Ophuizen.indirecte_calorimetrie

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.

I NDIRECT CALORIMETRY, 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 obesity23-35 and diabetes.36-40 The 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 increas- ing 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,6.45-50 it 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.

BACKGROUND

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 isother- mia, 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

Metabolism, Vol 37, No 3 (March), 1988: pp 287-301

energy to where it is needed. Chemical (biosyntheses), osmotic (active transports), and mechanical (muscular con- traction) work is thus made possible.

Although biochemical reactions in vivo flow through intri- cate 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

Enthalpy (H) = total heat content of a substance or physical system

Entropy (S) = degree in which the total energy of a system is uniformly distributed (random- ness) 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.

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. 00260495,88/3703-0015$03.00/0

287

288 ELEUTERIO FERRANNINI

where T = temperature R = gas constant

K’, = equilibrium constant = [prod] / [react] AGo = standard free-energy change

For AG = 0, we get

Equation C:

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 corresponding 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).

z L I 1 I I I I

0.01 1 100

EQUILIBRIUM CONSTANT, Keq

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).

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

AGo (in vitro) = - 7.3 kcal/mol AG” (in vivo) = - 12.5 kcal/mol

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.52 Clearly, a system with these kinetic character- istics 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, rounded- off 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 sub- jected 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.

DIRECT V INDIRECT CALORIMETRY

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 accu- rately 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,

INDIRECT CALORIMETRY 289

heat and energy can be used as synonyms. Any heat dissi- pated internally to increase body temperature or accumu- lated 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 degrada- tion 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 equation.48

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 OX currency.

The next step is to write the stoichiometry of the three oxidative reactions (box 4).

INDIRECT CALORIMETRY

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 con- ceptual, systematic errors.

Indirect calorimetry measures gas exchange, ie, whole- body 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 acids- The stoichiometry of protein oxidation varies within a nar- row 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,

+0.746LC02 + 0.6gHz0 (1)

1 g Lipid (L) + 2.029 L 0,

- 1.430 L CO, t I .09 g HZ0 (2)

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$ (3’)

one has:

1 gN + 6.04L0,+4.89LCOZ + 2.81gHz0 (3)

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?

(4)

(5)

(6)

i=(l.67+0,-+CO,)- l.92ti (7)

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 palmitoyl-oleoyl-stearoyl-triglyceride) oxidized by the body.

An alternative way of carrying out these calculations is to

Table 1. Energy Balance Sheet for the Three Main Fuels

Oxidized Fuel

(1 mall

0, Used CO, Produced Net ATP Yield Caloric Cost Oxygen Cost Caloric Equivalent ATP Equivalent

AGO of ATP of ATP of 0, of 0,

Ikcallmol) lmol) IL) hloll (L) RQ (mol) (kg) (kcal/mol) ~L/rnOl~ (kc&/L) (mol/mol)

Glucose* -673 6 134 6 134 1.000 36 18.3 18.7 3.72 5.02 3.00

Palmitate -2,398 23 515 16 358 0.695 131 66.4 18.3 3.93 4.66 2.85

Amino acidst -475 5.1 114 4.1 92 0.807 23 11.7 20.7 4.96 4.17 2.25

*Complete oxidation of glucose yields 38 mol of ATP per mol of glucose, but 2 ATP mol are used up during glycolysis.

tcomplete 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

2). 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 sim- plicity, the caloric equivalents are given in box 5 in the same units as the substrate oxidation rates (ie, per gram of substance).

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 kJ/g)

Protein (mol wt 116)

= AG; = -4.10 kcal/g (=-17.15 kJ/g)

Energy Production Rate (EPR)

= GAG; + ~AG; + PAG; (8)

From equations 3’, 6,7, and 8, one has:

EPR(kcal/min) = 3.91 VO, + l.10iC02 - 3.34 k (9)

The molecular weight indicated is that of an average constituent amino acid.45.55 It 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 biosyn- thetic processes involving gas exchange (eg, lipogenesis, gluconeogenesis, ketogenesis) takes place along with oxida- tions, then equation 9 really estimates net energy production or energy balance. This issue is dealt with in detail else- where.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 quanti- ties. 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 technique.

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 becomes:

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:

EPR/vO, = 3.91 + 1.10 RQ - 3.34 +J/irO, (10)

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

5.6

5.2 - < 3 0 4.8

5

N

.F 4.4

2

& 4.0

3.6

0.4 0.6 0.8 1.0 1.2 1.4

RQ

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 corra- sponds to 28 mg/min of protein oxidation, the lower dotted line to 112 mglmin.

