Quantitative Acid-Base Chemistry
& Acid-Base Physiology
(They are not the same)
P Wilkes MD, PhD, FRCP
University of Ottawa Heart Institute
Guiding Principles
Physiology will not violate the laws of
chemistry and physics
 There is a difference between cause and
effect vs. correlation (physics vs. math)
 In many ways – you do not know anything
unless you know everything

(If the devil is in the details – so is salvation)
Learning Objectives
The Chemistry
 The Physiology
 The Clinical Approach

The ‘Chemistry’ in the Text Books
‘The CO2 Hydration Reaction’
Chemical Description:
CO2 + H20
H2CO3
HCO3- + H+
Mathematical Description, the
Henderson-Hasselbalch equation:
pH = pK + log [HCO3-]
(.PCO2)
[HCO3-]
Resp acidosis
PCO2=60
PCO2=40
Metab alkalosis
30
PCO2=30
24
Metab acidosis
Resp alkalosis
14
7.0
7.4
7.6
PCO2=60
30
[HCO3-]
PCO2=40
Hg
PCO2=30
24
14
7.0
pH
7.4
7.6
BE = (1-0.014Hgb)(HCO3-24)+(1.43Hgb +7.7)(pH-7.4)
PCO2=40
PCO2=30
30
[HCO3-]
24
Base
Excess
Measured
Decrease
in [HCO3-]
14
7.0
pH
7.4
7.6
CO2 Hydration Reaction
What is the pH of water equilibrated to PCO2 =
40 mmHg?
? 7.4
? Higher
? Lower
 Answer 4.4
 What is the HCO3?
? 24 mEq/L
? Higher
? Lower
 Answer < 1 mEq/L

What is Going On?
 The
Problem:
The CO2 hydration reaction does not
predict what we measure in blood!!
Nevertheless, the HendersonHasselbalch equation does??
 The Answer:
The CO2 hydration reaction is either
wrong or incomplete
Modern Quantitative Acid – Base
Chemistry
(The Real Chemistry)
Can J Physio Pharmacol 61: 1444 - 1461, 1983
Peter A Stewart
Physical Chemistry of CO2 and Water
Condition:
Equations:
At pH 7.4
(i.e. [H+] = 4x10-5 mEq/L)
HCO3 = 24 mEq/L
How do you account
for electrical neutrality?
Solving:
PCO2 = 40 mmHg
[H+][OH-] = K’w
CO2(K1) = [HCO3-][H+]
[HCO3-](K2) = [CO3=][H+]
[H+] - [HCO3-] - [CO3=] - [OH-] = 0
[H+] = 0.036 mEq/L, pH = 4.44 !!
[HCO3-] = 0.036 mEq/L
[CO3=] and [OH-] < 1 x 10-6 mEq/L
[H+], [HCO3-], [CO3=], [OH-] are determined ONLY by PCO2 &
Dissociation Constants
How to Make Bicarb ?
NaOH = 5
HCO3 mmol/L
40
30
NaOH = 20
20
NaOH = 40
10
0
0
10
20
30
PCO2 (mmHg)
40
Necessary Condition
50
[fixed60+ charge]
&
PCO2
The Fixed Positive Charge and Other Acids



Plasma [Na+] + [K+] – [Cl-]
140 mEq/L + 4 mEq/L – 100 mEq/L
~ 44 mEq/L positive charge
This is the Strong Ion Difference (SID)
Other Acids ?




