All subjects were evaluated for the type and degree of SCI and disability by specialists in rehabilitation medicine, orthopedics, neurosurgery, neurology, and internal medicine (rheumatology division) at medical institutions equipped with diagnostic tools, including X-ray facilities. This study targeted individuals with SCI with the following selection criteria: 1) SCI of a non-progressive nature, whether due to trauma or other causes; 2) a confirmed injury level at or below the T2; 3) a minimum of one year since discharge from rehabilitation; 4) age ranging from 18 to 65 years; 5) regular use of a push-rim wheelchair, with the capability of propelling themselves over a distance of at least 100 meters unassisted; 6) utilization of wheelchairs equipped with quick-release axles. Participants were excluded from the study based on the following criteria: 1) those currently under palliative care; 2) SCI resulting from congenital anomalies, progressive neurological diseases, or Guillain-Barré syndrome; 3) presence of upper limb pain severe enough to restrict wheelchair propulsion; 4) past history of shoulder, elbow, or wrist fractures or dislocations that continue to cause discomfort; 5) a background of heart or lung conditions potentially aggravated by intense exercise.

The sample size was calculated using G*Power 3.1.9, as described previously [18]. Applying an effect size of 0.63, a power of 80%, and a significance level of 0.05, the sample size was calculated to be 20 individuals. In our study, the sample size was 32, with a power of 95%. Considering the dropout rate for reasons such as withdrawal from the experiment, insincerity, or pain complaints, 35 participants were initially selected. Eventually, 34 individuals participated in the study, with one withdrawing from the study due to personal reasons. The study cohort comprised 19 individuals with cervical spine injuries and 14 individuals with thoracic spine injuries. All the participants were fully informed about the study and voluntarily agreed to participate. All study procedures were approved by the Institutional Review Board of Dongseo University (2021-019-HR-02) and conducted in accordance with the Declaration of Helsinki.

Participants were asked to visit the laboratory twice. They were instructed to avoid strenuous exercise and physical activity within 24 hours before the visit and to ensure at least 6 hours of sleep before visiting the laboratory. In the initial session, participants underwent a body composition assessment using the Inbody BWA device (Biospace Ltd., Seoul, Korea) and a peak cardiopulmonary exercise evaluation using the Quark CPET system (Cosmed, Rome, Italy). Independence assessments and a Korean activities of daily living (K-ADL) scale, body circumference measurements, and pulmonary function tests (Quark CPET, Cosmed, Rome, Italy) were performed on the second visit, at least 72 hours later.

Height was measured in the lying position from the sole to the top of the head using a tape measure. Weight was measured using a wheelchair scale (WCS-200; CAS, Seoul, Korea) and the weight of the participants was obtained by subtracting the weight of the wheelchair from the total weight when seated in the wheelchair. Body composition analysis was performed using the InBody BWA (Biospace Ltd., Seoul, Korea), a bioelectrical impedance analysis device specifically designed for individuals with disabilities. The analysis measured body mass index (BMI), free fat mass (FFM), body fat (BF), percentage of BF.

A tape measure was used to measure the circumference of individuals with spinal cord injuries. The circumferences of the left and right biceps, forearm, wrist, waist, hip, thigh, calf, and ankle muscles were measured.

The graded exercise test (GXT) was based on a study by van der Scheer et al. [19]. The participants were advised to avoid intense physical activity 24 h before the GXT and to have a light meal two to three hours before the test while avoiding caffeine, alcohol, and smoking. Incremental exercise was measured using the Quark CPET System (Cosmed, Rome, Italy), with calibration of the testing equipment performed one hour before the experiment for accuracy. Upon arrival at the laboratory, the participants were thoroughly briefed about the test procedures and precautions, followed by stretching as guided by the examiner, and VO₂peak was measured using an arm ergometer. To ensure accurate gas analysis, masks fitting the face size were used to prevent air leakage, and resting values for the heart rate and respiratory variables were collected while the participants were sitting quietly before starting the measurement. Pedaling on the arm ergometer started at 60 rpm with no resistance and was increased by either 5 or 10 W/min (5 W/min for quadriplegic patients and 10 W/min for paraplegic patients) until the participant reached voluntary fatigue (i.e., was unable to maintain a speed of 30 rpm). The measurement was terminated if any of the early cessation criteria outlined in the American College of Sports Medicine guidelines were met, including a 2 mm descent in the ST segment, increased neurological symptoms (such as blurred vision and dizziness), persistent ventricular tachycardia, or chest discomfort. The GXT was concluded under the following criteria: Termination occurred when despite maximum effort, a plateau in heart rate (HR) was observed. Additionally, the test was stopped when the highest Respiratory Exchange Ratio (RER) reached ≥ 1.1. The test was also terminated when the participant voluntarily expressed a desire to stop [20].

