Le manque de produits pharmaceutiques destinés à la population pédiatrique est un problème auquel sont confrontés les professionnels de la santé. Les pharmaciens doivent fréquemment se tourner vers les médicaments destinés aux adultes afin de fournir aux jeunes patients les traitements adéquats. L’utilisation de préparations magistrales pour adapter les médicaments homologués aux besoins de la population pédiatrique reste, encore à ce jour, l’option la plus souvent utilisée. Dans ce mémoire, nous proposons le développement et l’évaluation de nouvelles formulations pharmaceutiques destinées à la population pédiatrique afin de bonifier les options thérapeutiques mises à la disposition des professionnels de la santé. De plus, nous avons exploré l’utilisation de nouvelles techniques spécialisées pour surmonter des défis analytiques rencontrés, ultimement dans le but de déterminer en toute confiance la stabilité et la sécurité de ces nouvelles formulations. La première étude visait à évaluer la stabilité de préparations magistrales de chlorhydrate de clonidine (20 µg/mL) préparées avec des comprimés dans le véhicule commercial Ora-Blend. Les formulations embouteillées ont été conservées à 25°C/60% RH pendant 90 jours. Les défis analytiques rencontrés lors de l’analyse de la stabilité chimique ont été surmontés par l’implémentation d'une nouvelle méthode d'extraction en phase solide, ayant permis d’optimiser la quantification du chlorhydrate de clonidine, se retrouvant qu’en très faible quantité dans les formulations orales. L'absence d'instabilités physiques, évaluée par des mesures qualitatives et quantitatives, et l’absence d'instabilités chimiques, mise en évidence par une méthode HPLC-UV indicatrice de stabilité, confirment qu’accorder une date de péremption de 90 jours à ces préparations magistrales serait approprié. La deuxième étude portait sur l’évaluation de la stabilité de préparations magistrales d’hydroxyurée (100 mg/mL) dans l’Ora-Blend. Dans le cadre de cette étude, différentes méthodes de préparation (mortier, mélangeur, QuartetRx) et différentes sources de principe actifs (poudre, contenu des capsules, capsules entières) ont été étudiées. Toutes les formulations ont été conservées à 25°C pendant 90 jours dans des bouteilles et 14 jours dans des seringues orales. Le développement d'une méthode HPLC indicatrice de stabilité impliquant la dérivation de l’hydroxyurée par le xanthydrol aura permis la rétention l’hydroxyurée sur une colonne à phase inverse de type C18. Plus de 90.0 % de la concentration initiale d’hydroxyurée a été conservé tout au long de l’étude, et ce, pour toutes les conditions testées. L’évaluation visuelle des préparations n’a révélé aucun changement au cours de l’étude de stabilité. Des changements de pH allant jusqu'à 1.6 unités ont toutefois été observés après 90 jours d’entreposage et ont mis en lumière une voie de dégradation de l’hydroxyurée, générant ultimement l’ion ammonium. Ce dernier a été quantifié et les concentrations mesurées, définies comme acceptables. Les résultats ont montré que toutes les formulations d’hydroxyurée étudiées sont demeurées stables jusqu’à 90 jours à 25°C. Pour terminer, une étude exploratoire ayant pour but d’évaluer des comprimés à croquer à saveur d’érable a été réalisée. Le sucre d’érable et un arôme naturel d’érable ont été ajoutés à la composition des comprimés afin d’obtenir une saveur suffisamment prononcée pour masquer le goût amer de l’acétaminophène. Une étude de stabilité préliminaire, impliquant une période de 30 jours d’entreposage dans des conditions de stabilité accélérées (40°C/75%RH), aura permis d’explorer les propriétés physico-chimiques de cette nouvelle formulation, de soulever les défis potentiels et de générer des hypothèses en lien avec l’augmentation de dureté observée après seulement 14 jours d’entreposage. Les résultats de cette étude préliminaire serviront de point de départ pour le futur développement de produits pharmaceutiques