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The Theoretical
Bases of Indirect Calorimetry:
A Review
Eleuterio Ferrannini
Indirect calorimetry is the method by which the type and rate of substrate utilization, and energy metabolism are estimated
in vivo starting from gas exchange measurements. This technique provides unique information, is noninvasive. and can be
advantageously combined with other experimental methods to investigate numerous aspects of nutrient assimilation,
thermogenesis, the energetics of physical exercise. and the pathogenesis of metabolic diseases. Since its use as a research
tool in metabolism is growing, the theoretical bases of indirect calorimetry are here reviewed in a detailed and orderly
fashion. Special cases, such as the occurrence of net lipid synthesis or gluconeogenesis, are formally considered with
derivation of explicit stoichiometric equations. The limitations of indirect calorimetry, both theoretical and technical, are
discussed in the context of circumstances of clinical interest in metabolism.
B 1988 by Grune & Stratton, Inc.
or the measurement of
metabolic free energy conversion, was developed at the
turn of the century’s2 as an application of thermodynamics to
animal life. Indirect calorimetry is the method by which
metabolic rate is estimated from measurements of oxygen
(0,) consumption and carbon dioxide (CO,) production.
Although it has long been recognized that indirect calorimetry can also provide information on the type and rate of
substrate utilization in vivo, 3 it is only recently that this
technique has been applied to clinical circumstances such as
acute illness and parenteral nutrition.4 Indirect calorimetry
has shed light on various aspects of nutrient assimilation,5m’5
thermogenesis,‘62’ the energetics of physical exercise,22ez4
and the pathogenesis of obesity23-35and diabetes.36-40The use
of indirect calorimetry in metabolic investigation is now
growing rapidly. Technology has made it possible to adapt
the technique to the sensitivity and time scale required for
long-term studies in humans.4’-44 At the present time, the
quality of information and the noninvasiveness of indirect
calorimetry make it easy to predict that it will gain increasing Favor among clinicians and clinical investigators.
The premise of the present review is that indirect calorimetry is not just a research method but a theory. As such, it
utilizes models and assumptions, of which one might not
always, or not entirely, be aware. While much of the information that follows can be recovered from specific literature
sources,6.45-50it may nevertheless be useful to lay out the
theoretical bases of indirect calorimetry in a simple and
orderly pattern, alerting the unfamiliar reader to those points
where an assumption creeps into the reasoning. The overall
purpose is to critically evaluate what indirect calorimetry can
do, with what limitations, and under what circumstances of
clinical interest in metabolism.
The ultimate goal of nutrient metabolism is to produce
energy. The most common way of extracting the chemical
energy of a substrate is to completely oxidize it to carbon
dioxide and water. The final common pathway of all cellular
fuels, ie, carbohydrates, fats, and proteins, therefore is
oxidation. The heat generated by biologic combustions is
utilized to maintain body temperature. Because of its isothermia, however, the body cannot use heat to perform work. The
chemical energy of oxidizable substrates is therefore transferred on to some all-purpose carriers, which bring the free
Vol 37,
No 3 (March), 1988: pp 287-301
energy to where it is needed. Chemical (biosyntheses),
osmotic (active transports), and mechanical (muscular contraction) work is thus made possible.
Although biochemical reactions in vivo flow through intricate networks of dynamic states,j’ the basic laws of equilibrium thermodynamics still apply to energy metabolism in
living organisms. Thus, energy can neither be created nor
destroyed, but can only be exchanged between the body and
its environment (first principle of thermodynamics). The
second principle of thermodynamics is illustrated in box 1 in
simple words: any change in the total energy content of a
system (eg, the heat of combustion in a biologic oxidation)
results in a change in both the free energy and the entropy of
the system. Since only the former can be utilized to perform
work of any kind, energy-yielding reactions invariably have
an efficiency (AG/AH) of less than 100%.
Box 1
(H) = total heat content of a substance or physical system
(S) = degree in which the total energy of a
system is uniformly distributed (randomness) and thus unavailable to do work
Free energy (G) = orderly energy, capable of doing work
Equation A:
AH = AG + TAS (where T is temperature)
In a biochemical reaction in which two reactants are
transformed into products, the change in free energy is
related to the concentrations of both reactants and products
as shown in box 2.
Equation B:
AG = AGo + RT In K’,
From the C.N.R. Institute of Clinical Physiology and the Second
Medical Clinic, University of Piss, Italy.
Address reprint requests to E. Ferrannini. MD, C.N.R. Institute
of Clinical Physiology, Via Savi. 8, 56100 Pisa. Italy.
Q 1988 by Grune & Stratton, Inc.
where T
gas constant
equilibrium constant = [prod] / [react]
standard free-energy change
Box 3
The ATP system (for a 70-kg adult)
Turnover rate = 1.3 mmol/min kg (or 66.4 kg/d)
Whole-body pool = 1.2 mmol/kg (or 42.6 mg)
Residence time (= pool/turnover rate) = 0.9 min
For AG = 0, we get
Equation C:
AGo (in vitro) = - 7.3 kcal/mol
AG” (in vivo) = - 12.5 kcal/mol
AG” = -RT In K’, = ZA”prod - LZAGVeact
Equation B says that the change in the free energy of a
reaction is related to the equilibrium constant of the reaction
through the standard free-energy change. The latter is a
constant for any given reaction, is defined as the free-energy
change occurring under standard concentration, temperature, and pressure conditions at the equilibrium point (ie,
AG = 0), and is inversely related to the equilibrium constant.
As depicted in Fig 1, equilibrium constants greater than 1
are associated with negative free-energy changes, ie, the
reaction produces energy (exergonic),
whereas energy-requiring
(endergonic) reactions absorb
energy. The standard free-energy change can also be viewed
as the difference between the sum of the free-energies of the
products and that of the reactants, all in standard state
(equation C).
As already mentioned, the chemical energy of a nutrient
liberated by oxidation is in part lost as heat and in part
trapped in a variety of so-called high-energy compounds, the
most important of which is ATP. Energy-rich phosphate
bonds are present in many biomolecules, but ATP is special
among them because its very function is energy transfer.
Thus, ATP accepts energy from richer compounds (eg,
phosphoenolpyruvate) as it is formed starting from ADP and
inorganic phosphorus, and donates it to less energized substrates (eg, glucose) through hydrolysis of its phosphate
group (back to ADP and inorganic phosphorus). As would be
expected of a carrier molecule, ATP has a very high turnover
rate and a small body pool (box 3).
Thus, a normal adult body contains only 42.6 mg of ATP
in the various water compartments, but this small pool is
completely renewed in less than one minute, so that during
24 hours an amount of ATP almost equal to body weight is
turned over.52Clearly, a system with these kinetic characteristics cannot serve as a reservoir, and in fact it is phosphocreatine that takes on this role by freely exchanging with
ATP. Thus, phosphorylation-dephosphorylation
of creatine,
which is abundant is vertebrate muscle and nerve tissue, is
the mechanism that the body relies on to store excess energy
and to finance energy debts in the longer term.
