1. The Four Minimum Points of Gait and Foot-line

The four minimum points of gait are:
1) step-heel-point,
2) step-pelvic joint,
3) rear-pelvic joint,
4) start-heel-point.

Deconstruction and simplification of the skeleton leaves the two heel-points as contact with the ground, and the pelvic joints as the only necessary rotation points, with 3 straight lines connecting the points. Measurements based on the projection of the 4 points onto any 2D plane gives all the distance and direction information for a person walking, wrt that plane.

The foot-line should be included if possible, but it isn't required. Without it, foot and push-off angles are recorded as a single angular change, and foot-line rotations over aberrations can't be determined.

Also, the heel-points are normally the points of contact with the ground if we had peg legs that went to points. So if a person was wearing shoes, the heel-point would be on the bottom of the shoe, not on the sole of the foot. However, this method allows for the choice of different points, eg. using the sole of the foot even though wearing shoes, as long as the interpretation takes it into account.

The entire measurement system is derived from the detailed analysis of the relationships between these 4 points and foot-line.

2. The Eight Fundamental Parameters of Gait

The 8 fundamental parameters of gait are lines and angles derived from the projection of the 4 minimum points of gait and foot-line, onto a specific 2D plane (usually the floor). They organize the contributions to distance and direction from specific body segments and rotation points (joints).

There must be a change in at least one of the fundamental parameters for there to be any change in distance and/or direction, and a change in any one must show as a change in distance and/or direction.

Distance:
1) rear-leg-line
2) step-out-line
3) straddle-line
4) pelvic-stretch

Direction:
4) foot offset
5) foot angle
6) push-off angle

Distance and direction:
7) aberration

Walking is the manipulation of these parameters.

1) and 2) are the 3rd and 4th straight lines over the step, resp.

Note: Step, stride and walking base are not fundamental parameters, they are products of them.

Also, 3) straddle-line and 4) pelvic-stretch, are the sides of a right triangle, with the pelvis-line as the hypotenuse. Technically, the pelvis-line should be the fundamental parameter (since it’s directly based on a body segment), not the other 2. However, since pelvic stretch and straddle-line are far more descriptive wrt the important elements of gait, I prefer to use them instead.

3. The Five Straight Lines Forward for a Single Step

The 4 minimum points and foot-line define a series of 5 "straight lines forward" which are relevant over the course of a single step. These lines describe sequential direction changes.

1) step-foot-line of the previous step,
2) foot-line after aberrations,
3) rear-leg-line,
4) step-out-line and,
5) step-foot-line of the current step.

The rear-leg and step-out lines are fundamental parameters, the foot-line isn't.

Foot-lines represent 3 of the straight lines, but, since it’s not a required element, only very useful. If there was no foot-line, there would be 2 straight lines. The first would be the rear-leg-line, and the second the step-out-line. This shows why adding the foot-line is desirable, it adds quite a bit of info because each foot-line is affected by different factors.

Each line represents what would be the straight line forward if there were no further direction changes. 1) would be the straight line if there were no foot offsets, foot or push-off angles, or aberrations. When there's an aberration, the foot-line, 2), becomes the straight line. When there's push-off angle, the rear-leg-line, 3) then becomes the straight line and, if there’s foot offset 4) becomes the straight line forward. 5) becomes the straight line if there’s foot angle. 5) is 1) for the next step. (4 and 5 occur at the same time.)

These represent a continuum which is defined by body segments, and allows the accurate determination of direction changes within the step, and over the entire path. This should help with the interpretation of data in many areas of gait research.

4. Real vs Apparent Rotation

Rotations at either pelvic joint or along the step-out-line axis result in direction changes, as well as others, but it doesn't have to be real rotation.

Since the step-out-line is a vector sum, the specific orientation of the component vectors could lead to a lateral heel-point shift without any actual rotation at the step-pelvic joint. (The specifics of this would have to be studied.) This would be measured as a rotation at the step-pelvic joint, even though it had nothing to do with it. Also, since this is a 2D projection, other movements along the z-axis may lead to apparent rotations.

Real vs apparent rotation is irrelevant to the measurements. It would be very important, though, to other aspects of a full clinical analysis. This highlights the fact that this method, though extensive, is still only one part of the greater analysis.

5. Walking is a Controlled Stagger

When a person walks, they are manipulating the 8 parameters. The degree of control over this manipulation is the factor which defines when a person is "staggering".

The distance parameters aren't as important, but variation of any of the direction parameters leads to a change in direction.

Distance deviations don't have to be compensated for, but if at any time there's a change to one of the direction parameters, there isn't only that turn, but there must be a future, compensating turn in order to stay on the straight path. This is by manipulation of the next parameters in that step, as well as the parameters for the next steps. If the compensating turn isn't exactly right, there has to be another compensating turn farther along the path, etc.

Someone who's drunk has less control over the direction changes, and the compensating turns, and shows greater lateral movement than normal, as well as other gait abnormalities. The classic drunken stagger.

For a sober person, each step virtually certainly has direction deviations and/or compensating turns. The upper body may be perfectly stable, but the lower frame is changing direction by small amounts. A well controlled stagger.

