Multiscale topology characterizes dynamic tumor vascular networks

Abstract

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.

Quantification of spatial and phenotypic heterogeneity in an agent-based model of tumour-macrophage interactions

“…Applying such statistics to medical images would enable their high-throughput, automated quantification and comparison in a manner that goes beyond expert visual inspection and is more interpretable than AI approaches [65,66]. We note also that while in this paper we focus on correlation functions, alternative metrics, including topological data analysis, can describe spatial features such as immune deserts that exist in noisy data [30], or changes in tumour and vascular architecture in response to radiotherapy [67]. Multiple spatial statistics can be combined to obtain more detailed descriptions of 2D data [68], or new statistics can be derived from networks of cell contact [69] or observations of immune cell locations [70,71].…”

Unsupervised segmentation of 3D microvascular photoacoustic images using deep generative learning

“…Common machine learning metrics do not provide a complete picture of image segmentation performance for tubular-like structures 45 . To evaluate our results, we calculated both standard segmentation metrics and a set of vascular descriptors 35,46 Statistical outliers were identified by five non-parametric tests: 1) Tukey's fences; 2) Median Absolute Deviation (MAD); 3) Modified Z-Score; 4) percentiles (5 th and 95 th percentile cuttoffs) and 5)…”

“…Standard machine learning metrics, such as F1 Score and Intersection over Union (IoU), do not provide a complete picture of segmentation performance in biomedical images, and so alternative metrics were employed. To evaluate segmentation more robustly, we computed established descriptors of network structure and topology on the skeletonised 3D vessel masks 35,46 for both VAN-GAN and RF segmentations (see Supplementary Table 3). VAN-GAN predicted greater network connectivity and maintained performance with increasing network complexity (Fig.…”

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

“…PH is readily computable ( 22 ), robust to noise ( 23 ) and its outputs are interpretable. In recent years, improved computational feasibility of PH has increased its applications to (high-dimensional) data in many contexts, including studies of the shape of brain arteries ( 25 ), neurons ( 26 ), the neural code ( 27 ), airways ( 28 ), stenosis ( 29 ), zebrafish patterns ( 30 ), ion aggregation ( 31 ), contagion dynamics ( 32 ), spatial networks ( 33,35–37 ), and geometric anomalies ( 38 ). In oncology, PH has been used to construct new biomarkers ( 35, 39, 40 ), to classify tumours ( 41, 42 ) and genetic alterations ( 43 ) and to quantify patterns of immune cell infiltration into solid tumours ( 44 ).…”