Tumour spheroids are widely used as an in vitro assay for characterising the dynamics and response to treatment of different cancer cell lines. Their popularity is largely due to the reproducible manner in which spheroids grow: the diffusion of nutrients and oxygen from the surrounding culture medium, and their consumption by tumour cells, causes proliferation to be localised at the spheroid boundary. As the spheroid grows, cells at the spheroid centre may become hypoxic and die, forming a necrotic core. The pressure created by the localisation of tumour cell proliferation and death generates an cellular flow of tumour cells from the spheroid rim towards its core. Experiments by Dorie et al. showed that this flow causes inert microspheres to infiltrate into tumour spheroids via advection from the spheroid surface, by adding microbeads to the surface of tumour spheroids and observing the distribution over time. We use an off-lattice hybrid agent-based model to reassess these experiments and establish the extent to which the spatio-temporal data generated by microspheres can be used to infer kinetic parameters associated with the tumour spheroids that they infiltrate. Variation in these parameters, such as the rate of tumour cell proliferation or sensitivity to hypoxia, can produce spheroids with similar bulk growth dynamics but differing internal compositions (the proportion of the tumour which is proliferating, hypoxic/quiescent and necrotic/nutrient-deficient). We use this model to show that the types of experiment conducted by Dorie et al. could be used to infer spheroid composition and parameters associated with tumour cell lines such as their sensitivity to hypoxia or average rate of proliferation, and note that these observations cannot be conducted within previous continuum models of microbead infiltration into tumour spheroids as they rely on resolving the trajectories of individual microbeads.

Autoantibodies against the extracellular domain of the N-methyl-d-aspartate receptor (NMDAR) NR1 subunit cause a severe and common form of encephalitis. To better understand their generation, we aimed to characterize and identify human germinal centres actively participating in NMDAR-specific autoimmunization by sampling patient blood, CSF, ovarian teratoma tissue and, directly from the putative site of human CNS lymphatic drainage, cervical lymph nodes. From serum, both NR1-IgA and NR1-IgM were detected more frequently in NMDAR-antibody encephalitis patients versus controls (both P < 0.0001). Within patients, ovarian teratoma status was associated with a higher frequency of NR1-IgA positivity in serum (OR = 3.1; P < 0.0001) and CSF (OR = 3.8, P = 0.047), particularly early in disease and before ovarian teratoma resection. Consistent with this immunoglobulin class bias, ovarian teratoma samples showed intratumoral production of both NR1-IgG and NR1-IgA and, by single cell RNA sequencing, contained expanded highly-mutated IgA clones with an ovarian teratoma-restricted B cell population. Multiplex histology suggested tertiary lymphoid architectures in ovarian teratomas with dense B cell foci expressing the germinal centre marker BCL6, CD21+ follicular dendritic cells, and the NR1 subunit, alongside lymphatic vessels and high endothelial vasculature. Cultured teratoma explants and dissociated intratumoral B cells secreted NR1-IgGs in culture. Hence, ovarian teratomas showed structural and functional evidence of NR1-specific germinal centres. On exploring classical secondary lymphoid organs, B cells cultured from cervical lymph nodes of patients with NMDAR-antibody encephalitis produced NR1-IgG in 3/7 cultures, from patients with the highest serum NR1-IgG levels (P < 0.05). By contrast, NR1-IgG secretion was observed neither from cervical lymph nodes in disease controls nor in patients with adequately resected ovarian teratomas. Our multimodal evaluations provide convergent anatomical and functional evidence of NMDAR-autoantibody production from active germinal centres within both intratumoral tertiary lymphoid structures and traditional secondary lymphoid organs, the cervical lymph nodes. Furthermore, we develop a cervical lymph node sampling protocol that can be used to directly explore immune activity in health and disease at this emerging neuroimmune interface.

