• Adjusting bone mass for differences in projected bone area and other confounding variables: an allometric perspective.

      Nevill, Alan M.; Holder, Roger L.; Maffulli, Nicola; Cheng, Jack C. Y.; Leung, Sophie S. S. F.; Lee, Warren T. K.; Lau, Joseph T. F. (American Society for Bone and Mineral Research, 2002)
      The traditional method of assessing bone mineral density (BMD; given by bone mineral content [BMC] divided by projected bone area [Ap], BMD = BMC/Ap) has come under strong criticism by various authors. Their criticism being that the projected bone "area" (Ap) will systematically underestimate the skeletal bone "volume" of taller subjects. To reduce the confounding effects of bone size, an alternative ratio has been proposed called bone mineral apparent density [BMAD = BMC/(Ap)3/2]. However, bone size is not the only confounding variable associated with BMC. Others include age, sex, body size, and maturation. To assess the dimensional relationship between BMC and projected bone area, independent of other confounding variables, we proposed and fitted a proportional allometric model to the BMC data of the L2-L4 vertebrae from a previously published study. The projected bone area exponents were greater than unity for both boys (1.43) and girls (1.02), but only the boy's fitted exponent was not different from that predicted by geometric similarity (1.5). Based on these exponents, it is not clear whether bone mass acquisition increases in proportion to the projected bone area (Ap) or an estimate of projected bone volume (Ap)3/2. However, by adopting the proposed methods, the analysis will automatically adjust BMC for differences in projected bone size and other confounding variables for the particular population being studied. Hence, the necessity to speculate as to the theoretical value of the exponent of Ap, although interesting, becomes redundant.
    • Allometric scaling of uphill cycling performance

      Jobson, Simon A.; Woodside, J.; Passfield, L.; Nevill, Alan M. (Georg Thieme Verlag, 2008)
      Previous laboratory-based investigations have identified optimal body mass scaling exponents in the range 0.79 - 0.91 for uphill cycling. The purpose of this investigation was to evaluate whether or not these exponents are also valid in a field setting. A proportional allometric model was used to predict the optimal power-to-mass ratios associated with road-based uphill time-trial cycling performance. The optimal power function models predicting mean cycle speed during a 5.3 km, 5.4 % road hill-climb time-trial were (V O (2max) . m (-1.24)) (0.55) and (RMP (max) . m (-1.04)) (0.54), explained variance being 84.6 % and 70.5 %, respectively. Slightly higher mass exponents were observed when the mass predictor was replaced with the combined mass of cyclist and equipment (m (C)). Uphill cycling speed was proportional to (V O (2max) . m (C)(-1.33)) (0.57) and (RMP (max) . m (C)(-1.10)) (0.59). The curvilinear exponents, 0.54 - 0.59, identified a relatively strong curvilinear relationship between cycling speed and energy cost, suggesting that air resistance remains influential when cycling up a gradient of 5.4 %. These results provide some support for previously reported uphill cycling mass exponents derived in laboratories. However, the exponents reported here were a little higher than those reported previously, a finding possibly explained by a lack of geometric similarity in this sample.
    • Determinants of 800-m and 1500-m Running Performance Using Allometric Models

      Ingham, Stephen A.; Whyte, Gregory P.; Pedlar, Charles R.; Bailey, David M.; Dunman, Natalie; Nevill, Alan M. (American College of Sports Medicine, 2008)
      Purpose: To identify the optimal aerobic determinants of elite, middle-distance running (MDR) performance, using proportional allometric models. Methods: Sixty-two national and international male and female 800-m and 1500-m runners undertook an incremental exercise test to volitional exhaustion. Mean submaximal running economy (ECON), speed at lactate threshold (speedLT), maximum oxygen uptake (V˙ O2max), and speed associated with V˙ O2max (speedV˙ O2max) were paired with best performance times recorded within 30 d. The data were analyzed using a proportional power-function ANCOVA model. Results: The analysis identified significant differences in running speeds with main effects for sex and distance, with V˙ O2max and ECON as the covariate predictors (P G 0.0001). The results suggest a proportional curvilinear association between running speed and the ratio (V˙ O2maxIECONj0.71)0.35 explaining 95.9% of the variance in performance. The model was cross-validated with a further group of highly trained MDR, demonstrating strong agreement (95% limits, 0.05 T 0.29 mIsj1) between predicted and actual performance speeds (R 2 = 93.6%). The model indicates that for a male 1500-m runner with a V˙ O2max of 3.81 LIminj1 and ECON of 15 LIkmj1 to improve from 250 to 240 s, it would require a change in V˙ O2max from 3.81 to 4.28 LIminj1, an increase of $0.47 LIminj1. However, improving by the same margin of 10 s from 225 to 215 s would require a much greater increase in V˙ O2max, from 5.14 to 5.85 LIminj1 an increase of $0.71 LIminj1 (where ECON remains constant). Conclusion: A proportional curvilinear ratio of V˙ O2max divided by ECON explains 95.9% of the variance in MDR performance.
    • Do sporting activities convey benefits to bone mass throughout the skeleton?

