Topological data analysis in biomedicine: A review

Sepsis endotypes identified by host gene expression across global cohorts

BACKGROUND

Sepsis from infection is a global health priority and clinical trials have failed to deliver effective therapeutic interventions. To address complicating heterogeneity in sepsis pathobiology, and improve outcomes, promising precision medicine approaches are helping identify disease endotypes, however, they require a more complete definition of sepsis subgroups.

METHODS

Here, we use RNA sequencing from peripheral blood to interrogate the host response to sepsis from participants in a global observational study carried out in West Africa, Southeast Asia, and North America (N = 494).

RESULTS

We identify four sepsis subtypes differentiated by 28-day mortality. A low mortality immunocompetent group is specified by features that describe the adaptive immune system. In contrast, the three high mortality groups show elevated clinical severity consistent with multiple organ dysfunction. The immunosuppressed group members show signs of a dysfunctional immune response, the acute-inflammation group is set apart by molecular features of the innate immune response, while the immunometabolic group is characterized by metabolic pathways such as heme biosynthesis.

CONCLUSIONS

Our analysis reveals details of molecular endotypes in sepsis that support immunotherapeutic interventions and identifies biomarkers that predict outcomes in these groups.

Metabolomics on depression: A comparison of clinical and animal research

BACKGROUND

Depression is a major cause of suicide and mortality worldwide. This study aims to conduct a systematic review to identify metabolic biomarkers and pathways for major depressive disorder (MDD), a prevalent subtype of clinical depression.

METHODS

We searched for metabolomics studies on depression published between January 2000 and January 2023 in the PubMed and Web of Science databases. The reported metabolic biomarkers were systematically evaluated and compared. Pathway analysis was implemented using MetaboAnalyst 5.0.

RESULTS

We included 26 clinical studies on MDD and 78 metabolomics studies on depressive-like animal models. A total of 55 and 77 high-frequency metabolites were reported consistently in two-thirds of clinical and murine studies, respectively. In the comparison between murine and clinical studies, we identified 9 consistently changed metabolites (tryptophan, tyrosine, phenylalanine, methionine, fumarate, valine, deoxycholic acid, pyruvate, kynurenic acid) in the blood, 1 consistently altered metabolite (indoxyl sulfate) in the urine and 14 disturbed metabolic pathways in both types of studies. These metabolic dysregulations and pathways are mainly implicated in enhanced inflammation, impaired neuroprotection, reduced energy metabolism, increased oxidative stress damage and disturbed apoptosis, laying solid molecular foundations for MDD.

LIMITATIONS

Due to unavailability of original data like effect-size results in many metabolomics studies, a meta-analysis cannot be conducted, and confounding factors cannot be fully ruled out.

CONCLUSIONS

This systematic review delineated metabolic biomarkers and pathways related to depression in the murine and clinical samples, providing opportunities for early diagnosis of MDD and the development of novel diagnostic targets.

Topological Data Analysis in Cardiovascular Signals: An Overview

Topological data analysis (TDA) is a recent approach for analyzing and interpreting complex data sets based on ideas a branch of mathematics called algebraic topology. TDA has proven useful to disentangle non-trivial data structures in a broad range of data analytics problems including the study of cardiovascular signals. Here, we aim to provide an overview of the application of TDA to cardiovascular signals and its potential to enhance the understanding of cardiovascular diseases and their treatment in the form of a literature or narrative review. We first introduce the concept of TDA and its key techniques, including persistent homology, Mapper, and multidimensional scaling. We then discuss the use of TDA in analyzing various cardiovascular signals, including electrocardiography, photoplethysmography, and arterial stiffness. We also discuss the potential of TDA to improve the diagnosis and prognosis of cardiovascular diseases, as well as its limitations and challenges. Finally, we outline future directions for the use of TDA in cardiovascular signal analysis and its potential impact on clinical practice. Overall, TDA shows great promise as a powerful tool for the analysis of complex cardiovascular signals and may offer significant insights into the understanding and management of cardiovascular diseases.

