An Index for Evaluating Exercise Capacity Improvement After Cardiac Rehabilitation in Patients After Myocardial Infarction : Journal of Cardiovascular Nursing

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An Index for Evaluating Exercise Capacity Improvement After Cardiac Rehabilitation in Patients After Myocardial Infarction

Nemati, Sepehr MD; Yavari, Tahereh MD; Tafti, Fahimeh MD; Hooshanginezhad, Zahra MD; Mohammadi, Tanya

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The Journal of Cardiovascular Nursing ():10.1097/JCN.0000000000000982, March 8, 2023. | DOI: 10.1097/JCN.0000000000000982
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Exercise intolerance is considered a predictor of poor outcomes in patients with cardiovascular disease.1,2 Cardiac rehabilitation plays an important role in caring for individuals with cardiovascular disease. The existing rehabilitation programs are not the same; however, the use of an exercise pretest and posttest and an analysis of the outcomes have been recommended.3 Meanwhile, there is no consensus on how to evaluate the effects of cardiac rehabilitation programs.4

Because of providing the most accurate, reliable, and reproducible information on exercise intolerance, cardiopulmonary exercise testing (CPX) is frequently used for evaluating exercise capacity.5,6 Assessment of peak oxygen consumption (peak VO2) yielded by CPX plays the main role in the assessment of exercise capacity.7,8 Reduced peak VO2 is associated with poor cardiovascular outcomes.2,9 A large number of researchers have focused on estimates of exercise tolerance in patients with heart failure.10–13 However, findings on the evaluation of exercise capacity after acute myocardial infarction (AMI) are still insufficient.2

Nevertheless, commercially available CPX units record a variety of outcomes including exercise time and workload, blood pressure and heart rate responses, and gas analyses for oxygen and carbon dioxide at rest and during exercise, among others.5 Moreover, attempts have been made to enrich CPX information with data on cardiac volumes and indices using stress echocardiography (SE).6,8,14–17 The large number of variables measured by CPX-SE allows profiling patients individually.18,19 Meanwhile, the development of treatment strategies relies on data-driven stratification regarding exercise capacity improvement.20 This leads to the challenging problem of finding patterns in high-dimensional data with correlated features. Typically, researchers investigate changes in clinical features after a rehabilitation program separately in subgroups of patients and use peak VO2 for defining success.2,14,15,18,20,21 To our knowledge, there is no study on identifying groups of patients based on response to treatment among individuals undergoing cardiac rehabilitation after an AMI.

Multiple cardiac and peripheral responses to dynamic exercise are used to evaluate exercise capacity in cardiovascular patients.14 Heart rate response, arteriovenous oxygen difference, early diastolic myocardial velocity, oxygen uptake, and left ventricular ejection fraction are examples of the proposed predictors for the success of cardiac rehabilitation programs.18 We conducted this study to investigate relationships among predictors of improvement in exercise capacity after cardiac rehabilitation programs in patients after AMI. We also sought to increase the accuracy of identifying patients' response to treatment. This would help to stratify patients regarding the efficacy of rehabilitation using a subset of CPX-SE outcomes. An accurate method for measuring response to treatment is important in designing efficient rehabilitation programs, improving survival, and lowering the likelihood of rehospitalization in post-MI patients.2,15,20 Our hypothesis was that patients could be clustered regarding the likelihood of progress in exercise tolerance based on CPX-SE measurements.


Design and Setting

We carried out a secondary analysis of data from a cohort of patients who experienced AMI (Grochowski Hospital, Warsaw, Poland). Smarz et al18 recruited individuals older than 18 years treated for the first AMI. Patients underwent cardiac rehabilitation between October 2015 and January 2019 and were assessed using CPX-SE before and after the intervention. They aimed to investigate the mechanisms of exercise capacity improvement after cardiac rehabilitation. A long list of exclusion criteria was established to prevent confounding the results. Specifically, individuals did not enter the study if they had left ventricular ejection fraction < 40% at least 4 weeks after AMI, congestive heart failure, anemia (hemoglobin < 12 g/dL), pulmonary limitations of exercise, and poor echocardiographic acoustic window. Response to treatment was defined as a rise in peak VO2 ≥ 1 mL/kg/min. Responders (N = 30) experienced 27% increase (P < .001), whereas nonresponders (N = 11) showed a 5% decrease in peak VO2. They concluded that cardiac rehabilitation improves exercise capacity in patients with preserved left ventricular ejection fraction after AMI and that the improvement is associated with an increased heart rate and peripheral oxygen extraction during exercise. We extended Smarz et al study results with principal component and cluster analyses and tried to extract further clinical implications from the data. Our study was carried out following the Declaration of Helsinki.

