Yonsei Med J.  2008 Aug;49(4):581-591. 10.3349/ymj.2008.49.4.581.

Numerical Simulation of the Effect of Sodium Profile on Cardiovascular Response to Hemodialysis

• Lim KM
• Choi SW
• Min BG
• Shim EB

• KMID: 1793193
• DOI: http://doi.org/10.3349/ymj.2008.49.4.581

Abstract

PURPOSE
We developed a numerical model that predicts cardiovascular system response to hemodialysis, focusing on the effect of sodium profile during treatment. MATERIALS and METHODS: The model consists of a 2-compartment solute kinetics model, 3-compartment body fluid model, and 12-lumped-parameter representation of the cardiovascular circulation model connected to set-point models of the arterial baroreflexes. The solute kinetics model includes the dynamics of solutes in the intracellular and extracellular pools and a fluid balance model for the intracellular, interstitial, and plasma volumes. Perturbation due to hemodialysis treatment induces a pressure change in the blood vessels and the arterial baroreceptors then trigger control mechanisms (autoregulation system). These in turn alter heart rate, systemic arterial resistance, and cardiac contractility. The model parameters are based largely on the reported values. RESULTS: We present the results obtained by numerical simulations of cardiovascular response during hemodialysis with 3 different dialysate sodium concentration profiles. In each case, dialysate sodium concentration profile was first calculated using an inverse algorithm according to plasma sodium concentration profiles, and then the percentage changes in each compartment pressure, heart rate, and systolic ventricular compliance and systemic arterial resistance during hemodialysis were determined. A plasma concentration with an upward convex curve profile produced a cardiovascular response more stable than linear or downward convex curves. CONCLUSION: By conducting numerical tests of dialysis/cardivascular models for various treatment profiles and creating a database from the results, it should be possible to estimate an optimal sodium profile for each patient.

Keyword

Hemodialysis; cardiovascular system; numerical simulation; sodium profile

MeSH Terms

Blood Pressure/drug effects
Cardiovascular System/*drug effects
*Computer Simulation
Models, Cardiovascular
*Renal Dialysis
Sodium/*pharmacology

Figure

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  Fig. 1 Schematic of our computational model.

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  Fig. 2 The compartment model used to describe body fluid exchange and solute kinetics. Dotted line, solute transport; solid line, fluid transport; ic, intracellular; is, interstitial; pl, plasma; ex, extracellular; d, dialysate; K, mass transfer coefficient between intracellular and extracellular compartments; KoA, mass transfer coefficient through the dialyzer membrane; V, compartment volume; Qinf, replacement fluid flow; Qf, ultrafiltration rate; C, concentration of solute; J, solute removal rate across the dialyzer; Rv, fluid reabsorption rate at venous capillaries; Fa, fluid filtration rate at arterial capillaries; Kf, osmotic filtration coefficient at the cellular membrane.

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  Fig. 3 Circuit representation of a single compartment. P, pressure; R, resistance; C, capacitance; q, blood flow; pis, interstitial pressure.

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  Fig. 4 Circuit diagram used for the hemodynamics of the cardiovascular system. lv, left ventricle; a, arterial; up, upper body; kid, kidney; sp, splanchnic; ll, lower limbs; avc, abdominal vena cava; ivc, inferior vena cava; svc, superior vena cava; rv, right ventricle; p, pulmonary; pa, pulmonary artery; pv, pulmonary vein; ro, right ventricular outflow; lo, left ventricular outflow; th, thoracic.

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  Fig. 5 Diagrammatic representation of the baroreceptor reflex model. CS, carotid sinus; CP, cardiopulmonary; ANS, autonomic nervous system; SA Node, sinoatrial node; Σ, summation.

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  Fig. 6 Comparison of the result for variation in urea concentration with Barth's experimental result.12 Straight line, intracellular pool with this model; dashed line, extracellular pool with this model; triangles, intracellular pool with the reference model; circles, extracellular pool with the reference model.

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  Fig. 7 Simulated pressure waveforms at several nodes. Straight line, left ventricle; dashed line, aorta; dotted line, right ventricle; dash-dot line, pulmonary artery.

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  Fig. 8 Sodium concentration profiles in plasma (A) and the dialysate obtained using the inverse algorithm (B). Straight line, Na+ profile with a convex downward curve; dashed line, linear decrease in the Na+ profile; dotted line, Na+ profile with a convex upward curve.

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  Fig. 9 Temporal variation in total blood volume. Straight line, Na+ profile with a convex downward curve; dashed line, linear decrease in the Na+ profile; dotted line, Na+ profile with a convex upward curve.

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  Fig. 10 Temporal variation in systemic arterial mean pressure. Straight line, Na+ profile with a convex downward curve; dashed line, linear decrease in the Na+ profile; dotted line, Na+ profile with a convex upward curve.

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  Fig. 11 Temporal variation in heart rate for the 3 dialysate sodium profiles. The first 4 hrs are for treatment and the last 2 hrs are an observation period. Straight line, Na+ profile with a convex downward curve; dashed line, linear decrease in the Na+ profile; dotted line, Na+ profile with a convex upward curve.

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  Fig. 12 Temporal variation in systolic compliance of the left (A) and right (B) ventricles for the 3 dialysate sodium profiles. Straight line, Na+ profile with a convex downward curve; dashed line, linear decrease in the Na+ profile; dotted line, Na+ profile with a convex upward curve.

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  Fig. 13 Temporal variation in peripheral resistance. Straight line, Na+ profile with a convex downward curve; dashed line, linear decrease in the Na+ profile; dotted line, Na+ profile with a convex upward curve.

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