Mathematical investigation of the interactions between the inflammatory response and mechanical aspects of dermal wound repair

Dermal wound repair involves complex interactions between cells, cytokines and mechanics to close injuries to the skin. In particular, we investigate the contribution of fibroblasts, myofibroblasts, TGFβ, collagen and local tissue mechanics to wound repair in the human dermis. We develop a morphoelastic model where a realistic representation of tissue mechanics is key, and a fibrocontractive model that involves a reasonable approximation to the true kinetics of the important bioactive species. We use each of these descriptions to elucidate the mechanisms that generate pathologies such as hypertrophic scars, contractures and keloids. We find that for hypertrophic scar and contracture development, factors regulating the myofibroblast phenotype are critical, with heightened myofibroblast activation, reduced myofibroblast apoptosis or prolonged inflammation all predicted as mediators for scar hypertrophy and contractures. Prevention of these pathologies is predicted when myofibroblast apoptosis is induced, myofibroblast activation is blocked or TGFβ is neutralised. To investigate keloid invasion, we develop a caricature representation of the fibrocontractive model and find that TGFβ spread is the driving factor behind keloid growth. Blocking activation of TGFβ is found to cause keloid regression. Thus, we recommend myofibroblasts and TGFβ as targets for clinicians when developing intervention strategies for prevention and cure of fibrotic scars.

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Optimal fluid injection strategies for in situ mineral leaching in two-dimensions

This paper examines the ground-water flow problem associated with the injection and recovery of certain corrosive fluids into mineral bearing rock. The aim is to dissolve the minerals in situ, and then recover them in solution. In general, it is not possible to recover all the injected fluid, which is of concern economically and environmentally. However, a new strategy is proposed here, that allows all the leaching fluid to be recovered. A mathematical model of the situation is solved approximately using an asymptotic solution, and exactly using a boundary integral approach. Solutions are shown for two-dimensional flow, which is of some practical interest as it is achievable in old mine tunnels, for example.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Sensors and imaging for wound healing : a review

Wound healing involves a complex series of biochemical events and has traditionally been managed with 'low tech' dressings and bandages. The concept that diagnostic and theranostic sensors can complement wound management is rapidly growing in popularity as there is tremendous potential to apply this technology to both acute and chronic wounds. Benefits in sensing the wound environment include reduction of hospitalization time, prevention of amputations and better understanding of the processes which impair healing. This review discusses the state-of-the-art in detection of markers associated with wound healing and infection, utilizing devices imbedded within dressings or as point-of-care techniques to allow for continual or rapid wound assessment and monitoring. Approaches include using biological or chemical sensors of wound exudates and volatiles to directly or indirectly detect bacteria, monitor pH, temperature, oxygen and enzymes. Spectroscopic and imaging techniques are also reviewed as advanced wound monitoring techniques. The review concludes with a discussion of the limitations of and future directions for this field.

Investigating epidermogenesis in a human skin equivalent model

Skin is the largest, and arguably, the most important organ of the body. It is a complex and multi-dimensional tissue, thus making it essentially impossible to fully model in vitro in conventional 2-dimensional culture systems. In view of this, rodents or pigs are utilised to study wound healing therapeutics or to investigate the biological effects of treatments on skin. However, there are many differences between the wound healing processes in rodents compared to humans (contraction vs. re-epithelialisation) and there are also ethical issues associated with animal testing for scientific research. Therefore, the development of skin equivalent (HSE) models from surgical discard human skin has become an important area of research. The studies in this thesis compare, for the first time, native human skin and the epidermogenesis process in a HSE model. The HSE was reported to be a comparable model for human skin in terms of expression and localisation of key epidermal cell markers. This validated HSE model was utilised to study the potential wound healing therapeutic, hyperbaric oxygen (HBO) therapy. There is a significant body of evidence suggesting that lack of cutaneous oxygen results in and potentiates the chronic, non-healing wound environment. Although the evidence is anecdotal, HBO therapy has displayed positive effects on re-oxygenation of chronic wounds and the clinical outcomes suggest that HBO treatment may be beneficial. Therefore, the HSE was subjected to a daily clinical HBO regime and assessed in terms of keratinocyte migration, proliferation, differentiation and epidermal thickening. HBO treatment was observed to increase epidermal thickness, in particular stratum corneum thickening, but it did not alter the expression or localisation of standard epidermal cell markers. In order to elucidate the mechanistic changes occurring in response to HBO treatment in the HSE model, gene microarrays were performed, followed by qRT-PCR of select genes which were differentially regulated in response to HBO treatment. The biological diversity of the HSEs created from individual skin donors, however, overrode the differences in gene expression between treatment groups. Network analysis of functional changes in the HSE model revealed general trends consistent with normal skin growth and maturation. As a more robust and longer term study of these molecular changes, protein localisation and expression was investigated in sections from the HSEs undergoing epidermogenesis in response to HBO treatment. These proteins were CDCP1, Metallothionein, Kallikrein (KLK) 1 and KLK7 and early growth response 1. While the protein expression within the HSE models exposed to HBO treatment were not consistent in all HSEs derived from all skin donors, this is the first study to detect and compare both KLK1 and CDCP1 protein expression in both a HSE model and native human skin. Furthermore, this is the first study to provide such an in depth analysis of the effect of HBO treatment on a HSE model. The data presented in this thesis, demonstrates high levels of variation between individuals and their response to HBO treatment, consistent with the clinical variation that is currently observed.

