# Delta Gap and Delta Ratio

Once one has calculated the anion gap and finds it raised, one is almost obliged to figure out whether those anions have been solely responsible for the acidosis, or whether another (non-anion-gap) cause is lurking in the background. A brief review of this can be found in the "Required Reading" section hidden among the CICM Fellowship Exam preparation material. For actual education, the exam candidates are directed to the LITFL delta ratio page, and to the excellent online works of Kerry Brandis.

## The delta gap

The delta gap is a straight-out difference between the change in anion gap and the change in bicarbonate.

**Delta gap = (change in anion gap) - (change in bicarbonate)**

(The normal anion gap is assumed to be 12, and the normal HCO_{3} is assumed to be 24.)

A simplified equation which does not require a bicarbonate value is also available:

**Delta gap = Na ^{+} - Cl^{-} - 36**

**Interpretation of the generated ratio:**

- -6 = Mixed high and normal anion gap acidosis
- -6 to 6 = Only a high anion gap acidosis exists
- over 6 = Mixed high anion gap acidosis and metabolic alkalosis

Delta gap is essentially a tool to determine whether or not there is also a normal anion gap metabolic acidosis present. The normal value for delta gap is zero, and it should remain zero as anion gap and bicarbonate change together (mole for mole, in opposite directions). If the bicarbonate is changing significantly less than the anion gap, the delta gap will become more and more positive, reflecting the fact that an alkalosis is present. If the change in bicarbonate is significantly greater than the change in anion gap, there is clearly some acidosis present which is unrelated to the anion gap rise, and the delta gap will be very negative.

Why -6 and +6? Keith Wrenn established these parameters in 1990, using the normal values supplied to him by the laboratory of Grady Memorial Hospital in Atlanta, Georgia. Those guys gave him an AG of 15 and a bicarbonate of 25. The standard deviation of these values over three months of testing was 3.2; and so Wrenn chose 6 as the threshold, it being two standard deviations from the mean value of 0.

One does not even need a bicarbonate value for this calculation. According to Tsapenko, the simplicity of his "Modified DG" calculation and the omission of bicarbonate from it is "an obvious advantage", presumably due to the fact that the bicarbonate is usually a calculated value and it is always better to rely on directly measured values. Generally this shortcut will work.

## The delta ratio

The delta ratio is a *ratio comparison* of the change in bicarbonate to the change in anion gap.

**Delta ratio = (change in anion gap) / (change in bicarbonate)**

(The normal anion gap is assumed to be 12, and the normal HCO_{3} is assumed to be 24.)

**Interpretation of the generated ratio:**

- 0.4 = normal anion gap metabolic acidosis
- 0.4-0.8 = mixed high and normal anion gap acidosis exists.
- 0.8-1.0 = purely due to a high anion gap metabolic acidosis
- 1.0-2.0 = still purely a high anion gap metabolic acidosis
- Over 2.0 = high anion gap acidosis with pre-existing metabolic alkalosis

So, basically acidic anions should titrate the bicarbonate stoichiometrically (mole for mole), generating a delta ratio of 1.0 (or up to 2.0 if the anions are polyvalent?) and if this does not appear to be the case, then a mixed disorder must be present.

Unfortunately, these relationships are largely unsubstantiated.

## Limitations of the delta method

Let us put aside concerns about laboratory error, though these may be valid. True, the delta ratio is two calculations removed from the actual laboratory values, and thus any existing error will be amplified - but this is not unique to the delta ratio.

Of greater relevance are the assumptions made about buffering in the body fluids.

These are as follows:

### Assumption: Acid anions are buffered 1:1 by bicarbonate

In actual fact, this is almost always false. Bicarbonate contributes about 75% of extracellular buffering in metabolic acid-base disorders. The rest is performed by haemoglobin and other proteins (to a lesser extent). The concentration of which will obviously vary, as will their buffering performance depending on a range of ambient physicochemical parameters (eg. haemoglobin is a better proton acceptor when it is fully deoxygenated).

