Mathematical models for chemotaxis and their applications in self-organisation phenomena

Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for attracting microbes to food, embryonic cells into developing tissues, immune cells to infection sites, animals towards potential mates, and mathematicians into biology. The Patlak-Keller-Segel (PKS) system forms part of the bedrock of mathematical biology, a go-to-choice for modellers and analysts alike. For the former it is simple yet recapitulates numerous phenomena; the latter are attracted to these rich dynamics. Here I review the adoption of PKS systems when explaining self-organisation processes. I consider their foundation, returning to the initial efforts of Patlak and Keller and Segel, and briefly describe their patterning properties. Applications of PKS systems are considered in their diverse areas, including microbiology, development, immunology, cancer, ecology and crime. In each case a historical perspective is provided on the evidence for chemotactic behaviour, followed by a review of modelling efforts; a compendium of the models is included as an Appendix. Finally, a half-serious/half-tongue-in-cheek model is developed to explain how cliques form in academia. Assumptions in which scholars alter their research line according to available problems leads to clustering of academics and the formation of "hot" research topics.Comment: 35 pages, 8 figures, Submitted to Journal of Theoretical Biolog

Surgical spectral imaging

Recent technological developments have resulted in the availability of miniaturised spectral imaging sensors capable of operating in the multi- (MSI) and hyperspectral imaging (HSI) regimes. Simultaneous advances in image-processing techniques and artificial intelligence (AI), especially in machine learning and deep learning, have made these data-rich modalities highly attractive as a means of extracting biological information non-destructively. Surgery in particular is poised to benefit from this, as spectrally-resolved tissue optical properties can offer enhanced contrast as well as diagnostic and guidance information during interventions. This is particularly relevant for procedures where inherent contrast is low under standard white light visualisation. This review summarises recent work in surgical spectral imaging (SSI) techniques, taken from Pubmed, Google Scholar and arXiv searches spanning the period 2013–2019. New hardware, optimised for use in both open and minimally-invasive surgery (MIS), is described, and recent commercial activity is summarised. Computational approaches to extract spectral information from conventional colour images are reviewed, as tip-mounted cameras become more commonplace in MIS. Model-based and machine learning methods of data analysis are discussed in addition to simulation, phantom and clinical validation experiments. A wide variety of surgical pilot studies are reported but it is apparent that further work is needed to quantify the clinical value of MSI/HSI. The current trend toward data-driven analysis emphasises the importance of widely-available, standardised spectral imaging datasets, which will aid understanding of variability across organs and patients, and drive clinical translation