Topological Data Analysis Captures Task-Driven fMRI Profiles in Individual Participants: A Classification Pipeline Based on Persistence

BOLD-based fMRI is the most widely used method for studying brain function. The BOLD signal while valuable, is beset with unique vulnerabilities. The most notable of these is the modest signal to noise ratio, and the relatively low temporal and spatial resolution. However, the high dimensional complexity of the BOLD signal also presents unique opportunities for functional discovery. Topological Data Analyses (TDA), a branch of mathematics optimized to search for specific classes of structure within high dimensional data may provide particularly valuable applications. In this investigation, we acquired fMRI data in the anterior cingulate cortex (ACC) using a basic motor control paradigm. Then, for each participant and each of three task conditions, fMRI signals in the ACC were summarized using two methods: a) TDA based methods of persistent homology and persistence landscapes and b) non-TDA based methods using a standard vectorization scheme. Finally, using machine learning (with support vector classifiers), classification accuracy of TDA and non-TDA vectorized data was tested across participants. In each participant, TDA-based classification out-performed the non-TDA based counterpart, suggesting that our TDA analytic pipeline better characterized task- and condition-induced structure in fMRI data in the ACC. Our results emphasize the value of TDA in characterizing task- and condition-induced structure in regional fMRI signals. In addition to providing our analytical tools for other users to emulate, we also discuss the unique role that TDA-based methods can play in the study of individual differences in the structure of functional brain signals in the healthy and the clinical brain.

Simplicial complex entropy for time series analysis

The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval), several methods have been proposed to evaluate their irregularity. However, for some types of dynamics such as stochastic and chaotic, new approaches are required that can provide a better characterization of them. In this paper we present the simplicial complex approximate entropy, which is based on the conditional probability of the occurrence of elements of a simplicial complex. Our results show that this entropy measure provides a wide range of values with details not easily identifiable with standard methods. In particular, we show that our method is able to quantify the irregularity in simulated random sequences and those from low-dimensional chaotic dynamics. Furthermore, it is possible to consistently differentiate cardiac interbeat sequences from healthy subjects and from patients with heart failure, as well as to identify changes between dynamical states of coupled chaotic maps. Our results highlight the importance of the structures revealed by the simplicial complexes, which holds promise for applications of this approach in various contexts.

Topological data analysis of the synchronization of a network of Rössler chaotic electronic oscillators

Synchronization study allows a better understanding of the exchange of information among systems. In this work, we study experimental data recorded from a set of Rössler-like chaotic electronic oscillators arranged in a complex network, where the interactions between the oscillators are given in terms of a connectivity matrix, and their intensity is controlled by a global coupling parameter. We use the zero and one persistent homology groups to characterize the point clouds obtained from the signals recorded in pairs of oscillators. We show that the normalized persistent entropy (NPE) allows us to characterize the effective coupling between pairs of oscillators because it tends to increase with the coupling strength and to decrease with the distance between the oscillators. We also observed that pairs of oscillators that have similar degrees and are nearest neighbors tend to have higher NPE values than pairs with different degrees. However, large variability is found in the NPE values. Comparing the NPE behavior with that of the phase-locking value (PLV, commonly used to evaluate the synchronization of phase oscillators), we find that for large enough coupling, PLV only displays a monotonic increase, while NPE shows a richer behavior that captures variations in the behavior of the oscillators. This is due to the fact that PLV only captures coupling-induced phase changes, while NPE also captures amplitude changes. Moreover, when we consider the same network but with Kuramoto phase oscillators, we also find that NPE captures the transition to synchronization (as it increases with the coupling strength), and it also decreases with the distance between the oscillators. Therefore, we propose NPE as a data analysis technique to try to differentiate pairs of oscillators that have strong effective coupling because they are first or near neighbors, from those that have weaker coupling because they are distant neighbors.

Computer-aided drug repurposing to tackle antibiotic resistance based on topological data analysis

The progressive emergence of antimicrobial resistance has become a global health problem in need of rapid solution. Research into new antimicrobial drugs is imperative. Drug repositioning, together with computational mathematical prediction models, could be a fast and efficient method of searching for new antibiotics. The aim of this study was to identify compounds with potential antimicrobial capacity against Escherichia coli from US Food and Drug Administration-approved drugs, and the similarity between known drug targets and E. coli proteins using a topological structure-activity data analysis model. This model has been shown to identify molecules with known antibiotic capacity, such as carbapenems and cephalosporins, as well as new molecules that could act as antimicrobials. Topological similarities were also found between E. coli proteins and proteins from different bacterial species such as Mycobacterium tuberculosis, Pseudomonas aeruginosa and Salmonella Typhimurium, which could imply that the selected molecules have a broader spectrum than expected. These molecules include antitumor drugs, antihistamines, lipid-lowering agents, hypoglycemic agents, antidepressants, nucleotides, and nucleosides, among others. The results presented in this study prove the ability of computational mathematical prediction models to predict molecules with potential antimicrobial capacity and/or possible new pharmacological targets of interest in the design of new antibiotics and in the better understanding of antimicrobial resistance.

