Lung Topology Characteristics in patients with Chronic Obstructive Pulmonary Disease

Quantification of Airway Structures by Persistent Homology

We propose two types of novel morphological metrics for quantifying the geometry of tubular structures on computed tomography (CT) images. We apply our metrics to identify irregularities in the airway of patients with chronic obstructive pulmonary disease (COPD) and demonstrate that they provide complementary information to the conventional metrics used to assess COPD, such as the tissue density distribution in lung parenchyma and the wall area ratio of the segmented airway. The three-dimensional shape of the airway and its abstraction as a rooted tree with the root at the trachea carina are automatically extracted from a lung CT volume, and the two metrics are computed based on a mathematical tool called persistent homology; treeH0 quantifies the distribution of branch lengths to assess the complexity of the tree-like structure and radialH0 quantifies the irregularities in the luminal radius along the airway. We show our metrics are associated with clinical outcomes.

Topological Data Analysis and Use of Mapper for Cerebral Aneurysm Rupture Status Discrimination Based on 3-Dimensional Shape Analysis

BACKGROUND AND OBJECTIVES

Topological data analysis (TDA), which identifies patterns in data through simplified topological signatures, has yet to be applied to aneurysm research. We investigate TDA Mapper graphs (Mapper) for aneurysm rupture discrimination.

METHODS

Two hundred sixteen bifurcation aneurysms (90 ruptured) from 3-dimensional rotational angiography were segmented from vasculature and evaluated for 12 size/shape and 18 enhanced radiomics features. Using Mapper, uniformly dense aneurysm models were represented as graph structures and described by graph shape metrics. Mapper dissimilarity scores (MDS) were computed between pairs of aneurysms based on shape metrics. Lower MDS described similar shapes, whereas high MDS represented shapes that do not share common characteristics. Ruptured/unruptured average MDS scores (how "far" an aneurysm is shape-wise to ruptured/unruptured data sets, respectively) were evaluated for each aneurysm. Rupture status discrimination univariate and multivariate statistics were reported for all features.

RESULTS

The average MDS for pairs of ruptured aneurysms were significantly larger compared with unruptured pairs (0.055 ± 0.027 vs 0.039 ± 0.015, P < .0001). Low MDS suggest that, in contrast to ruptured aneurysms, unruptured aneurysms have similar shape characteristics. An MDS threshold value of 0.0417 (area under the curve [AUC] = 0.73, 80% specificity, 60% sensitivity) was identified for rupture status classification. Under this predictive model, MDS scores <0.0417 would identify unruptured status. MDS statistical performance in discriminating rupture status was similar to that of nonsphericity and radiomics Flatness (AUC = 0.73), outperforming other features. Ruptured aneurysms were more elongated ( P < .0001), flatter ( P < .0001), and showed higher nonsphericity ( P < .0001) compared with unruptured. Including MDS in multivariate analysis resulted in AUC = 0.82, outperforming multivariate analysis on size/shape (AUC = 0.76) and enhanced radiomics (AUC = 0.78) alone.

CONCLUSION

A novel application of Mapper TDA was proposed for aneurysm evaluation, with promising results for rupture status classification. Multivariate analysis incorporating Mapper resulted in high accuracy, which is particularly important given that bifurcation aneurysms are challenging to classify morphologically. This proof-of-concept study warrants future investigation into optimizing Mapper functionality for aneurysm research.

A topological classifier to characterize brain states: When shape matters more than variance