à la saveur du Québec. Les techniques utilisées et les études réalisées dans le cadre de ce projet de maîtrise auront permis de générer des résultats robustes qui pourront être utilisés par les professionnels de la santé. Ces informations seront pertinentes à la pratique pharmaceutique et permettront d’offrir à la population pédiatrique des nouvelles options de traitement sécuritaires et efficaces. / The lack of pharmaceuticals intended to the pediatric population is an issue facing healthcare professionals. Pharmacists must frequently resort to adult treatments to provide adequate treatment to young patients. The use of compounding to adapt commercial drugs to the needs of the pediatric population is still, to this day, the most considered option. In this master’s thesis, we propose the development and evaluation of new medicinal preparations for pediatrics in order to improve and diversify the therapeutic options available to healthcare professionals. In addition, we have explored the use of new specialized techniques to overcome analytical challenges encountered, with the goal of confidently determining the stability and safety of these new formulations. The first study aimed to assess the stability of compound preparations of clonidine hydrochloride (20 µg / mL) prepared with tablets in the commercial vehicle Ora-Blend. Bottled formulations were stored at 25°C/60% RH for 90 days. The analytical challenges encountered during the analysis of chemical stability were overcome by the implementation of a new method of solid phase extraction, which allowed to optimize the quantification of clonidine hydrochloride, present in very small amount in oral formulations. The absence of physical instabilities, assessed by qualitative and quantitative measurements, and the absence of chemical instabilities, as demonstrated by a stability indicating HPLC-UV method, confirm that it would be appropriate to grant a 90-day expiration date to these compounded oral liquids. The second study evaluated the stability of compound preparations of hydroxyurea (100 mg / mL) in Ora-Blend. In this study, different preparation methods (mortar, mixer, QuartetRx) and different sources of hydroxyurea (powder, content of capsules, whole capsules) were studied. All formulations were stored at 25°C for 90 days in bottles and 14 days in oral syringes. The development of a stability indicating HPLC method involving the derivatization of hydroxyurea by xanthydrol will have enabled hydroxyurea retention on a C18 type reverse phase column. Over 90.0% of the initial hydroxyurea concentration was recovered throughout the study under all conditions tested. Visual evaluation of the preparations did not reveal any changes during the stability study. Changes in pH of up to 1.6 units were observed after 90 days of storage and revealed a degradation pathway for hydroxyurea, ultimately generating ammonium ion. The latter was quantified, and the measured concentrations defined as acceptable. The results showed that all hydroxyurea formulations studied were stable for up to 90 days at 25°C. Finally, an exploratory study to evaluate maple flavored chewable tablets was carried out. Maple sugar and a natural maple flavor have been added to the composition of the tablets to achieve a flavor strong enough to mask the bitter taste of acetaminophen. The pre-stability study, involving a period of 30 days of storage under accelerated stability conditions (40°C/75% RH), will have made it possible to explore the physicochemical properties of this new formulation, to raise the potential challenges and generate hypotheses related to the increase in hardness observed after only 14 days of storage. The results of this preliminary study will serve as a starting point for the future development of pharmaceutical products with a Quebec flavor. The techniques used and the studies performed will have generated robust results that could help healthcare professionals in their practice.

