Mostafa Bachar

Metabolic effects of dialyzate glucose in chronic hemodialysis: results from a prospective, randomized crossover trial

BACKGROUND There is no agreement concerning dialyzate glucose concentration in hemodialysis (HD) and 100 and 200 mg/dL (G100 and G200) are frequently used. G200 may result in diffusive glucose flux into the patient, with consequent hyperglycemia and hyperinsulinism, and electrolyte alterations, in particular potassium (K) and phosphorus (P). This trial compared metabolic effects of G100 versus G200. METHODS Chronic HD patients participated in this randomized, single masked, controlled crossover trial (www.clinicaltrials.gov: #NCT00618033) consisting of two consecutive 3-week segments with G100 and G200, respectively. Intradialytic serum glucose (SG) and insulin concentrations (SI) were measured at 0, 30, 60, 120, 180, 240 min and immediately post-HD; P and K were measured at 0, 120, 180 min and post-HD. Hypoglycemia was defined as an SG<70 mg/dL. Mean SG and SI were computed as area under the curve divided by treatment time. RESULTS Fourteen diabetic and 15 non-diabetic subjects were studied. SG was significantly higher with G200 as compared to G100, both in diabetic {G200: 192.8±48.1 mg/dL; G100: 154.0±27.3 mg/dL; difference 38.8 [95% confidence interval (CI): 21.2-56.4] mg/dL; P<0.001} and non-diabetic subjects [G200: 127.0±11.2 mg/dL; G100 106.5±10.8 mg/dL; difference 20.6 (95% CI: 15.3-25.9) mg/dL; P<0.001]. SI was significantly higher with G200 in non-diabetic subjects. Frequency of hypoglycemia, P and K serum levels, interdialytic weight gain and adverse intradialytic events did not differ significantly between G100 and G200. CONCLUSION G200 may exert unfavorable metabolic effects in chronic HD patients, in particular hyperglycemia and hyperinsulinism, the latter in non-diabetic subjects.

Modeling the Cardiovascular-Respiratory Control System: Data, Model Analysis, and Parameter Estimation

Several key areas in modeling the cardiovascular and respiratory control systems are reviewed and examples are given which reflect the research state of the art in these areas. Attention is given to the interrelated issues of data collection, experimental design, and model application including model development and analysis. Examples are given of current clinical problems which can be examined via modeling, and important issues related to model adaptation to the clinical setting.

Evaluation of treatment adherence in type 1 diabetes: a novel approach.

Background  Intensified insulin therapy requires outstanding compliance but no measure of therapy adherence has been agreed upon. The aim of the current study was to test the hypothesis that treatment adherence, as described by a novel multiple regression model, relates to glycosylated haemoglobin and hypoglycaemia frequency in type 1 diabetes. Furthermore, we sought to analyse the complex diurnal patterns of therapy adherence.

Delay differential equations: a partially ordered sets approach in vectorial metric spaces

AbstractIn this paper we develop a fixed point theorem in the partially ordered vector metric space C([−τ,0],Rn) by using vectorial norm. Then we use it to prove the existence of periodic solutions to nonlinear delay differential equations. MSC:06F30, 46B20, 47E10, 34K13, 34K05.

Parameter Estimation of a Model for Baroreflex Control of Unstressed Volume

The baroreflex involves a number of control pathways. In this chapter we consider in greater detail the role of the control of unstressed volume mobilization. We also consider an alternative approach for choosing parameters most likely to be estimable and we apply this method to a model incorporating the control of unstressed volume and compare to data.

New cubature formulas and Hermite–Hadamard type inequalities using integrals over some hyperplanes in the d-dimensional hyper-rectangle

Abstract This paper focuses on the problem of approximating a definite integral of a given function f when, rather than its values at some points, a number of integrals of f over certain hyperplane sections of a d -dimensional hyper-rectangle C d are only available. We develop several families of integration formulas, all of which are a weighted sum of integrals over some hyperplane sections of C d , and which contain in a special case of our result multivariate analogs of the midpoint rule, the trapezoidal rule and Simpson’s rule. Basic properties of these families are derived. In particular, we show that they satisfy a multivariate version of Hermite–Hadamard inequality. This latter does not require the classical convexity assumption, but it has weakened by a different kind of generalized convexity. As an immediate consequence of this inequality, we derive sharp and explicit error estimates for twice continuously differentiable functions. More precisely, we present explicit expressions of the best constants, which appear in the error estimates for the new multivariate versions of trapezoidal, midpoint, and Hammer’s quadrature formulas. It is shown that, as in the univariate case, the constant of the error in the trapezoidal cubature formula is twice as large as that for the midpoint cubature formula, and the constant in the latter is also twice as large as for the new multivariate version of Hammer’s quadrature formula. Numerical examples are given comparing these cubature formulas among themselves and with uniform and non-uniform centroidal Voronoi cubatures of the standard form, which use the values of the integrand at certain points.

Properties of Fixed Point Sets of Monotone Nonexpansive Mappings in Banach Spaces

ABSTRACT In this work, we discuss the properties of the common fixed points set of a commuting family of monotone nonexpansive mappings. In particular, we show that under suitable assumptions, this set is a monotone nonexpansive retract.

Impulsive mathematical modeling of ascorbic acid metabolism in healthy subjects.

In this work, we develop an impulsive mathematical model of Vitamin C (ascorbic acid) metabolism in healthy subjects for daily intake over a long period of time. The model includes the dynamics of ascorbic acid plasma concentration, the ascorbic acid absorption in the intestines and a novel approach to quantify the glomerular excretion of ascorbic acid. We investigate qualitative and quantitative dynamics. We show the existence and uniqueness of the global asymptotic stability of the periodic solution. We also perform a numerical simulation for the entire time period based on published data reporting parameters reflecting ascorbic acid metabolism at different oral doses of ascorbic acid.

Merging Mathematical and Physiological Knowledge: Dimensions and Challenges

This chapter introduces the main theoretical and practical topics which arise in the mathematical modeling of the human cardiovascular–respiratory system. These topics and ideas, developed in detail in the text, also represent a template for considering interdisciplinary research involving mathematical and life science disciplines in general. The chapter presents a multi-sided view of the modeling process which synthesizes the mathematical and life science viewpoints needed for developing and validating models of physiological systems. Particular emphasis is placed on the problem of coordinating model design and experimental design and methods for analyzing the model identification problem in the light of restricted data. In particular a variety of approaches based on information derived from parameter sensitivity are examined. The themes presented seek to provide a coordinated view of modeling that can aid in considering the current problem of patient-specific model adaptation in the clinical setting where data is in particular typically limited.

Approximate Fixed Points

In this chapter, we present some of the known results about the concept of approximate fixed points of a mapping. In particular, we discuss some new results on approximating fixed points of monotone mappings. Then we conclude this chapter with an application of these results to the case of a nonlinear semigroup of mappings. It is worth mentioning that approximate fixed points are useful when a computational approach is involved. In particular, most of the approximate fixed points discussed in this chapter are generated by an algorithm that allows its computational implementation.