Despite the remarkable accuracies attained by machine learning classifiers to separate complex datasets in a supervised fashion, most of their operation falls short to provide an informed intuition about the structure of data, and, what is more important, about the phenomena being characterized by the given datasets. By contrast, topological data analysis (TDA) is devoted to study the shape of data clouds by means of persistence descriptors and provides a quantitative characterization of specific topological features of the dataset under scrutiny. Here we introduce a novel TDA-based classifier that works on the principle of assessing quantifiable changes on topological metrics caused by the addition of new input to a subset of data. We used this classifier with a high-dimensional electro-encephalographic (EEG) dataset recorded from eleven participants during a previous decision-making experiment in which three motivational states were induced through a manipulation of social pressure. We calculated silhouettes from persistence diagrams associated with each motivated state with a ready-made band-pass filtered version of these signals, and classified unlabeled signals according to their impact on each reference silhouette. Our results show that in addition to providing accuracies within the range of those of a nearest neighbour classifier, the TDA classifier provides formal intuition of the structure of the dataset as well as an estimate of its intrinsic dimension. Towards this end, we incorporated variance-based dimensionality reduction methods to our dataset and found that in most cases the accuracy of our TDA classifier remains essentially invariant beyond a certain dimension.

A topological data analysis study on murine pulmonary arterial trees with pulmonary hypertension

Pulmonary hypertension (PH), defined by a mean pulmonary arterial blood pressure above 20 mmHg in the main pulmonary artery, is a cardiovascular disease impacting the pulmonary vasculature. PH is accompanied by chronic vascular remodeling, wherein vessels become stiffer, large vessels dilate, and smaller vessels constrict. Some types of PH, including hypoxia-induced PH (HPH), also lead to microvascular rarefaction. This study analyzes the change in pulmonary arterial morphometry in the presence of HPH using novel methods from topological data analysis (TDA). We employ persistent homology to quantify arterial morphometry for control and HPH mice characterizing normalized arterial trees extracted from micro-computed tomography (micro-CT) images. We normalize generated trees using three pruning algorithms before comparing the topology of control and HPH trees. This proof-of-concept study shows that the pruning method affects the spatial tree statistics and complexity. We find that HPH trees are stiffer than control trees but have more branches and a higher depth. Relative directional complexities are lower in HPH animals in the right, ventral, and posterior directions. For the radius pruned trees, this difference is more significant at lower perfusion pressures enabling analysis of remodeling of larger vessels. At higher pressures, the arterial networks include more distal vessels. Results show that the right, ventral, and posterior relative directional complexities increase in HPH trees, indicating the remodeling of distal vessels in these directions. Strahler order pruning enables us to generate trees of comparable size, and results, at all pressure, show that HPH trees have lower complexity than the control trees. Our analysis is based on data from 6 animals (3 control and 3 HPH mice), and even though our analysis is performed in a small dataset, this study provides a framework and proof-of-concept for analyzing properties of biological trees using tools from Topological Data Analysis (TDA). Findings derived from this study bring us a step closer to extracting relevant information for quantifying remodeling in HPH.

Persistent homology analysis distinguishes pathological bone microstructure in non-linear microscopy images

We present a topological method for the detection and quantification of bone microstructure from non-linear microscopy images. Specifically, we analyse second harmonic generation (SHG) and two photon excited autofluorescence (TPaF) images of bone tissue which capture the distribution of matrix (fibrillar collagen) structure and autofluorescent molecules, respectively. Using persistent homology statistics with a signed Euclidean distance transform filtration on binary patches of images, we are able to quantify the number, size, distribution, and crowding of holes within and across samples imaged at the microscale. We apply our methodology to a previously characterized murine model of skeletal pathology whereby vascular endothelial growth factor expression was deleted in osteocalcin-expressing cells (OcnVEGFKO) presenting increased cortical porosity, compared to wild type (WT) littermate controls. We show significant differences in topological statistics between the OcnVEGFKO and WT groups and, when classifying the males, or females respectively, into OcnVEGFKO or WT groups, we obtain high prediction accuracies of 98.7% (74.2%) and 77.8% (65.8%) respectively for SHG (TPaF) images. The persistence statistics that we use are fully interpretable, can highlight regions of abnormality within an image and identify features at different spatial scales.

