Mathematical modelling of nanoparticle delivery to vascular tumours

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.The goal of any cancer therapy is to achieve efficient, tissue-specific targeting of drugs to cancer cells. However, most anticancer agents act on healthy and malignant tissue alike, potentially resulting in side effects to healthy tissue. This has motivated the development of treatment strategies that are cancer-cell specific; one approach uses biomimetic polymer vesicles (BPV) to deliver chemotherapeutic drugs into cells before releasing them. BPVs are synthetic membrane enclosed, nanometre-sized structures, and provide ideal drug delivery vectors because specific targeting to cancer cells can be achieved by coating with tumourspecific molecules. We present several mathematical models covering a wide range of length-scales pertinent to BPV-mediated delivery protocols and focus on capturing the in vivo environment by evaluating the impact of the underlying vascular structure upon the governing transport mechanisms. Firstly, we present models of specific binding of BPVs to cancer cells. Subsequently we examine the implications of these model outputs in the contexts of both discrete capillary architectures and higher level homogenized-models that track blood and BPV transport at the tissue scale (both intra- and extra-tumorally). Numerical solutions are discussed, and recommendations are presented on that optimal integration of the models to generate quantitative predictions associated with BPV treatment efficacy

Hollow Fiber Bioreactors for In Vivo-like Mammalian Tissue Culture

Tissue culture has been used for over 100 years to study cells and responses ex vivo. The convention of this technique is the growth of anchorage dependent cells on the 2-dimensional surface of tissue culture plastic. More recently, there is a growing body of data demonstrating more in vivo-like behaviors of cells grown in 3-dimensional culture systems. This manuscript describes in detail the set-up and operation of a hollow fiber bioreactor system for the in vivo-like culture of mammalian cells. The hollow fiber bioreactor system delivers media to the cells in a manner akin to the delivery of blood through the capillary networks in vivo. The system is designed to fit onto the shelf of a standard CO2 incubator and is simple enough to be set-up by any competent cell biologist with a good understanding of aseptic technique. The systems utility is demonstrated by culturing the hepatocarcinoma cell line HepG2/C3A for 7 days. Further to this and in line with other published reports on the functionality of cells grown in 3-dimensional culture systems the cells are shown to possess increased albumin production (an important hepatic function) when compared to standard 2-dimensional tissue culture

Timescale analysis of a mathematical model of acetaminophen metabolism andtoxicity

Acetaminophen is a widespread and commonly used painkiller all over the world. However, it can cause liver damage when taken in large doses or at repeated chronic doses. Current models of acetaminophen metabolism are complex, and limited to numerical investigation though provide results that represent clinical investigation well. We derive a mathematical model based on mass action laws aimed at capturing the main dynamics of acetaminophen metabolism, in particular the contrast between normal and overdose cases, whilst remaining simple enough for detailed mathematical analysis that can identify key parameters and quantify their role in liver toxicity. We use singular perturbation analysis to separate the di fferent timescales describing the sequence of events in acetaminophen metabolism, systematically identifying which parameters dominate during each of the successive stages. Using this approach we determined, in terms of the model parameters, the critical dose between safe and overdose cases, timescales for exhaustion and regeneration of important cofactors for acetaminophen metabolism and total toxin accumulation as a fraction of initial dose

Microglial peri-somatic abutments classify two novel types of GABAergic neuron in the inferior colliculus

