The role of acidity in solid tumour growth and invasion

Acidic pH is a common characteristic of human tumours. It has a significant impact on tumour progression and response to therapies. In this paper, we develop a simple model of three-dimensional tumour growth to examine the role of acidosis in the interaction between normal and tumour cell populations. Both vascular and avascular tumour dynamics are investigated, and a number of different behaviours are observed. Whilst an avascular tumour always proceeds to a benign steady state, a vascular tumour may display either benign or invasive dynamics, depending on the value of a critical parameter. Analysis of the model allows us to assess novel therapies directed towards changing the level of acidity within the tumour

Achieving coexistence - Comment on "Modelling rain forest diversity:The role of competition by Bampfylde et al. (2005)

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Implementing vertex dynamics models of cell populations in biology within a consistent computational framework

The dynamic behaviour of epithelial cell sheets plays a central role during development, growth, disease and wound healing. These processes occur as a result of cell adhesion, migration, division, differentiation and death, and involve multiple processes acting at the cellular and molecular level. Computational models offer a useful means by which to investigate and test hypotheses about these processes, and have played a key role in the study of cell–cell interactions. However, the necessarily complex nature of such models means that it is difficult to make accurate comparison between different models, since it is often impossible to distinguish between differences in behaviour that are due to the underlying model assumptions, and those due to differences in the in silico implementation of the model. In this work, an approach is described for the implementation of vertex dynamics models, a discrete approach that represents each cell by a polygon (or polyhedron) whose vertices may move in response to forces. The implementation is undertaken in a consistent manner within a single open source computational framework, Chaste, which comprises fully tested, industrial-grade software that has been developed using an agile approach. This framework allows one to easily change assumptions regarding force generation and cell rearrangement processes within these models. The versatility and generality of this framework is illustrated using a number of biological examples. In each case we provide full details of all technical aspects of our model implementations, and in some cases provide extensions to make the models more generally applicable

Colorectal Cancer Through Simulation and Experiment

Colorectal cancer has continued to generate a huge amount of research interest over several decades, forming a canonical example of tumourigenesis since its use in Fearon and Vogelstein’s linear model of genetic mutation. Over time, the field has witnessed a transition from solely experimental work to the inclusion of mathematical biology and computer-based modelling. The fusion of these disciplines has the potential to provide valuable insights into oncologic processes, but also presents the challenge of uniting many diverse perspectives. Furthermore, the cancer cell phenotype defined by the ‘Hallmarks of Cancer’ has been extended in recent times and provides an excellent basis for future research. We present a timely summary of the literature relating to colorectal cancer, addressing the traditional experimental findings, summarising the key mathematical and computational approaches, and emphasising the role of the Hallmarks in current and future developments. We conclude with a discussion of interdisciplinary work, outlining areas of experimental interest which would benefit from the insight that mathematical and computational modelling can provide

Metabolic changes during carcinogenesis: Potential impact on invasiveness

Successful adaptation to varying microenvironmental constraints plays a crucial role during carcinogenesis. We develop a hybrid cellular automation approach to investigate the cell–microenvironmental interactions that mediate somatic evolution of cancer cells. This allows investigation of the hypothesis that regions of premalignant lesions develop a substrate-limited environment as proliferation carries cells away from blood vessels which remain separated by the intact basement membrane. We find that selective forces in tumoural regions furthest from the blood supply act to favour cells whose metabolism is best suited to respond to local changes in oxygen, glucose and pH levels. The model predicts three phases of somatic evolution. Initially, cell survival and proliferation is limited due to diminished oxygen levels. This promotes adaptation to a second phase of growth dominated by cells with constitutively up-regulated glycolysis, less reliant on oxygen for ATP production. Increased glycolysis induces acidification of the local environment, limiting proliferation and inducing cell death through necrosis and apoptosis. This promotes a third phase of cellular evolution, with emergence of phenotypes resistant to acid-induced toxicity. This emergent cellular phenotype has a significant proliferative advantage because it will consistently acidify the local environment in a way that is toxic to its competitors but harmless to itself. The model's results suggest this sequence is essential in the transition from self-limited premalignant growth to invasive cancer, and, therefore, that this transition may be delayed or prevented through novel strategies directed towards interrupting the hypoxia–glycolysis–acidosis cycle

Models for pattern formation in somitogenesis: a marriage of cellular and molecular biology

Somitogenesis, the process by which a bilaterally symmetric pattern of cell aggregations is laid down in a cranio-caudal sequence in early vertebrate development, provides an excellent model study for the coupling of interactions at the molecular and cellular level. Here, we review some of the key experimental results and theoretical models related to this process. We extend a recent chemical pre-pattern model based on the cell cycle Journal of Theoretical Biology 207 (2000) 305-316, by including cell movement and show that the resultant model exhibits the correct spatio-temporal dynamics of cell aggregation. We also postulate a model to account for the recently observed spatio-temporal dynamics at the molecular level

