Multiscale Topology Characterises Dynamic Tumour Vascular Networks

Abstract

Advances in imaging techniques enable high resolution 3D visualisation of vascular networks over time and reveal abnormal structural features such as twists and loops 1-6 . Quantitative descriptors of vascular networks are an active area of research 1, 2, 7 and often focus on a single spatial resolution. Simultaneously, topological data analysis (TDA) 8, 9 , the mathematical field that studies 'shape' of data, has expanded from theory to applications through advances in computation and machine learning integration. Fully characterising the geometric, spatial and temporal tissue organisation is challenging, and its quantification is necessary to assess treatment effects. Here we showcase TDA to analyse intravital and ultramicroscopy imaging modalities and quantify spatio-temporal variation of twists, loops, and avascular regions (voids) in 3D vascular networks. We propose two topological lenses to study vasculature which capture inherent multi-scale organisation and vessel connectivity invisible to existing methods. This topological approach validates and quantifies known qualitative trends; specifically, dynamic changes in tortuosity and loops in response to antibodies that modulate vessel sprouting. Using these topological descriptors, we show further how radiotherapy alters the structure of tumour vasculature. Topological data analysis offers great potential for relating the form and function of vascular networks, and proposing novel biomarkers for tumour progression and treatment.Introduction. The advent of high resolution imaging techniques has driven the development of reconstruction algorithms, which generate exquisitely detailed 3D renderings of biological tissues, such as tumour vascular networks 10,11 . Analyses of these images have quantified structural features and shape, including vessel density, number of vessels and branch points 7 , fractal dimension 12 , and lacunarity 13 , and highlighted their relevance for monitoring disease progression 14,15 and treatment 6 . Tumours may contain regions of high and low vessel density 2 , the latter corresponding to vascular voids which are associated with tumour hypoxia and necrosis, and lead to reduced survival in patients and poor responses to therapy 2 . Artificial intelligence and machine learning algorithms represent the state-of-the-art for learning how to segment images; we employ them here.

Quantification of vascular networks in photoacoustic mesoscopy

“…Next, we skeletonised each segmentation mask to enable us to perform statistical and topological data analysis (TDA) to test how each segmentation method quantitatively influences a core set of vessel network descriptors [33] . These descriptors allowed us to evaluate the performance of the different segmentation methods in respect of the biological characterisation of the tumour networks.…”

“…As blood vessel networks can be represented as complex, interconnected graphs, we performed statistical and topological data analyses [36] , [33] to further assess the strengths and weaknesses of our chosen segmentation methods.…”

“…Prior work applying topological data analysis after skeletonization of PAI data in a skin burn model also showed biologically relevant differences in between healthy and burnt skin in rats [37] . Looking further afield, vascular descriptors such as these have also shown response to anti-angiogenic drugs and radiotherapy, with decreased SOAM (tortuosity), loops and increased vessel lengths detected in response to treatment in mouse colon carcinomas [33] . Stolz et al also showed an increase in tortuosity and looping structures upon addition of a vascular-promoting agent.…”

What are higher-order networks?

“…Higher-order networks have also proven useful in genomics and evolutionary biology [57,220], structural biology [273], as well as for the analysis of structures such as vascular networks [23,47,253]. References overviewing the potential of topological techniques include [8,36,220,254].…”

“…Recent studies suggest that higher-order network structures and computational topol-ogy can be helpful for analyzing such models of biological systems [155,184,198,262]. Using higher-order networks to analyze diseases such as cancer [11,116,203,253] offers possibilities for combining data and mathematical models [252,268]. While the structure of some chemical reaction models can be distinguished using persistent homology [269], others are better encoded as a hypergraph and analyzed with discrete Ricci curvature [90].…”