Limitations of a laboratory scale model in predicting optimal pilot scale conditions for dilute acid pretreatment of sugarcane bagasse

Pilot and industrial scale dilute acid pretreatment data can be difficult to obtain due to the significant infrastructure investment required. Consequently, models of dilute acid pretreatment by necessity use laboratory scale data to determine kinetic parameters and make predictions about optimal pretreatment conditions at larger scales. In order for these recommendations to be meaningful, the ability of laboratory scale models to predict pilot and industrial scale yields must be investigated. A mathematical model of the dilute acid pretreatment of sugarcane bagasse has previously been developed by the authors. This model was able to successfully reproduce the experimental yields of xylose and short chain xylooligomers obtained at the laboratory scale. In this paper, the ability of the model to reproduce pilot scale yield and composition data is examined. It was found that in general the model over predicted the pilot scale reactor yields by a significant margin. Models that appear very promising at the laboratory scale may have limitations when predicting yields on a pilot or industrial scale. It is difficult to comment whether there are any consistent trends in optimal operating conditions between reactor scale and laboratory scale hydrolysis due to the limited reactor datasets available. Further investigation is needed to determine whether the model has some efficacy when the kinetic parameters are re-evaluated by parameter fitting to reactor scale data, however, this requires the compilation of larger datasets. Alternatively, laboratory scale mathematical models may have enhanced utility for predicting larger scale reactor performance if bulk mass transport and fluid flow considerations are incorporated into the fibre scale equations. This work reinforces the need for appropriate attention to be paid to pilot scale experimental development when moving from laboratory to pilot and industrial scales for new technologies.

Mathematical models for collective cell spreading

Collective cell spreading is frequently observed in development, tissue repair and disease progression. Mathematical modelling used in conjunction with experimental investigation can provide key insights into the mechanisms driving the spread of cell populations. In this study, we investigated how experimental and modelling frameworks can be used to identify several key features underlying collective cell spreading. In particular, we were able to independently quantify the roles of cell motility and cell proliferation in a spreading cell population, and investigate how these roles are influenced by factors such as the initial cell density, type of cell population and the assay geometry.

Computational modelling of bubbles, droplets and particles in metals reduction and refining

A multi-phase framework is typically required for the CFD modelling of metals reduction processes. Such processes typically involve the interaction of liquid metals, a gas (often air) top space, liquid droplets in the top space and injection of both solid particles and gaseous bubbles into the bath. The exchange of mass, momentum and energy between the phases is fundamental to these processes. Multi-phase algorithms are complex and can be unreliable in terms of either or both convergence behaviour or in the extent to which the physics is captured. In this contribution, we discuss these multi-phase flow issues and describe an example of each of the main “single phase” approaches to modelling this class of problems (i.e., Eulerian–Lagrangian and Eulerian–Eulerian). Their utility is illustrated in the context of two problems – one involving the injection of sparging gases into a steel continuous slab caster and the other based on the development of a novel process for aluminium electrolysis. In the steel caster, the coupling of the Lagrangian tracking of the gas phase with the continuum enables the simulation of the transient motion of the metal–flux interface. The model of the electrolysis process employs a novel method for the calculation of slip velocities of oxygen bubbles, resulting from the dissolution of alumina, which allows the efficiency of the process to be predicted.