6. The Primary Goals of Walking are Distance and Direction

Humans evolved the ability to walk in order to better get from point A to point B. Since a person's body is directional, the path to B will not only include a distance to be traveled, but also a direction change from straight ahead.

Physical processes developed to accomplish these goals, using the available framework, which also required the balancing of a large, gangly mass over the lower locomotion framework, the minimization of energy expenditure, the versatility necessary to traverse any terrain, and the breadth of control to quickly alter the walking pattern to suit virtually any immediate choice (such as jumping, changing speed or direction).

Extremely complex muscle controls have evolved, but, if distance and direction are the primary goals, then it’s reasonable to assume muscular and other controls developed to facilitate these, and, so, should be definable as specific sets associated with each.

That's why the plane of the floor is the most revealing, and why the 8 parameters should be the central correlation for all areas of gait research, since they directly show distance and direction changes involved during the step, defined wrt body segments and rotation points (ie., specific movements and muscle action).

Also, since each step is an individual, the ability to separate the unique direction and distance variations over each step, which are directly related to various mass movements, should aid in the analysis of vector data such as force, velocity, etc.

7. The Standard Start Position

Definition of the theoretical standard start position is required for the separation of step and carry lines. Only 3 of the minimum points of gait are needed to define it, the step and rear-pelvic joints and the start-heel-point, and it's the position when all changes due to the previous step are accounted for by rotations and/or heel-point shifts, and after aberration and push-off angle shifts and rotations.

The first 2 direction changes, aberrations and push-off angle, change the Step Model grid orientation, and, hence, the position of the standard start position.

To visualize it, imagine yourself frozen at the instant of heel-contact. Now draw yourself back along a straight line, keeping the same straddle-line, until you're standing straight up at a stop, with the step-foot in the air, and the left and right feet at a distance of straddle-line apart, not pelvis line.

If you had any pelvic stretch in that step (which everyone probably has), since this would decrease the straddle-line but have no effect on the pelvis-line, you couldn’t stand at the standard start position in real life. But, it's still a valid standard reference because of the vector nature of all the measured distances.

Also, the foot never has to pass over the standard position, and the person never has to take up the orientation of the standard grid except at heel-contact.

This provides a separate, consistent measurement standard, the reference-heel-point, which is still defined by the heel-contact (or any other) snapshots. In the Step Model, the reference and start foot-models define the standard start position.. The reference-foot model represents the foot that's in the air (the step-foot), and the reference-heel-point is the stop/start point for carry/step lines, resp.

8. Heel vs Heel-point Contact

The time of the snap-shot which defines the parameters is the instant of heel-contact. But, heel-edge is not the point used for measurements. All measurements are to and from heel-points.

The heel-contact time point is chosen so movements due to aberrations can be isolated. Usually, the heel-point is still in the air at heel-contact, but that doesn't matter to the measurements. Aberrations are highly variable, and the ability to separate the distance and direction changes they cause greatly simplifies the analysis and allows far greater accuracy.

The position of the heel-point contact is important, though, since this would be the best start/stop point for field measurements. This position, which can be estimated from a footprint, is the most accurate field determination of heel-point position. It includes all or part of an aberration, but may still be very close to it's position at heel-edge contact. A more detailed footprint analysis could estimate deviations.

As long as it's consistent, and since changes are the most important, any discrepancy in position of heel-point at heel-edge vs heel-point contact may be insignificant, or at least tolerable. This would be a matter for study.

Also, since the heel-point is a point on the body, not the floor, there's the potential for time dependant analysis of all the parameters. The 4 points and line are always definable, whether in the air or not, but the interpretation would have to be modified for movement through the air and angular transition wrt the pelvis and leg-lines.

Heel contact is considered the end of the current step and start of the next step.

9. Direction Changes Over the Step

The 4 direction parameters are not expressed at the same time, or in the same way, over the step.

Aberrations and push-off angle are due to movements associated with the planted (opposite) foot, over single and part of double stance phases.

Foot offset and foot angle occur over swing phase of the step foot, and are established at heel-contact.

So, aberrations is the 1st, push-off angle the 2nd, and foot angle and offset occur at the same time and are the 3rd and 4th direction changes.

7 of the 8 fundamental parameters are defined by a single snapshot, but aberrations require the comparison of consecutive snapshots, wrt foot angle change and heel-point shift of the planted foot.

Foot offset, aberrations and push-off angle require linear translation to express normally, while foot angle can be expressed while stepping in place.

Within the same step, foot offset and foot angle can compensate for aberration and push-off angle deviations, but not vice versa. Push-off angle can compensate for aberrations.

Only certain (real or apparent) actions can change direction:
1) aberrations – spins, slides and all other movements of the planted foot, between sequential heel-contacts
2) push-off angle - appropriate muscle action in the planted foot's leg and foot, as well as momentum and other path specifics
3) foot angle - rotation of the foot-line around the 3D axis of the step-out-line
4) foot offset - step and/or rear pelvic joint rotation (lateral and/or vertical), and rotation at the step-knee and/or ankle joint which leads to heel-point shift.

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