Development and validation of a regression equation for VO₂ peak prediction in patients with heart and neurologic diseases

Abstract

To develop and validate a peak oxygen consumption (VO₂ peak) prediction model for Korean patients with both cardiovascular and neurologic diseases, addressing limitations in existing models that fail to account for disease-specific physiological interactions. Retrospective observational cross-sectional study with model development and validation. Data were collected from a single tertiary care hospital, Myongji Hospital, South Korea. A total of 269 patients (mean age: 61.62 ± 13.37 years, 76% male) who underwent cardiopulmonary exercise testing (CPET) between 2019 and 2021. Predictor variables included age, sex, body mass index (BMI), presence of neurologic disease, and type of heart disease. The primary outcome was VO₂ peak, measured via CPET. The model’s predictive performance was evaluated using adjusted R² and root mean square error (RMSE) and compared with established equations by Wasserman, Hansen, Jones, and Dun. Leave-one-subject-out cross-validation (LOSO-CV) was performed to assess generalizability. The final model demonstrated an adjusted R² of 0.444 and RMSE of 5.798, outperforming existing prediction equations for patients with heart and neurologic diseases. VO₂ peak was negatively influenced by age, BMI, and neurologic disease, while coronary heart disease had a relatively positive association compared to other heart conditions. Validation using LOSO-CV showed an R² of 0.4335, indicating good predictive performance when accounting for disease-specific factors. This model provides an accurate, practical tool for estimating VO₂ peak in patients with both cardiovascular and neurologic conditions, supporting personalized rehabilitation and treatment planning. Future studies should aim to validate the model in diverse populations to enhance its generalizability.

1. Introduction

Heart and neurologic diseases share common risk factors, including hypertension, hyperlipidemia, smoking, and diabetes.^[1,2] The prevalence of these conditions has notably increased in recent years.^[3] These conditions often significantly limit patients’ aerobic capacity, adversely affecting their overall health.^[4,5] As a result, assessing aerobic capacity has become a key focus in clinical practice for guiding rehabilitation therapies.

Peak oxygen consumption (VO₂ peak), a primary measure of aerobic capacity, provides critical diagnostic and prognostic insights, especially for patients with heart or neurologic diseases.^[6] VO₂ peak reflects the efficiency of the respiratory, cardiovascular, and muscular systems during exercise and is influenced by cardiac output and the arteriovenous oxygen difference.^[7] The cardiopulmonary exercise test (CPET) is the gold standard for measuring VO₂ peak, as it involves respiratory gas analysis during submaximal or maximal exercise.^[8] However, CPET may not always be feasible due to patient burden or logistical constraints. To address this, predictive equations based on demographic and physiological factors – such as gender, age, body weight, height, and physical activity level – have been developed. For instance, Wasserman equations have been widely used to estimate VO₂ peak in healthy individuals.^[9]

Despite their utility, these predictive models are generally designed for healthy or general populations and may not accurately estimate VO₂ peak in patients with heart or neurologic diseases, particularly those with both conditions.^[10] Some studies have proposed new equations for estimating VO₂ peak in patients with heart failure using performance-based tests, such as treadmill speed and grade^[11] or the 6-minute walk test.^[12] However, patients with coexisting heart and neurologic diseases often exhibit compounded impairments in cardiac and pulmonary function, which further alters VO₂ peak values.^[13] These complexities underscore the need for more nuanced prediction models that account for the unique characteristics of patients with multiple comorbidities.^[14]

Additionally, the physiological impacts of heart diseases vary significantly. For example, coronary heart disease (CHD) primarily causes localized ischemic damage, whereas heart failure leads to structural dysfunction, often resulting in more severe reductions in aerobic capacity.^[15] Such differences highlight the importance of condition-specific models for predicting aerobic capacity, as the type and severity of heart disease can lead to distinct physiological limitations.

Therefore, this study aims to develop and validate a prediction equation for VO₂ peak specifically for Koreans with heart and neurologic diseases. The performance of the proposed equation was compared with established models developed by Jones,^[16] Hansen,^[17] Neder,^[18] and Dun,^[19] to evaluate its accuracy and clinical applicability in this patient population.