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 ignore.

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.

Other Metabolic Processes

Lipogenesis. 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

Lipogenesis from glucose:

1 g G - 0.52 g F + 0.31 L 02,

AGo= +1.22kcal/g (11)

1 g G + 0.045 L 0, - 0.35 g F + 0.25 L CO2 (12)

Lipogenesis from protein:

lgP-0.54gF+0.14L02,

AG” = + 1.07 kcal/g (13)

1 g P + 0.253 L O2 - 0.08 g F + 0.303 L CO2 (14)


i.v.Na H’CO, I

50

10

‘~co*(t~ = 54000 -0..6 t -0.073 t -o.ooast

+ 950. + 550

CO2 turnover = 9.4 mmdmln

co2 pool = 521mrnol

0 6.0 lit0 tie 240 300 360

TIME (mitt)

Fig 3. Disappearance of an intravenous bolus of NaH’4C0, from expired air in a healthy volunteer in the overnight fasted state. The 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)dtl x 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:

+O, = 0.746 b+ 6.04 ti - 0.60 i,, (15)

+CO, = 0.746 b+ 4.89 ti (16)

Solving for Lo,,:

i o,r = 1.67 (?CO, - $0,) + 1.92 ti (17)

Solving for C:

EPR =

G = 1.34 (+CO, - 4.88 ti) (18)

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 (19)

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 1 l), 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 (20)

hence:

1; = 6.25 ti - 1.84 i,, (21)

293

Since L,, is still given by equation 17, we get:

P =3.074 (CO, - +CO,) + 2.714 ti (22)

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.

Gluconeogenesis. Although lactate, pyruvate, and glyc- erol 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 (CO1 fixation), and energy is spent.

Box 9

Gluconeogenesis from alanine

2 alanine + CO, - glucose + urea,

AGo = 1.02 kcal/g (23)

1 g alanine + 0.126 L CO?

- 1.01 g G + 0.157 g N (23’)

6.37 g alanine + 0.801 L CO2

- 6.43 g G + 1 g N (23”)

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

-1.01gG+0.029LC0,+0.157gN (24)

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 (25)

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.

Box 10

Based on equations 4, 5, and 25, we get:

\j02 = 0.746 G + 2.029 i + 6.04 ti - 0.966 G, (26)

\ico z = 0.746 G + 1.430 i + 4.89 ti - 0.908 G, (27)

from which:

G = 4.55 irC0, - 3.21 ir0, - 2.87 I;r + 1.03 G, (28)

i = 1.67 (+O, - VCO,) - 1.92 ti + 0.097 GA (29)

Equations 28 and 29 are the same as equations 6 and 7, both

with an added term in GA. Therefore:

G calculated = G - G* (30)

Lcalculatcd = i - 0.097 G, (31)

Example:

\iO, = 0.389 L/min;

\jCOZ = 0.306 L/min; fi = 0.030 g/min

True Rates Calculated Rates % Difference

i;, = 0.090 gfmin -

NPRO = 0.779 NPRQ = 0.767 -2%

p = 0.100 gfmin p = 0.188 gfmin +88%

G = 0.150 g/min $, = 0.058 gfmin -62%

L = 0.090 g/min L = 0.081 g/min -10%

EPR = 1.733 kcalfmin EPR = 1.757 kcalfmin +1%

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

from alanine occurring together with net lipid synthesis from glucose.

Box 11

Gluconeogenesis + net lipid synthesis from glucose

Lo,, = 1.67 (irC0, - ir0,) + 1.92 ti - 0.097 G, (32)

G = 1.34 (+CO, - 4.88 ti) + 1.22 G, (33)

G = 21.004 (1.064 iTC0,

- ir0, + 0.838 rj - 0.6 i,,) (34)

Example:

$0, = 0.273 l/min; \jCOZ = 0.291 l/min;

fi = 0.030 g/min

True Rates Calculated Rates % Differences

6, = 0.090 gfmin - -

G = 0.300 gfmin ,Ci = 0.194gfmin -35%

L,,, = 0.080 gfmin LG,F = 0.088 gfmin +lo%

EPR = 1.252 kcal/min EPR = 1.286 kcal/min +5%

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

Let:

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 (35)

Pro = 1.01 G, (36)

Urinary nitrogen is the sum of protein oxidation and protein deamination for conversion into both lipid and glucose. Thus:

P + P,, + P,,, = 6.25 fi

From equations 35,36, and 37 we have: .