Ethical Considerations

Smarz et al's18 study was approved by the Institutional Ethics Committee of the Centre of Postgraduate Medical Education Bioethical Committee, Warsaw, Poland (protocol code: 16/PB/2015, approved on February 25, 2015). We did not carry out measurements on participants, nor did we had access to identifying information. This is a secondary analysis of open-access anonymized data.

Data Availability

The data set is publicly accessible at

Protocols and Measurements

The study protocols and measurements have been described elsewhere in detail.15,18 In summary, patients underwent cardiac rehabilitation either as a daily stationary program for 3 weeks or as an ambulatory program 3 times weekly, lasting 2 months. The program was based on endurance exercise and inspiratory muscle training. Maximal heart rate was used as the indicator of aerobic exercise intensity. Each training session included warming up, cycling for 60 minutes, and cooling down periods. Later in the process, a physician decided to increase training either 50% to 60% or 60% to 80% of the heart rate reserve for each patient. The CPX and SE were carried out at the same time both at rest and during exercise, and the results were interpreted by a cardiologist according to current guidelines.15,18,23–25 Patients were instructed to exercise at maximal effort. For each individual, peak VO2 (mL/kg/min) was averaged from the maximal 20 seconds of exercise. Stroke volume was calculated as 0.785 × squared left ventricular outflow tract diameter × velocity time integral. The arteriovenous oxygen difference was calculated according to the Fick equation.14


We performed a cluster analysis of the data using changed values detected with CPX-SE. The clustering tendency of the data was assessed with Hopkins statistic. The value of Hopkins statistic > 0.5 suggests that the data set has a significant clustering tendency. We carried out a hierarchical clustering with the Euclidean distance and the ward method of building trees and depicted a dendrogram to show the results. We also carried out a principal component analysis. The principal component analysis is used to extract information from multivariate data by representing linear combinations of the original variables. The idea is to identify directions along which the variation in data is maximal. The percentages of explained variances for each principal component were illustrated with a scree plot. The quality of representation for variables was plotted on the factor map using the squared coordinates (cos2). Then, we selected the most representative variables on the first component and calculated a composite index. In addition, the contribution of individuals to the first 2 principal components was illustrated with scatterplots. We represented individuals by their projections on and variables by their correlation with a principal component using biplots. The performance of the composite index in identifying patient clusters was compared with the definition of response to cardiac rehabilitation in Smarz et al's article. Results are presented as mean (SD) or median [interquartile range] for continuous variables and as absolute numbers (%) for categorical data. The level of significance was set at a 2-tailed α = .05. All data analyses were performed with R version 4.0.2 for Windows. R is a well-known open-source environment for computing and graphics (R Foundation for Statistical Computing, Vienna, Austria;



In total, the data set included 41 patients (Table 1). Twenty individuals (48.8%) underwent inpatient cardiac rehabilitation. Only 0.6% of the data was missing. We imputed missing data a single time using predictive mean matching with the maximum iteration of 5.

TABLE 1 - Patients' Demographic Characteristics
Characteristics n (%)
Age, mean (SD), y 57.5 (10.1)
BMI, mean (SD), kg/m2 27.2 (4.2)
Hemoglobin, mean (SD), g/dL 14.0 (1.1)
Creatinine clearance, mean (SD), mL/min 110.0 (32.0)
Male sex 28 (68.0)
Current smoking 23 (56.1)
Hypertension 23 (56.1)
Hyperlipidemia 34 (82.9)
DM/impaired glucose tolerance 15 (36.6)
STEMI 16 (39.0)
NSTEMI 23 (56.1)
Physical activity before MI
 Small 9 (22)
 Moderate 22 (54)
 High 10 (24)
Abbreviations: BMI, body mass index; DM, diabetes mellitus; MI, myocardial infarction; NSTEMI, acute myocardial infarction without ST-segment elevation; STEMI, acute myocardial infarction with ST-segment elevation.


