Analysis of particles size distribution on the agglomeration and shrinkage of alumina-zirconia compacts

The combination of Alumina and Zirconia has emerged as a promising ceramic structure for advance machine tool application. However, the particles of Alumina and Zirconia tend to agglomerate during mixture which affected shrinkage and dimension accuracy of the end product. This study focused on the analysis of the particle size of Alumina-Zirconia compacts and their relationship with the shrinkage and agglomerates. The particles size of single Alumina, Zirconia and ball-milled Alumina-Zirconia with 90-10 wt% ratio were examined by mastersizer. These powders then were compacted and sintered at 1400°C to examine their shrinkage. The results show that Alumina possesses larger particles size of 109.65 μm, which is 10 folds larger than Zirconia at 6.10 μm. When blended by ball mill, the Alumina�Zirconia particles were changed into 9.77 μm, showing that the ball mill to refine powder particles while reducing the risk of agglomeration. After sintering, the Alumina-Zirconia compacts were shrunk to maximum 9.56% when 75-25 wt% of Alumina-Zirconia. The combination of porosity, agglomerate and infiltration of zirconia between alumina grains were responsible for the shrinkage of Alumina-Zirconia compacts

The effects of time valuation in cancer optimal therapies: a study of chronic myeloid leukemia

Background The mathematical design of optimal therapies to fight cancer is an important research field in today’s Biomathematics and Biomedicine given its relevance to formulate patient-specific treatments. Until now, however, cancer optimal therapies have considered that malignancy exclusively depends on the drug concentration and the number of cancer cells, ignoring that the faster the cancer grows the worse the cancer is, and that early drug doses are more prejudicial. Here, we analyze how optimal therapies are affected when the time evolution of treated cancer is envisaged as an additional element determining malignancy, analyzing in detail the implications for imatinib-treated Chronic Myeloid Leukemia. Methods Taking as reference a mathematical model describing Chronic Myeloid Leukemia dynamics, we design an optimal therapy problem by modifying the usual malignancy objective function, unaware of any temporal dimension of cancer malignance. In particular, we introduce a time valuation factor capturing the increase of malignancy associated to the quick development of the disease and the persistent negative effects of initial drug doses. After assigning values to the parameters involved, we solve and simulate the model with and without the new time valuation factor, comparing the results for the drug doses and the evolution of the disease. Results Our computational simulations unequivocally show that the consideration of a time valuation factor capturing the higher malignancy associated with early growth of cancer and drug administration allows more efficient therapies to be designed. More specifically, when this time valuation factor is incorporated into the objective function, the optimal drug doses are lower, and do not involve medically relevant increases in the number of cancer cells or in the disease duration. Conclusions In the light of our simulations and as biomedical evidence strongly suggests, the existence of a time valuation factor affecting malignancy in treated cancer cannot be ignored when designing cancer optimal therapies. Indeed, the consideration of a time valuation factor modulating malignancy results in significant gains of efficiency in the optimal therapy with relevant implications from the biomedical perspective, specially when designing patient-specific treatments.This work was supported by projects MTM2014-56022-C2-2-P and MTM2017-85476-C2-1-P of the Spanish Office of Innovation and Competitiveness and European FEDER Funds, and by projects of the Castile and León Autonomous Government: VA041P17 (with European FEDER Funds), VA138G18 and VA148G18

Mathematical Models with Delays for Glucose-Insulin Regulation and Applications in Artificial Pancreas

Ph.DDOCTOR OF PHILOSOPH

Quantifying the insulin response in mouse C2C12 skeletal muscle: a minimal modelling approach

