Gait Speed Trajectory During the Six-Minute Walk Test in Multiple Sclerosis: A Measure of Walking Endurance

Background: The six-minute walk (6MW) test is a validated assessment method in Multiple Sclerosis (MS) research. While the total distance covered during six minutes (6MWTD) is often used as the standard measurement of gait capacity (i.e., the maximum distance one can achieve), we hypothesize that endurance (i.e., ability to maintain speed over a prolonged time) can be inferred by the gait speed trajectory (GST) during the 6MW test (6MWGST). Objective: To characterize group differences in 6MWGST between MS patients and healthy controls (HCs), and to assess information added by 6MWGST for discerning between MS patients and HCs. Methods: We performed a secondary data analysis on a cross-sectional cohort of 40 MS and 20 HC subjects with three repeated 6MW tests. We modeled 6MWGST using a linear mixed-effects model with time in minutes and replicated walks nested within individuals. We compared the discernibility of 6MWGST with that of conventional metrics using likelihood ratio tests and receiver operating characteristic (ROC) analysis on logistic regression models. Results: MS subjects showed a concave, quadratic GST during 6MW tests, slowing down more than the HC subjects, especially at the beginning of 6MW tests. Despite accelerating at the end of the 6MW, MS subjects were unable to attain or surpass their initial 6MW gait speeds. 6MWGST added useful information (p = 0.002) to the conventional metrics (e.g., 6MWTD) for discerning between MS and HC subjects, and increased the area under the ROC curve from 0.83 to 0.93 (p = 0.037). Conclusions: The distinctive 6MWGST pattern of MS patients provided increased discernibility compared with currently used gait metrics. Both gait capacity measured by the 6MWTD, and gait endurance measured by parameters of 6MWGST, are significant functional indicators for the MS population.


INTRODUCTION
Gait impairment is a central and ultimately inevitable aspect of multiple sclerosis (MS) that can be expressed as a decrease in gait speed, endurance, and balance. Thus, gait assessment is commonly employed in the evaluation of MS disability. Several timed-walk tests have been used in MS assessment that vary in the distance and duration of walking (e.g., timed 25foot walk, two-and six-minute walk tests) (1)(2)(3)(4). The sixminute walk (6MW) test has been used within MS studies and throughout health science. The 6MW total distance (6MW TD ) is a validated, standard outcome that has demonstrated added value over shorter distance walk tests in that it measures gait capacity (i.e., the ability to achieve maximal distance) (5), offers improved precision (1), correlates with habitual gait performance (6), and correlates with other physiological measures (7). Some researchers have also explored minute-by-minute 6MW data, by computing the percentage change in gait speed in the 6 th minute relative to the 1 st minute, sometimes referred to as the 6MW (2,3). In the largest study of 6MW in MS participants to date, Leone et al. (3) devised the distance walk index (DWI), which is the percentage change in gait speed in the nth minute relative to the 1 st minute. Specifically, they used DWI at the 6 th minute (i.e., 6MW as in other literature) to subgroup MS patients, demonstrating that more than 50% of their MS patients decelerated during 6MW tests. Van Geel et al. assessed the dayto-day reliability of 6MW, confirming consistent deceleration patterns in MS patients on two separate days (8). Ramari et al. demonstrated that in females with mild MS, knee flexor strength and balance are linked to the deceleration pattern in the 6MW test (9). Using temporally more continuous data collected by wearable sensors, Shema-Shiratzky et al. also demonstrated significant deterioration in cadence, stride regularity, and gait complexity among MS patients during 6MW tests (10).
Collectively, most literature on the 6MW test has been crosssectional and based on a single 6MW. Moreover, the existing metric for measuring within-walk performance, 6MW, relies on the assumption that change in gait speed is linear, and can thus be captured by the gait speed in the first and last minutes alone. However, it is more likely that changes in gait speed vary across all six minutes, and the gait speed trajectories in the 6MW (6MW GST ) may carry additional information which would more precisely measure endurance. We hypothesize that 6MW GST will provide additional information that goes beyond total distance (or equivalently, average gait speed), to give a true representation of endurance. In this manuscript, we analyze data from a previously published cohort (1), who performed three repeated 6MWs in a single day, using linear mixed-effects (LME) models. An LME model allows us to incorporate the full information from the minute-by-minute 6MW GST and assess the effect of MS status on gait endurance (measured by changes in 6MW GST ), whilst accounting for idiosyncratic differences in the baseline gait speed.

