Criteria for knee flexion range of motion and quadriceps strength to ascend and descend stairs 1 year after bilateral total knee arthroplasty: A cross-sectional study

Abstract

Background

Stair ascent/descent pose significant challenges after total knee arthroplasty (TKA); however, the exact knee flexion range of motion (ROM) and quadriceps strength requirements remain unclear.

Objective

To establish criteria for knee flexion ROM and quadriceps strength to determine independence in stair ascent/descent and evaluate the accuracy of the combination of these factors in patients with bilateral TKA.

Methods

Patients with bilateral TKA were cross-sectionally assessed at 1 year postoperatively for independence in stair ascent/descent. Receiver operating characteristic curves provided cutoff values for knee flexion ROM and quadriceps strength. The area under the curves (AUC) of each factor and logistic regression models including both factors were evaluated.

Results

Eighty-two participants were included. Fifty-eight participants could independently ascend and 52 could descend stairs, with equal cutoff values for both: 121° for knee flexion ROM (AUC: 0.66 and 0.67) and 1.09 Nm/kg for quadriceps strength (AUC: 0.70 and 0.73). Logistic regression models produced AUCs of 0.73 and 0.76 for ascent and descent, respectively.

Conclusions

A quadriceps strength of 1.09 Nm/kg is a useful cutoff for independent stair ascent/descent, but combining it with knee flexion ROM did not enhance accuracy. Other functions such as coordination of the knee or other joints may influence stair performance post-TKA.

Keywords

osteoarthritis knee range of motion articular stair climbing arthroplasty replacement quadriceps muscle

Introduction

Successful total knee arthroplasty (TKA) can improve daily functional capacity and relieve pain in individuals with end-stage knee osteoarthritis (OA).¹ However, even after general rehabilitation, some individual experience reduced muscle strength and limited mobility for certain activities, which remains a significant and persistent issue.^2,3 In particular, ascending and descending stairs are highly demanding activities for patients after TKA.⁴ Almost all patient-reported outcomes include elements regarding ascending and descending stairs,⁵ highlighting the importance of enhancing these functions for patient satisfaction after TKA.

Knee flexion range of motion (ROM) and quadriceps strength are crucial for ascending and descending stairs. Patients with unilateral TKA often exhibit a reduced peak internal knee extension moment and knee flexion angle during these activities.^6–10 While ascending, the vastus lateralis and semitendinosus exhibit 68% and 56% of maximum muscle activity on electromyography, respectively, in patients with unilateral TKA.⁷ Pozzi et al. reported that internal knee extension moment was reduced by 37.7% during the ascending phase and 18.9% during the descending phase compared to healthy controls.⁸ The quadriceps are the primary source of knee extension moment during both stair ascent and descent.¹⁰ Additionally, Stevens-Lapsley et al. reported that while both quadriceps and hamstring strength decrease after TKA, the reduction is greater in the quadriceps.¹¹ Therefore, quadriceps strength plays a key role in stair ascent and descent. Various compensation strategies, such as forward trunk lean and increased muscle activity in lower limb joints other than the knee, have been documented as specific features in patients with TKA. These tendencies are considered to be due to quadriceps weakness, reduction in knee flexion ROM, or efforts to avoid pain.^8–10 A few studies in patients with bilateral TKA revealed they exhibit similar tendencies to patients with unilateral TKA. However, no consensus has been established regarding the optimal compensation strategy for knee joint function, including reduction in quadriceps strength and knee flexion ROM, in patients with TKA.^12,13 Furthermore, pain and psychological status can affect stair performance.¹⁴ It is assumed that movement strategies for stair performance vary considerably in patients after TKA, particularly during the pull-up phase of stair ascent and weight acceptance phase of stair descent. Therefore, a certain level of knee flexion flexibility and knee extension strength is required to independently ascend and descend a standard staircase with a step height of 16–20 cm.¹⁵ Additionally, adapted movement strategies can vary widely among individuals after TKA, even in those with bilateral TKA. However, quadriceps strength and knee flexion ROM requirements for independent stair ascent and descent remain unclear.

Knee flexion ROM and quadriceps strength are easily evaluated in a clinical setting and serve as objective indicators of postoperative knee joint function.^16,17 Determining specific criteria, such as cutoff values for these two factors, is beneficial in assessing patients’ ability to ascend and descend stairs independently, thereby supporting improvements in knee joint function. Additionally, understanding the interrelationship between knee flexion ROM, quadriceps strength, and stair-use capability serves as an effective screening tool to broaden interventions for knee joint function beyond these parameters, such as coordination of the knee and other joints. In individuals with unilateral TKA, separating the effects of pain and deformity in the unoperated knee on stair performance is challenging. Conversely, studies on individuals with bilateral TKA allow for a more accurate assessment of knee function without the influence of an unoperated knee. Furthermore, the risk of contralateral replacement in patients undergoing unilateral TKA is approximately 40%.¹⁸ Given this high risk, recognizing the impact of bilateral TKA on stair ascent and descent is crucial.