© 2020 The Authors. European Journal of Neuroscience published by Federation of European Neuroscience Societies and John Wiley & Sons Ltd Emerging evidence suggests functional roles for microglia in the healthy, mature nervous system. However, we know little of the cellular density and ramified morphology of microglia in sensory systems, and even less of their inter-relationship with inhibitory neurons. We therefore conducted fluorescent multi-channel immunohistochemistry and confocal microscopy in guinea pigs of both sexes for Iba1, GAD67, GFAP, calbindin, and calretinin. We explored these markers in the inferior colliculi (IC), which contain sub-regions specialized for different aspects of auditory processing. First, we found that while the density of Iba1+ somata is similar throughout the IC parenchyma, Iba1+ microglia in dorsal cortex are significantly more ramified than those in the central nucleus or lateral cortex. Conversely, Iba1+ ramifications in ventral central nucleus, a region with the highest density of GAD67+ (putative GABAergic) neurons in IC, are longer with fewer ramifications. Second, we observed extensive abutments of ramified Iba1+ processes onto GAD67+ somata throughout the whole IC and developed novel measures to quantify these. Cluster analyses revealed two novel sub-types of GAD67+ neuron that differ in the quantity of Iba1+ somatic abutments they receive. Unlike previous classification schemes for GAD67+ neurons in IC, these clusters are not related to GAD67+ soma size. Taken together, these data demonstrate that microglial ramifications vary between IC sub-regions in the healthy, adult IC, possibly related to the ongoing demands of their niche. Furthermore, Iba1+ abutments onto neuronal somata are a novel means by which GAD67+ neurons can be classified

In silico-guided optimisation of oxygen gradients in hepatic spheroids

One of the key advantages of assessing the hepatotoxic potential of xenobiotics in spheroids rather than monolayer cell culture is the existence of a more physiologically relevant testing environment. Three-dimensional cultures support spatial gradients in nutrients such as oxygen that can be exploited to better represent in vivo gradients that exist along a fundamental sub-unit of liver microarchitecture, the liver sinusoid. The physical and physiological processes that result in the establishment of such gradients can be described mathematically. Quantification of the rates governing these processes and optimisation of cell culture conditions can be performed in silico to better inform experimental design. In this study, we take into account cell line-specific physiological properties, spheroid size and the impact of experimental equipment geometries in order to demonstrate how mathematical models can be optimised to achieve specific in vivo-like features in different scenarios. Furthermore, the sensitivity of such optimised gradients is analysed with respect to culture conditions and considerations are given to prevent the emergence of hypoxic regions in the spheroid. The methodology presented provides an enhanced understanding of the mechanisms of the system within this simulated in vitro framework such that experimental design can be more carefully calibrated when conducting experiments using hepatic spheroids. © 2019 Elsevier B.V

A combined in vitro/in silico approach to identifying off-target receptor toxicity

Many xenobiotics can bind to off-target receptors and cause toxicity via the dysregulation of downstream transcription factors. Identification of subsequent off-target toxicity in these chemicals has often required extensive chemical testing in animal models. An alternative, integrated in vitro/in silico approach for predicting toxic off-target functional responses is presented to refine in vitro receptor identification and reduce the burden on in vivo testing. As part of the methodology, mathematical modelling is used to mechanistically describe processes that regulate transcriptional activity following receptor-ligand binding informed by transcription factor signalling assays. Critical reactions in the signalling cascade are identified to highlight potential perturbation points in the biochemical network that can guide and optimise additional in vitro testing. A physiologically-based pharmacokinetic model provides information on the timing and localisation of different levels of receptor activation informing whole-body toxic potential resulting from off-target binding

Tuberculosis incidence correlates with sunshine : an ecological 28-year time series study

Birmingham is the largest UK city after London, and central Birmingham has an annual tuberculosis incidence of 80 per 100,000. We examined seasonality and sunlight as drivers of tuberculosis incidence. Hours of sunshine are seasonal, sunshine exposure is necessary for the production of vitamin D by the body and vitamin D plays a role in the host response to tuberculosis. Methods: We performed an ecological study that examined tuberculosis incidence in Birmingham from Dec 1981 to Nov 2009, using publicly-available data from statutory tuberculosis notifications, and related this to the seasons and hours of sunshine (UK Meteorological Office data) using unmeasured component models. Results: There were 9,739 tuberculosis cases over the study period. There was strong evidence for seasonality, with notifications being 24.1% higher in summer than winter (p<0.001). Winter dips in sunshine correlated with peaks in tuberculosis incidence six months later (4.7% increase in incidence for each 100 hours decrease in sunshine, p<0.001). Discussion and Conclusion: A potential mechanism for these associations includes decreased vitamin D levels with consequent impaired host defence arising from reduced sunshine exposure in winter. This is the longest time series of any published study and our use of statutory notifications means this data is essentially complete. We cannot, however, exclude the possibility that another factor closely correlated with the seasons, other than sunshine, is responsible. Furthermore, exposure to sunlight depends not only on total hours of sunshine but also on multiple individual factors. Our results should therefore be considered hypothesis-generating. Confirmation of a potential causal relationship between winter vitamin D deficiency and summer peaks in tuberculosis incidence would require a randomized-controlled trial of the effect of vitamin D supplementation on future tuberculosis incidence