Multiscale topology characterizes dynamic tumor vascular networks

Advances in imaging techniques enable high-resolution three-dimensional (3D) visualization of vascular networks over time and reveal abnormal structural features such as twists and loops, and their quantification is an active area of research. Here, we showcase how topological data analysis, the mathematical field that studies the "shape" of data, can characterize the geometric, spatial, and temporal organization of vascular networks. We propose two topological lenses to study vasculature, which capture inherent multiscale features and vessel connectivity, and surpass the single-scale analysis of existing methods. We analyze images collected using intravital and ultramicroscopy modalities and quantify spatiotemporal variation of twists, loops, and avascular regions (voids) in 3D vascular networks. This topological approach validates and quantifies known qualitative trends such as dynamic changes in tortuosity and loops in response to antibodies that modulate vessel sprouting; furthermore, it quantifies the effect of radiotherapy on vessel architecture.

Multiscale topology characterizes dynamic tumor vascular networks

Advances in imaging techniques enable high-resolution three-dimensional (3D) visualization of vascular networks over time and reveal abnormal structural features such as twists and loops, and their quantification is an active area of research. Here, we showcase how topological data analysis, the mathematical field that studies the "shape" of data, can characterize the geometric, spatial, and temporal organization of vascular networks. We propose two topological lenses to study vasculature, which capture inherent multiscale features and vessel connectivity, and surpass the single-scale analysis of existing methods. We analyze images collected using intravital and ultramicroscopy modalities and quantify spatiotemporal variation of twists, loops, and avascular regions (voids) in 3D vascular networks. This topological approach validates and quantifies known qualitative trends such as dynamic changes in tortuosity and loops in response to antibodies that modulate vessel sprouting; furthermore, it quantifies the effect of radiotherapy on vessel architecture.

Topological data analysis in biomedicine: A review

Significant technological advances made in recent years have shepherded a dramatic increase in utilization of digital technologies for biomedicine- everything from the widespread use of electronic health records to improved medical imaging capabilities and the rising ubiquity of genomic sequencing contribute to a "digitization" of biomedical research and clinical care. With this shift toward computerized tools comes a dramatic increase in the amount of available data, and current tools for data analysis capable of extracting meaningful knowledge from this wealth of information have yet to catch up. This article seeks to provide an overview of emerging mathematical methods with the potential to improve the abilities of clinicians and researchers to analyze biomedical data, but may be hindered from doing so by a lack of conceptual accessibility and awareness in the life sciences research community. In particular, we focus on topological data analysis (TDA), a set of methods grounded in the mathematical field of algebraic topology that seeks to describe and harness features related to the "shape" of data. We aim to make such techniques more approachable to non-mathematicians by providing a conceptual discussion of their theoretical foundations followed by a survey of their published applications to scientific research. Finally, we discuss the limitations of these methods and suggest potential avenues for future work integrating mathematical tools into clinical care and biomedical informatics.

Novel Insights into Aspergillus fumigatus Pathogenesis and Host Response from State-of-the-Art Imaging of Host-Pathogen Interactions during Infection

Aspergillus fumigatus spores initiate more than 3,000,000 chronic and 300,000 invasive diseases annually, worldwide. Depending on the immune status of the host, inhalation of these spores can lead to a broad spectrum of disease, including invasive aspergillosis, which carries a 50% mortality rate overall; however, this mortality rate increases substantially if the infection is caused by azole-resistant strains or diagnosis is delayed or missed. Increasing resistance to existing antifungal treatments is becoming a major concern; for example, resistance to azoles (the first-line available oral drug against Aspergillus species) has risen by 40% since 2006. Despite high morbidity and mortality, the lack of an in-depth understanding of A. fumigatus pathogenesis and host response has hampered the development of novel therapeutic strategies for the clinical management of fungal infections. Recent advances in sample preparation, infection models and imaging techniques applied in vivo have addressed important gaps in fungal research, whilst questioning existing paradigms. This review highlights the successes and further potential of these recent technologies in understanding the host-pathogen interactions that lead to aspergillosis.

