clin pharm 2005

Clin Pharmacokinet 2005; 44 (10): 1051-1065ORIGINAL RESEARCH ARTICLE 0312-5963/05/0010-1051/$34.95/0

2005 Adis Data Information BV. All rights reserved.

Quantification of Lean BodyweightSarayut Janmahasatian,1 Stephen B. Duffull,1,2 Susan Ash,3 Leigh C. Ward,4Nuala M. Byrne5 and Bruce Green1,2

1 School of Pharmacy, University of Queensland, Brisbane, Queensland, Australia2 Center for Drug Development Science, University of California San Francisco, Washington

Campus, Washington, DC, USA3 School of Public Health, Queensland University of Technology, Brisbane,

Queensland, Australia4 Department of Biochemistry and Molecular Biology, University of Queensland, Brisbane,

Queensland, Australia5 School of Human Movement Studies, Queensland University of Technology, Brisbane,

Queensland, Australia

Background: Lean bodyweight (LBW) has been recommended for scaling drugAbstractdoses. However, the current methods for predicting LBW are inconsistent atextremes of size and could be misleading with respect to interpretingweight-based regimens.Objective: The objective of the present study was to develop a semi-mechanisticmodel to predict fat-free mass (FFM) from subject characteristics in a populationthat includes extremes of size. FFM is considered to closely approximate LBW.There are several reference methods for assessing FFM, whereas there are noreference standards for LBW.Patients and methods: A total of 373 patients (168 male, 205 female) wereincluded in the study. These data arose from two populations. Population A (indexdataset) contained anthropometric characteristics, FFM estimated by dual-energyx-ray absorptiometry (DXA – a reference method) and bioelectrical impedanceanalysis (BIA) data. Population B (test dataset) contained the same anthropomet-ric measures and FFM data as population A, but excluded BIA data. The patientsin population A had a wide range of age (18–82 years), bodyweight(40.7–216.5kg) and BMI values (17.1–69.9 kg/m2). Patients in population B hadBMI values of 18.7–38.4 kg/m2. A two-stage semi-mechanistic model to predictFFM was developed from the demographics from population A. For stage 1 amodel was developed to predict impedance and for stage 2 a model that incorpo-rated predicted impedance was used to predict FFM. These two models werecombined to provide an overall model to predict FFM from patient characteristics.The developed model for FFM was externally evaluated by predicting intopopulation B.Results: The semi-mechanistic model to predict impedance incorporated sex,height and bodyweight. The developed model provides a good predictor ofimpedance for both males and females (r2 = 0.78, mean error [ME] = 2.30 × 10–3,root mean square error [RMSE] = 51.56 [approximately 10% of mean]). The finalmodel for FFM incorporated sex, height and bodyweight. The developed model

1052 Janmahasatian et al.

for FFM provided good predictive performance for both males and females (r2 =0.93, ME = –0.77, RMSE = 3.33 [approximately 6% of mean]). In addition, themodel accurately predicted the FFM of subjects in population B (r2 = 0.85, ME =–0.04, RMSE = 4.39 [approximately 7% of mean]).Conclusions: A semi-mechanistic model has been developed to predict FFM (andtherefore LBW) from easily accessible patient characteristics. This model hasbeen prospectively evaluated and shown to have good predictive performance.

Background where BWt is bodyweight and BMI is body massindex.

Obesity is recognised as a serious medical andSome authors have suggested that LBW is likelypublic health problem in both developed and devel-

to be a better predictor of drug dosage in the obese,[8]oping countries,[1] and is a major risk factor for

as good correlations between LBW and volume ofserious noncommunicable diseases such as diabetesdistribution have been seen for hydrophilic drugs.mellitus and cardiovascular disease.[1] Unfortunate-The current estimate of LBW[3] is, however, incon-ly, dosage recommendations in drug labels aresistent at extremes of size,[7] and could be mislead-predominantly developed from clinical trials thating with respect to interpreting bodyweight-basedexclude special patient populations such as theregimens as normal-weighted patients have a nor-obese, or have not specifically quantified how bodymal amount of fat mass, which is ignored in compu-composition affects the exposure response relation-tation of LBW. This has stimulated researchers toship. Drug administration in clinical practice isdevelop a new size descriptor termed ‘predictedtherefore based on the premise that structural andnormal bodyweight’ (PNWT), which can be used tofunctional aspects of the body are similar in obesepredict normal bodyweight for individuals who areand normal-weight patients, and can be scaled toobese.[9] Nevertheless, PNWT itself relies on thetotal bodyweight, usually presented in the drug labelcurrent equation[3] to predict LBW, which willas a dose per kilogram.therefore necessarily confer the same predictionSelecting a drug dose that is scaled according tolimitations seen with LBW. Refinement of thebodyweight is unlikely to result in comparable expo-PNWT equation with a more accurate equation forsures between obese and nonobese patients. Thispredicting LBW is therefore required.arises as body composition usually varies as a func-

tion of total bodyweight, with the ratio of adipose When considering human body composition, to-tissue to lean body mass increasing with body- tal bodyweight is believed to be comprised of fatweight.[2] Whilst bodyweight remains the most com- mass and fat-free mass (FFM). FFM consists ofmon size descriptor to scale drug dose, other muscle, bone, vital organs and extracellular fluid.descriptors such as lean bodyweight (LBW)[3] have Technically, LBW differs from FFM because lipidsbeen recommended for the drugs enoxaparin sodi- in cellular membranes, the CNS and bone marrowum,[4] amikacin[5] and suxamethonium chloride.[6] are included in LBW[10] but not in FFM. However,The most widely used equations to calculate LBW as lipid included with LBW is generally a smallare shown in the format described by Green and fraction of total bodyweight (approximately 3% inDuffull[7] (equations 1 and 2): males and 5% in females), the terms FFM and LBW

for the purposes of assessing body composition forLBW (male) = 1.10 × BWt – 0.0128 × BMI × BWtdrug administration can be considered interchangea-(Eq. 1)ble. Clinically, measuring body fat is difficult andno accurate method is available for routine clinicalLBW (female) = 1.07 × BWt – 0.0148 × BMI × BWt

use.[11] Measurement of FFM is easier and common-(Eq. 2)