Thus, this study aimed to establish reference values for knee flexion ROM and quadriceps strength and assess the accuracy of combining these variables for detecting independent stair ascent and descent ability in patients after bilateral TKA. We hypothesized that these two factors would demonstrate fair discriminatory accuracy and that combining these factors would enhance this accuracy.

Methods

Study population

This cross-sectional study enrolled individuals who underwent either staged or simultaneous bilateral TKA and met the following criteria: (1) completion of the final TKA more than 1 year before the study, and (2) a diagnosis of knee OA prior to TKA according to established guidelines.¹⁹ For patients who underwent staged TKA, at least 1 year should have passed since both the first and second TKA. For patients who underwent simultaneous bilateral TKA, at least 1 year should have passed since surgery. Evidence from a systematic review shows that considerable functional recovery typically stabilizes within 1 year following TKA.²⁰ The exclusion criteria were patients with (1) secondary knee OA such as rheumatoid arthritis, (2) revision TKA, (3) prior surgeries on the lower extremities (excluding TKA), (4) decline in cognitive function (a mini-mental state examination score of < 23), (5) other lower limb conditions, such as hip OA, and (6) severe illnesses, such as neurological disorders, that could influence test performance. Cognitive decline was set as an exclusion criterion because individuals with cognitive impairment tend to have difficulty understanding the commands for performance tests accurately.

The Tokushukai Group Ethics Committee approved the study protocol (Approval No. TGE02523-03). This study adhered to the principles outlined in the Declaration of Helsinki and followed the STROBE guidelines.²¹ Consent was obtained using an opt-out approach, with study details publicly accessible on the hospital's website before data collection. Eligible patients were provided a timeframe in which to opt out. Data were collected from patients’ clinical records. The opt-out notice was posted on June 1, 2024, and participants were identified at Shonan Kamakura General Hospital between June 1 and June 15, 2024. Data collection commenced on June 16, 2024. In total, 94 patients diagnosed with knee OA who underwent staged or simultaneous bilateral TKA between April 17, 2020, and March 31, 2023, and completed perioperative and postoperative physical therapy for 3 months were considered to be included in this study.

Procedure

The following data were extracted from medical records: knee flexion ROM, quadriceps strength, pain status, and stair ascent and descent capability as outcome measures; diagnosis, sex, age, body mass index, and Charlson comorbidity index²² as demographic data. In addition, the preoperative Japanese Orthopaedic Association (JOA) score for knee OA²³ and status of walking aid use before TKA were also collected as indices of functional status before TKA. The JOA score for knee OA is an evaluation system comprising four categories, with a total score of up to 100 points: walking distance with pain (30 points), stair performance with pain (25 points), knee flexion ROM (35 points), and joint swelling (10 points). Higher scores reflect better functional outcomes. All outcome measures were evaluated by well-trained physical therapists on the same day. For patients with simultaneous bilateral TKA, evaluation took place 1 year post-surgery; in contrast, for those with staged bilateral TKA, assessments were conducted 1 year after the final TKA. In other words, for patients with staged bilateral TKA, values were used for both knees assessed at more than 1 year after the first TKA and at 1 year after the last TKA.

Our clinical pathway for TKA is as follows. Two orthopedic surgeons specializing in knee arthroplasty performed all TKA. All knees were opened via a medial parapatellar approach under general anesthesia. A fixed-platform cruciate-retaining prosthesis without a patellar component was used for all knees. Actual ROM outcomes depend on postoperative rehabilitation and individual patient characteristics, though cruciate-retaining prosthesis allows a maximum flexion of approximately 150°.²⁴ For pain management, patients followed a standardized protocol: During surgery, an ultrasound-guided femoral nerve block with 0.75% ropivacaine (10–20 ml) was administered. Postoperatively, intravenous paracetamol (1000 mg) was administered three times at 6-h intervals, starting 6 h after surgery. For the first week, paracetamol (800 mg, three times/day) and celecoxib (100 mg, twice/day) were prescribed. From the second week, tramadol/paracetamol (37.5 mg/325 mg, twice/day) was introduced and continued for 1 to 2 months, depending on individual pain management needs.

Postoperative rehabilitation was started on the first postoperative day. Knee joint ROM exercises and knee muscle strengthening were performed for as long as the pain was tolerable. Active assistive ROM exercises were primarily used to improve knee joint mobility. Manual therapy and stretching were incorporated to enhance muscle flexibility. Continuous passive motion was not utilized. Knee muscle strengthening focused mainly on the quadriceps and hamstrings, employing manual resistance, rubber balls, or bands. The resistance load was gradually increased for each patient individually, ensuring that it did not exacerbate pain. Walking exercises with full weight bearing using a walker were initiated on the first postoperative day. Single- or double-cane walking was introduced by the second day. Ascending and descending stair exercises commenced on the seventh day. Patients were discharged on the tenth day and received outpatient physical therapy once or twice a week by the third month after TKA. Outpatient physical therapy included knee ROM exercises, knee muscle strengthening exercises, balance exercises, walking exercises, and stair ascending and descending exercises according to the condition of each patient. Follow up, including surgeon consultation, radiographic evaluation, and functional assessment by well-trained physical therapists, was conducted at 3 weeks and 1, 2, 3, 5, and 12 months postoperatively.

