A multiscale model for collagen alignment in wound healing

It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this process. We consider fibroblasts as discrete units moving within an extracellular matrix of collagen and fibrin modelled as continua. Our model includes flux induced alignment of collagen by fibroblasts, and contact guidance of fibroblasts by collagen fibres. We can use the model to predict the effects of certain manipulations, such as varying fibroblast speed, or placing an aligned piece of tissue in the wound. We also simulate experiments which alter the TGF-β concentrations in a healing dermal wound and use the model to offer an explanation of the observed influence of this growth factor on scarring

Cancer modelling: Getting to the heart of the problem

Paradoxically, improvements in healthcare that have enhanced the life expectancy of humans in the Western world have, indirectly, increased the prevalence of certain types of cancer such as prostate and breast. It remains unclear whether this phenomenon should be attributed to the ageing process itself or the cumulative effect of prolonged exposure to harmful environmental stimuli such as ultraviolet light, radiation and carcinogens (Franks and Teich, 1988). Equally, there is also compelling evidence that certain genetic abnormalities can predispose individuals to specific cancers (Ilyas et al., 1999). The variety of factors that have been implicated in the development of solid tumours stems, to a large extent, from the fact that ‘cancer’ is a generic term, often used to characterize a series of disorders that share common features. At this generic level of description, cancer may be viewed as a cellular disease in which controls that usually regulate growth and maintain homeostasis are disrupted. Cancer is typically initiated by genetic mutations that lead to enhanced mitosis of a cell lineage and the formation of an avascular tumour. Since it receives nutrients by diffusion from the surrounding tissue, the size of an avascular tumour is limited to several millimeters in diameter. Further growth relies on the tumour acquiring the ability to stimulate the ingrowth of a new, circulating blood supply from the host vasculature via a process termed angiogenesis (Folkman, 1974). Once vascularised, the tumour has access to a vast nutrient source and rapid growth ensues. Further, tumour fragments that break away from the primary tumour, on entering the vasculature, may be transported to other organs in which they may establish secondary tumours or metastases that further compromise the host. Invasion is another key feature of solid tumours whereby contact with the tissue stimulates the production of enzymes that digest the tissue, liberating space into which the tumour cells migrate. Thus, cancer is a complex, multiscale process. The spatial scales of interest range from the subcellular level, to the cellular and macroscopic (or tissue) levels while the timescales may vary from seconds (or less) for signal transduction pathways to months for tumour doubling times The variety of phenomena involved, the range of spatial and temporal scales over which they act and the complex way in which they are inter-related mean that the development of realistic theoretical models of solid tumour growth is extremely challenging. While there is now a large literature focused on modelling solid tumour growth (for a review, see, for example, Preziosi, 2003), existing models typically focus on a single spatial scale and, as a result, are unable to address the fundamental problem of how phenomena at different scales are coupled or to combine, in a systematic manner, data from the various scales. In this article, a theoretical framework will be presented that is capable of integrating a hierarchy of processes occurring at different scales into a detailed model of solid tumour growth (Alarcon et al., 2004). The model is formulated as a hybrid cellular automaton and contains interlinked elements that describe processes at each spatial scale: progress through the cell cycle and the production of proteins that stimulate angiogenesis are accounted for at the subcellular level; cell-cell interactions are treated at the cellular level; and, at the tissue scale, attention focuses on the vascular network whose structure adapts in response to blood flow and angiogenic factors produced at the subcellular level. Further coupling between the different spatial scales arises from the transport of blood-borne oxygen into the tissue and its uptake at the cellular level. Model simulations will be presented to illustrate the effect that spatial heterogeneity induced by blood flow through the vascular network has on the tumour’s growth dynamics and explain how the model may be used to compare the efficacy of different anti-cancer treatment protocols

Computational Modelling of Cancer Systems: From Individual to Collective Cell Behaviour

Debido a su complejidad, el cáncer sigue siendo una de las principales causas de muerte a nivel mundial. La creación de prácticas preventivas adecuadas y terapias innovadoras está limitada por la falta de comprensión de los mecanismos básicos que causan el cáncer. Como tal, se deben desarrollar métodos nuevos y más efectivos que avancen nuestra comprensión del cáncer. En los últimos años, se ha visto un aumento en el uso de modelos computacionales para explicar procesos biológicos que son costosos y difíciles de explorar en entornos experimentales. Estos métodos permiten la traducción de mecanismos biológicos en ecuaciones y suposiciones matemáticas que pueden evaluarse utilizando herramientas informáticas para producir nuevas hipótesis. Además, las tecnologías computacionales se están volviendo más potentes debido a la disponibilidad de datos y la amplia capacidad de procesamiento.El objetivo global de esta tesis es diseñar e implementar modelos computacionales de cáncer, comenzando con comportamientos simples y aislados y progresando hacia fenómenos más complejos. Se abordan tres campos de investigación específicos para lograr este objetivo general: (i) motilidad unicelular, (ii) crecimiento tumoral y (iii) formación de patrones. En el primer objetivo, se presenta un modelo computacional para simular la motilidad celular individual que considera las propiedades mecánicas y químicas del microambiente. Posteriormente, este trabajo fue ampliado para tener en cuenta las interacciones célula-célula y reproducir el crecimiento de estructuras tumorales multicelulares. Por último, todos los eventos biológicos mencionados anteriormente fueron considerados y se añadió la diferenciación celular como el bloque de construcción final de esta tesis para simular la formación de patrones espaciales.Además, esta tesis analiza la relevancia de integrar datos experimentales y métodos computacionales para mejorar la precisión biológica y confirmar los resultados del modelo. En particular, muestra cómo se pueden usar técnicas de calibración y optimización para considerar datos empíricos en el diseño y validación de modelos. Los resultados experimentales cualitativos y cuantitativos, tanto de la literatura como de nuevos experimentos, se reproducen en este artículo para mostrar diferentes enfoques en la integración de datos.En general, esta tesis proporciona un modelo de cómo se pueden utilizar los métodos computacionales para analizar y comprender problemas complejos en la biología del cáncer.Demuestra explícitamente cómo los componentes del modelo pueden representar ciertos aspectos de la biología del cáncer, que pueden mejorarse y reproducirse utilizando datos experimentales. En consecuencia, los comportamientos complejos, como el crecimiento tumoral y la formación de patrones, resultan de la intrincada interacción entre los componentes del modelo.<br /