Modelling the effects of glucagon during glucose tolerance testing

Background Glucose tolerance testing is a tool used to estimate glucose effectiveness and insulin sensitivity in diabetic patients. The importance of such tests has prompted the development and utilisation of mathematical models that describe glucose kinetics as a function of insulin activity. The hormone glucagon, also plays a fundamental role in systemic plasma glucose regulation and is secreted reciprocally to insulin, stimulating catabolic glucose utilisation. However, regulation of glucagon secretion by α-cells is impaired in type-1 and type-2 diabetes through pancreatic islet dysfunction. Despite this, inclusion of glucagon activity when modelling the glucose kinetics during glucose tolerance testing is often overlooked. This study presents two mathematical models of a glucose tolerance test that incorporate glucose-insulin-glucagon dynamics. The first model describes a non-linear relationship between glucagon and glucose, whereas the second model assumes a linear relationship. Results Both models are validated against insulin-modified and glucose infusion intravenous glucose tolerance test (IVGTT) data, as well as insulin infusion data, and are capable of estimating patient glucose effectiveness (sG) and insulin sensitivity (sI). Inclusion of glucagon dynamics proves to provide a more detailed representation of the metabolic portrait, enabling estimation of two new diagnostic parameters: glucagon effectiveness (sE) and glucagon sensitivity (δ). Conclusions The models are used to investigate how different degrees of pax‘tient glucagon sensitivity and effectiveness affect the concentration of blood glucose and plasma glucagon during IVGTT and insulin infusion tests, providing a platform from which the role of glucagon dynamics during a glucose tolerance test may be investigated and predicted

The Great American Biotic Interchange: Dispersals, Tectonics, Climate, Sea Level and Holding Pens

The biotic and geologic dynamics of the Great American Biotic Interchange are reviewed and revised. Information on the Marine Isotope Stage chronology, sea level changes as well as Pliocene and Pleistocene vegetation changes in Central and northern South America add to a discussion of the role of climate in facilitating trans-isthmian exchanges. Trans-isthmian land mammal exchanges during the Pleistocene glacial intervals appear to have been promoted by the development of diverse non-tropical ecologies

Modelling changes in glutathione homeostasis as a function of quinone redox metabolism

Redox cycling is an understated mechanism of toxicity associated with a plethora of xenobiotics, responsible for preventing the effective treatment of serious conditions such as malaria and cardiomyopathy. Quinone compounds are notorious redox cyclers, present in drugs such as doxorubicin, which is used to treat a host of human cancers. However, the therapeutic index of doxorubicin is undermined by dose-dependent cardiotoxicity, which may be a function of futile redox cycling. In this study, a doxorubicin-specific in silico quinone redox metabolism model is described. Doxorubicin-GSH adduct formation kinetics are thermodynamically estimated from 26 its reduction potential, while the remainder of the model is parameterised using oxygen consumption rate data, indicative of hydroquinone auto oxidation. The model is then combined with a comprehensive glutathione metabolism model, facilitating the simulation of quinone redox cycling, and adduct-induced GSH depletion. Simulations suggest that glutathione pools are most sensitive to exposure duration at pharmacologically and supra-pharmacologically relevant doxorubicin concentrations. The model provides an alternative method of investigating and quantifying redox cycling induced oxidative stress, circumventing the experimental difficulties of measuring and tracking radical species. This in silico framework provides a platform from which GSH depletion can be explored as a function of a compound’s physicochemical properties