One important consideration is the standard free-energy
change (AGO) for the hydrolysis of ATP to ADP and
phosphorus, or, in other words, the amount of energy that is
packed in the phosphate bond of ATP. When directly
measured or indirectly estimated in vitro, this amount is
- 7.3 kcal/mol.53 Under the conditions of pH, temperature,
and concentrations prevailing within the cell, however, the
AGo of ATP hydrolysis is much higher, an average, roundedoff value being - 12.5 kcal/mol.54
Another point to keep in mind is that the enzymatic
reactions by which energy is transferred to ATP are subjected to multiple regulation, and ATP itself, along with pH,
magnesium, ADP, and inorganic phosphorus, is an allosteric
regulator of many involved enzymes.
The notions so far recalled, which can be found in any
textbook of biochemistry (eg, reference 54), are necessary
and probably sufficient to understand the rationale of the
measurement of in vivo energy metabolism, that is, calorimetry.
Fig 1. Relationship between the standard free-energy change
of a reaction and its equilibrium constant (K’eq = (C + D)/(A + 6)
for a reaction A + B = C + D).
Direct calorimetry measures total heat loss from the body;
indirect calorimetry measures total energy production by the
body. With the former, the subject is placed in a thermically
isolated chamber, and the heat that he/she dissipates (by
evaporation, radiation, and conduction/convection)
is accurately collected and precisely measured.48 Indirect calorimetry, on the other hand, really measures O2 consumption and
CO2 production. On the assumption that all the oxygen is
used to oxidize degradable fuels and all the CO, thereby
evolved is recovered, it is possible to calculate the total
amount of energy produced. It should be clear that “energy
production” means conversion of the chemical free-energy of
nutrients into the chemical energy of ATP plus loss of some
energy during the oxidation process. Eventually, however, all
energy will be converted into heat. In this sense, therefore,
0, if derived from glucose, 3.93 L if obtained from palmitate,
and 4.96 L when protein is the substrate. Another way of
looking at the same fact is to calculate the caloric or ATP
equivalents of 0, (last two columns in Table l), that is, how
much energy or ATP we can generate with 1 L (or 1 mol) of
OZ. Again we find that glucose has the highest equivalent
followed by palmitate and protein. These calculations thus
demonstrate an important physiologic concept, that is, the
most efficient way of utilizing 0, to produce usable energy
(=ATP) is to oxidize glucose; fat and protein oxidation are
more costly in terms of OXcurrency.
The next step is to write the stoichiometry of the three
oxidative reactions (box 4).
heat and energy can be used as synonyms. Any heat dissipated internally to increase body temperature or accumulated in the form of energy-rich chemical bonds is not “seen”
by direct calorimetry. In the long run, however, (practically,
longer than 24 hours), the two techniques give convergent
estimates because: (1) the rates of formation and degradation of energy-rich bonds will be equal, and (2) all changes in
body temperature will cancel out. Under conditions of
unchanging temperature and energy store repletion, direct
and indirect calorimetry simply look at the two sides,
removal and production, respectively, of the heat balance
The Principle
Box 4
To fully appreciate the rationale as well as limitations of
indirect calorimetry, it is important to distinguish what is
measured from what is estimated; measurements, in fact, are
only fraught with experimental, random error, whereas
estimation calls on assumptions, which may introduce conceptual, systematic errors.
Indirect calorimetry measures gas exchange, ie, wholebody O2 uptake and CO, release. The next steps can be
illustrated with the help of Table 1. When 1 mol of either of
the three main fuels (glucose, palmitate, and amino acidsThe stoichiometry of protein oxidation varies within a narrow range according to the amino acid composition of a given
protein. The coefficients used are those of Consolazio et al.55)
is burnt up in a calorimetric bomb, the volumes of O2 used
and CO1 released and the amount of energy liberated as heat
(AC”) are those given in the corresponding columns of Table
1. The respiratory quotient (RQ, or the ratio of CO* to 0,) is
1.00 for glucose, 0.70 for fats, and 0.80 for proteins. When
the same oxidative reactions occur in the body, the amounts
of energy harnessed as chemical energy in ATP are given in
the “net ATP yield” column. Since, as previously mentioned,
the AGo of ATP in vivo is - 12.5 kcal/mol, one can assess the
efficiency with which the energy in the starting fuel is
conserved in ATP by multiplying the net ATP yield by 12.5
and dividing the result by the AG” of each fuel. We thus find
that glucose and palmitate are used with a net efficiency of
about 68%, amino acids with one of 61%; the differences,
32% and 39%, respectively, are lost as heat during the
oxidative process. We then calculate the cost of the ATP
generated in each oxidation both in terms of energy and in
terms of O2 used (Table 1). We find that the caloric cost of
ATP is higher for proteins than for either glucose or palmitate. Even more strikingly, each mole of ATP costs 3.72 L of
1 g Glucose (G) + 0.746 L 0,
+ 0.6gHz0
1 g Lipid (L) + 2.029 L 0,
1.430 L CO, t I .09 g HZ0
1 g Protein (P) + 0.966 L O2
0.782 L CO, + 0.45 g HZ0
Since nitrogen is about 16% of protein by weight, or
P = 6.25 x urine nitrogen (I$
one has:
1 gN + 6.04L0,+4.89LCOZ
+ 2.81gHz0
From 1,2, and 3 it follows:
CO, = 0.746 G + 2.029 i + 6.04 ti
?COZ = 0.746 G + 1.430 i + 4.89 i
Solving the system of equations 4 and 5:
G = 4.55 +COZ - 3.21 $0, ~- 2.87 Y?
With a few simple passages, equations 6 and 7 are derived,
which, having measured O2 consumption (.irOJ, CO, production (VCO,), and urinary nitrogen excretion (a), allow
one to estimate the amounts of glucose and lipid (a standard
oxidized by the body.
An alternative way of carrying out these calculations is to
Table 1. Energy Balance Sheet for the Three Main Fuels
0, Used
Oxidized Fuel
(1 mall
Amino acidst
CO, Produced
Caloric Cost
Oxygen Cost
Caloric Equivalent
of ATP
of ATP
of 0,
of 0,
Net ATP Yield
*Complete oxidation of glucose yields 38 mol of ATP per mol of glucose, but 2 ATP mol are used up during glycolysis.
