Effects of arterial oxygen tension and cardiac output on venous saturation: a mathematical modeling approach

OBJECTIVES: Hemodynamic support is aimed at providing adequate O-2 delivery to the tissues; most interventions target O-2 delivery increase. Mixed venous O-2 saturation is a frequently used parameter to evaluate the adequacy of O-2 delivery. METHODS: We describe a mathematical model to compare the effects of increasing O-2 delivery on venous oxygen saturation through increases in the inspired O-2 fraction versus increases in cardiac output. The model was created based on the lungs, which were divided into shunted and non-shunted areas, and on seven peripheral compartments, each with normal values of perfusion, optimal oxygen consumption, and critical O-2 extraction rate. O-2 delivery was increased by changing the inspired fraction of oxygen from 0.21 to 1.0 in steps of 0.1 under conditions of low (2.0 L.min(-1)) or normal (6.5 L.min(-1)) cardiac output. The same O-2 delivery values were also obtained by maintaining a fixed O-2 inspired fraction value of 0.21 while changing cardiac output. RESULTS: Venous oxygen saturation was higher when produced through increases in inspired O-2 fraction versus increases in cardiac output, even at the same O-2 delivery and consumption values. Specifically, at high inspired O-2 fractions, the measured O-2 saturation values failed to detect conditions of low oxygen supply. CONCLUSIONS: The mode of O-2 delivery optimization, specifically increases in the fraction of inspired oxygen versus increases in cardiac output, can compromise the capability of the "venous O-2 saturation" parameter to measure the adequacy of oxygen supply. Consequently, venous saturation at high inspired O-2 fractions should be interpreted with caution.

Do muscle strengthening exercises improve performance in the 6-minute walk test in postmenopausal women?

Background: Walking speed seems to be related to aerobic capacity, lower limb strength, and functional mobility, however it is not clear whether there is a direct relationship between improvement in muscle strength and gait performance in early postmenopausal women. Objective: To evaluate the effect of muscle strengthening exercises on the performance of the 6-minute walk test in women within 5 years of menopause. Methods: The women were randomized into control group (n=31), which performed no exercise, and exercise group (n=27), which performed muscle strengthening exercises. The exercises were performed twice a week for 3 months. The exercise protocol consisted of warm-up, stretching, and strengthening of the quadriceps, hamstring, calf, tibialis anterior, gluteus maximus, and abdominal muscles, followed by relaxation. Muscular strength training started with 60% of 1MR (2 series of 10-15 repetitions), reaching 85% until the end of the 3-month period (4 series of 6 repetitions each). Results: The between-group comparisons pre- and post-intervention did not show any difference in distance walked, heart rate or blood pressure (p>0.05), but showed differences in muscle strength post-intervention, with the exercise group showing greater strength (p<0.05). In the within-group comparison, there were differences in final heart rate and quadriceps and hamstring strength pre- and post-intervention in the exercise group (p<0.05). Conclusion: The results suggest that muscle strengthening of the lower limbs did not improve performance in the 6-minute walk test in this population of postmenopausal women. Trial registration ACTRN12609001053213.

MATHEMATICAL ANALYSIS OF MAXIMUM POWER GENERATED BY PHOTOVOLTAIC SYSTEMS AND FITTING CURVES FOR STANDARD TEST CONDITIONS

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I- 100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

Progress in the mathematical theory of quantum disordered systems

We review recent progress in the mathematical theory of quantum disordered systems: the Anderson transition, including some joint work with Marchetti, the (quantum and classical) Edwards-Anderson (EA) spin-glass model and return to equilibrium for a class of spin-glass models, which includes the EA model initially in a very large transverse magnetic field. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770066]

Mathematical modeling and analysis of the particle interactions in the direct filtration using the colloidal theory

This work used the colloidal theory to describe forces and energy interactions of colloidal complexes in the water and those formed during filtration run in direct filtration. Many interactions of particle energy profiles between colloidal surfaces for three geometries are presented here in: spherical, plate and cylindrical; and four surface interactions arrangements: two cylinders, two spheres, two plates and a sphere and a plate. Two different situations were analyzed, before and after electrostatic destabilization by action of the alum sulfate as coagulant in water studies samples prepared with kaolin. In the case were used mathematical modeling by extended DLVO theory (from the names: Derjarguin-Landau-Verwey-Overbeek) or XDLVO, which include traditional approach of the electric double layer (EDL), surfaces attraction forces or London-van der Waals (LvdW), esteric forces and hydrophobic forces, additionally considering another forces in colloidal system, like molecular repulsion or Born Repulsion and Acid-Base (AB) chemical function forces from Lewis.