Outcome measures

The staircase, comprising three steps, that was used to assess stair ascent and descent capability measured 20 cm in height, 26 cm in depth, and 92 cm in width, with handrails on both sides. Participants were instructed to ascend and descend the stairs in their usual way, using a handrail for balance if necessary while avoiding excessive force, as recommended for the stair-climbing test.¹⁵ Participants who demonstrated the ability to ascend and descend in a step-over-step pattern were deemed capable of independent ascent and descent, since ascending and descending stairs in a step-by-step pattern takes longer and can restrict activities. Additionally, previous studies have focused on a step-over-step pattern.¹⁰ Ascending and descending data were extracted separately.

The maximum passive knee flexion angle in the supine position was measured with a goniometer (Matsuyoshi & Co., Ltd, Tokyo, Japan) to assess knee flexion ROM in both knees.²⁵ Quadriceps strength was measured isometrically in both knees with a handheld dynamometer (μ-tus; Anima Co., Tokyo, Japan) while the participants were seated on a flat bed with their hips and knees flexed at 90°. The sensor of the dynamometer was placed at the top of the medial malleolus and restrained at the foot of the bed using a belt. Participants were subsequently instructed to exert maximal knee extension force. This method has high intraclass correlation coefficients (ICC [2,1] = 0.98).²⁶ The length between the center of the sensor and the center of the knee joint was measured using a tape measure as the arm length for torque. Torque per body weight (Nm/kg: [sensor force × arm length]/body weight) was calculated. These evaluations were conducted in both knees, and the lower value was selected for analysis.

Pain intensity and psychological aspects of pain were collected as potential covariates because pain status can cause poor stair ascent and descent performance.¹⁴ The 11-item numeric rating scale (NRS) was employed to evaluate the knee pain intensity while ascending and descending stairs.²⁷ The four-item short form of Pain Self-Efficacy Questionnaire measures self-efficacy regarding the ability to function despite pain, with scores of 0–24; higher scores indicate greater confidence.²⁸ Similarly, the six-item short form of Pain Catastrophizing Scale quantifies catastrophic thoughts about pain on a scale of 0–24, with higher scores indicating increased catastrophic thoughts about pain.²⁹ These were assessed for psychological aspects of pain. Pain status was assessed simultaneously with other outcome measures.

Statistical analysis

The participants were allocated as follows: those who could ascend or descend using the step-over-step pattern were categorized into the step-over-step group, whereas those who used the step-by-step pattern were categorized into the step-by-step group. Group comparisons of outcome measures, demographic data, and preoperative functional status data were conducted separately for ascending and descending situations. Categorical variables were analyzed using the chi-square test or Fisher's exact test. The Student's t-test was used to analyze normally distributed variables, whereas the Mann–Whitney U test was used to analyze non-normally distributed variables. Additionally, all demographic data, outcome measures, and preoperative functional status were compared between participants who underwent staged and simultaneous bilateral TKA.

Receiver operating characteristic (ROC) curves were used to evaluate the accuracy of quadriceps strength and knee flexion ROM to distinguish between step-over-step and step-by-step stair ascent or descent. Similarly, the binary logistic regression model, incorporating these two factors as independent variables, was evaluated using the ROC curve to assess their combined discriminatory accuracy. The optimal cutoff value for these two factors to balance sensitivity and specificity was determined as the point nearest to [0, 1] on the ROC curve.³⁰ Discriminatory accuracy was assessed based on the area under the curve (AUC). For internal validation, we used the bootstrap method, which involved resampling the model 1000 times to estimate the bootstrap-corrected AUC and its 95% confidence interval (CI).³¹ These analyses were conducted in both ascending and descending situations. A higher AUC value indicates greater discriminatory accuracy, where a value closer to 1 indicates ideal accuracy and a value closer to 0.5 indicates poor accuracy. For the AUC to be considered satisfactory, it must be at least 0.7.³⁰

Sample size requirements were calculated using the Obuchowski method, assuming a one-to-one of cases (patients able to use the step-over-step pattern) to controls (patients using the step-by-step pattern).³² A minimum of 48 participants, including 24 cases, was required to detect an AUC > 0.7, with an alpha risk of 0.05 and a power of 0.8. R version 4.4.0 (R Foundation for Statistical Computing, Vienna, Austria) was used for all analyses, with statistical significance set at P < 0.05 for all tests.

