SHORT COMMUNICATION Brain Size, Body Size and Longevity

A Peters1, B Hitze1, D Langemann2, A Bosy-Westphal3 and MJ Mu¨ller3

1Medical Clinic 1, University of Luebeck, Luebeck, Germany; 2Institute of Computational Mathematics, Technical University Braunschweig, Braunschweig, Germany and 3Institute of Human Nutrition and Food Science, Christian-Albrechts-University Kiel, Kiel, Germany

In this analysis, we bring together two research fields that have never been associated before: the clinical issue ‘Que´telet’s body-mass index and longevity’ and the comparative biological issue ‘body–brain allometry’. Comparison of medical and biological data supports the view that body mass index is just a one-to-one mapping of the body–brain–energy balanceFa biological variable indicating that an individual maintains its systemic energy homeostasis and therefore is likely to perform well in the coming years. International Journal of Obesity (2010) 34, 1349–1352; doi:10.1038/ijo.2010.65; published online 30 March 2010

Keywords: brain size; body size; body mass index; longevity

One currently prevailing myth is that a large cerebral As body metabolism increases, brain metabolism increases capacity should guarantee a long life. Here we suggest that in a so-called ‘isometric’ manner, that is, it follows a ‘linear’ there might indeed be a hidden link between brain size function. ‘Isometric’ functions number among a larger class and longevity. of so-called ‘allometric’ functions that are often used in Focussing on humans alone, clinicians ascertained that comparative biology, and all of which follow the power body mass is related to life span.1–3 As long ago as 1835, the function Y ¼ kXa. Such allometric functions are used, for mathematician Adolphe Que´telet analyzed human data sets example, to describe the nonlinear relationship between with the intention of finding a statistical variable that would brain mass and body mass, or the relationship between body allow him to identify ‘healthy’ humans whom he considered metabolism and body mass among different species where to be of ‘normal’ stature.4 He achieved a little success the allometric exponents have been reported to be around in this task in finding that a man or woman displaying a 0.7.9,10 Allometric functions have also been reported for the mass/height2 ratio of B24 kg mÀ2 matched his image of nonlinear relationship between brain mass and life span.11,12 being ‘normal’. Later on, insurance companies used his Remarkably, the relationship between brain energy metabo- concept to calculate the health risks for humans. Que´telet’s lism (Y) and body energy metabolism (X) is particularly ratio is now referred to as the ‘body mass index’ (BMI). simple, as the exponent a has been found to be very close to Recent studies confirm that a BMI of between 22.5 and 1.0.8 As already mentioned, such special linear relationships 25.0 kg mÀ2 is a strong predictor for maximal longevity are referred to as ‘isometric’ by biologists. In vertebrates (Figure 1c).1,2 It is known that in mice, less insulin-like ranging in size and metabolism from goldfishes to elephants, signalling throughout the body or just in the brain consi- brains become proportionally larger and hence utilize a derably extends the life span.5,6 It is unknown, however, larger amount of energy when body metabolism increases. whether brain energy metabolism specifically can predict In the research field of neuroenergetics, there is interest in longevity. knowing how the control system (brain) and the executor Taking the broader perspective of comparative biology, system (periphery) of a given vertebrate species compete vertebrate brain metabolism has been found to be strictly for the available energy resources within the organism.13 The proportional to body energy metabolism (Figure 1b).7,8 brains of Homo sapiens not only use a larger proportion of the organism’s energy supply (20%) than do those of rats, cats and dogs (4–6%), but also are the largest compared with their Correspondence: Dr A Peters, Clinical Research Group SELFISH BRAIN, Brain body size, with humans exhibiting a relatively gracile metabolism, Neuroenergetics, Obesity and Diabetes, Medical Clinic I, physique.7,8,14 We therefore consider the ‘body–brain– University of Luebeck, Ratzeburger Allee 160, Luebeck 23538, Germany. energy balance’ (X/Y) to be a variable indicating the E-mail: [email protected] Received 17 December 2009; revised 10 February 2010; accepted 19 February proportion of energy used to cover the individual cerebral 2010; published online 30 March 2010 need in an individual subject. In this body–brain–energy Body–brain–energy balance A Peters et al 1350 8 80 Y= 1/5 ·X 7 70

