## Introduction

Musculoskeletal deteriorations are closely related to balance and gait problems, a major contributor to accidental falls in the older population1,2,3. A musculoskeletal disorder most prevalent in the elderly is knee osteoarthritis (OA), a degenerative disease in which the joint cartilage wears away progressively4,5. About 50% of the elderly population above 60 years old have knee OA4,6,7, resulting in restricted physical activities with pain and symptoms such as joint swelling and stiffness, muscle weakness, and limited range of motion8. These symptoms and the accompanied alterations in joint biomechanics have a direct impact on the gait patterns and balance control9,10,11,12. Therefore, knowledge of the balance control during gait in people with knee OA may provide useful information for the management of fall risks in this patient population.

Previous studies have reported decreased standing postural stability in older people with unilateral and bilateral knee OA12,13,14,15. However, clinical observations indicated that falls most frequently occur during activities involving larger displacement of the body’s center of mass (COM), such as walking16. Therefore, quantifying standing postural stability alone is not sufficient to describe dynamic balance, and monitoring of the motion of the COM is essential.

Quantifying the motion of the body’s COM relative to the center of pressure (COP) has been used to evaluate the body’s balance control during locomotion17,18. A common measure is the COM–COP separation defined by the horizontal distance between the COP and the vertical projection of the COM on the ground. In contrast to static balance during which the downward vertical projection of the COM has to be kept close to the COP, during walking the projected COM can be further away from the COP without loss of balance as long as the COM is controlled at an appropriate velocity relative to the COP19. It follows that the COM–COP separation alone cannot indicate the actual control of the COM relative to the COP, as it does not consider the velocity of the COM relative to the COP, nor the influence of the body height or leg length. To overcome the limitations of COM–COP separations, another approach that uses the COM–COP inclination angle (IA) formed by the COM–COP vector and the vertical, and the rate of change of IA (RCIA) has been proposed. The IA combines both the information of COM–COP separation and the height of the COM, and the RCIA integrates the information of the velocity of the COM relative to the COP. The IA and RCIA together provide a more complete description of the COM–COP control, and better enable comparisons between people of different statures17,20,21. Generally, interpretation of the IA and RCIA data of a patient group should be made with reference to those of healthy controls in order to identify any particular balance control strategies adopted. For example, an increased IA may suggest a poor balance control, but if one is able to generate an appropriate RCIA either by changing the velocity of the COM or that of the COP or both, the combined changes are considered a successful balance control strategy.

The study of balance control strategies during dynamic activities in terms of IA and RCIA has been reported in various populations18,20,22. However, previous studies on patients with knee OA have been limited, and have focused mainly on the COM and IA without considering the velocities of the COM relative to the COP23,24. Mandeville et al.23 studied the balance control in patients before and after unilateral total knee replacement, examining the maximum COM–COP inclination angles without considering data at gait events and during phases, nor the velocities of the COM relative to the COP. These studies have limited the correct interpretation of the COM–COP data of the knee OA patient group. To the best knowledge of the authors, no study has investigated the effects of knee OA on the balance control in terms of IA and RCIA of the COM motions relative to the COP during level walking.

The purpose of the current study was to identify the effects of bilateral medial knee OA on whole body balance control in older people during level walking, in terms of IA and RCIA. It was hypothesized that older people with severe medial OA would walk with altered, more conservative COM–COP control with increased IA but decreased RCIA when compared to healthy controls.

## Methods

All experiments of the current study were conducted under the approval of Taiwan Adventist Hospital Institutional Review Board (IRB No. 106-E-15). All the experiments and procedures conformed to the Ethical Principles for Medical Research Involving Human Subjects (World Medical Association Declaration of Helsinki). Fifteen older patients with bilateral medial knee OA (OA group), and 15 healthy controls (Control group) matching with the OA group for sex, age and BMI participated in the current study with written informed consent (Table 1). All the patients were determined radiographically to have severe bilateral medial knee OA (KL grade 4) by a senior consultant orthopaedic surgeon with more than 30 years of experience (HCL) using Kellgren and Lawrence criteria25 (Table 1). They were also assessed via the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) questionnaire. Participants were excluded from the study if they had received an intra-articular corticosteroid injection in the previous two months, or if they had other neuromusculoskeletal diseases or neurological pathology that might affect gait. An a priori power analysis for a two-group independent sample t test for the comparison of IA and RCIA between older adults with knee OA and healthy controls based on pilot results using GPOWER26 determined that a projected sample size of five subjects for each group would be needed with a power of 0.8 and a large effect size (Cohen's d = 0.8) at a significance level of 0.05. Thus, 15 subjects for each group were more than adequate for the main objectives of the current study.

In a gait laboratory, each subject walked at a self-selected, comfortable pace on a 10-m walkway. The motions of their body segments were tracked by 39 infrared retro-reflective markers placed on specific anatomical landmarks, namely ASISs, PSISs, greater trochanters, mid-thighs, medial and lateral epicondyles, heads of fibulae, tibial tuberosities, medial and lateral malleoli, navicular tuberosities, fifth metatarsal bases, big toes and heels, and mandibular condylar processes, acromion processes, C7, medial and lateral humeral epicondyles, and ulnar styloids21,27,28. Three-dimensional (3D) trajectories of the markers were measured using an 8-camera motion analysis system (Vicon MX T-40, UK) at 120 Hz while the ground reaction forces (GRF) were measured simultaneously at 1080 Hz using three forceplates (50.8 cm × 46.2 cm, OR-6-7-1000, AMTI, USA). The motion analysis system has been shown to have a high precision and accuracy with a mean absolute error of 0.15 mm and a variability lower than 0.025 mm29, which was considered appropriate for the purpose of the current study. The subjects were allowed to walk on the walkway several times before data collection. Data of a total of six trials, each containing a complete gait cycle for each lower limb, were obtained for each subject.

