Trakia Journal of Sciences, Vol. 12, Suppl. 1, pp 70-73, 2014
Copyright © 2014 Trakia University
Available online at:
http://www.uni-sz.bg
ISSN 1313-7050 (print)
ISSN 1313-3551 (online)
ALOMETRIC RELATIONSHIPS BETWEEN THE BODY-MASS INDEX,
MASS TO SURFACE RATIO AND THE LENGTH OF PREGNANCY IN
SOME MAMMALS (Metatheria and Placentalia)
A. Atanasov1*, M. Todorova2, D. Valev3, R. Todorova4
1
Department of Physics and Biophysics, Faculty of Medicine, Trakia University, Stara Zagora, Bulgaria
2
Department of Obstetrics and Gynecology, Faculty of Medicine, Trakia University, Stara Zagora,
Bulgaria
3
Space Research and Technology Institute, Stara Zagora, Departments, Bulgarian Academy of Sciences,
Bulgaria
4
Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia
ABSTRACT
Body mass index (BMI) is characteristics in human physiology represented by the ratio between the body
mass and the square of body height, i.e. BMI = Mass/Height 2. In the case of animals (mammals) the BMI
can be defined by the length of the body i.e. BMI = Mass/Legth 2. In manuscript is showed existence of
relationship between the body mass M(kg), length L(m), surface S(m 2), body mass to surface ratio M/S
(kg/m2 ) as well as body mass index BMI(kg/m2) and the length of pregnancy T (days).
Key words: body mass index, length, surface, pregnancy, human, veterinary medicine.
INTRODUCTION
Body mass index (BMI) is a physiological
characteristics represented by the ratio of body
mass and the square of body height, i.e. BMI =
Mass/Height2. Body mass index is characteristics
often used for purpose of diagnostics in Human
medicine (1). But BMI is not well developed like
prognostic
characteristics
in
Veterinary
medicine. In case of mammals the BMI can be
defined by the length of the body i.e. BMI =
Mass/Legth2. The field of Veterinary medicine
contained
wide
spectrum
of
animals
(Poikilotherms, Mammals and Aves) with wide
spectrum of characteristics: body mass, length
and lifetime characteristics (lifespan, length of
pregnancy, during puberty, during excretion of
drugs) that differs some orders of magnitude
between them. However, the connection between
BMI and these characteristics is not study. The
aim of the work is to investigate the alometric
_________________________________
*Correspondence to: Atanas Todorov Atanasov,
Medical Faculty, Dept. Physics and
Biophysics,Trakia University, Armeiska Str. 11, Stara
Zagora, BULGARIA, E-mail: [email protected]
70
relationship between the body mass, body
length, body surface, body mass to surface ratio
and the body mass index and the length of
pregnancy in Mammals.
MATERIALS AND METHODS
The data for the 103 studied mammal species
Metatheria and Placentalia (from Common
shrew to Killer whale), their body mass, body
length and pregnancy length were collected from
the review papers (2-5). The body surface S (m2)
were calculated by formula S=0.1M0.67, where
the body mass M is given in kg (6, 7).The body
length of animals H (m) was given to be from
head to tail i.e. the length of head plus length of
spinal cord, without length of the tail.
RESULTS
The relationships between the body mass M
(kg), square of body length H2 (m2), body length
H (m), body surface S (m2), body mass to
surface ratio M/S (kg/m2) and body-mass index
M/H2) as a function of length of pregnancy T(d)
are given on Table 2. On Figure 1 are compared
relationships of BMI, M/S ratio as functions of
the length of pregnancy T.
Trakia Journal of Sciences, Vol. 12, Suppl. 1, 2014
ATANASOV A., et al.
Table 1.. Experimental and calculated data for Mammals.
