Use of allometry in predicting anatomical and physiological parameters of mammals

One challenge for veterinarians, animal facilities and research scientists is the making of physiological estimates appropriate to a variety of species for which data are often either completely lacking or are incomplete. Our intent in compiling the data in this paper is to provide the best possible database of normal physiological and anatomical values primarily (though not exclusively) for four common mammalian model species: mouse, rat, dog and man. In order to make those data as accessible and applicable as possible, we have presented the results of this study in the form of body-size dependent allometric equations in which some variable (Y) is expressed as a dependent function of body mass (M) in the power-law equation, Y = aM(b). By compiling these data, it is apparent that the resultant equations are quantitatively grouped (with similar slope or 'b' values). These emergent patterns provide insights into body-size dependent 'principles of design' that seem to dictate several aspects of design and function across species among all mammals. In general, the weights of most individual organs scale as a constant fraction of body mass (i.e. the body mass exponent, b approximately equal to 1.0). Biological rates (e.g. heart rate, respiratory rate) scale as b approximately equal to -1/4. Finally, volume-rates (the product of volume and rate) such as cardiac output, ventilation and oxygen uptake vary as b approximately equal to 3/4.     

The principle of laplace and scaling of ventricular wall stress and blood pressure in mammals and birds

Maximum left ventricular wall stress is calculated at end-diastolic volume and systemic arterial diastolic blood pressure, according to a thick-walled model for the principle of Laplace. Stress is independent of body mass and averages 13.9 kPa (+/-2.3; 95% confidence interval) in 24 species of mammals weighing 0.025-4,000 kg and 15.5 kPa (+/-4.7) in 12 birds weighing 0.014-110 kg. Birds have higher arterial blood pressures and larger hearts than mammals. Systolic and diastolic arterial blood pressures increase with body mass according to M(0.05) in mammals, and heart mass increases according to M(1.06) in the same species, further supporting the principle. However, blood pressure in birds is independent of body mass, and heart mass scales isometrically. End-diastolic stress values, calculated according to Laplace, are about one-third of peak stresses recorded in isolated mammalian myocardial preparations.     

An allometric analysis of the giraffe cardiovascular system

There has been co-evolution of a long neck and high blood pressure in giraffes. How the cardiovascular system (CVS) has adapted to produce a high blood pressure, and how it compares with other similar sized mammals largely is unknown. We have measured body mass and heart structure in 56 giraffes of both genders ranging in body mass from 18 kg to 1500 kg, and developed allometric equations that relate changes in heart dimensions to growth and to cardiovascular function. Predictions made from these equations match measurements made in giraffes. We have found that heart mass increases as body mass increases but it has a relative mass of 0.51 ± 0.7% of body mass which is the same as that in other mammals. The left ventricular and interventricular walls are hypertrophied and their thicknesses are linearly related to neck length. Systemic blood pressure increases as body mass and neck length increase and is twice that of mammals of the same body mass. Cardiac output is the same as, but peripheral resistance double that predicted for similar sized mammals. We have concluded that increasing hydrostatic pressure of the column of blood during neck elongation results in cardiac hypertrophy and concurrent hypertrophy of arteriole walls raising peripheral resistance, with an increase in blood pressure following.     

The maximum oxygen consumption and aerobic scope of birds and mammals: getting to the heart of the matter

Resting or basal metabolic rates, compared across a wide range of organisms, scale with respect to body mass as approximately the 0.75 power. This relationship has recently been linked to the fractal geometry of the appropriate transport system or, in the case of birds and mammals, the blood vascular system. However, the structural features of the blood vascular system should more closely reflect maximal aerobic metabolic rates rather than submaximal function. Thus, the maximal aerobic metabolic rates of birds and mammals should also scale as approximately the 0.75 power. A review of the literature on maximal oxygen consumption and factorial aerobic scope (maximum oxygen consumption divided by basal metabolic rate) suggests that body mass influences the capacity of the cardiovascular system to raise metabolic rates above those at rest. The results show that the maximum sustainable metabolic rates of both birds and mammals are similar and scale as approximately the 0.88 +/- 0.02 power of body mass (and aerobic scope as approximately the 0.15 +/- 0.05 power), when the measurements are standardized with respect to the differences in relative heart mass and haemoglobin concentration between species. The maximum heart beat frequency of birds and mammals is predicted to scale as the -0.12 +/- 0.02 power of body mass, while that at rest should scale as -0.27 +/- 0.04.     

