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{{short description|Formula for identifying acid-base disorders}}

In [[nephrology]], the '''delta ratio''', or "'''delta-delta'''" (denoted {{math|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.

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==Equation==
The equation for calculating the delta ratio is<ref>{{Cite web |url=http://fitsweb.uchc.edu/student/selectives/TimurGraham/Delta_Ratio.html |title=Delta Gap: Acid Base Tutorial, University of Connecticut Health Center |access-date=2014-03-30 |archive-url=https://web.archive.org/web/20131204164220/http://fitsweb.uchc.edu/student/selectives/TimurGraham/Delta_Ratio.html |archive-date=2013-12-04 |url-status=dead }}</ref>
<math chem display=block>\begin{align}
  \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{align}</math>

where AG is the anion gap, {{chem2|1=AG = [Na+] \– ([Cl-] + [HCO3-])}}, which reflects either an increase in the anion gap or a decrease in the [[bicarbonate]] concentration ({{chem2|[HCO3-]}}).<ref>{{cite book|last1=Marini|first1=John|title=Critical Care Medicine: The Essentials|date=16 June 2014|publisher=Lippincott Williams & Wilkins|isbn=978-0781798396|page=236|edition=4th}}</ref>

==Results==
The ratio gives one of four results:{{cn|date=November 2024}}

# <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 disorder]]s.

Results 1. and 4. are oddities, mathematically speaking:{{cn|date=November 2024}}

Result 1: if there is a normal anion gap acidosis, the {{math|(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 {{chem2|[Cl-]}} or {{chem2|[HCO3-]}} concentrations. So the AG doesn't change; but to maintain electrical equilibrium, if {{chem2|[Cl-]}} goes up, {{chem2|[HCO3-]}} must come down. Hence, hyperchloremia always causes a metabolic acidosis as {{chem2|[HCO3-]}} must fall; alternatively, if the {{chem2|[HCO3-]}} rises, the {{chem2|[Cl-]}} must fall. For a list of the common causes of this change in bicarbonate or chloride, see  [[normal anion gap acidosis]].{{cn|date=November 2024}}

Results 2–4 all involve HAGMAs. A [[high anion gap metabolic acidosis]] usually  occurs because of an increase in anions. So in the equation:
<math chem display=block>\text{AG} = [\ce{Na+}] - \Bigl([\ce{Cl-}] + [\ce{HCO3-}] + [\ce{A-}] \Bigr)</math>
it is the {{chem2|[A-]}} that is the cause.
For a list of the common anions responsible, see [[high anion gap metabolic acidosis]]. [[High anion gap metabolic acidosis#Causes|KULT]] is probably the easiest of the mnemonics to use (Ketones, Uremia, Lactate, Toxins). Toxins are an uncommon cause of high anion gap metabolic acidosis – a list of the commonest toxins is ACE GIFTs [ibid]. [[Metformin]] as a pure toxicological cause is vanishingly rare.{{cn|date=November 2024}}

Result 4: if the result of the ratio is greater than 2 in a high anion gap metabolic acidosis, it is usually because there was a pre-existing higher than normal bicarbonate level. This is commonly found in people with chronic [[respiratory acidosis]] from chronic lung disease such as chronic obstructive pulmonary disease ([[COPD]]), who can't breathe off their excess carbon dioxide owing to poor lung function, and retain bicarb in order to counteract the acidosis caused by the retained {{chem2|CO2}}. Alternatively it could be caused by a concurrent [[metabolic alkalosis]] such as vomiting causing acid loss and hence alkalosis, or diuretic use with loss of {{chem2|[Cl-]}} and a compensatory bicarb retention in order to maintain plasma electrical neutrality.<ref>UpToDate.com The Δanion gap/ΔHCO3 ratio in patients with a high anion gap metabolic acidosis</ref>

Mathematically this is reflected in a high anion gap, but because the bicarbonate was high to start, it will appear to fall only a small amount. When this happens the numerator is large, the denominator is small, and the result is a delta ratio which is high (>2). This means a combined high anion gap metabolic acidosis and a pre-existing either respiratory acidosis or metabolic alkalosis (causing the high bicarbonate) – i.e. a mixed acid–base metabolic acidosis.{{cn|date=November 2024}}

Result 3: if there is a pure HAGMA, the bicarb would be expected to fall at a similar rate as the anion gap rises, since one molecule of acid combines with one molecule of bicarb buffer. So the equation above should be balanced as the change in the AG away from normal (12) is similar to the change in bicarb away from normal (24). Mathematically, if the change in the numerator is similar to the change in the denominator, the delta ratio will be close to 1. Since the anions are unable to diffuse out of the bloodstream, while bicarbonate and hydrogen ions diffuse with ease (as {{chem2|H2CO3}}, [[carbonic acid]]), the usual result will be closer to a delta ratio of 1 to 2.<ref>{{Cite news|url=http://lifeinthefastlane.com/ccc/delta-ratio/|title=Delta Ratio|work=LITFL • Life in the Fast Lane Medical Blog|access-date=2018-03-23|language=en-US}}</ref><ref name=":0">{{Cite web|url=http://www.anaesthesiamcq.com/AcidBaseBook/ab3_3.php|title=3.3 The Delta Ratio|website=www.anaesthesiamcq.com|access-date=2018-03-23}}</ref> [[Lactic acidosis]] usually causes a ratio of 1.6.<ref name=":0" />

Result 2: if the delta ratio is somewhere between low (<0.4) and high (1–2), then it is usually due to a combination of high anion gap metabolic acidosis and normal anion gap acidosis.<ref>{{cite journal|last1=Rastegar|first1=Asghar|title=Use of the ΔAG/ΔHCO3− Ratio in the Diagnosis of Mixed Acid–Base Disorders|journal=Journal of the American Society of Nephrology|date=26 July 2007|volume=18|issue=9|pages=2429–2431|url=http://jasn.asnjournals.org/content/18/9/2429.full|accessdate=16 June 2014|doi=10.1681/asn.2006121408|pmid=17656477 |doi-access=free}}</ref> For example, a person with [[cholera]] may have a normal anion gap acidosis due to diarrhea, but becomes progressively dehydrated and develops a lactic acidosis from shock, and proceeds to develop a high anion gap metabolic acidosis – i.e. a mixed acid–base disorder.{{cn|date=November 2024}}

== References ==
{{reflist}}
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{{Renal physiology}}
{{DEFAULTSORT:Acid-base homeostasis}}

[[Category:Acid–base disturbances]]