ATP Equivalent
oxidation of amino acids yields 28.8 mol ATP, but 5.8 mol are consumed in the process.
first derive the nonprotein RQ from equations 4 and 5 (ie,
NPRQ = @CO, - 4.89 N)/(QOz - 6.04 I$), and then
read off the corresponding amounts of oxygen used for
glucose and lipid oxidation in ad hoc tables (eg, reference
Once the rates of glucose, lipid, and protein oxidation have
been computed, the total rate of energy production can be
estimated directly by taking into account the caloric equivalent of the three substrates (ie, the standard free-energy
changes associated with their oxidation, Table I). For simplicity, the caloric equivalents are given in box 5 in the same
units as the substrate oxidation rates (ie, per gram of
Box 5
Caloric equivalents of fuels:
Glucose (mol wt 180)
= AGE = - 3.74 kcal/g (= - 15.65 kJ/g)
Fat (mol wt 861) = AG: = -9.50 kcal/g (=-39.75
Protein (mol wt 116)
= AG; = -4.10 kcal/g (=-17.15
Energy Production Rate (EPR)
= GAG; + ~AG; + PAG;
From equations 3’, 6,7, and 8, one has:
= 3.91 VO, + l.10iC02
- 3.34 k
The molecular weight indicated is that of an average
constituent amino acid.45.55It should be noted that 1 g of
protein (heat of combustion = 5.65 kcal/g) upon hydrolysis
yields 1.15 g of constituent amino acids. Furthermore, urinary nitrogenous compounds (urea, uric acid, creatinine,
creatine, ammonia, etc) have an average heat of combustion
of 7.89 kcal/g N (or 1.26 kcal/g of protein oxidized). The
metabolizable energy of protein would therefore be 4.39
kcal/g.56 The metabolizable energy of free amino acids
derived from either endogenous or dietary protein is 4.39/
1.15 = 3.82 kcal/g, from which the heat of hydrolysis (0.03 1
kcal/g) must be substracted. The value of 4.1 kcal/g here
used assumes equal contribution of protein and free amino
acids to total protein oxidation.55
Two comments are in order here. First, the rate of energy
production obtained by indirect calorimetry is most often
referred to as energy expenditure. This is somewhat of a
misnomer because indirect calorimetry measures respiratory
gas exchange and estimates energy production. Obviously,
production and expenditure will be equal in the steady state,
ie, when there is no net gain or loss in energy in the form of
heat (= change in body temperature) or chemical potential
(= ATP or phosphocreatine stores). In vivo, ATP hydrolysis
triggers ATP synthesis; this suggests that energy flow is
controlled on the demand rather than the supply side. This
may not be true, however, under all circumstances. In any
case, energy expenditure or dissipation or utilization is not
what indirect calorimetry measures. It would therefore seem
that using the term production rate (EPR) is generally
correct, whether or not the steady state case applies,
although it may be advisable to conform to prevalent or
conventional use.56 It is important to stress that when biosynthetic processes involving gas exchange (eg, lipogenesis,
gluconeogenesis, ketogenesis) takes place along with oxidations, then equation 9 really estimates net energy production
or energy balance. This issue is dealt with in detail elsewhere.47V48
The second comment is that energy production is
estimated by indirect calorimetry under the same set of
assumptions as are utilized to calculate the rates of glucose,
lipid, and protein oxidation, namely, on the basis of the
stoichiometry of the oxidative reactions of these fuels. Any
deviation from the assumed model will introduce an error
both in the relative amounts of substrate oxidized and in the
corresponding energy production rate. The impact of these
errors on the physiologic interpretation of calorimetric measurements may be very different. The only variable that does
not depend on any assumed pattern of biochemical reactions
is the RQ, which is only a function of the measured quantities. Unfortunately,
the RQ provides merely qualitative
indications, and occasionally is difficult to interpret.
The Assumptions
Indirect calorimetry makes use of a number of assumptions, both theoretical and operational. To spell out these
assumptions and to appraise their impact on the interpretation of the results is the key to a correct use of this
Stoichiometry of the oxidative reactions in vivo. The
equations in boxes 4 and 5 can be written with slightly
different coefficients,45 but they all describe the same pattern
of O2 utilization and CO2 production. [When there is reason
to believe that tissue glycogen rather than free glucose is the
predominant form of carbohydrate being oxidized, then it
should be considered that hydrolysis of glycogen yields 1.11 g
of glucose per gram of glycogen (= 180/ 162). Therefore,
complete oxidation of glycogen requires 0.746 x 1.11 =
0.829 L of OZ. and produces 0.829 L of CO*. Equation 6 then
G (glycogen) = 4.09 \iCO, - 2.88 ‘?OZ - 2.59 fi
(6 bis)
Alternatively, one can use equation 6 as is, and multiply the
result by l/l .l 1 = 0.9. In either case, the caloric equivalent
of glycogen (4.15 kcal/g) should be used to calculate EPR.4S
The choice between glucose and glycogen as the assumed
carbohydrate fuel should be based on independent information on the physiologic condition under study. After an
overnight fast, for example, roughly three fourths of plasma
glucose turnover is derived from liver glycogenolysis,
whereas this quantity is substantially reduced in the postprandial state. In the absence of any information on the type
of carbohydrate used, it would seem unlikely that assuming
exclusive glucose oxidation might introduce a major error.]
To the extent that O2 and/or CO, are used in other ways, the
estimates of substrate oxidation rates are in error. It is
important to emphasize, however, that the estimates of EPR,
though based on the same reactions, are much more robust.
Consider equation 9 in box 5. If both sides are divided by
$‘O,, we obtain:
= 3.91 + 1.10 RQ - 3.34 +J/irO,
which shows that the caloric equivalent of O2 (EPR/vO,, cfr
Table 1) is linearly related to the RQ. If protein oxidation is
taken to be nil, one gets the solid line in Fig 2, which predicts
that the caloric equivalent of pure fat (RQ = 0.70) is 4.66
kcal/L and that of glucose (RQ = 1.00) is 5.02 kcal/L.
These values, and those in between on the connecting line,
are experimentally verified (cfr Table 1). Thus, the EPR
estimates at zero protein oxidation only depend on the RQ
(the nonprotein RQ in this case). If protein oxidation does
occur, the intercept but not the slope of the line will change,
and the line will be shifted downwards (Fig 2); the more the
shift, the higher the protein oxidation rate. The shaded area
in Fig 2 denotes a fourfold range of protein oxidative rate. If
this rate were misjudged by 50% (eg, the true rate is 0.8
mg/min kg in a 70-kg subject with an 0, consumption of
0.24 L/min, but 0.4 or 1.2 mg/min kg is erroneously
measured), it can be calculated that the corresponding EPRs
would be in error by about 1.2%. However, the glucose
oxidation rate would be off by 13% (equation 6), and lipid
oxidation by 15% (equation 7). This numerical example
illustrates the point that energy metabolism estimation is
affected by a roughly tenfold smaller error than is the
estimation of carbohydrate v lipid oxidation when the starting experimental data are gas exchange measurements and
urine nitrogen excretion.
Gas exchange measurements.
