## Abstract

Conventional bioimpedance analysis (BIA) methods now simplify the representation of lower limb geometry and electrical properties for body composition estimation. In the present study, a three-dimensional model of the lower limb was assembled by segmentation of magnetic resonance cross-sectional images (MRI) for adipose tissue, skeletal muscle, and bone. An electrical network was then associated with this model. BIA and MRI measurements were made in six lean subjects (3 men and 3 women, age 32.2 ± 6.9 yr). Assuming 0.85 S/m for the longitudinal conductivity of the muscle, the model predicted in the examined subjects an impedance profile that conformed well to the BIA impedance profile; predicted and measured resistances were similar (261.3 ± 7.7 vs. 249 ± 9 Ω; *P* = not significant). The resistance profile provided, through a simpler model, muscle area estimates along the lower limb and total leg muscle volume (mean 4,534 cm^{3} for men and 4,071 cm^{3} for women) with a mean of the absolute value of relative error with respect to MRI of 6.2 ± 3.9. The new approach suggests that BIA can reasonably estimate the distribution and volume of muscles in the lower extremities of lean subjects.

- bioimpedance analysis
- body composition
- nutritional assessment
- magnetic resonance imaging

the study of human body composition in health and disease is of increasing interest in both research and clinical practice (13). The availability of advanced techniques, such as computed tomography (CT) and magnetic resonance imaging (MRI), allows accurate and reproducible estimates of major tissue and organ compartments (10, 14). However, CT and MRI can be performed only in specialized research units, since the availability of instrument time is limited, the evaluation cost is high, and technical expertise is required for image analysis (20).

In the past decade, bioimpedance analysis (BIA) has been advocated as a simple method for body composition estimation in humans because it is noninvasive, inexpensive, and well suited for epidemiological studies (3). However, current BIA electrical and geometric models are oversimplified, and results are often inaccurate (3,6). Typically, BIA estimates of total body water are based on equations in which the fat-free compartment is assumed to be a cylinder with uniform electrical characteristics, and between-individual differences in electrical path length are accounted for by measured height. The conventionally used electrical path is arm to leg, although measurement of isolated limbs or trunk impedance is now gaining recognition (2, 18, 19). Recently, a detailed analysis of resistance data of the human thigh was reported by Aaron et al. (1), and resistance data from the thigh and calf were analyzed in association with MRI body composition estimates by Fuller et al. (7).

The aim of the present study was to evaluate the feasibility of using multiple BIA measurements for quantifying muscle volume and for reconstructing the profile of the muscle cross-sectional area along the lower limb. Our study was based on a mathematical model that describes the electrical characteristics of the lower limb in healthy lean subjects. The lower limb was selected as the study site since it has a simple geometry and tissue composition compared with the trunk. The mathematical model uses a realistic reconstruction of limb geometry and tissue composition obtained from MRI measurements. The model provides the distribution of electrical potential and the fluxes of current induced in the lower limb by an externally applied current and thus allows for a comparison with BIA measurements at multiple sites along the lower limb. Furthermore, on the basis of the results obtained by the model, a method for reconstructing muscle cross-sectional area along the lower limb from BIA data is proposed.

## METHODS

#### Subjects and anthropometry.

Six volunteers (3 men and 3 women, age 32.2 ± 6.9 yr, body mass index 22.4 ± 1.4 kg/m^{2}) were enrolled in the study. All subjects were in good health, as assessed by clinical and laboratory examinations, were not taking medications, and did not participate in intensive physical activity. The women were studied in the follicular phase of the menstrual cycle. Body weight was measured to the nearest 0.1 kg by a beam scale and height to the nearest 0.5 cm was measured using a stadiometer (Holatin, Crosswell, Wales, UK). The protocol conformed to the directives given by the Ethical Committee of the Institutional Health Review Board of the Catholic University, School of Medicine, in Rome. Informed consent was obtained in all cases.

#### MRI.

Subjects completed an MRI scan of the lower limb using a 0.5-T scanner (model Vectra 0.5; General Electric, Milwaukee, WI) with an axial T_{1} weighted spin echo sequence. Axial views were acquired with 10-mm slice thickness and a 50-mm interslice gap in five subjects and 10 mm in one subject. The lower limb lengths corresponding to the scan views are reported in Table 1. The area and volume of skeletal muscle within each slice were calculated by a trained observer using the VECT image analysis software (Martel).