Results

Among the 94 patients initially considered, 6 were excluded due to rheumatoid arthritis (n = 2), previous lower extremities surgeries except for knees (n = 2), or revision TKA (n = 2). Of the remaining 88 patients, 6 were excluded because of missing data regarding outcome measures. Therefore, the final analysis included 82 patients (36 with staged bilateral TKA and 46 with simultaneous bilateral TKA) (Figure 1 and Table 1).

Figure 1.

Participant selection flow chart. TKA: Total knee arthroplasty.

Table 1.

Participants characteristics.

Variable	N = 82
Age (y); mean ± SD	73.1 ± 9.2
Female; n [%]	70 [85.3]
Body mass index (kg/m²); mean ± SD	26.1 ± 3.7
Charlson comorbidity index; median (IQR)	0 (0–1.0)
Preoperative Kellgren–Lawrence score on the right side
III; n [%]	8 [9.8]
IV; n [%]	74 [90.2]
Preoperative Kellgren–Lawrence score on the left side
III; n [%]	10 [12.2]
IV; n [%]	72 [87.8]
Preoperative JOA total score; median (IQR)	50 (45–50)
Use of walking aid during walking; n [%]	37 [45.1]
Simultaneous bilateral TKA; n [%]	46 [56.1]
Staged bilateral TKA; n [%]	36 [43.9]
Duration between the primary TKA and contralateral side TKA (month); median (IQR)	5.5 (4.0–7.0)

IQR, Interquartile range; JOA, Japanese Orthopaedic Association; TKA, Total knee arthroplasty.

In this cohort, 58 participants (70.7%) used a step-over-step pattern for ascent; in contrast, 52 participants (63.4%) used this pattern for descent (Table 2). Notably, all participants who could descend with the step-over-step pattern could also ascend in the same manner. Table 2 shows that the step-over-step group had significantly higher knee flexion ROM and quadriceps strength during both ascent and descent compared with the step-by-step group. During descent, the step-over-step group reported significantly lower NRS pain values. The step-over-step group had higher preoperative JOA scores for knee OA and a lower rate of walking aid use before TKA compared to the step-by-step group. No significant differences were found in demographic data or assessment measures between patients with staged and simultaneous bilateral TKA (Table 3).

Table 2.

Differences between groups of patients with different patterns of stair ascent and descent.

	Stair ascent				Stair descent
Variable	Step-by-step (n = 24)	Step-over-step (n = 58)	P	Effect size	Step-by-step (n = 30)	Step-over-step (n = 52)	P	Effect size
Age (y); mean ± SD	75.5 ± 10.7	72.1 ± 8.4	0.13	0.19	75.3 ± 10.2	71.8 ± 8.4	0.06	0.21
Female; n [%]	22 [91.7]	48 [83.0]	0.49		28 [93.3]	42 [80.8]	0.19
Body mass index (kg/m²); mean ± SD	26.6 ± 4.0	25.9 ± 3.6	0.38	0.1	26.9 ± 3.9	25.6 ± 3.6	0.14	0.16
Charlson comorbidity index; median (IQR)	0 (0–1.0)	0 (0–1.0)	0.25	0.13	0 (0–1.0)	0 (0–1.0)	0.55	0.07
Preoperative Kellgren–Lawrence score on the right side
III; n [%]	4 [16.7]	4 [6.9]	0.22		4 [13.3]	3 [5.8]	0.25
IV; n [%]	20 [83.3]	54 [93.1]			26 [86.7]	49 [94.2]
Preoperative Kellgren–Lawrence score on the left side
III; n [%]	1 [4.2]	7 [12.1]	0.4		3 [10.0]	5 [9.6]	1
IV; n [%]	23 [95.8]	51 [87.9]			27 [90.0]	47 [90.4]
Preoperative JOA score for knee OA; median (IQR)	45.0 (40.0–50.0)	50.0 (45.0–53.8)	0.02	0.25	45.0 (40.0–50.0)	50.0 (45.0–55.0)	0.003	0.33
Use of walking aid during walking before TKA; n [%]	17 [70.8]	20 [38.5]	0.003	0.33	21 [70.0]	16 [30.7]	< 0.001	0.38
Simultaneous bilateral TKA; n [%]	13 [54.2]	33 [56.9]	0.82	0.03	16 [53.3]	30 [57.7]	0.73	0.02
Staged bilateral TKA; n [%]	11 [45.8]	25 [43.1]			14 [46.7]	22 [42.3]
Duration between the primary TKA and contralateral side TKA (months); n [%]	5.5 (4.0–7.5)	5.5 (4.0–7.0)	0.88	0.01	5.5 (4.0–7.5)	5.5 (4.0–7.0)	0.9	0.01
Knee flexion range of motion (°); mean ± SD	121.2 ± 10.1	127.0 ± 11.9	0.5	0.23	120.9 ± 11.5	127.8 ± 11.1	0.01	0.28
Quadriceps strength (Nm/kg); mean ± SD	1.02 ± 0.37	1.29 ± 0.46	0.04	0.28	1.00 ± 0.39	1.33 ± 0.45	< 0.001	0.39
NRS during ascending stairs; median (IQR)	0 (0–1.0)	0 (0–0)	0.46	0.1	0 (0–2.0)	0 (0–0)	0.01	0.31
Four-item short form of pain self-efficacy questionnaire; median (IQR)	4.0 (0–11.5)	4.0 (0–10.8)	0.11	0.08	16.0 (13.0–22.0)	20.0 (14.5–24)	0.08	0.19
Six-item short form of pain catastrophizing scale; median (IQR)	16.0 (13.0–22.0)	20.0 (13.5–24)	0.49	0.18	5.0 (0.5–11.0)	3.5 (0–10.3)	0.18	0.15
Use of handrail during stair performance; n [%]	24 [100.0]	45 [77.6]	0.01		30 [100.0]	43 [82.6]	0.02

