Spatiotemporal Parameters (STP) are a reliable gait measurement as proven by scientific literature. All STP are derived from measuring the spatiality and temporality of foot-based placements.

The first step in measuring gait analysis is to isolate the gait cycle. Computerized systems such as ProtoKinetics’ Zeno Walkway collect key event data, based on direct acquisition of the spatial coordinates of the feet on the ground and the contact times. Zeno Walkway then separates this data into different phases and quantifying measurements to characterize movement.

(this is part 2 of 2. Read part 1, Measuring Time & Stance Phase)

### Measuring Spatial Parameters

Spatial parameters reflect the antero-posterior and medio-lateral movements of the feet during walking.

• Stride length (m or cm): distance traveled during a gait cycle, measured as the length between the most rearward point of two successive footprints of the same foot (often the heel).

To calculate stride length, it is necessary to know the coordinates of the furthest point of the footprints and calculate the distance between these two points.

For example, point #1 (764.253; 28.798) and #2 (637.172; 24.508):

Stride length = √ ((764.253-637.172) ^ 2 + (28.798-24.508) ^ 2) = 127.15 cm

• Step length (m or cm): distance between the most rearward point of two successive footprints (often the heel), measured parallel to the direction of progression of the ipsilateral stride. Same logic as the stride length for calculation.
• Stride width or base of support (cm): the distance between the feet during walking. Different modes of calculation can be found, but it is usually defined as the perpendicular distance between the line connecting two heels of the same foot (cycle) and the heel of the contralateral foot. This calculation is recommended because it is more robust and valid, even in the case of deviation of the axis of progression during walking (Huxham et al., 2006).
• Internal/External Angle (°): An angle between the direction of progression and the angle of the foot that results in a positive angle when the foot is turned outward and in a negative angle when the foot is turned inward.

Angle int/ext = angle of the footprint – direction of progression

Example: 7,754 – (-10,165) = 14,144°

The stride length is the relative distance to the gait cycle but, in practice, the step length is more informative because it makes it possible to evaluate the symmetry between the two members.

The step length is directly related to the length of the lower limb and is partly dependent on the contralateral support.  If support is weak, the foot will be rested on the ground more quickly and less far. Step length is often reduced in pathologies impacting walking, while the cadence is increased to maintain speed.

When step length is calculated according to the anteroposterior axis of progression, it is possible to observe a zero or negative step length when the hind foot is not brought back beyond the front foot. It is also possible to look at the overall displacement length of the foot in space, called the absolute step length, which is the direct distance between the two successive supports (measurement takes into account the anteroposterior distance and the lateral distance).

The stride width or base of support is usually between 8 and 12 cm in the child and the adult, but wider in the toddler (once normalized by the width of the pelvis) and in the elderly. When there is a dynamic balance problem, the subject enlarges the support polygon to better control walking and reduce the risk of falls. This is the main front-end compensation mechanism to increase the margin of safety between the center of mass and the limits of the base of support. This may be effective or not, but always signifies the presence of a balance disorder. A negative support base can also be found in the presence of step crosses, as in the “pseudo-drunkenness” or ataxic gait.

In an asymptomatic subject, the stride width decreases when they are asked to walk faster than at spontaneous speed, which is explained by the geometric ratio between step length and cycle width.

The angle of progression of the step (about 0 to 15° in the adult control) accounts for the position of the foot (in abduction, adduction or neutral) during support. This is a very individual characteristic, mainly related to the motor habits and bone architecture of the lower limb. A difference of less than or equal to 5° between the two feet may be considered normal.

Excessive internal and external rotations are frequently observed in subjects with cerebral palsy. These excessive rotations are the result of architectural defects that appear progressively during growth (rotation anomalies of the femoral and tibial segment, fixed or irreducible deviations of the foot in varus adductus or valgus abductus).

The validity and the reproducibility of these parameters are dependent on completely laying the foot flat on the ground. This is an important point, as the spatial and temporal accuracy of the measurements are derived from it.