To obtain the discretized three-dimensional geometric model and tissue composition of the lower limb, as required by the BIA mathematical model, the MRI were scanned (Epson scanner Perfection model 1200Photo) with a resolution of 300 pixels/in. and then digitized. Each digitized image was then processed to identify the regions corresponding to the different tissues. Only three tissue types, namely bone, muscle, and adipose tissue, were distinguished; cartilage and tendon were assigned to bone, vascular tissue to muscle, and skin to adipose tissue. Each tissue type was labeled by a different color. Each image was then subdivided into 22 × 22 square cells of 1 cm side, and cells were assigned to the prevailing tissue or to external air.

In the final step, a text file was formed as a stack of discretized images. To have images at 1-cm intervals when the 50-mm interslice gap was used in the MRI scan, each of the available images was replicated four times (2 times the initial and the final image). The stack provided a three-dimensional model of lower limb geometry and tissue composition with a total, including the external air, of 22 × 22 × *N* cubic cells of 1 cm side, *N*depending on the length of the subject's lower limb (*N* from 72 to 77; see Table 1).

#### Bioelectrical impedance analysis.

Resistance and capacitive reactance were determined using a multifrequency BIA system (Human-IM DIP; DS-Medigroup, Milan, Italy) with a delivered current of 800 μA at a frequency of 50 kHz. The current-injection electrodes were positioned on the middorsum of the right hand, just proximal to the metacarpal phalangeal joint line, and on the middorsum of the right foot, just proximal to metatarsal phalangeal joint line (3).

To determine the impedance profile along the lower limb, one of the voltage electrodes was positioned on the middorsum of the right wrist and kept fixed. The other electrode was positioned at various contiguous levels along the lower limb at 2.5-cm intervals, starting from the midanterior right ankle up to the midline of the anterior surface of the right thigh at about the level of the inguinal crease. By subtracting the measured impedances from whole body impedance, we obtained the impedance profile along the lower limb, as would be measured between an electrode located at different levels along lower limb from the ankle to the hip and an electrode located at the ankle.

#### BIA mathematical model.

As seen in the
, the mathematical model for BIA consists of a set of equations of the form of *Eq. 7A
*, one for each cell of the discretized three-dimensional model of the lower limb. These equations associate an electrical network composed of admittances with the body region of interest, and the admittance values depend on the electrical characteristics of the various tissues.

The electrical characteristics of tissues were obtained from literature data. For the conductivity of skeletal muscle in the longitudinal direction (ς_{mz}), taken as the dominant direction of muscle fibers in the lower limb and corresponding to the*z*-axis in the model, we considered the values of 0.67 and 0.85 S/m according to the resistivity values reported by Fuller et al. (7, 8). The muscle conductivity in the transverse direction (ς_{mx} = ς_{my}) was set to 0.13 S/m, as reported in Ref. 1. Both adipose tissue (at) and bone (b) were assumed to be isotropic tissues, with conductivity ς_{at} = 0.064 and ς_{b} = 0.013 S/m, respectively (1, 5). The tissue permittivities were assumed to depend on the frequency (f, in Hz) of the applied current according to the following expressions (5)
where ɛ is the permittivity of muscle in the transverse direction (mx and my), in the longitudinal direction (mz), and of adipose tissue (at) and bone (b); ɛ_{0} = 10^{−9}/(36π)F/m is the permittivity of free space. Conductivity and permittivity of external air were set equal to zero.

Concerning the externally applied currents (the term *I* in*Eq. 7A
*) that simulate the current delivered to the body during BIA, we had to take into account that, in the present measurements of lower limb bioimpedance, the current-injecting electrodes were placed at locations that are far from the body region considered (i.e., in the ipsilateral hand and foot) to minimize the influence of current injection on the potential measurement. This condition was simulated by replicating the terminal cross sections of the three-dimensional model of the lower limb (one in the ankle and the other in the thigh) to create 10-cm extra spaces below the ankle and above the thigh. The external current was impressed in nodes of the electrical network located at the extreme of these extra spaces, so the region in which the distribution of electrical potential was calculated was at least 10 cm away from the points where the external current was applied.

Under the applied current, the network generated the distribution of the electrical potential in the body region considered and thus allowed us to compute impedance values that were compared with data provided by BIA. The set of equations composing the model was solved by the technique of successive overrelaxation (5, 11).

