Kinematic modelling of the foot-ankle complex for gait analysis

The functional role of the foot-ankle complex is critical in terms of providing support and mobility to the whole human body. Besides those associated with common lesions or damages of its structures (e.g. sprains, bone fractures), impairments in the foot may also cause secondary chronic pathologies. Thus, a quantitative assessment of the mechanical behaviour of the joints within the foot-ankle complex is certainly of clinical value. Gait analysis is used to assess lower limb joint kinematics during walking, and is usually performed using stereophotogrammetric systems. Conventionally, the foot is considered as a rigid segment. This oversimplification has been overcome with the use of multi-segment models to describe foot kinematics. However, these models have been only partially validated, limiting their widespread adoption. This Thesis aims at filling the gap of a repeatability and reproducibility analysis of the outcomes of the available foot modelling techniques, providing guidelines and reference values to be used in future applications, and establishing a standard for the kinematic assessment of the foot-ankle complex in gait analysis. As a first step, different indices to quantify repeatability and reproducibility of model outcomes have been critically compared and investigated, including Linear Fit Method coefficients (LFM), Coefficient of Multiple Correlation (CMC), Mean Absolute Variability (MAV), and Root Mean Square Error (RMSE). A sensitivity analysis was performed to this purpose using artificially created curves, which were varied by imposing a set of realistic alterations in their shapes, joints’ range of motion, sample by sample amplitude variability, offset, and time shift. The CMC values were found to be sensible to different curve shapes, and, as well as the LFM coefficients, were independent from the range of motion. Complex values of the CMCs were observed when large offset and time shift occurred. The LFM coefficients worsened with the time shift, invalidating the assumption of linear relationship among curves. Nonetheless, these coefficients, when used with measurement of absolute differences (e.g., MAV or RMSE), were found to be the most suitable to be used for gait curve comparisons. The instrumental error associated with different procedures that can be adopted to calibrate a stereophotogrammetric system has then been assessed for two different systems. The results of this part of the Thesis showed that the errors are independent on the adopted calibration. In fact, the between-calibration CMC of joint kinematics were never lower than 0.93. The average differences between measured and known values of distances between pair of markers were lower than 1.7 mm. Instead, the average differences between measured and known values of angles between markers 0.7°. These findings suggest that relevant procedures do not affect the metrological performance of the systems under test and the associated errors can be neglected. As a following step, the experimental error associated to the marker placement was quantified for the four most adopted multi-segment models of the foot. The repeatability and reproducibility of the relative measurements were assessed by comparing joint sagittal kinematics obtained when: a) the same operator placed the markers on thirteen young healthy adults in two different sessions; b) three operators placed the markers for three times on three randomly selected participants, respectively. The two most repeatable and reproducible models, according to the validated similarity and correlation indices (i.e., the LFM coefficient), displayed averaged correlation higher than 0.72, with the lowest values obtained for the between-subject comparison of the midfoot kinematics (0.69 and 0.55). Results showed that foot kinematics have low overall repeatability when evaluated with the existing models, and normative bands should be adopted with caution when used for comparison with patient data, especially when dealing with joints that interacts with the mid-foot and display range of motions smaller than 10°. Finally, to overcome the limitations highlighted by the assessment of the existing models, a novel kinematic model of the foot-ankle complex has been designed, and the repeatability and reproducibility of the relevant sagittal kinematics have also been quantified. Results showed an improvement, especially for the joint enclosed between the mid-foot and the hindfoot, with correlation higher than 0.82. In conclusion, the new model paves the way to a more reliable modelling of the foot and, represents an improvement with respect to the existing techniques

Effect of the calibration procedure of an optoelectronic system on the joint kinematics

Optoelectronic systems are largely employed for human movement analysis, where marker trajectories are used to estimate the articular joint kinematics. From a literature analysis it emerged that the error associated to the joint kinematics can be reduced performing the data collection in the center of the system calibration volume. According to human movement analysis literature, the foot-ankle complex appears to be the anatomical joint most affected by instrument inaccuracy, as it moves in the lower bound of the calibration volume during the gait cycle. A multi-segment marker-based model of the lower limb-including the pelvis, thigh, tibia, hindfoot, forefoot and hallux-was investigated in this paper. One healthy subject was asked to walk on the central and on two boundary areas of the capture volume calibrated for the experiments. The calibration procedure was focused on the exploitation of the effects on the joint angles of: (i) calibration volumes (i.e. the global one and two of its sub-volumes) and (ii) number of frames acquired for the calibration procedure (refinement frames). In order to quantify the precision of estimating the joint kinematics when changing the calibration procedure, the RMSE among different refinement frames using both the global volume and the two sub-volumes was computed as an index of the joint angles variation estimated on the sagittal plane. Two two-way ANOVAs were performed to evaluate whether the calibration volumes or the walking areas affect the kinematics. The statistical analysis highlighted a good robustness of the reconstruction algorithm implemented by the optoelectronic system manufacturer. Few variables showed significant differences for the RMSEs, with p-values lower than 0.05. No clear dependence on the body segments here analyzed emerged from the analysis. The coefficient of Multiple Correlations was computed in order to enlighten the similarities among the joint angles time patterns. We conclude that reconstructed trajectories can be affected by the same magnitude errors, regardless to the calibrated volume or the considered walking area. This finding allows conducting the gait analysis without paying attention when calibrating the system and without having to impose excessive restrictions to the tested subjects, allowing to keep their movement as natural as possible