      Nevill, Alan M.; Holder, Roger L.; Stewart, Arthur D. (Taylor & Francis, 2004)
      It is well known that sport and exercise play an important role in stimulating site-specific bone mineral density (BMD). However, what is less well understood is how these benefits dissipate throughout the body. Hence, the aim of the present study was to compare the BMD (recorded at nine sites throughout the skeleton) of 106 male athletes (from nine sports) with that of 15 male non-exercising age-matched controls. Given that BMD is known to increase with body mass and peak with age, multivariate and univariate analyses of covariance were performed to compare the BMD of the nine sports groups with controls (at all sites) using body mass and age as covariates. Our results confirmed a greater adjusted BMD in the arms of the upper-body athletes, the right arm of racket players and the legs of runners (compared with controls), supporting the site-specific nature (i.e. specific to the externally loaded site) of the bone remodelling response (all P <0.01). However, evidence that bone mass acquisition is not just site-specific comes from the results of the rugby players, strength athletes, triathletes and racket players. The rugby players' adjusted BMD was the greatest of all sports groups and greater than controls at all nine sites (all P <0.01), with differences ranging from 8% greater in the left arm to 21% in the lumbar spine. Similarly, the strength athletes' adjusted BMD was superior to that of controls at all sites (P <0.05) except the legs. The adjusted BMD of the triathletes was significantly greater than that of the controls in both the arms and the legs as well as the thoracic and lumbar spine. The racket players not only had significantly greater right arm BMD compared with the controls but also a greater BMD of the lumbar spine, the pelvis and legs. In contrast, the low-strain, low-impact activities of keep-fit, cycling and rowing failed to benefit BMD compared with the age-matched controls. These results suggest that sporting activities involving high impact, physical contact and/or rotational forces or strains are likely to convey significant benefits not only to the loaded sites, but also to other unloaded peripheral and axial sites throughout the skeleton.
    • Modeling elite male athletes' peripheral bone mass, assessed using regional dual x-ray absorptiometry.

      Nevill, Alan M.; Holder, Roger L.; Stewart, Arthur D. (Elsevier Science Direct, 2003)
      There is still considerable debate as to whether bone mineral content (BMC) increases in proportion to the projected bone area, A(p), or an estimate of the skeletal bone volume, (A(p))(3/2), being assessed. The results from this study suggest that the bone mass acquisition of elite athletes' arms and legs increases in proportion to the projected bone area, A(p), having simultaneously controlled/removed the effect of the confounding variables of body mass and body fat. Although this supports the use of the traditional bone mineral density ratio (BMD=BMC/A(p)), it also highlights the dangers of overlooking the effect of known confounding variables. Ignoring the effect of such confounding variables, athletic groups whose activities involve upper body strength (rugby, rock climbing, kayaking, weight lifting) had the highest arm BMD, while runners were observed to have the lowest arm BMD (lower than that of the controls). Similarly, leg BMD was highest in rugby players, whose activities included both running and strength training. However, the rugby players were also observed to have the greatest body mass. When the important determinants of body mass, body fat, as well as projected bone area, A(p), were incorporated as covariates into a proportional allometric ANCOVA model for BMC, different conclusions were obtained. The introduction of these covariates had the effect of reducing the sporting differences on adjusted arm BMC, although the "sport" by "side" interaction still identified racket players as the only group with a greater dominant arm BMC (P < 0.05). In contrast, sporting differences in adjusted leg BMC remained highly significant, but with a rearranged hierarchy. The runners replaced the rugby players as having the greatest adjusted leg BMC. The results confirm the benefits of activity on peripheral bone mass as being site-specific but reinforce the dangers of making generalizations about the relative benefits of different exercises ignoring the effects of known confounding variables, such as body size, body composition, and age.
    • Modeling physiological and anthropometric variables known to vary with body size and other confounding variables

