# Metabolic rate and body mass relationship accompanying

The relationship between mammalian basal metabolic rate (BMR, ml of O2 per h) and body mass (M . Relationship between body mass (M, g) and body temperature (Tb, °C) for eutherians .. Aschoff J. In: A Companion to Animal Physiology. Furthermore, many metabolic scaling relationships have been found As he remarked at the end of a paper on the body-mass scaling of . In short, mammalian metabolic rate and its scaling with body size . rapid increases in heat production accompanying maturation of the thermoregulatory system [18]. For Higher Biology, learn how metabolic rates are measured and the different ways in which oxygen The relationship between body mass and metabolic rate .

In addition, we hypothesized that less energy spent on activity AEE during the premenarcheal period is an additional independent risk factor for increased weight gain over the adolescence period.

## Metabolic rate

Unlike RMR, the energy spent on activity can be altered by individual behavior. In this study, we examined the changes in body mass index BMI z score and in body fatness as measured by bioelectrical impedance analysis BIA to test our hypothesis that RMR, AEE, and TEE in normal-weight premenarcheal girls are associated with increased body fat or relative weight gain during the pubertal period.

The longitudinal nature of the study and the annual measures of physical activity level and dietary intake allowed us to control for changes in activity and diet over the study period. Premenarcheal girls aged 8—12 y were recruited from the Cambridge and Somerville public schools in Massachusetts, the MIT summer day camp, and friends and siblings of enrolled subjects.

All participants were healthy, free of disease, and not taking any medication that affected body composition or EE.

Study protocol Initial study visit Details of the baseline visit are described elsewhere Girls admitted to the Clinical Research Center at MIT for an overnight visit arrived in the late afternoon at which time a physician obtained a medical history and examined each girl to ensure that she was in good health. Girls were asked to complete a physical activity questionnaire and a food-frequency questionnaire.

Subjects wearing a hospital gown and slippers were weighed on a Seca scale Seca, Hanover, MD accurate to 0. Height was measured to 0. RMR was measured by indirect calorimetry after an overnight fast and a min rest period as previously described 22 At the baseline and exit visits 4 y after menarcheand other visits when TBW was measured, body weight and BIA were measured after an overnight fast. On annual visits, body weight and BIA were measured either after an overnight fast or 2 h after a meal.

Most but not all of the visits were measured in the fasting state. Weight was measured in a hospital gown on all visits. Two weeks later the participants returned to the Clinical Research Center after an overnight fast.

Collection of a urine sample the second void of the day marked the end of the EE period.

The subjects were weighed, and their RMR was measured. Annual visits Girls were seen annually on the anniversary of their baseline visit. Diet and activity questionnaires, anthropometric measures, and BIA measurements were repeated. Girls completed the study when they were 4 y postmenarche. Criteria for acceptance values were a SE for replicate measures of 0.

Body fatness by bioelectrical impedance Body fatness was estimated for each follow-up with prediction equations developed in this cohort that used available measures of TBW by isotopic dilution of HO as the criterion method A correction factor was applied to the predicted body fat measures for each girl to address the discontinuity that arises from using 2 independently generated equations. The average correction was 0. A total of measurements from girls were used in the development of these equations.

The distribution of measurement numbers were as follows: Relative weight To provide a measure of relative weight, a BMI z score was calculated for each BMI measure with the reference to age- and sex-specific limits provided by the Centers for Disease Control and Prevention growth reference standards Three limits were estimated: The equation for the LMS is the following: The final set of percentile curves available from the Centers for Disease Control and Prevention was produced by using the modified LMS estimation procedure, as described in detail in the documentation that accompanied the release of these growth charts These limits are based on BMIs calculated from heights and weights from national surveys conducted in the United States between and Physical activity and inactivity measures Participants completed a questionnaire that identified usual patterns of physical activity.

Participants were presented with two h timetables school day and weekend day and asked to recall, on an hour-by-hour basis, their participation in 5 types of activities during each time block: In addition, participants completed a similar grid on which they reported television-viewing time on an hourly basis including time spent watching videos or playing video games.

Information on the reliability of this physical activity assessment protocol was published elsewhere To develop an index to assess the time spent and level of physical activity, we examined the relation between AEE adjusted for body weight and time spent sleeping, sitting, standing, walking, in vigorous activity, and television viewing. We then created an activity variable to reflect time spent and intensity of vigorous activity and walking and an inactivity variable to reflect time spent sitting, standing, and sleeping.

