Inertial-Sensor-Based Monitoring of Sample Entropy and Peak Frequency Changes in Treadmill Walking during Recovery after Total Knee Arthroplasty

Abstract

This study aimed to investigate whether sample entropy (SEn) and peak frequency values observed in treadmill walking could provide physical therapists valuable insights into gait rehabilitation following total knee arthroplasty (TKA). It was recognized that identifying movement strategies that during rehabilitation are initially adaptive but later start to hamper full recovery is critical to meet the clinical goals and minimize the risk of contralateral TKA. Eleven TKA patients were asked to perform clinical walking tests and a treadmill walking task at four different points in time (pre-TKA, 3, 6, and 12 months post-TKA). Eleven healthy peers served as the reference group. The movements of the legs were digitized with inertial sensors and SEn and peak frequency of the recorded rotational velocity-time functions were analyzed in the sagittal plane. SEn displayed a systematic increase during recovery in TKA patients (p < 0.001). Furthermore, lower peak frequency (p = 0.01) and sample entropy (p = 0.028) were found during recovery for the TKA leg. Movement strategies that initially are adaptive, and later hamper recovery, tend to diminish after 12 months post-TKA. It is concluded that inertial-sensor-based SEn and peak frequency analyses of treadmill walking enrich the assessment of movement rehabilitation after TKA.

Keywords: entropy; gait; inertial measurement units; knee replacement surgery; power spectral density analysis.

Figure 1

The sensor placement in both the TKA and control groups during treadmill walking (left) and depiction of the definition of the amplitude of angular excursion (right; see [41]).

Figure 2

The angular position (degrees) time series of the thigh and shank of one trial performed by a control participant during treadmill walking at CWS. The eight black circles represent a representative subset of the peaks from the shank identified by the peak-to-peak detection algorithm. The black arrow between two successive peaks in the angular position–time function of the shank depicts the angular excursion of the IMU on the shank (due to its fixation around its Y-axis) in one cycle ranging between +40 to −40 deg, in a total of 80 degrees. Peak-to-peak detection was visually checked and was subjected to the constraint that positive peak values were always followed by negative peak values, thus eliminating the highly frequent three-peak sequences that can be discerned in the thigh angular position–time function around +10 degrees.

Figure 3

Mean and standard error of the CWS (left upper panel), 6 MWT (right upper panel), and TUG (central lower panel) of the TKA group (n = 9) and the control group (n = 11). The * indicates a significant difference between the TKA and control group at T3. T0, T1, T2, and T3 represent pre-TKA, 3, 6, and 12 months post-TKA, respectively.

Figure 4

Mean and standard error of the cadence (left upper panel), peak frequency (right upper panel), amplitude of angular excursion (left lower panel), and SEn (right lower panel) of the TKA group (n = 9) and control group (n = 11). The * indicates a significant difference between the TKA and control group at T3. T0, T1, T2, and T3 represent pre-TKA, 3, 6, and 12 months post-TKA, respectively. Note that the ** indicates a significant difference between the TKA and control group for both the non-affected / right shank and the affected / left shank at T3.