All the equations so far
derived apply to the case in which all the O2 in breath is used
to oxidize substrates and all the CO* is that evolved from
those oxidative reactions. In situations where there is a
postexercise excess oxygen consumption, a shift in acid-base
Other Metabolic Processes
As can be appreciated from the simple
diagram of Fig 4, the acetyl-CoA pool in the mitochondrion
is a busy crossroad; oxidation of all the three substrates feeds
this pool, and lipid synthesis draws from it. Therefore, the
carbon moieties of either glucose or protein can end up in
lipid and then go back to acetyl-CoA as lipid is oxidized. In
other words, there can be lipogenesis from glucose or protein
going on concomitantly with the oxidative reactions. The
stoichiometry of glucose and protein conversion into fat is
given below.45-47,62,63
Box 6
balance such as acidosis or alkalosis, or hyperventilation/
hypoventilation, gas movements reflect other, nonmetabolic
processes, and indirect calorimetric measurements will be
substantially invalidated. By very much the same token, CO,
losses through the skin or other routes also are potential
sources of error, which it is customary to either control for or
A special problem is represented by equilibration of
expired gases in body pools. Oxygen consumption measured
at the mouth follows very quickly whole-body oxygen consumption because there is virtually no oxygen reserve within
the body.48 Endogenously (ie, cellular) produced CO*, on the
other hand, enters the rather large bicarbonate pool, which
has complex kinetics. For example (Fig 3) an intravenous
bolus of NaHi4C0, is eliminated with expired air in a
multiexponential time course, indicating that the body bicarbonate system consists of several interchanging compartments.” Graphical analysis of the data in Fig 3 allows one to
peel off three exponential components, from which it can be
estimated that the healthy subject studied has a total body
bicarbonate pool of 821 mmol and a COZ turnover rate of 9.4
mmol/min; the mean transit time of a CO2 molecule through
the system (pool/turnover rate) therefore is 87 minutes. This
value, which falls into the range of those reported in the
literature,58-6’ clearly indicates that changes in metabolic
CO* production give rise to changes in expired CO* concentrations with some time delay. The impact of such a delay on
the calorimetric estimates of fuel oxidation has not been
formally evaluated. The interpretation of time patterns of
gaseous exchange should therefore be cautious, and an
attempt should be made to obtain measurements under
steady state conditions of CO2 output.
Lipogenesis from glucose:
1g G -
0.52 g F + 0.31 L 02,
Fig 2.
Relationship between the caloric equivalent of 0, and
the respiratory quotient at zero protein oxidation (solid line) and
over a wide range of protein oxidation rates (shaded area). EPR,
energy production rate (kcal/min). The upper dotted line corrasponds to 28 mg/min of protein oxidation, the lower dotted line to
112 mglmin.
1 g G + 0.045 L 0, -
AGo= +1.22kcal/g
0.35 g F + 0.25 L CO2
Lipogenesis from protein:
1 g P + 0.253 L O2 -
AG” = + 1.07 kcal/g
0.08 g F + 0.303 L CO2
i.v.Na H’CO,
-0..6 t
+ 950.
+ 550
= 9.4 mmdmln
= 521mrnol
Disappearance of an intravenous bolus of NaH’4C0, from expired air in a healthy volunteer in the overnight fasted state. The
Fig 3.
solid line is the fitting function (sum of three exponentials) obtained by a peeling-off algorithm. Integration of this function yields a value for
whole-body CO, turnover (Dose/ lo” ‘*COJt)dt) of 9.4 mmol/min. Since the subject’s total venous CD, content was 23.5 mmol/L, the
clearance rate of bicarbonate is estimated at 9.4/23.5
= 0.4 Llmin. The body bicarbonate pool is the product of total distribution volume
and total CD, content. Total plasma-equivalent volume. Cs,” t?D,(t)dt/
J0m14C0,(t)dtlx clearance rate, was equal to 35 L. or about 49%
of body weight.
As can be seen from equation 11, on the basis of stoichiometry alone glucose would turn into fat (a low-oxygen molecule) with a -50% yield gram per gram, and evolve 0,, the
reaction being endergonic. Since evolution of 0, does not
occur in vivo and the energy requirement of the synthetic
reaction must be met, lipogenesis is assumed to be coupled
with glucose oxidation with the overall stoichiometry shown
by equation 12. The same rationale applies when lipid is
formed from acetyl-CoA derived from protein oxidation
(equations 13 and 14). The RQ of lipogenesis is very high
(5.6 in equation 12). Therefore, the simultaneous occurrence
of lipogenesis and carbohydrate oxidation can be reflected in
RQ values greater than 1. In such cases, the problem is
threehold: (1) What are the rates of lipid oxidation v lipid
synthesis? (2) What is the true rate of glucose oxidation? (3)
What is the corresponding rate of energy production? The
answer requires setting up the stoichiometric equations for
the new situation.
Box 7
Let Lo., be the rate of lipid synthesis from glucose and C&
the rate of glucose conversion into fat. From Equations 1, 3,
CO,+ H,O
Fig 4.
A simple scheme of glucose oxidation (1). lipid oxidation
(2). protein oxidation (31, lipid synthesis (41, and gluconeogenesis
from protein sources (5). OAA. oxaloecetic acid: Ac.CoA. acetyl-CoA.
and 1 I:
Since L,, is still given by equation 17, we get:
= 0.746 b+
6.04 ti - 0.60 i,,
= 0.746 b+
4.89 ti
Solving for Lo,,:
i o,r = 1.67 (?CO,
- $0,)
+ 1.92 ti
Solving for C:
G = 1.34 (+CO, - 4.88 ti)
EPR = PAG; + Ge
- io,r~G:.r
6.25 ti 4.1 + G 3.74 - 1.92 Go,r 1.22
3.91 $0,
+ 1.10 \jco,
- 3.34 +I
As can be seen, lipid synthesis turns out to be dependent
upon O2 utilization, CO* production, and nitrogen excretion
with the same coefficients as lipid oxidation, only with the
opposite sign, ie, Lo,r = -L. This means that either equation
17 or equation 7 can be used to estimate the rate of net lipid
synthesis; in particular, a positive solution of equation 17
indicates net lipid synthesis, a negative solution denotes net
lipid oxidation. In addition, and most importantly, if net
lipogenesis is assumed to occur, then equation 18 and not
equation 6 must be used to estimate glucose oxidation. Using
equation 6 overestimates glucose oxidation by an amount
equal to that used to synthesize fat. Based on Fig 4, if routes
2 and 4 are identical, the glucose-derived acetyl-CoA lost to
route 4 is exactly replaced through route 2, ie, only
exchanged, and this metabolic loop will not affect the flux
through Krebs’ cycle as judged from gaseous measurements.
For example, if the RQ is 1.08, net lipid synthesis if 0.044
g/min (equation 17), glucose oxidation is 0.200 g/min
according to equation 18 and 0.282 according to equation 6
(with protein oxidation = 0.01 g/min). The difference
between these two estimates of glucose oxidation, 0.082
g/min, corresponds to 0.044 g/min of lipid (equation 1l), ie,
it is equal to net fat synthesis. The final point in box 7 is that
the equation for EPR derived for the case of net lipid
synthesis represents net energy production, and is identical
with equation 8, the general formula to estimate energy
production. Thus, net energy production is not affected by
the presence of net lipid synthesis.
Equivalent reasoning applies to lipid syntheis from protein, as shown in box 8.
Box 8
Let L,, be the rate of lipid synthesis from protein, and P,,
the flux of protein to lipid (Pr,r = 1.84 L,,, equation 13).