Cardiac Output and Its Interorgan Distribution in Mammals at Rest

A review is presented on published equations connecting the cardiac output per minute (COM) with the body weight (BW) in mammals with different BW under the conditions of the relative motor rest. The entire series of these animals with the BW from several grams to many tons is well described by the equation -BW^0.75, in which the coefficient changes parabolically by increasing to the smallest and largest animals. According to it, the BW increase from 20 g to 70 kg is accompanied by an 8-fold decrease of the specific COM from 72 to 9 ml/min × 100 g. As judged from publications, this COM decrease is accompanied by changes of its interorgan distribution. The volume rate of the blood flow (per 100 g of the organ) is preserved in kidney, decreases approximately 3 times in heart and organs of v. hepatica, remaining higher in heart, and decreases markedly in skin (14 times), in skeleton (18 times), and skeletal muscles (21 times). The mechanisms of such changes of the organ blood flow are different changes of the organ parts of COM and relative body weights of the organs.     

The Organ Blood Flow under Conditions of Motor Rest in Rodents with Different Body Mass

The volume velocity of organ blood flow (VVBF) was measured using ⁸⁶RbCl in anesthetized wild rodents (birch mouse, narrow-skulled vole, and common hamster) as well as in wakeful and anesthetized Wistar rats and Balb mice. It has been shown that with increase of the rodent body mass (from 8 g to 760 g) and decrease of the specific minute volume of blood circulation (VVBF/100 g organ), VVBF is unchanged in kidney, decreases, although to a lesser extent than cardiac output (CO), in digestive tract, liver, spleen, and heart, whereas in supporting-motor and covering structures it decreases to a greater extent than CO.     

Scaling laws for capillary vessels of mammals at rest and in exercise

A general derivation is presented for the scaling laws governing the size and number of capillary blood vessels in mammals. The derivation is based on the assumption of three idealized similarity principles known to apply, at least approximately, to resting mammals: (i) size-invariant blood pressure; (ii) size-invariant fraction of blood in the capillaries; and (iii) size-invariant oxygen consumption and uptake, per unit of body mass, during each heart cycle. Results indicate that the radius and length of capillaries, and the number that are open and active in the resting state, should scale with mammal mass to the powers 1/12, 5/24 and 5/8, respectively, consistent with earlier work by the author. Measurements are presented supporting the results. Physiological changes accompanying strenuous exercise are accounted for by a change in the scaling law for capillary number, from scaling exponent 5/8 to 3/4.     

Fetal heart rate in relation to body mass

In contrast to the inverse relation of heart rate to body mass in adult mammals, the heart rate of immature fetuses is unrelated to body mass and approximately constant among different species. With maturation, fetal heart rate decreases in a large mammal but tends to increase in a small mammal. These maturational changes reduce the difference between the heart rate of a term fetus and the heart rate which is "appropriate for body mass" as calculated by means of the allometric equation for adults. The comparative physiology of fetal heart rate supports the hypothesis that immature fetuses of small and large mammals have similar oxygen consumption rates per unit body mass.     