[pt] O Método Híbrido dos Elementos de Contorno foi formulado em 1987. Desde então, este método tem sido aplicado com sucesso a diversos tipos de problemas de elasticidade e potencial, inclusive problemas dependentes do tempo. Porém, alguns aspectos importantes do método permaneceram abertos a investigação. Esta dissertação apresenta três contribuições, com desenvolvimentos feitos para problemas de elasticidade, mas prontamente extensíveis a problemas de potencial. Numa primeira etapa, desenvolve-se uma expressão para os resultados de deslocamentos no domínio, levando-se em conta corretamente a parcela de deslocamentos de corpo rígido. A partir deste primeiro desenvolvimento, é proposta uma formulação simplificada do método, na qual uma matriz de flexibilidade é obtida diretamente, num procedimento que dispensa qualquer tipo de integração. Esta nova formulação, como mostrado nos exemplos numéricos, é extremamente precisa e de simples implementação computacional. No entanto, por não ter uma base variacional, esta formulação conduz a uma matriz de rigidez não-simétrica. Na terceira contribuição, o Método Híbrido dos Elementos de Contorno e o Método Híbrido Simplificado dos Elementos de Contorno são aplicados a problemas gerais de meio infinito, para qualquer tipo de condições de contorno. Para isto é mostrado que as propriedades espectrais de ambos os métodos estão interrelacionadas. Apresenta-se um grande número de resultados numéricos de problemas bidimensionais, para validação dos desenvolvimentos teóricos realizados. / [en] The hybrid boundary element method was introduced in 1987. Since then, the method has been applied successfully to different problems of elasticity and potential, including time-dependent problems. However, some important aspects of the method have remained open to investigation. This dissertation consists in a threefold contribution, with developments outlined for elasticity, but readily extensible to potential problems. The first step is aimed at improving the expression of displacement results in the domain by taking correctly into account the amount of rigid body movements. Based on the assessment of displacements, a simplified formulation of the method is proposed, in which a flexibility-like matrix is directly obtained, in a procedure that requires no integration at all. This novel formulation, as shown in the numerical examples, is extremely accurate and rather inexpensive. Since it lacks a variational basis, however, the method leads to a non-symmetric stiffness matrix. In a third step, both hybrid and simplified boundary element methods are extended to general problems in an infinite domain, for any type of boundary conditions. It is shown that the matrices of both methods are spectrally interrelated. A large number of numerical results of two-dimensional problems validate the theoretical achievements. / [es] El Método Híbrido de los Elementos de Contorno fue formulado en 1987. Desde entonces, este método ha sido aplicado con éxito a diversos tipos de problemas de elasticidad y potencial, incluso en problemas dependientes del tiempo. No obstante, algunos aspectos importantes del método han permanecido abiertos a la investigación. Esta disertación presenta tres contribuciones, desarrolladas para problemas de elasticidad, pero perfectamente extendibles a problemas de potencial. En una primeira etapa, se desarrolla una expresión para los resultados de deslocamientos en el dominio, teniendo en cuenta la parcela correcta de deslocamientos del cuerpo rígido. A partir de este primer desarrollo, se propone una formulación simplificada del método, en el cual, se obtiene una matriz de flexibilidad diretamente, a través de un procedimiento que dispensa cualquier tipo de integración. Esta nueva formulación, como muestran los ejemplos numéricos, es extremamente precisa y de simple implementación computacional. Sin embargo, por no tener una base variacional, esta formulación conduce a una matriz de rígidez no simétrica. En la tercera contribución, se aplican el Método Híbrido de los Elementos de Contorno y el Método Híbrido Simplificado de los Elementos de Contorno a problemas gerales de medio infinito, para cualquier tipo de condiciones de contorno. Para ello, se demuestra que las propriedads espectrales de ambos métodos están interrelacionadas. Con el objetivo de evaluar los desarrollos teóricos aquí abordados se presentan un gran número de resultados numéricos de problemas bidimensionales.

No description available.

Yes / Two different types of dry powder inhalers (Easyhaler® and RS01®) were used in this work to evaluate the ex vivo and in vitro performance of a budesonide inhaled formulation with recrystallised mannitol, commercial DPI-grade mannitol, or lactose. The aerodynamic performance of the budesonide formulation with recrystallised mannitol was superior when RS01® was used (FPF = 45.8%) compared to Easyhaler® (FPF = 14%). However, the aerodynamic profile was very poor in both devices when commercial mannitol was used. Interestingly, the aerosol performance of the marketed budesonide formulation significantly improved when RS01® was used compared to Easyhaler® (the original device for the formulation). Due to the significant increases in the surface energy of the commercial mannitol formulation, the aerodynamic performance of the formulation was very poor. This work demonstrates the impact of inhaler devices on the performance of inhaled formulations and considers the particle surface energy during formulation development.

