotid artery bifurcation models. We developed subject-specific computational fluid dynamics models of the human carotid bifurcation from magnetic resonance (MR) geometry data and phase contrast MR velocity data measured in vivo. Two simulations were conducted with identical geometry, flow rates, and fluid parameters: (1) Simulation 1 used in vivo measured velocity distributions as time-varying boundary conditions and (2) Simulation 2 used idealized fully-developed velocity profiles as boundary conditions. The position and extent of negative axial velocity regions (NAVRs) vary between the two simulations at any given point in time, and these regions vary temporally within each simulation. The combination of inlet velocity boundary conditions, geometry, and flow waveforms influences NAVRs. In particular, the combination of flow division and the location of the velocity peak with respect to individual carotid geometry landmarks (bifurcation apex position and the departure angle of the internal carotid) influences the size and location of these reversed flow zones. Average axial wall shear stress (WSS) distributions are qualitatively similar for the two simulations; however, instantaneous WSS values vary with the choice of velocity boundary conditions. By developing subject-specific simulations from in vivo measured geometry and flow data and varying the velocity boundary conditions in otherwise identical models, we isolated the effects of measured versus idealized velocity distributions on blood flow patterns. Choice of velocity distributions at boundary conditions is shown to influence pathophysiologically relevant flow patterns in the human carotid bifurcation. Although mean WSS distributions are qualitatively similar for measured and idealized inlet boundary conditions, instantaneous NAVRs differ and warrant imposing in vivo velocity boundary conditions in computational simulations. A simulation based on in vivo measured velocity distributions is preferred for modeling hemodynamics in subject-specific carotid artery bifurcation models when studying atherosclerosis initiation and development.

3D modeling of patient-specific geometries of portal veins using MR images

In this note, we present an approach for developing patient-specific 3D models of portal veins to provide geometric boundary conditions for computational fluid dynamics (CFD) simulations of the blood flow inside portal veins. The study is based on MRI liver images of individual patients to which we apply image registration and segmentation techniques and inlet and outlet velocity profiles acquired using PC-MRI in the same imaging session. The portal vein and its connected veins are then extracted and visualized in 3D as surfaces. Image registration is performed to align shifted images between each breath-hold when the MRI images are acquired. The image segmentation method first labels each voxel in the 3D volume of interest by using a Bayesian probability approach, and then isolates the portal veins via active surfaces initialized inside the vessel. The method was tested with two healthy volunteers. In both cases, the main portal vein and its connected veins were successfully modeled and visualized.

Harmonic skeleton guided evaluation of stenoses in human coronary arteries

This paper presents a novel approach that three-dimensionally visualizes and evaluates stenoses in human coronary arteries by using harmonic skeletons. A harmonic skeleton is the center line of a multi-branched tubular surface extracted based on a harmonic function, which is the solution of the Laplace equation. This skeletonization method guarantees smoothness and connectivity and provides a fast and straightforward way to calculate local cross-sectional areas of the arteries, and thus provides the possibility to localize and evaluate coronary artery stenosis, which is a commonly seen pathology in coronary artery disease.

Multiscale 3D shape analysis using spherical wavelets

Shape priors attempt to represent biological variations within a population. When variations are global, Principal Component Analysis (PCA) can be used to learn major modes of variation, even from a limited training set. However, when significant local variations exist, PCA typically cannot represent such variations from a small training set. To address this issue, we present a novel algorithm that learns shape variations from data at multiple scales and locations using spherical wavelets and spectral graph partitioning. Our results show that when the training set is small, our algorithm significantly improves the approximation of shapes in a testing set over PCA, which tends to oversmooth data.

A Hamilton-Jacobi-Bellman approach to high angular resolution diffusion tractography

This paper describes a new framework for white matter tractography in high angular resolution diffusion data. A direction-dependent local cost is defined based on the diffusion data for every direction on the unit sphere. Minimum cost curves are determined by solving the Hamilton-Jacobi-Bellman using an efficient algorithm. Classical costs based on the diffusion tensor field can be seen as a special case. While the minimum cost (or equivalently the travel time of a particle moving along the curve) and the anisotropic front propagation frameworks are related, front speed is related to particle speed through a Legendre transformation which can severely impact anisotropy information for front propagation techniques. Implementation details and results on high angular diffusion data show that this method can successfully take advantage of the increased angular resolution in high b-value diffusion weighted data despite lower signal to noise ratio.

The 3D structure of real polymer foams

The intricate structure of polymeric foams may be examined using 3D imaging techniques such as MRI or X-ray tomography followed by image processing. Using a new 3D image processing technique, six images of polyurethane foams were analyzed to create computerized 3D models of the samples. Measurements on these models yielded distributions of many microstructural features, including strut length and window and cell shape distributions. Nearly 8000 struts, 4000 windows, and 376 cells were detected and measured in six polyurethane foam samples. When compared against previous theories and studies, these measurements showed that the structure of real polymeric foams differs significantly from both equilibrium models and aqueous foams. For example, previous studies of aqueous foams showed that about 70% of foam windows were pentagons. In the polymeric sample studied here, only 55% of windows were pentagonal.

Optical flow: a curve evolution approach

A novel approach for the computation of optical flow based on an L (1) type minimization is presented. It is shown that the approach has inherent advantages since it does not smooth the flow-velocity across the edges and hence preserves edge information. A numerical approach based on computation of evolving curves is proposed for computing the optical flow field. Computations are carried out on a number of real image sequences in order to illustrate the theory as well as the numerical approach.