The average daily hours spent walking and in vigorous activity were combined and weighted by their intensity using a metabolic equivalent value to create an activity index.

Average hours spent daily in sleeping or lying down, sitting, and standing were summed to create an inactivity index. Dietary assessment All participants completed a semiquantitative food-frequency questionnaire designed for children aged 9—18 y and based on one validated for adults Similar to the adult version, this questionnaire was designed to be self-administered, but participants were given oral or written instructions or both on how to complete the forms properly.

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Specific details about the questionnaire are described elsewhere With data from questionnaires, we calculated daily servings of fruit and vegetables, percentage of daily calories from sugar-sweetened soda, and percentage of daily calories from macronutrients. Widely accepted exponents for these powers are 0. In addition, recent analyses established the validity of a range of numerical values for the BMR and MMR power exponents with 0.

Hence, for example, the fractal dimensions of the athletic, nonathletic, and combined species collections would be 2. Consequently, it will be shown here that the scaling exponent of BMR with body mass can be obtained by taking body composition into account in the product of the scaling exponents of MMR and visceral mass.

On the other hand, the visceral contribution to BMR would scale as visceral. The key to scaling visceral BMR with is Pace et al.

Hence, visceral BMRwith the exponent 0. Denotingand visceralthis finding generalizes to However, it is important to realise that whole body BMR contains a skeletal muscle contribution in addition to the main visceral component Schmidt-Nielsen, The scaling of the muscle BMR can be derived from an argument based on shared blood flow from the heart into main arteries connected to muscle and viscera. Presumably, the shared cardio-vascular system also causes blood flow during rest in skeletal muscle in order to be proportional to the visceral requirements.

Locally, this can be mediated by capillary closure because of precapillary sphincter muscles or by bypass vessels or shunts. This means that the functional muscle capillaries and, consequently, muscle BMR can scale to muscle mass, according to formulas derived in Roux in correspondence with visceral BMR scaling with body mass.

Body composition To investigate the magnitude and nature of visceral BMR, an assessment of the scaling of viscera and its component organs with total body mass is needed. This is given in Tables 2 and 3. The scaling of carcass, visceral and skin masses in Table 2 is from Pace et al. Carcass mass includes muscle and skeletal mass, with fat and blood not being accounted for by Pace et al. The sources for estimates of the fat and blood contributions are indicated in Table 2. The intercepts add to almost one, as they should if almost all the constituents of body mass have been accommodated.

To obtain the logically required estimate of unity for the exponent of the sum of the body components it is necessary to average the exponent numbers weighed by their intercepts. This result indicates that such weighing is a useful procedure to obtain the scaling of sums of body components, so that it will also be employed in Tables 3 - 6.

The sum of the intercepts of Table 3 of 0. For birds, the exponent for the gut may not be reliable, as indicated by the length of its CI. The average with the gut deleted is in fair agreement with the mammalian estimate.

Presumably, the maximum workload of the digestive and elimination organs can be assumed to scale like MMR. Table 3 shows scaling approximately like MMR see values in Introduction for the liver, gut and kidneys in mammals.

This supports the scaling in Table 3suggesting that the homeostatic control function workload of the brain may scale like BMR. The heart and lungs scale almost isometrically to body mass in Table 3. It follows from the exponent averages in Tables 2 and 3 that variations owing to the different types of deviations from the workload scaling proportional to MMR appear to be cancelled out.

Especially remarkable is the lung and brain average exponent of 0. Hence, the conclusion that the combined visceral mass scaling power exponent can be approximated by the MMR scaling power exponent.

The first approach is to obtain estimates of metabolic rates MR by applying in vitro specific MR from tissue slices to the mammalian organ scalings in Table 3. The second is to obtain maximum potential MR scalings from mitochondrial surface areas, and the third to estimate the scaling contributions of the visceral organs to whole body BMR from in vivo blood oxygen transport.

Tissue Slices In the first way to investigate the scaling of the metabolic rates of the visceral organs, the specific metabolic rates of tissue slices on mice, rats, and dogs from Field et al. The results are in Table 4. In Table 4 the scaling exponents of the individual organs are somewhat heterogeneous. It is mainly with the averages that regularities appear. Combined with the visceral scaling in Table 3this gives 0.