Thesis (PhD)--Stellenbosch University, 2021.ENGLISH ABSTRACT: The insulin signalling cascade is one of the most important regulatory and signalling pathways in humans. Dysregulation or dysfunction of the insulin signalling path- ways often underlies the molecular ætiology of diseases such as diabetes, obesity, and Alzheimer’s. In turn, these diseases are the harbingers of various co-morbidities such as cardio-vascular disease, chronic inflammation, and dementia. The healthcare, eco- nomic, personal, and mortality burden of these diseases cannot be overstated. Mathematical modelling of insulin signalling is indispensable in the effort to un- derstand the dynamics of the insulin signalling cascade and how malfunctions therein lead to disease. However, despite the availability and complexity of existing models, few have explicitly connected the signalling cascade, glucose transporter activity, and metabolism with one another. In order to study these interactions, a ‘three-module’ approach was adopted that defined the signalling cascade, glucose transporter activ- ity, and metabolism as core, ‘input-output’ modules. The present work is limited to the signalling cascade and glucose transporter activity modules whereas work by Dr. Cobus van Dyk is concerned with the metabolic module. With this in mind, this thesis sets forth three aims. Firstly, to establish standard- ised culturing conditions which can be used to determine the basal state of insulin signalling and glucose transporter activity. Secondly, to develop a core, mathemati- cal model based on Western blotting and radio-labelled glucose -assay data which is able to describe the concentration- and time-dependence of the signalling cascade and glucose transporter activity in response to insulin. Thirdly, to determine the clustering behaviour of GFP-tagged GLUT4 molecules in response to insulin. The first goal was to standardise culturing conditions. Herein, the ability of high (25mM), medium (15mM), and low (5mM) glucose culturing conditions were evalu- ated with regards to their ability to sensitise or desensitise the insulin signalling cascade as well as the degree to which they are able to induce the differentiation of C2C12 my- oblasts into myocytes. The glucose and lactate concentrations in the external media were used to determine the glucose-lactate flux of the C2C12 cells. This served as a proxy for the induction of insulin-dependent glucose transport and metabolism. A modified Ladd staining protocol was used to assess the degree to which C2C12 cells could differentiate under the culturing protocols. The second goal was to construct a core, mathematical model of insulin signalling and glucose transporter activity. The time-dependent phosphorylation and dephos- phorylation of the insulin receptor and the serine 473 and threonine 308 sites of Akt in response to varying insulin concentrations was investigated using Western blotting techniques. The glucose transporter (GLUT4) activity was assayed using radio-carbon glucose. The data were used to optimise parameters for a core, ODE-based model of the signalling and glucose transporter modules. The third goal, to investigate the clustering behaviour of GLUT4 in response to insulin, was investigated by using confocal microscopy to image GFP-tagged GLUT4 molecules before and after being stimulated with insulin. A hierarchical clustering algorithm as well as further geometric and statistical analyses were used to determine the number, size, density, and distribution of GLUT4 clusters pre and post insulin exposure. Of the remaining chapters, Chapter 1 discusses the background, context, scope, and aims of this study as well as further elaborating on the ‘three module’ approach. The literature review in Chapter 2 provides an overview of the relevant literature as delineated by the scope and aims of this study. The materials and methods are provided in Chapter 3, with specific alterations or methodologies being further discussed in the relevant experimental chapters. The final chapter, Chapter 7, provides the reader with general discussions, limitations, and final thoughts concerning this work.AFRIKAANSE OPSOMMING: Die insulien seinkaskade is een van die belangrikste regulerings- en sein padweë in mense. Disregulering of disfunksie van die insulien sinweë is dikwels onderliggend aan die molekulêre etiologie van siektes soos diabetes, vetsug en Alzheimers. Verder is hierdie siektes die draers van verskillende ko-morbiditeite soos hartvatsiektes, chroniese ontsteking, demensie en ander. Die gesondheids, ekonomiese, persoonlike en sterftes- las van hierdie siektes kan nie oorskat word nie. Wiskundige modellering van insulien seinweë is onontbeerlik in die poging om die dinamika van die insulien seinkaskade te verstaan en hoe wanfunksies daarin tot siektes lei. Ondanks die beskikbaarheid en ingewikkeldheid van die bestaande mod- elle, het min die seinkaskade, glukose-vervoerderaktiwiteit en metabolisme egter ek- splisiet met mekaar verbind. Ten einde hierdie interaksies te bestudeer, is ‘n ‘drie- module’-benadering aangewend wat die seinkaskade, glukose-vervoerderaktiwiteit en metabolisme as kernmodules as ‘n ’inset-uitset’ model gedefinieer het. Die huidige werk is beperk tot die seinkaskade en glukose-vervoerdersaktiwiteitsmodules, terwyl werk deur dr. Cobus van Dyk gemoeid is met die metaboliese module. Met die oog hierop stel hierdie proefskrif drie doelstellings. Eerstens, om ges- tandaardiseerde kweektoestande vas te stel wat gebruik kan word om die basale toe- stand van insulien seine en glukose-vervoerderaktiwiteit te bepaal. Tweedens, om ‘nkern, wiskundige model te ontwikkel gebaseer op Westerse klad-tegnieke en radio- toetsdata, wat die konsentrasie en tydafhanklikheid van die seinkaskade en glukosever- voerder kan beskryf as ‘n gevolg van insulien blootstelling. Derdens, om die groeper- ingsgedrag van GFP-gemerkte GLUT4-molekules in reaksie op insulien te bepaal. Die eerste doelwit, met betrekking tot gestandaardiseerde kweektoestande, word aangebied in hoofstuk 4. Hierin is die vermoë van hoë (25mM), medium (15mM) en lae (5mM) kweektoestande geëvalueer met betrekking tot hul kapasiteit om die insulien seinkaskade te sensitiseer of te desensitiseer, asook die mate waarin hulle die differensiasie van C2C12-myoblaste in miosiete kan veroorsaak. Die skynbare glukose-laktaatvloei in die eksterne media dien as ‘n gevolmagtigde maatstaf vir die induksie van insulienafhanklike glukosevervoer en metabolisme. ‘n Gemodifiseerde LADD-kleuringprotokol is gebruik om die mate waarin C2C12-selle kan onderskei te bepaal. Die tweede doelwit, om ‘n kern, wiskundige model van insulien seinweë en die glukosevervoerder aktiwiteit te konstrueer, word in hoofstuk 5 nagestreef. Die fos- forilering en ontfosforylering van die insulienreseptor en die serien 473 en treonien 308-posisies van die intermediêre seinmolekule (Akt) in reaksie op wisselende in- sulienkonsentrasies, sowel as tyd, is met behulp van Westerse klad-tegnieke onder- soek. Die glukose-vervoerder (GLUT4) -aktiwiteit is met behulp van radio-koolstof glukose ondersoek. Die data is gebruik om parameters te optimaliseer vir ‘n kern- GDV-gebaseerde model van die sein en glukose-vervoermodules. Die derde doelwit, wat die groeperingsgedrag van GLUT4 in reaksie op insulien ondersoek het, word in hoofstuk 6 aangebied. Konfokale mikroskopie is gebruik om GFP-gemerkte GLUT4-molekules wat sonder en met insulien gestimuleer is te analiseer. ‘n Hiërargiese groeperingsalgoritme sowel as verdere meetkundige en statistiese ontledings is gebruik om die aantal, grootte, digtheid en verspreiding van GLUT4- groepe voor en na insulienblootstelling te bepaal. Van die hoofstukke wat nog nie hier bespreek is nie, bied hoofstuk 1 die agter- grond, konteks, omvang en doelstellings van hierdie studie, asook die uitwerking van die ‘drie module’-benadering. Terwyl die literatuuroorsig in hoofstuk 2 bied ‘n onder- soek van die relevante literatuur soos uiteengesit in die omvang en doelstellings van hierdie studie. Die materiaale en metodes word in hoofstuk 3 verskaf, met spesifieke wysigings of metodologieë wat in die betrokke eksperimentele hoofstukke verder be- spreek word. Die finale hoofstuk, hoofstuk 7, sal die leser voorsien met algemene besprekings, beperkings en afsluitende gedagtes rakende hierdie werk.Doctora

