Body Size and Scaling Size Matters in Physiology.
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Transcript of Body Size and Scaling Size Matters in Physiology.
![Page 1: Body Size and Scaling Size Matters in Physiology.](https://reader035.fdocuments.net/reader035/viewer/2022062308/56649d135503460f949e71e0/html5/thumbnails/1.jpg)
Body Size and Scaling
Size Matters in Physiology
![Page 2: Body Size and Scaling Size Matters in Physiology.](https://reader035.fdocuments.net/reader035/viewer/2022062308/56649d135503460f949e71e0/html5/thumbnails/2.jpg)
Living Organisms Come in a Huge Range of Sizes!
• Pleuropneumonia-like organisms (Mycoplasma) – 0.1 pg (10-13 g)
• Rotifers– 0.01 μg (10-8 g)
• Blue Whale (Balaenoptera musculus)– 10,000 kg (108 g)
• Giant Redwood Trees (Sequoia spp.) = even bigger!• Living organisms range 1021+ in size • Animals range 1016 in size
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Size Profoundly Influences Physiology
• Gravity– Circulation
– Movement and Locomotion
• Surface Area/Volume Ratio– Respiration
– Digestion
– Water Balance
– Thermoregulation
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Scaling
• Changes in body proportion often accompany changes in body size– both ontogenic and phylogenic– e.g. changes in proportions from human fetus
to adult
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Allometry
1. The study of differential growth
2. The study of biological scaling
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Allometric Equation
• Y = aXb (a power function)
– Y = body part being measured in relationship to the size of the organism
– X = measure of size used for basis of comparison • usually a measure of whole body size
– a = initial growth index • size of Y when X = 1
– b = scaling exponent • proportional change in Y per unit X
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The Scaling Exponent (b) Defines the Type of Scaling Relationship
• If b = 1, there is no differential growth– the relative size of Y to X is
the same at all values of X
– isometry (geometric similarity)
0
10
20
30
40
50
0 200
400
600
800
100
0
120
0
140
0
Body Mass vs. Liver Mass
Live
r M
ass
(g)
Body Mass (g)
y = 0.04 * x1.00
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The Scaling Exponent (b) Defines the Type of Scaling Relationship
• If b < 1, Y increases at a slower rate than X– as X increases, Y becomes
relatively smaller
– negative allometry
Hea
d Le
ngth
(cm
)
0
0.5
1
1.5
2
2.5
3
3.5
4
0 2 4 6 8 10 12 14 16
Head Length vs. Body Length
Hea
d Le
ngth
(cm
)
Body Length (cm)
y = 0.5 * x0.72
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The Scaling Exponent (b) Defines the Type of Scaling Relationship
• If b > 1, Y increases at a faster rate than X– as X increases, Y becomes
relatively larger
– positive allometry
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5 2 2.5 3 3.5
Forelimb Length vs. Body Length
For
elim
b Le
ngth
(m
)
Body Length (m)
y = 0.32 * x1.28
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Allometry
• Allometric Data Can Also Be Expressed as Linear Functions of Log-Transformed Data
Y = aXb
log Y = log a + b log X
– the slope of the line (b) indicates the type of scaling relationship
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Types of Scaling Relationships
• If b = 1, isometry (geometric similarity)• If b < 1, negative allometry• If b > 1, positive allometry
• The Catch: – Above is true only when we compare like dimensions
(e.g. length to length, mass to mass).
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Isometry for Different Dimensions
• Example: Head Length vs. Body Length– Linear dimension (m1) vs. linear dimension (m1)– Isometry: m1/m1, b = 1/1 = 1.0
• Example: Head Length vs. Body Mass– Linear Dimension (m1) vs. Cubic Dimension (m3)– Isometry: m1/m3, b = 1/3 = 0.33
• Example: Surface Area vs. Body Mass– Square Dimension (m2) vs. Cubic Dimension (m3)– Isometry: m2/m3, b = 2/3 = 0.67
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Differential Scaling is Common
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1 cm
1 cm
10 cm
10 cm 10 cm
Limb cross-sectional area = 1 cm X 1 cm = 1 cm2
Volume = 10 cm X 10 cm X 10 cm = 1000 cm3
Estimated mass = 1000 g
Weight loading on limb = 1000g / 1 cm2
Hypothetical one-legged cuboid animal…
Example: Support of Weight by the Limbs
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10 cm
10 cm
100 cm
100 cm 100 c
m
Limb cross-sectional area = 10 cm X 10 cm = 100 cm2
Volume = 100 cm X 100 cm X 100 cm = 1,000,000 cm3
Estimated mass = 1,000,000 g
Weight loading on limb = 1,000,000g / 100 cm2 = 10,000 g/cm2
Increase all linear dimensions tenfold…
Example: Support of Weight by the Limbs
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33.3 cm
33.3
cm100 cm
100 cm 100 c
m
Limb cross-sectional area = 33.3 cm X 33.3 cm = 1000 cm2
Volume = 100 cm X 100 cm X 100 cm = 1,000,000 cm3
Estimated mass = 1,000,000 g
Weight loading on limb = 1,000,000g / 1000 cm2 = 1000 g/cm2
Need a proportionately thicker limb bone to support the increased mass
Example: Support of Weight by the Limbs
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Scaling of Skeleton Mass
• Expect b = 1 for isometry
• However, because of increased weight loading, may expect b > 1
• Typical scaling: b = 1.12– skeleton becomes relatively more massive with
increased body size– compensates for increased weight loading
![Page 18: Body Size and Scaling Size Matters in Physiology.](https://reader035.fdocuments.net/reader035/viewer/2022062308/56649d135503460f949e71e0/html5/thumbnails/18.jpg)
Scaling of Skeleton Mass• Scaling of 1.12 does not fully compensate
for weight loading with increased mass:– Length Mass1/3
– Skeletal Mass Cross-Sectional Area * Length– Cross-Sectional Area Body Mass– Skeletal Mass Body Mass * Length– Skeletal Mass Body Mass * Body Mass1/3
– Skeletal Mass4/3
– Skeletal Mass1.33 expected for isometry of weight loading
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Scaling of Skeleton Mass
• Why not scale at 1.33?
– Mass of skeleton contributes to mass of animal
– increased skeletal mass limits movement and ability of skeleton to absorb physical shocks
• the thicker the skeleton, the greater the chance of fracture
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Scaling of Skeleton Mass
• How can animals increase in size without becoming “all skeleton”?– Animals accept lower safety factor
• generally, skeleton is about 10x as strong as needed to support the animal’s weight
– Decreased locomotor performance
– Alter morphology to reduce stress on the skeleton
– Alter chemical composition of skeleton• e.g. human limb bones - relatively more slender in adults
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How Does Differential Scaling Arise?
• Differences in size among animals are due primarily to differences in cell number
• During embryonic development, cells differentiate and give rise to germinal centers
– each part of an organism arises from one or more germinal centers
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How Does Differential Scaling Arise?
• Rate at which a part grows depends on number of germinal centers and rate of cell division
• For Y = aXb
– a number of germinal centers contributing to a particular body region
– b ratio of the frequencies of cell division between Y and X