Scaling the physiological effects of exposure to radiofrequency electromagnetic radiation: consequences of body size

We have demonstrated that a comparative analysis of the physiological effects of exposure of laboratory mammals to radiofrequency electromagnetic radiation (RFR) may be useful in predicting exposure thresholds for humans if the effect is assumed to be due only to heating of tissue. The threshold specific absorption rate (SAR) necessary to affect a thermoregulatory parameter shows an inverse and linear relationship to body mass. The inverse relationship between threshold SAR and body mass is attributed to a surface area: body mass relationship. In comparison to small mammals, relatively large mammals have a reduced capacity to dissipate an internal heat load passively, and are therefore physiologically more sensitive to RFR exposure. The threshold for a thermoregulatory response depends on the type of response measured, species, ambient temperature, etc. By extrapolation, it can be shown that a SAR of only 0.2-0.4 W/kg is required to promote a thermoregulatory response in a mammal with a body mass of 70 kg (e.g. weight of adult human). The specific absorption rate bioeffects data collected from laboratory mammals can be related by means of a simple power formula: threshold SAR (W/kg) = aMb, where M is body mass in kg, a is a constant and b is equal to approximately -0.5. Through this equation we have illustrated that a threshold SAR measured in a species weighing 100 g would be 10 times greater than that of a species weighing 10 000 g. Accordingly, a relatively low SAR that is physiologically ineffective in small mammals may be stressful to larger species.     

Function of alveoli as a result of evolutionary development of respiratory system in mammals

Reaction of hemoglobin oxygenation is known to occur for 40 femtoseconds (40 × 10^?15 s). However, the process of oxygen diffusion to hemoglobin under physiologic conditions decelerated this reaction approximately billion times. In mammalian lungs, blood is moving at a high rate and in a relatively high amount. The human lung mass is as low as 600 g, but the complete cardiac output approaches 6 l/min. In rat, from 20 to 40 ml of blood is passed for one minute through the lung whose mass is about 1.5 g. Such blood flow rate is possible, as in lungs of high animals there exists a dense network of relatively large microvessels with diameter from 20 to 40 μm and more. In spite of a large volume and a high blood flow rate hampering oxygen diffusion, the complete blood oxygenation occurs in lung alveoli. This is due to peculiar mechanisms that facilitate markedly the oxygen diffusion and that developed in alveoli of mammals in the course of many million years of evolution of their respiratory system. Thus, alveolus is not a bubble with air, but a complex tool of fight with inertness of diffusion. It is interesting that in lungs of the low vertebrates, neither such system of blood vessels nor alveoli exist, and their blood flow rate is much lower than in mammals.     

Locomotor mode, maximum running speed, and basal metabolic rate in placental mammals

The locomotor performance (absolute maximum running speed [MRS]) of 120 mammals was analyzed for four different locomotor modes (plantigrade, digitigrade, unguligrade, and lagomorph-like) in terms of body size and basal metabolic rate (BMR). Analyses of conventional species data showed that the MRS of plantigrade and digitigrade mammals and lagomorphs increases with body mass, whereas that of unguligrade mammals decreases with body mass. These trends were confirmed in plantigrade mammals and lagomorphs using phylogenetically independent contrasts. Multiple regression analyses of MRS contrasts (dependent variable) as a function of body mass and BMR contrasts (predictor variables) revealed that BMR was a significant predictor of MRS in the complete data set, as well as in plantigrade and nonplantigrade mammals. However, there was severe multicollinearity in the nonplantigrade model that may influence the interpretation of these models. Although these data show mass-independent correlation between BMR and MRS, they are not necessarily indicative of a cause-effect relationship. However, the analyses do identify a negligible role of body size associated with MRS once phylogenetic and BMR effects are controlled, suggesting that the body size increase in large mammals over time (i.e., Cope's rule) can probably rule out MRS as a driving variable.     

Adrenergic control of venous capacitance during moderate hypoxia in the rainbow trout (Oncorhynchus mykiss): role of neural and circulating catecholamines