Albumin
Phosphate
Albumin + Phosphate = [Atot]
~ Total Protein (g/L) x 0.25 = Atot (mEq/L)
The Chemically Complete
Solution
 Multiple
components
CO2 hydration reaction
Weak Acids (Blood is thicker than water)
Electrical Neutrality
 Systems Approach:
Solve All Equations Simultaneously
Independent vs. Dependent Variables
Water dissociation equilibrium
[H+] x [OH-] = K’w
Weak acid dissociation equilibrium
[H+] x [A-] = KA x [HA]
Conservation of mass for “A”
[HA] + [A-] = [ATOT]
Bicarbonate ion formation equilibrium
[H+] x [HCO3-] = KC x pCO2
Carbonate ion formation equilibrium
[H+] x [CO32-] = K3 x [HCO3-]
Electrical neutrality
[SID] + [H+] - [HCO3-] - [A-] - [CO32-] - [OH-] = 0
SID – HCO3 – [A-] ~0
Na + K – Cl – HCO3 ~ [A-] (Is this familiar?)
[A-] is the anion gap
• Only the whole set of six equations
can explain the quantitative
properties of the system, and
permit evaluation of any of the
dependent variables
• No one of the six equations is
more, or less, important than the
others. All six are essential
Solve for [H+] and get a big wet kiss:
Please put away all calculators, you have 30
seconds beginning now
[H+]4 + {KA+[SID]} [H+]3 +
{KA([SID]-[Atot])-(K1.CO2+K’w)} [H+]2 {KA(K1.CO2+K’w)+K2.K1.CO2} [H+] KA.K2.K1.CO2 = 0
A[X]4 + B[X]3 + C[X]2 + D[X] + E = 0
A Fourth Order
Polynomial !?!
DUOH !?!
Now what do I do??
I know – Use a computer ! ?
Insert:
SID = Na+K-Cl = 140 + 4 -100
= 44 mEq/L
PCO2 = 40 mmHg
Tprot = 80 g/L = 20 mEq/L
[H+]4 + {KA+ [44] } [H+]3 +
{KA( [44] - [20] )-(K1.40+K’w)} [H+]2 {KA(K1.40+K’w)+K2.K1.40} [H+] KA.K2.K1.40 = 0
[H+] = 3.98 x 10–8
-Log 3.98 x 10-8 = 7.4
Why Does the Henderson-Hasselbalch Equation
Seem to Work?
Water dissociation equilibrium
[H+] x [OH-] = K’w
Weak acid dissociation equilibrium
[H+] x [A-] = KA x [HA]
Conservation of mass for “A”
[HA] + [A-] = [ATOT] (20 mEq/L)
Bicarbonate ion formation equilibrium
[H+] x [HCO3-] = KC x pCO2 (40 mmHg)
Carbonate ion formation equilibrium
[H+] x [CO32-] = K3 x [HCO3-]
Electrical neutrality
[SID] (44 mEq/L) + [H+] - [HCO3-] - [A-] - [CO32-] - [OH-] = 0
[H+] is determined by SID, PCO2 and Atot
[H+] = 3.98x10-8 Eq/L (pH=7.4) in all 6 equations only if
SID=44 mEq/L, PCO2=40mmHg and Atot=20 mEq/L
Therefore [HCO3] must be ~ 24 mM/L
(math not chemistry)
Paradigm Shift
[H+] = 3.98 x 10-8 Eq/L (i.e. pH=7.4) AND HCO3 = 24 mmol/L because:
SID = 44 mEq/L
PCO2 = 40 mmHg
Tprot = 80 g/L (~20 mEq/L)
1) [H+] and [HCO3] DO NOT INFLUENCE EACH OTHER
2) The CO2 hydration reaction:
a) incomplete chemical description of the system
b) predicts acid-base but does not offer a cause/effect explanation
3) You must understand normal acid-base before you can understand
abnormal acid-base
Does the Equation Work?
pH Calculated
7.7
7.6
y = 1.1101x - 0.8447
7.5
R2 = 0.8092
7.4
7.3
7.2
7.1
7.2
7.3
7.4
7.5
7.6
7.7
pH Measured
(Wilkes AJP:1998)
Independent vs. Dependent
In Vitro
In Vivo
Independent
CO2
Na+, Cl-
PCO2 = ƒ(VCO2, VA)
SID = ƒ(dIn/dOut, Vd), Na, Cl
Atot = ƒ(dIn, dOut, Vd)
Dependent
Protein
H, HCO3, CO3, Prot, ProtH, OH
(not functions of dIn, dOut or Vd)
Summary
Cause and Effect
[OH-]
PCO2
[SID]
[Tprot]
[H+]
[H+] = ƒ([SID], PCO2, [Tprot])
[HCO3-]
A(X)4 + B(X)3 + C(X)2 + D(X) + E = 0
[CO3=]
[Prot.H]
[Prot-]
Conceptual Consequences
The model predicts what we measure
 H+ and HCO3 are both determined by
chemistry IN PLASMA, NOT physiology
 H+ and HCO3 are not determined by intake
or loss – the kidney is irrelevant!!
 What does physiology control?
1) The concentrations of Na, K, Cl
and thus the strong ion difference
2) PCO2
3) Total weak acid concentration