Since protein loses the nitrogen whether it is oxidized or
converted to fat, it must be:
P + PP.r = 6.25 ti
1; = 6.25 ti - 1.84 i,,
P =3.074 (CO, - +CO,) + 2.714 ti
In this case, glucose oxidation is given by equation 6, lipid
synthesis by equation 17, and the correct rate of protein
oxidation by equation 22. Again, the use of equation 3 in
place of equation 22 leads to an overestimation of protein
oxidation. Also, it can be easily shown that EPR still is as per
equation 8. Of note is that nonoxidative deamination of
protein sources for lipogenesis or gluconeogenesis yields
falsely elevated rates of urinary nitrogen excretion, from
which an incorrect value for the nonprotein RQ is derived. A
useful rule of thumb therefore is to solve equation 17 first: if
the result is positive, glucose oxidation is obtained from
equation 18; if the result is negative, equation 6 is used. If
there is reason to believe that amino acids are contributing to
lipid synthesis, true protein oxidation can be estimated from
equation 22.
Although lactate, pyruvate, and glycerol all are substrates for gluconeogenesis, their conversion to
glucose does not involve gas exchange. Alanine, on the other
hand, can be effectively converted into glucose in the liver;
when this happens, the amino group of alanine is transferred
via glutamate to the urea cycle to form urea. In this latter
process, CO* is used to give carbamoyl-phosphate
fixation), and energy is spent.
Box 9
Gluconeogenesis from alanine
2 alanine + CO, -
glucose + urea,
AGo = 1.02 kcal/g
1.01 g G + 0.157 g N
1 g alanine + 0.126 L CO?
6.37 g alanine + 0.801 L CO2
6.43 g G + 1 g N
If it is assumed& that the energetic cost of reaction 23 is met
by lipid oxidation, the overall stoichiometry is:
1 g alanine + 0.11 g palmitate + 0.22 L O2
with an RQ of 0.13
Several problems arise when the gluconeogenic flux is
significant. First, nitrogen excretion reflects both protein
oxidation and alanine deamination. Indicating gluconeogenesis from alanine with GjA,it is:
P + G;A= 6.25 fi
Second, the rates of glucose oxidation calculated from equation 6 are the algebraic sum of glucose oxidation and glucose
synthesis rate, ie, they underestimate glucose oxidation by an
amount equal to de novo glucose synthesis from amino acids.
Third, the rate of lipid oxidation is systematically, if not
greatly, underestimated. Finally, EPR calculations also bear
a systematic error. The 0, and CO, balances and derived
formulas in case of active gluconeogenesis from alanine are
those outlined in box 10.
from alanine occurring together with net lipid synthesis from
Box 10
Box 11
Based on equations 4, 5, and 25, we get:
\j02 = 0.746 G + 2.029 i + 6.04 ti - 0.966 G,
\ico z = 0.746 G + 1.430 i + 4.89 ti - 0.908 G,
+ net lipid synthesis from glucose
Lo,, = 1.67 (irC0,
- ir0,)
+ 1.92 ti - 0.097 G,
G = 1.34 (+CO, - 4.88 ti) + 1.22 G,
G = 21.004 (1.064 iTC0,
from which:
G = 4.55 irC0,
i = 1.67 (+O, - VCO,) - 1.92 ti + 0.097 GA
Equations 28 and 29 are the same as equations 6 and 7, both
with an added term in GA. Therefore:
G calculated
= G - G*
$0, = 0.273 l/min; \jCOZ = 0.291 l/min;
fi = 0.030 g/min
= i - 0.097 G,
True Rates
6, = 0.090
- ir0, + 0.838 rj - 0.6 i,,)
- 3.21 ir0, - 2.87 I;r + 1.03 G,
L,,, = 0.080
EPR = 1.252 kcal/min
% Differences
,Ci = 0.194gfmin
LG,F= 0.088
EPR = 1.286 kcal/min
\iO, = 0.389 L/min;
\jCOZ = 0.306 L/min; fi = 0.030 g/min
True Rates
i;, = 0.090
NPRQ = 0.767
NPRO = 0.779
% Difference
p = 0.188
G = 0.150
$, = 0.058
L = 0.090
L = 0.081
p = 0.100
EPR = 1.733 kcalfmin
EPR = 1.757 kcalfmin
Equation 30 confirms that the calculated rate of glucose
oxidation is the net balance of glucose oxidation and synthesis. From equation 31 we learn that the calculated rate of
lipid oxidation is less than the true one by a quantity equal to
9% to 10% of the gluconeogenic rate. This result could be
explained on the basis of equation 24, which shows that for
each gram of glucose formed from alanine, about 0.1 of
palmitate is oxidized to provide for the energetic cost of this
endergonic reaction. This amount of palmitate would produce 0.166 L of CO2 on complete oxidation but only 0.029 L
evolve, the remainder being incorporated into new glucose.
The difference, 0.166 - 0.029 = 0.137 L CO,, corresponds
to the lipid oxidation rate of 0.09 g (per gram of new glucose)
that is missing from the gas balances, in keeping with
equation 3 1.
The example in box 10 assumes a subject who is making
glucose from protein at a rate of 0.09 g/min at the same time
as he/she oxidizes lipid, protein, and glucose at the rates
indicated. As can be seen, the use of the standard calorimetric equations leads to a gross underestimation of glucose
oxidation, a large overestimation of protein oxidation, and a
10% underestimation of lipid oxidation. Of interest is that
the calculated NPRQ and the energy production rate are
much less affected.
Let us now consider a composite case, ie, gluconeogenesis
As can be seen, the calculation of net lipid synthesis and
that of glucose oxidation both must be corrected for gluconeogenesis. In particular, the rate of new glucose formation
must be subtracted from the expression used to compute net
lipid synthesis in the absence of gluconeogenesis (equation
17) and added to the one derived for glucose oxidation during
concomitant lipid synthesis (equation 18). The numerical
example set up in box 11 shows that the use of standard
formulas in this case underestimate glucose oxidation by 35%
and overestimate net lipid synthesis by 10%. EPR would be
overestimated by 5%. Obviously, equations 32 and 33 cannot
be solved unless GA is known.
Finally, let us draw up the O2 and CO, balances for the
most complicated case, ie, the concomitance of gluconeogenesis from protein and net lipid synthesis from both glucose
and protein.
Box I2
Pr,r = rate of protein conversion into lipid
Pr,o = rate of protein conversion into glucose
From equations 13 and 23’ we have:
Pr,r = 1.84 Lr,r
Pro = 1.01 G,
Urinary nitrogen is the sum of protein oxidation and protein
deamination for conversion into both lipid and glucose.