2005 Adis Data Information BV. All rights reserved. Clin Pharmacokinet 2005; 44 (10)

Quantification of Lean Bodyweight 1053

ly performed using bioelectrical impedance analysis reactance is approximately 10% of the resistance,[12]

(BIA) or dual-energy x-ray absorptiometry (DXA). and very small relative to impedance (<4%),[10] it isoften assumed that resistance and impedance are

Objective approximately equivalent and are used interchange-ably.[10,12,14] At present, a variety of equations have

The objective of this study was to develop a been presented in the literature to compute FFMsemi-mechanistic model for predicting FFM from from resistance or impedance, although it remainssubject characteristics. The study was conducted in controversial as to which one is the most accuratetwo parts. The first part involved the development of and reliable.a semi-mechanistic model for prediction of impe-dance from anthropometric measures. The second Dual-Energy X-raypart incorporated a semi-mechanistic model to link Absorptiometry (DXA)the prediction of impedance from part 1 to estimates

DXA is regarded as a reference method for FFMof FFM.estimation.[15] This method assumes that the body iscomprised of three components, which can be dis-Bioelectrical Impedance Analysis (BIA)tinguished by their x-ray attenuation properties. Thethree components are lean tissue mass, fat mass andBIA is a readily accessible method of assessingbone mineral mass, and FFM is made up of leanFFM. It is noninvasive, portable, inexpensive andtissue mass and bone mineral mass.[16] To measureprovides immediate results. Although BIA is gener-body composition using DXA, two differing low-ally known as a method of measuring FFM, it actu-energy x-ray beams are passed through the body.ally estimates total body water. As water is a con-Since the density of fat and lean tissues is different,stant fraction of FFM (around 72% in males andthe beams are attenuated to differing degrees. The73% in females),[10] FFM can be estimated as theattenuation ratio, which is the ratio of beam attenua-ratio of total body water to the constant water frac-tion at the lower energy to higher energy, can thention. BIA measures the impedance or opposition ofbe applied to established mass attenuation equa-biological tissue to the flow of an alternating electrictions[17] to estimate the mass of each component.current. In the body, lean tissue preferentially con-

ducts electricity since it contains water and electro-Patients and Methodslytes, while fat mass impedes the current flow as it is

largely anhydrous. It can be readily shown that themeasured impedance of a body is inversely related Patientsto total conductive volume (V) and to the length of

This study comprises data from two populations.the conductor (L). This relationship can be ex-Population A was comprised of 303 subjects (146pressed as shown in equation 3:[12]

males and 157 females), of whom 88 (39 males andV = rL2/R 49 females) were normal weight (BMI <25 kg/m2)

(Eq. 3) and 215 (107 males and 108 females) were over-where ρ is the resistivity constant and R is the weight or obese (BMI ≥25 kg/m2). The normal-resistance. In practice, application of BIA theory to weight subjects, including students and staff, werethe human body is that the body is considered to be a recruited from the University of Queensland, Bris-single cylinder of length equal to stature height bane, QLD, Australia. Approval for collection of(Ht)[13] and the conductive volume is that of total these data was obtained from the Ethics Committee,body water (TBW) and is therefore proportional to School of Pharmacy, University of Queensland,the term Ht2/R, which is termed the impedance Australia. All subjects gave informed consent toindex or quotient.[14] Impedance actually comprises participate in the study. Both anthropometric andtwo components, resistance and reactance. As the BIA data were recorded. Subjects who were (or



could have been) pregnant were excluded, together and ankle at the mid-line between the bonywith those who had medical electronic devices such prominences. Subjects were asked to empty theiras pacemakers. The data for overweight and obese bladders before the measurement and not to takesubjects (BMI ≥25 kg/m2) arose from two sites. strenuous exercise 12 hours before the measure-Anthropometric measures and BIA data were avail- ments. BIA instruments from different manufactur-able from a de-identified database of patients attend- ers were used at the different sites: a Bodystat 1500ing the Department of Diabetes and Endocrinology (Bodystat Ltd, Douglas, Isle of Man, UK) singleObesity Clinic, at the Princess Alexandra Hospital, frequency (50 kHz) instrument was used at PrincessBrisbane, QLD, Australia, and were completed by Alexandra Hospital, and an SEAC SFB3 multifre-one observer. This database was collected for quency instrument (Impedimed Pty Ltd, Brisbane,clinical reasons. Anthropometric measures, BIA and QLD, Australia) was used at the University ofDXA data were also provided from a BIA database Queensland and Queensland University of Technol-maintained at the Department of Biochemistry and ogy. All measurements were performed in accor-Molecular Biology, University of Queensland. Ethi- dance with the manufacturer’s manual. In the case ofcal approval was obtained for both datasets. the SFB3 multifrequency instrument, impedance

