Delta ratio
formula for identifying acid-base disorders
In nephrology, the delta ratio, or "delta-delta" (denoted Δ/Δ), is a formula that can be used to evaluate whether a mixed acid–base disorder (metabolic acidosis) is present, and if so, assess its severity. The anion gap (AG) without potassium is calculated first and if a metabolic acidosis is present, results in either a high anion gap metabolic acidosis (HAGMA) or a normal anion gap acidosis (NAGMA). A low anion gap is usually an oddity of measurement, rather than a clinical concern.
Equation
The equation for calculating the delta ratio is
Δ
/
Δ
=
Δ
AG
Δ
[
HCO
3
−
]
=
measured AG
−
normal AG
normal
[
HCO
3
−
]
−
measured
[
HCO
3
−
]
=
[
AG
]
−
12
24
−
[
HCO
3
−
]
{\displaystyle {\begin{aligned}\Delta /\Delta &={\frac {\Delta {\text{ AG}}}{\Delta \ [{\ce {HCO3-}}]}}\\[4pt]&={\frac {{\text{measured AG}}-{\text{normal AG}}}{{\text{normal }}[{\ce {HCO3-}}]-{\text{measured }}[{\ce {HCO3-}}]}}\\[4pt]&={\frac {[{\ce {AG}}]-12}{24-[{\ce {HCO3-}}]}}\end{aligned}}}
where AG is the anion gap, AG = [Na+] - ([Cl−] + [HCO−3]), which reflects either an increase in the anion gap or a decrease in the bicarbonate concentration ([HCO−3]).
Results
The ratio gives one of four results:
<0.4 due to a pure NAGMA
0.4–0.8 due to a mixed NAGMA + HAGMA
0.8–2.0 due to a pure HAGMA
>2.0 due to a mixed HAGMA + metabolic alkalosis
Results 2 and 4 are the ones which have mixed acid–base disorders.
Results 1. and 4. are oddities, mathematically speaking:
Result 1: if there is a normal anion gap acidosis, the (AG – 12) part of the equation will be close to zero, the delta ratio will be close to zero and there is no mixed acid–base disorder. Your calculations can stop here. A normal anion gap acidosis (NAGMA) has more to do with a change in [Cl−] or [HCO−3] concentrations.
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