a) Briefly explain the concept of the quantitative approach (Stewart's approach) to acid-base analysis.

b) How does the quantitative approach classify acid-base disturbances?

a)
The quantitative approach to acid-base chemistry provides a mathematical explanation of the relevant variables that control H+ in body fluids and their interactions. The approach treats body fluids as a sys- tem that contains multiple interacting constituents.
The Henderson-Hasselbach approach to evaluating acid-base status considers the interactions of only a few variables in the system, such as pH, PCO2, and bicarbonate, whereas Stewart considers the interactions among more variables and allows one to identify the variables that control H+.
Quantitative approach uses physical laws of aqueous solutions to write equations that describe the interactions among the variables in the system. These laws are the maintenance of electrical neutrality, the satisfaction of the dissociation equilibria for weak electrolytes (partially dissociated when dissolved in water), and the conservation of mass.

An important basic concept of Stewart's principles is the classification of variables in a system as independent or dependent. Independent variables can be altered from outside the system without affecting each other. Dependent variables are thought of as internal to the system. Their values depend on the values of the independent variables and reflect the behaviour of the equilibrium reactions in the system.
Three independent parameters are known to control acidity in arterial or venous plasma. These parameters are the strong ion difference (SID), which summarises the strong or fully dissociated electrolytes, the total weak acid concentration (Atot), which summarises the non-volatile weak or partially dissociated electrolytes, and the partial pressure of carbon dioxide (PCO2). It is these 3 independent variables that control [H+].
Basic equation such as below should feature:
[SID] = [Na+] + [K+] + [Ca2+] + [Mg2+] - [CL-] - [Other Strong Anions/lactate].
[ATOT] = [PiTOT] + [PrTOT] + albumin.
b)
Classification of Primary Acid–Base Disturbances
Respiratory ↑ PCO2 ↓ PCO2
Non-Respiratory
a. Abnormal SID
i .Water excess/deficit ↓ SID, ↓ [Na+] ↑ SID, ↑ [Na+]
ii. Imbalance of strong anions
Chloride excess/ deficit ↓ SID, ↑ [Cl-] ↑ SID, ↓ [Cl-]
Unidentified anion excess ↓ SID, ↑ [XA-]
b. Non-volatile weak acids
i. Serum albumin ↑ [Alb] ↓ [Alb]
ii. Inorganic phosphate ↑ [Pi] ↓ [Pi]

Indicate essential points to achieve pass:

Clear description of the quantitative approach. This question is not intended to be answered at PhD biochemistry level but rather at a level that demonstrates a good consultant understanding of the issues e.g. if asked by a visiting team about quantitative acid-base.

Examiners' comments: Candidates were not expected to have an advanced knowledge of biochemistry but an overall understanding of the principles involved e.g. to allow an explanation of the issues to colleagues.

## Discussion

A concept requiring a 504-page book to explain needs to be compacted into a 10-minute exam answer. The college has this editorial from 2004 on their site, titled "What exactly is the strong ion gap and does anybody care?"

In its briefest form:

• The acid-base system is an interaction of several variables
• There are independent variables, which can be altered from outside the system.
• There are dependent variables which are altered by changes in the independent variables.
• pH and HCO3- are dependent variables.
• The independent variables are:
• SID - the strong ion difference
• ATOT - the total weak acid concentration
• PaCO2
• Thus, changes in any of the independent variables can cause a change in pH and HCO3-, i.e. acidosis and alkalosis.

Thus, acid-base disorders can be classified as:

• Respiratory: increased or decreased PaCO2
• SID changes:
• due to excess or deficit of water
• due to excess or deficit of strong ions
• ATOT changes: excess or deficit of inorganic phosphate or albumin

• Quantitative mathematical explanation of acid-base disorders
• A more scientific approach - applies the concepts of physical chemistry to traditional acid-base concepts
• Accessible, logical framework for the design of resuscitation fluids

• Complex
• Substantially different to the well-validated classical approach; thus, produces confusion
• Numerous variables, each measured with a small error, are combined- thus amplifying the measurement error
• Fails to incorporate the buffering contribution of haemoglobin
• No evidence that this approach has any influence on mortality

### References

References

Morgan, T. J. "What exactly is the strong ion gap, and does anybody care?" Critical Care and Resuscitation (2004) 6: 155-166.

Sirker, A. A., et al. "Acid− base physiology: the ‘traditional’and the ‘modern’approaches."  Anaesthesia 57.4 (2002): 348-356.

Story, D. A., S. Poustie, and R. Bellomo. "Quantitative physical chemistry analysis of acid− base disorders in critically ill patients." Anaesthesia 56.6 (2001): 530-533.