Supplemental oxygen and hyperbaric treatment at high altitude: Cardiac and respiratory response

Introduction: The most effective treatment for high altitude sickness is prompt descent. However, rapid descent is sometimes impossible and alternative solutions are desirable. Supplemental oxygen at ambient pressure and hyperbaric oxygen in a hyperbaric tent have both been demonstrated to improve symptoms and increase arterial oxygenation (SaO(2)) in those with high altitude sickness; however, their use in combination has not previously been described in a controlled study. Methods and Results: In this feasibility study, the SaO(2) of six healthy, well-acclimatized participants rose from 76.5 to 97.5% at 4900 m and 72.5 to 96.0% at 5700 m following the administration of oxygen via a nasal demand circuit (33 ml of oxygen per pulse) inside a hyperbaric tent (107 mmHg above ambient barometric pressure) (p

Topical bacteriophage therapy of the infected diabetic foot

Tese de doutoramento, Medicina (Medicina Interna), Universidade de Lisboa, Faculdade de Medicina, 2014

Oxygen exchange in galls of Eurosta solidaginis (Diptera: Tephritidae)

Hypoxia in plant tissue should affect animals living within. Gallmakers stimulate their plant hosts to produce the gall they inhabit and feed on, and also influence the gall phenotype for other adaptations, such as defense against predators. The potential for hypoxia in galls of Eurosta solidaginis was studied in the context of potential adaptations to gall oxygen level, using a combination of direct measurement, mathematical modelling, and respirometry on both gallmakers and hosts. Modelling results suggested mild hypoxia tolerable to the larva persists for most of the growth season, whereas more severe hypoxia may occur earlier in fully-grown young galls. Field data from one of the two years studied showed hypoxia more severe than expected, and coincided with adverse weather conditions and high larval mortality. The hypoxia may be related to host response to adverse weather. Whether hypoxia directly caused larval mortality requires further study.

