Assessment of Body Proportions BPK303 Assessment of Body Proportions Summer 2015

Height Distance & Velocity Curves Adolescent growth spurt growth most rapid in first two years

Height Velocity Curves Indicator of maturity Needs longitudinal data Other “systems” have similar curves

Upper Arm Maturity Gradient

Maturity Gradients Adult proportions are a result of complex genetic and environmental influences

Shape Changes with Age

Proportional Changes

Quantifying Proportions Allometry a general assessment Phantom a detailed assessment

Allometry Growth of one part in relation to the growth of another part Isometry - same proportions maintained during growth (same shape)

Physical Dimensions [L] = Length [T] = Time [M] = Mass

VELOCITY = DISTANCE / TIME = [L]/[T] = [L]1[T]-1

Geometrical Similarity System with increase or decrease in size there is no change in shape or body composition

Geometrical Similarity System Length = [L]1 Mass = [L]3 Time = [L]1

VELOCITY = DISTANCE / TIME = [L]1/[L]1 = [L]1[L]-1 = [L]0

Huxley’s Allometric Curve Y = aXb

Huxley’s Allometric Curve Log10Y = log10a + blog10X Curve is linearized by “logging” both sides “b-value” is used to describe relative growth

Human Architecture Growth - longitudinal Adult – Cross-sectional As children grow they tend to become more linear, less weight for height Head becomes proportionally smaller Limbs become proportionally longer Adult – Cross-sectional Tall more linear (less ponderous) Tall proportionally longer limbs Tall proportionally weaker

Allometric Analysis Log10 Y [L]yd Log10 X [L]xd Geometrical Expectancy Slope = b = yd/xd Log10 Y [L]yd Actual Data Slope = b = ? Log10 X [L]xd

Longitudinal Allometric Analysis

Cross-sectional Allometric Analysis

Galileo’s Cube-Square Law

Large relative to what?

Doryphorus (Spearbearer) Polykleitos (750 BC ) Canon of ideal proportions Combination of the best parts of 23 men

Da Vinci’s Vitruvian Man Canon of perfect proportions eg Navel is the centre of the circle described by the hands at head height and the feet when legs describe an equilateral triangle

(x - mean) / standard deviation Standard Score z-score (x - mean) / standard deviation

Phantom is a list of means (P) and standard deviations (s)

Phantom Formula standard score in comparison to a unisex reference proportionality score

Geometrical Similarity System with increase or decrease in size there is no change in shape or body composition

Geometrical Scaling d = 1 for linear measures [L]1 (lengths, skinfolds etc) d = 2 for measures of dimension [L]2 (areas, strength) d = 3 for measures of dimension [L]3 (weight, volumes) & weight)

Interpretation of z-values Phantom is not a norm Proportionally bigger (+) or smaller (-) than the Phantom (so what?) Compare z-values

Bivariate Plotting of Z-values 2 1 -1 Time

Weight

Sitting Height

Upper Arm Length

Foot Length

Skinfold-adjusted Arm Girth

Proportionality Profile -1 1 Weight Arm Length Triceps Skinfold Arm Girth

Standard Error of the Mean

Visual Test of Significant Difference between Means 1 Standard Error of the Mean No significant difference Significant difference

Proportionality Profile -1 1 Weight Arm Length Triceps Skinfold Arm Girth

Kin 303 Proportionality Profile Fall 2009 Males Black Boxes (n=10) Females Open Boxes (n=15) Means ± 1 SEM