Nonsteroidal anti-inflammatory drugs (NSAIDs) are widely used in the treatment of inflammation and pain (Escribano et al., 2003:203). Diclofenac, a classical NSAID, is considerably more effective as an analgesic, antipyretic and anti-inflammatory drug than other traditional NSAIDs, like indomethacin and naproxen (Grosser et al., 2011:986). However, the use of diclofenac is known for its many side effects, such as gastric disorders, while fluid and sodium retention are also commonly observed (Rossiter, 2012:391). Since topical diclofenac offers a more favourable safety profile, it is a valuable substitute for oral NSAID therapy in the treatment of osteoarthritis (Roth & Fuller, 2011:166). The benefits of topically applied NSAIDs, compared to oral administration and systemic delivery, include the easy cessation of treatment, should effects become troublesome (Brown et al., 2006:177), the avoidance of extensive, first-pass metabolism (Cleary, 1993:19; Kornick, 2003:953; Prausnitz & Langer, 2008:1261; Lionberger & Brennan, 2010:225), reduced systemic side effects (Colin Long, 2002:41), convenience of application and improved patient compliance (Cleary, 1993:19; Prausnitz & Langer, 2008:1261). An approach that is often applied in optimising the solubility and dissolution rate of poorly water soluble, weak electrolytes is to prepare a salt of the active pharmaceutical ingredient (API) (Minghetti et al., 2007:815; O’Connor & Corrigan, 2001:281-282). Diclofenac is frequently administered as a salt, due to the high partition coefficient and very low water solubility of this molecule (Fini et al., 1999:164). Formulating for efficacy (FFETM) is a software programme designed by JW Solutions to facilitate the formulation of cosmetic ingredients or solvents into a product that would optimally deliver active ingredients into the skin. The notion is built upon solubility, i.e. solubility of the active ingredient in the formulation and solubility of the formulation in the skin. This programme could also be employed to optimise amounts of predetermined ingredients, to propose formulations that would ensure optimal drug delivery, to calculate the skin delivery gap (SDG) and to demonstrate transdermal permeation of active ingredients and excipients (JW Solutions Software, 2013a). When the SDG is known, it mathematically indicates the optimal active ingredient and topical delivery vehicle to use (JW Solutions, 2013b). In this study, diclofenac sodium (DNa), diclofenac diethylamine (DDEA) and diclofenac N-(2- hydroxyethyl) pyrrolidine (DHEP) were each formulated in the following emulgels: * An emulgel optimised towards the stratum corneum (SC) (enhancing drug delivery into this layer and deeper tissues) (oily phase ~30%), * A more hydrophilic emulgel (oily phase ~15%), and * A more lipophilic emulgel (oily phase ~45%). Components of the oily phase and its respective amounts, as well as the SDG of formulations were determined by utilising the FFETM software of JW Solutions (2013a). The aqueous solubilities of DNa, DDEA and DHEP were determined and their respective values were 11.4 mg/ml, 8.0 mg/ml and 11.9 mg/ml, all indicative of effortless percutaneous delivery (Naik et al., 2000:319). Log D (octanol-buffer distribution coefficient) (pH 7.4) determinations for DNa, DDEA and DHEP were performed and their values established at 1.270 (DNa), 1.291 (DDEA) and 1.285 (DHEP). According to these values, diclofenac, when topically applied as a salt in a suitable vehicle, should permeate transdermally without the aid of radical intervention (Naik et al., 2000:319; Walters, 2007:1312). Membrane release studies were also carried out in order to determine the rate of API release from these new formulations. Results confirmed that diclofenac was indeed released from all nine of the formulated emulgels. The more hydrophilic DNa formulation released the highest average percentage of diclofenac (8.38%) after 6 hours. Subsequent transdermal diffusion studies were performed to determine the diclofenac concentration that permeated the skin. The more hydrophilic DNa emulgel showed the highest average percentage skin diffusion (0.09%) after 12 hours, as well as the highest average flux (1.42 ± 0.20 μg/cm2.h). The concentrations of diclofenac in the SC-epidermis (SCE) and epidermis-dermis (ED) were determined through tape stripping experiments. The more lipophilic DNa emulgel demonstrated the highest average concentration (0.27 μg/ml) in the ED, while the DNa emulgel that had been optimised towards the SC, had the highest concentration in the SCE (0.77 μg/ml). / MSc (Pharmaceutics), North-West University, Potchefstroom Campus, 2014