All participants (N = 82) were analyzed.

IQR, Interquartile range; JOA, Japanese Orthopaedic Association; NRS, Numeric rating scale; TKA, Total knee arthroplasty.

Cramér's V for categorical variables and r for continuous variables are used to estimate effect size.

Table 3.

Differences between simultaneous and staged bilateral TKA.

Variable	Simultaneous (n = 46)	Staged (n = 36)	P	Effect size
Age (y); mean ± SD	73.7 ± 10.6	72.6 ± 8.0	0.61	0.06
Female; n [%]	34 [78.3]	34 [94.4]	0.06
Body mass index (kg/m²); mean ± SD	26.4 ± 3.3	25.8 ± 4.0	0.50	0.08
Charlson comorbidity index; median (IQR)	0 (0–1.0)	0 (0–1.0)	0.13	0.17
Preoperative JOA score for knee OA; median (IQR)	45.0 (40.0–50.0)	50.0 (45.0–53.7)	0.10	0.17
Use of walking aid during walking before TKA; n [%]	22 [47.8]	15 [41.6]	0.58	0.06
Knee flexion range of motion; mean ± SD	124.1 ± 10.6	126.2 ± 12.5	0.47	0.08
Quadriceps strength; mean ± SD	1.16 ± 0.45	1.25 ± 0.46	0.51	0.07
NRS during ascending and descending stairs; median (IQR)	0 (0–0)	0 (0–0.0)	0.50	0.07
Four-item short form of pain self-efficacy questionnaire; median (IQR)	17.5 (14.5–22.0)	20.0 (13.0–24.0)	0.58	0.06
Six-item short form of pain catastrophizing scale; median (IQR)	4.0 (0–11.0)	4.0 (0.0–10.8)	0.81	0.03
Ascending stairs in step-over-step pattern; n [%]	33 [71.7]	25 [69.4]	0.82	0.03
Descending stairs in step-over-step pattern; n [%]	20 [65.2]	22 [61.1]	0.70	0.04
Use of handrail during ascending; n [%]	37 [80.4]	32 [88.9]	0.30	0.12
Use of handrail during descending; n [%]	39 [84.5]	34 [94.4]	0.16	0.15

All participants (N = 82) were analyzed.

IQR, Interquartile range; JOA, Japanese Orthopaedic Association; NRS, Numeric rating scale; TKA, Total knee arthroplasty.

Cramér's V for categorical variables and r for continuous variables are used to estimate effect size.

For stair ascent, the cutoff values were 121° for knee flexion ROM and 1.09 Nm/kg for quadriceps strength. The AUC for knee flexion ROM was 0.66 (95% CI: 0.53–0.78); in contrast, the AUC for quadriceps strength was 0.70 (95% CI: 0.58–0.82) (Table 4). The logistic regression model yielded an AUC of 0.73 (95% CI: 0.61–0.85), and quadriceps strength was identified as a significant independent predictor (Table 5 and Figure 2). The bootstrap-corrected AUCs were 0.70 (95% CI: 0.57–0.82) for quadriceps strength, 0.66 (95% CI: 0.49–0.78) for knee flexion ROM, and 0.73 (95% CI: 0.62–0.85) for the logistic regression model (Tables 4 and 5).

Figure 2.

Receiver operating characteristic curves for the ability of quadriceps strength, knee flexion range of motion, and the binary logistic regression model to discriminate those who can ascend stairs in a step-over-step pattern. The logistic regression model includes quadriceps strength and knee flexion ROM as independent variables. NRS: Numeric rating scale, ROM: Range of motion.

Table 4.

Discriminative accuracy of measurements in patients ascending or descending stairs using a step-over-step pattern.