Population B was comprised of 70 subjects (22 data at 50 kHz only were used, comparable with thatmales and 48 females), of whom 24 (4 males and 20 of the Bodystat instrument. Measurements per-females) were normal weight (BMI <25 kg/m2) and formed with reference resistors showed that there46 (18 males and 28 females) were overweight or was no difference between the two instruments.obese (BMI ≥25 kg/m2). This population was ob-tained from body composition studies being under- DXAtaken at the School of Human Movement Studies,

Whole-body and regional (trunk, arm and leg)Queensland University of Technology, Brisbane,lean and fat tissue were determined with the use ofQLD, Australia, under ethics approval from the in-DXA (DPX-L, Lunar Radiation Corp., Madison,stitution’s Human Research Ethics Committee. ThisWI, USA). The scans were analysed with the use ofpopulation contained the same anthropometric dataADULT software, version 1.33 (Lunar Radiationand FFM data as population A but excluded BIACorp., Madison, WI, USA). The calculation of ap-data.pendicular lean and fat mass was made according to

Anthropometric Measurements the approach described by Heymsfield et al.[18] WithHeight (cm), bodyweight (kg), waist circumfer- the use of specific anatomic landmarks, the legs and

ence (cm) and hip circumference (cm) were mea- arms are isolated on the skeletal x-ray planogramsured. Height was measured to the nearest 1mm (anterior view). The arm encompasses all soft tissueusing a stadiometer, and bodyweight was measured extending from the centre of the arm socket to theto 0.1kg using digital scales. BMI was calculated as phalange tips, and contact with the ribs, pelvis orbodyweight (kg) divided by the square of height greater trochanter is avoided. The leg consists of all(m2). Waist and hip circumference were measured soft tissue extending from an angled line drawnwith a tape measure. The waist-to-hip circumference through the femoral neck to the phalange tips. Theratio was calculated as waist circumference (cm) system software provides the total mass, ratio of softdivided by hip circumference (cm). tissue attenuations, and bone mineral mass for the

isolated regions. The ratio of soft tissue attenuationBIAfor each region was used to divide bone mineral-freeImpedance was measured using a conventionaltissue of the extremities into fat and lean compo-tetrapolar technique while subjects were in a supinenents. Limb fat and lean tissue were calculated fromposition. Electrodes that provided alternating cur-summed arm and leg fat, and lean tissues, respec-rent were placed at the base of the fingers and toes,tively.with voltage sensing electrodes placed on the wrist



Model Development anistic model to describe FFM from impedance(model 4) was developed using NONMEM version

This study used impedance rather than resistance 5 (Globomax, Hanover, MD, USA).[19]

to develop a new model for predicting FFM. Tworesponses were available for model development – Model Performanceimpedance and DXA-estimated FFM. These two

The predictive performance of all models wasresponses were modelled sequentially, anthropo-assessed in terms of the mean error (ME) and rootmorphic measures to impedance and impedance tomean square error (RMSE).[20] ME is a measure ofFFM, in order to provide a basis for development ofbias in prediction and the 95% confidence intervaltwo semi-mechanistic models. These models canshould include zero for a nonbiased model. RMSE isultimately be applied individually (if impedance isa measure of the precision of the model predictions.available clinically) or as a combined full model toThe predictive loss is presented as a ratio of thepredict FFM from patient anthropomorphic charac-mean squared error of the semi-mechanistic modelteristics. The two responses were also modelledover the saturated model. Interpretation is intendedempirically, therefore providing four models for de-to be considered only in terms of the fractional lossvelopment:and not to have any specific statistical qualities.1. an empirical model to describe impedance fromFinally, the semi-mechanistic FFM model was eval-anthropometric features;uated against an independent population (population2. a semi-mechanistic model to predict impedanceB). The predictive performance in terms of ME andfrom anthropomorphic features;RMSE was computed.3. an empirical model to predict FFM from anthro-

pometric features; Model 1: Empirical Model for Impedance4. a semi-mechanistic model to predict FFM from The empirical model was derived through step-impedance. wise multiple regression of population A. The de-

Both empirical models were developed using a pendent variable was the impedance measurementdata-driven approach, whereas the semi-mechanistic from the BIA, and the explanatory variables weremodels were developed based on biological knowl- the subjects’ anthropometric measures. The best em-edge of the interactions between variables. pirical model was selected using the Akaike Infor-

mation Criterion (AIC),[21] which is a measure of theThe empirical models were allowed to include updifference between goodness-of-fit and model com-to ten anthropometric measures with second levelplexity. The model with the smallest AIC is consid-interaction terms. The empirical models were usedered the model with the best overall statisticalto represent a saturated model, i.e. the best possibleproperties and parameter balance.model to describe the data, and were not intended

for routine clinical use. The intended use of the Model 2: Semi-Mechanistic Model for Impedancesaturated model was to determine the predictive loss The semi-mechanistic model was developedassociated with assuming a priori the functional based on the assumption that the body is describedrelationships inherent in the semi-mechanistic mod- as various cylindrical conductors (arms, legs andels. torso), and resistance for each cylindrical conductor