Deconstructing the Mapper algorithm to extract richer topological and temporal features from functional neuroimaging data

Capturing and tracking large-scale brain activity dynamics holds the potential to deepen our understanding of cognition. Previously, tools from Topological Data Analysis, especially Mapper, have been successfully used to mine brain activity dynamics at the highest spatiotemporal resolutions. Even though it is a relatively established tool within the field of Topological Data Analysis, Mapper results are highly impacted by parameter selection. Given that non-invasive human neuroimaging data (e.g., from fMRI) is typically fraught with artifacts and no gold standards exist regarding "true" state transitions, we argue for a thorough examination of Mapper parameter choices to better reveal their impact. Using synthetic data (with known transition structure) and real fMRI data, we explore a variety of parameter choices for each Mapper step, thereby providing guidance and heuristics for the field. We also release our parameter-exploration toolbox as a software package to make it easier for scientists to investigate and apply Mapper on any dataset.

MapperPlus: Agnostic clustering of high-dimension data for precision medicine

One of the goals of precision medicine is to classify patients into subgroups that differ in their susceptibility and response to a disease, thereby enabling tailored treatments for each subgroup. Therefore, there is a great need to identify distinctive clusters of patients from patient data. There are three key challenges to three key challenges of patient stratification: 1) the unknown number of clusters, 2) the need for assessing cluster validity, and 3) the clinical interpretability. We developed MapperPlus, a novel unsupervised clustering pipeline, that directly addresses these challenges. It extends the topological Mapper technique and blends it with two random-walk algorithms to automatically detect disjoint subgroups in patient data. We demonstrate that MapperPlus outperforms traditional agnostic clustering methods in key accuracy/performance metrics by testing its performance on publicly available medical and non-medical data set. We also demonstrate the predictive power of MapperPlus in a medical dataset of pediatric stem cell transplant patients where a number of cluster is unknown. Here, MapperPlus stratifies the patient population into clusters with distinctive survival rates. The MapperPlus software is open-source and publicly available.

The shape of cancer relapse: Topological data analysis predicts recurrence in paediatric acute lymphoblastic leukaemia

Although children and adolescents with acute lymphoblastic leukaemia (ALL) have high survival rates, approximately 15-20% of patients relapse. Risk of relapse is routinely estimated at diagnosis by biological factors, including flow cytometry data. This high-dimensional data is typically manually assessed by projecting it onto a subset of biomarkers. Cell density and "empty spaces" in 2D projections of the data, i.e. regions devoid of cells, are then used for qualitative assessment. Here, we use topological data analysis (TDA), which quantifies shapes, including empty spaces, in data, to analyse pre-treatment ALL datasets with known patient outcomes. We combine these fully unsupervised analyses with Machine Learning (ML) to identify significant shape characteristics and demonstrate that they accurately predict risk of relapse, particularly for patients previously classified as 'low risk'. We independently confirm the predictive power of CD10, CD20, CD38, and CD45 as biomarkers for ALL diagnosis. Based on our analyses, we propose three increasingly detailed prognostic pipelines for analysing flow cytometry data from ALL patients depending on technical and technological availability: 1. Visual inspection of specific biological features in biparametric projections of the data; 2. Computation of quantitative topological descriptors of such projections; 3. A combined analysis, using TDA and ML, in the four-parameter space defined by CD10, CD20, CD38 and CD45. Our analyses readily extend to other haematological malignancies.

Supervised topological data analysis for MALDI mass spectrometry imaging applications

BACKGROUND

Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) displays significant potential for applications in cancer research, especially in tumor typing and subtyping. Lung cancer is the primary cause of tumor-related deaths, where the most lethal entities are adenocarcinoma (ADC) and squamous cell carcinoma (SqCC). Distinguishing between these two common subtypes is crucial for therapy decisions and successful patient management.