Modelling, optimisation and model predictive control of insulin delivery systems in Type 1 Diabetes Mellitus

Type 1 Diabetes Mellitus is a metabolic disease requiring lifelong treatment with exogenous insulin which significantly affects patient’s lifestyle. Therefore, it is of paramount importance to develop novel drug delivery techniques that achieve therapeutic efficacy and ensure patient safety with a minimum impact on their quality of life. Motivated by the challenge to improve the living standard of a diabetic patient, the idea of an artificial pancreas that mimics the endocrine function of a healthy pancreas has been developed in the scientific society. Towards this direction, model predictive control has been established as a very promising control strategy for blood glucose regulation in a system that is dominated by high intra- and inter-patient variability, long time delays, and presence of unknown disturbances such as diet, physical activity and stress levels. This thesis presents a framework for blood glucose regulation with optimal insulin infusion which consists of the following steps: 1. Development of a novel physiologically based compartmental model analysed up to organ level that describes glucose-insulin interactions in type 1 diabetes, 2. Derivation of an approximate model suitable for control applications, 3. Design of an appropriate control strategy and 4. In-silico validation of the closed loop control performance. The developed model’s accuracy and prediction ability is evaluated with data obtained from the literature and the UVa/Padova Simulator model, the model parameters are individually estimated and their effect on the model’s measured output, the blood glucose concentration, is identified. The model is then linearised and reduced to derive low-order linear approximations of the underlying system suitable for control applications. The proposed control design aims towards an individualised optimal insulin delivery that consists of a patient-specific model predictive controller, a state estimator, a personalised scheduling level and an open loop optimisation problem subjected to patient specific process model and constraints. This control design is modifiable to address the case of limited patient data availability resulting in an “approximation” control strategy. Both designs are validated in-silico in the presence of predefined, measured and unknown meal disturbances using both the proposed model and the UVa/Padova Simulator model as a virtual patient. The robustness of the control performance is evaluated in several conditions such as skipped meals, variability in the meal content, time and metabolic uncertainty. The simulation results of the closed loop validation studies indicate that the proposed control strategies can achieve promising glycaemic control as demonstrated by the study data. However, further prospective validation of the closed loop control strategy with real patient data is required.Open Acces