On the basis of Smarz et al's study results, we selected all features with significant or near-significant change (P ≤ .078) assessed by CPX-ES before and after the cardiac rehabilitation program. Then, we calculated the difference and carried out a cluster analysis of the change values. The Hopkins statistic was 0.625, showing a significant clustering tendency of the data. The hierarchical clustering algorithm identified 2 distinct clusters among patients using the scaled difference values (Figure 1A). The average proportion of nonoverlap and the average distance between means were 0.002 and 0.024, respectively. These small values indicated stable clustering outcomes. We used the Ward method and Euclidean distance to build the tree hierarchy. Clusters 1 and 2 included 17 and 24 patients, respectively. Figure 1B was depicted using cluster membership. It shows that the 2 clusters are relatively well identified. Cluster 2 represents patients with a higher change in exercise capacity. The clusters were significantly different in the proportion of responders (peak VO2 ≥ 1 mL/kg/min), that is, 47% versus 92% in clusters 1 and 2, respectively, χ2(1) = 7.942, P = .005.

A, Dendrogram for hierarchical clustering of patients. B, Representation of the individuals on the first 2 principal components using clustered data. The colored concentration ellipses represent patients' clusters.

Principal Component Analysis

Figure 2A shows the scree plot of the 8 components with an eigenvalue ≥ 1 representing a cumulative 78.8% of the total variance. The first component alone explained 28.6% of the variance. On the basis of the scree plot, we considered the first 5 components for further interpretations. Figure 2B enumerates the included variables and illustrates their quality of representation using the squared coordinates of variables on the first 5 principal components (cos2). We selected O2 uptake and CO2 output at peak exercise (liters per minute), minute ventilation at peak (liters per minute), load achieved at peak exercise (watts), and exercise time (seconds) from the first component with the coordinates of 0.86, 0.86, 0.83, 0.81, and 0.78, respectively. The scores showed that the variables are all important in describing the change in exercise capacity. Meanwhile, the scores are roughly rounded to 0.8. Therefore, instead of a weighted mean, we proposed a composite index (we call it the improvement index thereafter) as the arithmetic mean of the selected variables.

A, The scree plot of the principal components with an eigenvalue ≥ 1. B, The quality of representation for variables on each principal component using the squared coordinates of variables (cos2).

Peak VO2 vs Improvement Index

Figure 3 shows the biplot of the 5 selected variables, improvement index, and individuals colored according to their cluster membership. Each solid circle represents an individual, and the size of each circle corresponds to the patient's improvement index. The arrows show the correlation between a variable and the principal components. Well-represented features are farther from the origin. The patient on the same side of a given variable has a high value and the individual on the opposite side has a low value for that particular variable. Oxygen uptake and carbon dioxide output at peak exercise, minute ventilation at peak, load achieved at peak exercise, and exercise time plausibly point to the area of cluster 2. However, the improvement index is the best-representing feature in expressing the program's effect than the other 5 variables. The area under the receiver operating characteristic curve for the improvement index was larger than the area for O2 uptake at peak (Figure 4). There was a significant difference in the improvement index between nonresponders and responders (peak VO2 ≥ 1 mL/kg/min) with the mean (SD) of −0.86 (0.76) and 0.32 (0.66), respectively, t15.748 = −4.508, P < .001.

Biplot of individuals and selected variables on the first 2 principal components using clustered data. The colored concentration ellipses represent patients' clusters. The size of each point corresponds to the patient's improvement index. VO2 pk, oxygen uptake at peak exercise; VCO2 pk, carbon dioxide output at peak exercise; Vent pk, minute ventilation at peak; Load max, load achieved at peak exercise; Excerc t, exercise time.
Receiver operating characteristic curve for the improvement index (impr idx) and O2 uptake at peak (pk).