Influence of [SID]
[Na+] = 137 mEq/L
[K+] = 4 mEq/L
[Cl-] = 105 mEq/L
[SID] = 36 mEq/L
PCO2 = 40 mmHg
[Tprot] = 80 g/L
[Na+] = 143 mEq/L
[K+] = 4 mEq/L
[Cl-] = 96 mEq/L
[SID] = 51 mEq/L
PCO2 = 40 mmHg
[Tprot] = 80 g/L
pH = 7.29
[HCO3-] = 20 mEq/L
[Prot-] = 16 mEq/L
pH = 7.51
[HCO3-] = 34 mEq/L
[Prot-] = 17 mEq/L
‘Electrolyte’ Acidosis
Usually iatrogenic
Assumed to be ‘benign’
However:
Gut hypoperfusion/Post Op N/V
(Gan, Anesth.1999; Williams, Anesth Analg. 1999)
Impaired Renal Blood Flow, GFR
(Wilcox, J Clin Invest, 1983)
Difficulty diagnosing Lactacidosis?
First Patient
 74
yo male, 48 hrs post MI, on BIPAP
 S. aureus infection, osteomyolytis (by
MRI for neck pain) vs. endocarditis (by
ECHO)
 Mod MR, EF 50%, no inotropes, stable
BP (No Swan)
 COPD, DM, Creat 173
 7.29/42/80/20/-6.7
AG = 15
 Are you worried ?
First Patient: Approach
Electrolytes:
Na = 132, K = 4.9, Cl = 102
SID = 34 mEq/L
 Total Protein:
64 g/L ~ 15 mEq/L
 Electrical Neutrality:
SID – HCO3 – Prot- ~ 0
34 - 20
- 15 = -1
 Lactate = 1.5 mEq/L
 Electrolyte based acidosis, low SID

SID and Acid-Base
160
160
140
120
100
80
[Prot-]
140
[HCO3-]
120
80
[Cl-]
[Na +]
60
40
40
20
20
0
0
Cations
[HCO3-]
100
[Na +]
60
[Prot-]
Anions
Very common cause of met acidosis
Iatrogenic hyperchloremic metabolic acidosis
How does this occur?
[Cl-]
Cations
Anions
Influence of Plasma Protein
Normal Protein = 80 g.L-1
SID = 44 mEq.L-1
PCO2 = 40 mmHg
pH = 7.42
[HCO3-] = 27 mmol.L-1
[Prot-] = 16.8 mEq.L-1
Low Protein = 40 g.L-1
SID = 44 mEq.L-1
PCO2 = 40 mmHg
pH = 7.533
[HCO3-] = 35 mEq.L-1
[Prot-] = 8.7 mEq.L-1
Hypoproteinemic Metabolic
Alkalosis
160
160
140
120
100
Prot-
140
HCO3
120
100
80
60
ProtHCO3
80
Na
Cl
60
40
40
20
20
0
0
Cations
Anions
Na
Cl
Cations
Anions
Hypoproteinemia
 Decrease
in COP (Schupbach et al., Vox Sang
35:332, 1978; Zabala Ann Ital Chir LXIV 4:387, 1993)
Fluid Shifts/Retention
 Glomerular Filtration Pressure

 Metabolic Alkalosis (McAuliffe et al., Am J Med
81:86, 1986)
Consequences of
Hypoproteinemic Metabolic
Alkalosis
Hypoventilation (McAuliffe AJM, 1986)
Hyperventilation ! (Rossing, J Lab Clin Med, 1988)
Difficulty assessing acid-base status
Anion gap = (Na + K – Cl – HCO3-) = ProtHides lactacidosis
Case #3: POD #1 2200 hr,
Emergency CABG
 LV
III, Inotropic support, IABP
 105/60, 38/20, CI = 2.0, SVR = 1200
 ABG = 7.45/40/155/29/-2.2
 Anion gap = Na + K – Cl – HCO3 = 17
 Are you concerned ?
Third Patient: Approach
Step 1: Electrolytes and SID
Na = 139
K = 3.5
Cl = 96
SID = 46 mEq/L
Step 2: Total Protein = 40 g/L
Convert to mEq/L: 40 g/L x 0.25 = 10 mEq/L
Third Patient: Approach
Step 3: Electrical Neutrality
SID – HCO3 – Prot- ~ 0 + 5 mEq/L
46.5 – 29 – 10 = 7.5 mEq/L
Either:
Lab variation (~ 2%)
Unmeasured acid
Lactate = 8 mEq/L (Type A)
Dead gut on laparotomy
The Danger of Hypoproteinemic
Alkalosis
160
160
140
-
[Prot ]
120
[HCO3-]
100
80
140
[Prot-]
120
[Lact-]
[HCO3-]
100
[Na +]
60
80
[Cl-]
60
40
40
20
20
0
0
Cations
Anions
[Na +]
[Cl-]
Cations
Anions
How does Stewart approach affect
concept of Anion Gap ?
160
140
120
SID
Prot AG
HCO3
100
80
60
Na
Cl
Cations
Anions
40
20
0
AG = Na+K-Cl-HC03
= [Prot-]
= [A-]
from [HA]Ka = [A-][H+]
[Atot] = [HA] + [A-]
[A-] = KaAtot
Ka+[H+]
Therefore: AG can be
measured directly
How does the Stewart approach affect
concept of BE?




