Mathematical modelling of solid tumour growth: a Dynamical Density Functional Theory-based model

We present a theoretical framework based on an extension of Dynamical Density Functional Theory (DDFT) to describe the structure and dynamics of cells in living tissues and tumours. DDFT is a microscopic statistical mechanical theory for the time evolution of the density distribution of interacting many-particle systems. The theory accounts for cell pair-interactions, different cell types, phenotypes and cell birth and death processes (including cell division), in order to provide a biophysically consistent description of processes bridging across the scales, including the description of the tissue structure down to the level of the individual cells. Analysis of the model is presented for a single species and a two-species cases, the latter describing competition between a cancerous and healthy cells. In suitable parameter regimes, model results are consistent with biological observations. Of particular note, divergent tumour growth behaviour, mirroring metastatic and benign growth characteristics, are shown to be dependent on the cell pair-interaction parameters

Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

 تقدم هذه الورقة البحثية طريقة  لايجاد الحل التقريبي لمؤثر فولتيرا التكاملي  الثلاثي الأبعاد غير الخطي في  R3. حيث يتم استخدام مفهوم (Majorant function) وباستخدام طريقة نيوتن المعدلة  لتحويل مؤثر فولتيرا التكاملي  الثلاثي الأبعاد غير الخطي  إلى متتالية  لمؤثر فولتيرا التكاملي  الثلاثي الأبعاد الخطي ومن يتم استخدام طريقة (Gaussian-Legendre)  التربيعية لايجاد الحل التقريبي لمؤثر فولتيرا التكاملي  الثلاثي الأبعاد الخطي من خلال التعامل مع نظام جبري خطي.تم مناقشة وجود ووحدانية الحل للطريقة المستخدمة مع اعطاء أمثلة توضيحية لإظهار دقة وكفاءة الطريقة.In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model. Mathematical Subject Classification (2010):  45P05, 45G10, 47H9

Dynamic properties of crushed glass and tyre rubber in unbound pavement applications

Flexible pavements consist of treated unbound materials between the surface, typically bituminous, and the natural subgrade layer. A laboratory study was conducted to assess the dynamic behavior under the influence of repeated loads of the two most common global waste materials for their performance as road materials. The study investigated the behavior and properties of crushed rock (R) blended with waste glass (G) and tyre rubber (T) and evaluated them as alternatives to natural unbound materials. Preliminary tests included Modified Proctor compaction and Particle Size Distribution tests (before and after the compaction stage), and a more specialised test to determine the resilient modulus (Mr) and the permanent deformation values; the Repeated Triaxial Load Test (RLTT). The mixtures were prepared at different percentages of the whole specimen's total dry weight: from 12 to 45 % waste glass, and from 5 to 15 % tyre rubber. To simulate typical in situ materials, the mixtures were also prepared at the lower target moisture contents of 70% and 80% of OMC. The moisture content and the dry density after the RLTT were measured. Results showed a positive correlation between permanent deformation and glass content, while glass content can improve Mr value of rock specimens by up to 50%. Under RLTT, the addition of tyre rubber to crushed rock decreased permanent deformation

Estimation of the Degree of Diversity for Some Iraqi Wheat Varieties through ISSR, SRAP and RAPD Markers

DNA-based molecular markers such as Inter Simple Sequence Repeat (ISSR), Sequence-Related Amplified polymorphism (SRAP) and Random Amplified Polymorphic DNA (RAPD) were used in this study to examine the genetic differences among sixteen Iraqi wheat varieties. Seventy three primers out of 177 were reproducible and showed clear amplified bands. The degree of genetic diversity, Polymorphism information content (PIC) and resolving power (RP) were estimated. All the studied molecular markers were informative and showed good ability to classify and distinguish 16 wheat varieties. Total number of polymorphic bands is 134, 221 and 55 for ISSR, SRAP and RAPD respectively. PIC and RP values were 0.259, 0.264 and 0.262 and 9.06, 7.87 and 2.7

Study on effect of extraction techniques and seed coat on proteomic distribution and cheese production from soybean milk