#### Estimation of muscle cross-sectional area and volume.

A very simplified version of the model in the can provide estimates of muscle cross-sectional area and volume from BIA data, as detailed below.

Because the longitudinal conductivity of muscle is much larger than all other conductivities, and the contribution of the reactive component of impedance is small at 50 kHz, we assumed that the *z*-directed current flowing in the lower limb during BIA is essentially carried by the resistive component of muscle, at least in lean subjects. Moreover, we assumed that, at locations remote from the current-injecting electrodes, the total *z*-directed current in a cross section is equal to the total current (*
*) delivered by the current-injecting electrodes. Thus, denoting the cross-sectional area by *S* and the muscle area by *S*
_{m} (these areas change with the level *z* along the lower limb), and considering the component in the *z*-direction of the real part of the current density *J* (see the
), we may write
Equation 1where d*s* is the element of the cross-sectional area. Moreover, according to *Eqs. 1-4
* of the
, we have
Equation 2In a region far from current-injecting electrodes, the electrical potential is likely to be approximately constant over the cross section; thus, *V* can be considered a function,*V*(*z*), of *z *only. If the potential at the ankle (*z* = 0) is set to zero, the quantity*V*(*z*)/*
* can be interpreted as the resistance between a point of the lower limb at distance *z*from the ankle and a point on the ankle itself. Denoting this resistance as *R*(*z*), we have
Equation 3Thus *Eqs. 1-3
* give for any level *z*along the lower limb the equation
Equation 4and an estimate [*Ŝ*
_{m}(*z*)] of muscle cross-sectional area at the level *z* is obtained as
Equation 5To evaluate the derivative in *Eq. 5
*, the resistance data obtained by BIA were approximated by a weighted sum of two Gaussian cumulative functions plus a straight line according to
Equation 6where F(*z*;μ,ς) denotes the cumulative function of a Gaussian with mean μ and SD ς [note that it should be*R̂*(0) = 0]. The two cumulative Gaussians represent the specific increase of resistance that is observed in the regions of the ankle and of the knee. The parameters c_{1}, c_{2}, c_{3}, ς_{1}, μ_{2}, and ς_{2} of the fitting function were determined by minimization of a weighted least squares index, and*Eq. 5
* was then applied with *R*(*z*) = *R̂*(*z*) and ς_{mz} = 0.85 S/m. The integral over*z* of the estimated cross-sectional area of muscle provided the total muscle volume of the lower limb.

## RESULTS

#### Discretized model of the lower limb.

Although the discretization of MRI with cells of 1 cm side may seem approximate, the three-dimensional reconstruction of the geometry and tissue composition of the lower limb appeared in general to be rather accurate, at least as the content of muscle tissue is concerned. Figure1 presents the cross-sectional area of the muscle (*S*
_{m}) as computed on the original MRI in the 78 cross sections of the lower limb of the subject in which the MRI scan was performed with a 10-mm interslice gap. Moving from left to right (*z* = 0 corresponds to the ankle), the regions corresponding to the ankle, the calf, the knee, and the thigh are easily recognized. The total volume of muscle in the lower limb region considered, as measured from the original MRI in this subject, was equal to 5,751 cm^{3}.

The muscle areas given by the discretized three-dimensional model are also reported in Fig. 1. It is seen that the approximation becomes less accurate in the regions of the ankle and of the knee, where*S*
_{m} is smaller. Considering all 78 cross sections, the mean error of the area was 0.2 cm^{2}. The total volume of muscle in the discretized model was equal to 5,784 cm^{3}. Figure 1 also shows the less accurate approximation that was obtained for this subject when a reduced number of cross sections at 5-cm intervals was used. Although the muscle area errors are larger, the total volume of muscle given by the model in this case was equal to 5,945 cm^{3}, with an error smaller than 4% with respect to the original MRI data. Similar error values are likely to be found for the other subjects in which the discretized reconstruction of the lower limb was obtained from MRI taken at 5-cm intervals.

The volumes of muscle in the part of the lower limb considered in this study are reported in Table 1 (V_{MRI}) for the six subjects. For *subject 1*, for whom MRI at 1-cm intervals were available, the volume measured on the original images is given.