6 in] (Y) 60 X/Y =5 Y= 0. 20 X0.99 / m

5 2 50

4 40

3 30 Y= 0.07 X0.99

body metabolism (X) / metabolism body (X) brain metabolism (Y) 2 20 -- vertebrates (Mink, 1981) — humans (Mink, 1981) 1 10 • normal-weight subjects;

brain metabolism [cm³ O this MRI study (n=89) 0 0 0 5 10 15 20 25 30 35 40 45 50 0 200 400 600 800 1000

BMI [kg/m²] body metabolism [cm³ O2 / min] (X)

1700

1600 1500

BMI = 24 kg/m² 1400 1300 35 30 1200 25

brain mass [g] 1100 20 15 1000 10 900 5 0 800 yearlydeath per 1000 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 BMI [kg/m²] BMI [kg/m²]

Figure 1 (a) Scatter plot of the body–brain–energy balance (X/Y) and body mass index (BMI) in our human magnetic-resonance imaging/calorimetric study (n ¼ 208).17 At a BMI of 24 kg/m2 we measured a body–brain–energy balance of 5.0 (black bold graph). (b) Allometric brain-to-body functions in vertebrates (dashed gray graph) and humans (solid gray graph) according to Mink.8 Note: the dashed gray graph actually covers a larger scope of values than depicted here, 3 À1 that is, bodies ranging in size from that of a goldfish to an elephant (0.04–6000.00 cm O2 min ). In (a), we considered the function X/Y ¼ 5 (black bold), which applies for humans exhibiting a BMI of 24 kg mÀ2, and integrated it (black bold graph) into (b), the large-scaled body–brain plot. The human-specific function (black bold) assessed here is a good approximation to the function (solid gray) based on the general power law. (c) Annual death rate related to body-mass index in females (solid line) and males (dashed line) according to Whitlock et al.1 Optimal survival is observed in humans with a BMI of B24 kg mÀ2.(d) Plot of brain mass and BMI in our human magnetic-resonance imaging/indirect calorimetry study (n ¼ 208). Brain mass is found to be independent from the BMI (women: r ¼ 0.131, NS; men: r ¼ 0.079, NS), as is consistent with the observation that the brain mass is maintained even when body mass changes dramatically.15

balance, the denominator, ‘brain metabolism’ (Y), ade- already well established over a wider range of body sizes quately fulfils the criteria for reference variables, as cerebral ranging in size from the goldfish to the elephant? morphological and energetic changes are known to be very In order to address the first question, we used magnetic- small even under conditions of long-term or short-term resonance imaging to measure brain size and indirect 15,16 3 À1 energy depletion. Every individual subject appears to calorimetry to measure body metabolism (cm O2 min )as strive for an optimal allocation of energy resources between described earlier.17 In all, 104 women and 104 men of widely the brain and the periphery in order to realize its best varying weight (underweight to obesity) participated in the adaptive capacity. Considering this background, the follow- study. We took the product of the subject’s individual brain 3 À1 À1 ing two questions are posed here: (1) is the relationship size and 0.0349 cm O2 min gbrain (that is, cerebral oxygen between body and brain energy metabolism somehow linked consumption according to Sokoloff18) in order to estimate to longevity in humans?, and (2) if so, can we integrate such their brain energy metabolism. We found that the body– a finding into the laws of body–brain allometry that are brain–energy balances (X/Y) were correlated with the