Measurements	Cutoff value	AUC	95% CI	Bootstrap-corrected AUC	95% CI	Sensitivity (%)	Specificity (%)
Ascending
Knee flexion range of motion (°)	121	0.66	0.53–0.78	0.66	0.49–0.78	54.2	67.2
Quadriceps strength (Nm/Kg)	1.09	0.70	0.58–0.82	0.70	0.57–0.82	70.1	67.2
Descending
Knee flexion range of motion (°)	121	0.67	0.55–0.80	0.67	0.54–0.79	56.6	71.1
Quadriceps strength (Nm/Kg)	1.09	0.73	0.62–0.85	0.74	0.63–0.85	70.0	71.1

All participants (N = 82) were analyzed.

AUC, Area under the curve; CI, Confidence interval; ROM, Range of motion.

Table 5.

Discriminate accuracy for ascending stairs in a step-over-step pattern of the binary logistic regression model.

Variables	Beta-coefficient	Standard error	Crude odds ratio	Adjusted odds ratio	95% CI	P
Knee flexion range of motion	0.05	0.02	1.05	1.04	0.99–1.08	0.13
Quadriceps strength	1.53	0.72	5.6	4.61	1.13–18.8	0.03
Intercept	–5.20	2.87

Sensitivity = 65.5%; specificity = 79.1% (threshold: p = 0.72); AUC = 0.73 (95% CI: 0.61–0.85); Hosmer–Lemeshow test = 0.35; bootstrap-corrected AUC = 0.73 (95% CI: 0.62–0.85).

All participants (N = 82) were analyzed.

AUC, Area under the curve; CI, Confidence interval.

For stair descent, the cutoff values were 121° for knee flexion ROM and 1.09 Nm/kg for quadriceps strength. The AUC for knee flexion ROM was 0.67 (95% CI: 0.55–0.80), and the AUC for quadriceps strength was 0.73 (95% CI: 0.58–0.82) (Table 4). The logistic regression model (Model 1) showed an AUC of 0.76 (95% CI: 0.65–0.87), identifying quadriceps strength as a significant independent predictor. Given the significantly higher NRS values for descending stairs in the step-by-step group than in the step-over-step group, a logistic regression model (Model 2) was created, including the NRS for descending stairs as an additional independent variable. As in Model 1, only quadriceps strength was identified as a significant independent variable (Table 6 and Figure 3). The bootstrap-corrected AUCs were 0.74 (95% CI: 0.63–0.85) for quadriceps strength, 0.67 (95% CI: 0.54–0.79) for knee flexion ROM, and 0.74 (95% CI: 0.62–0.86) for the first logistic regression model (Tables 4 and 6).

Figure 3.

Receiver operating characteristic curves for the ability of quadriceps strength, knee flexion range of motion, and the binary logistic regression model to discriminate those who can descend stairs in a step-over-step pattern. The logistic regression model 1 includes quadriceps strength and knee flexion ROM as independent variables. The logistic regression model 2 includes quadriceps strength, knee flexion ROM, and NRS during descending stairs as independent variables. NRS: Numeric rating scale, ROM: Range of motion.

Table 6.

Discriminate accuracy for descending stairs in a step-over-step pattern of the binary logistic regression model.

Variables	Beta-coefficient	Standard error	Crude Odds ratio	Adjusted Odds ratio	95% CI	P
Model 1
Knee flexion range of motion	0.05	0.02	0.95	1.05	1.00–1.10	0.051
Quadriceps strength	1.92	0.73	8.21	6.84	1.84–33.03	0.01
Intercept	–7.42	3.03
Model 2
Knee flexion range of motion	0.05	0.03	0.95	1.05	1.00–1.10	0.06
Quadriceps strength	1.85	0.74	8.21	6.37	1.67–31.3	0.01
Numeric rating scale	–0.37	0.22	0.66	0.69	0.43–1.04	0.09
Intercept	–7.36	3.27

Model 1: Sensitivity = 71.1%; specificity = 80.0% (threshold: p = 0.65); AUC = 0.76 (95% CI: 0.65–0.87); Hosmer–Lemeshow test = 0.16; bootstrap-corrected AUC = 0.74 (95% CI: 0.62–0.86).

Model 2: Sensitivity = 69.2%; specificity = 90.0% (threshold: p = 0.68); AUC = 0.80 (95% CI: 0.70–0.90); Hosmer–Lemeshow test = 0.53; bootstrap-corrected AUC = 0.76 (95% CI: 0.63–0.88).

All participants (N = 82) were analyzed.

AUC, Area under the curve; CI, Confidence interval.

Discussion

In this study, we aimed to establish reference values for knee flexion ROM and quadriceps strength and to examine the discriminatory accuracy of detecting independent stair ascent and descent ability by combining the two factors. The AUC for quadriceps strength showed fair discriminatory accuracy, whereas the AUC for knee flexion ROM showed poor accuracy. Combining these two factors did not significantly improve the AUC, which partially supports our hypothesis. These tendencies were the same for ascending and descending stairs.