#### Mathematical model of BIA and analysis of bioimpedance data.

The distribution of the electrical potential provided by the BIA model shows that, in the proximity of the current-injecting electrodes, the potential varies considerably in the cross section from the points closer to the electrode to the points far from it. This effect is markedly reduced in a cross section at a distance of 10 cm. The variability of the potential *V* in the cross section was quantified by computing the ratio (*V*
_{max} −*V*
_{min})/*V*
_{mean} in all of the cross sections, including those of the added extra spaces where the external current was applied. In the cross sections containing the electrodes, the above ratio was in the order of 10, whereas this ratio decreased to values lower than 0.3 in the cross sections at least 10 cm away from the electrodes. However, in the region of the knee where the content of muscle tissue is lower, the ratio was larger, and values up to 1.9 were achieved. When only the cells that form the border of a cross section were considered, remarkable variations of the potential were still found in the region of the knee. Thus the location of the voltage electrode along the circumference of the limb at a given cross section is likely to affect the determination of the resistance.

The model also provided the currents that flow through the various tissues at each location within the lower limb. As expected, the currents flowing in the longitudinal direction (*z* direction) in the muscle were markedly larger than the currents flowing in the other tissues. Far from the current-injecting electrodes, >90% of the*z*-directed current was carried by the muscle, except in the region of the knee where this percentage decreased to values of ∼70%. These results show that the assumptions leading to *Eq.5
* may be considered substantially fulfilled.

The total resistance *R*
_{BIA} and the capacitive reactance *X*
_{BIA} of the part of the lower limb considered, as measured by BIA, are shown in Table2. The mean lower limb resistance was 243.7 Ω for men and 255.3 Ω for women. Reactances were in the range 31–38 Ω. These data were compared with the resistance and reactance computed by the mathematical model of BIA described in the
. Because this model substantially utilizes the lower limb geometry observed by MRI, the discrepancies between data and model predictions should be mainly because of the interindividual variability of the electrical parameters. As expected, the most influent parameter was the conductivity ς_{mz} of skeletal muscle in the longitudinal direction. When ς_{mz} was set at 0.85 S/m, the model slightly overestimated the total resistance of the lower limb (see values of *R*
_{MOD} in Table 2), with the relative errors ranging from ∼0 to 10%. Even larger values of*R*
_{MOD} were predicted with a muscle conductivity of 0.67 S/m, so the value of 0.85 S/m was assumed in the subsequent analysis. Moreover, the model underestimated the reactance of the lower limb (see *X*
_{MOD} in Table 2), confirming, however, the small contribution of the reactive component of the impedance at the frequency of 50 kHz.

The resistance profile along the lower limb found by BIA in the subject in whom the MRI were available at 1-cm intervals is shown in Fig.2. The experimental values of the resistance are plotted at 2.5-cm intervals. The data show that the resistance increases more rapidly in the regions of the ankle and of the knee, where the content of low resistivity muscle tissue is smaller. Figure 2 also presents the profile of the resistance given by the model in the
, computed at each level* z* along the lower limb. The profile of the resistance obtained from the model when using the coarser discretization (i.e., MRI data at 5-cm intervals) is also reported in Fig. 2 and shows that the general pattern of the profile is still adequately reproduced by the BIA model when larger intervals are used for MRI. Figure 3 shows the experimental and predicted profiles for the lower limb of a woman.

#### Estimation of muscle cross-sectional area and volume.

The profile of muscle cross-sectional area along the lower limb and the muscle volume were estimated on the basis of the model of *Eqs.5
* and *
6
* (with ς_{mz} = 0.85 S/m), using the experimental BIA data. Means ± SD of the estimated parameters of *Eq. 6
* (except μ_{2}, which depends on the lower limb length) were as follows: c_{1} = 194.2 ± 46.0 Ω, ς_{1} = 10.4 ± 1.7 cm, c_{2} = 73.2 ± 7.6 Ω, ς_{2} = 8.9 ± 1.7 cm, c_{3} = 1.0 ± 0.2 Ω/cm.