The Spinal Cord Independence Measure III (SCIM III) assesses independence and is composed of three main categories: self-care, respiration, sphincter management, and mobility, and is divided into 19 sub-categories. Points were allocated as 20, 40, and 40 for each category, respectively, with a total score of 100. The Korean Activities of Daily Living (K-ADL) scale was used to measure the individual’s ability to perform daily activities. It comprises seven parameters, including ‘changing clothes,’ ‘washing face,’ ‘brushing teeth,’ ‘washing hair,’ ‘taking a bath or shower,’ ‘eating prepared meals,’ ‘getting up from bed and going out of the room,’ ‘using the toilet,’ and ‘managing bowel and bladder control.’ The total score ranges from a minimum of 7 to a maximum of 21, with higher scores indicating greater dependence on others for daily activities.

Pulmonary function was measured using Quark CPET (Cosmed, Rome, Italy) to assess forced vital capacity (FVC), peak expiratory flow (PEF), and maximal voluntary ventilation (MVV). Pulmonary volume measurements were conducted with the participants standing upright, with their noses clipped, and breathing through a mouthpiece. After normal breathing for two to three breaths, the participants took a deep breath and exhaled forcefully and rapidly without interruption, continuing the exhalation effort for five to six seconds, with a minimum duration of at least three seconds. This test was repeated at least three times to determine the maximal values of FVC and PEF. MVV, which measures the total capacity of respiratory effort, was assessed by instructing the participant to breathe as deeply and rapidly as possible through a spirometer for a predetermined period, typically lasting 15 to 30 seconds.

In the multiple regression model, the following key assumptions were met: (1) linearity; (2) homoscedasticity; (3) independence of errors; (4) normality; and (5) independence of independent variables [21]. The mean and standard deviation were calculated for all measured parameters. The Shapiro-Wilk test was used to check the normal distribution of all outcome variables. Regression coefficients (β values) were examined to validate independent variables for linear regression analysis. Regression analysis using the forward selection method was conducted to predict VO₂peak using age; height; weight; BMI; FFM; BF; percentage of BF; circumference of upper arm, forearm, wrist, waist, belly, thigh, calf, and ankle; SCIM III; K-ADL; FVC; PEF; and MVV. To compare the observed and estimated VO₂peak, a paired t-test was utilized. The research rigorously followed the fundamental principles of regression analysis, ensuring linearity, independence, homoscedasticity, normal distribution, absence of autocorrelation, and outlier exclusion. The bias was determined by the discrepancy between the actual and predicted VO₂peak values. For statistical evaluations, SPSS version 25.0 (IBM Corporation, Armonk, NY, USA) was used; the threshold for statistical significance was set at a p-value of 0.05.

Outliers were screened using a criterion where standard residual absolute values exceeded 3; no outliers were found in the VO₂peak prediction model. Furthermore, a forward selection method was employed for estimating the regression model. Correlations between the observed VO₂peak and the dependent variables are detailed in Table 2.

The validity of each regression model was evaluated using an F-test, while the significance of the regression coefficients of independent variables was determined through a t-test. Following an exploratory data analysis, integrated regression models that were statistically significant were formulated using chosen independent variables. These models were applicable to all patients with traumatic spinal cord injury (TSCI) and specifically to those with cervical (CI) and thoracic injuries (TI). For patients with SCI, the variables were height, calf circumference, independence index, and PEF; for patients with CI, the variables were height, calf circumference, and MVV; and for patients with TI, the variable was calf circumference. These results were statistically significant, as shown in Table 3.

To assess the performance of the regression models, we calculated the coefficient of determination (R²), the adjusted R², and the standard error of estimate (SEE). VO₂peak regression models for all patients with SCI and specifically for patients with cervical or thoracic spinal cord injury were developed using their respective independent variables. The average explanatory power of the VO₂peak regression model for all patients with SCI was 70.3% (R²) and 66.2% (adjusted R²), with an average SEE of 2.94 ml/kg/min. For patients with cervical spinal cord injury, the average explanatory powers were 71.7% (R²) and 66.1% (adjusted R²), with an average SEE of 1.88 ml/kg/min. For patients with thoracic spinal cord injury patients, the average explanatory powers were 55.9% (R²) and 52.5% (adjusted R²), with an average SEE of 3.41 ml/kg/min (Table 4).

In this study, no significant difference was found between the VO₂peak measured using a metabolic gas analyzer and the VO₂peak predicted by the equation for all patients with SCI and for each type of injury. The average bias between the measured VO₂peak and the predicted VO₂peak was as follows: TSCI (total spinal cord injury) = 0.00 ml/kg/min, CI (cervical injury) = −0.05 ml/kg/min, TI (thoracic Injury) = −0.01 kcal, as shown in Table 5. The measured VO₂peak and predicted VO₂peak showed similar average values, and the correlation coefficients indicated a significant correlation (TSCI: R = 0.839, p = 0.000; CI: R = 0.847, p = 0.000; TI: R = 0.748, p = 0.001), as depicted in Figure 1.