 ### Description

The distribution of head circumference for young boys age 0-3 years can be used to evaluate the physical development of a child.

month

5th%

10th%

25th%

50th%

75th%

90th%

95th%

0

32.6

33

33.9

34.8

35.6

36.6

37.2

1

34.9

35.4

36.2

37.2

38.1

39

39.6

3

38.4

38.9

39.7

40.6

41.7

42.5

43.1

6

41.5

42

42.8

43.8

44.7

45.6

46.2

9

43.5

44

44.8

45.8

46.6

47.5

48.1

12

44.8

45.3

46.1

47

47.9

48.8

49.3

18

46.3

46.7

47.4

48.4

49.3

50.1

50.6

24

47.3

47.7

48.3

49.2

50.2

51

51.4

30

48

48.4

49.1

49.9

51

51.7

52.2

36

48.6

49

49.7

50.5

51.5

52.3

52.8

Polynomial equations approximating this data were calculated in JMP, as follows:

5th% for head circumference in centimeters =

= ((-8.4 * 10^(-8) * ((months)^6)) + (0.0000106 * ((months)^5)) - (0.000546 * ((months)^4)) + (0.0149958 * ((months)^3)) - (0.243795 * ((months)^2)) + (2.5218565 * (months)) + 32.610369)

10th% for head circumference in centimeters =

= ((-9 * 10^(-8) * ((months)^6)) + (0.0000113 * ((months)^5)) - (0.000575 * ((months)^4)) + (0.0156669 * ((months)^3)) - (0.25234 * ((months)^2)) + (2.570534 * (months)) + 33.032701)

25th% for head circumference in centimeters =

= ((-9.2 * 10^(-8) * ((months)^6)) + (0.0000111 * ((months)^5)) - (0.000547 * ((months)^4)) + (0.0146785 * ((months)^3)) - (0.239547 * ((months)^2)) + (2.5080993 * (months)) + 33.915289)

50th% for head circumference in centimeters =

= ((-9.4 * 10^(-8) * ((months)^6)) + (0.0000114 * ((months)^5)) - (0.000568 * ((months)^4)) + (0.0152087 * ((months)^3)) - (0.245625 * ((months)^2)) + (2.537425 * (months)) + 34.835751)

75th% for head circumference in centimeters =

= ((-1.6 * 10^(-7) * ((months)^6)) + (0.0000186 * ((months)^5)) - (0.00087 * ((months)^4)) + (0.0212998 * ((months)^3)) - (0.303215 * ((months)^2)) + (2.7456556 * (months)) + 35.622878)

90th% for head circumference in centimeters =

= ((0.0000019 * ((months)^5)) - (0.000217 * ((months)^4)) + (0.0094392 * ((months)^3)) - (0.20525 * ((months)^2)) + (2.4391856 * (months)) + 36.684292)

Note: This equation is fifth order, while the others in the series are sixth order. The sixth order equation for the 90th percentile data gave less accurate results, while the fifth order was appropriate. The sixth order equation is: (((-1) * (10^(-7)) * ((months)^6)) + (0.0000126 * ((months)^5)) - (0.000625 * ((months)^4)) + (0.0165703 * ((months)^3)) - (0.260665 * ((months)^2)) + (2.5934976 * (months)) + 36.62589).

95th% for head circumference in centimeters =

= ((-1.2 * 10^(-7) * ((months)^6)) + (0.000014 * ((months)^5)) - (0.000674 * ((months)^4)) + (0.0173798 * ((months)^3)) - (0.267385 * ((months)^2)) + (2.6135233 * (months)) + 37.218546)

Distribution of Head Circumference by Month

If the same data is analyzed for each month, then the percentile represented by a given head circumference can be derived. Initially third and fourth order polynomial equations were tried, but were found to be inaccurate. Using 2 second order polynomials for above and below the 50th percentile gave equations adequate for most clinical situations.

5 to 50%ile

age in years

coefficient

0

5.4214884

-345.1254

5494.6317

0.08

4.4424819

-300.5708

5083.6509

0.25

5.7694287

-435.255

8211.3065

0.5

4.4424819

-359.2115

7260.9325

0.75

4.4424819

-376.9815

7997.1255

1

5.7694287

-509.1037

11233.2540

1.5

3.5763125

-316.9954

7014.9580

2

4.7788310

-437.0868

9987.0102

2.5

7.0078568

-662.3134

15649.8410

3

7.0078568

-670.7228

16049.7520

51 to 95%ile

age in years

coefficient

0

-7.058069

526.58004

-9727.045

0.08

-5.941966

475.05468

-9399.272

0.25

-3.840346

339.70583

-7411.976

0.5

-5.941966

553.48863

-12793.46

0.75

-7.345051

709.07271

-17018.08

1

-5.724594

570.75769

-14129.92

1.5

-5.769429

591.70332

-15073.26

2

-3.885224

411.3931

-10785.85

2.5

-3.213161

347.99741

-9314.465

3

-4.442482

478.64054

-12792.01