The empirical models to predict BIA (model 1) is proportional to length (L) and inversely propor-and FFM (model 3) from anthropometric data were tional to cross-sectional area (A). Resistance (R)developed using the statistical program NCSS 2001 also depends on the composition of the cylinder.and PASS Trial (Number Cruncher Statistical Sys- This relationship can be shown by the followingtems, Kaysville, UT, USA). The semi-mechanistic equation (equation 4):model for BIA (model 2) was developed usingMATLAB student version 6.5 (The MathWorks, R µ L/A ´ composition

Inc., San Diego, CA, USA). Finally, the semi-mech- (Eq. 4)



In BIA, the resistive component is considered to where θ1 and θ2 are parameters to be estimated indominate the impedance, as discussed in the back- the model that may vary between males and females.ground section, and overall cylindrical length is The semi-mechanistic model was developedapproximated as height; therefore, impedance (Z) based on population A using a cross-validation tech-can be expressed as equation 5: nique. In cross-validation, the population was split

into two groups by random sampling without re-Z µ Ht/A ´ composition placement. The first group comprised 90% of the

(Eq. 5) total subjects and was used to estimate the modelIn this approximation we assume that the compo- parameters, and the second group, comprising 10%

sition of the body is similar between obese and of the total subjects, was used to evaluate the predic-nonobese subjects. As the body consists of fat mass tive performance of the developed model. This pro-and FFM, and we propose impedance is proportion- cess was repeated 5000-fold to provide parameteral to the concentration of fat mass, therefore (equa- estimates.tion 6):

Model 3: Empirical Model to Predict Fat-FreeZ µ Ht/A ´ [fat mass] Mass (FFM)

(Eq. 6) The empirical model was developed using step-An indicator of the concentration of fat mass may wise multiple regression analysis, and the best

be gained by considering the density of the body, model was again selected using the AIC.[21]

since fat mass has lower density than FFM. If weModel 4: Semi-Mechanistic Model to Predict FFMassume that the composition of the body is uniformModel 4 was a semi-mechanistic model that in-then it would seem reasonable to propose the rela-

corporated the prediction for impedance (fromtionship shown in equation 7:model 2) into a widely accepted model to predictFFM from BIA data.[22] This model takes the generalZ µ Ht/A ´ density

−1

form shown in equation 13:(Eq. 7)Since density = bodyweight/body volume, and if FFM µ Ht2/Z

we approximate body volume = A × Ht, then (equa- (Eq. 13)tions 8, 9 and 10):

where is the predicted impedance.Z µ Ht/A ´ [BWt/(A Ht)]−1

Although the exact nature of the BIA index ap-(Eq. 8) pears to have been empirically derived, it is biologi-

cally reasonable that FFM is inversely proportionalZ µ Ht ´ [BWt/Ht)]−1

to impedance but proportional to body size. On the(Eq. 9) basis of this relationship, the model to predict FFM

from height and our predicted impedance is given asZ µ Ht2/BWt shown in equation 14:

(Eq. 10)As BMI = BWt/Ht2, thus (equation 11):

5

4

Z

Ht 3 θ

θθ=FFM

(Eq. 14)Z µ 1/BMI

The effect of sex on the model used to predict(Eq. 11)FFM was also investigated, by allowing the parame-Finally, a regression model is proposed such thatter values (θ1, θ2, θ3, θ4, θ5) to vary between males(equation 12):and females. Standard goodness-of-fit criteria, such

Z = q1/BMI + q2 as assessment of the objective function and parame-(Eq. 12) ter estimates, and diagnostic plots were assessed.



Between-subject variance (BSV) for each parameterwas also estimated. Goodness-of-fit was assessed bythe objective function value of NONMEM and stan-dard diagnostic plots. A statistically significant im-provement in model fit was based on a drop in theobjective function value of >3.84 units between twonested models (α = 0.05, degrees of freedom = 1,χ2).

Ultimately, models 4 and 2 would be combinedto provide a single model for predicting FFM frompatient characteristics. The developed model forFFM was externally evaluated by predicting intopopulation B.

Results

A total of 373 subjects (168 males and 205 fe-males) were studied. The anthropometric and BIAcharacteristics for each population are shown intable I. The data used to develop the model topredict impedance comprised of patient body-weights that ranged from 40.7–216.5kg and BMIthat ranged from 17.1–69.9 kg/m2.

Development of Models toPredict Impedance

Model 1: Empirical Model for ImpedanceThe empirical (saturated) model that best predict-

ed impedance was found to be a function of sex,bodyweight, age, waist size, height and hip size, andwas described by the following equation 15:

Z = 521 + (200 × sex) – (10.1 × bodyweight) –

(8.23 × age) + (3.17 × waist) – (1.05 × waist × sex) +

(4.31 × age × height) + (92.8 × height2) +

(0.019 × bodyweight2) + (0.010 × hip2)

ˆ

(Eq. 15)where height is measured in metres, bodyweight isin kilograms, waist circumference is in centimetres,hip circumference is in centimetres and sex is codedas 0 for males and 1 for females. The predictiveperformance for the developed empirical model isshown in table II.


Tab

le I

. A

nthr

opom

etric

, bi

oele

ctric

al im

peda

nce

anal

ysis

and

dua

l-ene

rgy

x-ra

y ab

sorp

tiom

etry

cha

ract

eris

tics

of s

tudy

pop

ulat

ions

a

Par

amet

erM

ale

Fem

ale

popu

latio

n A

popu

latio

n B

popu

latio

n A

popu

latio

n B

(n =

146

)(n

= 2

2)(n

= 1

57)

(n =

48)

Age

(y)

18–8

2 (4

1 ±

11.7

)29

–64

(49

± 9.