International Journal of Obesity Body–brain–energy balance A Peters et al 1351 BMIs (r ¼ 0.553; Po0.001) (see Figure 1a). The regression able to find a simple ‘statistically derived’ variable, that is, equation read as follows: the BMI, which allowed him to identify humans who were X expecting maximal longevity. However, although Que´telet’s ¼ 0:085 Á BMI þ 2:961 ð1Þ Y variable is predictive, it is also only a descriptive measure. Does it in fact make any biological sense? Here, we made If a BMI of 24 kg mÀ2 is inserted in Equation (1), a body– an attempt to replace the descriptive ratio BMI (mass (kg) brain–energy balance (X/Y) of 5.0 is obtained. As such, the divided by area (m2)) with a variable representing a relevant optimal survival of humans with a BMI of 24 kg mÀ2 as biological feature. reported by Whitlock et al.1 is associated with a body–brain– In conclusion, we brought two research fields together energy balance of 5, or put otherwise, with a relative that have never been associated before, that is, the clinical brain energy consumption of 20%. In contrast, underweight issue ‘Que´telet-index and longevity’ and the comparative subjects showed a higher relative brain energy consumption biological issue ‘body–brain allometry’. It should be noted of 22.0±0.1% (mean±s.e.m.), and obese subjects a lower here that the general biological ‘constancy of the body– one, of 17.2±0.1%. Specifically, we obtained a linear brain–energy balance’ rule shows a wider ‘scope of validity’ dependency for Homo sapiens, which applies for subjects than Que´telet’s index, as it is based on data sets assessed with a BMI of 24 kg mÀ2 who have been reported to expect in the subphylum of vertebrata (including humans) and is the highest longevity: not merely restricted to the human species. Comparison of 1 medical and biological data supports the view that the BMI is Y ¼ Á X ð2Þ 5 just a one-to-one mapping of the body–brain–energy This function (Equation (2)) can then be depicted balanceFa biological variable indicating that an individual by means of a commonly used brain-to-body allometric plot maintains its systemic energy homeostasis and therefore is (Figure 1b; black bold graph). likely to perform well in the coming years. Interestingly, this We then attempted to integrate this finding into the more performance depends largely on a competent ‘brain-pull’ general laws of body–brain allometry. We used the known mechanism, that is, on the ability of the brain to compe- allometric function derived from a data set assessed in tently demand energy from the body, as recent research from vertebrates (including humans)8 to calculate the brain-to- the field of neuroenergetics has shown.19 body allometric function, which satisfactorily applies for normal-weight humans. In vertebrates, Mink found that brain energy metabolism depends on body energy metabo- Conflict of interest lism according to the isometric function Y ¼ 0.07X0.99. We assume that the functions applying for humans on the The authors declare no conflict of interest. one hand and vertebrates on the other show the same ‘isometric exponent’ a ¼ 0.99, but differ regarding their ‘coefficient’ (k). According to Mink’s data analysis, which is based on invasive cerebral measurements, the coefficient Acknowledgements k is 0.20 in humans and 0.07 in vertebrates. These coefficients indicate that a human subject has an approxi- This work was supported by grants from the German mately threefold higher brain energy metabolism than an Research Foundation (DFG Mu¨ 714/8-3 and Clinical average vertebrate with an equivalent body metabolism. Research Group KFO-126). According to Mink’s study, the following function therefore applies for humans with their narrow body-metabolism range: References Y ¼ 0:20X0:99 ð3Þ 1 Whitlock G, Lewington S, Sherliker P, Clarke R, Emberson J, We can also depict this function (Equation (3)) using a brain- Halsey J et al. Body-mass index and cause-specific mortality in to-body allometric plot (Figure 1b; solid gray graph). 900 000 adults: collaborative analyses of 57 prospective studies. Lancet 2009; 373: 1083–1096. In summary, we compared the function obtained by our 2 Pischon T, Boeing H, Hoffmann K, Bergmann M, Schulze MB, magnetic-resonance imaging and indirect calorimetry study Overvad K et al. General and abdominal adiposity and risk of in humans (Equation (2)) with the isometric function death in Europe. N Engl J Med 2008; 359: 2105–2120. applying for Homo sapiens derived from a larger data set8 3 Bales CW, Buhr GT. Body mass trajectory, energy balance, and weight loss as determinants of health and mortality in older assessed in vertebrates and humans (Equation (3)), adults. Obes Facts 2009; 2: 171–178. and were able to show that the first one was a good 4 Que´telet MA. A Treatise on Man and the Development of His approximation of the second (Figure 1b, bold black vs solid Faculties. William and Robert Chambers: Edinburgh, 1842. gray graph). 5 Holzenberger M, Dupont J, Ducos B, Leneuve P, Geloen A, Even PC et al. IGF-1 receptor regulates lifespan and Referring back to the biological context, it is not surprising resistance to oxidative stress in mice. Nature 2003; 421: that Que´telet, when analyzing data from humans alone, was 182–187.

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