Mathematical Modelling of Cancer Treatments Involving Radiation Therapy and Hypoxia-Activated Prodrugs

Cancer is one of the world's deadliest diseases despite immense investments into oncological research in recent years. Although great strides have been made in our understanding of cancer, much remains unknown regarding its genesis, progression, and optimal treatment. The benefits of mathematical modelling have been realized in many fields of science, and oncology is no exception. Mathematical modelling has become increasingly popular in recent years and today, studies involving both biologists and mathematicians are rather commonplace. This thesis focuses on mathematical oncology, detailing three distinct research works involving the mathematical analysis of cancer. They specifically focus on modelling the applications of various treatment methods including external-beam radiation therapy, hypoxia-activated prodrugs, antiangiogenic agents, and drug-carrying nanocells. The mathematics involves partial differential equation models solved analytically and by using various computational methods. Altogether, the analyses herein show that mathematical modelling is an invaluable tool in oncology which will be a crucial part of future research

Applications of Deep Learning to Differential Equation Models in Oncology

The integration of quantitative tools in biology and medicine has led to many groundbreaking advances in recent history, with many more promising discoveries on the horizon. Conventional mathematical models, particularly differential equation-based models, have had great success in various biological applications, including modelling bacterial growth, disease propagation, and tumour spread. However, these approaches can be somewhat limited due to their reliance on known parameter values, initial conditions, and boundary conditions, which can dull their applicability. Furthermore, their forms are directly tied to mechanistic phenomena, making these models highly explainable, but also requiring a comprehensive understanding of the underlying dynamics before modelling the system. On the other hand, machine learning models typically require less prior knowledge of the system but require a significant amount of data for training. Although machine learning models can be more flexible, they tend to be black boxes, making them difficult to interpret. Hybrid models, which combine conventional and machine learning approaches, have the potential to achieve the best of both worlds. These models can provide explainable outcomes while relying on minimal assumptions or data. An example of this is physics-informed neural networks, a novel deep learning approach that incorporates information from partial differential equations into the optimization of a neural network. This hybrid approach offers significant potential in various contexts where differential equation models are known, but data is scarce or challenging to work with. Precision oncology is one such field. This thesis employs hybrid conventional/machine learning models to address problems in cancer medicine, specifically aiming to advance personalized medicine approaches. It contains three projects. In the first, a hybrid approach is used to make patient-specific characterizations of brain tumours using medical imaging data. In the second project, a hybrid approach is employed to create subject-specific projections of drug-carrying cancer nanoparticle accumulation and intratumoral interstitial fluid pressure. In the final project, a hybrid approach is utilized to optimize radiation therapy scheduling for tumours with heterogeneous cell populations and cancer stem cells. Overall, this thesis showcases several examples of how quantitative tools, particularly those involving both conventional and machine learning approaches, can be employed to tackle challenges in oncology. It further supports the notion that the continued integration of quantitative tools in medicine is a key strategy in addressing problems and open questions in healthcare

A Multiscale Approach to Blast Neurotrauma Modeling: Part I – Development of Novel Test Devices for in vivo and in vitro Blast Injury Models

The loading conditions used in some current in vivo and in vitro blast-induced neurotrauma models may not be representative of real-world blast conditions. To address these limitations, we developed a compressed-gas driven shock tube with different driven lengths that can generate Friedlander-type blasts. The shock tube can generate overpressures up to 650 kPa with durations between 0.3 and 1.1 ms using compressed helium driver gas, and peak overpressures up to 450 kPa with durations between 0.6 and 3 ms using compressed nitrogen. This device is used for short-duration blast overpressure loading for small animal in vivo injury models, and contrasts the more frequently used long duration/high impulse blast overpressures in the literature. We also developed a new apparatus that is used with the shock tube to recreate the in vivo intracranial overpressure response for loading in vitro culture preparations. The receiver device surrounds the culture with materials of similar impedance to facilitate the propagation of a single overpressure pulse through the tissue. This method prevents pressure waves reflecting off the tissue that can cause unrealistic deformation and injury. The receiver performance was characterized using the longest helium-driven shock tube, and produced in-fluid overpressures up to 1500 kPa at the location where a culture would be placed. This response was well correlated with the overpressure conditions from the shock tube (R2 = 0.97). Finite element models of the shock tube and receiver were developed and validated to better elucidate the mechanics of this methodology. A demonstration exposing a culture to the loading conditions created by this system suggest tissue strains less than 5% for all pressure levels simulated, which was well below functional deficit thresholds for strain rates less than 50 s−1. This novel system is not limited to a specific type of culture model and can be modified to reproduce more complex pressure pulses

