Modelling and simulation of vascular architecture aims at locating potential vascular pathologies which cannot be observed by direct visualization of the angiography. Arteriovenous vascularization has two basic functions: the first one is the distributive function and the other one consists in the hemodynamic concepts. This paper approaches the study of fractal properties based on hemodynamic function. Arterial and venous vascular tree is designed to perform both functions, but it is very important to make the distinction between them, because they are carried out by different parts of the vascular pressure and venous structures. While the distributive function is linked to the geometric appearance of the vascular tree, the hemodynamic one is related to the dynamics of the blood flow. Previous studies of fractal character of the vascular tree have focused in particular on the distributive function. This paper approaches the study of fractal properties based on hemodynamic function. The simulation of blood flow and pressure in compliant vessels requires the definition of three differential equations. In order to build a structural tree at the level of large arteries terminals, the characters of small vessels must be modeled. The relevant parameters are the radius, bifurcation, asymmetry and area ratio, length and compliance. The mathematical model of uncontrolled circulation can be used in multiple cases: (a) to study the properties of flow self-regulation, irrespective of external control mechanisms; (b) to explain the need for external control mechanisms; (c) to serve as foundation for the construction of a simple model to control the flow. With the help of MatLab software, it was possible to build a graphical user interface to display and process ultrasound images and to simulate the mathematical calculation of the blood flow. This interface is based on two modules: one for acquisition and image processing and the second one for measurement and analysis registration. The modules highlight the modification of the parameters when the patient has cardio vascular diseases and teach the user to make the difference between a normal and a pathological disposition.

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Multiple Attribute Decision Making (MADM) is an intensive area of research subject and applications both with many methods applied both in for crisp numbers and in condition of uncertainty, that is, fuzzy framework. In this last case, fuzzy linguistic variables and fuzzy numbers (triangular, trapezoidal or generalized fuzzy) are the along with arithmetic operations are the most common approaches. Depending on distance similarity between fuzzy numbers, the results, no matter the proposed methods, can have slightly different results in intermediary matrices of fuzzy numbers used in calculation. Despite of MADM popularity and usage, in many papers the part that show intermediary results in matrix of fuzzy numbers cover pages and, in this form, it is difficult for the reader to follow all the values in the process of learning these methods. More, if the matrices have higher dimensions and a user (student, e.g.) wants to test some hypothesis, the reproduction of algorithms can be very difficult because of abundance of data. An educational tool is proposed especially for biomedical engineering students, in this stage of development made by two modules: Fuzzy TOPSIS method and fuzzy VIKOR method. Two types of fuzzy numbers are taken into account (triangular fuzzy numbers and trapezoidal fuzzy numbers) and three distance similarity between fuzzy numbers (vertex method, Hausdorff metric and normalized Hamming metric) are three options proposed to used. The user interface (GUI) offers the possibility to visualize all the matrices involved in methods, the steps of algorithms, and also the possibility to select a particular index from matrices.

Biomedical Engineering (BME) is different from other engineering or medical areas, in the sense that the results are obtained usually by experimental procedures and the simulation using mathematical approaches are familiar to them without a very deep knowledge of medical subjects specific to physicians. The tool proposes one and two compartment models for mathematical model of skin absorption selected from models in literature. The compartments models are described by system of differential equations that are solved by numerical methods. The user has the possibility to select the model and the parameters of the models (the Graphical User Interface - GUI) is automatically updated according the selected model along with a graphical image of compartments and the variables that are assigned to interaction among compartments. The parameter for simulation (the solving of system of differential equations) are adjusted optimally according to selected model but they can be also modified by the user in order to test the sensitivity of the models to different value of parameters. The dosage substrate and/or inhibitors can be calculated by user using this tool. The constant of permeability and diffusion, deduced by experimental data, can be included and saved for future use using a selection panel. The implementation is made as a Matlab application with a GUI designed as a friendly user interface. The graphic of evolution of variable are displayed in a window, and the user has the possibility to select the group of variables to be visualized. The tool is accompanied by a small user's manual with a set of practical tests in the form of laboratories in order to improve the e-learning process. A more concise form of the mathematical model can be used by students in Balneo-Physio-Kinetotherapy (BFKT) by simulated be the Sulphur absorption by skin in sludge therapy.

Salmonella is a zoonotic disease that is transmitted from animal products by contact with sick animals or the environments where these animals are living. The mathematical model of transmission disease improve the students' understanding of pathogen dynamics, the role of factors that influence the transmission and control of a specific pathogen and the trend of antimicrobial resistance for this pathogen. The tendency to increase of resistance of Salmonella to antibiotic and combination of antibiotics suggest that models are useful in simulation of different scenarios for dynamic of transmission of this disease. There are two main Salmonella types: Typhimurium serotype and Enteritidis serotype. Both types are included in the software toolbox in a tutorial and interactive manners. The three models of Salmonella compartmental are presented in friendly manner to user with possibility to automatically generation of system equations using built-in templates. Tools that calculate the R0 number and stability analysis are provided as modules in order to evaluate how the experimental data are fit to model or to evaluate the influence of constant coefficients over mathematical model. Because Salmonella typhi bacteria is responsible for a communicable disease, Typhoid fever, an optional module is append to main software in order to give to student the possibility to improve the knowledge with mathematical model of this disease as direct result of a particular bacteria from a larger group of bacteria. The educational software has a friendly GUI (Graphic User Interface) that help student to understand better the dynamic of a specific pathogen modeled by class of larger mathematical models, the compartmental models.