Published in:
01-05-2010 | Correspondence
Reply to Agrafiotis
Published in: Intensive Care Medicine | Issue 5/2010
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Dear editor: Dr. Agrafiotis suggested that in vivo the mechanism of dilutional acidosis is more complicated than what we proposed in our “plasma model” and focused on the Gibbs-Donnan equilibrium as a possible additional mechanism. No doubt that, in vivo, the whole picture is far more complicated than whatever available model. In fact, beside the Gibbs-Donnan equilibrium, the presence of red cells, the kidney and lung actions, the capillary permeability in the different body regions, etc., all contribute to acid-base/electrolytes behavior. However, to answer to Dr. Agrafiotis (and for intellectual divertissement), we quantitatively analyzed a model including two interacting compartments [plasma/protein-free interstitial fluid (ISF)], separated by a membrane permeable to electrolytes and impermeable to proteins. Composition and electrical charges of plasma and ISF were derived from Stewart’s [1] (see Table 1 for baseline). “Permeable cations” represent the sum of all permeable positively charged ions (Na+, K+, Mg++, Ca++), “permeable anions” are the sum of all permeable negatively charged ions (Cl−, Lactate−, HCO3 −), and “impermeable anions” are the negatively charged plasma proteins (according to Stewart’s terminology, A−) to which the membrane is impermeable. In Table 1, we report the effects of plain dilution (100% dilution with the same three SID = 0 solutions used in our paper) on the concentrations of permeable cations, permeable anions and impermeable anions, ignoring the Gibbs-Donnan equilibrium, as if the two compartments behave as separated entities. Interestingly the percentage error on Gibbs-Donnan effect computed as ([Permeable Cations plasma] × [Permeable Anions plasma] − [Permeable Cations ISF] × [Permeable Anions ISF]/([Permeable Cations plasma] × [Permeable Anions plasma]) was 2.44% in all steps, regardless of dilution. This small inaccuracy was likely due to baseline data approximation. In Table 2, we report the effects of the same dilutions on electrolyte composition taking into account not only the electroneutrality and the mass conservation laws, but also the Gibbs-Donnan equilibrium. Accordingly:
Table 1
Effects of plain dilution on the concentrations of permeable cations, permeable anions and impermeable anions, ignoring the Gibbs-Donnan equilibrium
|
Baseline
|
Dilution distilled water
|
Dilution normal saline
|
Dilution lactated Ringer’s
|
|||||
|---|---|---|---|---|---|---|---|---|
|
ISF
|
Plasma
|
ISF
|
Plasma
|
ISF
|
Plasma
|
ISF
|
Plasma
|
|
|
Volume (l)
|
13.2
|
3.3
|
26.4
|
6.6
|
26.4
|
6.6
|
26.4
|
6.6
|
|
Permeable cations (mEq/l)
|
143
|
150
|
71.5
|
75.5
|
148.5
|
152
|
140
|
143.5
|
|
Permeable anions (mEq/l)
|
143
|
133
|
71.5
|
66.5
|
148.5
|
143.5
|
140
|
135
|
|
Impermeable anions (mEq/l)
|
0
|
16.6
|
0
|
8.3
|
0
|
8.3
|
0
|
8.3
|
Table 2
Effects of the same dilutions on electrolyte composition taking into account not only the electroneutrality and the mass conservation laws, but also the Gibbs-Donnan equilibrium
|
Baseline
|
Dilution distilled water
|
Dilution normal saline
|
Dilution lactated Ringer’s
|
|||||
|---|---|---|---|---|---|---|---|---|
|
ISF
|
Plasma
|
ISF
|
Plasma
|
ISF
|
Plasma
|
ISF
|
Plasma
|
|
|
Volume (l)
|
13.2
|
3.3
|
26.4
|
6.6
|
26.4
|
6.6
|
26.4
|
6.6
|
|
Permeable cations (mEq/l)
|
142.7
|
151.2
|
71.3
|
75.6
|
148.4
|
152.6
|
139.9
|
144.1
|
|
Permeable anions (mEq/l)
|
142.7
|
134.6
|
71.3
|
67.3
|
148.4
|
144.3
|
139.9
|
135.8
|
|
Impermeable anions (mEq/l)
|
0
|
16.6
|
0
|
8.3
|
0
|
8.3
|
0
|
8.3
|
1.
Gibbs-Donnan equilibrium:
$$ \left[ {Permeable\,Cations_{{{\mathbf{ISF}}}} } \right] \times \left[ {Permeable\,Anions_{{{\mathbf{ISF}}}} } \right] \, = \left[ {Permeable\,Cations_{{{\mathbf{plasma}}}} } \right] \times \left[ {Permeable\,Anions_{{{\mathbf{plasma}}}} } \right]. $$
2.
ISF electroneutrality:
$$ \left[ {Permeable\,Cations_{{{\mathbf{ISF}}}} } \right]-\left[ {Permeable\,Anions_{{{\mathbf{ISF}}}} } \right] \, = \, {\mathbf{0}}. $$
3.
Plasma electroneutrality:
$$\left[ {Permeable\,Cations_{{{\mathbf{plasma}}}} } \right]-\left[ {Permeable\,Anions_{{{\mathbf{plasma}}}} } \right]-\left[ {Impermeable\,Anions_{{{\mathbf{plasma}}}} } \right]={\mathbf{0}}.$$
4.
Mass conservation:
$$ \left[ {Permeable\,Cations_{{{\mathbf{ISF}}}} } \right] \cdot V_{{{\mathbf{ISF}}}} \, + \, \left[ {Permeable\,Cations_{{{\mathbf{plasma}}}} } \right] \cdot V_{{{\mathbf{plasma}}}} = \, \left[ {Permeable\,Cations_{{{\mathbf{TOT}}}} } \right] \cdot V_{{{\mathbf{TOT}}}}. $$