**Question 1:**

PH = 7.19, that is severe acidaemia.

HCO3 = 14 mmol/L, So we have metabolic acidosis. Next, we need to calculate respiratory compensation and anion gap.

To calculate respiratory compensation we use Winter’s formula, that is:

Expected pCO2 = 1.5 x HCO3 + 8 (+/- 2).

Accordingly, expected pCO2 for this patient should be 1.5 x 14 + 8= 29 mmHg. Or the expected range is 27 to 31. pCO2 here is higher than that (39), So we have additional respiratory acidosis.

Next we will calculate the Anion Gap for this patient. AG is calculated as:

AG = Na – (Cl + HCO3) = 130 – (107+ 14) = 9. According to this calculation we have normal anion gap metabolic acidosis ***

(This doesn’t fit with the rest of the results we have for this patient).

These results show elevated glucose level, elevated lactate, elevated ketones and high urea. All these cause HAGMA.

However, Na level is falsely reduced in the presence of high glucose level. To calculate the corrected Na level to glucose level we use the following formula:

Corrected Na = Measured Na + (Glucose – 5)/3 = 135 mmol/L.

Using the corrected Na level to calculate the anion gap =135 -(107+14) = 14, we end up with high anion gap which fits the presentation for this patient.

The other abnormal finding is elevated creatinine, 141.

We can calculate the Urea/Creatinine ratio for this patient. The formula for that is:

Urea x 1000 / Creatinine.

For this patient the ratio is: 18 x 1000 / 141 = 127.6. Ratio above 100 indicates prerenal causes (Usually dehydration).

- Ratio > 100 indicates a pre-renal cause.
- Ratio of 100 – 40 is normal or post renal cause of acute kidney injury
- Ratio < 40 indicates intrinsic renal damage.

This patient had Acidosis, Hyperglycemia and high ketones, that fits the definition of DKA. DKA is usually associated with high lactate due to the dehydration and reduced tissue perfusion.

** Question 2:**

Na is an essential cation for the calculation of anion gap and important osmotically active ion for the calculation of osmolarity.

Na is a positively charged ion while glucose is neutral. That is why we use the corrected Na level when we calculate the anion gap as we are dealing with the electrical neutrality.

While for the calculation of osmolarity, both sugar and Na are osmotically active. That is why we use the measured Na level to calculate the osmolarity.