COMBINED EFFECT OF THERMAL LOAD AND MECHANICAL LOAD IN TRANSTIBIAL PROSTHESIS. AN EMPIRICAL STUDY.

UNLABELLED: Probably the most important factor in evaluating a patient's prosthesis is quality of life. Transtibial amputations, are among the most frequently performed major limb amputations. Many individuals with transtibial amputations successfully achieve rehabilitation at or near their preamputation levels. Discomfort in prosthetic sockets continues to be a critical challenge faced by both prosthetists and amputees. MATERIAL AND METHODS: This paper proposes a fusion Graphic User Interface that combines two types of information (pressure and temperature). Data from pressure sensors and thermistors (an electrical resistor whose resistance is greatly reduced by heating, used for measurement and control) placed on the stump in transtibial prosthetics are collected in real time using a National Instruments Data Acquisition device. RESULTS: All the data stored in files are available for offline processing. The user has the possibility to analyse the signal by zooming or positioning the marker and window on different parts of signal. A complex analysis that involves the pressure and temperature for a location (where both sensors are placed) is available in time domain. CONCLUSIONS: Blunt-prosthesis interface is characterized by few parameters among the most important are pressure and friction. The action of these parameters during static and dynamic stage is very important because their actions can produce lesions of skin at the level of interface. Despite the advancements in surgical techniques and prostheses, much still needs to be done. We made certain that the sensors were in the same location by pressing on specific cells on the residual limb during various stages of the experimentation. The highest pressures recorded were during the stance phase of walking. The curve that shows the temperature evolution or pressure in one point could differ in different points from patient to patient.

GRAPHICAL USER INTERFACE WITH APPLICATIONS IN SUSCEPTIBLE-INFECTIOUS-SUSCEPTIBLE MODELS.

UNLABELLED: Practical significance of understanding the dynamics and evolution of infectious diseases increases continuously in contemporary world. The mathematical study of the dynamics of infectious diseases has a long history. AIM: By incorporating statistical methods and computer-based simulations in dynamic epidemiological models, it could be possible for modeling methods and theoretical analyses to be more realistic and reliable, allowing a more detailed understanding of the rules governing epidemic spreading. MATERIAL AND METHODS: To provide the basis for a disease transmission, the population of a region is often divided into various compartments, and the model governing their relation is called the compartmental model. To present all of the information available, a graphical user interface provides icons and visual indicators. The graphical interface shown in this paper is performed using the MATLAB software ver. 7.6.0. MATLAB software offers a wide range of techniques by which data can be displayed graphically. The process of data viewing involves a series of operations. To achieve it, I had to make three separate files, one for defining the mathematical model and two for the interface itself. RESULTS: Considering a fixed population, it is observed that the number of susceptible individuals diminishes along with an increase in the number of infectious individuals so that in about ten days the number of individuals infected and susceptible, respectively, has the same value. If the epidemic is not controlled, it will continue for an indefinite period of time. By changing the global parameters specific of the SIS model, a more rapid increase of infectious individuals is noted. CONCLUSIONS: Using the graphical user interface shown in this paper helps achieving a much easier interaction with the computer, simplifying the structure of complex instructions by using icons and menus, and, in particular, programs and files are much easier to organize. Some numerical simulations have been presented to illustrate theoretical analysis.

Analyse of socket-prosthesis-blunt complex for lower limb amputee using objective measure of patient's gait cycle.

UNLABELLED: The prosthetic application is a highly complex process. Modeling and simulation of biomechanics processes in orthopedics is a certainly field of interest in current medical research. Optimization of socket in order to improve the quality of patient's life is a major objective in prosthetic rehabilitation. A variety of numerical methods for prosthetic application have been developed and studied. MATERIAL AND METHODS: An objective method is proposed to evaluate the performance of a prosthetic patient according to surface pressure map over the residual limb. The friction coefficient due to various liners used in transtibial and transfemoral prosthesis is taken into account also. RESULTS: Creation of a bio-based modeling and mathematical simulation allows the design, construction and optimization of contact between the prosthesis cup and lack of functionality of the patient amputated considering the data collected and processed in real time and non-invasively. The von Mises stress distribution in muscle flap tissue at the bone ends shows a larger region subjected to elevated von Mises stresses in the muscle tissue underlying longer truncated bones. CONCLUSIONS: Finite element method was used to conduct a stress analysis and show the force distribution along the device. The results contribute to a better understanding the design of an optimized prosthesis that increase the patient's performance along with a god choice of liner, made by an appropriate material that fit better to a particular blunt. The study of prosthetic application is an exciting and important topic in research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical orthopedics.

Taguchi method for partial differential equations with application in tumor growth.

UNLABELLED: The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. MATERIAL AND METHODS: Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. RESULTS: First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. CONCLUSIONS: Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Differential equations with applications in cancer diseases.