P + P,, + P,,, = 6.25 fi
From equations 35,36, and 37 we have:
P = 6.25 ti - 1.84 Lr,r - 1.01 G,
The O2 and CO, balances
1.105 g palmitate
GO, = 0.746 G + 0.966 F - 0.6 L,,r - 0.258 i,,
+ 0.675 1 O2 -
1.74 g AcAc~
1 g Acetone
+ 0.386 L CO,
Ketone body oxidation
= 0.746 G + 0.782 P - 0.126 G,
Introducing equation
39 and 40 for Lr,o,
is = i,,r
+ i,,
38 and solving the system of equations
1 g AcAc-
= 1.67 &CO,
2 B-OH-
- +O,)
+ 1.923 ti - 0.1 G,
t 0.887 L 0, -
+ 9 O2 + 2 H’ -
1 g B-OH-
_ 2.87 rj - 1.93 i,,
Example: VCO, = 0.283 L/min;
0.03 19 g/min
True Rates
+ 3 O2 -
G = 4.55 i’COZ - 3.21 i’OZ
+ 1.033 G,
GO, = 0.278 L/min;
p = 0.090
b (equation
18) = 0.17
L;p,F = 0.010
i (equation
17) = 0.070
L G,F = 0.050
6 (equation
3’) = 0.199
1 g/min
3 CO, + 3 H,O
for ketogenesis:
0, Consumption
CO, Production
0, and CO2 balances
GP = 0.090
1.739 L CO*
Calculated Rates
0, and CO2 balances
fi =
8 CO* + 8 Hz0
+ 1.956 L O2 -
Solving for G:
0.887 L CO2
for ketone body oxidation:
0, Consumption
CO, Production
CO2 Correction
Since it is:
AGo of L,,
= + 1.961 kcal/g
AGo of Lo,, = t2.340
AGo of G, = + 1.023 kcal/g
EPR (true) = 1.262 kcal/min
EPR (equation 9) = 1.292 kcal/min
(+ 2%)
As shown in Box 12, provided that some estimate of the
rate is available, it is still possible to derive
total net lipogenesis from equation 41 and true glucose
oxidation from equation 42, whereas the standard formulas
lead to an overestimation
of the oxidative rates of both
protein and lipid and a large underestimation
of glucose
oxidation. Of note is that in this case equation 6 estimates
glucose oxidation (0.304 g/min) more closely than equation
18 in spite of the presence of net lipid synthesis. Finally, EPR
again is off by only about 2%.
Ketone body metabolism.
Production of ketone bodies is
an oxygen-requiring
metabolic process (see box 13). Therefore, if ketone bodies are formed in excess of their oxidation,
they influence gas exchange.
Box 13
2 palmitate
+ 14 O2 -
0.635 g palmitate
8 AcAc-
+ 0.388 L O2 -
t 8H’ + 8 HZ0
1 g AcAc+ 0.0099 g H’
0.648 g palmitate
+ 0.396 L O1 AcAc-
+ (0.5 0,)
1.02 g AcAc~
1 g B-OH + (0.109 L 0,)
+ CO*
The O2 and CO, balances show that for acetoacetic acid
and /3-hydroxybutyric
acid the process of synthesis from lipid
is associated with release of hydrogen ions, which at physiologic pH are almost entirely dissociated from the ketoacids.
If these hydrogen ions were to displace equivalent amounts of
CO* from the bicarbonate pool, then CO, production would
take on the values indicated as “CO2 corrections” in box 13.
Conversely, during oxidation of acetoacetate and &hydroxybutyrate COZ is retained as bicarbonate to make up for the
consumption of hydrogen ions associated with the oxidative
process. However, whether these compensatory shifts in COZ
actually occur, and if so to what extent, is
What we learn here is that ketone bodies partake of
gaseous exchange both as they are formed and as they are
oxidized. Therefore, whenever their circulating concentrations change, gas exchange measurements
should be corrected accordingly. If the concentrations
rise, then production is in excess of disposal, and the 0, and CO, balances for
ketogenesis should be used, vice versa in case of falling levels.
The amount of ketone bodies formed in excess of oxidation
can be estimated by adding up ketone excretion in the urine
(and in breath for acetone) and accumulation
in their body
distribution volume.
Lactate metabolism.
The case for lactate is in some
respect similar to that for ketone bodies. Accumulation
lactate (as lactic acid) will cause addition of hydrogen ions,
with the possibility of displacing CO*. Net loss of lactate by
on the other hand, consumes hydrogen ions,
leading to CO, trapping as bicarbonate.
The quantitative
influence of lactate changes can be appreciated
from the
following experiment.
Sodium lactate was infused into a
healthy subject (72 kg) at a constant rate of 25 pmol/min
kg for three hours. At the end of the infusion, blood lactate
had risen from 0.9 to 2.4 mmol/L, but arterial blood
bicarbonate had increased by 7 mmol/L (metabolic alkalosis). Thus, 324 mmol of sodium lactate had caused the
retention of 205 mmol (or 4.6 L) of CO2 (assuming a
bicarbonate volume of 400 mL/kg). 0, consumption did not
change during the infusion (averaging 215 mL/min), but
CO* output fell from 175 to 148 mL/min. This change in RQ
(from 0.81 to 0.69) is, however, an artifact; if the CO,
retained in the body (205 mmol over three hours) is added to
the CO, recovered in the expired air, one gets a total
metabolic CO2 production of 174 mL/min, ie, an RQ similar
to the basal one.
Indirect calorimetry is a powerful research tool for studies
of metabolism. There is no simpler way, at present, of
obtaining the sort of information that gas exchange measurement can provide. The technical requirements4*21*41-44S@67
strict, if relatively few: (1) an air-tight canopy with a
constant air flow to be adjusted to give O2 and CO* concentrations within the workable range (Fig 5); (2) sensitive,
stable O2 and CO1 analyzers for continuous sampling of the
expired air; (3) a calibration routine using standard gas
mixtures; (4) some system to trap or condense out the
moisture of the expired air line feeding into the sensors; and
(5) a software to store and manipulate the data in any small
desktop computer. Particular attention should be paid to
ensure adequate drying of any sampled expired air, especially in long studies. Humidity alters fractional gas concentrations, and can interfere with the response of the analyzers.
Also, it is critical that apparatus be calibrated frequently
during the course of a study, so that any drift in analyzer
sensitivity can be corrected for.65A7The technique is touchy,
and currently available instrumentation is far from perfect;
as with most experimental apparatuses, expertise and a
patient attitude are unrelenting conditions to obtain reliable
The measurement of urinary nonprotein nitrogen excretion is essential. Ideally, one would want to measure all the
nitrogen deriving exclusively from protein oxidation, lost
through whatever route.68*6gIn practice, urinary excretion is
by far the predominant (~90%) mechanism of nitrogen
removal in normal subjects. Gastrointestinal and skin losses
become important in patients with renal failure. The Kjeldahl method, or any modification thereof, is the assay for
nonprotein nitrogen that most prefer. However, in case of
Fig 5.
