We investigated TF amputee pelvic motions (pelvic tilt, pelvic obliquity, pelvic rotation) and their relationship with hip rotation. This data was used to develop an algorithm to calculate hip angles throughout the gait cycle, from pelvic motion while walking on a treadmill with no incline. Hip angles calculated by the algorithm were compared with measured (motion-captured) hip angles to quantify algorithm. This study focused on analyzing model performance during steady-state walking.

Databases

Two databases of transfemoral amputee gait were used in this study, for algorithm development and validation. Dataset selection requirements were: all participants must be TF amputees; participants must ambulate without relying on walking assistive devices such as canes, walkers, or treadmill assistive bars; gait data must be from steady-state sequences of level walking tests.

A database from a group of 10 people with unilateral transfemoral amputation with K3 and K4 activity levels [18] was used for algorithm development. Data were collected in the CAREN Extended virtual reality laboratory at The Ottawa Hospital Rehabilitation Centre and processed with C-motion Visual 3D (version 6) using six degrees of freedom model and MATLAB software version 2021a [19,20,21,22]. People walked on a treadmill (level walking) at self-selected walking speeds (1.05 ± 0.27m/s), and ten strides per person were extracted (a total of 100 strides). The development group's mean age was 47 (± 9.4) years, weight was 85 (± 8.6) kg, and height was 176 (± 9) cm. The gait events were processed using foot velocity relative to the pelvis method [23] and through manual verification. This database has been utilized in various biomechanics-related studies published in literature [21, 24, 25]. The Ottawa Health Science Network Research Ethics Board approved the secondary use of this dataset.

Testing group data were obtained from a recently published database ([26, 27]) that used 10 VICON 3D motion capture cameras and a dual belt instrumented Bertec treadmill. Ten people with unilateral transfemoral amputation with K2 and K3 activity levels met our inclusion criteria. Participants walked at different fixed speeds based on their activity level. People with K2 activity levels completed separate walking trials at 0.4, 0.5, 0.6, 0.7, and 0.8 m/s. Those with K3 activity levels walked at 0.6, 0.8, 1.0, 1.2, and 1.4 m/s. The marker data were then processed using modified Vicon plug-in-gait model to obtain the hip and knee kinematics [28, 29]. The pelvic kinematic data were processed using a CODA pelvic model in MATLAB™ R2021a [30]. The testing group's mean age was 47 (± 15) years, weight was 84.5 (± 17.6) kg, and height was 177 (± 11) cm.

Differences between the development and testing groups for activity level, walking speed, or prosthetic components are desirable when evaluating model performance on different groups of participants. This helps to determine model generalizability and avoid cases where better results are due to training and testing on the same group. Prosthesis details for both groups are presented in Tables 1 and 2.

Table 1 Testing group detailsTable 2 Development group detailsAlgorithm development

Pelvic movement in sagittal (anterior/posterior tilt), frontal (lateral tilt or obliquity), and transverse (pelvic rotation) planes were investigated, and gait phase transition timing was assessed to determine their correlation with hip angle throughout the gait cycle.

In this study, any posterior movement of the pelvis and hip joints were considered as positive angular displacement (posterior pelvic tilt, forward pelvic rotation, and hip flexion), while anterior movements were considered as negative angular displacement (anterior pelvic tilt, backward pelvic rotation, and hip extension).

The hip angle calculation algorithm development required:

A.

Hip angle features: Temporal and spatial hip angle features to calculate hip angular velocity.

B.

Correlations: Analyze pelvic motion and stance time data to determine common features and correlations with hip angle features.

C.

Hip angle feature calculation equations: Develop regression equations to calculate the hip angle features using the identified pelvic features in step B.

D.

Identification of per-person constants: Determine constant parameters unique to each person's gait characteristics that could be used for algorithm development.

E.

Sequential hip angle calculation: Develop an algorithm for real-time hip angle calculation using parameters obtained in steps C and D.

F.

Algorithm performance analysis: Evaluate the model with a new data set (testing group).

Each of these will be considered in turn.

A.

Hip angle features

A typical gait cycle for people with transfemoral amputation includes ([17, 31]): foot contacts the ground (foot strike) with the hip flexed to ~ 30°; hip moves to ~ 5° of extension at the end of stance; hip starts to flex ~ 35° until 80%-90% of stride; and hip flexion decreases ~ 5° in terminal swing to ensure that the prosthetic knee is fully extended before the next foot-strike [32,33,34,35].