RESULTS

We propose a new algebraic topological framework, which obtains intrinsic information from MALDI data and transforms it to reflect topological persistence. Our framework offers two main advantages. Firstly, topological persistence aids in distinguishing the signal from noise. Secondly, it compresses the MALDI data, saving storage space and optimizes computational time for subsequent classification tasks. We present an algorithm that efficiently implements our topological framework, relying on a single tuning parameter. Afterwards, logistic regression and random forest classifiers are employed on the extracted persistence features, thereby accomplishing an automated tumor (sub-)typing process. To demonstrate the competitiveness of our proposed framework, we conduct experiments on a real-world MALDI dataset using cross-validation. Furthermore, we showcase the effectiveness of the single denoising parameter by evaluating its performance on synthetic MALDI images with varying levels of noise.

CONCLUSION

Our empirical experiments demonstrate that the proposed algebraic topological framework successfully captures and leverages the intrinsic spectral information from MALDI data, leading to competitive results in classifying lung cancer subtypes. Moreover, the framework's ability to be fine-tuned for denoising highlights its versatility and potential for enhancing data analysis in MALDI applications.

Spatiochemical Characterization of the Pancreas Using Mass Spectrometry Imaging and Topological Data Analysis

Mass Spectrometry Imaging (MSI) is a technique used to identify the spatial distribution of molecules in tissues. An MSI experiment results in large amounts of high dimensional data, so efficient computational methods are needed to analyze the output. Topological Data Analysis (TDA) has proven to be effective in all kinds of applications. TDA focuses on the topology of the data in high dimensional space. Looking at the shape in a high dimensional data set can lead to new or different insights. In this work, we investigate the use of Mapper, a form of TDA, applied on MSI data. Mapper is used to find data clusters inside two healthy mouse pancreas data sets. The results are compared to previous work using UMAP for MSI data analysis on the same data sets. This work finds that the proposed technique discovers the same clusters in the data as UMAP and is also able to uncover new clusters, such as an additional ring structure inside the pancreatic islets and a better defined cluster containing blood vessels. The technique can be used for a large variety of data types and sizes and can be optimized for specific applications. It is also computationally similar to UMAP for clustering. Mapper is a very interesting method, especially its use in biomedical applications.

Multiscale geometric and topological analyses for characterizing and predicting immune responses from single cell data

Single cell genomics has revolutionized our ability to map immune heterogeneity and responses. With the influx of large-scale data sets from diverse modalities, the resolution achieved has supported the long-held notion that immune cells are naturally organized into hierarchical relationships, characterized at multiple levels. Such a multigranular structure corresponds to key geometric and topological features. Given that differences between an effective and ineffective immunological response may not be found at one level, there is vested interest in characterizing and predicting outcomes from such features. In this review, we highlight single cell methods and principles for learning geometric and topological properties of data at multiple scales, discussing their contributions to immunology. Ultimately, multiscale approaches go beyond classical clustering, revealing a more comprehensive picture of cellular heterogeneity.

Enriching representation learning using 53 million patient notes through human phenotype ontology embedding

The Human Phenotype Ontology (HPO) is a dictionary of >15,000 clinical phenotypic terms with defined semantic relationships, developed to standardize phenotypic analysis. Over the last decade, the HPO has been used to accelerate the implementation of precision medicine into clinical practice. In addition, recent research in representation learning, specifically in graph embedding, has led to notable progress in automated prediction via learned features. Here, we present a novel approach to phenotype representation by incorporating phenotypic frequencies based on 53 million full-text health care notes from >1.5 million individuals. We demonstrate the efficacy of our proposed phenotype embedding technique by comparing our work to existing phenotypic similarity-measuring methods. Using phenotype frequencies in our embedding technique, we are able to identify phenotypic similarities that surpass current computational models. Furthermore, our embedding technique exhibits a high degree of agreement with domain experts' judgment. By transforming complex and multidimensional phenotypes from the HPO format into vectors, our proposed method enables efficient representation of these phenotypes for downstream tasks that require deep phenotyping. This is demonstrated in a patient similarity analysis and can further be applied to disease trajectory and risk prediction.