The comparison between participants who underwent staged and simultaneous bilateral TKA revealed no differences in demographics or outcome measures; hence, we believe this difference had little effect on the results. The two-group comparison for both stair ascent and descent revealed no significant differences in the scores for psychological aspects of pain. During descent, the step-by-step group had significantly higher pain intensity; however, this was not identified as a significant independent variable in the logistic regression model. A previous study showed that pain intensity and psychological status can affect stair performance.¹⁴ However, in this study, only 1 patient complained of high-intensity pain (NRS > 5) and 13 patients (15.8%) of low-intensity pain (NRS < 3) while descending stairs. The pain caused by surgery is assumed to have subsided since all participants had undergone TKA more than a year before. Furthermore, participants with severe psychological statuses related to pain were few, since pain intensity correlates with psychological status. Therefore, the impact of pain intensity and related psychological status on stair performance was low in this study population.

The cutoff values for knee flexion ROM and quadriceps strength for both ascending and descending stairs were identical. A systematic review has shown that the requirements for these are greater for descending stairs than for ascending stairs.¹⁰ In this study population, six participants could not descend with a step-over-step manner but could ascend using this pattern. Additionally, no participant could descend with a step-over-step manner but could not ascend in the same manner. These results are supported by a previous systematic review.¹⁰ However, the variability of the population between the ascending and descending groups was small, which may have contributed to the similar cutoff values suggested.

The AUC can be interpreted as follows: a test with a value exceeding 0.9 demonstrates high accuracy, while values between 0.7 and 0.9 reflect moderate accuracy.³⁰ The AUCs and bootstrap-corrected AUCs of quadriceps strength in ascending and descending stairs were > 0.7, validating the cutoff value as a useful clinical criterion. A cohort study on stair ascent reported average quadriceps strengths of 3.2 N/kg for the step-by-step pattern and 3.8 N/kg for the step-over-step pattern in patients with unilateral TKA.³³ In our study, quadriceps strength was 3.3 N/kg for the step-by-step group and 4.0 N/kg for the step-over-step group in both ascending and descending stairs, supporting the validity of our findings. Hasegawa et al.³⁴ found that a quadriceps strength cutoff of 2.8 N/kg can distinguish older adults who can ascend stairs without using a handrail. Our cutoff value for quadriceps strength was 3.3 N/kg. We allowed the use of a handrail, which likely reduced the muscle strength required compared with ascending and descending stairs without a handrail. However, our cutoff and average quadriceps strength values were higher than those of older adults in the study mentioned above.³⁴

Previous studies have shown that the internal knee extension moment during ascending and descending stairs is typically lower in patients with TKA than in the unoperated side and age-matched controls.^7–9 A comparative analysis of ascending stairs revealed that the internal knee extension moment in the TKA groups exhibited a lower value in comparison to the control group; however, muscle activity levels, particularly in the vastus lateralis and semitendinosus, did not significantly differ between groups.⁷ Furthermore, patients after TKA tend to experience increased co-activation of the hamstrings during isometric quadriceps contractions and walking, which can impair movement smoothness and weaken the quadriceps.^11,35 Considering the role of the hamstrings during ascending stairs is particularly important, as they serve as hip extensors in the pull-up phase. However, excessive co-activation of the hamstrings can also impede knee extension. It is assumed that this co-activation also occurs during ascending and descending stairs. A systematic review exploring biomechanical analysis during stair navigation highlighted several changes in kinetics and kinematics in the sagittal plane, as well as delayed quadriceps activity in patients with knee OA.³⁶ These features are similar to those observed in patients after TKA.^8–10,12,13 This suggests that preoperative compensatory strategies cannot be improved merely by alleviating pain or strengthening the quadriceps. Therefore, preoperative compensatory strategies to reduce knee joint load can be implemented after TKA, despite the improvement in pain status. The surgical impact of TKA on the quadriceps can lead to significant weakness, particularly within the first month postoperatively.¹¹ Additionally, arthrogenic inhibition of the quadriceps has been observed after TKA due to swelling and inflammatory responses, which should be considered in post-TKA rehabilitation.³⁷^,³⁸ However, since all participants in our study underwent TKA more than a year prior, these effects are likely minimal. Accordingly, we considered that our study population might experience difficulty ascending and descending stairs using the quadriceps effectively because of excessive co-activation of the hamstrings or their movement strategy. Consequently, the cutoff value for quadriceps strength may be higher than that of older adults.

Regarding knee flexion ROM, the AUC did not reach 0.7, and the logistic regression models with quadriceps strength as an independent variable did not significantly improve the AUC compared with that of quadriceps strength in both ascending and descending stairs. Therefore, the impact of passive maximum knee flexion ROM on ascending and descending stairs was small. The required knee flexion angle increases with increase in step height and is greater for stair descent than for ascent.⁹ In previous studies, the height of the stairs was 18 cm, which is 2 cm lower than the stairs in our study. Bjerke et al.⁶ analyzed stair descent without handrails, and reported a peak knee flexion angle was 89.0° during descent, with an average passive knee flexion ROM of 111°, which is lower than our cutoff value. Additionally, a previous retrospective study showed that patients who can flex the knee joint > 125° demonstrate optimal stair function¹⁷; thus, being able to flex the knee deeply is a strong advantage for ascending and descending stairs. However, our findings suggest that in patients with bilateral TKA, factors beyond ROM, such as the coordination of the knee and other joints during knee flexion, significantly contribute to stair ascent and descent.

