The biomechanical response of persons with transfemoral amputation to variations in prosthetic knee alignment during level walking

Biomechanical characteristics of transfemoral bone-anchored prostheses during gait: A review of literature

BACKGROUND

Osseointegration (OI) is an emerging technique that allows a direct connection between the bone and a titanium metal implant, allowing the direct attachment of bone-anchored prostheses (BAP) to address the problems associated with socket prostheses. This review article aims to compare the biomechanical features of gait when using a transfemoral BAP in comparison to healthy gait, and in comparison to the gait of traditional transfemoral socket prosthesis users.

METHODS

A computer-based literature search of electronic databases since inception (ranging from 1967 to 2004 depending on the database) to June 14, 2022, identified peer-reviewed articles focusing on the temporal-spatial, kinematic, kinetic, and electromyography data related to transfemoral BAP gait. Eight articles were included that focused on these biomechanical features of gait in adults with BAP and were compared with socket prosthesis users or healthy gait.

RESULTS

Compared with healthy participants, prosthesis users after OI surgery have slower speed and cadence, lower symmetry, longer duration of swing phase, increased pelvic and trunk motion, more hip extension, larger moments on the intact limb, and lower forces on the prosthetic side. Compared with transfemoral socket prosthesis gait, BAP gait shows faster cadence and longer duration of support phase. There are limited and inconsistent data on changes in trunk, pelvic, and hip motion with OI.

CONCLUSION

Based on this review, transfemoral BAP improve spatial-temporal parameters closer to normal gait when compared to socket gait, but there are persisting deficits compared with healthy gait. Additional studies are needed to confirm the changes in kinematics and kinetics when walking with a BAP.

Transfemoral prosthetic simulators versus amputees: ground reaction forces and spatio-temporal parameters in gait

This study aimed to compare the ground reaction forces (GRFs) and spatio-temporal parameters as well as their asymmetry ratios in gait between individuals wearing a transfemoral prosthetic simulator (TFSim) and individuals with unilateral transfemoral amputation (TFAmp) across a range of walking speeds (2.0-5.5 km h-1). The study recruited 10 non-disabled individuals using TFSim and 10 individuals with unilateral TFAmp using a transfemoral prosthesis. Data were collected using an instrumented treadmill with built-in force plates, and subsequently, the GRFs and spatio-temporal parameters, as well as their asymmetry ratios, were analysed. When comparing the TFSim and TFAmp groups, no significant differences were found among the gait parameters and asymmetry ratios of all tested metrics except the vertical GRFs. The TFSim may not realistically reproduce the vertical GRFs during the weight acceptance and push-off phases. The structural and functional variations in prosthetic limbs and components between the TFSim and TFAmp groups may be primary contributors to the difference in the vertical GRFs. These results suggest that TFSim might be able to emulate the gait of individuals with TFAmp regarding the majority of spatio-temporal and GRF parameters. However, the vertical GRFs of TFSim should be interpreted with caution.

Quantification of push-off and collision work during step-to-step transition in amputees walking at self-selected speed: Effect of amputation level

Maintaining forward walking during human locomotion requires mechanical joint work, mainly provided by the ankle-foot in non-amputees. In lower-limb amputees, their metabolic overconsumption is generally attributed to reduced propulsion. However, it remains unclear how altered walking patterns resulting from amputation affect energy exchange. The purpose of this retrospective study was to investigate the impact of self-selected walking speed (SSWS) on mechanical works generated by the ankle-foot and by the entire lower limbs depending on the level of amputation. 155 participants, including 47 non-amputees (NAs), 40 unilateral transtibial amputees (TTs) and 68 unilateral transfemoral amputees (TFs), walked at their SSWS. Positive push-off work done by the trailing limb (WStS+) and its associated ankle-foot (Wankle-foot+), as well as negative collision work done by the leading limb (WStS-) were analysed during the transition from prosthetic limb to contralateral limb. An ANCOVA was performed to assess the effect of amputation level on mechanical works, while controlling for SSWS effect. After adjusting for SSWS, NAs produce more push-off work with both their biological ankle-foot and trailing limb than amputees do on prosthetic side. Using the same type of prosthetic feet, TTs and TFs can generate the same amount of prosthetic Wankle-foot+, while prosthetic WStS+ is significantly higher for TTs and remains constant with SSWS for TFs. Surprisingly and contrary to theoretical expectations, the lack of propulsion at TFs' prosthetic limb did not affect their contralateral WStS-, for which a difference is significant only between NAs and TTs. Further studies should investigate the relationship between the TFs' inability to increase prosthetic limb push-off work and metabolic expenditure.