2. Materials and methods

2.1. Participants

This study analyzed data from 421 patients referred to the cardiac rehabilitation program at Myongji Hospital following cardiac surgery or intervention between January 1, 2019, and December 31, 2021. Of these, 152 were excluded due to medical conditions or refusal, resulting in a final sample of 269 patients (Fig. 1). A power analysis indicated that a minimum of 82 participants was required (f² = 0.15, α = 0.05, power = 0.80; Fig. 1). As this was a retrospective study, no personally identifiable patient information was collected or recorded. The study protocol was approved by the Myongji Hospital Institutional Review Board (MJH2025-12-033) and registered with the Clinical Research Information Service (CRIS; KCT0011472).

Figure 1.

Flowchart of study participation. CHD = coronary heart disease, CPET = cardiopulmonary exercise testing, HD = heart diseases, ND = neurologic disease.

Patients received personalized treatments, including medication, percutaneous coronary intervention (PCI), coronary artery bypass grafting, and valve replacement, with most undergoing procedures within a week of admission. Cardiopulmonary exercise testing was conducted during hospitalization, and patients who were unable or unwilling to participate were excluded.

To develop a predictive equation, participants were categorized into those with coronary heart disease and those with neurologic disease (ND). Among them, 201 had CHD, while 68 had other heart diseases (HD), such as heart failure, valvular disease, atrial fibrillation, and peripheral artery occlusive disease. Neurologic disease cases primarily included stroke, with some instances of dementia or peripheral neuropathy.

2.2. Cardiopulmonary exercise test

Cardiopulmonary exercise testing assessed VO₂ peak using either a leg ergometer or a treadmill, following the guidelines of the American College of Sports Medicine.^[20] Physicians determined the need for testing and selected the protocol based on individual clinical status. The CASE T2100 system (GE Healthcare, Chicago) and the Quark gas analysis system (COSMED, Rome, Italy) measured maximal aerobic capacity and respiratory gas exchange.

Before testing, patients completed a 3-minute baseline assessment while seated. The test consisted of a warm-up phase, an exercise phase with incremental workload increases (e.g., the Bruce protocol, Bruce ramp protocol, or ergometer increments of 5–15 W every 3 minutes), and a recovery phase. Hemodynamic variables, including heart rate and systolic blood pressure, were recorded every 3 minutes, while respiratory gas exchange was continuously measured and standardized into 15-second averages. VO₂ peak was defined as the highest oxygen uptake averaged over a 20-second interval.

Cardiopulmonary exercise testing ended when patients reached standard termination criteria, such as excessive fatigue or physiological thresholds. Trained physical therapists and nurses continuously monitored participants using a 12-lead ECG to ensure safety. For further methodological details, refer to previous studies.^[21]

2.3. Develop the prediction equation

A linear regression model with a forward stepwise approach developed the prediction equation. The multivariate regression model followed the equation:

$${\displaystyle \begin{array}{l}{\displaystyle Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+{\beta }_3{X}_3+{\beta }_4{X}_4+{\beta }_5{X}_5+\epsilon ,}\end{array}}$$

where Y represents VO₂ peak, β denotes regression coefficients, and X₁, X₂, X₃, X₄, and X₅ correspond to Age, BMI, Sex, ND, and CHD, respectively. The error term appears as ε. The coding scheme assigned female = 0 and male = 1 for sex, while ND and CHD followed No = 0 and Yes = 1. Age, BMI, and sex influenced cardiac output, while ND and CHD accounted for neurologic and cardiac conditions. Group imbalance between ND and CHD remained minimal and did not impact model validity (see Section 3).

Model development began with a single predictor from Age, BMI, Sex, ND, and CHD. The process introduced additional predictors one at a time, expanding the model incrementally until it included all predictors. The anova() function in R^[22] compared models using an F test. Predictors that failed to improve the model were removed. Each predictor required statistical significance (P < .05, based on the t-value). Nonsignificant predictors did not appear in the final model.