Nonsteroidal anti-inflammatory drugs (NSAIDs) are widely used in the treatment of inflammation and pain (Escribano et al., 2003:203). Diclofenac, a classical NSAID, is considerably more effective as an analgesic, antipyretic and anti-inflammatory drug than other traditional NSAIDs, like indomethacin and naproxen (Grosser et al., 2011:986). However, the use of diclofenac is known for its many side effects, such as gastric disorders, while fluid and sodium retention are also commonly observed (Rossiter, 2012:391). Since topical diclofenac offers a more favourable safety profile, it is a valuable substitute for oral NSAID therapy in the treatment of osteoarthritis (Roth & Fuller, 2011:166). The benefits of topically applied NSAIDs, compared to oral administration and systemic delivery, include the easy cessation of treatment, should effects become troublesome (Brown et al., 2006:177), the avoidance of extensive, first-pass metabolism (Cleary, 1993:19; Kornick, 2003:953; Prausnitz & Langer, 2008:1261; Lionberger & Brennan, 2010:225), reduced systemic side effects (Colin Long, 2002:41), convenience of application and improved patient compliance (Cleary, 1993:19; Prausnitz & Langer, 2008:1261). An approach that is often applied in optimising the solubility and dissolution rate of poorly water soluble, weak electrolytes is to prepare a salt of the active pharmaceutical ingredient (API) (Minghetti et al., 2007:815; O’Connor & Corrigan, 2001:281-282). Diclofenac is frequently administered as a salt, due to the high partition coefficient and very low water solubility of this molecule (Fini et al., 1999:164). Formulating for efficacy (FFETM) is a software programme designed by JW Solutions to facilitate the formulation of cosmetic ingredients or solvents into a product that would optimally deliver active ingredients into the skin. The notion is built upon solubility, i.e. solubility of the active ingredient in the formulation and solubility of the formulation in the skin. This programme could also be employed to optimise amounts of predetermined ingredients, to propose formulations that would ensure optimal drug delivery, to calculate the skin delivery gap (SDG) and to demonstrate transdermal permeation of active ingredients and excipients (JW Solutions Software, 2013a). When the SDG is known, it mathematically indicates the optimal active ingredient and topical delivery vehicle to use (JW Solutions, 2013b). In this study, diclofenac sodium (DNa), diclofenac diethylamine (DDEA) and diclofenac N-(2- hydroxyethyl) pyrrolidine (DHEP) were each formulated in the following emulgels: * An emulgel optimised towards the stratum corneum (SC) (enhancing drug delivery into this layer and deeper tissues) (oily phase ~30%), * A more hydrophilic emulgel (oily phase ~15%), and * A more lipophilic emulgel (oily phase ~45%). Components of the oily phase and its respective amounts, as well as the SDG of formulations were determined by utilising the FFETM software of JW Solutions (2013a). The aqueous solubilities of DNa, DDEA and DHEP were determined and their respective values were 11.4 mg/ml, 8.0 mg/ml and 11.9 mg/ml, all indicative of effortless percutaneous delivery (Naik et al., 2000:319). Log D (octanol-buffer distribution coefficient) (pH 7.4) determinations for DNa, DDEA and DHEP were performed and their values established at 1.270 (DNa), 1.291 (DDEA) and 1.285 (DHEP). According to these values, diclofenac, when topically applied as a salt in a suitable vehicle, should permeate transdermally without the aid of radical intervention (Naik et al., 2000:319; Walters, 2007:1312). Membrane release studies were also carried out in order to determine the rate of API release from these new formulations. Results