An example of the reconstruction of the profile of muscle cross-sectional area along the limb is shown in Fig.4. Figure 4 shows the experimental profile of resistance together with the fitted profile*R̂*(*z*) and the estimated muscle cross-sectional area *Ŝ*
_{m}(*z*) obtained by *Eq. 5
* together with the areas given by MRI. Although the estimated general pattern was reasonable, large errors may be found at specific locations, such as the knee and the extreme sections of the thigh. Table 1 shows, for each subject, the average error on the cross-sectional area computed as ɛ_{S} = 100 × Σ‖*S*
_{MRI} −*S*
_{BIA}‖*/*Σ*S*
_{MRI}, where *S*
_{MRI} is the muscle cross-sectional area measured by MRI, *S*
_{BIA} is the estimated area*Ŝ*
_{m}(*z*) evaluated at the same level of the MRI, and the sum is carried over all the cross sections considered. The errors on the cross-sectional areas did not cause a large effect on the estimate of total lower limb muscle volume. Table 1reports the estimates of muscle volume for all subjects with the relative error ɛ_{V} = 100 × (V_{MRI} − V_{BIA})/V_{MRI} with respect to the volume measured by MRI. Note that, by definition, it is ɛ_{S} ≥ ‖ɛ_{V}‖. The mean ± SD over the subjects of the absolute value of the error on volume was 6.2 ± 3.9%.

## DISCUSSION

In the past few years, a great deal of attention has focused on the evaluation of skeletal muscle mass as a means of assessing the nutritional status of individuals with various clinical conditions (9, 15, 16). For instance, protein-energy malnutrition is a frequent feature in elderly patients in acute-care settings. Critical illnesses and hospitalization result in catabolic stress, anorexia, and immobilization, which worsen the nutritional status of elderly subjects. Disuse of muscles because of bed rest or chair rest leads to a loss of muscle mass in a range of 1.5%/day in adults (4). In critically ill elderly patients, anorexia and functional dependency, resulting in decreased energy and protein intake, could further contribute to decreased muscle mass. Conversely, adequate muscle mass appears to be the best predictor of good prognosis in critical illness. Loss of skeletal muscle tissue also occurs in patients after major accidents of the spinal cord, and it is important and useful to monitor improvements in skeletal muscle mass and function with rehabilitation therapy (17, 21, 24). Furthermore, the possibility of obtaining a profile of the lower limb skeletal muscle might be useful to follow training athletes during the time. Skeletal muscle (SM) represents the largest fraction of body mass in nonobese adults (22). Because the muscle mass of the limbs accounts for an estimated 75–80% of total body muscle mass (12), appendicular muscle mass has been endorsed as a simple means of quantifying total body muscle mass with the exception of body builders or weight lifters.

The mathematical model of BIA developed here, which used the discretized reconstruction of lower limb geometry and tissue composition obtained by MRI, predicted the pattern of resistance along the lower limb, as measured by BIA. Because the model showed that the electrical current in the lower limb is essentially carried by muscle, the pattern of resistance appears to be mainly dependent on the profile of muscle cross-sectional area along the lower limb and appears to thus contain the information needed for recovering the muscle volume from BIA data. Thus an approach based on BIA data seems to be feasible, allowing avoidance of the more sophisticated and expensive technique based on MRI, at least in clinical practice and particularly when several measurements are required, as in the present study.

Although some anatomical detail is lost with MRI with cells of 1-cm side, the gross structure appeared still to be represented in the discretized three-dimensional model of the lower limb. Figure 1 shows that the profile of muscle area along the limb was accurately reproduced, even when MRI cross-sectional images at 5-cm intervals were available. Thus the duration of the exposure during the MRI scans can be reduced. We note, however, that, with cells of 1-cm side, the skin cannot be represented, even if its contribution to the flow of current across the limb is not negligible in the regions where the content of muscle and adipose tissue is reduced.

The model of BIA reproduced the general behavior of impedance along the lower limb, as shown in Figs. 2 and 3, at least when the value of the longitudinal conductivity of muscle (ς_{mz}) was set to a value of 0.85 S/m. It was found that the electrical potential along the border of a cross section of the limb can show marked changes, as also seen by BIA measurements (1). This effect is particularly remarkable in the proximity of the current-injecting electrodes and in the region of the knee, confirming that the location of the voltage electrodes may be critical in bioimpedance analysis.

As shown in Figs. 2 and 3, the resistance profile given by the model did not precisely follow the experimental BIA data in the regions of the ankle and the knee, where the predicted resistance showed larger variations than those experimentally observed. A number of factors can cause the observed discrepancies: *1*) the predicted profile was obtained from the mean potential over the adipose tissue of the cross section, whereas the experimental measurements were obtained by voltage electrodes at specific locations; *2*) because of the discretization with cells of 1-cm side, anatomical structures such as ligaments, tendons, and sinovial fluid were disregarded, and these structures may present larger conductivities than those assumed in the model, thus giving smaller increments in observed resistance;*3*) the value of the longitudinal conductivity of muscle, ς_{mz}, which was assumed as a constant in the present model, may be partially dependent on interindividual variability and on the arrangement and orientation of muscle fibers, which are different in the thigh and in the calf (1).