From BE = (1-0.014Hgb)(HCO3-24)+(1.43Hgb +7.7)(pH-7.4)
BE = 0 when pH = 7.4 and [HCO3] = 24
From Stewart:
pH and [HCO3] are dependent upon prevailing PCO2, SID and Atot
Therefore BE is also a function of PCO2, SID and Atot
Atot and SID can both be altered by pathophysiology such that
neither pH or HCO3 change
Both Atot and SID should be assessed during a clinical evaluation
Information from BE
BE = (1-0.014Hgb)(HCO3-24)+(1.43Hgb +7.7)(pH-7.4)
HgB = 14
pH = 7.4
HCO3 = 24
PCO2 = 40
BE = 0
Na = 140
K=4
Cl = 100
AG = 16
SID = 44
Tprot = 20 mEq/L
SID-HCO3-TP~0
44 – 24 – 20 ~ 0
pH = 7.3
HCO3 = 16
PCO2 = 30
BE = -9.2
Na = 140
K=4
Cl = 100
AG = 24
pH = 7.24
HCO3 = 16
PCO2 = 35
BE = -10.9
Na = 130
K=4
Cl = 105
AG = 9
Lact = 10
SID = 44 (-10)
Tprot = 20 mEq/L
SID-HCO3-TP~0
34 – 16 – 20 = 2
SID = 29
Tprot = 15
SID-HCO3–TP~ 0
29 – 16 – 15 = -2
Lact = 0
pH = 7.38
HCO3 = 25
PCO2 = 40
BE = +1.2
Na = 140
K=4
Cl = 100
AG = 15
SID = 44
Tprot = 10 mEq/L
SID-HCO3-TP~10
44 – 25 – 10 = 9
Lact = 10
Model Summary
SID (electrolyte or metabolic) 
SID (electrolyte)

acidosis
alkalosis
Weak acid (protein)
(Weak acid (phos-, protein)


alkalosis
acidosis)


acidosis
alkalosis
PCO2
PCO2
Compensatory Responses

Metabolic acidosis

Metabolic alkalosis
 2nd low protein

2nd increased SID

Respiratory acidosis

Respiratory alkalosis
Hyperventilate
Lower PCO2
Decrease SID
by increase Cl
Hypoventilate
Increase PCO2
Increase SID by
decreasing Cl
?increase protein
?decrease SID
Permissive Hypercapnia
(Wilkes, unpublished)
PCO2 (mmHg)
100
90
80
70
60
50
40
30
20
10
0
[HCO3-] (mEq/L)
[SID] (mEq/L)
0
5
10
15
Days
20
25
30
Permissive Hypercapnia
mEq.L-1
(Wilkes, unpublished)
160
140
120
100
80
60
40
20
0
[Na+],(mEq/L)
[Cl-], (mEq/L)
[SID], (mEq/L)
0
5
10
15
Days
20
25
30
Respiratory Acidosis