A pelvic kinematic approach for calculating hip angles for active hip disarticulation prosthesis control

BACKGROUND

Control system design for a microprocessor-controlled hip-knee-ankle-foot (HKAF) prosthesis is a challenge since hip disarticulation amputees lack the entire leg and, therefore, only have pelvis movement as user-guided input. This research proposes a method for determining hip joint angles from pelvis movement in a control system for the next generation of powered prostheses.

METHOD

Three-dimensional pelvic motion and stance time of 10 transfemoral (TF) prosthetic users were used to identify important features and to develop an algorithm to calculate hip angles from pelvis movement based on correlation and linear regression results. The algorithm was then applied to a separate (independent) TF group to validate algorithm performance.

RESULTS

The proposed algorithm calculated viable hip angles during walking by utilizing pelvic rotation, pelvic tilt, and stance time. Small angular differences were found between the algorithm results and motion capture data. The greatest difference was for hip maximum extension angle (2.5 ± 2.0°).

CONCLUSIONS

Since differences between algorithm output and motion data were within participant standard deviations, the developed algorithm could be used to determine the desired hip angle from pelvis movements. This study will aid the future development of gait control systems for new active HKAF prostheses.

Unilateral transfemoral osseointegrated prostheses improve joint loading during walking

People with unilateral transfemoral amputation using socket prostheses are at increased risk for developing osteoarthritis in both the residual hip and intact lower-limb joints. Osseointegrated prostheses are a surgical alternative to socket prostheses that directly attach to the residual femur via a bone-anchored implant, however their multi-joint loading effect is largely unknown. Our objective was to establish how osseointegrated prostheses influence joint loading during walking. Motion capture data (kinematics, ground reaction forces) were collected from 12 participants at baseline, with socket prostheses, and 12-months after prosthesis osseointegration during overground walking at self-selected speeds. Subject-specific musculoskeletal models were developed at each timepoint relative to osseointegration. Internal joint moments were calculated using inverse dynamics, muscle and joint reaction forces (JRFs) were estimated with static optimization. Changes in internal joint moments, JRFs, and joint loading-symmetry were compared using statistical parametric mapping (p≤ 0.05) before and after osseointegration. Amputated limb hip flexion moments and anterior JRFs decreased during terminal stance (p = 0.002, <0.001; respectively), while amputated limb hip abduction moments increased during mid-stance (p < 0.001), amputated hip rotation moment changed from internal to external throughout early stance (p < 0.001). Intact limb hip extension and knee flexion moments (p = 0.028, 0.032; respectively), superior and resultant knee JRFs (p = 0.046, 0.049; respectively) decreased during the loading response following prosthesis osseointegration. These results may indicate that the direct loading transmission of these novel prostheses create a more typical mechanical environment in bilateral joints, which is comparable with loading observed in able-bodied individuals and could decrease the risk of development or progression of osteoarthritis.

Comparison of clinical and biomechanical characteristics between individuals with lower limb amputation with and without lower back pain: A systematic review and meta-analysis

BACKGROUND

Lower back pain is a debilitating condition common to individuals with lower limb amputation. It is unclear what risk factors contribute to the development of back pain. This study systematically reviewed and analyzed the available evidence regarding the clinical and biomechanical differences between individuals with amputation, with and without lower back pain.

METHODS

A literature search was conducted in PubMed, Web of Science, Scopus, and CINAHL databases in November 2020 and repeated in June 2021 and June 2022. Studies were included if they reported comparisons of demographic, anthropometric, biomechanical, and other clinical variables between participants with and without LBP. Study quality and potential for reporting bias were assessed. Meta-analyses were conducted to compare the two groups.

FINDINGS

Thirteen studies were included, with aggregated data from 436 participants (239 with LBP; 197 pain free). The median reporting quality score was 37.5%. The included studies enrolled participants who were predominantly male (mean = 91.4%, range = 77.8-100%) and with trauma-related amputation. Meta-analyses showed that individuals with LBP exhibited moderate (3.4 out of 10) but significantly greater pain than those without LBP. We found no between-group differences in age, height, weight, BMI, and time since amputation (p = 0.121-0.682). No significant differences in trunk/pelvic kinematics during gait were detected (p = 0.07-0.446) between the groups.