With the use of the simplified mathematical model of *Eqs. 5
* and *
6
*, the total muscle volume was estimated from the experimental BIA data with an acceptable error with respect to the reference value provided by MRI. The estimation of muscle cross-sectional area from the profile of resistance along the lower limb appears to be feasible, as shown by Fig. 4, although the average estimation error on this area will be larger than the error on volume, as shown in Table 1. Because the measured potential can change when the voltage electrode is moved circumferentially at a given level of the limb, it is suggested that the measurement of the potential at more than a single point in a given cross section (e.g., in both the anterior and the posterior aspects of the limb at the level of the knee) might provide an improved determination of resistance and thus a more accurate reconstruction of the muscle cross-sectional areas.

In conclusion, the mathematical model described in the present paper allows for predicting with good accuracy the volume of lower limb skeletal muscle mass by using BIA, thus representing a first step toward advancing BIA as a replacement for CT and MRI when evaluating the composition of the lower limb in lean subjects.

## Acknowledgments

We thank Drs. A. Scarfone and P. Morini for technical assistance.

## Appendix

#### Mathematical model of BIA.

Under the quasi-static approximation, valid at the frequency*f* = 50 kHz used in the present bioimpedance measurements, the electric field *E *(V/m) in the body region considered is related to the potential *V* (V) by the following equation
Equation 1AMoreover, for the electric current density *J*(A/m^{2}), we can write the continuity equation
Equation 2Awhere *I *(A/m^{3}) is the externally applied current per unit volume. Assuming harmonic fields, *J* is related to *E* by
Equation 3Awhere *k* (S/m) is the complex conductivity tensor given by
Equation 4Awith ς being the conductivity and ɛ the permittivity of the media.

From *Eqs. 1-3
* we obtain the following equation for the complex potential
Equation 5Ato be solved in the region of interest with the appropriate boundary conditions (11). If the electric field is referred to Cartesian coordinates, all nondiagonal elements of the tensor *k*(*x,y,z*) are zero and *k* = diag(*k _{x}
*,

*k*,

_{y}*k*). Thus

_{z}*Eq. 5A*becomes Equation 6AThe three components of the tensor

*k*at a given point (

*x*,

*y*,

*z*) are possibly different because of tissue anisotropy, but the complex conductivity of a given tissue is assumed to be independent of the spatial position.

To solve *Eq. 6A
* we used the finite difference method (5, 23), with the nodal points taken coincidently with the centers of the cells that form the three-dimensional model of the lower limb (see Fig. 5). The finite differences lead to the following equation (5)
Equation 7Awhere *V* is the electrical potential in the node located at the center (*x*, *y*, *z*) of a cell, *V*
_{i} are the potentials at the six neighboring nodes [(*x* − Δ*x, y, z*), (*x* + Δ*x, y, z*), and so on; see Fig. 5],*Y _{i}
* are the complex admittances between the nodes (denoted as

*Y*

_{x−},

*Y*

_{x+}, and so on in Fig.5), and

*I*denotes the external current impressed at the node (

*x*,

*y*,

*z*). It is

*I*≠ 0 only at the nodes representing the current-injecting electrodes. The values of the admittances depend on the types of tissue associated with the various cells. For instance, the admittance

*Y*

_{x+}between the nodes (

*x*,

*y*,

*z*) and (

*x*+ Δ

*x*,

*y*,

*z*), which may be associated with different tissues, has the expression Equation 8Aand similarly for the other admittances. The impedances to be compared with BIA data were computed from the mean value of the electrical potential of cells that represent the adipose tissue at a given level

*z*along the lower limb.

## Footnotes

Address for reprint requests and other correspondence: S. Salinari, Dip. Informatica e Sistemistica, Università di Roma “La Sapienza,” Via Eudossiana, 18 00184 Rome, Italy (E-mail:salinari{at}dis.uniroma1.it).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “

*advertisement*” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.First published November 20, 2001;10.1152/ajpendo.00109.2001

- Copyright © 2002 the American Physiological Society