Response to Treatment vs Improvement Index Cut Point

Smarz et al defined response to rehabilitation as a rise in peak VO2 ≥ 1 mL/kg/min. To compare the diagnostic performance of response to rehabilitation in Smarz et al's study with the improvement index in recognizing patient clusters, we selected a cut point for the index. The optimal cut point of 0.12 for the improvement index separated 2 groups of 21 and 20 patients as rehabilitation failure and success, respectively. Table 2 shows the performance of both instruments for identifying the patients' clusters. The improvement index was remarkably more accurate and sensitive with a higher negative predicted value, whereas Smarz et al's response to rehabilitation was only 8% more specific. Overall, the performance of the improvement index was far better than the criterion of peak VO2 ≥ 1 mL/kg/min, with a C-statistic of 91.7% and 72.3%, respectively.

TABLE 2 - Comparison of the 2 Criteria for Response to Rehabilitation, Peak VO2 ≥ 1 mL/kg/min, and the Improvement Index ≥ 0.12 for Identifying Patient Clusters
Performance Criteria
Smarz's Response to Rehabilitation, VO2 ≥ 1 mL/kg/min Improvement Index ≥ 0.12
Observed Observed
Failure Success Failure Success
Predicted Failure 9 2 17 4
Success 8 22 0 20
Accuracy (95% CI), % 75.6 (59.7, 87.6) 90.2 (76.9, 97.3)
Sensitivity, % 52.9 100.0
Specificity, % 91.6 83.3
Positive predicted value, % 81.8 80.9
Negative predicted value, % 73.3 100.0
C-statistic, % 72.3 91.7
Abbreviation: CI, confidence interval.


We assessed the change values extracted from CPX-SE, clustered patients, and investigated relations among predictors of improvement in exercise capacity after cardiac rehabilitation programs in patients after AMI. Our clustering algorithm showed the existence of 2 distinct clusters among patients. The clusters were significantly different in response to the rehabilitation program. Moreover, the principal component analysis enabled us to propose a composite index of improvement in exercise tolerance. This study showed that an index composed of informative variables would outperform mere peak VO2 ≥ 1 mL/kg/min in discerning clusters of responsive versus unresponsive patients. The new composite index is the average of scaled oxygen uptake at peak exercise, carbon dioxide output at peak exercise, minute ventilation at peak, load achieved at peak exercise, and exercise time. Instruments can be programmed to automatically calculate the improvement composite index. To the best of our knowledge, there is no other study similar to this in the algorithmic application of cluster and principal component analyses, and calculating an index for testing the effectiveness of cardiac rehabilitation programs in patients after AMI.

Exercise intolerance is defined by an abnormally low VO2 at maximal exercise.7 According to the Fick equation, oxygen uptake depends on arterial and mixed venous oxygen contents, heart rate, and stroke volume.7 In healthy individuals, the VO2 plateau at near maximal exercise is used to estimate maximum VO2. In practice, a discernible plateau is not reached unless symptom limitation of exercise occurs.7 Consequently, the peak VO2 serves as a surrogate for maximal VO2.7 Moreover, pulmonary, musculoskeletal, and hematological conditions affect maximal VO2 by changing arterial or mixed venous oxygen content.6,7 Research suggested that calculated arterial-venous oxygen content difference is also a predictor of peak VO2 in patients with heart failure.8,12 This signifies the effects of noncardiac contributors on exercise intolerance. In addition, peak VO2 (mL/kg/min) is averaged from the maximal 20 seconds of exercise.18 In summary, the assessment of exercise intolerance is open to the inexactness of estimation.

