The kinetic modeling parts of the model simply assign masses and radii of gyration to the segments defined in the kinematic model. An estimate of the position of the center of mass is required in the segment. This is defined as a point at a given proportion along a line from the distal joint center (normally the origin of the segment) towards the proximal joint center of a "typical" segment. The masses of each segment are calculated as a proportion of the total body mass. The principal axes moments of inertia are calculated from (mass) normalized radii of gyration from these tables too. In general the moment is considered to be zero around the longitudinal axis of most segments. Since experimental data were not available, estimates have been made for the radii of gyration of the pelvis and thorax. You can change these values in the **Properties** pane of the **Process Dynamic Plug-in Gait Model** pipeline operation.

The following diagram shows the kinetic hierarchy.

Note that the clavicles are not considered to have mass in themselves, so reactions for the humerus segments are consider to act directly on the thorax.

The feet are only 'connected' to the forceplates where forceplate measurements and marker data indicate a match. Only one segment is chosen to be in contact with a given forceplate for each frame.

Note also that the "untortioned" tibiae are used for the kinetic modeling. This means that where the KAD and a tibial torsion have been used, and the proximal frame is chosen to reference the ankle moments, the flexion and abduction moments will not correspond to the axes used to calculate the ankle angles. Having said that, the axes are calculated with a "floating axis" definition, so even for corresponding segments the axes will not be coincident.

Even though the "untortioned" tibiae are used for the reference frames, a difference in moments will be observed if the trial is processed with a different tibial torsion. When the tibial torsion is applied in the static trial, the ankle joint center is moved backwards, then the "untortioned" tibia is calculated by rotating the tortioned tibia round the Z axis, keeping the ankle joint center in position. Thus, for a given trial, as tibial torsion is increased, and the joint center is rotated backwards around the ankle marker, the ankle flexion moment will generally become more positive.

Segment | CoM | Mass | Radius of gyration |
---|---|---|---|

Pelvis^{a} | 0.895 | 0.142 | 0.31 |

Femur | 0.567 | 0.1 | 0.323 |

Tibia | 0.567 | 0.0465 | 0.302 |

Foot | 0.5 | 0.0145 | 0.475 |

Humerus | 0.564 | 0.028 | 0.322 |

Radius | 0.57 | 0.016 | 0.303 |

Hand^{b} | 0.6205 | 0.006 | 0.223 |

Thorax^{c} | 0.63 | 0.355 | 0.31 |

Head^{d} | see below | 0.081 | 0.495 |

a) Pelvis: The center of mass is defined along a line from the midpoint of the hip joint centers, to the center of the top surface of the Lumbar 5 vertebra. For simplified scaling, this distance is defined as 0.925 times the distance between the hip joint centers, and the Lumbar5 is defined as lying directly on the Z axis (derived by inspection from the bone mesh used in Polygon). The radius of gyration for the pelvis is an estimate, and is applied round all three axes.

b) Hand: The length of the hand in this model is defined as the distance from the wrist joint center to the finger tip. An estimate of 0.75 is taken as the proportion of this length to the "Knuckle II" reference point referred to in the Dempster data.

c) Thorax: The thorax length is taken as the distance between an approximation to the C7 vertebra and the L5 vertebra in the Thorax reference frame. C7 is estimated from the C7 marker, and offset by half a marker diameter in the direction of the X axis. L5 is estimated from the L5 provided from the pelvis segment, but localized to the thorax, rather than the pelvis. The positions are calculated for all frames in the trial, and averaged to give the mean length. The Center of mass is deemed to lie at a proportion of 0.63 along this line.

d) Head: The center of mass of the head is defined as being 0.52 * the distance from the front to the back of the head along the X axis from the head origin (the midpoint of the front head markers). The length of the head used for the inertial normalization is the distance from this point to the C7 vertebra (the mean position localized to the head segment). The inertia value for the head is applied around all three axes.

## Whole body center of mass

The center of mass is calculated whenever the head or thorax segment is present. A weighted sum of all the centers of mass of all the segments is made, where segments are defined by markers. The sum is still made if segments, such as the hands, for example, do not have markers. The center of mass is the center of mass of all the modeled segments.

**Caution**

Note that this center of mass algorithm has not been clinically tested, and may be misleading in some clinical situations. In particular, the thorax segment is modeled kinetically as a rigid body which includes the mass of the abdomen (which is not independently modeled). The markers which define the thorax are at the top of the thorax, and the center of mass is assumed to be on a line directed towards the L5 vertebra. Any bending of the trunk in the upper lumbar region will cause this assumption to fail, which may cause a significant error in the position of the center of mass for the whole body.

The projection of the center of mass onto the floor is made simply by setting the Z value to zero.