## Anthropometric Relationships of body and body segment moments of inertia

Reference | >Anthropometric Relationships of body and body segment moments of inertia |

Journal | AFAMRL-TR-80-119 |

Author | J.T. McConville |

Item | V COV I PAI(Principal Axis of Inertia) |

State | Living |

Sample number | 31 |

Sex | Male |

Age | 27.45±5.64 |

Measurement year | n/a |

Race | Caucasian |

Measurement place | USA |

Measurement technique | Photogrammetry |

Rawdata accessibility | NG |

#### (1)Definition of Body segment

24segments:head，Neck，Thorax，Abdomen，Pelvis，Upper arm，Forearm，Hand，Flap，Thigh，Calf，Foot，Thigh―Flap，Lower Arm＋Hand

a.Head―Neck

The cut plane passes through the left and right gonial points and nuchale

b.Neck―Thorax

The compound plane consists of two components. The horizontal plane originates at the cervicale, and passes anteriorly parallel with the standing surface.

The second plane originates at the lower of the two clavicale landmarks, rises 45 degree from the horizontal, and passes diagonally superiorly-posteriorly until it intersects with the horizontal plane.

c.Thorax―Abdomen

The cut plane begins at the 10th rib mid-spine landmark and passes through the torso parallel with the standing surface.

d.Abdomen―Pelvis

The cut plane begins at the higher of the two ilio-cristale landmarks and passes through the torso parallel with the standing surface.

e.Pelvis―Thigh

The cut plane begins at the center of the crotch and passes laterally midway between the anterior superior iliac spine and trochanteric landmarks along the line of the right and left inguinal ligaments.

f.Thigh－Flap

The cut plane begins at the gluteal furrow landmark and passes through the thigh parallel to the standing surface

g.Thigh―Calf

The cut plane passes through the lateral femoral epicondyle landmark parallel to the standing plane.

h.Calf―Foot

The cut plane begins at the sphyrion landmark and passes through the ankle parallel to the standing height.

i.Thorax―Upper Arm

The cut plane begins at the acromion landmark and passes downward through the anterior and posterior scye creases at the level of the axilla.

j.Upper arm―Forearm

The cut plane begins at the olecranon landmark and passes through the medial and lateral humeral epicondyle landmarks.

k.Forearm―Hand

The cut plane begins at the ulnar and radial styloid landmark and passes through the wrist perpendicular to the long axis of the forearm.

#### (2)Predictive model

- The center of volume is calculated as the mean distance from the anatomical axis origin of each segments
- The principal axes of inertia are calculated as the mean angle with respect to the anatomical axis of each segments.
- Volume and principal moment of inertia are calculated using regression equations, as follows．
- A.Volume and principal moment of inertia are predicted using equations including body weight and stature.
- B.Volume and principal moment of inertia are predicted using equations including the three anthropometric variables that have the first, second and third greatest correlation coefficients of all variables.

#### (3)Validation

- Comparison of measurement of principal moments of inertia of the whole body between the photogrammetry method and mechanical vibration method. -> X: -12.96, Y: -4.05 Z: -1.08%
- Comparison of measurement of principal moments of inertia of all segments between the photogrammetry method and the cadaver segmentation method of Chandler -> The values by photogrammetry method are almost consistently larger than those by cadaver segmentation method

# Regression coefficients

## Definition of the anatomical axis origin of each segment.

- Three landmarks are used to establish the original plane.
- Two additional landmarks are used to establish a plane perpendicular to the first plane.
- A single landmark is used to establish a plane perpendicular to first two planes.

The origin of each axis system is the common point of intersection of the three planes. +Z is the direction from the origin towards the head; +X is the direction from the origin towards the front of the body; +Y is the direction from the origin towards the left of the body.