In Smarz et al's18 study, 27% of patients did not show improvement in their exercise capacity after the rehabilitation program. However, our study showed that approximately half of the patients failed to meaningfully improve exercise capacity after cardiac rehabilitation. The difference might be due to the application of the more accurate instrument (the improvement index) for justifying the improvement. Our results were more compatible with the findings of a study conducted by Nichols et al.26 They compared 48 patients who underwent cardiac rehabilitation with 22 controls in a variety of features and reported that the rehabilitation program is unlikely to improve long-term physiological outcomes. However, in another study, Witvrouwen et al27 investigated predictors of response to exercise training in patients with coronary artery disease. They also used peak VO2 < 1 mL/kg/min as the definition of response to treatment and estimated a failure rate of 14%. Of course, the lack of standards in designing rehabilitation programs is another source of ambiguity.3,4 Patients' comorbidities and personal characteristics or heritable factors (eg, changes in hemodynamic response and skeletal muscle characteristics) contribute to the variability of results as well.28 In addition, current guidelines for comprehensive cardiovascular rehabilitation includes parallel modification of behavioral variables such as nutritional counseling, smoking cessation, lowering alcohol consumption, patient education, psychosocial support, and lifestyle interventions for patients after AMI.29 Moreover, the mechanism of the improvement seems to be different in patients with or without preserved ejection fraction.30 Overall, we believe that the notion of “improvement” in exercise capacity needs to be revisited by considering a set of informative features instead of simplifying the concept by measuring a single variable.

Quantification of cardiac chamber size and function plays an important role in the diagnostic workup of patients with heart disease. Overall, SE is the most commonly used noninvasive technique for imaging and quantification of cardiac structure and function.31 In addition to its availability and portability, SE provides real-time images of the beating heart. Study authors suggested that CPX combined with SE allows for better evaluation of effort intolerance.8,14,15 Our goal in our study was not to evaluate the advantages of combining CPX and SE. We agree with the application of CPX-SE because it plausibly provides more information for individualized decision making. Meanwhile, the most informative diagnostic features in our study were based on CPX evaluations.


A limitation of our study was the small sample size. In Smarz et al's study, there were no significant differences between responders (N = 30) and nonresponders (N = 11) in patients' characteristics and clinical features. A large enough sample size allows cluster profiling by calculating adjusted odds ratios and provides better discriminating power. Meanwhile, our cluster analysis revealed 2 more balanced groups within the study sample (24 vs 17 patients). In a guideline of appropriate sample size for various statistical techniques, it was reported that there is no generally accepted rule of thumb concerning minimum sample sizes for cluster analysis.32 However, in a recent article on statistical power for cluster analysis in biomedical research, Dalmaijer et al33 investigated sample size for different algorithms including hierarchical clustering with Ward linkage. They showed that sufficient statistical power is achieved with N = 20 per subgroup. This is near to the size of our smaller cluster (N = 17). Moreover, we had a large Hopkins statistic, well-separated clusters in the visualizations, small stability metrics, and a highly significant difference in the improvement index between the 2 clusters. These suggested that the relatively small size of the study sample did not probably affect the clustering results.

In addition, time-variant outcome data enable us to compare the prognostic value of our composite index with other rehabilitation response criteria.2 A large longitudinal study is required for developing reliable prognostic prediction models. This gives the opportunity to externally validate the improvement index for the assessment of cardiac rehabilitation success, to investigate whether it could predict the survival of patients similar to peak VO2, and to provide stronger evidence that supports the practicality of the index. The diversity of methods used to conduct and investigate exercise programs implies that assessment protocols should still be improved to optimize patient rehabilitation.4,26 The establishment of the improvement index would help in improving or comparing different cardiac rehabilitation programs as well.4


Our study showed that, in patients after AMI, the assessment of exercise tolerance after cardiac rehabilitation programs is more accurate when incorporating more information into the existing models. Two patient clusters were identified with different responses to treatment. We introduced a composite index for the assessment of change in exercise capacity after rehabilitation programs in post-AMI patients. On the basis of the current definition of response to treatment (peak VO2 ≥ 1 mL/kg/min), the patient clusters were recognized as the nonresponder and responder groups. However, the composite index outperformed the current definition in identifying the 2 clusters. The index can be used in comparing different rehabilitation programs. Our study design could be used as a basis for the establishment of composite indices for patient evaluations. Longitudinal studies are required for prognostic assessment of our composite improvement index.

What’s New and Important

  • The effect of cardiac rehabilitation could be assessed more exactly.
  • Two patient clusters were identified with different responses to rehabilitation.
  • We proposed a composite index for the assessment of change in exercise capacity.
  • The new index outperformed current definitions in identifying responder patients.
  • The index can be used in comparing different rehabilitation programs.


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cardiac; cardiopulmonary; echocardiography; exercise; myocardial infarction; rehabilitation

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