CT Radiomic Features of Superior Mesenteric Artery Involvement in Pancreatic Ductal Adenocarcinoma: A Pilot Study

Background Current imaging methods for prediction of complete margin resection (R0) in patients with pancreatic ductal adenocarcinoma (PDAC) are not reliable. Purpose To investigate whether tumor-related and perivascular CT radiomic features improve preoperative assessment of arterial involvement in patients with surgically proven PDAC. Materials and Methods This retrospective study included consecutive patients with PDAC who underwent surgery after preoperative CT between 2012 and 2019. A three-dimensional segmentation of PDAC and perivascular tissue surrounding the superior mesenteric artery (SMA) was performed on preoperative CT images with radiomic features extracted to characterize morphology, intensity, texture, and task-based spatial information. The reference standard was the pathologic SMA margin status of the surgical sample: SMA involved (tumor cells ≤1 mm from margin) versus SMA not involved (tumor cells >1 mm from margin). The preoperative assessment of SMA involvement by a fellowship-trained radiologist in multidisciplinary consensus was the comparison. High reproducibility (intraclass correlation coefficient, 0.7) and the Kolmogorov-Smirnov test were used to select features included in the logistic regression model. Results A total of 194 patients (median age, 66 years; interquartile range, 60-71 years; age range, 36-85 years; 99 men) were evaluated. Aside from surgery, 148 patients underwent neoadjuvant therapy. A total of 141 patients' samples did not involve SMA, whereas 53 involved SMA. A total of 1695 CT radiomic features were extracted. The model with five features (maximum hugging angle, maximum diameter, logarithm robust mean absolute deviation, minimum distance, square gray level co-occurrence matrix correlation) showed a better performance compared with the radiologist assessment (model vs radiologist area under the curve, 0.71 [95% CI: 0.62, 0.79] vs 0.54 [95% CI: 0.50, 0.59]; P < .001). The model showed a sensitivity of 62% (33 of 53 patients) (95% CI: 51, 77) and a specificity of 77% (108 of 141 patients) (95% CI: 60, 84). Conclusion A model based on tumor-related and perivascular CT radiomic features improved the detection of superior mesenteric artery involvement in patients with pancreatic ductal adenocarcinoma. © RSNA, 2021 Online supplemental material is available for this article. See also the editorial by Do and Kambadakone in this issue.

Multiparameter persistent homology landscapes identify immune cell spatial patterns in tumors

Highly resolved spatial data of complex systems encode rich and nonlinear information. Quantification of heterogeneous and noisy data-often with outliers, artifacts, and mislabeled points-such as those from tissues, remains a challenge. The mathematical field that extracts information from the shape of data, topological data analysis (TDA), has expanded its capability for analyzing real-world datasets in recent years by extending theory, statistics, and computation. An extension to the standard theory to handle heterogeneous data is multiparameter persistent homology (MPH). Here we provide an application of MPH landscapes, a statistical tool with theoretical underpinnings. MPH landscapes, computed for (noisy) data from agent-based model simulations of immune cells infiltrating into a spheroid, are shown to surpass existing spatial statistics and one-parameter persistent homology. We then apply MPH landscapes to study immune cell location in digital histology images from head and neck cancer. We quantify intratumoral immune cells and find that infiltrating regulatory T cells have more prominent voids in their spatial patterns than macrophages. Finally, we consider how TDA can integrate and interrogate data of different types and scales, e.g., immune cell locations and regions with differing levels of oxygenation. This work highlights the power of MPH landscapes for quantifying, characterizing, and comparing features within the tumor microenvironment in synthetic and real datasets.

A homological approach to a mathematical definition of pulmonary fibrosis and emphysema on computed tomography