Participants
A previously published cross-sectional study with a cohort of 60 subjects was analyzed (1). This cohort included 40 MS patients and 20 HC subjects who completed three repeated 6MW tests in a single day (1). Ethical approval for this study was obtained from the Cleveland Clinic Foundation Institutional Review Board (IRB). All participants provided written informed consent prior to any study procedures. The University of Virginia IRB provided approval for secondary analyses of the de-identified data presented herein.
The MS subjects had a diagnosis of clinically definite MS according to the McDonald Criteria (11) and were recruited from outpatients at the Cleveland Clinic neurology department. HC subjects were recruited through MS subjects (e.g., a spouse or a friend). All subjects were aged 18-64 years old, reported being able to walk for six minutes, and had an EDSS (Expanded Disability Status Scale) score no higher than 6.5. Exclusion criteria for all subjects included neurological impairment from other diagnoses, orthopedic limitations, morbid obesity (BMI > 40), or known cardiac or respiratory disease. All fatigue-related medications (e.g., dalfampridine or modafinil) were withheld 48 hours before the study visit to avoid underlying changes in gait function being obscured. Additional details regarding the study population can be found in the primary publication (1).

Clinical Assessment and Disability Measures
Baseline demographics, medical history, and medications were documented. MS-related disability was assessed using the EDSS (12). EDSS severity was further classified by a certified Neurostatus examiner [MDG]. The MS Functional Composite was also collected for further disability assessment. The MSFC is a composite measure of disability that includes a quantitative test of ambulation (timed 25-foot walk, T25FW) (13).

Six-Minute Walk (6MW) Tests
All 6MW tests took place in a 175-foot hallway using the protocol developed and validated by Goldman et al. (1). Subjects were asked to walk as far and as fast as possible and used their usual assistive devices. Subjects arrived at 9:00 a.m. for 6MW tests to eliminate any time-of-day variability and completed three 6MW tests (i.e., three replicates) during a single visit. To eliminate residual fatigue from the previous walk, subjects rested at least 30 minutes between tests. The minute-by-minute distance was recorded for each walk using floor markers at 8.5foot intervals. Thus, each subject's 6MW test had one repeatedmeasure outcome at six time points for gait speed (i.e., distance walked per minute), and three explanatory variables-Time (indexed as 0, 1, 2, 3, 4, 5), Replicate (indexed as 0, 1, 2) as a categorical variable, and the MS status of the subject as a binary indicator (MS =1, HC = 0).