Indirect calorimetry with the canopy.
significant aminoaciduria, eg, during parenteral alimentation with amino acid mixtures, nonprotein nitrogen will be
falsely elevated. It is then necessary to separately measure
urine amino acids, or alpha-amino nitrogen as a whole, to be
subtracted from the value for nonprotein nitrogen given by
the Kjeldahl technique. Another question concerns the timing of urine collection. Urine output is better estimated over
longer periods of time. As the time-scale is lengthened,
however, the metabolic state of the study subject invariably
changes, and the assumption that protein oxidation remains
constant may become more questionable. This is all more the
case if manipulations known to affect protein metabolism,
eg, insulin administration or catecholamine infusion, are part
of the study protocol. Information in this specific area is
The experimental circumstances offer other possible
sources of error. On a good day, a tranquil, collaborative
subject is lying supine in bed, breathing calmly and regularly
in the canopy as he/she reads or dozes on and off, with very
few other stimuli from a thermo-regulated, quiet environment. RestIessness, hyperventilation/hypoventiIation,
like perturbations all impinge upon the assumption that the
volumes of gases exchanged only reflect metabolic events.
An issue that haunts any investigator submitting calorimetric results to peer review is how to express the data in
order to take body mass and composition into appropriate
account. Intuitively, the same rate of glucose oxidation will
have a very different meaning if observed in a 60-kg habitual
jogger or a 90-kg sedentary person. Metabolic functions
should be normalized by the metabolically active body mass.
How can the latter be estimated? What should be used as the
denominator of substrate or metabolic rates? Body weight
would at first appear to be unacceptable, because it comprises metabolically inert parts, such as bone minerals,
extracellular fluid, and fat.” It should be noted that adipose
tissue is all but metabolically inactive, but its energyexchanging processes involve only adipocyte cytoplasm,
which is a small proportion (less than 10%) of triglyceride
stores. The lean, or fat-free, body mass can be estimated by
anthropometric,7’-73 densitometric,74 and isotopic techniques.” Body surface area (as predicted from height and
weight according to DuBois’ formula), body mass index
and various powers of body weight
(usually 0.75) are easy but crude indices. Of them, body
surface area has been shown to bear a very good correlation
with the lean body mass estimated from the antipyrine
space73 or by underwater weighing.76 Densitometry, on the
other hand, counts the fat-free tissues but also the extracellular fluid, thereby overestimating the body cell mass by an
amount that might be quite different in subjects of different
age and body weight. Also, underwater weighing is cumbersome and impractical in many clinical settings. Isotopes of
water or potassium are no less laborious. Direct or indirect
measurement of whole-body potassium theoretically should
come closest to estimating the component of all tissues that
contains the oxygen-exchanging, work performing mass
(body cell mass). However, it is pertinent to note that the
densitometric and isotopic methods are much less precise
than measuring height and weight.
Table 2.
of Various Body Size Factors to Normalize
Weight (kg)
ESA (rn’)
BMI (kg/m’)
FFM (kg)
EPR (kcal/min)
Glucose oxidation (mglmin)
Glucose oxidation/weight (mg/min kg)
Glucose oxidation/BSA (mg/min m2)
Glucose oxidation/EM1 (mg m’/min kg)
Glucose oxidation/FFM (mg/min kg)
Glucose oxidation/EPR (mg/kcal)
Height (cm)
% Difference
_ 16%
Body size data from Bogardus et alSoand Lillioja et al.”
The various factors to correct substrate rates are compared in Table 2, where it is assumed that the same absolute
rate of glucose oxidation is measured in two subjects of
widely different body weight. The values are the mean group
data in reference 50 for the obese case, and in reference 76
for the lean subject; in these studies, fat-free mass was
determined by underwater weighing. It can be seen that
correcting the oxidation rate by the fat-free mass gives the
same percent difference between the two subjects as does
correcting for total body weight, whereas both the body
surface area and the body mass index underestimate the
impairment in glucose oxidation of the obese subject. Thus,
contrary to what is commonly heId, the highly disreputed
correction for body weight reproduces the difference indicated by the fat-free mass correction relatively faithfully,
while the other anthropometric corrections provide rather
conservative estimates of the same difference. Whether this
result applies to the host of body sizes and compositions that
clinical investigation offers is uncertain. One easy as well as
sound alternative is to use the basal energy production rate as
the correction factor.” In fact, nothing is a better function of
the body cell mass than its heat production, ie, an integrated
index of all metabolic activities. That energy production
correlates tightly with body size over a wide range of values
has long been known4 For example, Table 2 shows that
correcting glucose oxidation for EPR (typical values for
normal and obese people3’) gives a percent difference very
similar to that obtained with fat-free mass. Using a functional rather than anatomical factor has the additional
advantage of directly indicating the proportion of energy
balance that is derived from carbohydrate or lipid oxidation.78 In the example in Table 2, the obese draws 52% of
each kilocalorie from glucose oxidation v a corresponding
figure of 72% in the nonobese. Clearly, however, experience
with this index is needed before it can be strenuously
defended against currently accepted indices.
An important aspect of indirect calorimetry is that it can
be, and usually is, combined with other research methods.
For example, tracer techniques can be used in concomitance
with indirect calorimetry to measure the turnover rate of
various substrates. With regard to this, it is useful to recall
that indirect calorimetry estimates whole-body rates of substrate oxidation while the great majority of tracer techniques
are based on plasma (or blood) measurements whereby
plasma (or blood) turnover rates are calculated. Consider the
case where indirect calorimetry is done during a constant
infusion of labeled palmitate, and the labeled CO, in expired
air is collected at timed intervals. The rate of oxidation
calculated from the labeled CO, data need not be, and in fact
hardly ever is, the same as the lipid oxidation rate obtained
from calorimetry because lipids that undergo oxidation without ever passing through the circulation are “read” by
calorimetry but do not dilute the tracer. Thus, oxidation of
circulating FFA is only 30% to 60% of total lipid oxidation.”
A further complication is that as tracer infusion is continued,
equilibration of labeled CO2 in the bicarbonate pool becomes
more complete and the cellular lipid pool, which turns over
more slowly than plasma FFA, is progressively labeled. As a
result, the ratio of tracer-determined to calorimetric rates of
lipid oxidation may change with time.
Another relevant example is glucose. Rates of glucose
oxidation by indirect calorimetry generally are a fraction of
the corresponding rates of plasma glucose turnover, which
includes nonoxidative pathways of glucose disposal. During
insulin-induced hypoglycemia, however, one can encounter
rates of glucose oxidation in excess of simultaneously measured rates of exogenous glucose infusion or plasma glucose
disappearance. This result is not an artifact but reflects the
breakdown of glycogen depots in muscle in response to
hypoglycemia itself and/or to the associated counter-regulatory hormone release (Ferrannini et al, unpublished observations) .
Finally, as far as the theoretical aspects of calorimetry are
concerned, the present state of affairs can be summarized as
1. We have exact equations to calculate lipid, glucose, and
protein oxidation, and net lipid synthesis from either glucose
or protein (equations 3’, 6, 7, 17, 18, and 22).
2. The equation giving the energy production rate is one
and the same (equation 9) when the metabolic processes
involving gaseous exchange are those in (1).
3. Approximate corrections can be applied to the measured gas Aows to account for ketone body and lactate
metabolism (box 13).
4. The presence of gluconeogenesis from amino acids,
whether occurring alone or in combination with net lipid
synthesis from any source, introduces an unknown, which
indirect calorimetry cannot estimate.