2.4. Cross-validation and correlation

Leave-one-subject-out cross-validation (LOSO-CV)^[23] validated the regression model for VO₂ peak. Given the variability in VO₂ peak across ND and CHD (Table 2), LOSO-CV provided a more reliable alternative to traditional cross-validation methods. The process systematically excluded 1 participant’s data, trained the model on the remaining dataset, and tested it using the withheld data. This procedure repeated for all participants, and the results were averaged. Agreement between measured and predicted VO₂ peak was assessed using Pearson or Spearman correlation coefficients and R² values.

Table 2.

General characteristics and VO₂ peak values of participants (n = 269).

Characteristics	Full data (n = 269)	Heart disease only	Heart and neurologic diseases
		CHD only (n = 172)	Other HD only (n = 31)	CHD + ND (n = 29)	Other HD + ND (n = 37)
Age (yr)	61.62 ± 13.37†	58.53 ± 11.01	60.29 ± 14.32	72.41 ± 13.50*	68.62 ± 15.85*
Weight (kg)	67.11 ± 11.70	69.45 ± 11.67	65.92 ± 10.77	62.17 ± 9.19*	61.07 ± 11.20*
Height (cm)	166.4 ± 8.87	168.18 ± 7.69	163.41 ± 9.91*	164.59 ± 10.54	161.89 ± 9.53*
BMI	24.19 ± 3.47	24.49 ± 3.4	24.68 ± 3.49	23.31 ± 3.9	22.98 ± 2.89
Sex (F/M)	65/204	27/145	9/22	12/17	17/20
VO2 peak (mL/kg/min)	16.56 ± 7.76	19.59 ± 7.06	14.41 ± 6.47*	10.61 ± 5.47*	8.96 ± 4.29*

BMI = body mass index, CHD = coronary heart disease, ND = neurologic disease, Other HD = heart conditions other than CHD, VO₂ peak = peak oxygen consumption.

^*Different from CHD only.

^†Mean ± standard deviation.

2.5. Comparison to other equations

VO₂ peak was recalculated using the 4 different prediction equations proposed by Jones, Hansen, Wasserman, and Dun. Detailed information about these prediction equations is provided in Table 1. The agreement between the measured VO₂ peak and the VO₂ peak estimated by each equation, including our model, was assessed using several metrics: mean comparison (independent t test), R², root mean squared error (RMSE), Normalized RMSE (NRMSE), and mean absolute error (MAE). The mean difference between measured and estimated VO₂ peak was tested using the independent t test with 0.05 of significance level. The R² value indicates how well the regression model fits the observed data, with a higher R² from the final model suggesting better predictive performance for the VO₂ peak. Root mean squared error is calculated as the square root of the average squared difference between the actual and predicted values, while MAE represents the average absolute difference between the actual and predicted values. Root mean squared error is more sensitive to data with outliers, making it a stronger metric in such cases. Normalized RMSE was computed by dividing the RMSE by the range of the observed VO₂ peak values (i.e., the difference between the minimum and maximum values). Lower values of RMSE, NRMSE, and MAE indicate better model performance.

Table 1.

Previous equations for VO₂ peak calculations.

Models	Country	Sex	Equations for VO2 peak (mL/min)
Jones[16],*	Canada	Male	VO2 peak = − 3760 + 34 × Height + 22 × Weight − 28 × Age
		Female	VO2 peak = − 2260 + 25 × Height + 10 × Weight − 18 × Age
Hansen et al[17]	United States	Male	VO2 peak = [50.75 − (0.37 × Age)] × Weight
		Female	VO2 peak = (Weight + 43) × [22.78 − (0.17 × Age)]
Neder[18]	Brazil	Male	VO2 peak =  702 + 9.8 × Height + 12.5 × Weight − 24.3 × Age
		Female	VO2 peak =  372 + 7.4 × Height + 7.5 × Weight − 13.7 × Age
Dun et al[19]	China	Male	VO2 peak = 1532.58 + 11.593 × Weight − 9.951 × Age
		Female	VO2 peak = 1204.34 + 11.593 × Weight − 9.951 × Age

VO₂ peak = peak oxygen consumption.