Statistical Analysis
We performed data analysis in Matlab 2019b (Mathworks Inc., Natick, Massachusetts) and R Studio (R version 3.6.3, RStudio Inc., Boston, Massachusetts). To accommodate the temporal variation in speed, and replicated walks nested within subjects, we fit LME models with the minute-by-minute gait speed data (or distance walked per minute) as the outcome variable. As preliminary analysis of the collected data revealed quadratic trajectories, we fit and tested the subject-specific linear and quadratic effects of time for MS and HC subjects. We also tested these temporal effects moderated by MS status. LME models allow us to estimate the random variation of the 6MW GST over time, controlling for the effects of MS and other covariates. To demonstrate this advantage, we fit an LME model after dropping all MS status related terms, and estimated parameters of subject-specific 6MW GST (i.e., subject-specific intercepts and linear and quadratic slopes). These subject-specific metrics were then used as the predictors of a logistic regression model with MS status as the outcome variable. We compared the discernibility of the predicted subject-specific 6MW GST with other conventional metrics such as 6MW TD , 6MW, and T25FW. The 6MW (3, 14) is calculated as: D 6 is the gait speed (or distance covered) in the 6 th minute and D 1 is the gait speed in the 1 st minute. For comparison, we used the MS status as a binary outcome, and developed five nested logistic regression models: (1) Model A contains parameters of subject-specific 6MW GST (i.e., subject-specific intercepts and linear and quadratic slopes estimated from an LME model) and the 6MW TD ; (2) Model B uses 6MW and 6MW TD (3) Model C uses 6MW TD ; (4) Model D uses the T25FW test (short-distance timed walk test); (5) Model E uses two covariates, age and sex, and is the baseline model in our study. Models A, B, C, and D were all adjusted for age and sex. For each model, we obtained the area under the receiver operating characteristic curve (AUROC) and the likelihood ratio χ 2 statistic (tested against an interceptonly null model). We tested added information by comparing AUROC using DeLong's tests and likelihood ratio tests across pairs of models (15).

RESULTS
60 subjects (40 MS and 20 HC) participated in the study. Baseline characteristics for both study populations are presented in Table 1. In our MS sample, there were 3.4 times as many females as males. This is consistent with the prevalence of MS, i.e., females are three times more likely to develop MS than males. HC subjects were predominantly male, since we actively recruited spouses of MS patients as HC subjects. For the MS sample, the median EDSS was 3 with a range of 0-6.5. Apart from sex and height, there were no significant differences in baseline demographic characteristics between MS and HC participants [age (p = 0.461), height (p = 0.038), weight (p = 0.225) and BMI (p = 0.882)]. There were, however, significant differences in gait function. MS subjects covered less distance in the first minute, the last minute, and across the 6 minutes, than HC subjects [Gait speed in 1 st min (p < 0.001), Gait speed in 6 th min (p < 0.001), Total distance (p < 0.001)].
Results from the LME model are listed in Table 2. To obtain the nadir times (here 2.7 for the HC, and 4.13 for the MS patients) of the estimated quadratic curves, we rearranged the quadratic time effects by completing the squares:  Table 2.
We first adjusted for age, sex, height, and weight, and then removed these variables from the final model as their effects are insignificant. On average, MS subjects walked 42.73 feet/minute slower than the HCs at the baseline (p = 0.003). After the baseline, using the trajectory −42.73−4.45×Time+.37×Time 2 , MS patients continued to walk 46.81, 50.15, 52.75, 54.61, 55.73 feet/minute slower than the HCs in the subsequent minutes. Both MS and HC subjects decelerated during the first half of the 6MW, but the MS patients decelerated by 4.5, 3.5, 3.0 feet/minute 2 more severely in the 2 nd to the 4 th minutes. In the second half of the 6MW, the HC subjects began to accelerate following a nadir in the 3 rd minute. In contrast, MS participants were unable to accelerate as early as HCs. As a result, at the end of the 6MW, HC subjects were able to walk as fast as at the baseline, whereas MS subjects ended up far below their baseline speed. Over the repeated walks, the HC group increased gait speed during the second walk (by 9.9 feet/minute, p = 0.003) and the third walk (by 7.5 feet/minute, p = 0.021), whereas the MS group only slightly increased gait speed over the repeated walks. Figure 1 shows the predicted trajectories of MS patients and HCs over replicated 6MW tests, as an illustration of our findings detailed in Table 2. First, there is a large difference in gait speed between the groups. HC subjects, despite decelerating in the first half of the 6MW test, exhibit acceleration over the second half of the 6MW test. In contrast, MS participants decelerate more rapidly in the first half of the 6MW and are unable to return to their baseline speed in the final minute. Moreover, while the HCs are able to improve their speeds over the replicated walks, the MS patients show no significant change in their gait speed over repeated walks. These findings suggest such differences are more likely to reflect the inherent pathology among MS subjects.
Using nested logistic regression models, we compared the conventional metrics such as 6MW TD , 6MW, and T25FW with the 6MW GST parameters estimated by the LME model as explained in the Statistical Analysis section. Table 3 shows model comparison results. Our Model A (6MW GST + 6MW TD ) added