Central venous blood pressure (P(ven)) increases in response to hypoxia in rainbow trout (Oncorhynchus mykiss), but details on the control mechanisms of the venous vasculature during hypoxia have not been studied in fish. Basic cardiovascular variables including P(ven), dorsal aortic blood pressure, cardiac output, and heart rate were monitored in vivo during normoxia and moderate hypoxia (P(W)O(2) = approximately 9 kPa), where P(W)O(2) is water oxygen partial pressure. Venous capacitance curves for normoxia and hypoxia were constructed at 80-100, 90-110, and 100-120% of total blood volume by transiently (8 s) occluding the ventral aorta and measure P(ven) during circulatory arrest to estimate the mean circulatory filling pressure (MCFP). This allowed for estimates of hypoxia-induced changes in unstressed blood volume (USBV) and venous compliance. MCFP increased due to a decreased USBV at all blood volumes during hypoxia. These venous responses were blocked by alpha-adrenoceptor blockade with prazosin (1 mg/kg body mass). MCFP still increased during hypoxia after pretreatment with the adrenergic nerve-blocking agent bretylium (10 mg/kg body mass), but the decrease in USBV only persisted at 80-100% blood volume, whereas vascular capacitance decreased significantly at 90-110% blood volume. In all treatments, hypoxia typically reduced heart rate while cardiac output was maintained through a compensatory increase in stroke volume. Despite the markedly reduced response in venous capacitance after adrenergic blockade, P(ven) always increased in response to hypoxia. This study reveals that venous capacitance in rainbow trout is actively modulated in response to hypoxia by an alpha-adrenergic mechanism with both humoral and neural components.     

The impact of locomotor energetics on mammalian foraging

The ecological impact of energy expended on an activity stems from its effect on foraging requirements. For locomotion, the effect of moving each additional unit distance probably depends on the proportional increase in energy expenditure. Other common measures of the cost of locomotion do not reflect the impact of energy expenditure on foraging requirements. In terrestrial mammals, both the effect of body mass and the unit cost itself are very small: moving one kilometre requires less than 2% of all other energy expenditures combined. Total locomotor energy expenditure ranges from 1/2% of daily metabolism for a 10 g mammal to 6% for an elephant. Potential sources of bias in the estimation of these costs include systematic bias in estimates of distance traversed and extra energy required for non-linear locomotion. Because larger mammals can readily locomote at greater speeds, the primary locomotor advantage of large size may not be conservation of energy but of time, which can mean greater safety and more or better food.     

Unifying principles in terrestrial locomotion: do hopping Australian marsupials fit in?

Mammalian terrestrial locomotion has many unifying principles. However, the Macropodoidea are a particularly interesting group that exhibit a number of significant deviations from the principles that seem to apply to other mammals. While the properties of materials that comprise the musculoskeletal system of mammals are similar, evidence suggests that tendon properties in macropodoid marsupials may be size or function dependent, in contrast to the situation in placental mammals. Postural differences related to hopping versus running have a dramatic effect on the scaling of the pelvic limb musculoskeletal system. Ratios of muscle fibre to tendon cross-sectional areas for ankle extensors and digital flexors scale with positive allometry in all mammals, but exponents are significantly higher in macropods. Tendon safety factors decline with increasing body mass in mammals, with eutherians at risk of ankle extensor tendon rupture at a body mass of about 150 kg, whereas kangaroos encounter similar problems at a body mass of approximately 35 kg. Tendon strength appears to limit locomotor performance in these animals. Elastic strain energy storage in tendons is mass dependent in all mammals, but exponents are significantly larger in macropodid. Tibial stresses may scale with positive allometry in kangaroos, which result in lower bone safety factors in macropods compared to eutherian mammals.     

The Abdominal Circulatory Pump

Blood in the splanchnic vasculature can be transferred to the extremities. We quantified such blood shifts in normal subjects by measuring trunk volume by optoelectronic plethysmography, simultaneously with changes in body volume by whole body plethysmography during contractions of the diaphragm and abdominal muscles. Trunk volume changes with blood shifts, but body volume does not so that the blood volume shifted between trunk and extremities (Vbs) is the difference between changes in trunk and body volume. This is so because both trunk and body volume change identically with breathing and gas expansion or compression. During tidal breathing Vbs was 50–75 ml with an ejection fraction of 4–6% and an output of 750–1500 ml/min. Step increases in abdominal pressure resulted in rapid emptying presumably from the liver with a time constant of 0.61±0.1SE sec. followed by slower flow from non-hepatic viscera. The filling time constant was 0.57±0.09SE sec. Splanchnic emptying shifted up to 650 ml blood. With emptying, the increased hepatic vein flow increases the blood pressure at its entry into the inferior vena cava (IVC) and abolishes the pressure gradient producing flow between the femoral vein and the IVC inducing blood pooling in the legs. The findings are important for exercise because the larger the Vbs the greater the perfusion of locomotor muscles. During asystolic cardiac arrest we calculate that appropriate timing of abdominal compression could produce an output of 6 L/min. so that the abdominal circulatory pump might act as an auxiliary heart.     

