Prediction of Solute Kinetics, Acid-Base Status, and Blood Volume Changes During Profiled Hemodialysis

Abstract

A mathematical model of solute kinetics oriented to the simulation of hemodialysis is presented. It includes a three-compartment model of body fluids (plasma, interstitial and intracellular), a two-compartment description of the main solutes (K+, Na+, Cl-, urea, HCO3-, H+), and acid-base equilibrium through two buffer systems (bicarbonate and noncarbonic buffers). Tentative values for the main model parameters can be given a priori, on the basis of body weight and plasma concentration values measured before beginning the session. The model allows computation of the amount of sodium removed during hemodialysis, and may enable the prediction of plasma volume and osmolarity changes induced by a given sodium concentration profile in the dialysate and by a given ultrafiltration profile. Model predictions are compared with clinical data obtained during 11 different profiled hemodialysis sessions, both with all parameters assigned a priori, and after individual estimation of dialysances and mass-transfer coefficients. In most cases, the agreement between the time pattern of model solute concentrations in plasma and clinical data was satisfactory. In two sessions, blood volume changes were directly measured in the patient, and in both cases the agreement with model predictions was acceptable. The present model can be used to improve the dialysis session taking some characteristics of individual patients into account, in order to minimize intradialytic unbalances (such as hypotension or disequilibrium syndrome).

A Bio-Hydraulic Modelling Approach to Control the Hemodialysis Patient Status—Calculus and Validation

“…The change of carbon dioxide concentration is determined by a balance between the net rate of carbon dioxide transported to the tissues by the blood and the net rate at which carbon dioxide is produced by the tissues. By assuming that the gas tensions in the body tissues are uniform and at every instant equal to those in the mixed venous blood returning to the lungs, the mass balance equations for the tissue compartment and the related formulas can be written [5][6][7][8][9][10][11]: σ and k are constant parameters Generally, we assume the equality between left cardiac output, right cardiac output, the systemic blood flow and the pulmonary blood flow [11]. The results of those equations will be used to model the production and elimination of acids and bases wastes, subject of the following paragraph.…”

“…For this goal, I will begin with introducing relationships among blood pressures (systolic/diastolic pressures), respiration, peripheral resistance, and sympathetic nerve activity [2][3][4]. Then, I will propose a quantitative description of the respiratory processes responsible for the regulation of acid-base balance in man [5][6][7][8]. This will be done by formulating the carbon dioxide concentration and its arterial blood pressure for the brain compartment, lung compartment and body tissue compartment.…”

Mathematical Modeling of Cardiovascular System Dynamics Using a Lumped Parameter Method

“…By contrast, Heldt et al [23] In the hemodialysis simulations using a lumped model done by Ursino's group [45][46][47], mass transfer in the blood-tissue-dialysate system was simulated with a model having three compartments: intracellular, interstitial, and plasma compartments. Fluid exchange between the intracellular and interstitial compartments depends on the osmotic concentration, whereas the hydraulic and osmotic pressure gradients at the capillary compartment determine fluid exchange between the interstitial fluid and plasma.…”

“…For example, some models assume that the microcirculation is a resistor [24,33] whose value is nearly 1 PRU, and others use a multibranched approximation for the microcirculation [31,32]. The microcirculation is especially important in hemodialysis simulation [45][46][47] and microgravity modeling of the circulation [23,48].…”

“…Melchior et al [55] first introduced modeling of the cardiopulmonary reflex to simulate orthostatic intolerance. This model, combined with that of the arterial baroreflex, was modified by Ursino et al [56] to mathematically investigate physiological factors involved in hemodialysis hypotension. Heldt et al [29] integrated the arterial baroreflex and cardiopulmonary reflex loop in their lumped parameter model.…”