^*Jones equation (sex-specific).

2.6. Statistical analysis

All statistical analyses were performed using RStudio version 1.2 (RStudio Inc., Boston). General characteristics, including age, weight, height, body mass index (BMI), and VO₂ peak, were summarized using descriptive statistics. Based on the assumption that VO₂ peak may be influenced by the type of heart disease and the presence of neurological disease, we divided the participants into 4 subgroups: those with coronary heart disease only (CHD only), those with other heart diseases (Other HD only), those with both CHD and neurological disease (CHD + ND), and those with both Other HD and neurological disease (Other HD + ND). All general characteristics were analyzed using these subgroups.

For development of the VO₂ peak prediction equation, the presence of coronary heart disease and neurological disease was coded as dummy variables (No = 0, Yes = 1). Differences in VO₂ peak by gender, type of heart disease, and presence of neurological disease were tested using either independent t test or Mann–Whitney U test, depending on data normality, which was evaluated using the Shapiro–Wilk test.

3. Results

3.1. General characteristics of participants

Table 2 presents the general characteristics of all subjects and those stratified by the presence of CHD and ND. The mean age of the participants was 61.62 ± 13.37 years. Most participants were men (76%, n = 204). Among the participants, 172 (63.94%) had CHD only, 31 (11.52%) had other HD only, 29 (10.78%) had both CHD and ND, and 37 (13.75%) had both other HD and ND. Participants with heart disease only (either CHD only or other HD only) were younger than those with both heart and neurological diseases (CHD + ND, or other HD + ND). There was no significant age difference between participants with CHD only and those with other HD only. BMI did not differ significantly among participants, regardless of whether they had heart diseases, neurological diseases, or both.

Male participants exhibited higher VO₂ peak values than female participants (18.06 ± 7.51 mL/kg/min for males and 11.82 ± 5.61 mL/kg/min for females; w = 3441, P < .001; Fig. 2A). Participants with CHD showed higher VO₂ peak values than those with other HD (w = 10,477, P < .001; Fig. 2B), whereas participants with ND showed lower VO₂ peak values than those without ND (w = 1979, P < .001; Fig. 2C). Participants with CHD only demonstrated the highest VO₂ peak, followed by those with other HD only, then participants with both CHD and ND, and finally, participants with both other HD and ND (Table 2 and Fig. 2D).

Figure 2.

VO₂ peak for the participants. (A) VO₂ peak for female and male participants: Male participants exhibited higher VO₂ peak values than female participants. (B) VO₂ peak comparison based on types of heart disease and (C) the presence of neurologic disease: Participants with CHD or without neurologic disease exhibited higher VO₂ peak values. (D) VO₂ peak across the subgroups of participants: Participants with CHD only demonstrated the highest VO₂ peak among all other disease subgroups. ***P < .001. CHD = coronary heart disease, HD = heart diseases, ND = neurologic disease, VO₂ peak = peak oxygen consumption.

3.2. Equation for the prediction of oxygen consumption in patients with heart and neurological diseases

Multivariate regression analysis identified age, gender, BMI, ND, and heart disease type (CHD or not) as key predictors of VO₂ peak (Table 3). Among single-predictor models, age (model 1) and ND presence (model 4) showed the strongest associations, while gender (model 3), CHD (model 5), and BMI (model 2) had weaker effects. Expanding to a 2-predictor model, combining ND and age (model 6) improved model fit (adjusted R² = 0.39, F = 48.563, P < .001). Performance improved further by incorporating gender (model 7), BMI (model 8), and CHD (model 9), leading to the final model:

Table 3.

Developed the models for calculating VO₂ peak.