INTERPRETATION

Demographic, anthropometric, biomechanical, and simple clinical outcome variables may be insufficient for differentiating the risk of developing back pain after amputation. Investigators should be aware of the existing gender bias in sampling and methodological limitations, as well as to consider incorporating psychosocial measures when studying LBP in this clinical population.

Swing phase considerations in prosthetic knee design: Case series to validate simulations

BACKGROUND

Previously reported simulations comparing a new polycentric knee (called IPK) and a single-axis knee suggested that polycentricity could lead to improved performance during swing phase and negate the need for an extension assist. They also showed that an anteriorly translated socket adapter for enhanced stance stability compromises foot clearance during swing.

OBJECTIVES

The objectives of this study are to validate those findings using gait trials to enable further improvement in the IPK design before mass production.

METHODS

Three subjects regularly using three different passive knees, single-axis knee without extension assist, single-axis knee with extension assist (SAK-EA), and polycentric knee with extension assist (Mobility India-sourced polycentric knee), participated in this study. Their gait with their regular prosthesis and with IPK (having no extension assist) were analyzed, compared, and broadly correlated with simulation results.

RESULTS

Extension assist in single-axis knee with extension assist improved swing performance, affected foot clearance in Mobility India-sourced polycentric knee, and was found to be unnecessary in the IPK. With an anteriorly placed socket adapter in the IPK, compensatory strategies were necessary for foot clearance. The IPK was found to provide better knee extension characteristics with lower hip effort (up to 42% reduction) than other knees.

CONCLUSIONS

This case series confirmed previously reported simulation results on the swing phase behavior of passive prosthetic knees. The performance of the IPK during swing obviated the need for an extension assist, thereby simplifying the design. Appropriate design changes in the IPK's socket adapter location are required to achieve both stance stability and reduce gait compensations for foot clearance.

Investigating the Effect of Real-Time Center of Pressure (CoP) Feedback Training on the Swing Phase of Lower Limb Kinematics in Transfemoral Prostheses with SACH foot

Transfemoral amputee often encounters reduced toe clearance resulting in trip-related falls. Swing phase joint angles have been shown to influence the toe clearance therefore, training intervention that targets shaping the swing phase joint angles can potentially enhance toe clearance. The focus of this study was to investigate the effect of the shift in the location of the center of pressure (CoP) during heel strike on modulation of the swing phase joint angles in able-bodied participants (n=6) and transfemoral amputees (n=3). We first developed a real-time CoP-based visual feedback system such that participants could shift the CoP during treadmill walking. Next, the kinematic data were collected during two different walking sessions- baseline (without feedback) and feedback (shifting the CoP anteriorly/posteriorly at heel strike to match the target CoP location). Primary swing phase joint angle adaptations were observed with feedback such that during the mid-swing phase, posterior CoP shift feedback significantly increases (p<0.05) the average hip and knee flexion angle by 11.55 degrees and 11.86 degrees respectively in amputees, whereas a significant increase (p<0.05) in ankle dorsiflexion, hip and knee flexion angle by 3.60 degrees, 3.22 degrees, and 1.27 degrees respectively compared to baseline was observed in able-bodied participants. Moreover, an opposite kinematic adaptation was seen during anterior CoP shift feedback. Overall, results confirm a direct correlation between the CoP shift and the modulation in the swing phase lower limb joint angles.

The impact of transfemoral socket adduction on pelvic and trunk stabilization during level walking - A biomechanical study

BACKGROUND

It is common practice to align transfemoral prosthetic sockets in adduction, due to the physiologic, adducted femoral alignment in unimpaired legs. An adducted femoral and socket alignment helps tightening hip abductors to stabilize the pelvis and reduce pelvic and trunk related compensatory movements.

RESEARCH QUESTION

How do different socket adduction conditions (SAC) of transfemoral sockets affect pelvic and trunk stabilization during level ground walking in the frontal plane?