Highly resolved spatial data of complex systems encode rich and nonlinear information. Quantification of heterogeneous and noisy data—often with outliers, artifacts, and mislabeled points—such as those from tissues, remains a challenge. The mathematical field that extracts information from the shape of data, topological data analysis (TDA), has expanded its capability for analyzing real-world datasets in recent years by extending theory, statistics, and computation. An extension to the standard theory to handle heterogeneous data is multiparameter persistent homology (MPH). Here we provide an application of MPH landscapes, a statistical tool with theoretical underpinnings. MPH landscapes, computed for (noisy) data from agent-based model simulations of immune cells infiltrating into a spheroid, are shown to surpass existing spatial statistics and one-parameter persistent homology. We then apply MPH landscapes to study immune cell location in digital histology images from head and neck cancer. We quantify intratumoral immune cells and find that infiltrating regulatory T cells have more prominent voids in their spatial patterns than macrophages. Finally, we consider how TDA can integrate and interrogate data of different types and scales, e.g., immune cell locations and regions with differing levels of oxygenation. This work highlights the power of MPH landscapes for quantifying, characterizing, and comparing features within the tumor microenvironment in synthetic and real datasets.

Purpose-Tumor hypoxia fuels an aggressive tumor phenotype and confers resistance to anticancer treatments. We conducted a clinical trial to determine whether the antimalarial drug atovaquone, a known mitochondrial inhibitor, reduces hypoxia in non-small cell lung cancer (NSCLC).Patients and methods-Patients with NSCLC scheduled for surgery were recruited sequentially into two cohorts: Cohort 1 received oral atovaquone at the standard clinical dose 750 mg twice-daily, whilst Cohort 2 did not. Primary imaging endpoint was change in tumor hypoxic volume (HV) measured by hypoxia PET-CT. Inter-cohort comparison of hypoxia gene expression signatures using RNA sequencing from resected tumors was performed.Results-Thirty patients were evaluable for hypoxia PET-CT analysis, 15 per cohort. Median treatment duration was 12 days. Eleven (73.3%) atovaquone-treated patients had meaningful HV reduction with median change −28.0% [95% confidence interval (CI), −58.2 to −4.4]. In contrast, median change in untreated patients was +15.5% (95% CI, −6.5 to 35.5). Linear regression estimated the expected mean HV was 55% (95% CI, 24% to 74%) lower in Cohort 1 compared to Cohort 2 (p=0.004), adjusting for cohort, tumor volume and baseline HV. A key pharmacodynamic endpoint was reduction in hypoxia regulated genes, which were significantly downregulated in atovaquone-treated tumors. Data from multiple additional measures of tumor hypoxia and perfusion are presented. No atovaquone-related adverse events were reported.Conclusions-This is the first clinical evidence that targeting tumor mitochondrial metabolism can reduce hypoxia and produce relevant anti-tumor effects at the mRNA level. Repurposing atovaquone for this purpose may improve treatment outcomes for NSCLC.

Over the past twenty-five years there has been an unparalleled increase in understanding of cancer biology. This transformation is exemplified by Hanahan and Weinberg's decision in 2011 to expand their original Hallmarks of Cancer from six traits to ten! At the same time, mathematical modelling has emerged as a natural tool for unravelling the complex processes that contribute to the initiation and progression of tumours, for testing hypotheses about experimental and clinical observations, and assisting with the development of new approaches for improving its treatment. This article starts by reviewing some of the earliest models of tumour growth and tumour responses to radiotherapy. Following Hanahan and Weinberg's lead, attention then focuses on how closer collaboration with cancer scientists and access to experimental data is stimulating the development of new and increasingly detailed models which account, for example, for tumour-immune interactions and immunotherapy. The article concludes by discussing the ways in which mathematical modelling is being integrated with experimental and clinical work and outlining how this could improve disease diagnosis and the delivery of effective personalised treatments to cancer patients. As such, the article serves as an introduction to mathematical modelling of cancer and its treatments, suitable for researchers seeking to enter the field.