Correlation Between Trochlear Groove Depth and Patellar Position During Open and Closed Kinetic Chain Exercises in Subjects With Anterior Knee Pain

The purpose of this study was to correlate the trochlear shape and patellar tilt angle and lateral patellar displacement at rest and maximal voluntary isometric contraction (MVIC) exercises during open (OKC) and closed kinetic chain (CKC) in subjects with and without anterior knee pain. Subjects were all women, 20 who were clinically healthy and 19 diagnosed with anterior knee pain. All subjects were evaluated and subjected to magnetic resonance exams during OKC and CKC exercise with the knee placed at 15, 30, and 45 degrees of flexion. The parameters evaluated were sulcus angle, patellar tilt angle and patellar displacement using bisect offset. Pearson's r coefficient was used, with p < .05. Our results revealed in knee pain group during CKC and OKC at 15 degrees that the increase in the sulcus angle is associated with a tilt increase and patellar lateral displacement. Comparing sulcus angle, patellar tilt angle and bisect offset values between MVIC in OKC and CKC in the knee pain group, it was observed that patellar tilt angle increased in OKC only with the knee flexed at 30 degrees. Based on our results, we conclude that reduced trochlear depth is correlated with increased lateral patellar tilt and displacement during OKC and CKC at 15 degrees of flexion in people with anterior knee pain. By contrast, 30 degrees of knee flexion in CKC is more recommended in rehabilitation protocols because the patella was more stable than in other positions.

Postural control in elderly women with osteoporosis: comparison of balance, strengthening and stretching exercises. A randomized controlled trial

Objective: To compare the efficacy of balance training associated with muscle strengthening or stretching, relative to no intervention, in the postural control of elderly women with osteoporosis. Design: A randomized, controlled trial. Subjects and interventions: Sample consisted of 50 women aged 65 years or older, with osteoporosis, randomized into one of three groups: strengthening group (n = 17) performed balance training with muscle strengthening; stretching group (n = 17) performed balance training with stretching; and control group (n = 16), no activities. Interventions lasted eight weeks, twice a week, 60 minutes a day. Main measures: Postural control was evaluated by the modified Clinical Test of Sensory Interaction for Balance (CTSIBm) and Limits of Stability Test. Strength was assessed by dynamometry and the shortening of the hamstrings by goniometry. Results: Relative to controls, participants in the strengthening group displayed significantly increased dorsiflexion strength and knee flexion strength, as well as centre of pressure velocity, directional control, and oscillation velocity (CTSIBm test). The stretching group had significantly improvements in hamstring length, knee flexion strength, centre of pressure velocity, and amplitude of movements. Relative to the stretching group, the strengthening group yielded better knee extension strength and directional control. Conclusion: The results suggest that both interventions are effective in improving postural control when compared to the control group, and the strengthening group was superior to the stretching group in knee extension strength and in directional control.

Efficacy of low level laser therapy associated with exercises in knee osteoarthritis: a randomized double-blind study

Objectives: To estimate the effects of low level laser therapy in combination with a programme of exercises on pain, functionality, range of motion, muscular strength and quality of life in patients with osteoarthritis of the knee. Design: A randomized double-blind placebo-controlled trial with sequential allocation of patients to different treatment groups. Setting: Special Rehabilitation Services. Subjects: Forty participants with knee osteoarthritis, 2-4 osteoarthritis degree, aged between 50 and 75 years and both genders. Intervention: Participants were randomized into one of two groups: the laser group (low level laser therapy dose of 3 J and exercises) or placebo group (placebo laser and exercises). Main measures: Pain was assessed using a visual analogue scale (VAS), functionality using the Lequesne questionnaire, range of motion with a universal goniometer, muscular strength using a dynamometer, and activity using the Western Ontario and McMaster Universities Osteoarthritis (WOMAC) questionnaire at three time points: (T1) baseline, (T2) after the end of laser therapy (three weeks) and (T3) the end of the exercises (11 weeks). Results: When comparing groups, significant differences in the activity were also found (P = 0.03). No other significant differences (P > 0.05) were observed in other variables. In intragroup analysis, participants in the laser group had significant improvement, relative to baseline, on pain (P = 0.001), range of motion (P = 0.01), functionality (P = 0.001) and activity (P < 0.001). No significant improvement was seen in the placebo group. Conclusion: Our findings suggest that low level laser therapy when associated with exercises is effective in yielding pain relief, function and activity on patients with osteoarthritis of the knees.

Freeze-drying microscopy in mathematical modeling of a biomaterial freeze-drying

Transplantation brings hope for many patients. A multidisciplinary approach on this field aims at creating biologically functional tissues to be used as implants and prostheses. The freeze-drying process allows the fundamental properties of these materials to be preserved, making future manipulation and storage easier. Optimizing a freeze-drying cycle is of great importance since it aims at reducing process costs while increasing product quality of this time-and-energy-consuming process. Mathematical modeling comes as a tool to help a better understanding of the process variables behavior and consequently it helps optimization studies. Freeze-drying microscopy is a technique usually applied to determine critical temperatures of liquid formulations. It has been used in this work to determine the sublimation rates of a biological tissue freeze-drying. The sublimation rates were measured from the speed of the moving interface between the dried and the frozen layer under 21.33, 42.66 and 63.99 Pa. The studied variables were used in a theoretical model to simulate various temperature profiles of the freeze-drying process. Good agreement between the experimental and the simulated results was found.

Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

An in-depth analysis of the HIV-1/AIDS dynamics by comprehensive mathematical modeling

This work presents major results from a novel dynamic model intended to deterministically represent the complex relation between HIV-1 and the human immune system. The novel structure of the model extends previous work by representing different host anatomic compartments under a more in-depth cellular and molecular immunological phenomenology. Recently identified mechanisms related to HIV-1 infection as well as other well known relevant mechanisms typically ignored in mathematical models of HIV-1 pathogenesis and immunology, such as cell-cell transmission, are also addressed. (C) 2011 Elsevier Ltd. All rights reserved.

Efficacy of graded activity versus supervised exercises in patients with chronic non-specific low back pain: protocol of a randomised controlled trial

Abstract Background Low back pain is a relevant public health problem, being an important cause of work absenteeism worldwide, as well as affecting the quality of life of sufferers and their individual functional performances. Supervised active physical routines and of cognitive-behavioral therapies are recommended for the treatment of chronic Low back pain, although evidence to support the effectiveness of different techniques is missing. Accordingly, the aim of this study is to contrast the effectiveness of two types of exercises, graded activity or supervised, in decreasing symptoms of chronic low back pain. Methods/design Sample will consist of 66 patients, blindly allocated into one of two groups: 1) Graded activity which, based on an operant approach, will use time-contingent methods aiming to increase participants’ activity levels; 2) Supervised exercise, where participants will be trained for strengthening, stretching, and motor control targeting different muscle groups. Interventions will last one hour, and will happen twice a week for 6 weeks. Outcomes (pain, disability, quality of life, global perceived effect, return to work, physical activity, physical capacity, and kinesiophobia) will be assessed at baseline, at treatment end, and three and six months after treatment end. Data collection will be conducted by an investigator blinded to treatment allocation. Discussion This project describes the randomisation method that will be used to compare the effectiveness of two different treatments for chronic low back pain: graded activity and supervised exercises. Since optimal approach for patients with chronic back pain have yet not been defined based on evidence, good quality studies on the subject are necessary. Trial registration NCT01719276

Voyages as exercises of the gaze

This article focuses the relationship between journeys and photographs especially among anthropologists who travel. Having travelled to the Upper Negro River as an advisor of a PhD student, I discuss what digital photographs may mean in a context where verbal communication is impossible. Real or imaginary journeys are a source of images, reports, or travel logs in which it is difficult to discern what is real and what is fiction. After discussing a few famous scientific and literary journeys, the article focuses on some anthropological journeys and concludes that images produced by anthropologists are a result of trained intuition, a sensitive gaze, and memories of former travels. The article includes photographic essays that incorporate pictures I took in February 2012 among the Hupd'äh, in the Upper Negro River region.

A mathematical model for optimizing the indications of liver transplantation in patients with hepatocellular carcinoma

Abstract Background The criteria for organ sharing has developed a system that prioritizes liver transplantation (LT) for patients with hepatocellular carcinoma (HCC) who have the highest risk of wait-list mortality. In some countries this model allows patients only within the Milan Criteria (MC, defined by the presence of a single nodule up to 5 cm, up to three nodules none larger than 3 cm, with no evidence of extrahepatic spread or macrovascular invasion) to be evaluated for liver transplantation. This police implies that some patients with HCC slightly more advanced than those allowed by the current strict selection criteria will be excluded, even though LT for these patients might be associated with acceptable long-term outcomes. Methods We propose a mathematical approach to study the consequences of relaxing the MC for patients with HCC that do not comply with the current rules for inclusion in the transplantation candidate list. We consider overall 5-years survival rates compatible with the ones reported in the literature. We calculate the best strategy that would minimize the total mortality of the affected population, that is, the total number of people in both groups of HCC patients that die after 5 years of the implementation of the strategy, either by post-transplantation death or by death due to the basic HCC. We illustrate the above analysis with a simulation of a theoretical population of 1,500 HCC patients with tumor size exponentially. The parameter λ obtained from the literature was equal to 0.3. As the total number of patients in these real samples was 327 patients, this implied in an average size of 3.3 cm and a 95% confidence interval of [2.9; 3.7]. The total number of available livers to be grafted was assumed to be 500. Results With 1500 patients in the waiting list and 500 grafts available we simulated the total number of deaths in both transplanted and non-transplanted HCC patients after 5 years as a function of the tumor size of transplanted patients. The total number of deaths drops down monotonically with tumor size, reaching a minimum at size equals to 7 cm, increasing from thereafter. With tumor size equals to 10 cm the total mortality is equal to the 5 cm threshold of the Milan criteria. Conclusion We concluded that it is possible to include patients with tumor size up to 10 cm without increasing the total mortality of this population.