From the measured marker and GRF data, the mass and position of the COM for each of the body segments were obtained using an optimization-based method28, and the body’s COM was calculated as the mass-weighted sum of the COMs of all body segments using a 13-body-segment model. This approach has been shown to have reduced errors in the calculated COM motion when compared to traditional prediction methods28. The COP position of the whole body was calculated using the forceplate data. The IA of the COM–COP vector in the sagittal and frontal planes were then calculated as follows:

$$\vec{t}=\left(\vec{Z}\times \frac{{\vec{P}}_{COM-COP}}{\left|{\vec{P}}_{COM-COP}\right|}\right)$$
(1)
$$\mathrm{Sagittal}\,\mathrm{IA}={\mathrm{sin}}^{-1}\left({t}_{Y}\right)$$
(2)
$$\mathrm{Frontal}\,\mathrm{IA}=\left\{\begin{array}{c}{-\mathrm{sin}}^{-1}\left({t}_{X}\right), for\,\,the\,\,right\,\,limb\\ {\mathrm{sin}}^{-1}\left({t}_{X}\right), for\,\,the\,\,left\,\,limb\end{array}\right.$$
(3)

where $${\vec{P}}_{COM-COP}$$ was the vector pointing from the COP to the COM, $$\vec{Z}$$ was the vertical unit vector, and $$\vec{X}$$ was the unit vector pointing in the direction of progression (Fig. 1). The RCIA were calculated by smoothing and differentiating the IA trajectories using the GCVSPL method30. A positive sagittal and frontal IA indicate that the COM is anterior to and away from the COP towards the contralateral limb, respectively. The greater the IA, the greater the horizontal projection of the COM deviates from the COP, and the greater the effort needed to maintain or reduce the deviation unless accompanied by an appropriate RCIA, corresponding to the position and velocity control of the COM as described by Pai and Patton31. All the data analyses and graphics generation in the current study were performed using programs in Matlab (R2017b, MathWorks, USA) developed in-house.

For statistical analysis, the values of the IA and RCIA in the sagittal plane and frontal plane at heel-strike and toe-off of both limbs were obtained for each trial and each subject. The ranges of IA and RCIA during the gait cycle, and time-averaged IA over the phases of initial and terminal double-limb support (DLS), single-limb support (SLS) and swing were also obtained. For each of the above-mentioned variables, data from the six trials were averaged. Each of the variables was first tested for normality using a Shapiro–Wilk test. For variables of normal distribution, the between-group differences were tested using independent t tests. A significance level of α = 0.05 was set for all tests. All statistical analyses were performed using SPSS version 20 (SPSS Inc., Chicago, IL, USA).

## Results

The average WOMAC subscale values for the OA group were 43 (SD 15.8) for pain, 39.2 (SD 16.9) for stiffness, and 38.3 (SD 7.5) for physical function. Compared to Control, the OA group showed significantly decreased walking speed and cadence with significantly increased step width (Table 2). No significant differences were found in the stride length and step length between the groups (Table 2).

Both Control and the OA group showed similar patterns in the IA curves but quite different RCIA curves between OA and Control groups, especially during DLS (Fig. 2). In the sagittal plane, compared to Control, the OA group showed significantly decreased IA at heel-strike but increased average IA during DLS (Fig. 3). The OA group also showed significantly decreased RCIA at heel-strike and toe-off, and during DLS, as well as significantly decreased average and range of RCIA during SLS and swing (Table 3; Fig. 3). In the frontal plane, compared to Control, the OA group showed significantly decreased RCIA at heel-strike and toe-off, and average RCIA during terminal DLS (Fig. 3). They also showed significantly decreased range of RCIA during SLS and swing (Table 4).

## Discussion

The current study aimed to identify the effects of bilateral medial compartment knee OA on the whole-body balance control during level walking, in terms of COM–COP IA and RCIA. The OA group was found to walk with an altered COM–COP control throughout the gait cycle, when compared to healthy controls. In the sagittal plane, the patients showed increased IA during DLS but decreased RCIA throughout the gait cycle, while in the frontal plane the IA was not altered but the RCIA was decreased during DLS. These results suggest that bilateral severe medial compartment knee OA compromised the COM–COP control in older adults during gait, which may be related to the increased risk of falling in this population as reported in the literature.

Patients with knee OA in the current study showed increased pain and stiffness, as well as decreased mobility during activities of daily living as indicated by the WOMAC results, in agreement with the literature23. These symptoms appeared to contribute to the compromised performance of gait in these patients. For example, decreased gait speed and cadence, and increases in step width may be related to joint stiffness, limited mobility and/or attempts to minimize pain. These gait deviations also contributed directly to the changes in the control of the COM relative to the COP.