A Multiscale Approach to Blast Neurotrauma Modeling: Part II: Methodology for Inducing Blast Injury to in vitro Models

Due to the prominent role of improvised explosive devices (IEDs) in wounding patterns of U.S. war-fighters in Iraq and Afghanistan, blast injury has risen to a new level of importance and is recognized to be a major cause of injuries to the brain. However, an injury risk-function for microscopic, macroscopic, behavioral, and neurological deficits has yet to be defined. While operational blast injuries can be very complex and thus difficult to analyze, a simplified blast injury model would facilitate studies correlating biological outcomes with blast biomechanics to define tolerance criteria. Blast-induced traumatic brain injury (bTBI) results from the translation of a shock wave in-air, such as that produced by an IED, into a pressure wave within the skull–brain complex. Our blast injury methodology recapitulates this phenomenon in vitro, allowing for control of the injury biomechanics via a compressed-gas shock tube used in conjunction with a custom-designed, fluid-filled receiver that contains the living culture. The receiver converts the air shock wave into a fast-rising pressure transient with minimal reflections, mimicking the intracranial pressure history in blast. We have developed an organotypic hippocampal slice culture model that exhibits cell death when exposed to a 530 ± 17.7-kPa peak overpressure with a 1.026 ± 0.017-ms duration and 190 ± 10.7 kPa-ms impulse in-air. We have also injured a simplified in vitro model of the blood–brain barrier, which exhibits disrupted integrity immediately following exposure to 581 ± 10.0 kPa peak overpressure with a 1.067 ± 0.006-ms duration and 222 ± 6.9 kPa-ms impulse in-air. To better prevent and treat bTBI, both the initiating biomechanics and the ensuing pathobiology must be understood in greater detail. A well-characterized, in vitro model of bTBI, in conjunction with animal models, will be a powerful tool for developing strategies to mitigate the risks of bTBI

Role of hypoxia-activated prodrugs in combination with radiation therapy: An in silico approach

Tumour hypoxia has been associated with increased resistance to various cancer treatments, particularly radiation therapy. Conversely, tumour hypoxia is a validated and ideal target for guided cancer drug delivery. For this reason, hypoxia-activated prodrugs (HAPs) have been developed, which remain inactive in the body until in the presence of tissue hypoxia, allowing for an activation tendency in hypoxic regions. We present here an experimentally motivated mathematical model predicting the effectiveness of HAPs in a variety of clinical settings. We first examined HAP effectiveness as a function of the amount of tumour hypoxia and showed that the drugs have a larger impact on tumours with high levels of hypoxia. We then combined HAP treatment with radiation to examine the effects of combination therapies. Our results showed radiation-HAP combination therapies to be more effective against highly hypoxic tumours. The analysis of combination therapies was extended to consider schedule sequencing of the combination treatments. These results suggested that administering HAPs before radiation was most effective in reducing total cell number. Finally, a sensitivity analysis of the drug-related parameters was done to examine the effect of drug diffusivity and enzyme abundance on the overall effectiveness of the drug. Altogether, the results highlight the importance of the knowledge of tumour hypoxia levels before administration of HAPs in order to ensure positive results

Antimicrobial assays of three native British plants used in Anglo-Saxon medicine for wound healing formulations in 10th century England

Ethnopharmacological relevance: Three important Anglo-Saxon medical texts from the 10th century contain herbal formulations for over 250 plant species, many of which have yet to be evaluated for their phytochemical and/or pharmacological properties. In this study, three native British plants were selected to determine antimicrobial activity relevant to treating bacterial infections and wounds. Materials and methods: Several preparations of Agrimonia eupatoria L., Arctium minus (Hill) Bernh. and Potentilla reptans L. were screened for antimicrobial activity against selected Gram-positive and Gram-negative bacteria of relevance in wounds using a 96 well plate microdilution method (200, 40 and 8 µg/mL). Minimum inhibitory concentration (MIC) values were determined for the most potent extracts from 2-0.004 mg/mL and HPLC chromatograms examined by multivariate analysis. Principle components analysis (PCA) was used to identify chemical differences between antimicrobial activity of the crude extracts. Results: The HPLC-PCA score plots attributed HPLC peaks to the antimicrobial activity with all three plants inhibiting growth of Gram-positive Staphylococcus aureus by >50% in four or more extracts. The first two principal components (PC) represented 87% of the dataset variance. The P. reptans 75% ethanol root extract exhibited the greatest range of activity with MIC50 at 31.25 µg/mL to a total MIC that was also the minimum bactericidal concentration (MBC) at 1 mg/mL. Additionally, the root of P. reptans inhibited growth of Gram-negative bacteria with the 75% ethanol extract having a MIC50 at 1 mg/mL against Pseudomonas aeruginosa and the decoction a MIC50 at 3.9 µg/mL against Escherichia coli. Conclusions: The results indicate a moderate antimicrobial activity against common wound pathogens for P.reptans suggesting it may well have been effective for treating wound and bacterial infections. Anglo-Saxon literary heritage may provide a credible basis for researching new antimicrobial formulations. Our approach encompassing advanced analytical technologies and chemometric models paves the way for systematic investigation of Anglo-Saxon medical literature for further therapeutic indications to uncover knowledge of native British plants, some of which are currently lost to modern Western herbal medicine