UNLABELLED: Mathematical modeling is a process by which a real world problem is described by a mathematical formulation. The cancer modeling is a highly challenging problem at the frontier of applied mathematics. A variety of modeling strategies have been developed, each focusing on one or more aspects of cancer. MATERIAL AND METHODS: The vast majority of mathematical models in cancer diseases biology are formulated in terms of differential equations. We propose an original mathematical model with small parameter for the interactions between these two cancer cell sub-populations and the mathematical model of a vascular tumor. We work on the assumption that, the quiescent cells' nutrient consumption is long. One the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. RESULTS: MATLAB simulations obtained for transition rate from the quiescent cells' nutrient consumption is long, we show a similar asymptotic behavior for two solutions of the perturbed problem. In this system, the small parameter is an asymptotic variable, different from the independent variable. The graphical output for a mathematical model of a vascular tumor shows the differences in the evolution of the tumor populations of proliferating, quiescent and necrotic cells. The nutrient concentration decreases sharply through the viable rim and tends to a constant level in the core due to the nearly complete necrosis in this region. CONCLUSIONS: Many mathematical models can be quantitatively characterized by ordinary differential equations or partial differential equations. The use of MATLAB in this article illustrates the important role of informatics in research in mathematical modeling. The study of avascular tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Ordinary differential equations with applications in molecular biology.

UNLABELLED: Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. MATERIAL AND METHODS: The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. RESULTS: We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. CONCLUSIONS: Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances. Ordinary differential equations are used to model biological processes on various levels ranging from DNA molecules or biosynthesis phospholipids on the cellular level.

[Mathematical modelling of drug addiction]. / Modelarea matematica a fenomenului de drogodependenta.

AIM: To describe and assess the phenomenon of drug addiction by the use of a system of linear differential equations. MATERIAL AND METHODS: For analytical purposes, the study population (1020 individuals) was divided into three groups: likely to use drugs, drug users, and recovered (S-D model). RESULTS: The number of individuals likely to use drugs decreases with the increase in the number of infected ones; thus, in about 10 days, the number of infected individuals matches the number of those likely to use drugs. If the global parameters of the study model are changed, a more rapid increase in the number of infected individuals is noticed. Also noticed is the fact that the number of recoveries is likely to decrease with the increase in the number of infected individuals. CONCLUSIONS: Although numerical techniques are often preferable, the analytical ones have some advantages. Thus, an analytical approach may provide a deeper understanding of the mechanism of a given phenomenon, so it is more convenient to describe the state variables in terms of parameters than in terms of numerical approximation. To assess to role of hazard and uncertain associations in the future statistical methods will be used.

Assessment of the correlation between two defining criteria for bidirectional isthmic block in the ablation of typical atrial flutter.

BACKGROUND: A complete, bidirectional conduction block in the cavotricuspid isthmus (CTI) represents the end-point of the typical atrial flutter ablation. We investigated the correlation between two criteria for successful ablation, one based on the atrial bipolar electrogram morphology before and after complete CTI conduction block, compared to the standard criteria of differential pacing and reversal in the right atrial depolarization sequence during coronary sinus (CS) pacing. METHOD: We conducted a retrospective study in 111 patients (81 males, average age 62±10 years) who underwent an atrial flutter ablation during September 2007 - July 2009 in the Cardiology - Rehabilitation Hospital, UMF Cluj-Napoca. We assessed the presence of a bidirectional block at the end of the procedure using the standard criteria. We then analyzed the morphology of the bipolar atrial electrograms adjacent to the ablation line, before and after CTI conduction block. RESULTS: A change from a qRs morphology to a rSr' morphology when pacing from the coronary sinus and from a rsr' morphology to a QRS morphology when pacing from the low-lateral right atrium was associated with a CTI conduction block. Sensitivity (Se), specificity(Sp), positive predictive value (PPV), negative predictive value (NPV) were 96%, 89%, 99% and 67% respectively. CONCLUSION: Our study suggests that the analysis of the atrial bipolar electrogram next to the ablation line before and after CTI ablation may be used as a reliable criterion to validate CTI conduction block due to its high sensitivity, specificity and positive predictive value.

Differential equations with small parameter with applications in radioimmunotherapy.

The Akzo Nobel research laboratories formulated this problem in their study of the penetration of radio-labeled antibodies into a tissue that has been infected by a tumor. This study was carried out for diagnostic as well as therapeutic purposes. The treatment of malignant diseases, after its primary treatment by surgery, is either by external beam radiotherapy, which is effective but local, or by chemotherapy, which is effective but not selective. The radiotherapy labelled antibody has to be able to penetrate the whole of the tumour, whereas for imaging only uptake on the surface of the tumour is needed. Factors such as dose, rate delivered, tumor size, and radiosensitivity play a major role in determining therapeutic response, while target-to-nontarget ratios and, particularly, circulating radioactivity to the bone marrow determine the major dose-limiting toxicities. In this article, we introduced a system of differential equations with small parameter with applications in radioimmunotherapy. The problem consists of two partial differential equations. Both the equation of this system includes small parameter epsilon. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. We write solution of this system in a small parameter, and investigation of asymptotic solution for system. Using the program Matlab and numerical method Runge-Kutta, I did various simulations for different values of biological parameters presented in the model studied.

Ischemic preconditioning during successive exercise testing.

It was suggested recently that ischemic preconditioning can occur in clinical practice. We investigated this hypothesis in 26 patients with old myocardial infarction (MI) or stable angina pectoris, subjected to two successive exercise testings at 1 hour interval. The ST depression was significantly lesser during the second exercise testing (1.83 +/- 0.12 mm, vs 1.02 +/- 0.14 mm p < 0.01) at the same double product (DP) (24.877 +/- 1206 vs 24.711 +/- 1152 p > 0.05) and peak effort (76.92 +/- 6.63 w vs 75.96 +/- 6.27 w p > 0.05). The improvement was attributed to ischemic preconditioning.