For example, in the case of equine varus gait, with exclusive forefoot placement, the angle given by a system based on pressure sensors will be incorrect, often with an overestimation of the internal rotation. By indicating the measurements of the foot (length and width), some software programs can indicate the effective foot surface in contact with the ground, which then gives an idea of the validity of the measurement of foot rotation.

In addition, if the patient does not always have the same ground support (once on the forefoot and then on the hindfoot), the measurements of the step lengths and strides are affected. What software sees as the heel for equine support is the forefoot. To solve this problem, some software (for example, PKMAS from ProtoKinetics) leaves the choice of the reference to the user (hindfoot, center of the footprint or forefoot).

### Measuring Speed

Speed and Walk Ratio are not strictly temporal or spatial parameters but relate to both aspects at the same time.

• Speed (m/s or cm/s): distance traveled over time. It is usually measured by dividing the sum of all cycle lengths by the sum of all cycle times.

It is also possible to calculate a speed for each cycle by dividing the length of a specific cycle by its duration. If you average these speeds per cycle, the result will be slightly different from the overall speed. Indeed, the calculation of the average speed amounts to applying a statistical weight equivalent to all the cycles, whereas the calculation of the speed of the cycle is affected by the duration of each cycle.

Average speed = (Cycle length (1) + Cycle length (2) + … + Cycle length (n)) / (Cycle time (1) + Cycle time (2) + … + Cycle time (n))

Speed represents the overall performance of walking. Each subject has a preferential spontaneous speed (a comfort zone of speed), determined at plus or minus 1 km/h around the average value, in which there is no significant difference in energy cost. A speed range of between 4.3 km/h and 5.8 km/h can be agreed, i.e. between 1.2 m/s and 1.6 m/s in adults.

But considering only the walking speed of a subject is not enough to correctly analyze their progress and the evolution of their walking speed over time.

Speed can simply be calculated as the distance traveled divided by the time needed, but it is also the product of the step length and cadence. In other words, it is possible to produce the same speed via multiple configurations ranging from very fast small steps to slow big steps. Moreover, while the cadence increases linearly, the step length, more constrained by the physical aspect, increases logarithmically, changing much at low speed, but tending to stabilize at higher speeds.

A normal walking speed can result from an adequate cadence and step length (asymptomatic walking), such as walking with small steps compensated by an increase in frequency. But if the compensation is insufficient, the speed will also be reduced.

In healthy adults, if the preferential walking speed is very close to the one that minimizes the energy expenditure per unit of distance, this is accurate only if the pace rate is also freely chosen. Zarrugh and Radcliffe (1978) have shown that this preferential step frequency is that which requires the least oxygen consumption irrespective of the speed. Any other constrained rate for the same walking speed increases the cost of oxygen compared to that required for an unconstrained rate.

### Measuring Walk Ratio

To overcome this informational lack of speed, a parameter called walk ratio can be used.

• Walk ratio (cm/step/min): step length divided by the cadence.

The walk ratio represents the relationship between the amplitude and the frequency of the movements of the legs and is calculated as the average step length divided by the cadence.

In adults, walk ratio is relatively stable in a range of speeds from very slow to very fast and is independent of speed (Sekiya et al., 1996). Walking with an invariant walk ratio would be optimal in terms of energy expenditure, temporal variability, spatial variability, and attentional demand. This is an important metric for the longitudinal follow-up of a patient, particularly during rehabilitation, as it demonstrates the rhythmic organization of walking.

The walk ratio obtained from the step length in centimeters and the cadence in steps/minute is on average 0.58 (0.06) in adults and decreases when the person walks with a lot of little steps. It should be noted that these reference values change depending on the parameters (step length, stride length); the units used (cm, m); and any normalization variables (leg length, size).

Looking only at walking speed gives a fragmentary view of the patient’s walk. A therapeutic evaluation or a protocol should not be based on this parameter alone.