Modeling of mouse experiments suggests that optimal anti-hormonal treatment for breast cancer is diet-dependent

Estrogen receptor positive breast cancer is frequently treated with anti-hormonal treatment such as aromatase inhibitors (AI). Interestingly, a high body mass index has been shown to have a negative impact on AI efficacy, most likely due to disturbances in steroid metabolism and adipokine production. Here, we propose a mathematical model based on a system of ordinary differential equations to investigate the effect of high-fat diet on tumor growth. We inform the model with data from mouse experiments, where the animals are fed with high-fat or control (normal) diet. By incorporating AI treatment with drug resistance into the model and by solving optimal control problems we found differential responses for control and high-fat diet. To the best of our knowledge, this is the first attempt to model optimal anti-hormonal treatment for breast cancer in the presence of drug resistance. Our results underline the importance of considering high-fat diet and obesity as factors influencing clinical outcomes during anti-hormonal therapies in breast cancer patients.Comment: 44 pages, 21 figure

Spectral Observations of Optical Emissions Associated With Terrestrial Gamma-Ray Flashes

The Atmosphere-Space Interactions Monitor measures Terrestrial Gamma-Ray Flashes (TGFs) simultaneously with optical emissions from associated lightning activity. We analyzed optical measurements at 180–230, 337, and 777.4 nm related to 69 TGFs observed between June 2018 and October 2019. All TGFs are associated with optical emissions and 90% of them are at the onset of a large optical pulse, suggesting that they are connected with the initiation of current surges. A model of photon delay induced by cloud scattering suggests that the sources of the optical pulses are from 0.7 ms before to 4.4 ms after the TGFs, with a median of −10 ± 80 µs, and 1–5 km below the cloud top. The pulses have rise times comparable to lightning but longer durations. Pulse amplitudes at 337 nm are ∼3 times larger than at 777.4 nm. The results support the leader-streamer mechanism for TGF generation.publishedVersio

Regional performance variation in external validation of four prediction models for severity of COVID-19 at hospital admission: An observational multi-centre cohort study

Background Prediction models should be externally validated to assess their performance before implementation. Several prediction models for coronavirus disease-19 (COVID-19) have been published. This observational cohort study aimed to validate published models of severity for hospitalized patients with COVID-19 using clinical and laboratory predictors. Methods Prediction models fitting relevant inclusion criteria were chosen for validation. The outcome was either mortality or a composite outcome of mortality and ICU admission (severe disease). 1295 patients admitted with symptoms of COVID-19 at Kings Cross Hospital (KCH) in London, United Kingdom, and 307 patients at Oslo University Hospital (OUH) in Oslo, Norway were included. The performance of the models was assessed in terms of discrimination and calibration. Results We identified two models for prediction of mortality (referred to as Xie and Zhang1) and two models for prediction of severe disease (Allenbach and Zhang2). The performance of the models was variable. For prediction of mortality Xie had good discrimination at OUH with an area under the receiver-operating characteristic (AUROC) 0.87 [95% confidence interval (CI) 0.79–0.95] and acceptable discrimination at KCH, AUROC 0.79 [0.76–0.82]. In prediction of severe disease, Allenbach had acceptable discrimination (OUH AUROC 0.81 [0.74–0.88] and KCH AUROC 0.72 [0.68–0.75]). The Zhang models had moderate to poor discrimination. Initial calibration was poor for all models but improved with recalibration. Conclusions The performance of the four prediction models was variable. The Xie model had the best discrimination for mortality, while the Allenbach model had acceptable results for prediction of severe disease

Early Embryonic Vascular Patterning by Matrix-Mediated Paracrine Signalling: A Mathematical Model Study

During embryonic vasculogenesis, endothelial precursor cells of mesodermal origin known as angioblasts assemble into a characteristic network pattern. Although a considerable amount of markers and signals involved in this process have been identified, the mechanisms underlying the coalescence of angioblasts into this reticular pattern remain unclear. Various recent studies hypothesize that autocrine regulation of the chemoattractant vascular endothelial growth factor (VEGF) is responsible for the formation of vascular networks in vitro. However, the autocrine regulation hypothesis does not fit well with reported data on in vivo early vascular development. In this study, we propose a mathematical model based on the alternative assumption that endodermal VEGF signalling activity, having a paracrine effect on adjacent angioblasts, is mediated by its binding to the extracellular matrix (ECM). Detailed morphometric analysis of simulated networks and images obtained from in vivo quail embryos reveals the model mimics the vascular patterns with high accuracy. These results show that paracrine signalling can result in the formation of fine-grained cellular networks when mediated by angioblast-produced ECM. This lends additional support to the theory that patterning during early vascular development in the vertebrate embryo is regulated by paracrine signalling

A review of mathematical models for the formation of vascular networks

Two major mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former term describes the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter term describes the sprouting of new vessels from an existing capillary or post-capillary venule. Similar mechanisms are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis. A number of mathematical approaches have been used to analyse these phenomena. In this article, we review the different types of models, with special emphasis on their ability to reproduce different biological systems and to predict measurable quantities which describe the overall processes. Finally, we highlight the advantages specific to each of the different modelling approaches. The research that led to the present paper was partially supported by a grant of the group GNFM of INdA

Mathematical models of vascular development

The present dissertation is devoted to mathematical modelling and simulation of a specific problem in early vascular morphogenesis, a process that constitutes the initial step in the generation of the vascular system in vertebrates. More precisely, a combined mathematical, computational and experimental approach is used to get new insights into key molecular and cellular mechanisms underlying the self-assembly of new blood vessels. The thesis is divided in three main sections: Preliminaries (Chapter 1), Research Work (Chapters 2 and 3) and Perspectives and Conclusions (Chapters 4 and 5). An overview of the field together with an introduction to the main problem is presented in Chapter 1, where the main literature on the subject is reviewed from a critical point of view. In Chapter 2, a new mechanism and a new hybrid mathematical model for early vascular patterning in the embryo are proposed and examined. The study of the proposed model raises a number of new biological hypotheses, many of which are beyond the current experimental reach. In some particular cases, however, they have been validated in a controlled situation using simplified in vitro assays, as shown in Chapter 3. While doing so, relevant quantitative information related with the kinetic and diffusive properties of a key molecule in vascular development (VEGF) was also obtained. Chapter 4 is devoted to future perspectives in the field under consideration. In particular, two ongoing projects that are extensions of the work here considered are outlined. Finally, the main conclusions of this study are gathered in Chapter 5

Modelling vascular morphogenesis: current views on blood vessels development

In this work we present a comprehensive account of our current knowledge on vascular morphogenesis, both from a biological and a mathematical point of view. To this end, we first describe the basic steps in the known mechanisms of blood vessel morphogenesis, whose structure, function and unfolding properties are examined. We then provide a wide, although by no means exhaustive, account of mathematical models which are used to describe and discuss particular aspects of the overall biological process considered. We finally summarize the approaches presented, and suggest possible directions for future research. Details about some of the major signalling molecules involved are included in a first Appendix at the end of the paper. A second Appendix provides a brief overview of design principles for vascular nets, a subject that has deserved considerable attention over the years