A "Trojan horse" strategy to reverse drug-resistance in brain tumors

Los gliomas malignos representan una de las formas más agresivas de los tumores del sistema nervioso central (SNC). De acuerdo con la clasificación de los tumores cerebrales de la Organización Mundial de la Salud (OMS), los astrocitomas han sido categorizados en cuatro grados, determinados por la patología subyacente. Es así como los gliomas malignos (o de alto grado) incluyen el glioma anaplásico (grado III) así como el glioblastoma multiforme (GBM, grado IV),estos últimos los más agresivos con el peor pronóstico (1). El manejo terapéutico de los tumores del SNC se basa en la cirugía, la radioterapia y la quimioterapia, dependiendo de las características del tumor, el estadio clínico y la edad (2),(3), sin embargo ninguno de los tratamientos estándar es completamente seguro y compatible con una calidad de vida aceptable (3), (4). En general, la quimioterapia es la primera opción en los tumores diseminados, como el glioblastoma invasivo y el meduloblastoma de alto riesgo o con metástasis múltiple, pero el pronóstico en estos pacientes es muy pobre (2),(3). Solamente nuevas terapias dirigidas (2) como las terapias anti-angiogénicas (4); o terapias génicas muestran un beneficio real en grupos limitados de pacientes con defectos moleculares específicos conocidos (4). De este modo, se hace necesario el desarrollo de nuevas terapias farmacológicas para atacar los tumores cerebrales. Frente a las terapias los gliomas malignos son con frecuencia quimioresistentes, y esta resistencia parece depender de al menos dos mecanismos: en primer lugar, la pobre penetración de muchas drogas anticáncer a través de la barrera hematoencefálica (BBB: Blood Brain Barrier), la barrera del fluido sangre-cerebroespinal (BCSFB: Blood-cerebrospinal fluid barrier) y la barrera sangre-tumor (BTB: blood-tumor barrier). Dicha resistencia se debe a la interacción de la droga con varios transportadores o bombas de eflujo de droga ABC (ABC: ATP-binding cassette) que se sobre expresan en las células endoteliales o epiteliales de estas barreras. En segundo lugar, estos transportadores de eflujo de drogas ABC propios de las células tumorales confieren un fenotipo conocido como resistencia a multidrogas (MDR: multidrug resistance), el cual es característico de varios tumores sólidos. Este fenotipo también está presente en los tumores del SNC y su papel en gliomas es objeto de investigación (5). Por consiguiente el suministro de medicamentos a través de la BBB es uno de los problemas vitales en los tratamientos de terapia dirigida. Estudios recientes han demostrado que algunas moléculas pequeñas utilizadas en estas terapias son sustratos de la glicoproteína P (Pgp: P-gycoprotein), así como también de otras bombas de eflujo como las proteínas relacionadas con la resistencia a multidrogas (MRPs: multidrug resistance-related proteins (MRPs) o la proteína relacionada con cáncer de seno (BCRP: breast-cancer resistance related protein)) que no permiten que las drogas de este tipo alcancen el tumor (1). Un sustrato de Pgp y BCRP es la DOXOrubicina (DOXO), un fármaco utilizado en la terapia anti cáncer, el cual es muy eficaz para atacar las células del tumor cerebral in vitro, pero con un uso clínico limitado por la poca entrega a través de la barrera hematoencefálica (BBB) y por la resistencia propia de los tumores. Por otra parte las células de BBB y las células del tumor cerebral tienen también proteínas superficiales, como el receptor de la lipoproteína de baja densidad (LDLR), que podría utilizarse como blanco terapéutico en BBB y tumores cerebrales. Es asi como la importancia de este estudio se basa en la generación de estrategias terapéuticas que promuevan el paso de las drogas a través de la barrera hematoencefalica y tumoral, y a su vez, se reconozcan mecanismos celulares que induzcan el incremento en la expresión de los transportadores ABC, de manera que puedan ser utilizados como blancos terapéuticos.Este estudio demostró que el uso de una nueva estrategia basada en el “Caballo de Troya”, donde se combina la droga DOXOrubicina, la cual es introducida dentro de un liposoma, salvaguarda la droga de manera que se evita su reconocimiento por parte de los transportadores ABC tanto de la BBB como de las células del tumor. La construcción del liposoma permitió utilizar el receptor LDLR de las células asegurando la entrada a través de la BBB y hacia las células tumorales a través de un proceso de endocitosis. Este mecanismo fue asociado al uso de estatinas o drogas anticolesterol las cuales favorecieron la expresión de LDLR y disminuyeron la actividad de los transportadores ABC por nitración de los mismos, incrementando la eficiencia de nuestro Caballo de Troya. Por consiguiente demostramos que el uso de una nueva estrategia o formulación denominada ApolipoDOXO más el uso de estatinas favorece la administración de fármacos a través de la BBB, venciendo la resistencia del tumor y reduciendo los efectos colaterales dosis dependiente de la DOXOrubicina. Además esta estrategia del "Caballo de Troya", es un nuevo enfoque terapéutico que puede ser considerado como una nueva estrategia para aumentar la eficacia de diferentes fármacos en varios tumores cerebrales y garantiza una alta eficiencia incluso en un medio hipóxico,característico de las células cancerosas, donde la expresión del transportador Pgp se vió aumentada. Teniendo en cuenta la relación entre algunas vías de señalización reconocidas como moduladores de la actividad de Pgp, este estudio presenta no solo la estrategia del Caballo de Troya, sino también otra propuesta terapéutica relacionada con el uso de Temozolomide más DOXOrubicina. Esta estrategia demostró que el temozolomide logra penetrar la BBB por que interviene en la via de señalización de la Wnt/GSK3/β-catenina, la cual modula la expresión del transportador Pgp. Se demostró que el TMZ disminuye la proteína y el mRNA de Wnt3 permitiendo plantear la hipótesis de que la droga al disminuir la transcripción del gen Wnt3 en células de BBB, incrementa la activación de la vía fosforilando la β-catenina y conduciendo a disminuir la β-catenina nuclear y por tanto su unión al promotor del gen mdr1. Con base en los resultados este estudio permitió el reconocimiento de tres mecanismos básicos relacionados con la expresión de los transportadores ABC y asociados a las estrategias empleadas: el primero fue el uso de las estatinas, el cual condujo a la nitración de los transportadores disminuyendo su actividad por la via del factor de transcripción NFκB; el segundo a partir del uso del temozolomide, el cual metila el gen de Wnt3 reduciendo la actividad de la via de señalización de la la β-catenina, disminuyendo la expresión del transportador Pgp. El tercero consistió en la determinación de la relación entre el eje RhoA/RhoA quinasa como un modulador de la via (no canónica) GSK3/β-catenina. Se demostró que la proteína quinasa RhoA promovió la activación de la proteína PTB1, la cual al fosforilar a GSK3 indujo la fosforilación de la β-catenina, lo cual dio lugar a su destrucción por el proteosoma, evitando su unión al promotor del gen mdr1 y por tanto reduciendo su expresión. En conclusión las estrategias propuestas en este trabajo incrementaron la citotoxicidad de las células tumorales al aumentar la permeabilidad no solo de la barrera hematoencefálica, sino también de la propia barrera tumoral. Igualmente, la estrategia del “Caballo de Troya” podría ser útil para la terapia de otras enfermedades asociadas al sistema nervioso central. Por otra parte estos estudios indican que el reconocimiento de mecanismos asociados a la expresión de los transportadores ABC podría constituir una herramienta clave en el desarrollo de nuevas terapias anticáncer.