Energetic benefits and adaptations in mammalian limbs: Scale effects and selective pressures

Differences in limb size and shape are fundamental to mammalian morphological diversity; however, their relevance to locomotor costs has long been subject to debate. In particular, it remains unknown if scale effects in whole limb morphology could partially underlie decreasing mass‐specific locomotor costs with increasing limb length. Whole fore‐ and hindlimb inertial properties reflecting limb size and shape—moment of inertia (MOI), mass, mass distribution, and natural frequency—were regressed against limb length for 44 species of quadrupedal mammals. Limb mass, MOI, and center of mass position are negatively allometric, having a strong potential for lowering mass‐specific locomotor costs in large terrestrial mammals. Negative allometry of limb MOI results in a 40% reduction in MOI relative to isometry's prediction for our largest sampled taxa. However, fitting regression residuals to adaptive diversification models reveals that codiversification of limb mass, limb length, and body mass likely results from selection for differing locomotor modes of running, climbing, digging, and swimming. The observed allometric scaling does not result from selection for energetically beneficial whole limb morphology with increasing size. Instead, our data suggest that it is a consequence of differing morphological adaptations and body size distributions among quadrupedal mammals, highlighting the role of differing limb functions in mammalian evolution.     

The morphological development of the locomotor and cardiac muscles of the migratory barnacle goose (Branta Leucopsis)

The masses of the locomotor and acardiac muscles of wild barncale goose gollings, from migratory population, were examined systematically during development and their values compared to those of pre-migratory geese. Pre-flight development was typified by approximately linear increases of body, leg, and heart ventricular mass with respect to age. Flight muscle showed an exponential increase in mass. Pectoralis muscle mass was 14.2 ± 0.3% of body mass (1297 ± 73g, n=7) in early flying goslings compared to 16.6 ± 0.3% of body mass (2318 ± 109g, n=8) in pre-migratory geese. Post-flight development was typified by stasis of leg muscle mass but hypertrophy of Ventricular and pectoralis muscle mass in proportion to body mass. Ventricular mass relative to body mass showed the lowest values at 5 weeks of age (0.62 ± 0.01%) with peak values at 1 week of age (10.4 ± 0.04%). The latter may be associated with both requirements of thermoregualation in these precocial, arctic breeding geese and the need to forage approximately 24 hours post-hatch. Peak values for leg muscle mass, relative to body mass, were found at 3 weeks of age (12.7 ± 0.36%), with lowest values in the pre-migratory geese (6.7 ± 0.21%), while peak values for pectoralis muscle mass were expressed in the premigratory geese with lowest values at 1 week of age (0.94 ± 0.07%). Ventricular mass was proportional to leg muscle mass up to 5 weeks of age (M_v= 0.38M_t^0.68, r²=0.95), but subsequent increase in ventricular mass was proportional to pectoralis muscle mass (M_v= 0.25M_p^0.73, r²= 0.81).     

An allometric study of pulmonary morphometric parameters in birds, with mammalian comparisons