confirmed that diclofenac was indeed released from all nine of the formulated emulgels. The more hydrophilic DNa formulation released the highest average percentage of diclofenac (8.38%) after 6 hours. Subsequent transdermal diffusion studies were performed to determine the diclofenac concentration that permeated the skin. The more hydrophilic DNa emulgel showed the highest average percentage skin diffusion (0.09%) after 12 hours, as well as the highest average flux (1.42 ± 0.20 μg/cm2.h). The concentrations of diclofenac in the SC-epidermis (SCE) and epidermis-dermis (ED) were determined through tape stripping experiments. The more lipophilic DNa emulgel demonstrated the highest average concentration (0.27 μg/ml) in the ED, while the DNa emulgel that had been optimised towards the SC, had the highest concentration in the SCE (0.77 μg/ml). / MSc (Pharmaceutics), North-West University, Potchefstroom Campus, 2014

Aims Novel low toxicity formulations using biomaterial (i.e. gelatin) for triggered release and controlled manner of formulated therapeutic agent for treatment of immuno-inflammatory disease on the skin were studied in the PhD project. It is a challenging concept because of difficulties in targeting and controlling for the releases that is tailored to disease severity or lesional inflammation extent. Background Psoriasis is a complicated disease with multi-factorial pathogenesis. Potent anti-psoriatic drugs are available but for managing the symptoms of the disease. Due to the toxicity of the therapeutic agents, different strategies have been suggested to avoid severe side effects from long term or high dose usage. Psoriasis is an optimal representative for this investigation in terms of the toxicities of recognized drugs, unpredictable or relapsed nature of the disease or even life threatening developments if generalised symptoms develop as they can in some types. Method Using the rheometry in temperature sweep mode, a series of concentrations of pure gelatin and gelatin mixture were developed. In addition, using tryptic enzyme, their action was studied rheologically. A Petri dish observational method was used to investigate the permeability of formulations chosen on the basis of the rheometric performance. Then, combining the Copley diffusion cell kit and UV/VIS spectrophotometer, the release of the model drug was investigated in porous artificial membranes and porcine skin for one or more of the formulations. The preliminary part using porous artificial membranes was to investigate the amount of the release of tartrazine from a candidate gel into the circulation system. In this part, alternatives were considered for dealing with gelatin or gelatin/carbomer swelling by using mechanical stress approach or changing to octanol solvent. For the latter a dye, rhodamine, which would partition into octanol had to be substituted for tartrazine (which has iv negligible organic solubility). In the final part, using skin membrane, the amount of the release tartrazine to the skin was measured because in this, skin staining, rather than partition was needed. Results Promising results were observed in each stage. The rheological investigation on the developed gelatin/water system and gelatin/carbomer intimate system in absence and presence of tryptic enzyme showed that a responsive but convenient formulation was possible and was independent of the presence of tartrazine. Analysis of these resulting rheological profiles suggested a prediction for the best gelatin/carbomer formulations to select for the permeability tests. The latter used Petri dishes to compare differential diffusion of these candidates showed the carbomer was able to stop three-dimensional spreading of the dye through the pure gelatin or its residue (after enzyme action). The drug release studies using artificial porous membranes for preliminary work showed significant differential release between enzyme free and enzyme treated versions of the 20% gelatin/0.9% carbomer formulation. The final success was the in vitro skin experiment in which the result was obtained for the pure gelatin and shown to deliver very substantially more to areas with applied enzyme s a simulated lesion.