Breast Cancer: Modelling and Detection

This paper reviews a number of the mathematical models used in cancer modelling and then chooses a specific cancer, breast carcinoma, to illustrate how the modelling can be used in aiding detection. We then discuss mathematical models that underpin mammographic image analysis, which complements models of tumour growth and facilitates diagnosis and treatment of cancer. Mammographic images are notoriously difficult to interpret, and we give an overview of the primary image enhancement technologies that have been introduced, before focusing on a more detailed description of some of our own recent work on the use of physics-based modelling in mammography. This theoretical approach to image analysis yields a wealth of information that could be incorporated into the mathematical models, and we conclude by describing how current mathematical models might be enhanced by use of this information, and how these models in turn will help to meet some of the major challenges in cancer detection

Clinical and economic consequences of hospital-acquired resistant and multidrug-resistant Pseudomonas aeruginosa infections: a systematic review and meta-analysis

Background Increasing rates of resistant and multidrug-resistant (MDR) P. aeruginosa in hospitalized patients constitute a major public health threat. We present a systematic review of the clinical and economic impact of this resistant pathogen. Methods Studies indexed in MEDLINE and Cochrane databases between January 2000-February 2013, and reported all-cause mortality, length of stay, hospital costs, readmission, or recurrence in at least 20 hospitalized patients with laboratory confirmed resistant P. aeruginosa infection were included. We accepted individual study definitions of MDR, and assessed study methodological quality. Results The most common definition of MDR was resistance to more than one agent in three or more categories of antibiotics. Twenty-three studies (7,881 patients with susceptible P. aeruginosa, 1,653 with resistant P. aeruginosa, 559 with MDR P. aeruginosa, 387 non-infected patients without P. aeruginosa) were analyzed. A random effects model meta-analysis was feasible for the endpoint of all-cause in-hospital mortality. All-cause mortality was 34% (95% confidence interval (CI) 27% – 41%) in patients with any resistant P. aeruginosa compared to 22% (95% CI 14% – 29%) with susceptible P. aeruginosa. The meta-analysis demonstrated a > 2-fold increased risk of mortality with MDR P. aeruginosa (relative risk (RR) 2.34, 95% CI 1.53 – 3.57) and a 24% increased risk with resistant P. aeruginosa (RR 1.24, 95% CI 1.11 – 1.38), compared to susceptible P. aeruginosa. An adjusted meta-analysis of data from seven studies demonstrated a statistically non-significant increased risk of mortality in patients with any resistant P. aeruginosa (adjusted RR 1.24, 95% CI 0.98 – 1.57). All three studies that reported infection-related mortality found a statistically significantly increased risk in patients with MDR P. aeruginosa compared to those with susceptible P. aeruginosa. Across studies, hospital length of stay (LOS) was higher in patients with resistant and MDR P. aeruginosa infections, compared to susceptible P. aeruginosa and control patients. Limitations included heterogeneity in MDR definition, restriction to nosocomial infections, and potential confounding in analyses. Conclusions Hospitalized patients with resistant and MDR P. aeruginosa infections appear to have increased all-cause mortality and LOS. The negative clinical and economic impact of these pathogens warrants in-depth evaluation of optimal infection prevention and stewardship strategies

Explaining rain forest diversity

This group, which is concerned with the applications of mathematics to agricultural science, was formed in 1970 and has since met at approximately yearly intervals in London for one-day meetings. The thirty-third meeting of the group, chaired by Professor P. K. Maini of the Mathematical Institute, University of Oxford, was held in the Kohn Centre at the Royal Society, 6 Carlton House Terrace, London on Friday, 6 April 2001 when the following papers were read

Computer-Assisted Precision Surgery in the Ear

Chirurgische Eingriffe am Ohr stellen aufgrund der komplexen Anatomie und der Grössenverhältnisse der beteiligten anatomischen Strukturen eine Herausforderung für den HNO-Chirurgen dar. In diesem Beitrag wird ein Ansatz für die roboterbasierte Navigation zur Hörgeräteimplantation vorgestellt. Insbesondere wird auf die Möglichkeit des Fräsens von Implantatlagern im Felsenbein eingegangen. Je präziser ein Implantat im Schädel verankert werden kann, desto einfacher ist der chirurgischen Ablauf. Weiterhin, profitieren Patienten von verkürzten Operationszeiten und weniger schmerzhaften Eingriffen.Traditional surgical procedures involving the implantation of artificial hearing devices in the inner ear are challenging due to the size and complexity of anatomical structures within the temporal bone. To date, no stereotactic instrument guidance technology providing the necessary levels of accuracy is available. This work presents an approach to robot assisted implantation of hearing devices. Specifically, the robot system was used to milla cavity to for a direct acoustical stimulation implant. As the precision of such cavities increases, so also can future implant generations improve in terms of size, complexity and cost effectiveness. Additionally, patients themselves would profit from shorter procedure times and less painful interventions