Animals
M (kg)*
Tpr (d)*
S (m2)
1. Sorex araneus
2. Mus musculus
3. Cricetulus migratorius
4. Myomimus personatus
5. Mustela nivalis
6.Rattus rattus
7.Chinchilla laniger
8.Rattus norvegicus
9.Cricetus cricetus
10.Gavia porcellus
11.Sciurus vulgaris
12.Mustela lutreola
13.Erinaceum europaeus
14.Ondatra zibethica
15.Citellus major
16.Mustela vison
17.Lepus tolai
18.Marmota bobac
19.Lepus europaeus
20.Lepus timidis
21.Felis libyca
22.Felis silvestris
23.Alopex lagopus
24.Marmota marmota
25.Urocyon cinereoargentus
26.Myocastor coypus
27.Felis familiaris
28.Dasypus novemcinctus
29.Vulpes vulpes
30.Nyctereutes
procyonoides
31.Procyon lotor
32.Canis aureus
33.Hylobacter lar
34.Canis latrans
35.Capreolus capreolus
36.Gulo gulo
37.Lynx lynx
38.Gazella subgutturosa
39.Rupicapra rupicapra
40.Capra aegagrus
41.Panthera pardus
42.Canis lupus
43.Ovis aries
44.Pan troglodytes
45.Homo sapiens
46.Saiga tatarica
47.Canis lupus
48.Ovis orientalis
49.Delphinus delphis
50.Canis familiaris
51.Crocuta crocuta
52.Macropus rufus
53.Panthera pardus
54.Dama dama
55.Zalophus californianus
56.Felis concolor
57.Sus scrofa
58.Ovis ammon
59.Capra falconeti
60.Capra ibex
61.Tursiops truncatus
0.008-0.015
0.021
0.021
0.024-0.025
0.1
0.20-0.35
0.30-0.60
0.384
0.40-0.50
0.51
0.18-1.0
1
0.7-1.0
0.95
1.05
1.5
3.0-4.0
4.5-6.0
4.0-5.0
3.0-5.0
5
6
6
4.0-8.0
7
up to 6
up to 6
6
6-10
20
19-20
20
20-25
54
20-24
108-112
21-22
30
68
38-44
42-46
49
25
30
34-78
50
30
44
47-55
60
63
52
35
63
130
60-63
120
49-58
5.00×10-3
7.514×10-3
7.514×10-3
8.33×10-3
0.0214
0.0421
0.0585
0.0526
0.0586
0.0637
0.0702
0.1
0.0897
0.0966
0.103
0.312
0.231
0.304
0.274
0.253
0.294
0.332
0.332
0.332
0.372
0.332
0.332
0.332
0.403
M/S
(kg/m2)
2.3
2.795
2.795
2.941
4.673
6.535
7.7
7.3
7.68
8
8.4
10
9.48
9.83
10.1
11.43
15.12
17.28
16.43
15.8
17
18.06
18.06
18.06
18.81
18.06
18.06
18.07
19.86
6-10
7-8
7-13
10
13
20-37
30
32
33
25-45
up to 38
32-40
32-50
49
70
60
60
up to 65
46-79
53
65
59-82
80-150
75
100
100
up to 105
60-150
100-170
109
110
120
65
63
60-63
210
60-66
165
120
63-70
150-180
180
150
90
65-75
148
270
280
150
60-65
150
300-330
64-68
110
275
90
240
360
90
124-140
150-180
150-180
154-161
330-360
0.403
0.386
0.468
0.468
0.558
0.943
0.976
1.012
1.04
1.083
1.144
1.103
1.204
1.356
1.723
1.554
1.554
1.64
1.597
1.43
1.64
1.731
2.403
1.804
2.188
2.188
2.26
2.26
2.675
2.318
2.332
2.472
19.86
19.44
21.38
21.38
23.31
30.2
30.73
31.38
31.7
32.17
33.21
32.63
34.06
36.12
40.63
38.61
38.61
39.65
39.04
37.07
39.65
40.73
47.87
41.57
45.71
45.71
46.45
46.45
50.47
47.03