Topological data analysis in medical imaging: current state of the art

Machine learning, and especially deep learning, is rapidly gaining acceptance and clinical usage in a wide range of image analysis applications and is regarded as providing high performance in detecting anatomical structures and identification and classification of patterns of disease in medical images. However, there are many roadblocks to the widespread implementation of machine learning in clinical image analysis, including differences in data capture leading to different measurements, high dimensionality of imaging and other medical data, and the black-box nature of machine learning, with a lack of insight into relevant features. Techniques such as radiomics have been used in traditional machine learning approaches to model the mathematical relationships between adjacent pixels in an image and provide an explainable framework for clinicians and researchers. Newer paradigms, such as topological data analysis (TDA), have recently been adopted to design and develop innovative image analysis schemes that go beyond the abilities of pixel-to-pixel comparisons. TDA can automatically construct filtrations of topological shapes of image texture through a technique known as persistent homology (PH); these features can then be fed into machine learning models that provide explainable outputs and can distinguish different image classes in a computationally more efficient way, when compared to other currently used methods. The aim of this review is to introduce PH and its variants and to review TDA's recent successes in medical imaging studies.

Characterizing emerging features in cell dynamics using topological data analysis methods

Filament-motor interactions inside cells play essential roles in many developmental as well as other biological processes. For instance, actin-myosin interactions drive the emergence or closure of ring channel structures during wound healing or dorsal closure. These dynamic protein interactions and the resulting protein organization lead to rich time-series data generated by using fluorescence imaging experiments or by simulating realistic stochastic models. We propose methods based on topological data analysis to track topological features through time in cell biology data consisting of point clouds or binary images. The framework proposed here is based on computing the persistent homology of the data at each time point and on connecting topological features through time using established distance metrics between topological summaries. The methods retain aspects of monomer identity when analyzing significant features in filamentous structure data, and capture the overall closure dynamics when assessing the organization of multiple ring structures through time. Using applications of these techniques to experimental data, we show that the proposed methods can describe features of the emergent dynamics and quantitatively distinguish between control and perturbation experiments.

Systems Biology in Asthma

The application of mathematical and computational analysis, together with the modelling of biological and physiological processes, is transforming our understanding of the pathophysiology of complex diseases. This systems biology approach incorporates large amounts of genomic, transcriptomic, proteomic, metabolomic, breathomic, metagenomic and imaging data from disease sites together with deep clinical phenotyping, including patient-reported outcomes. Integration of these datasets will provide a greater understanding of the molecular pathways associated with severe asthma in each individual patient and determine their personalised treatment regime. This chapter describes some of the data integration methods used to combine data sets and gives examples of the results obtained using single datasets and merging of multiple datasets (data fusion and data combination) from several consortia including the severe asthma research programme (SARP) and the Unbiased Biomarkers Predictive of Respiratory Disease Outcomes (U-BIOPRED) consortia. These results highlight the involvement of several different immune and inflammatory pathways and factors in distinct subsets of patients with severe asthma. These pathways often overlap in patients with distinct clinical features of asthma, which may explain the incomplete or no response in patients undergoing specific targeted therapy. Collaboration between groups will improve the predictions obtained using a systems medicine approach in severe asthma.

Personalized Medicine for the Critically Ill Patient: A Narrative Review

Personalized Medicine (PM) is rapidly advancing in everyday medical practice. Technological advances allow researchers to reach patients more than ever with their discoveries. The critically ill patient is probably the most complex of all, and personalized medicine must make serious efforts to fulfill the desire to “treat the individual, not the disease”. The complexity of critically ill pathologies arises from the severe state these patients and from the deranged pathways of their diseases. PM constitutes the integration of basic research into clinical practice; however, to make this possible complex and voluminous data require processing through even more complex mathematical models. The result of processing biodata is a digitized individual, from which fragments of information can be extracted for specific purposes. With this review, we aim to describe the current state of PM technologies and methods and explore its application in critically ill patients, as well as some of the challenges associated with PM in intensive care from the perspective of economic, approval, and ethical issues. This review can help in understanding the complexity of, P.M.; the complex processes needed for its application in critically ill patients, the benefits that make the effort of implementation worthwhile, and the current challenges of PM.