(37)

P = 6.25 ti - 1.84 Lr,r - 1.01 G, (38)


The O2 and CO, balances are:

GO, = 0.746 G + 0.966 F - 0.6 L,,r - 0.258 i,, (39)

+CO, = 0.746 G + 0.782 P - 0.126 G, (40)

Introducing equation 38 and solving the system of equations

39 and 40 for Lr,o,

is = i,,r + i,, = 1.67 &CO, - +O,)

+ 1.923 ti - 0.1 G, (41)

Solving for G:

G = 4.55 i’COZ - 3.21 i’OZ

_ 2.87 rj - 1.93 i,, + 1.033 G, (42)

Example: VCO, = 0.283 L/min; GO, = 0.278 L/min; fi =

0.03 19 g/min

True Rates Calculated Rates

GP = 0.090 g/min -

p = 0.090 g/min 6 (equation 3’) = 0.199 g/min +120%

G 5 0.300 g/min b (equation 18) = 0.17 1 g/min -43%

L;p,F = 0.010 g/min i (equation 17) = 0.070 g/min +16%

L G,F = 0.050 g/min

Since it is:

AGo of L,, = + 1.961 kcal/g

AGo of Lo,, = t2.340 kcal/g

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

gluconeogenic 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). There- fore, if ketone bodies are formed in excess of their oxidation,

they influence gas exchange.

Box 13

2 palmitate + 14 O2 - 8 AcAc- t 8H’ + 8 HZ0 (43)

0.635 g palmitate + 0.388 L O2 - 1 g AcAc-

+ 0.0099 g H’

AcAc + NADH - B-OH- + (0.5 0,) (44)

0.648 g palmitate + 0.396 L O1 - 1.02 g AcAc~

- 1 g B-OH + (0.109 L 0,)

AcAc- - Acetone + CO* (45)

1.105 g palmitate + 0.675 1 O2 - 1.74 AcAc~ g

- 1 g Acetone + 0.386 L CO,

Ketone body oxidation

AcAc+40,+H+-4CO,+3H,O (46)

1 AcAc- t 0.887 L 0, - 0.887 L CO2 g

2 B-OH- + 9 O2 + 2 H’ - 8 CO* + 8 Hz0 (47)

1 B-OH- + 1.956 L O2 - 1.739 L CO* g

Acetone + 3 O2 - 3 CO, + 3 H,O (48)

lgAcetone+ 1.158L02~l.158LC01

0, and CO2 balances for ketogenesis:

0, Consumption CO, Production CO, Correction

AcAc- (g) 0.388 L 0 (+0.222 L)

B-OH- (g) 0.287 L 0 (+0.217 L)

Acetone (g) 0.675 L 0.386 L

0, and CO2 balances for ketone body oxidation:

0, Consumption CO, Production CO2 Correction

AcAc- Ig) 0.687 L 0.887 L (-0.222 L)

B-OH- (g) 1.956 L 1.739 L (-0.217 L)

Acetone (g) 1.158L 1.158L -

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 physio-

logic 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 &hydroxy- butyrate 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 distribution actually occur, and if so to what extent, is

uncertain.4’

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 concentra-

tions change, gas exchange measurements should be corrected accordingly. If the concentrations rise, then produc-

tion 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 of lactate (as lactic acid) will cause addition of hydrogen ions, with the possibility of displacing CO*. Net loss of lactate by oxidation, 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.

COMMENTS

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 are 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, espe- cially 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.65A7 The 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 results.

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*6g In 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 Kjel- dahl 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 alimenta- tion 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 tim- ing 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 scanty.

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, and 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 com- prises 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 energy- exchanging 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 (weight/height*), 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 cumber- some 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. Comparison of Various Body Size Factors to Normalize Substrate Metabolism Rates

Normal Obese % Difference

Height (cm) 161.1 170

Weight (kg) 75.3 104.3

ESA (rn’) 1.795 2.144

BMI (kg/m’) 29 36.1

FFM (kg) 46.6 67.8

EPR (kcal/min) 1.04 1.44

Glucose oxidation (mglmin) 200 200

Glucose oxidation/weight (mg/min kg) 2.66 1.92

Glucose oxidation/BSA (mg/min m2) 112 93

Glucose oxidation/EM1 (mg m’/min kg) 6.90 5.54

Glucose oxidation/FFM (mg/min kg) 4.20 2.95

Glucose oxidation/EPR (mg/kcal) 192 139

+6%

+39%

120%

+24X

+42%

+38% -

-28% _ 16%

-20%

-30%

-28%

Body size data from Bogardus et alSo and Lillioja et al.”