47.17
48.54
H (m)*
0.06-0.09
0.11
0.13
0.11
0.28
0.13-0.24
0.27
0.18-0.25
0.24-0.32
0.28-0.30
0.19-0.29
0.43
0.20-0.30
0.25-0.30
0.23-0.33
0.4
0.4-0.53
0.5-0.7
0.5-0.7
0.44-0.74
0.7
0.75
0.5-0.75
0.57
0.5-0.8
0.6-0.8
0.3-0.4
0.8
0.6-0.9
BMI
(kg/m2)
2.044
17.36
12.43
2.025
1.276
8.041
6.173
8.312
5.74
6.064
8.682
5.408
13.6
12.6
13.4
9.375
7.527
14.58
12.5
11.49
10.2
10.67
15.34
18.4
16.59
12.24
48.98
9.38
14.22
0.65-08
0.5-0.6
0.7-1
1
0.7-10
1.2
0.8
1.2
1.16
1.2
1.5
1.8
1.3
1.3
1.5
1.65
1.14
1-1.6
1.47
2.5
1
1.3
2-3
1.8
1.4
1.75
1.3
2
2
1.7
1.6
3
15.22
24.8
13.84
10
18
19.8
46.87
22.22
24.52
24.3
16.9
11.11
24.11
28.8
31.11
22
46.5
38.23
28.9
8.48
65
41.47
18.4
23.15
51
32.65
61.76
26.25
33.75
37.7
43
13.33
Trakia Journal of Sciences, Vol. 12, Suppl. 1, 2014
71
ATANASOV A., et al.
62.Ursus thibetanus
63.Capra sibirica
64.Phoca vitulina
65.Lama glama
66.Ovis ammon
67.Pagopoca groenlandica
68.Cervus nippon
69.Panthera leo
70.Gorilla gorilla
71.Tapirus terrestris
72.Panthera tigris
73.Ursus arctos
74.Pongo pigmaeus
75.Monachus monachus
76.Cervus elaphus
77.Ovibos moschatus
78.Equus burchelli
79.Cystophora cristata
80.Kogia breviceps
81.Camelus bactrianus
82.Ursus maritimus
83.Bison bonasus
84.Poephagus gruniens
85.Equus cabalus
86.Ursus horribilis
87.Bubalus caffer
88.Giraffa camelopardalis
89.Bison bison
90.Delphinapterus leucas
91.Bubalus aranee
92.Syncerus caffer
93.Tapirus indicus
94.Diceros bicornis
95.Rhinoceros unicornis
96.Hippopotamus amphibius
97.Ceratotherium simum
98.Elephas maximum
99.Loxodonta africana
100.Orcinus orca
101.Balaenoptera physalus
102.Balaena mysticetus
103.Balaenoptera musculus
140
100-130
150
up to 101
100-170
170
148
180-240
110-300
200
227-272
250
up to 250
300
300-340
up to 300
up to 350
400
400-500
450-490
700
600-800
up to 720
up to 700
up to 800
800-1000
1000
1000
1000
1000-1200
1000-1200
1500
up to 2000
up to 2000
3200
3000
5000
7500
12500
100000
100000
160000
210
170-180
270-300
330-397
150-180
330
240
105-112
270
390-400
95-154
180-240
270
315
165-224
270
361-390
330
270
365-440
230-250
270
255-304
350
250
270-280
420-446
265-270
330-360
300-328
330
390-395
450-548
484.5
210-240
540
607-641
660
480
360
360
420
The correlation coefficients R2 of relationships
given on Table 2 vary between 0.612 and 0.941.
This shows that the relationships are not random.
The power and linear coefficients in the
relationships for body surface and the square of
body length differ negligible i.e. these
relationships are nearly equivalently in relation
to the length of pregnancy.
