RESUMEN
Regional citrate anticoagulation use in intermittent hemodialysis is limited by the increased risk of metabolic complications due to faster solute exchanges than with continuous renal replacement therapies. Several simplifications have been proposed. The objective of this study was to validate a mathematical model of hemodialysis anticoagulated with citrate that was then used to evaluate different prescription scenarios on anticoagulant effectiveness (free calcium concentration in dialysis filter) and calcium balance. A study was conducted in hemodialyzed patients with a citrate infusion into the arterial line and a 1.25 mmol/L calcium dialysate. Calcium and citrate concentrations were measured upstream and downstream of the citrate infusion site and in the venous line. The values measured in the venous lines were compared with those predicted by the model using Bland and Altman diagrams. The model was then used with 22 patients to make simulations. The model can predict the concentration of free calcium, bound to citrate or albumin, accurately. Irrespective of the prescription scenario a decrease in free calcium below 0.4 mmol/L was obtained only in a fraction of the dialysis filter. A zero or slightly negative calcium balance was observed, and should be taken into account in case of prolonged use.
Asunto(s)
Anticoagulantes , Calcio , Ácido Cítrico , Diálisis Renal , Humanos , Diálisis Renal/métodos , Anticoagulantes/administración & dosificación , Femenino , Masculino , Persona de Mediana Edad , Calcio/metabolismo , Calcio/sangre , Anciano , Modelos Teóricos , Simulación por ComputadorRESUMEN
Calcium has two important roles in haemodialysis. It participates in the activation of blood coagulation and calcium intakes have a major impact on patient mineral and bone metabolism. The aim of this article is to propose a mathematical model for calcium ions concentration in a dialyzer during haemodialysis using a citrate dialysate. The model is composed of two elements. The first describes the flows of blood and dialysate in a dialyzer fibre. It was obtained by asymptotic analysis and takes into account the anisotropy of the fibres forming a dialyzer. Newtonian and non-Newtonian blood rheologies were tested. The second part of the model predicts the evolution of the concentration of five chemical species present in these fluids. The fluid velocity field drives the convective part of a convection-reaction-diffusion system that models the exchange of free and complexed calcium. We performed several numerical experiments to calculate the free calcium concentration in the blood in a dialyzer using dialysates with or without citrate. The choice of blood rheology had little effect on the fluid velocity field. Our model predicts that only a citrate based dialysate without calcium can decrease free calcium concentration at the blood membrane interface low enough to inhibit blood coagulation. Moreover for a given calcium dialysate concentration, adding citrate to the dialysate decreases total calcium concentration in the blood at the dialyzer outlet. This decrease of the calcium concentration can be compensated by infusing in the dialyzed blood a quantity of calcium computed from the model.
Asunto(s)
Calcio/metabolismo , Ácido Cítrico/química , Soluciones para Hemodiálisis/química , Modelos Biológicos , Diálisis Renal/métodos , Algoritmos , Coagulación Sanguínea , Calcio/sangre , Simulación por Computador , Hemorreología , Humanos , Transporte Iónico , Conceptos Matemáticos , Diálisis Renal/estadística & datos numéricosRESUMEN
This paper describes a rigorous framework for reconstructing MR images of the heart, acquired continuously over the cardiac and respiratory cycle. The framework generalizes existing techniques, commonly referred to as retrospective gating, and is based on the properties of reproducing kernel Hilbert spaces. The reconstruction problem is formulated as a moment problem in a multidimensional reproducing kernel Hilbert spaces (a two-dimensional space for cardiac and respiratory resolved imaging). Several reproducing kernel Hilbert spaces were tested and compared, including those corresponding to commonly used interpolation techniques (sinc-based and splines kernels) and a more specific kernel allowed by the framework (based on a first-order Sobolev RKHS). The Sobolev reproducing kernel Hilbert spaces was shown to allow improved reconstructions in both simulated and real data from healthy volunteers, acquired in free breathing.
Asunto(s)
Algoritmos , Corazón/anatomía & histología , Aumento de la Imagen/métodos , Interpretación de Imagen Asistida por Computador/métodos , Imagen por Resonancia Cinemagnética/métodos , Mecánica Respiratoria , Humanos , Imagen por Resonancia Cinemagnética/instrumentación , Movimiento (Física) , Fantasmas de Imagen , Reproducibilidad de los Resultados , Sensibilidad y EspecificidadRESUMEN
This article describes a general framework for multiple coil MRI reconstruction in the presence of elastic physiological motion. On the assumption that motion is known or can be predicted, it is shown that the reconstruction problem is equivalent to solving an integral equation--known in the literature as a Fredholm equation of the first kind--with a generalized kernel comprising Fourier and coil sensitivity encoding, modified by physiological motion information. Numerical solutions are found using an iterative linear system solver. The different steps in the numerical resolution are discussed, in particular it is shown how over-determination can be used to improve the conditioning of the generalized encoding operator. Practical implementation requires prior knowledge of displacement fields, so a model of patient motion is described which allows elastic displacements to be predicted from various input signals (e.g., respiratory belts, ECG, navigator echoes), after a free-breathing calibration scan. Practical implementation was demonstrated with a moving phantom setup and in two free-breathing healthy subjects, with images from the thoracic-abdominal region. Results show that the method effectively suppresses the motion blurring/ghosting artifacts, and that scan repetitions can be used as a source of over-determination to improve the reconstruction.