Three-dimensional imaging is essential to evaluate local abnormalities and understand structure-function relationships in an organ. However, quantifiable and interpretable methods to localize abnormalities remain unestablished. Visual assessments are prone to bias, machine learning methods depend on training images, and the underlying decision principle is usually difficult to interpret. Here, we developed a homological approach to mathematically define emphysema and fibrosis in the lungs on computed tomography (CT). With the use of persistent homology, the density of homological features, including connected components, tunnels, and voids, was extracted from the volumetric CT scans of lung diseases. A pair of CT values at which each homological feature appeared (birth) and disappeared (death) was computed by sweeping the threshold levels from higher to lower CT values. Consequently, fibrosis and emphysema were defined as voxels with dense voids having a longer lifetime (birth-death difference) and voxels with dense connected components having a lower birth, respectively. In an independent dataset including subjects with idiopathic pulmonary fibrosis (IPF), chronic obstructive pulmonary disease (COPD), and combined pulmonary fibrosis and emphysema (CPFE), the proposed definition enabled accurate segmentation with comparable quality to deep learning in terms of Dice coefficients. Persistent homology-defined fibrosis was closely associated with physiological abnormalities such as impaired diffusion capacity and long-term mortality in subjects with IPF and CPFE, and persistent homology-defined emphysema was associated with impaired diffusion capacity in subjects with COPD. The present persistent homology-based evaluation of structural abnormalities could help explore the clinical and physiological impacts of structural changes and morphological mechanisms of disease progression.NEW & NOTEWORTHY This study proposes a homological approach to mathematically define a three-dimensional texture feature of emphysema and fibrosis on chest computed tomography using persistent homology. The proposed definition enabled accurate segmentation with comparable quality to deep learning while offering higher interpretability than deep learning-based methods.

Comprehensive Analysis of Heat and Water Exchanges in the Human Lungs

This work presents a new mathematical model of the heat and water exchanges in the human lungs (newborn to adult). This model is based on a local description of the water and energy transports in both the lumen and the surrounding tissues, and is presented in a comprehensive, dimensionless framework with explicitly stated assumptions and a strong physiological background. The model is first used to analyze and quantify the key phenomena and dimensionless numbers governing these heat and water exchanges and then it is applied to an adult in various situations (varying atmospheric conditions, exercising…). The results highlight several interesting physiological elements. They show that the bronchial region of the lungs is able to condition the air in all the considered situations even if, sometimes, for instance when exercising, distal generations have to be involved. The model also shows that these distal generations are super-conditioners. Moreover, the results quantify the key role of the submucosal glands in mucus hydration. They also show that, during expiration, a significant cooling of the air and condensation of water occur along the respiratory tract as the vascularization of the tissues surrounding the airways is not able to maintain these tissues at body temperature during inspiration. Due to the interaction between several phenomena, it appears that the ratio of the amount of water returned to the mucosa during expiration to the amount extracted during inspiration is almost independent of the breathing conditions (around 33%). The results also show that, in acute situations, such as suffering from a pathology with airway dysfunction, when being intubated or when exercising above an intensity threshold, the heat and water exchanges in the lungs may be critical regarding mucus hydration. In proximal generations, the evaporation may overwhelm the ability of the submucosal glands to replenish the airway surface liquid with water. In some situations, the cooling of the mucosa may be very important; it can even become colder than the inspired air, due to evaporative cooling. Finally, the results show that breathing cold air can significantly increase the exchanges between the lungs and the environment, which can be critical regarding disease transmission.

Radiomics approach for survival prediction in chronic obstructive pulmonary disease

OBJECTIVES

To apply radiomics analysis for overall survival prediction in chronic obstructive pulmonary disease (COPD), and evaluate the performance of the radiomics signature (RS).

METHODS

This study included 344 patients from the Korean Obstructive Lung Disease (KOLD) cohort. External validation was performed on a cohort of 112 patients. In total, 525 chest CT-based radiomics features were semi-automatically extracted. The five most useful features for survival prediction were selected by least absolute shrinkage and selection operation (LASSO) Cox regression analysis and used to generate a RS. The ability of the RS for classifying COPD patients into high or low mortality risk groups was evaluated with the Kaplan-Meier survival analysis and Cox proportional hazards regression analysis.

RESULTS

The five features remaining after the LASSO analysis were %LAA_-950, AWT_Pi10_6^th, AWT_Pi10_heterogeneity, %WA_heterogeneity, and VA_18mm. The RS demonstrated a C-index of 0.774 in the discovery group and 0.805 in the validation group. Patients with a RS greater than 1.053 were classified into the high-risk group and demonstrated worse overall survival than those in the low-risk group in both the discovery (log-rank test, < 0.001; hazard ratio [HR], 5.265) and validation groups (log-rank test, < 0.001; HR, 5.223). For both groups, RS was significantly associated with overall survival after adjustments for patient age and body mass index.