Comprehensive pulmonary morphometric data from 42 species of birds representing ten orders were compared with those of other vertebrates, especially mammals, relating the comparisons to the varying biological needs of these avian taxa. The total lung volume was strongly correlated with body mass. The volume density of the exchange tissue was lowest in the charadriiform and anseriform species and highest in the piciform, cuculiform and passeriform species. The surface area of the blood-gas (tissue) barrier, the volume of the pulmonary capillary blood and the total morphometric pulmonary diffusing capacity were all strongly correlated with body mass. The harmonic mean thickness of both the blood-gas (tissue) barrier and the plasma layer were weakly correlated with body mass. The mass-specific surface area of the blood-gas (tissue) barrier (surface area per gram body mass) and the surface density of the blood-gas (tissue) barrier (i.e. its surface area per unit volume of exchange tissue) were inversely correlated (though weakly) with body mass. The passeriform species exhibited outstanding pulmonary morphometric adaptations leading to a high specific total diffusing capacity per gram body mass, consistent with the comparatively small size and energetic mode of life which typify passeriform birds. The relatively inactive, ground-dwelling domestic fowl (Gallus gallus) had the lowest pulmonary diffusing capacity per gram body mass. The specific total lung volume is about 27% smaller in birds than in mammals but the specific surface area of the blood-gas (tissue) barrier is about 15% greater in birds. The ratio of the surface area of the tissue barrier to the volume of the exchange tissue was also much greater in the birds (170-305%). The harmonic mean thickness of the tissue barrier was 56-67% less in the birds, but that of the plasma layer was about 66% greater in the birds. The pulmonary capillary blood volume was also greater (22%) in the birds. Except for the thickness of the plasma layer, these morphometric parameters all favour the gas exchange capacity of birds. Consequently, the total specific mean morphometric pulmonary diffusing capacity for oxygen was estimated to be about 22% greater in birds than in mammals of similar body mass. This estimate was obtained by employing oxygen permeation constants for mammalian tissue, plasma and erythrocytes, as avian constants were not then available.(ABSTRACT TRUNCATED AT 400 WORDS)     

WISE 2005: stroke volume changes contribute to the pressor response during ischemic handgrip exercise in women.

The mechanism of the pressor response to small muscle mass (e.g., forearm) exercise and during metaboreflex activation may include elevations in cardiac output (Q) or total peripheral resistance (TPR). Increases in Q must be supported by reductions in visceral venous volume to sustain venous return as heart rate (HR) increases. Therefore, this study tested the hypothesis that increases in Q, supported by reductions in splanchnic volume (portal vein constriction), explain the pressor response during handgrip exercise and metaboreflex activation. Seventeen healthy women performed 2 min of static ischemic handgrip exercise and 2 min of postexercise circulatory occlusion (PECO) while HR, stroke volume and superficial femoral artery flow (Doppler), blood pressure (Finometer), portal vein diameter (ultrasound imaging), and muscle sympathetic nerve activity (MSNA; microneurography) were measured followed by the calculation of Q, TPR, and leg vascular resistance (LVR). Compared with baseline, mean arterial blood pressure (MAP) (P < 0.001) and Q (P < 0.001) both increased in each minute of exercise accompanied by a approximately 5% reduction in portal vein diameter (P < 0.05). MAP remained elevated during PECO, whereas Q decreased below exercise levels. MSNA was elevated above baseline during the second minute of exercise and through the PECO period (P < 0.05). Neither TPR nor LVR was changed from baseline during exercise and PECO. The data indicate that the majority of the blood pressure response to isometric handgrip exercise in women was due to mobilization of central blood volume and elevated stroke volume and Q rather than elevations in TVR or LVR resistance.     

Longitudinal measurements of blood volume and essential body mass in human subjects.

Repeated determinations of blood volume and body density were made on 34 Chinese subjects (28 men and 6 women) in Taiwan over a period of 12 yr, as the mean age increased from 31 to 43 yr. Essential body mass calculated from body density and body weight showed no significant change over the 12-yr period. Changes in body weight (mean gain equals 6.0 kg) were attributable to alterations in adipose tissue weight, the density of which was found to be 0.948 g/cm3. In two-thirds of the subjects the second blood volume increased by more than 5% over the first determination, and the mean blood volume for all subjects increased by 7.5% (P less than 0.01). Correlation of the blood volume data with the findings on essential body mass and adipose tissue mass suggests that blood content per unit tissue mass increased in the second determination. This interpretation is supported by the increase in nutrient availability in Taiwan over the 12-yr period, and it may explain the lack of blood volume increase in an earlier longitudinal study on American subjects with stable nutrient availability.