Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis

Nardini, John T.; Stolz, Bernadette J.; Flores, Kevin; Harrington, Heather A.; Byrne, Helen M.

doi:10.1371/journal.pcbi.1009094

Cited by 29 publications

(26 citation statements)

References 79 publications

(138 reference statements)

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“…We specifically chose descriptors that are simple summaries of PH barcodes so that we can interpret biological differences between networks. In other biological applications, barcodes have been successfully analyzed by their vectorization, for example, by using persistence images (58) or persistence landscapes (59,60) and classifying them using methods from machine learning; see, for example, (22,36,(61)(62)(63)(64). Here, this type of transformation is not suitable because of the variation of initial vasculature within a treatment group and small sample size common to mouse model experiments.…”

Section: Discussionmentioning

confidence: 99%

Multiscale topology characterizes dynamic tumor vascular networks

et al. 2022

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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.

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Section: Discussionmentioning

confidence: 99%

Multiscale topology characterizes dynamic tumor vascular networks

et al. 2022

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“…Therefore, we map all persistence diagrams into two-dimensional persistence images (PIs) of the same size and convert the PIs into vectors of a fixed length (Figure 3). The resulting topological descriptor vectors are stable to perturbations in data and can be used for machine learning and data science algorithms [20,32,40]. 5.…”

Section: Persistence Imagesmentioning

confidence: 99%

“…Topological and statistical analyses, on the other hand, generate metrics that are interpretable. In future work, we plan to combine topological and statistical methods with machine learning algorithms and mathematical modeling to infer the mechanisms that lead to diabetic retinopathy and other microvascular diseases of the retina [32,51].…”

Section: Interpretation Of the Topological Descriptor Vectorsmentioning

confidence: 99%

“…PH has been applied to vascular network data previously: Bendich et al showcased how PH summaries can reveal the effects of aging on brain vascular morphology [30], and Stolz et al used PH to uncover effects of radiotherapy on tumor vascular structure not seen using statistical methods [31]. We recently applied PH computations and a machine learning algorithm to cluster a large collection of simulated vessel networks according to their topological features [32]. We found that simulations within the same clusters were generated from similar input model parameters.…”

Section: Introductionmentioning

confidence: 99%

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Statistical and Topological Summaries Aid Disease Detection for Segmented Retinal Vascular Images

Nardini¹,

Pugh²,

Byrne³

2022

Preprint

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Disease complications can alter vascular network morphology and disrupt tissue functioning. Diabetic retinopathy, for example, is a complication of type 1 and 2 diabetes mellitus that can cause blindness. Microvascular diseases are assessed by visual inspection of retinal images, but this can be challenging when diseases exhibit silent symptoms or patients cannot attend in-person meetings. We examine the performance of machine learning algorithms in detecting microvascular disease when trained on either statistical or topological summaries of segmented retinal vascular images. We apply our methods to four publicly-available datasets and find that the fractal dimension performs best for high resolution images. By contrast, we find that topological descriptor vectors quantifying the number of loops in the data achieve the highest accuracy for low resolution images. Further analysis, using the topological approach, reveals that microvascular disease may alter morphology by reducing the number of loops in the retinal vasculature.Our work provides preliminary guidelines on which methods are most appropriate for assessing disease in high and low resolution images. In the longer term, these methods could be incorporated into automated disease assessment tools.

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“…This repeated outgrowth of vessels through a persistent tunic also presents a platform for a broader question: to what extent can an extracellular medium, unmodified during vessel retraction, influence the formation of successive generations of vasculature? Such a property is not one that has been extensively explored in the context of chemotaxis-driven systems, though is reminiscent of hypotheses of wound healing and the accompanying angiogenesis [33,34]. With the tunic of B. schlosseri potentially facilitating such a persisting memory of the vessel network, we consider this question of long-term influence and remodelling in the context of our agent-based framework, revealing principles underlying dynamics of guided and temporally convergent vascular growth in response to mechanical cues.…”

Section: Introductionmentioning

confidence: 99%

Modelling mechanically dominated vasculature development

Walker¹,

Dawes²

2022

Preprint

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Vascular networks play a key role in the development, function, and survival of many organisms, facilitating transport of nutrients and other critical factors within and between systems. The development of these vessel networks has been thoroughly explored in a variety of in vivo, in vitro and in silico contexts. However, the role of interactions between the growing vasculature and its environment remains largely unresolved, particularly concerning mechanical effects. Motivated by this gap in understanding, we develop a computational framework that is tailored to exploring the role of the mechanical environment on the formation of vascular networks. Here, we describe, document, implement, and explore an agent-based modelling framework, resolving the growth of individual vessels and seeking to capture phenomenology and intuitive qualitative mechanisms. In our explorations, we demonstrate that such a model can successfully reproduce familiar network structures, whilst highlighting the roles that mechanical influences could play in vascular development. For instance, we illustrate how an external substrate could act as an effective shared memory for the periodic regrowth of vasculature. We also observe the emergence of a nuanced collective behaviour and clustered vessel growth, which results from mechanical characteristics of the external environment.

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Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis

Cited by 29 publications

References 79 publications

Multiscale topology characterizes dynamic tumor vascular networks

Multiscale topology characterizes dynamic tumor vascular networks

Statistical and Topological Summaries Aid Disease Detection for Segmented Retinal Vascular Images

Modelling mechanically dominated vasculature development

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