### Assumption: All buffering occurs in the extracellular fluid

But it does not - in fact, buffering by the intracellular compartment may be very important, depending on whether the acid being buffered has any access to the cytosol. If, like lactate, it can easily enter and exit the cell - then this assumption does not hold up. Generally, Brandis remarksthat intracellular protein and phosphate may contribute about 60% of the total buffering in metabolic acidosis, and perhaps 30% in metabolic alkalosis.

### Assumption: Acid anions have the same distribution space and clearance mechanisms as the H^{+}

But they dont. Indeed the discrepancies between anion clearance rates give rise to strange "rules of extensively observed pattern" which you will sometimes see. For instance, it is said that with lactic acidosis, the "traditional" delta ratio is 1.6, because the lactate has poor renal clearance and undergoes intracellular metabolism, whereas in DKA the ketones are rapidly cleared renally, keeping the ratio closer to 1.0. A NEJM article reports that "In lactic acidosis, the decrease in the concentration of bicarbonate is 0.6 times the increase in the anion gap". In fact the published authorities seem to disagree extensively as to what the "usual" delta ratio should be for a given acid-base disturbance, and so there may be little value in these rules when it comes to making a diagnosis. If your delta ratio is 1.6, that does not mean you have a lactic acidosis; but it does mean that you should think about checking the lactate levels.

## So, is the delta ratio a waste of time?

No, it is not. Provided one does not abuse the concept.

One should not expect this method to yield an accurate stoichiometric information- at best, it may point one to the existence of another acid-base disorder, which may cause one to reconsider that extra bottle of bicarbonate, or bag of saline.

Thus, one can make use of this concept to identify mixed acid-base disorders, provided one is

- conscious of the abovementioned limitations,
- confident of the quality of one's measurements,
- careful in one's clinical assessment of the patient.

Because to blindly apply a method like this without any information from history and examination could lead you to wildly ridiculous conclusions.

## Use of the Standard Base Excess instead of Actual Bicarbonate

T.J. Morgan's chapter on acid-base disorders in Oh's Manual describes (p.944) the use of anion gap together with the Standard Base Excess. This method may answer the complaints about the buffering assumptions made by delta ratio users. The SBE accounts for non-bicarbonate buffering, so it should be somewhat more accurate.

The theory goes that an elevated anion gap should be accompanied by an equal decrease in the SBE.

For instance, a raised anion gap in the presence of a normal SBE suggests that a metabolic alkalosis is present; similarly an anion gap which has changed more than the SBE suggests that a non-anion-gap acidosis is also present.

Morgan does not reference this method, and it is difficult to track down where it originates, or whether anybody has made any attempt to validate it. It also appears in J-L. Vincent's *Textbook of Critical care*, and in Chapter 121 of *Critical Care Nephrology* by Ronco Bellomo and Kellum. On face value, it would appear to be a sensible alternatve to the use of bicarbonate for a delta ratio calculation, particularly when (like in our local machine) the *actual* bicarbonate is not reported.

## References

Wrenn, Keith. "The delta (Δ) gap: An approach to mixed acid-base disorders."*Annals of emergency medicine* 19.11 (1990): 1310-1313.

Reddy, P., and A. D. Mooradian. "Clinical utility of anion gap in deciphering acid–base disorders." *International journal of clinical practice* 63.10 (2009): 1516-1525.

Jones, B. J., and P. J. Twomey. "The anion gap revisited." *International journal of clinical practice* 63.10 (2009): 1409-1412.

Tsapenko, Mykola V. "Modified Delta Gap Equation for Quick Evaluation of Mixed Metabolic Acid-Base Disorders." *Oman medical journal* 28.1 (2013): 73.

Oosthuizen, Nicholette M. "Approach to acid-base disorders–a clinical chemistry perspective: acid-base disorders are frequently encountered in clinical practice and have a significant impact on patient morbidity and mortality." CME July 2012 Vol. 30 No. 7

Rastegar, Asghar. "Use of the ΔAG/ΔHCO3− Ratio in the Diagnosis of Mixed Acid-Base Disorders." *Journal of the American Society of Nephrology* 18.9 (2007): 2429-2431.

Dinubile, MarkJ. "The increment in the anion gap: overextension of a concept?." *The Lancet* 332.8617 (1988): 951-953.