Mathematical Optimization Applied to Thermal and Electrical Energy Systems

This Thesis aims at building and discussing mathematical models applications focused on Energy problems, both on the thermal and electrical side. The objective is to show how mathematical programming techniques developed within Operational Research can give useful answers in the Energy Sector, how they can provide tools to support decision making processes of Companies operating in the Energy production and distribution and how they can be successfully used to make simulations and sensitivity analyses to better understand the state of the art and convenience of a particular technology by comparing it with the available alternatives. The first part discusses the fundamental mathematical background followed by a comprehensive literature review about mathematical modelling in the Energy Sector. The second part presents mathematical models for the District Heating strategic network design and incremental network design. The objective is the selection of an optimal set of new users to be connected to an existing thermal network, maximizing revenues, minimizing infrastructure and operational costs and taking into account the main technical requirements of the real world application. Results on real and randomly generated benchmark networks are discussed with particular attention to instances characterized by big networks dimensions. The third part is devoted to the development of linear programming models for optimal battery operation in off-grid solar power schemes, with consideration of battery degradation. The key contribution of this work is the inclusion of battery degradation costs in the optimisation models. As available data on relating degradation costs to the nature of charge/discharge cycles are limited, we concentrate on investigating the sensitivity of operational patterns to the degradation cost structure. The objective is to investigate the combination of battery costs and performance at which such systems become economic. We also investigate how the system design should change when battery degradation is taken into account.

Modelling of transient heat transfer in annealing furnaces

This is a study of heat transfer in a lift-off furnace which is employed in the batch annealing of a stack of coils of steel strip. The objective of the project is to investigate the various factors which govern the furnace design and the heat transfer resistances, so as to reduce the time of the annealing cycle, and hence minimize the operating costs. The work involved mathematical modelling of patterns of gas flow and modes of heat transfer. These models are: Heat conduction and its conjectures in the steel coils;Convective heat transfer in the plates separating the coils in the stack and in other parts of the furnace; and Radiative and convective heat transfer in the furnace by using the long furnace model. An important part of the project is the development of numerical methods and computations to solve the transient models. A limited number of temperature measurements was available from experiments on a test coil in an industrial furnace. The mathematical model agreed well with these data. The model has been used to show the following characteristics of annealing furnaces, and to suggest further developments which would lead to significant savings: - The location of the limiting temperature in a coil is nearer to the hollow core than to the outer periphery. - Thermal expansion of the steel tends to open the coils, reduces their thermal conductivity in the radial direction, and hence prolongs the annealing cycle. Increasing the tension in the coils and/or heating from the core would overcome this heat transfer resistance. - The shape and dimensions of the convective channels in the plates have significant effect on heat convection in the stack. An optimal design of a channel is shown to be of a width-to-height ratio equal to 9. - Increasing the cooling rate, by using a fluidized bed instead of the normal shell and tube exchanger, would shorten the cooling time by about 15%, but increase the temperature differential in the stack. - For a specific charge weight, a stack of different-sized coils will have a shorter annealing cycle than one of equally-sized coils, provided that production constraints allow the stacking order to be optimal. - Recycle of hot flue gases to the firing zone of the furnace would produce a. decrease in the thermal efficiency up to 30% but decreases the heating time by about 26%.