3)19

–79

(40

± 12

.0)

21–6

2 (4

5 ±

10.5

)

Hei

ght

(cm

)15

9.0–

208.

9 (1

77.5

± 7

.8)

159.

0–18

9.0

(177

± 8

.0)

137.

8–18

5.0

(164

.0 ±

7.0

)15

1.0–

187.

0 (1

65.0

± 6

.0)

Bod

ywei

ght

(kg)

60.6

–216

.5 (

108.

4 ±

34.6

)63

.8–1

31.7

(90

.3 ±

15.

3)40

.7–1

96.2

(93

.5 ±

33.

7)47

.6–1

05.9

(71

.4 ±

14.

7)

Bod

y m

ass

inde

x (k

g/m

2 )18

.2–6

9.9

(34.

5 ±

11.0

)22

.4–3

7.7

(28.

6 ±

3.7)

17.1

–66.

3 (3

4.7

± 12

.3)

18.7

–38.

4 (2

6.2

± 5.

0)

Wai

st c

ircum

fere

nce

(cm

)73

.0–1

74.0

(11

1.5

± 27

.1)

82.0

–116

.5 (

97.9

± 9

.8)

61.0

–171

.0 (

100.

0 ±

27.3

)63

.0–1

11.0

(81

.0 ±

12.

3)

Hip

circ

umfe

renc

e (c

m)

88.0

–184

.0 (

116.

4 ±

21.0

)92

.0–1

22.0

(10

5.7

± 7.

06)

82.0

–187

.0 (

121.

5 ±

25.0

)84

.0–1

33.0

(10

5.3

±11.

0)

Wai

st-t

o-hi

p ra

tio0.

79–1

.22

(0.9

5 ±

0.09

)0.

80–1

.06

(0.9

3 ±

0.07

)0.

65–1

.03

(0.8

1 ±

0.08

)0.

69–0

.95

(0.7

7 ±

0.06

)

Impe

danc

e (o

hm)

262.

0–63

1.0

(428

.9 ±

76.

4)N

A32

5.0–

862.

0 (5

29.9

± 1

13.9

)N

A

Fat

-fre

e m

ass

(kg)

44.8

–106

.3 (

72.2

± 1

2.0)

40.7

–78.

8 (6

1.2

± 8.

7)28

.1–7

9.7

(50.

5 ±

9.9)

34.4

–73.

8 (4

4.4

± 5.

6)

aV

alue

s ar

e ex

pres

sed

as r

ange

(m

ean

± S

D).

NA

= n

ot a

vaila

ble.


Table II. The predictive performance of the empirical model for impedance

Sex r2 Mean error Mean square error Root mean square error(95% CI) (95% CI) (95% CI)

Male 0.73 –1.94 (–9.78, 5.89) 1.81 × 103 (1.05 × 103, 2.57 × 103) 42.5 (32.4, 50.7)

Female 0.79 5.81 (–3.84, 15.4) 3.12 × 103 (2.23 × 103, 4.01 × 103) 55.9 (47.2, 63.3)

Combined 0.82 2.16 (–4.15, 8.47) 2.50 × 103 (1.91 × 103, 3.10 × 103) 50.0 (43.7, 55.7)

Model 2: Semi-Mechanistic Model for Impedance

A reasonably strong relationship was found be-FFM = (1.59 × bodyweight) – (0.087 × hip × sex) –

(0.003 × hip × waist) – (0.004 × bodyweight2)– 16.2tween impedance and the inverse of BMI. The asso-

(Eq. 18)ciation was found to be different between males andfemales (r2 = 0.54 and 0.64, respectively) and is where bodyweight is in kilograms, hip circumfer-shown in figure 1. The equations for predicting ence is in centimetres, waist circumference is inimpedance from BMI are given for males (equation centimetres and sex is coded as 0 for males and 1 for16) and females (equation 17): females. The predictive performance for the devel-

oped empirical model is shown in table IV.216

1068.6 ˆ

3

+

´

=

BMIZ (male)

Model 4: Semi-Mechanistic Model to Predict FFM(Eq. 16)Based on the BIA index Ht2/Z hypothesis, the

general predictive model for FFM (equation 14)244BMI

1078.8Z

3

(female) +´

=

generated using NONMEM was found to be (equa-(Eq. 17)tion 19):Table III summarises the cross-validation results

and the predictive performance for the semi-mech-anistic models. The semi-mechanistic models incor-porated bodyweight and height as a metric of BMI,while the empirical model incorporated bodyweight,height, age and waist and hip circumference. Fromthe plot of predicted impedance versus measuredimpedance (figure 2), it is seen that the semi-mech-anistic model for impedance provides a good predic-tor of the impedance for both males and females (r2

= 0.67 and 0.74, respectively). There was no appar-ent bias for the semi-mechanistic model. The appar-ent loss in predictive performance was approximate-ly 6%, where the ratio of the MSE for the semi-mechanistic model over the saturated empiricalmodel for both sexes combined was 1.06. This ap-pears to be an acceptably small loss of informationassociated with the biologically more plausible andsimpler semi-mechanistic model. The absolute sizeof the precision (RMSE) was approximately 10% ofthe average value of impedance.

Model 3: Empirical Model to Predict FFMThe best empirical model to predict FFM was

found to be (equation 18):

0100200300400500600700800900

1000

0100200300400500600700800900

1000

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

BMI−1

Impe

danc

e (o

hm)

a

b

Fig. 1. Relationship between impedance and the inverse of bodymass index (BMI) in (a) males and (b) females.