Segment | XY plane | YZ plane | XZ plane |

a.head | The plane passes through the right and left tragion and right infraorbitale | The plane passes through right and left tragion, perpendicular to XY plane | The plane passese through sellion, perpendicular to XY and YZ plane |

b.neck | The plane passes through Adam's apple, cervicale and suprasternale. | The plane passes through one- half the distance between the right clavicale and cervicale and the left clavicale and cervicale, perpendicular to XZ plane. | The plane passes through cervicale, perpendicular to XZ and XY plane. |

c.Thorax | The plane passes through suprasternale, cervicale and mid-spine at level of 10th rib. | The plane passes through cervicale and 10th rib level at mid-spine, perpendicular to XZ plane. | The plane passes through 10th rib level at mid-spine, perpendicular to XZ and YZ plane. |

d.Abdomen | The plane passes through right and left 10th rib and at mid-spine at level of 10th rib. | The plane passes through right and left 10th rib, perpendicula to XY plane. | The plane passes through 10th rib mid-spine, perpendicular to XY and YZ plane. |

e.Pelvis | The plane passes through right and left anterior superior iliac spine and symphsion. | The plane passes through right and left anterior superior iliac spine, perpendicular to YZ plane. | The plane passes through mid-spine at level of posterior superior iliac spine, perpendicular to YZ and XY plane. |

f.Right and left upper arm | The plane passes through acromion and right and left humeral epicondyles. | The plane passes through lateral epicondyle and acromion, perpendicular to YZ plane. | The plane passes through acromion, perpendicular to YZ and XZ plane |

g.Right and left forearm, forearm + hand | The plane passes through distal end of the ulnar and radial styloid processes and radiale. | The plane passes through distal end of the ulnar styloid process and radiale, perpendicular to YZ plane. | The plane passes through radiale, perpendicular to YZ and XZ plane. |

h.Right and left hand | The plane passes through dactylion and the lateral aspect of the metacarpal-phalangeal joint of degits 2 and 4. | The plane passes through the lateral aspect of the metacarpal-phalangeal joint of digits 2 and 4, perpendicular to YZ plane. | The plane passes through metacarpale 3, perpendicular to YZ and XY plane. |

i.Right and left thigh, flap, thigh-flap | The plane passes through trochanterion and right and left lateral femoral epicondyles. | The plane passes through lateral femoral epicondyles and trochanterion, perpendicular to YZ plane. | The plane passes through trochanterion, perpendicular to YZ and XZ plane. |

j.Right and left calf | The plane passes through tibiale, sphyrion and the lateral malleolus. | The plane passes through sphyrion and tibiale, perpendicular to YZ plane. | The plane passes through tibiale, perpendicular to YZ and XZ plane. |

j.Right and left foot | The plane passes through metatarsal-phalangeal 1 and 5 landmarks and the posterior calcaneous. | The plane passes through tip of digit 2 and posterior calcaneous, perpendicular to plane. | The plane passes through metatarsal-phalangeal 1 landmark, perpendicular to XY and XZ plane. |

## The center of volume

The following table shows the mean distance from the anatomical axis origin of each segments.

Note:The dimension in the table is cm.

## Principal axes of inertia

The following table shows mean principal axes of inertia with respect to anatomical axes cosine matrix expressed in degrees.

**Ex.) **

## Volume (independent variables: body weight and stature)

The following table shows regression coefficients.

Note:Volume in cm^{3}, weight in lb, body fat in mm and all other dimensions in cm.

**Ex.)
Head volume(cm ^{3})=2806+6.84×stature(cm)+2.05×body weight(lb)**

## Principal moment of inertia (independent variables: body weight and stature)

The following table shows regression coefficients.

Note:Weight in lb, body fat in mm, moment of inertia in g・cm^{2}, all other dimension in cm.

**Ex.)
Principal moment of inertia around x-axis(g・cm ^{2})=36972+859×stature(cm)+86×body weight(lb)**

## Volume (independent variables: three anthropometric variables)

The following table shows regression coefficients.

Note:Volume in cm^{3}, weight in lb, body fat in mm, all other dimensions in cm.

**Ex.)
Head volume(cm ^{3})=-5593.6+216.18×head circumference(cm)-121.84×head length(cm)**

## Principal moment of inertia around x-axis (independent variables: three anthropometric variables)

The following table shows regression coefficients. -> Yp, Zp

Note:Weight in lb, body fat in mm, moment of inertia in g・cm^{2}, all other dimension in cm.

**Ex.)
Principal moment of inertia around x-axis(g・cm ^{2})=-625049+11639×head circumference(cm)+10605×head length(cm)
**

## Principal moment of inertia around y-axis (independent variables: three anthropometric variables)

The following table shows regression coefficients. -> Xp, Zp

Note:Weight in lb, body fat in mm, moment of inertia in g・cm^{2}, all other dimension in cm.

**Ex.)
Principal moment of inertia around y-axis(g・cm ^{2})=-794181+17924×head circumference(cm)**