Hip angle kinematics can be divided into three periods (Fig. 1), with each period having a linear progression of hip angle by time (i.e., constant slope or constant angular velocity).

Period 1 (hip extension): Initiates at foot-strike and ends at 50–60% of the gait cycle. The angular velocity vector is always negative.

Period 2 (hip flexion): Initiates at hip max extension and continues through the stance-to-swing transition with minor angular velocity change. The velocity vector is always positive.

Period 3 (knee control): Knee joint behavior directly affects hip rotation in this period, with hip rotation acting to keep the prosthetic knee fully extended. For this study, hip angle throughout period 3 was assumed to be constant (angular velocity is zero) until the next foot strike.

Fig. 1

Three hip angle periods during gait cycle: hip rotation toward negative angle (extension), hip rotation toward positive angle (flexion), constant angle. Measured curve is the average of 100 strides in the development group

Hip angular velocity was assumed to remain mostly constant throughout each period, simplifying the hip angle calculation. Five features were present for all participants; therefore, these features were used to calculate the constant angular velocity during each period. Spatial features were hip angle at foot strike (HθFS), maximum hip extension angle (HθE), and maximum hip flexion angle (HθF). Temporal features were maximum hip extension time (HτE) and maximum hip flexion time (HτF).

For period 1 (hip extension), the constant angular velocity was calculated using HθFS, HθE, and the difference in time between the two features. For period 2 (hip flexion), the constant angular velocity was calculated using HθE, HθF, and the difference in time between the two features. In period 3 (knee control), hip angle was assumed to be constant at HθF (i.e., zero angular velocity).

The algorithm uses these angular velocity values to calculate hip angle at each time point. Therefore, equations that define the relationships between pelvic kinematics and hip features are required.

B.

Correlations

Pelvic angular velocity, pelvic tilt, pelvic obliquity, pelvic rotation, and stance time per stride for each person in the development group were analyzed to determine common features that could be used to calculate the constant hip angular displacement and velocities. Twenty-two features were identified as potential candidates. Next, p-earson correlation analyses were applied to each feature candidate to determine which features were most related to the hip angle features. The strongest correlations were (Fig. 2):

Pelvic tilt angle at foot strike (PTθ) and hip angle at foot-strike (HθFS): r = 0.95

Timing of pelvic rotation angular velocity zero-crossing in early stance (PRZC) and the hip rotation angle range of motion during that period (ΔH): r = -0.75

Timing of pelvic tilt angular velocity first zero crossing in midstance (PTZC) and hip max extension time (HτE): r = 0.90

PTZC and hip max flexion time (HτF): r = 0.82

Stance time (τs) and hip max flexion time (HτF): r = 0.93.

Fig. 2

Pelvic feature and stance time correlation with hip angle features. A Pelvic tilt angle at foot strike (PTθ) and hip angle at foot-strike (HθFS), B timing of pelvic angular velocity zero-crossing in early stance (PRZC) and hip angle range of motion during that period (ΔH), C timing of pelvic tilt angular velocity first zero crossing in midstance (PTZC) and hip max extension time (HτE), D timing of pelvic tilt angular velocity first zero crossing in mid-swing (PTZC) and hip max flexion time (HτF), E stance time (τs) and hip max flexion time (HτF)

PTZC (Timing of pelvic rotation angular velocity zero-crossing in early stance) can be detected in real-time by continuously monitoring the 10 most recent pelvic tilt angular velocity data samples. If the most recent sample is positive while the prior 10 samples are negative, positive zero-crossing is detected (Fig. 3).

Fig. 3

Pelvic tilt angular displacement (A) and corresponding pelvic tilt angular velocity (B). The red square represents the most recent sample, while the blue stars represent the 10 data samples prior to the most recent sample

PRZC (timing of pelvic tilt angular velocity first zero crossing in mid-swing) is detectable by measuring the pelvic rotation angular velocity zero-crossing (Fig. 4). Initially, angular velocity should be in the positive region. The crossing instance is marked if the angular velocity vector crosses the zero value into the negative angular velocity region.

Fig. 4

Pelvic rotation angular displacement (A) and corresponding pelvic rotation angular velocity (B)

C.