Z

Ht(m) 10 9.27 FFM

23´´=

(Eq. 19)where θ3 is 9.27 × 103, θ4 was fixed at 2.00, and θ5was fixed at 1. Estimating θ4 did not improve the fitof the model and the estimated value was 1.7. Fixingthe value to 1.7 or 2.0 yielded the same objectivefunction value from NONMEM, therefore the valueof 2 was chosen. Estimating θ5 yielded a value thatwas 0.922 and no improvement in model fit. Thisvalue was then fixed to 1.0. BSV was only able to beestimated for θ3, and the variability between patientswas found to be negligible (coefficient of variation =0.27%). No statistical interaction was found be-tween sex and any of the BIA index parameters. Asshown in figure 3, the new model correlated wellwith the FFM measured by DXA with ME = –0.01(95% CI –0.24, 0.22), RMSE = 1.07 (95% CI 0.90,1.22) for FFM measured by DXA versus each indi-vidual’s value of predicted FFM. The plots betweenresidual and weighted residual versus model predic-tions from the new model against predicted popula-tion FFM are shown in figure 4. It can be seen thatthere was no evidence of bias in the model predic-tion.

The loss of information associated with thechoice of a semi-mechanistic model, compared withthe saturated empirical model, was 35%. This ishigher than for the loss associated with the impe-dance model (6%). Estimation of the parameters θ4and θ5 for the BIA index did not reveal a differentrelationship for this population, which addscredence to the model. The actual value of RMSEfor the model was 3.3, which is only 6% of theaverage FFM estimated by DXA. This level of im-precision is of limited clinical concern.

Model to Predict FFM fromPatient Characteristics

When the semi-mechanistic model for and

FFM (from ), corresponding to models 2 and 4,were combined and simplified, the final model isshown in equations 20 and 21.


Tab

le I

II.

Sem

i-mec

hani

stic

mod

els

for

impe

danc

e de

velo

ped

usin

g cr

oss-

valid

atio

n te

chni

que

Sex

Mod

elS

D o

f th

eS

D o

f th

er2

Mea

n er

ror

Mea

n sq

uare

err

orR

oot

mea

n sq

uare

err

orsl

ope

inte

rcep

t(9

5% C

I)(9

5% C

I)(9

5% C

I)M

ale

117.

993.

960.

67– 1

.62

× 10

– 2 (

– 7.0

8, 7

.05)

1.89

× 1

03 (

1.32

× 1

03,

2.46

× 1

03)

43.4

(36

.3,

49.6

)

Fem

ale

146.

554.

440.

741.

96 ×

10–

2 (–

9.10

, 9.

14)

3.38

× 1

03 (

2.49

× 1

03,

4.26

× 1

03)

58.1

(49

.9,

65.3

)

Com

bine

dN

AN

A0.

782.

30 ×

10–

3 (–

5.81

, 5.

82)

2.66

× 1

03 (

2.12

× 1

03,

3.20

× 1

03)

51.6

(46

.0,

56.6

)

BM

I =

bod

y m

ass

inde

x; N

A =

not

app

licab

le;

SD

= s

tand

ard

devi

atio

n;

= p

redi

cted

impe

danc

e.


Table IV shows the FFM predictive performancefor the developed semi-mechanistic model.

The new model for FFM (equations 20 and 21)was used to predict FFM from population B, fromsubject characteristics in this population. The pre-dicted FFM was plotted versus their observed valueof FFM (from DXA) [figure 5]. Table V shows thepredictive performance for the final model for FFMwhen used to predict FFM for subjects in populationB. It can be seen that the new developed model topredict FFM from subject characteristics is not bi-ased and the value of RMSE is approximately 7.3%that of the average value for FFM. In addition, whenthe model is applied to a typical range of heights andbodyweights, it concords well with the current equa-tion for LBW.[3] Importantly, however, the estimateof LBW does not decline as bodyweight increases,nor does it lead to computation of a negative valueof LBW at extremes of BMI (figure 6).

Discussion

This study reports on the development of a semi-mechanistic model for predicting FFM from theindividual characteristics of patients. Demographics

200

300

400

500

600

700

200

300

400

500

600

700

800

900

200 300 400 500 600 700 800 900

Measured Z

Pre

dict

ed Z

a

b

200 300 400 500 600 700

Line of identity

Fig. 2. Plot of predicted vs measured impedance (Z) for (a) malesand (b) females. of the patients used to develop the model spanned a

wide range of bodyweights (from 40.7 to 216.5kg)and BMI values (from 17.1 to 69.9 kg/m2). It shouldbe noted that 71% of the study patients were over-

weight or obese. Although this study involved the(Eq. 20) development of a predictive equation for FFM, in

the clinical setting it is reasonable for FFM andLBW to be considered as equivalent descriptors, and

hence this equation could be used to predict LBW.(Eq. 21) FFM differs from LBW in that FFM describes the

Table IV. The predictive performance of the model for fat-free mass

Model r2 Mean error Mean square error Root mean square error(95% CI) (95% CI) (95% CI)

Empirical model

Male 0.82 –0.71 (–1.74, 0.33) 8.27 (3.86, 12.7) 2.88 (1.96, 3.56)

Female 0.81 –0.72 (–1.72, 0.32) 8.82 (4.33, 13.1) 2.97 (2.08, 3.62)