VO2 peak models
Parameters	1	2	3	4	5	6	7	8	9
Age	−0.31***					−0.23***	−0.21***	−0.21***	−0.22***
BMI		0.01						−0.24*	−0.23*
Gender (male)			6.24***				2.61**	2.62**	2.24*
ND (yes)				−9.11***		−6.47***	−6.02***	−6.30***	−4.85***
CHD (yes)					6.85***				3.63***
Constant	35.49***	16.35***	11.83***	18.80***	11.44***	32.32***	28.95***	35.08***	32.26***
Observations	269	269	269	269	269	269	269	269	269
R 2	0.28	0.001	0.12	0.26	0.15	0.39	0.41	0.42	0.46
Adjusted R2	0.28	−0.004	0.12	0.25	0.14	0.39	0.40	0.41	0.44
Residual standard error	6.60	7.78	7.30	6.71	7.18	6.08	6.00	5.96	5.80
F statistic	103.73***	0.004	35.97***	91.69***	46.16***	85.38***	61.18***	47.86***	43.85***

BMI = body mass index, CHD = coronary heart disease , ND = neurologic disease, R² = R squared, VO₂ peak = peak oxygen consumption.

^*P < .05.

^**P < .01.

^***P < .001.

$${\displaystyle \begin{array}{l}{\displaystyle \begin{array}{lll}& {\displaystyle \mathrm{V}{\mathrm{O}}_2\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}=32.26+(-.22\times \mathrm{a}\mathrm{g}\mathrm{e})+(-.23\times \mathrm{B}\mathrm{M}\mathrm{I})}& {\displaystyle +(2.24\times \mathrm{S}\mathrm{e}\mathrm{x})+(-4.85\times \mathrm{N}\mathrm{D})+(3.63\times \mathrm{C}\mathrm{H}\mathrm{D}).}\end{array}}\end{array}}$$

For a female patient with other HD only, the equation simplifies to:

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{V}{\mathrm{O}}_2\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}=32.26-.22\times \mathrm{a}\mathrm{g}\mathrm{e}-.23\times \mathrm{B}\mathrm{M}\mathrm{I}).}\end{array}}$$

For a male patient with both ND and CHD, the equation becomes:

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{V}{\mathrm{O}}_2\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}=32.26-.22\times \mathrm{a}\mathrm{g}\mathrm{e}-.23\times \mathrm{B}\mathrm{M}\mathrm{I}+2.24-4.85+\mathrm{3.63.}}\end{array}}$$

Validation using leave-one-subject-out cross-validation(LOSO-CV) produced R² = 0.43, RMSE = 5.84, and MAE = 4.52. The final model’s predicted VO₂ peak strongly correlated with actual values (ρ = 0.67, Spearman correlation, P < .001).

3.3. Comparison with other equations

Table 4 shows that the measured VO₂ peak values closely matched the values predicted by the final model, whereas other equations either overestimated or underestimated VO₂ peak. The lowest RMSE, MAE, and normalized RMSE confirmed that the final model provided the most accurate VO₂ peak predictions compared to other estimations. The mean and median values of the final model’s measured and predicted VO₂ peak showed no statistically significant differences.

Table 4.

Statistical values of the equations.

Sex	Statistic measurements	Measured VO2 peak	Our model	Jones	Hansen	Neder	Dun
Female	Mean	11.82	11.83	16.68***	19.51***	17.77***	20.86***
	Minimum	2.30	2.39	2.38	13.25	11.90	16.80
	Maximum	29.00	21.6	37.88	33.76	32.05	31.36
	SD	6.60	5.34	6.97	4.70	4.60	3.13
	R 2	–	0.54	0.26	0.28	0.27	0.25
	RMSE	–	4.46	8.29	9.60	8.25	10.67
	MAE	–	3.33	6.40	8.43	7.09	9.68
	Normalized RMSE	–	0.38	0.70	0.81	0.70	0.90
Male	Mean	18.07	18.07	26.74***	28.67***	25.71***	25.23***
	Minimum	2.10	6.75	−0.56	18.35	15.63	19.93
	Maximum	47.20	25.91	43.77	39.932	39.34	32.89
	SD	7.51	4.24	6.40	4.50	4.30	2.23
	R 2	–	0.35	0.195	0.21	0.20	0.06
	RMSE	–	6.06	11.40	12.56	10.20	10.22
	MAE	–	4.74	6.78	11.11	8.56	8.38
	Normalized RMSE	–	0.33	0.63	0.70	0.56	0.57

MAE = mean absolute error, RMSE = root mean squared error, R² = R squared, SD = standard deviation, VO₂ peak = peak oxygen consumption.