      Nevill, Alan M.; Bate, Stuart; Holder, Roger L. (Wiley Interscience, 2005)
      This review explores the most appropriate methods of identifying population differences in physiological and anthropometric variables known to differ with body size and other confounding variables. We shall provide an overview of such problems from a historical point of view. We shall then give some guidelines as to the choice of body-size covariates as well as other confounding variables, and show how these might be incorporated into the model, depending on the physiological dependent variable and the nature of the population being studied. We shall also recommend appropriate goodness-of-fit statistics that will enable researchers to confirm the most appropriate choice of model, including, for example, how to compare proportional allometric models with the equivalent linear or additive polynomial models. We shall also discuss alternative body-size scaling variables (height, fat-free mass, body surface area, and projected area of skeletal bone), and whether empirical vs. theoretical scaling methodologies should be reported. We shall offer some cautionary advice (limitations) when interpreting the parameters obtained when fitting proportional power function or allometric models, due to the fact that human physiques are not geometrically similar to each other. In conclusion, a variety of different models will be identified to describe physiological and anthropometric variables known to vary with body size and other confounding variables. These include simple ratio standards (e.g., per body mass ratios), linear and additive polynomial models, and proportional allometric or power function models. Proportional allometric models are shown to be superior to either simple ratio standards or linear and additive polynomial models for a variety of different reasons. These include: 1) providing biologically interpretable models that yield sensible estimates within and beyond the range of data; and 2) providing a superior fit based on the Akaike information criterion (AIC), Bayes information criterion (BIC), or maximum log-likelihood criteria (resulting in a smaller error variance). As such, these models will also: 3) naturally lead to a more powerful analysis-of-covariance test of significance, which will 4) subsequently lead to more correct conclusions when investigating population (epidemiological) or experimental differences in physiological and anthropometric variables known to vary with body size.
    • Modelling the relationship between isokinetic muscle strength and sprint running performance.

      Dowson, M. N.; Nevill, Mary E.; Lakomy, H. K.; Nevill, Alan M.; Hazeldine, R. J. (London: Taylor & Francis Ltd., 1998)
      Muscle strength is thought to be a major factor in athletic success. However, the relationship between muscle strength and sprint performance has received little attention. The aim of this study was to examine the relationship in elite performers of isokinetic muscle strength across three lower limb joints and sprinting performance, including the use of theoretical models. Eight rugby players, eight track sprinters and eight competitive sportsmen, all elite national or regional competitors, performed sprints over 15 m and 35 m with times recorded over 0-15 m and 30-35 m. Isokinetic torque was measured at the knee, hip and ankle joints at low (1.05 rad s(-1)), intermediate (2.09 or 2.62 rad s(-1)) and high (3.14 or 4.19 rad s(-1)) speeds during concentric and eccentric muscle actions. Using linear regression and expressing sprint performance as time, the strongest relationship, for the joint actions and speeds tested, was between concentric knee extension at 4.19 rad s(-1) and sprint performance (0-15 m times: r=-0.518, P< 0.01; 30-35 m times: r=-0.688, P< 0.01). These relationships were improved for 0-15 m, but not for 30-35 m, by expressing torque relative to body mass (0-15 m times: r=-0.581; 30-35 m times: r=-0.659). When 0-15 m performance was expressed as acceleration rather than time, the correlation was improved slightly (r=0.590). However, when the data (0-15 m times) were fitted to the allometric force model proposed by Gunther, 77% of the variance in concentric knee extension torque at 4.19 rad s(-1) could be explained by 0-15 m times, limb length (knee to buttocks) and body mass. The fitted parameters were similar to those from the theoretical model. These findings suggest that the relationship between isokinetic muscle strength and sprint performance over 0-15 m (during the acceleration phase) is improved by taking limb length and body mass into account.
    • Scaling maximal oxygen uptake to predict cycling time-trial performance in the field: a non-linear approach.