Hip angle feature calculation equations

A series of linear regression equations were determined to calculate the hip angle features based on the linear relationships and correlations between pelvic motion features, gait events, and hip rotation features (Fig. 2). These regression equations are calculated sequentially (from Eqs. 1–5) as the pelvic features and gait events are detected (Fig. 6).

When foot strike is detected, regression Eq. 1 is used to calculate hip angle.

$$_=24.27+\left(1.45\times PT\theta \right)$$

(1)

where HθFS is hip angle at foot strike and PTθ is pelvic tilt angle at foot strike.

Once pelvic rotation zero crossing is detected (Fig. 4), regression Eq. 2 is used to determines ΔH.

$$\Delta H=-0.6261-\left(59.04\times _\right)$$

(2)

where PRZC is the difference between the time of pelvic rotation angular velocity first zero crossing and foot-strike time. ΔH is the difference between hip angle at foot-strike and hip angle at PRZC time.

Approaching the end of stance phase, pelvic tilt zero crossing is detected (Fig. 3) and used to calculate hip max extension time using regression Eq. 3 and hip max flexion time using Eq. 4.

$$_=0.3461 +\left(1.35\times _\right)$$

(4)

where PTZC is the time of pelvic tilt angular velocity zero crossing, HτE is the hip max extension time, and HτFα is the hip max flexion time at the PTZC instant.

During the foot-off instance, HτF is recalculated again in Eq. 5 to take advantage of the higher HτF and τS correlation value (R = 0.94) compared to HτF and PTZC (R = 0.84).

$$_=0.0874 +\left(1.18\times _\right)$$

(5)

where τS is the gait stance time, and HτFβ is max hip flexion time at foot-off.

D.

Per person, unique constants

For hip angle calculation using the developed algorithm, two unique input constants were defined for each person after analyzing the development dataset: mean hip max extension and mean hip max flexion angles. In practice, during the fitting process, a prosthetist would increase or decrease these constants for each patient until results are satisfactory [36]. That is, iterative changes are made to the values during the prosthetic fitting process until gait is acceptable to the end-user and clinician, similar to the process for tuning other microprocessor controlled prosthetic joints.

Hip max extension and max flexion angles tended to be in a unique but limited range for each TF amputee in the development group. Studies suggested that this unique hip ROM is due to prosthesis user control strategies to maintain balance during walking [37, 38]. The per-person-specific hip max extension and max flexion angle constants for both development and testing groups are provided in Table 3.

Table 3 Per-person unique constants of development and testing group datasets E.

Hip angle calculation

Figure 5 shows the general block diagram of the hip angle calculation algorithm for steady state gait. Initially, pelvic features are extracted from pelvic motion data. Then, using the hip angle feature calculation equations and foot-off time, the hip parameters necessary for constant hip angular velocity calculations are obtained. In the algorithm's last two stages, the calculated hip features are used to calculate hip angular velocity and hip angle.

Fig. 5

Gait cycle hip angle calculation block diagram

The six sequences shown in Fig. 6 represent five different hip angle equations used in the algorithm. Since the algorithm was developed to run in real-time, pelvic features are detected by the algorithm at different times during the gait cycle (since people walk at different speeds). Therefore, different hip calculation equations are used depending on the timing of each pelvic feature detection. The hip extension angle (period 1) is calculated during the first three sequences. During sequences 4 and 5, the hip angle during hip flexion (period 2) is calculated, and during sequence 6 the hip angle during period 3 is calculated. For detailed mathematics of hip calculations for each sequence see Additional file 1.

Fig. 6

Calculated hip angle throughout the gait cycle. PRZC: pelvic rotation zero-crossing time, PTZC: pelvic tilt zero-crossing time, HτE: hip max extension time, τs: stance time, HτF: hip max flexion time. Sequences are foot-strike to PRZC (sequence 1, solid red line), PRZC to PTZC (sequence 2, solid black line), PTZC to HτE (sequence 3, solid blue line), HτE to τFO (sequence 4, red dashed line), τFO to HτF (sequence 5, blue dashed line), and HτF to the end of the gait cycle (sequence 6, black dashed line)

F.

Algorithm evaluation

The developed algorithm was applied to both testing and development groups. Algorithm performance was assessed by calculating hip angle feature differences between calculated (algorithm) and motion capture system data (ground truth). To provide a reference for whether the differences were appropriate or beyond typical participant variability, the calculated differences were compared with participant averaged hip feature standard deviations in the testing and development set.