^***Different from measured VO₂ peak, P < .001.

For men, VO₂ peak values estimated by the Jones, Hansen, Neder, and Dun equations significantly differed from measured values. A similar trend appeared in female participants. However, VO₂ peak values for women were predicted more accurately than those for men using the final model (R² = 0.54 for women vs R² = 0.35 for men).

4. Discussion

This study developed and validated a novel model for predicting VO₂ peak in elderly patients with heart and neurologic diseases. By integrating demographic and clinical variables through multiple regression analysis, the model significantly improved prediction accuracy compared to existing models.

The final model (model 9, Table 3), which incorporated age, gender, BMI, ND presence, and heart disease type (CHD or not), demonstrated the highest explanatory power (R² = 0.46), accounting for 45.5% of VO₂ peak variability while maintaining the lowest residual standard error (5.80). In contrast, single-variable models (models 1–4) exhibited lower explanatory power (R² = 0.26–0.28) and higher residual errors (6.60–7.78). Incrementally adding variables (models 6–9) progressively improved model performance, emphasizing the importance of key variable interactions in VO₂ peak prediction.

The distinct features of this model, compared to previous VO₂ peak estimation models, highlight the significant roles of neurologic disease and coronary heart disease in influencing VO₂ peak among elderly individuals. Kokkinos et al (2020) developed a prediction equation for VO₂ peak in patients with heart failure using parameters such as speed, grade, or work rate from treadmill or cycle ergometer protocols, based on data from the Fitness Registry and the Importance of Exercise National Database (FRIEND).^[11] In contrast, the proposed model relies on basic patient characteristics to enable a simpler estimation of VO₂ peak. Specifically, the presence of ND significantly decreased VO₂ peak (model 9, β = −4.85, P < .001), whereas the presence of CHD increased VO₂ peak (β = 3.63, P < .001). Variations in aerobic capacity among heart disease patients closely relate to the type and severity of the condition. For example, CHD, often characterized by a sudden onset and managed with minimally invasive interventions such as stent insertion, tends to preserve higher aerobic capacity. In contrast, patients with chronic conditions such as heart failure or valvular heart disease, which impose prolonged cardiac stress, exhibit significantly reduced aerobic capacity.^[24] CHD patients may retain partial oxygen delivery capacity during exercise, whereas other heart diseases more profoundly impair peak cardiac output due to reduced contractility or blood regurgitation.^[15] These findings emphasize the importance of distinguishing CHD from other heart diseases when estimating VO₂ peak, as demonstrated by the final model’s performance.

Patients with neurologic diseases, particularly stroke survivors, often exhibit significantly lower VO₂ peak compared to non-neurologic populations. This decline arises from several physiological mechanisms. Reduced central drive impairs cardiovascular fitness by disrupting the transmission of motor commands from the brain and spinal cord, limiting physical activity capacity and reducing pulmonary muscle engagement during exertion.^[25] Additionally, muscle atrophy, caused by decreased physical activity, leads to peripheral muscular changes characterized by a shift from slow-twitch (type I) fibers to fast-twitch (type II) fibers, reducing muscular endurance and increasing fatigue during exercise.^[26] These physiological changes collectively contribute to the lower VO₂ peak observed in neurologic disease patients, underscoring the necessity of targeted rehabilitation strategies aimed at improving both muscle function and cardiovascular fitness.^[27]