      Nevill, Alan M.; Jobson, Simon A.; Palmer, G.S.; Olds, Tim (Springer Berlin / Heidelberg, 2005)
      The purpose of the present article is to identify the most appropriate method of scaling VO2max for differences in body mass when assessing the energy cost of time-trial cycling. The data from three time-trial cycling studies were analysed (N = 79) using a proportional power-function ANCOVA model. The maximum oxygen uptake-to-mass ratio found to predict cycling speed was VO2max(m)(-0.32) precisely the same as that derived by Swain for sub-maximal cycling speeds (10, 15 and 20 mph). The analysis was also able to confirm a proportional curvilinear association between cycling speed and energy cost, given by (VO2max(m)(-0.32))0.41. The model predicts, for example, that for a male cyclist (72 kg) to increase his average speed from 30 km h(-1) to 35 km h(-1), he would require an increase in VO2max from 2.36 l min(-1) to 3.44 l min(-1), an increase of 1.08 l min(-1). In contrast, for the cyclist to increase his mean speed from 40 km h(-1) to 45 km h(-1), he would require a greater increase in VO2max from 4.77 l min(-1) to 6.36 l min(-1), i.e. an increase of 1.59 l min(-1). The model is also able to accommodate other determinants of time-trial cycling, e.g. the benefit of cycling with a side wind (5% faster) compared with facing a predominately head/tail wind (P<0.05). Future research could explore whether the same scaling approach could be applied to, for example, alternative measures of recording power output to improve the prediction of time-trial cycling performance.
    • Scaling, normalizing, and per ratio standards: an allometric modeling approach.

      Nevill, Alan M.; Holder, Roger L. (Bethesda, MD: The American Physiological Society, 1995)
      The practice of scaling or normalizing physiological variables (Y) by dividing the variable by an appropriate body size variable (X) to produce what is known as a "per ratio standard" (Y/ X), has come under strong criticism from various authors. These authors propose an alternative regression standard based on the linear regression of (Y) on (X) as the predictor variable. However, if linear regression is to be used to adjust such physiological measurements (Y), the residual errors should have a constant variance and, in order to carry out parametric tests of significance, be normally distributed. Unfortunately, since neither of these assumptions appear to be satisfied for many physiological variables, e.g., maximum oxygen uptake, peak and mean power, an alternative approach is proposed of using allometric modeling where the concept of a ratio is an integral part of the model form. These allometric models naturally help to overcome the heteroscedasticity and skewness observed with per ratio variables. Furthermore, if per ratio standards are to be incorporated in regression models to predict other dependent variables, the allometric or log-linear model form is shown to be more appropriate than linear models. By using multiple regression, simply by taking logarithms of the dependent variable and entering the logarithmic transformed per ratio variables as separate independent variables, the resulting estimated log-linear multiple-regression model will automatically provide the most appropriate per ratio standard to reflect the dependent variable, based on the proposed allometric model.
    • The ecological validity of laboratory cycling: Does body size explain the difference between laboratory- and field-based cycling performance?

      Jobson, Simon A.; Nevill, Alan M.; Palmer, G.S.; Jeukendrup, A.E.; Doherty, Michael; Atkinson, Greg (Taylor & Francis, 2007)
      Previous researchers have identified significant differences between laboratory and road cycling performances. To establish the ecological validity of laboratory time-trial cycling performances, the causes of such differences should be understood. Hence, the purpose of the present study was to quantify differences between laboratory- and road-based time-trial cycling and to establish to what extent body size [mass (m) and height (h)] may help to explain such differences. Twenty-three male competitive, but non-elite, cyclists completed two 25 mile time-trials, one in the laboratory using an air-braked ergometer (Kingcycle) and the other outdoors on a local road course over relatively flat terrain. Although laboratory speed was a reasonably strong predictor of road speed (R2=69.3%), a significant 4% difference (P < 0.001) in cycling speed was identified (laboratory vs. road speed: 40.4 +/- 3.02 vs. 38.7 +/- 3.55 km . h-1; mean +/- s). When linear regression was used to predict these differences (Diff) in cycling speeds, the following equation was obtained: Diff (km . h-1)=24.9 - 0.0969 . m - 10.7 . h, R2=52.1% and the standard deviation of residuals about the fitted regression line=1.428 (km . h-1). The difference between road and laboratory cycling speeds (km . h-1) was found to be minimal for small individuals (mass=65 kg and height=1.738 m) but larger riders would appear to benefit from the fixed resistance in the laboratory compared with the progressively increasing drag due to increased body size that would be experienced in the field. This difference was found to be proportional to the cyclists' body surface area that we speculate might be associated with the cyclists' frontal surface area.