Les travaux réalisés concernent l'opération de foisonnement en continu. Les résultats ont montré que la modification de la conduite de l'opération lors de l'ajout d'ingrédients dans une formulation doit tenir compte de trois effets à conditions opératoires fixées : l'augmentation de la viscosité de la matrice qui favorise la rupture des billes mais réduit la capacité à incorporer le gaz ; l'augmentation éventuelle de l'élasticité qui favorise la stabilisation des bulles en inhibant la coalescence, mais rend la rupture plus difficile ; les interactions protéines-polysaccarides qui peuvent favoriser ou défavoriser la stabilisation du gaz. Le rotor-stator n'est pas le disperseur le plus efficace ; son efficacité est proche de celle de la colonne de foisonnement qui permet en plus d'obtenir des bulles plus petites. La méthode d'analyse dimensionnelle permettant le calcul des contraintes à appliquer afin de maintenir d32 constant lors de l'extrapolation d'un foisonneur a pu être validée.

L'objectif principal était de développer un outil de formulation dédié à l'inertage des déchets par des liants minéraux (laitiers, fondus, portland..) pour un stockage en décharge classée ou pour valorisation sous la forme d'Eco-matériaux. Deux voies de recherches se sont déroulées en parallèle, d'une part la caractérisation multi-échelles du 'composite liant/déchet' pour qualifier l'efficacité de l'inertage,d'autre part, la mesure des propriétés rhéologiques et mécaniques du 'composite liant/déchet' pour mieux cibler son domaine d'emploi. Il est apparu rapidement que pour fonder l'outil de formulation, une description fine du réseau poreux obtenu (diamètre et connectivité des capillaires, distribution de taille et morphologie des pores) associée à une étude des microstructures formées seraient impératives. Pour ce faire des expériences multi-échelles à caractère novateur ont été mises en place (ICP-OES couplée avec de la conductimètrie, cartographie MEB) et appliquées à 8 couples liant/ polluant. Elles ont confirmé une intégration des polluants sous diverses formes microstructurales dans de nouveaux composés Pour mieux prédire les cinétiques de rejet, dans le cadre d'une mise en décharge, les lois classiques de diffusion ont été revisitées sur une période d'étude de [3min-24mois] et les coefficients de diffusion de Fick ont été calculés globalement ou par partie.

The principal aim of the project has been to investigate formulation-solution processes and the extent to which these processes lead to better guidance and understanding of teaching, learning, and assessment in mathematical modelling. The following main activities have been carried out in support of this aim: the development of case studies of the mathematical modelling approaches that may be used in the solution of practical problems; the design of teaching and learning experiments carried out mainly with undergraduates with some knowledge of physics and teachers on an MSc course in mathematical education; the theoretical development of formulation-solution processes by means of a concept matrix and a relationship level graph; the analysis of a selection of students' modelling attempts; an investigation of assessment methods and the implications of the theoretical development of formulation solution processes for these methods. The case studies were based on possible modelling approaches to practical problems which are connected in some way with every-day reality. These studies were used in seventeen experiments with students working in a genuine educational environment under the usual time constraints. Most of the students involved had little or no modelling experience. Results have shown that students have a common set of difficulties, and a set of learning heuristics has been devised in an attempt to overcome these. The theoretical development of formulation-solution processes has identified the following main characteristics in early model development: distribution of features from global (difficult to quantify) to specific (easily quantified) concepts; basic relationships are often generated as solution proceeds; relationships can occur in either general or specific forms; general progress is gauged by relationship 'level'; most variables and constants are generated with relationships; partitioning a problem into sub-problems may be possible initially, but such break-down into distinct parts is often only possible after having seen a pattern of linkages in a relationship level graph. Finally, the implications for assessment methods are examined, and suggestions for further research investigations are made.