Ascending and descending stairs in the step-by-step pattern take longer than in the step-over-step pattern, and slower stair performance can restrict physical activity.³⁹ Therefore, the capability of ascending and descending stairs using a step-over-step pattern is highly valued. This study is the first to determine reference values for knee flexion ROM and quadriceps strength while assessing the accuracy of combining these two factors to detect the independent capability of ascending and descending stairs in patients after bilateral TKA. Although patients with bilateral TKA show various kinds of compensation strategies,^12,13 the importance of quadriceps strength and knee flexion ROM in stair negotiation remains unchanged.

Including additional performance tests, such as the timed up and go test or chair stand test,¹⁵ could improve the model's discriminatory accuracy. However, this study primarily aimed to assess the efficacy of quadriceps strength, knee flexion ROM, and their combination as indicators for targeted interventions. This information may be used as a criterion to broaden exercises for movement strategies or other functions, such as coordination of the knee and other joints. Furthermore, adding additional variables could destabilize our logistic model owing to the limited sample size, even though our sample size exceeded the minimum required to validate discriminatory accuracy.⁴⁰^,⁴¹ The strength of this study lies in providing easily measurable clinical criteria for quadriceps strength and knee flexion ROM. Particularly, the discriminative accuracy of quadriceps strength was clinically useful, and its significance remained after adjusting for pain status, which can affect movement ability. As a result, we consider our cutoff value for quadriceps strength to be a useful criterion.

There were some limitations in this study. First, the quality of the movements could not be evaluated because movement analysis was not performed. Strategies such as using the knee and other joints should be considered to improve ascending and descending stairs after bilateral TKA. Compared to other studies that evaluated the JOA score for knee before TKA, our study population did not exhibit substantially deteriorated functional status and pain.⁴² However, as the functional status before TKA was better in those who could ascend and descend using a step-over-step pattern than in those who could not, complex functional factors, including movement strategy and other joint functions, present before TKA cannot be ignored. Second, our cutoff value may have varied depending on the step height and how participants used the handrail. However, the stairs used in our study had standardized specifications. Additionally, participants were instructed not to use a handrail beyond maintaining balance, as recommended.²⁰ Third, most of our study population was female. The sex ratio did not differ between the two groups; however, sex differences may have affected the cutoff values. Fourth, because this study population was limited to those who underwent fixed-platform cruciate-retaining prostheses without a patellar component, opened via a medial parapatellar approach, our cutoff point may differ in populations with other types of TKA or other approaches. Fourth, although all AUCs and 95% CIs were almost the same as the bootstrap-corrected AUCs and 95% CIs, and a sufficient sample size was collected to detect useful discriminatory accuracy,³² our results were not validated in an external sample. Finally, this study relied on past patient records for demographic data and clinical information. These results do not fully reflect the specific rehabilitation programs or the detailed aspects of patients’ daily living conditions, such as standing time per day. While these results provide valuable insights, the retrospective nature of data collection carries a potential risk of selection bias; therefore, the generalizability of these findings should be treated with caution.

Conclusion

This study revealed that 1.09 Nm/kg of isometric quadriceps strength could be a useful cutoff value for discriminating between those who can ascend and descend stairs using a step-over-step pattern in a clinical setting. However, discriminatory accuracy was not significantly improved by combining it with knee flexion ROM. This result implies that interventions to improve stair performance after bilateral TKA should consider other knee joint functions that ROM cannot measure, such as the coordination of the knee and other joints. Future studies investigating stair ascent and descent biomechanics based on quadriceps strength and knee flexion ROM must validate our findings and incorporate performance tests to extend our findings in patients with bilateral TKA. Additionally, further research is needed to examine the recovery of knee flexion ROM and muscle strength required for stair ascent and descent, as well as changes in stair performance over time.

Footnotes

Acknowledgments

We wish to thank physical therapists D. Kurihara, K. Suda, G. Tamura, K. Yoshida, and I. Sato for their assistance in gathering data.

Funding

The authors report no funding.

Declaration of conflicting interests

Ryutaku Kaneyama received royalties from the Teijin Nakashima Medical and Surgical Alliance. Tetsuya Jinno has received grants or royalties from Stryker, B. Braun Aesculap, Kyocera, Smith & Nephew, Zimmer Biomet, and Johnson & Johnson.

Data accessibility statement

The data supporting the findings of this study can be obtained from the corresponding author, [K.N.], upon reasonable request.

ORCID iD

Keigo Nanjo

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