METHODS

Seven persons with transfemoral amputation with medium residual limb length participated in this study. The prosthetic alignment in the sagittal plane was performed according to established recommendations. SAC varied (0°, 3°, 6°, 9°). Kinematic and kinetic parameters were recorded in a gait laboratory with a 12-camera optoelectronic system and two piezoelectric force plates embedded in a 12-m walkway. The measurements were performed during level ground walking with self-selected comfortable gait speed.

RESULTS

In the frontal plane, nearly all investigated kinematic and kinetic parameters showed a strong correlation with the SAC. The pelvis was raised on the contralateral side throughout the gait cycle with increasing SAC. During the prosthetic side stance phase, the mean shoulder obliquity and mean lateral trunk lean to the prosthetic side tended to be reduced with increased SAC. Prosthetic side hip abduction moment decreased with increasing SAC.

SIGNIFICANCE

The results confirm that transfemoral SAC contributes to pelvic stabilization and reduced compensatory movements of the pelvis and trunk. Transfemoral SAC of 6 ± 1° for bench alignment seems adequate for amputees with medium residual limb length. However, the optimum value for the individual patient may differ slightly.

Innovative alignment of sprinting prostheses for persons with transfemoral amputation: Exploratory study on a gold medal Paralympic athlete

BACKGROUND

Recommendations for the alignment of the socket and foot in the sprinting prosthesis of athletes with transfemoral amputation are either based on walking biomechanics or lack public scientific evidence.

OBJECTIVES

To explore the biomechanical changes and the sensations of a gold medal Paralympic sprinter, while running with three bench alignments: a conventional reference (A0), an innovative alignment based on the biomechanics of elite able-bodied sprinters (A2), and an intermediate alignment (A1).

STUDY DESIGN

Single subject with repeated measures.

METHODS

A1 and A2 feature a progressively greater socket tilt and a plantar-flexed foot compared to A0. The 30-year-old female athlete trained with three prostheses, one per alignment, for at least 2 months. We administered a questionnaire to collect her impressions. Then, she ran on a treadmill at full speed (5.5 m/s). We measured the kinematics and moments of the prosthetic side, and the ground reaction forces of both sides.

RESULTS

A2 reduced the prosthetic side hip extension at foot-off while preserving hip range of motion, decreased the impulse of the hip moment, and increased the horizontal propulsion, leaving sufficient margin to prevent knee buckling without increasing sound side braking forces. Biomechanical outcomes matched well with subjective impressions.

CONCLUSIONS

A2 appears promising to improve the performance and comfort of sprinters with transfemoral amputation, without compromising safety.

CLINICAL RELEVANCE

Observation of elite able-bodied sprinters led to the definition of a new specific alignment for the sprinting prosthesis of athletes with transfemoral amputation, which appears promising to improve performance and comfort, without compromising safety. This may constitute a major improvement compared to alignments based on walking biomechanics.

Using a Simple Walking Model to Optimize Transfemoral Prostheses for Prosthetic Limb Stability-A Preliminary Study

The interaction between the prescribed prosthetic knee and foot is critical to the safety of transfemoral prosthesis users primarily during the stance phase of the gait, when knee buckling can result in a fall. Nonetheless, there is still a need for standardized approaches to quantify the effects of prosthetic component interactions and associated mechanical function on user gait biomechanics. A numerical model was defined to simulate sagittal plane prosthetic limb stance based on a single inverted pendulum and predict effects of prosthetic knee alignment and foot stiffness on knee moment to identify optimal solutions. Model validation against laboratory gait data suggests it is appropriate to preliminary simulate prosthetic gait during single-limb support, when prosthetic knee stability may be most at risk given reliance on the prosthetic limb and proximal anatomy, but only for knees with flexion smaller than 4°. Model predictions identify a solution space containing those combinations of knee alignment and foot stiffness (via roll-over shape radius) guaranteeing knee stability in early and mid- single-limb support, whilst facilitating knee break at the end of it. Specifically, a posterior to in-line knee alignment should be combined with low to medium ankle-foot stiffness, whereas anterior knee alignments and rigid feet should likely be avoided. Clinicians can use these solution spaces to optimize transfemoral prostheses including knees with little to no change in stance flexion, ensuring the safety of users. Model prediction can further inform in-vivo investigations on commercial device interactions, providing evidence for future Clinical Practice Guidelines on transfemoral prostheses design.