The scaling for muscle from the tissue average is given by These exponents are in good agreement with their corresponding averages in Table 4. Although the body mass power exponents of the MR of visceral organs are somewhat variable, their weighed average of 0. In contrast, the exponent from the muscle slices of 0. On the other hand, if organ mass instead of body mass is used as a reference mass in the scaling of sliced tissue MR, the weighed average visceral organ exponent is 0.

It is confirmed by the results in Table 4 that the exponent for BMR can be obtained from the relationship between visceral MR and body mass. The necessary accompanying modification of the relationship between muscle metabolic rate and body mass in vivo under resting conditions follows plausibly by assuming that blood flow for BMR is determined by visceral requirements. This would imply the closure of some muscle capillaries causing a scaling of the remaining open capillaries, according to Roux The closure of muscle capillaries has been observed by Kroghand the modification of blood flow according to physiological demand is well known.

Under these assumptions the validity of Equation 1 can be illustrated from Tables 43 and 2 by 0. Mitochondrial inner membrane The amount of mitochondrial inner membrane can be used as an indicator of a cell's maximum aerobic capacity because most ATP is of aerobic origin and each cell must manufacture its own ATP.

The scaling for mitochondrial surface areas m2J with body and organ mass g is in Table 5. The scaling pattern is remarkably similar to that from sliced tissue respiration in Table 4and the conclusions are therefore the same. The average organ mass exponent of the visceral organ masses and the muscle organ mass exponent are precisely equal to 0.

This is according to expectation from the argument that the whole body fractal vascular scaling is also applicable to organ mass of separate organs or their collections. Note that the unweighed visceral average is also 0. Blood oxygen transport Based on five species and six experiments, Wang et al. Blood oxygen transport is estimated by in vivo measurement of arterio-venous differences in oxygen concentration, together with simultaneous blood flow measurements across organs.

The estimated specific resting metabolic rate of five organ-tissue components in Table 1 of Wang et al.

### BBC Bitesize - Higher Biology - Metabolic rate - Revision 1

The scaling of BMR of the visceral organs with whole body mass is the same as that of Wang et al. The scaling of the remaining tissues residual differs because of an apparent error in Table 1 of Wang et al.

In contrast to the results in Table 4 in which the weighed visceral average body mass power exponent is very near to the in vivo BMR exponent, the weighed visceral average body mass exponent in Table 6 of 0. This may be explained by the low exponent and high intercept of the liver, which, in the absence of the gut and lungs, has a dominant contribution to the average visceral exponent.

It is likely that higher values for the gut and lungs contributing to the residual might have caused the higher value of 0. These results therefore cannot be taken as invalidating the hypothesis of Equation 1 that the scaling of BMR with whole body mass is caused by the scaling of visceral mass to body mass. In contrast to the situation in the average visceral exponent of BMR scaling with whole body mass, the weights in the average visceral scaling with organ mass are not dominated by the liver, so that a comparatively high value of 0.

Fromcalculated from Table 3Equation 1 gives 0.

The conclusion therefore follows that the evidence in Table 6 can be regarded as supporting the postulate of Equation 1 that BMR can be derived from the power exponent scaling of the viscera with whole body mass. The total estimate from Table 6 is in conspicuous agreement with the combined mammalian estimate from Sieg et al. Oxygen partial pressure and basic metabolic rate A comparison of Tables 2 and 3 with Tables 45and 6 establishes that the power exponent scaling of visceral mass with whole body mass is at least approximately equal to the scaling of MMR with whole body mass.

This allows the estimation of BMR from the power exponent scaling of oxygen half saturation pressure P50 with body mass from Equations 2 and 3. A comparison of the estimates b2 obtained via Equations 2 and 3 with the conventional fasting BMR estimates c is in Table 7.

It is important to note the substantial overlap in the Cl-s for each pair of estimates. Together with equal average values of 0. In the construction of Table 7heterogeneities in the estimates of BMR have been taken into account. The mammalian category in the estimate of c includes the 5 out of 10 orders not significantly different from each other and from 0.

Where adequate numbers of observations are available, the other clades or orders are accommodated separately. The values for lizards in Table 7 are calculated from the observations for mature animals listed by Pough aexcept for the deletion of the extraordinarily low P50 value of Hemidactylus bibroni, which is about half the value of the next lowest observation.