DISCUSSION
In this study, we demonstrate consistent and significant deceleration patterns, an indicator of diminished endurance, among MS patients during repeated 6MW tests. Our finding underscores that the less-investigated aspect of the 6MW teststhe temporal change in minute-by-minute gait speed-offers a unique characterization of gait beyond 6MW TD . By testing the group differences in gait speed trajectories between MS and HC subjects, our LME model confirms a deterioration in both gait capacity and endurance among MS subjects. The LME model takes into consideration sources of variation in the gait speed outcome such as the subject-specific baseline gait speed and repeated walks, thus better elicits gait degradation due to MS-disability status. Using this model, we identified no significant change in 6MW GST over repeated 6MW tests among MS patients, indicating that a single 6MW test may be adequate to assess gait endurance for MS patients. With the MS status as a binary outcome, we also compared logistic regression models using parameters of 6MW GST estimated by an LME model against models using other conventional metrics (i.e., 6MW, 6MW TD , and the T25FW metric). Ultimately, our analysis showed that the subject-specific parameters of 6MW GST capture additional information about gait endurance in the MS population, beyond the gait capacity measured by total distance. MS patients are recognized to have denuded axons due to demyelination. The consequence of this is impaired nerve conduction. Fampridine, a potassium channel blocker, has been demonstrated to improve gait speed with a presumed mechanism of action of sustained conduction across demyelinated axons secondary to increased potassium availability (16). We posit that the differences in the subject-specific temporal variation in gait speed may be an indicator of this recognized conduction failure in MS individuals. Specifically, a deceleration pattern in the 6MW GST may be due to conduction failure among those MS patients with denuded axons. Were this to be the case, 6MW GST could serve as a potential biomarker when screening subjects for future remyelination trials, enrolling only decelerators as a recruitment enrichment strategy. The underlying pathophysiology driving 6MW deceleration in MS warrants further investigation which is not explored in this manuscript.
Although other studies found a strong correlation between gait speeds measured in 6MW and 2MW tests, the latter can only capture gait capacity (17,18), and are unable to assess gait endurance. Similarly, the 500-meter walk of the EDSS, and the T25FW test provide only a single endpoint for gait capacity evaluation, omitting the rich within-subject temporal patterns during walking. Given that the time needed to complete the 6MW (i.e., six minutes) is not substantially greater than the time needed for the 500-meter walk of the EDSS, and that the 6MW test can provide critical information about endurance and gait capacity at the same time, the 6MW test could be integrated into the EDSS as a substitute for the 500-meter walk.
One limitation of this work is the recruitment of patients' spouses as HC subjects. As MS is three times more prevalent in females (19), our control subjects tended to be male. Although we did not find any gender or height effect on the outcome, a potential gender confounding effect may exist in our data (e.g., females tend to walk slower than males). It is worth noting that while this confounding factor may impact 6MW TD , by focusing on the within-subject pattern, our proposed 6MW GST is robust to height or baseline gait speed differences. Also, although our sample size is sufficient to carry out the LME modeling, it is too small for developing diagnostic prediction models that could validate 6MW GST metrics. Lastly, we cannot track whether these 6MW GST metrics worsen longitudinally as these data were collected on a single day. Additional studies with larger sample sizes will be required to further characterize the longitudinal changes in 6MW GST among MS patients.
In conclusion, 6MW GST is a promising measure for assessing impaired gait function that merits further investigation. Our results demonstrate that the 6MW GST quantified by LME models is more informative than other gait outcome measures. Further studies will be necessary to confirm and expand our understanding of the potential underlying pathobiological relationship between the deceleration slope and associated measures of axonal integrity and myelination.