Combined 0.95 –0.73 (–1.45, –0.01) 8.25 (5.16, 11.4) 2.87 (2.27, 3.38)

Semi-mechanistic model

Male 0.75 –1.27 (–2.49, –0.06) 12.4 (5.11, 19.7) 3.52 (2.26, 4.44)

Female 0.76 –0.28 (–1.43, 0.88) 9.79 (5.21, 14.4) 3.13 (2.28, 3.79)

Combined 0.93 –0.77 (–1.62, 0.07) 11.1 (6.82, 15.4) 3.33 (2.61, 3.92)



obese; however, the study was not designed for thispurpose and hence may have inherent limitationswhen extrapolated to this application. Recently, ithas been suggested that the Cheymol/James equa-tion for LBW leads to inconsistencies in the estima-tion of LBW at extremes of bodyweight and height.These inconsistencies lead to estimation of lowervalues of LBW at extremes of bodyweight thanwould seem reasonable and in some circumstanceseven lead to computation of negative values ofLBW.[7] These inconsistencies are most likely due tothe empirical nature of the evaluation of LBW as thedifference between bodyweight and fat bodyweight(FBW), but where the predictor of FBW was basedon a population where <10% of the study subjectswere obese. Clearly, the population in the Jamesstudy differs from the population demographics oftoday.

FFM is another size descriptor presented in thepharmacokinetic literature. Of the current work un-dertaken in this area, the simpler methods available

a

b

30

40

50

60

70

80

90

30

40

50

60

70

80

90

30 40 50 60 70 80 90

Predicted individual FFM

FF

M (

by D

XA

)

Predicted population FFM

Line of identity

Fig. 3. Plot of fat-free mass (FFM) measured by dual-energy x-rayabsorptiometry (DXA) vs (a) predicted population FFM and (b) pre-dicted individual FFM calculated using the developed model forFFM.

mass of the body after excluding all fat content,whereas LBW is the mass of the body excluding fatcontent other than the lipids in cellular membranes,the CNS and bone marrow.[10] Nevertheless, lipidincluded within the descriptor LBW is a small frac-tion of total bodyweight (3% in males and 5% infemales). The terms FFM and LBW are thereforeused interchangeably.[23]

LBW is often used as a size descriptor to scaledrug dose.[2] The equation currently used for LBW(see Cheymol[3] for details) was derived based onthe study of James,[24] which included 133 patientsfrom three studies.[25-27] The purpose of the Jamesreport was to provide a size descriptor that could belinked to mortality data for life insurance tables.This has provided a convenient application in thearea of drug administration for patients who are

−10

−5

0

5

10

Res

idua

l

−3

−2

−1

0

1

2

3

30 40 50 60 70 80 90

Predicted population FFM

Wei

ght r

esid

ual

a

b

Fig. 4. Relationship between (a) residual and (b) weight residualfrom the developed model for fat-free mass (FFM) plotted againstpredicted population FFM.



are better predictors of body fat percentage thanBMI.[32,33] Nevertheless, skinfold thickness mea-surements require a considerable amount of techni-cal skill in order to obtain accurate results. Addition-ally, skinfold thickness measurements cannot beperformed in some obese patients because of theinadequate size of the calipers.[34] Although predic-tion equations to estimate FFM from skinfold thick-ness measurements have been published, it is likelythat such equations are age, sex and populationspecific, which may lead to biased estimates of FFMwhen the equations are applied to a different popula-tion.

BIA is considered the most accurate of the ‘sim-ple’ methods for estimation of FFM; however, theaccuracy of BIA depends on the parameters andstructure of the regression equation that links impe-dance with FFM.[35] To date, a variety of regressionequations to predict FFM for BIA have been devel-oped. Unfortunately, no well validated equation hasbeen developed from obese subjects, which maylead to inconsistencies in prediction when theseequations are extrapolated to an obese population. Inaddition, the clinical applicability of an equationthat relies on an actual BIA measurement will be

a

b

20

30

40

50

60

70

80

90

20

30

40

50

60

70

80

90

20 30 40 50 60 70 80 90

Predicted FFM (kg)

Mea

sure

d F

FM

(kg

)

Line of identity

Fig. 5. Plot of predicted fat-free mass (FFM) using the new devel-oped model vs FFM measured using dual-energy x-ray absorpti-ometry (population B) for (a) males and (b) females.

limited owing to the requirement for validated BIAequipment at all clinical locations. Hence, an accu-for estimation of FFM are BMI, skinfold thicknessrate method that relies only on easily measuredmeasurements and BIA. BMI or ‘Quetelet’s index’subject characteristics (e.g. bodyweight, height andis widely used to classify obesity and is easy tosex) would be of significant clinical value.perform.[28] To date, several equations for predicting

body fat percentage from BMI have been devel- The development of the semi-mechanistic modeloped[29,30] and FFM can be calculated as the differ- for predicting FFM from patient demographics inence between bodyweight and body fat. However, this study was conducted in two parts. The first partthese equations were not developed from the popu- was to develop a semi-mechanistic model to predictlation with a wide range of bodyweight. impedance from subject characteristics, and the sec-

Skinfold thickness measurement is one of the ond part was to incorporate the semi-mechanisticreliable methods for evaluating adiposity.[31] It has model for impedance into an overall model to pre-been reported that skinfold thickness measurements dict FFM. We use the term semi-mechanistic to