An Extensive Set of Kinematic and Kinetic Data for Individuals with Intact Limbs and Transfemoral Prosthesis Users

This paper introduces an extensive human motion data set for typical activities of daily living. These data are crucial for the design and control of prosthetic devices for transfemoral prosthesis users. This data set was collected from seven individuals, including five individuals with intact limbs and two transfemoral prosthesis users. These data include the following types of movements: (1) walking at three different speeds; (2) walking up and down a 5-degree ramp; (3) stepping up and down; (4) sitting down and standing up. We provide full-body marker trajectories and ground reaction forces (GRFs) as well as joint angles, joint velocities, joint torques, and joint powers. This data set is publicly available at the website referenced in this paper. Data from flexion and extension of the hip, knee, and ankle are presented in this paper. However, the data accompanying this paper (available on the internet) include 46 distinct measurements and can be useful for validating or generating mathematical models to simulate the gait of both transfemoral prosthesis users and individuals with intact legs.

Can high-functioning amputees with state-of-the-art prosthetics walk normally? A kinematic and dynamic study of 40 individuals

BACKGROUND

Previous work has highlighted the highly functional post-rehabilitation level of military individuals who sustained traumatic amputation. Understanding how these individuals walk with their prosthesis could be key to setting a precedent for what is realistically possible in the rehabilitation of individuals with amputations.

OBJECTIVE

The aim of this paper is to answer how "normal" should the gait of an individual with an amputation(s) be and can we aspire to mimic able-bodied gait with the most advanced prosthetics in highly functioning individuals?

METHODS

This was a cross-sectional study comparing the gait of severely injured and highly functional UK trans-tibial (n=10), trans-femoral (n=10) and bilateral trans-femoral (n=10) military amputees after completion of their rehabilitation programme to that of able-bodied controls (n=10). Joint kinematics and kinetics of the pelvis, hip, knee and ankle were measured with 3-D gait analysis during 5min of walking on level ground at a self-selected speed. Peak angle, moment or range of motion of intact and prosthetic limbs were compared to control values.

RESULTS

Joint kinematics of unilateral trans-tibial amputees was similar to that of controls. Individuals with a trans-femoral amputation walked with a more anterior tilted pelvis (P=0.006), with reduced range of pelvic obliquity (P=0.0023) and ankle plantarflexion (P<0.001) than controls. Across all amputee groups, hip joint moments and power were greater and knee and ankle joint moments were less than for controls.

CONCLUSIONS

This is the first study to provide a comprehensive description of gait patterns of unilateral trans-tibial, trans-femoral and bilateral trans-femoral amputees as compared with healthy able-bodied individuals. The groups differed in joint kinematics and kinetics, but these can be expected in part because of limitations in prosthesis and socket designs. The results from this study could be considered benchmark data for healthcare professionals to compare gait patterns of other individuals with amputation who experienced similar injuries and rehabilitation services.

The effect of prosthetic alignment on hip and knee joint kinetics in individuals with transfemoral amputation

BACKGROUND

Prosthetic alignment directly affects the biomechanical loading in individuals with lower-limb amputation, and improper alignment may be contribute to the high incidence of hip and knee osteoarthritis (OA). The biomechanical changes caused by different alignments should be considered in prosthetic fitting. However, the quantitative effect of alignment on the kinetic features of individuals with transfemoral amputation remains unclear.

RESEARCH QUESTION

As important kinetics indexes, how are the hip and knee joint moments affected by prosthetic alignment in individuals with transfemoral amputation?

METHODS

Gait tests of ten individuals with transfemoral amputation and fifteen individuals without amputation (control group) were performed. Several prosthetic alignment conditions were used, including the so-called "initial" alignment and eight malalignments. The hip and knee joint moments of the individuals with amputation under various alignments were analysed and compared with those of the control group. Statistical analyses were performed by one-way ANOVA, repeated measure multivariate ANOVA, and paired t tests.

RESULTS

The peaks and impulses of the hip abductor and external rotator moments on the residual side were significantly smaller than those of the control group (P < 0.0056). The peaks of the hip extensor, adductor and external rotator moments on the intact side were significantly larger than those on the residual side (P < 0.05). Alignment significantly affected the intact hip and knee joint moments for each individual with amputation (P < 0.00625), but there was no consistent effect among individuals.