Soybean-based food products are a major source of protein. In the present study, proteins in soybean milk from seeds of the cultivar Bunya (Glycine max) were extracted using the cheesecloth and the centrifuge methods. The milk was produced through mechanical crushing of both whole and split seeds in water. Following separation by either the cheesecloth or centrifuge, proteins were isolated from the soybean milk by using thiourea/urea solubilisation and then separated them using two-dimensional polyacrylamide gel electrophoresis. The isolated proteins were identified by mass spectrometry. A total of 97 spots were identified including 49 that displayed different abundances. Of the two separation techniques, centrifuge separation gave higher protein extraction and more intense protein spots than cheesecloth separation. Eleven of the β-subunits of β-conglycinin, three of the α-subunits of β-conglycinin, and four of the mutant glycinin showed different levels of abundances between separation techniques, which might be related to subsequent cheese quality. Notably, split-seed soybean milk has less allergenic proteins with four α-subunits of β-conglycinin compared to whole-seed milk with eight of those proteins. The sensory evaluation showed that the cheese produced from split-soybean milk received higher consumer preferences compared to that of whole seed, which could be explained by their proteomic differences. The demonstrated reference map for whole and split-seed soybean milk could be further utilized in the research related to soybean cheesemaking

Proteomic characterisation of lupin (Lupinus angustifolius) milk as influenced by extraction techniques, seed coat and cultivars

Lupin seeds are rich in proteins and other essential ingredients that can help to improve human health. The protein contents in both whole and split seeds of two lupin cultivars (Mandleup and PBA Jurien) were used to produce the lupin milk using the cheesecloth and centrifuge method. Proteins were extracted from the lupin milk using thiourea/urea solubilization. The proteins were separated by a two-dimensional polyacrylamide gel electrophoresis and then identified with mass spectrometry. A total of 230 protein spots were identified, 60 of which showed differential abundances. The cheesecloth separation showed protein extractability much better than that of the centrifuge method for both the cultivars. The results from this study could offer guidance for future comparative analysis and identification of lupin milk protein and provide effective separation technique to determine specific proteins in the cheese-making process

Dynamical density functional theory based modelling of tissue dynamics: application to tumour growth

We present a theoretical framework based on an extension of dynamical density functional theory (DDFT) for describing the structure and dynamics of cells in living tissues and tumours. DDFT is a microscopic statistical mechanical theory for the time evolution of the density distribution of interacting many-particle systems. The theory accounts for cell pair-interactions, different cell types, phenotypes and cell birth and death processes (including cell division), in order to provide a biophysically consistent description of processes bridging across the scales, including describing the tissue structure down to the level of the individual cells. Analysis of the model is presented for a single species and a two-species cases, the latter aimed at describing competition between tumour and healthy cells. In suitable parameter regimes, model results are consistent with biological observations. Of particular note, divergent tumour growth behaviour, mirroring metastatic and benign growth characteristics, are shown to be dependent on the cell pair-interaction parameters

Research of pressure drop and efficiency of new design of valve tray

The article represents a new type of valve tray which is used in tray columns. This type is the result of optimization of the common valve tray. This article includes a design of a new type of the valve tray and experimental results of its efficiency and pressure drop which are illustrated in the diagrams

Research of pressure drop and efficiency of new design of valve tray

The article represents a new type of valve tray which is used in tray columns. This type is the result of optimization of the common valve tray. This article includes a design of a new type of the valve tray and experimental results of its efficiency and pressure drop which are illustrated in the diagrams

An investigation into the roles of chlorides and sulphate salts on the performance of low salinity injection in sandstone reservoirs : experimental approach

Numerous studies have been carried out to ascertain the mechanisms of low salinity and smart water flooding technique for improved oil recovery. Focus were often on brine composition and, specifically the cationic content in sandstone reservoirs. Given the importance of the salt composition and concentration, tweaking the active ions which are responsible for the fluids-rock equilibrium will bring into effect numerous mechanisms of displacement which have been extensively debated. This experimental study, however, was carried out to evaluate the extent of the roles of chloride and sulphate-based brines in improved oil recovery. To carry this out, 70,000 ppm sulphates and chloride-based brines were prepared to simulate formation water and 5,000ppm brines of the same species as low salinity displacement fluids. Core flooding process was used to simulate the displacement of oil by using four (4) native sandstones core samples, obtained from Burgan oil field in Kuwait, at operating conditions of 1500 psig and 50oC. The core samples were injected with 70,000 ppm chloride and sulphates and subsequently flooded with the 5,000 ppm counterparts in a forced imbibition process. Separate evaluations of chloride and sulphate-based brines were carried out to investigate the displacement efficiencies of each brine species. The results showed that the in both high and low salinity displacement tests, the SO4 brine presented better recovery of up to 89% of the initial oil saturation (Soi). Several mechanisms of displacement were observed to be responsible for improved recovery during SO4 brine displacement. IFT measurement experiments also confirmed that there was reduction in IFT at test conditions between SO4 brine and oil and visual inspection of the effluent showed a degree emulsification of oil and brines. Changes in pH were observed in the low salinity flooding and negligible changes were noticed in the high salinity floods. These results provide an insight into the roles of chloride and sulphate ions in the design of smart “designer” water and low salinity injection scenarios