Maternal Programming of Sexual Behavior and Hypothalamic-Pituitary-Gonadal Function in the Female Rat

Variations in parental care predict the age of puberty, sexual activity in adolescence and the age at first pregnancy in humans. These findings parallel descriptions of maternal effects on phenotypic variation in reproductive function in other species. Despite the prevalence of such reports, little is known about potential biological mechanisms and this especially true for effects on female reproductive development. We examined the hypothesis that parental care might alter hypothalamic-pituitary-ovarian function and thus reproductive function in the female offspring of rat mothers that vary pup licking/grooming (LG) over the first week postpartum. As adults, the female offspring of Low LG mothers showed 1) increased sexual receptivity; 2) increased plasma levels of luteinizing hormone (LH) and progesterone at proestrus; 3) an increased positive-feedback effect of estradiol on both plasma LH levels and gonadotropin releasing-hormone (GnRH) expression in the medial preoptic region; and 4) increased estrogen receptor α (ERα) expression in the anterioventral paraventricular nucleus, a system that regulates GnRH. The results of a cross-fostering study provide evidence for a direct effect of postnatal maternal care as well as a possible prenatal influence. Indeed, we found evidence for increased fetal testosterone levels at embryonic day 20 in the female fetuses of High compared to Low LG mothers. Finally, the female offspring of Low LG mothers showed accelerated puberty compared to those of High LG mothers. These data suggest maternal effects in the rat on the development of neuroendocrine systems that regulate female sexual behaviour. Together with studies revealing a maternal effect on the maternal behavior of the female offspring, these findings suggest that maternal care can program alternative reproductive phenotypes in the rat through regionally-specific effects on ERα expression

Writing in Britain and Ireland, c. 400 to c. 800

No abstract available

Age Affects the Expression of Maternal Care and Subsequent Behavioural Development of Offspring in a Precocial Bird

Variations of breeding success with age have been studied largely in iteroparous species and particularly in birds: survival of offspring increases with parental age until senescence. Nevertheless, these results are from observations of free-living individuals and therefore, it remains impossible to determine whether these variations result from parental investment or efficiency or both, and whether these variations occur during the prenatal or the postnatal stage or during both. Our study aimed first, to determine whether age had an impact on the expression of maternal breeding care by comparing inexperienced female birds of two different ages, and second, to define how these potential differences impact chicks’ growth and behavioural development. We made 22 2-month-old and 22 8-month-old female Japanese quail foster 1-day-old chicks. We observed their maternal behaviour until the chicks were 11 days old and then tested these chicks after separation from their mothers. Several behavioural tests estimated their fearfulness and their sociality. We observed first that a longer induction was required for young females to express maternal behaviour. Subsequently as many young females as elder females expressed maternal behaviour, but young females warmed chicks less, expressed less covering postures and rejected their chicks more. Chicks brooded by elder females presented higher growth rates and more fearfulness and sociality. Our results reveal that maternal investment increased with age independently of maternal experience, suggesting modification of hormone levels implied in maternal behaviour. Isolated effects of maternal experience should now be assessed in females of the same age. In addition, our results show, for first time in birds, that variations in maternal care directly induce important differences in the behavioural development of chicks. Finally, our results confirm that Japanese quail remains a great laboratory model of avian maternal behaviour and that the way we sample maternal behaviour is highly productive

Outside the gate: sub-urban legal practices in early medieval England

Many aspects of English early medieval (Anglo-Saxon) legal landscapes can be discerned in archaeological and toponymic evidence, ranging from the locations of legislative councils and judicial assemblies to sites of capital punishment. Among the corpus of such sites a striking group can be detected at the periphery of urban spaces. Gates into a number of towns appear to have functioned as legislative meeting-places, and even gave their names to some legally constituted communities, while suburban locations also feature prominently as sites of gallows and public punishment. In this paper historical, archaeological and toponymic evidence is used to examine this phenomenon of suburban legal practices and to pose questions about the wider dimensions of the early medieval legal landscape