SIGNIFICANCE

The significantly larger hip joint moment on the intact side of individuals with transfemoral amputation may be associated with the higher incidence of hip OA on the intact side. Alignment significantly affects the hip and knee joint moments of each individual with transfemoral amputation, but the individual responses to alignment changes are different. This situation may imply that the method for optimizing alignment should be personalized.

A characterisation of established unilateral transfemoral amputee gait using 3D kinematics, kinetics and oxygen consumption measures

BACKGROUND

Persons with unilateral transfemoral (UTF) amputation are known to walk with less efficiency than able-bodied individuals, therefore understanding the gait deviations that drive this inefficiency was considered to be important.

RESEARCH QUESTIONS

What are the differences in gait outcomes between persons with UTF amputation and able-bodied persons? What is the prevalence of specific gait deviations within this group?

METHODS

Using a cross-sectional study design, the level over ground gait of established prosthetics service users with UTF amputation using mechanical knee joints (n=60) were compared with able-bodied persons (n=10). Gait profile score, walking velocity, step length, step length symmetry ratio, step time symmetry ratio, vertical ground reaction force symmetry index, base of support, centre of mass deviation and metabolic energy expenditure were measured. All data were captured during walking on level ground at a self-selected speed. Prevalence of gait deviations for each UTF participant were assessed by inspection, using a predefined list of lower limb kinematic, upper body kinematic, ground reaction force and lower limb kinetic gait deviations.

RESULTS

Statistically significant between-groups differences across all outcome measures were found, with all p-values <0.005, and effect sizes ranging from 'large' to 'huge'. The most prevalent gait deviations included: lack of prosthetic knee flexion in early stance (98%); lack of hip extension on the prosthetic side in late stance (82%): increased trunk side flexion range of motion across the gait cycle (92%); reduced anterior propulsion force on the prosthetic side in late stance (100%) and reduced prosthetic hip adduction moment in early stance (96%).

SIGNIFICANCE

The results of this study indicate that the magnitude of the differences between UTF amputees and able-bodied persons, across a comprehensive range of gait measures, are such that significant research into all aspects of prosthetic rehabilitation to reduce these differences is clearly justified.

Comparative biomechanical evaluation of two technologically different microprocessor-controlled prosthetic knee joints in safety-relevant daily-life situations

Safety-relevant gait situations (walking on stairs and slopes, walking backwards, walking with small steps, simulated perturbations of swing phase extension) were investigated in a motion analysis laboratory with six unilateral transfemoral amputees using two different microprocessor-controlled prosthetic knee joints (Rheo Knee XC, C-Leg). A randomized crossover design was chosen. The study results imply that the performance and safety potential of a microprocessor-controlled knee joint can be associated with the individual control algorithms and the technological concepts that are implemented to generate motion resistances for controlling flexion and extension movements. When walking with small steps, advantages of the "default swing" concept used in the Rheo Knee XC were identified due to a highly reproducible swing phase release. However, when walking backwards, this concept may lead to an uncontrolled knee flexion which partly resulted in falls. When walking down stairs, walking on slopes or while recovering from a stumble after perturbations of the swing phase extension, the C-Leg demonstrated a reliable prosthetic side load-bearing capacity resulting in reduced loading on the residual body. In contrast, the Rheo Knee XC required increased compensatory movements of the remaining locomotor system in order to compensate for reduced load-bearing and safety reserves.

Sockets for Limb Prostheses: A Review of Existing Technologies and Open Challenges

In the prosthetics field, one of the most important bottlenecks is still the human-machine interface, namely the socket. Indeed, a large number of amputees still rejects prostheses or points out a low satisfaction level, due to a sub-optimal interaction between the socket and the residual limb tissues. The aim of this paper is to describe the main parameters (displacements, stress, volume fluctuations and temperature) affecting the stump-socket interface and reducing the comfort/stability of limb prostheses. In this review, a classification of the different socket types proposed in the literature is reported, together with an analysis of advantages and disadvantages of the different solutions, from multiple viewpoints. The paper then describes the technological solutions available to face an altered distribution of stresses on the residual limb tissues, volume fluctuations affecting the stump overtime and temperature variations affecting the residual tissues within the socket. The open challenges in this research field are highlighted and the possible future routes are discussed, towards the ambitious objective of achieving an advanced socket able to self-adapt in real-time to the complex interplay of factors affecting the stump, during both static and dynamic tasks.