CONCLUSIONS

A radiomics approach for survival prediction and risk stratification in COPD patients is feasible, and the constructed radiomics model demonstrated acceptable performance. The RS derived from chest CT data of COPD patients was able to effectively identify those at increased risk of mortality.

KEY POINTS

• A total of 525 chest CT-based radiomics features were extracted and the five radiomics features of %LAA_-950, AWT_Pi10_6^th, AWT_Pi10_heterogeneity, %WA_heterogeneity, and VA_18mm were selected to generate a radiomics model. • A radiomics model for predicting survival of COPD patients demonstrated reliable performance with a C-index of 0.774 in the discovery group and 0.805 in the validation group. • Radiomics approach was able to effectively identify COPD patients with an increased risk of mortality, and patients assigned to the high-risk group demonstrated worse overall survival in both the discovery and validation groups.

Modeling of the Transport and Exchange of a Gas Species in Lungs With an Asymmetric Branching Pattern. Application to Nitric Oxide

Over the years, various studies have been dedicated to the mathematical modeling of gas transport and exchange in the lungs. Indeed, the access to the distal region of the lungs with direct measurements is limited and, therefore, models are valuable tools to interpret clinical data and to give more insights into the phenomena taking place in the deepest part of the lungs. In this work, a new computational model of the transport and exchange of a gas species in the human lungs is proposed. It includes (i) a method to generate a lung geometry characterized by an asymmetric branching pattern, based on the values of several parameters that have to be given by the model user, and a method to possibly alter this geometry to mimic lung diseases, (ii) the calculation of the gas flow distribution in this geometry during inspiration or expiration (taking into account the increased resistance to the flow in airways where the flow is non-established), (iii) the evaluation of the exchange fluxes of the gaseous species of interest between the tissues composing the lungs and the lumen, and (iv) the computation of the concentration profile of the exchanged species in the lumen of the tracheobronchial tree. Even if the model is developed in a general framework, a particular attention is given to nitric oxide, as it is not only a gas species of clinical interest, but also a gas species that is both produced in the walls of the airways and consumed within the alveolar region of the lungs. First, the model is presented. Then, several features of the model, applied to lung geometry, gas flow and NO exchange and transport, are discussed, compared to existing works and notably used to give new insights into experimental data available in the literature, regarding diseases, such as asthma, cystic fibrosis, and chronic obstructive pulmonary disease.

Deep Small Bowel Segmentation with Cylindrical Topological Constraints

We present a novel method for small bowel segmentation where a cylindrical topological constraint based on persistent homology is applied. To address the touching issue which could break the applied constraint, we propose to augment a network with an additional branch to predict an inner cylinder of the small bowel. Since the inner cylinder is free of the touching issue, a cylindrical shape constraint applied on this augmented branch guides the network to generate a topologically correct segmentation. For strict evaluation, we achieved an abdominal computed tomography dataset with dense segmentation ground-truths. The proposed method showed clear improvements in terms of four different metrics compared to the baseline method, and also showed the statistical significance from a paired t-test.

The shape of things to come: Topological data analysis and biology, from molecules to organisms

Shape is data and data is shape. Biologists are accustomed to thinking about how the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. Less often do we consider that data itself has shape and structure, or that it is possible to measure the shape of data and analyze it. Here, we review applications of topological data analysis (TDA) to biology in a way accessible to biologists and applied mathematicians alike. TDA uses principles from algebraic topology to comprehensively measure shape in data sets. Using a function that relates the similarity of data points to each other, we can monitor the evolution of topological features-connected components, loops, and voids. This evolution, a topological signature, concisely summarizes large, complex data sets. We first provide a TDA primer for biologists before exploring the use of TDA across biological sub-disciplines, spanning structural biology, molecular biology, evolution, and development. We end by comparing and contrasting different TDA approaches and the potential for their use in biology. The vision of TDA, that data are shape and shape is data, will be relevant as biology transitions into a data-driven era where the meaningful interpretation of large data sets is a limiting factor.