Compensatory response to
hypercapnea in severe COPD is to
increase SID by lowering Cl (Alfero 1996)
Influence of [Atot] on [SID]
160
[Na+]=0.18[Atot]+134.6
-1
[Na ], [Cl ], [SID] (mEq.L )
(Wilkes AJP 1998)
140
120
-
[Cl ]=-0.66[Atot]+110.7
100
+
-
80
[SID]=0.99[Atot]+24.7
60
40
20
8
10
12
14
Atot (mEq.L-1)
16
18
20
Influence of [Atot] on [Prot-], [HCO3-]
and [H+]
+
40
-
[Prot ], [HCO3 ], [H ]
50
-
60
[H+], nEq.L-1
30
[HC03-], mEq.L-1
20
[Prot-], mEq.L-1
10
0
8
10
12
14
16
-1
Atot (mEq.L )
18
20
The Law of Electrical Neutrality
A Law of Physics – it ALWAYS exist
SID + H+ - HCO3- - Prot- - Phos- - CO3= - OH- =0
SID – HCO3- - Prot- - Phos- ~ 0
{HCO3- + Prot- + Phos-} ~ SID
{HCO3- - Prot- - Phos-} ~ {Na + Mg + Ca + K – Cl – Lact}
What if electrical neutrality APPEARS not to exist?
Influence of Apparent Charge Imbalance
[SID] - [HCO3-] - [Prot-] ~ 0
(Wilkes, AJP, 1998)
0.3
y = -0.0146x + 0.0214
R2 = 0.8599
pH(msd-calc)
0.2
0.1
if UMI = 0, dpH = 0.0214
0
-0.1
-0.2
-0.3
-15
-10
-5
0
5
10
Un-Measured Ions (UMI), (mEq/L)
15
20
Explanations of The Strong Ion Gap
SID + H+ - HCO3- - Prot- - CO3= - OH- =0
SID – HCO3- - Prot- = 0
SID = HCO3- + ProtIf SID = HCO3- + Prot- (Strong Ion Gap)?
1.
2.
Measurement error (Na, Cl + 2%) (Jones 1993)
Error of omission - lactate, ketoacids,
krebs cycle intermediates (Gilfix 1993, Forni 2005,
Moviat 2008)
3.
Ionic concentration vs. activity (Stewart 1978)
Acids – Bases & Salts & Ionic Activity
If NS is equal parts Na and Cl (SID=0) how
can you explain the pH = 5.5?
1) Electrical neutrality refers to ionic
activity (functional concentration) not
ionic concentration (actual concentration)
2) NS is also equal parts HCl and NaOH
and HCl is a stronger acid than NaOH is
base (Wilkes, 2009)
Strong Ion Gap (SIG)
In the Critically Ill (Kellum 1998)

Increased SIG in pts with:
 Sepsis (Reeves, 1983, Mehta 1986)
 Liver disease (Kellum 1995, Kirschbaum 1997)
 Critical illness (Mehta 1986)
 Animal studies with endotoxemia (Kellum
1995)
Critically ill pts with ARF (Rocktaeschel 2003)
 May be a predictor of mortality (Kellum 2004)

Clinical Outcome
(Gunnerson CC: 2005)
Definitions of Acid-Base Disturbances
Consistent definitions are a necessity to
assess incidence and outcome
 Respiratory disturbances are straight
forward
 Metabolic acidosis secondary to high
chloride is not equivalent to high lactate
 Organic vs. electrolyte
 Metabolic alkalosis from elevated SID or
hypoproteinemia
 Organic vs. electrolyte

SID and the ICU
Need to define acid-base disorders
based on physical principles, not HCO3
and H+
 Clinical outcome may be a function of
underlying physical principle more so
than the actual pH
 Need to define what is normal for a
given population
 We still do not have a complete
understanding of the physical chemistry

Basic Clinical Approach at 02:00




pH=7.05, HCO3=12, BE=-12, PCO2=30
ETT, O2, #14 iv and volume, inotropes, Sx and/or antibx
Most other cases
Measure electrolytes – calculate SID
Normal is 40-44 mEq/L
Measure TPrt x 0.25 = Atot (mEq/L)
Estimate electrical neutrality from
[SID] – Atot – [HCO3] + 5
If >5 then check lactate
If lactate normal then +SIG (equally bad)
Case 2: POD # 0, Elective CABG



PMHx:
79 yo male with peripheral, cerebral vascular
disease
Intra Op:
SVG x 2, off CPB with mil/levo
increased abdominal girth
CI=1.8, SVR=1477, BP=115/55, Ppa 50/20
7.35/36/104/20/-5.4
AG = 9.2
Are you worried ?
Second Patient: Approach
1) Electrolytes:
Na = 136
K = 5.2
Cl = 112
SID = 29.2 mEq/L
2) Total Protein = 33 g/L ~ 7.6 mEq/L
3) Electrical Neutrality:
29.2 – 20 – 7.6 = 1.6 mEq/l
4) Lactate = 2 mEq/L
5) Compensated hypoproteinemic alkalosis
(Wilkes, AJP, 1998)
Questions