Our model confirmed that age, gender, and BMI significantly influence VO₂ peak, aligning with previous findings.^[16-19] VO₂ peak decreases by approximately 0.22 units per additional year of age (model 9, P < .001). Male participants demonstrated VO₂ peak values roughly 2.24 units higher than females (model 9, P < .05). Although BMI had a weaker correlation with VO₂ peak, the relationship remained significant, with higher BMI negatively affecting VO₂ peak (model 9: β = −0.23, P < .05). Unlike some previous models that relied on height or weight alone,^[17] this study incorporated BMI (calculated as body weight [kg] divided by height squared [m²]) as an indirect measure of body fat. Excess adipose tissue, a non-metabolically active mass, diverts oxygen away from active muscles, reducing effective oxygen delivery and lowering VO₂ peak. Moreover, elevated BMI increases the workload on the cardiovascular and respiratory systems, reducing oxygen transport efficiency and further impairing VO₂ peak during exertion. These findings reinforce BMI as a reliable indicator of body composition and its influence on cardiorespiratory fitness in VO₂ peak prediction models.

Compared to existing models, the proposed model demonstrated superior performance based on error metrics such as RMSE, MAE, and NRMSE (Table 4). Previous equations, including those developed by Jones, Hansen, Neder, and Dun, were not designed for patients with cardiovascular and cerebrovascular diseases, leading to significant overestimations of VO₂ peak.^[16-19] Among men, all existing equations consistently overestimated VO₂ peak, as they were developed for young, healthy adults without neurologic or heart diseases, failing to account for disease-specific VO₂ peak reductions. Among women, although predictions were slightly more accurate, a similar overestimation trend emerged. In contrast, the proposed model produced predictions closely aligned with measured values, exhibiting the lowest variability in residual analysis. These findings highlight the limitations of conventional VO₂ peak prediction equations and underscore the necessity of tailored models for patients with cardiovascular and cerebrovascular diseases.

The proposed model offers a precise tool for assessing VO₂ peak by incorporating patient-specific factors such as age, gender, BMI, and the presence of neurologic disease and coronary heart disease. By enhancing the accuracy of VO₂ peak estimation, this model supports the development of personalized exercise and rehabilitation plans tailored to each patient’s physical condition. Additionally, it helps manage multimorbidity by quantifying the impact of conditions like ND and CHD on VO₂ peak, enabling the design of rehabilitation strategies that address the complex interactions between comorbid conditions. Furthermore, as VO₂ peak is a key indicator of patient outcomes, its assessment can be valuable for monitoring treatment effectiveness and long-term disease progression.

Despite its strengths, this study has several limitations that warrant further investigation. The study population consisted exclusively of Korean patients, necessitating validation across diverse racial and regional groups to ensure broader applicability. Additionally, incorporating variables such as medication use, neuromuscular function, and cardiovascular responses to exercise may enhance the predictive accuracy of the model. Moreover, since this study relied on cross-sectional data, longitudinal research is required to evaluate changes in VO₂ peak over time and verify the long-term reliability of the model.

5. Conclusion

This study developed a novel multiple regression model for accurately predicting VO₂ peak in patients with heart and neurological diseases. The proposed model exhibited greater explanatory power and lower error metrics than existing equations, highlighting its potential for clinical application. Future research should focus on expanding the model’s applicability and improving reliability through validation in diverse patient populations.

Acknowledgments

The authors thank the staff of the cardiopulmonary exercise testing (CPET) laboratory and the Department of Rehabilitation Medicine at Myongji Hospital for their assistance with data acquisition and clinical coordination. We also appreciate the contributions of colleagues who provided methodological input during model development.

Author contributions

Conceptualization: Sujin Kim.

Data curation: Jeong Jae Lee, Sujin Kim.

Formal analysis: Jeong Jae Lee, Sujin Kim.

Methodology: Jeong Jae Lee, Sujin Kim.

Project administration: Jeong Jae Lee.

Resources: Jeong Jae Lee.

Validation: Jeong Jae Lee.

Visualization: Jeong Jae Lee.

Writing – original draft: Jeong Jae Lee, Sujin Kim.

Writing – review & editing: Jeong Jae Lee, Sujin Kim.