2.741
2.4
2.87
2.202
2.675
3.122
2.845
3.596
3.539
3.481
4.037
4.042
4.042
4.567
4.77
4.567
5.064
5.535
5.993
6.17
8.058
8.058
8.211
8.058
8.812
9.535
10.23
10.23
10.23
10.9
10.9
13.43
16.28
16.28
22.31
21.36
30.08
39.47
55.58
223.87
223.87
306.73
51.07
47.87
52.25
45.86
47
54.46
52.02
58.39
57.93
57.45
61.81
61.85
61.85
65.68
67.1
65.68
69.11
66.74
75.087
76.175
86.87
86.87
87.69
86.87
86.87
90.78
94.4
97.75
97.75
97.75
100.92
100.92
111.7
122.85
143.43
140.45
166.2
190
224.9
446.69
446.69
521.68
2
1.65
1.8
1.6
2
2
1.18
2.7
2
1
2.9
2
1.5
2.75
2.4
2.4
2.5
2.8
3
3
2.5
3.5
4
3
2.75
2.75
4
3
5
1.9
2.2
2.5
3.8
3.15
4.5
4.5
5
5
8
25
21
32
35
42.3
42.3
39
33.75
42.5
106
28.8
51.25
200
29.73
62.5
111.1
39.7
55.55
52.08
56
51
50
52
112
57.14
45
77.8
105.8
132.3
62.5
111.1
40
160.34
227
240
138.5
201.5
158
148.14
200
300
195.3
160
226
161.24
The Figure 1 shows that the scaling exponent of
relationships: M/S = 0.3474 T 0.9768 and M/H2 =
0.2184 T 0.9968 differ negligible (0.9768 and
0.9968), as well as the linear coefficient (0.3474
and 02184), and corresponding coefficients
(0.753 and 0.612) in two relationships. Thus, the
BMI and M/S ratio are equivalently in relation to
the length of pregnancy too.
Table 2. Alometric relationships between the body parameters and the length of pregnancy
n
1.
2.
3.
4.
5.
6.
7.
72
EQUATIONS
M = 2.248×10-5 T 2 . 9744
H2 = 9.85×10-5 T 1. 9864
H = 9.81×10-3 T 0.9931
S = 8.093×10-5 T 1.9844
M/S = 0.3474 T 0.9768
M/H2 = 0.2184 T 0.9968
H2 = 1.123 S 0. 9906
Correlation coefficient R2
R2 = 0.7553
R2 = 0.7244
R2 = 0.7283
R2 = 0.7539
R2 = 0.7534
R2 . = 0.612
R2 = 0.941
Trakia Journal of Sciences, Vol. 12, Suppl. 1, 2014
ATANASOV A., et al.
3
BMI
M/S
BMI (M/S), kg/m2
2,5
y = 0.9968x - 0.6571
R2 = 0.612
2
1,5
1
0,5
y = 0.9768x - 0.5254
R2 = 0.7534
0
0
0,5
1
1,5
Tpr, days
2
2,5
3
Figure 1. Linear relationships between BMI, M/S ratio and length of pregnancy T in 103 Metatheria
and Placentalia. The power coefficients 0.9968 and 0.9768 in two relationships are very near to 1.0.
The found relationships can be used for
prognostic purpose in the human and the
veterinary medicine.
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Maternal obesity and labour complications
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2. Atanasov, A.T., Possible metabolism-body
weight effect on prolongation and reduction
of pregnancy duration. Medical Hypotheses
64, 1247-1248, 2005.
3. Atanasov, A.T., Allometric relationship
between the length of pregnancy and body
4.
5.
6.
7.
weight in mammals. Bulgarian Journal of
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Grant, V., Evolution of the organisms, Mir,
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Markov, G., Animals, 2nd ed., Science,
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Rübner, M., Ueber den Einfluss der
Körpergrösse auf Stoffund Kraftwechsell, Z.
Biol. 19: 535-562, 1883.
Atanasov, A. T., Prognosis of Prolongation
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