The various factors to correct substrate rates are com- pared 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 func- tional 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 observa- tions) .

Finally, as far as the theoretical aspects of calorimetry are concerned, the present state of affairs can be summarized as follows:

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

298 ELEIJTERIO FERRANNINI

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

Table 3. Changes in Fuel Utilization and Energy Production

in Diabetic Ketoacidosis

Corrected Initial Data Final Data Final

Energy production

Plasma glucose (mg/dL)

Plasma FFA (mmol/L)

Blood acetoacetate fmmol/L)

Blood fi-OH-butyrate

(mmol/L)

Blood acetone (mmol/L)

Breath acetone output

(Amol/min)

itO, Urnin)

QCO, (L/min)

Fuel utilization

Glucose oxidation fg/min)

Lipid oxidation (g/min)

Protein oxidation (g/min)

Energy production rate

fkcal/min)

% of EPR as G, L, P

179 451 -

0.78 1.74 -

0.66 3.74 -

1.10 12.07 -

1.92 5.02 -

66 159 -

0.188 0.259 -

0.158 0.172 -

0.124 - 0.080 0.038

0.029 0.124 0.083

0.029 0.029 0.029

0.858 1.165 1.050

54132114 ? 14/75/l 1

Urine nitrogen excretion was 0.011 g/min, and did not change

between 0 and 12 hours. In keeping with the authors’ assumption,

nitrogen was taken to derive from both protein oxidation and deamination

in the proportion 0.42/0.58. Gluconeogenesis was therefore calculated

to be 0.040 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

acetoacetate and P-OH-butyrate, and 0.7 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

corresponding correction was therefore ignored. The mean rates of net

ketone body production over 12 hours were calculated to be: 0.015

g/min for acetoacetate, 0.055 g/min for @-OH-butyrate, and 0.021

g/min for acetone.

Data from Owen et al.”

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 hyperke- tonemic 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 interac- tions of glucose and lipid metabolism.

APPENDIX I

For a circuit like that depicted in Fig 5, the general equations are:

VO, = V, x FI02 - V,, x FEO,

Vi” = V, + V* + V,,,

(a)

(b) . V,“, = v, + \i, + v,,, + vco* - Go,

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:

Vo, = (VO”, - V, - VEWL)(FI02 - FEO,)/

- [l - (1 - RQ) x FIOJ (d)

The fractional concentrations of O1 in the incoming and outgoing airflows (FIO, and FEO,) are altered by the added volumes.of water V, and VEWL *’ The error involved with the calculation of V, due to 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:

VO, = Vs x (FIO, - FEO,)/[l - (1 - RQ) x FIO,] (e)

or

VO, = V, x (FIO* - FEOJ - VCOl x FIO,/(l - FIO1) (f)

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 underestimated.

APPENDIX II

Calculating energy metabolism from ir0, alone** leads to a 20%

underestimation (cfr equation 9), which is partially compounded (down to 15%) by also neglecting protein excretion.


Fig 6. Relationship between the RQ calculated

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 functions 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:

RQ = (FECO, - FECOl x FIO,)/

FIOz - FEOl - FECO, x FIOz) (g)

If the correction term FECO, x F102 is neglected, RQ becomes

simply:

1.2

1 1

1 .o

0.9

0.8

0.7

/ ’ /

/ /

/ /

0.7 0.8 09 10 1 1 12

RQ measured

*RQ = FEC02/(FI02 - FEO,)

These two expressions of RQ are related to one another as follows:

RQ = (1 - FIO,) x *RQ/(l - F102 x *RQ) (h)

The nonlinear function h is plotted in Fig 6 over the range of RQ

values observed under ordinary circumstances. As can be seen, *RQ

overestimates RQ for values >l, and underestimates it for values

tl. In other words, omitting Haldane’s correction introduces a

systematic error that depends on RQ itself.

ACKNOWLEDGMENT

Professor Eric J&quier, of the University of Lausanne, Switzer-

land, 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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