5. We have derived equations that give the coefficients for
the known variables (Q02, %‘COZ,&;, I+ and P) when the
unknown, ie, gluconeogenesis, is present.
6. In general, gluconeogenesis from protein sources
causes an underestimation of lipid oxidation equal to 0.09
times its own rate and one of 1.03 times its own rate for
glucose oxidation. Protein oxidation is definitely overestimated if gluconeogenesis is active.
7. The estimation of energy production rate is relatively
more resistant to the impact of gluconeogenesis.
Thus, a correct use of indirect calorimetry calls for a
preliminary evaluation of the metabolic condition to be
studied. Is gluconeogenesis likely to be operative at a significant rate in the subject? Are any of the manipulations of the
experimental protocol likely to change its rate? Can it be
estimated independently with any degree of confidence? The
equations to take formal account of the various metabolic
phenomena are there, but as usual they cannot replace
physiologic knowledge and clinical judgement.
To conclude, Table 3 illustrates a case-study exquisitely
germaine to metabolism, i.e. a calorimetric evaluation of
patients in diabetic ketoacidosis (DKA). The data are those
of Owen et al (Tables 3 and 4”) who carried out indirect
calorimetry on patients admitted to the hospital in DKA,
then rehydrated and subsequently treated with insulin. The
authors obtained sequential readings over 12 hours, but we
have used only the initial and final data. Also, for illustrative
purpose, we have reversed the real time sequence, ie, we
imagine that a representative diabetic subject on insulin
(initial data) stops taking insulin and, over the course of the
following 12 hours, drifts into DKA (final data). As can be
seen, the patient is moderately hyperglycemic and hyperketonemic before stopping insulin, then becomes severely
hyperglycemic and ketotic. Both v02 and %‘CO, are now
increased, but the glucose oxidation rate calculated from
these gas flows is --0.08 g/min, ie, an inconceivable rate.
By taking ketogenesis and gluconeogenesis into consideration, we get a drastically different picture; glucose oxidation
is low (0.038 mg/min - kg) and less than one third the
baseline value, and the reliance of energy production on lipid
oxidation is increased twofold. This shift in fuel utilization is
fully consistent with the rise in FFA levels, the known effects
of insulin on lipolysis and glucose uptake, and the interactions of glucose and lipid metabolism.
For a circuit like that depicted in Fig 5, the general equations
Table 3. Changes in Fuel Utilization and Energy Production
VO, = V, x FI02 - V,, x FEO,
in Diabetic Ketoacidosis
Vi” = V, + V* + V,,,
V,“, =
Energy production
Plasma glucose (mg/dL)
Blood acetoacetate fmmol/L)
Blood fi-OH-butyrate
Blood acetone (mmol/L)
Breath acetone output
v, + \i, + v,,,+vco*
- Go,
Vo, = (VO”,- V, - VEWL)(FI02 - FEO,)/
itO, Urnin)
QCO, (L/min)
- [l - (1 - RQ) x FIOJ
Fuel utilization
Glucose oxidation fg/min)
- 0.080
Lipid oxidation (g/min)
Protein oxidation (g/min)
Energy production rate
% of EPR as G, L, P
Urine nitrogen excretion was 0.011
nitrogen was taken to derive from both protein oxidation and deamination
to be 0.040
Gluconeogenesis was therefore calculated
g/min both initially and at 12 hours. The correction for blood
ketones was made by using 0.5
L/kg as the distribution volume of
and 0.7
and P-OH-butyrate,
L/kg as that of acetone.
According to the authors’ measurements, ketonuria was not significantly
different between the beginning and the end of the study, and the
VO, = Vs x (FIO, - FEO,)/[l
VO, = V, x (FIO* - FEOJ - VCOl x FIO,/(l
Data from Owen et al.”
g/min for @-OH-butyrate, and 0.021
- FIO1)
For example, if the air leaving the canopy were saturated at 37OC
(water vapor pressure of 47 torr), the error of VO, (as calculated
from equation f) would be +6.2%, and the value of RQ would be
ketone body production over 12 hours were calculated to be: 0.015
g/min for acetoacetate,
- (1 - RQ) x FIO,]
corresponding correction was therefore ignored. The mean rates of net
g/min for acetone.
The fractional concentrations of O1 in the incoming and outgoing
airflows (FIO, and FEO,) are altered by the added volumes.of water
*’ The error involved with the calculation of V, due to
V, and VEWL
ambient and evaporative water is nonproportional (because VEWL
only alters FE02), and is an overestimation equal to (V, + V,,)/
V,,. Ifall water vapor isabsorbed prior to entry into the O2 analyzer,
then VA = VEWL= 0, V,, becomes Va (= outflow at STPD), and
equation d can be written as:
and did not change
between 0 and 12 hours. In keeping with the authors’ assumption,
in the proportion 0.42/0.58.
where Vi, and V,, are airflow rates into and out of the canopy under
standard temperature and pressure conditions (STP), V, is the
inflow rate of dry air (STPD), VA is the flow rate (STP) of ambient
water vapor, and VEWt,is the flow rate (STP) of the subject’s
evaporative water loss. By substituting equations b and c into
equation a, one obtains:
Plasma FFA (mmol/L)
energy metabolism from ir0,
alone** leads to a 20%
(cfr equation 9), which is partially compounded
(down to 15%) by also neglecting protein excretion.
1 1
Relationship between the RQ calculated
Fig 6.
with the use of Haldane’s correction
and that
obtained without such correction
(solid curve).
The dotted line is the identity line.
Energy metabolism can be determined
on the basis of ‘?O, and
vCO1 alone without measuring
urinary nitrogen excretion. The
error introduced
by using respiratory
alone has been
estimated to be about 4% in the fasting condition (and to decrease as
the metabolic rate increases) when a constant value for nitrogen
output is assumed.“.**
Also of interest is that if Haldane’s correction for the fractional
gas concentration
in a gas mixture is neglected, the error on the RQ
is a function of RQ itself. Consider that ‘irC0, is equal to ‘?r
(FEC02 - FICO,); since, however, FIC02 is negligibly small, it is
i’C02 = .irr x FECO>.
Using equation f of Appendix I, the true, corrected RQ is:
x FIO,)/
If the correction
x F102 is neglected,
x FIOz)
RQ becomes
These two expressions
1 1
= FEC02/(FI02
of RQ are related to one another
RQ = (1 - FIO,)
x *RQ/(l
The nonlinear function h is
values observed under ordinary
RQ for values
In other words, omitting
systematic error that depends
as follows:
- F102 x *RQ)
plotted in Fig 6 over the range of RQ
As can be seen, *RQ
>l, and underestimates
it for values
on RQ itself.
Professor Eric J&quier, of the University of Lausanne, Switzerland, and Drs Ralph A. DeFronzo and Riccardo Bonadonna, of Yale
University School of Medicine, New Haven, USA, offered useful
criticism to this paper. Special thanks are due to Daniela Banti for
her expert assistance in the preparation of the manuscript.
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