Table V. The predictive performance of the semi-mechanistic model for fat-free mass (FFM) when used to predict FFM for subjects inpopulation B

Sex r2 Mean error Mean square error Root mean square error(95% CI) (95% CI) (95% CI)

Male 0.72 –2.74 (–4.76, –0.73) 28.6 (13.6, 43.7) 5.35 (3.69, 6.61)

Female 0.61 1.14 (0.07, 2.20) 15.2 (6.51, 23.8) 3.90 (2.55, 4.88)

Combined 0.85 –0.04 (–1.09, 1.00) 19.3 (11.6, 26.9) 4.39 (3.41, 5.19)



−80−60−40−20

030406080

100

−500

−100

−50

0

50

100

170180

160150

140130

120 6080 100

120 140160

180

Height (cm) Total bodyweight (kg)

LBW

(kg

)

a

b

The newequation

The Cheymolequation

The newequation

The Cheymolequation

Fig. 6. Estimated lean bodyweight (LBW) for (a) males and (b) females according to the Cheymol[3] equation and our equations for LBW.

illustrate that the structural form of the relationship was encouraging to note that when we estimated thebetween patient demographics and impedance was exponents of the relationship the original form wasdeveloped based on a priori knowledge rather than preferred, i.e. that the exponent for height was twoon BIA measurements. We therefore believe that the and for predicted impedance was one.model incorporates biologically reasonable features The final model for predicting FFM from patientand hence would be of more use for extrapolation characteristics is based on bodyweight, height andthat is inevitable in any clinical application of the

sex. Given the wide range of bodyweights of sub-equation than a model that was developed from an

jects enrolled in this study it is likely that the modelempirical relationship derived from the data withoutwill have good predictive performance with mini-reference to understanding how impedance of a cur-mal need for extrapolation to patients who haverent through biological tissues might arise. Incorpo-more extreme BMI values. The predictive perform-ration of the ‘semi-mechanistic’ model for impe-ance of the model was assessed using both internaldance into an overall model to predict FFM wasand external evaluation. The external evaluation as-based on a standard relationship (Ht2/Z) that hassessed the ability of the model to predict FFM inbeen described before.[22] This relationship has beenpatients who were not used for model building. Thisfound to provide a good predictor of FFM fromis a strong test of the ability of the model to performimpedance over a wide range of subject characteris-well when used to predict into a new population.tics (aged 18–50 years and FFM 34–96kg).[36] AgainThe prediction error was acceptably small, as indi-we did not change the structural relationship of this

model, but rather estimated the parameter values. It cated by the ME of –0.04 and RMSE of 4.39.



It is also encouraging to note that our model for AcknowledgementsFFM provides predictions that are very similar to

We would like to acknowledge Christine Staatz, PhD, forthat of the Cheymol/James for subjects with BMI her assistance in conducting the study. S. Janmahasatian wasvalues that are <35 kg/m2. Hence, for patients of funded by a scholarship from the Australian Agency for

International Development (AusAID). The authors have nonormal weight to moderately obese (which corre-potential conflicts of interest that are directly relevant to thesponds to the demographics of the subjects in thecontents of this study.original James[24] study) either of the predictive

equations for LBW/FFM could be used with reason-Referencesable accuracy. However, for patients who are mor-

1. Kopelman PG. Obesity as a medical problem. Nature 2000; 404bidly obese it would seem prudent not to use the (6778): 635-432. Green B, Duffull SB. What is the best size descriptor to use forCheymol/James equation, and it is in this circum-

pharmacokinetic studies in the obese? Br J Clin Pharmacolstance that the current work will provide some ad-2004; 58 (2): 119-33

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enoxaparin in obese patients. Br J Clin Pharmacol 2002; 56:bodyweights and BMI (population A), the data used 96-103to evaluate the model (population B) were limited to 5. Sarubbi Jr FA, Hull JH. Amikacin serum concentrations: predic-

tion of levels and dosage guidelines. Ann Intern Med 1978; 89be between the bodyweights of 47.6–131.7kg (BMI(5 Pt 1): 612-8

values of 18.7–38.4 kg/m2). Therefore, further work 6. Wulfsohn NL. Succinylcholine dosage based on lean bodymass. Can Anaesth Soc J 1972; 19 (4): 360-72on evaluation would be prudent. A further potential

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8. Morgan DJ, Bray KM. Lean body mass as a predictor of drugsult in systematic differences in the impedance mea-dosage: implications for drug therapy. Clin Pharmacokinet

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obese? Clin Pharmacokinet 2004; 43 (15): 1167-78Based on this empirical test it seems that any differ-10. Roche AF, Heymsfield SB, Lohman TG, editors. Human bodyence would indeed be small and of doubtful clinical composition. Champaign (IL): Human Kinetics, 1996

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12. Bioelectrical impedance analysis in body composition measure-populations. Nevertheless, it has been reported that ment. Bethesda (MD): National Institutes of Health, Public

Health Service, 1994 Dec 12-14variation between observer of DXA and BIA mea-13. Liedtke RJ. Fundamentals of bioelectrical impedance analysissurements is not significant.[37,38]

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24. James W. Research on obesity. London: Her Majesty’s Station-35. Kyle UG, Genton L, Karsegard L, et al. Single predictionery Office, 1976

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density and total body potassium content. Clin Sci 1972; 43 36. Lukaski HC, Bolonchuk WW, Hall CB, et al. Validation of(3): 469-75

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