A Method for Predicting the Main Indicators of Cardiopulmonary Stress Testing for Patients with Chronic Heart Failure

A Method for Predicting the Main Indicators of Cardiopulmonary Stress Testing for Abstract Introduction. Cardiopulmonary stress testing provides significant diagnostic and prognostic information on the condition of patients with cardiovascular and pulmonary diseases. However, the final stage of such tests requires significant physical effort from the patient, which may aggravate the existing cardiovascular or pulmonary pathology. A possible solution consists in the development of methods for calculating the final-stage testing parameters on the basis of the data obtained at the initial test stages. Aim. To develop a method for calculating the values of peak heart rate and peak oxygen consumption for patients with chronic heart failure at the end of a cardiopulmonary stress test on the basis of the data obtained at the initial test stages. Materials and methods. 149 anonymized rhythmograms and oxygen consumption records for chronic heart failure patients were used. The patients underwent a cardiopulmonary stress test using a bicycle ergometer. The load was raised gradually by increasing the load power by 10 W following each 1-minute stage. Results. Following an analysis of the data obtained, a method for evaluating the maximum values of heart rate and oxygen consumption in patients with chronic heart failure was developed. Conclusion. When calculating peak heart rate values, the relative error did not exceed 10%, which renders this method feasible for practical application. When calculating the peak oxygen consumption after completing 70% of the load protocol, the relative error did not exceed 20% in most cases. Further research should be aimed at im-proving the accuracy of the method for use in medical applications testing the performance of the cardiopulmonary system. Main Indicators

Introduction. The growing incidence of cardiovascular pathologies among the human population requires the development of non-invasive diagnostic methods aimed at early detection and prevention of such conditions. Load stress testing ( Fig. 1) [1] is most frequently used as a non-invasive and reproducible method for diagnosing the performance of the cardiovascular system and predicting treatment outcomes of cardiovascular diseases [2]. The system of load stress testing includes equipment for performing physical exercise of various intensity (a bicycle ergometer or a treadmill), sensors for recording human biological signals (e.g., electrocardiogram, blood pressure, etc.) and computing devices for processing the data using software applications [3].
Cardiopulmonary stress testing (CPST) refers to load stress testing with an additional measurement of gas exchange parameters at rest, during exercise and during recovery. As a rule, the following main indicators are measured: the volume of oxygen consumed   V ventilation parameters, as well as the electrocardiographic parameters, such as heart rate (HR) and blood pressure. Fig. 1, a exemplifies a system for simultaneous monitoring of respiration, blood pressure and pulse during exercise. CPST is a reliable diagnostic tool that provides significant clinical and prognostic information about the condition of patients with cardiovascular and pulmonary diseases, thus allowing treatment outcomes to be predicted [4,5].
When conducting clinical load testing, the selection of its modality and protocol is of decisive importance ( Fig. 1, b). Existing protocols typically include an initial warm-up period followed by a progressive dosed load and a recovery period after maximum effort.
The selection of a workload protocol depends on the purpose of testing. The most frequently used protocol is that based on a stepwise increase of the load [3,6,7]. The as-obtained data is continuously displayed on a monitor and recorded in the device memory for further processing (Fig. 1, c).
A serious problem in the application of CPST consists in the increased risk of overload at maximal exercise for some patients, which may lead to aggravating the patient's physical condition. This is why CPST is performed only at medical institutions having intensive care units. A possible solution to this problem is the development of methods for calculating (predicting) the functional state of patients at the end stage of the load protocol based on the data registered at initial test stages.
This article proposes an approach, according to which only the initial SPST cycle, rather the entire load protocol, is realized. The parameters obtained at the initial stages are further used to calculate the results of the final, most energy-consuming phase of peak VO2 SPST. Thus, it becomes possible to reduce the risk of overburdening the patient by decreasing the duration of the load protocol without losing diagnostically important information. The task of predicting some CPST indicators was considered in previous research. Thus, [8][9][10][11] investigated the possibility of predicting HR at peak loads in patients with cardiovascular pathologies using linear regression equations. A similar approach was applied in [12-14] to obtain the peak oxygen consumption ( V was proposed in [15]. However, in all the aforementioned works, the main SPST parameters were evaluated on the basis of the data obtained during the resting state, not taking into account the information received at the initial stages of the load protocol. Thus, the dynamic properties of biological signals during load testing were actually ignored.
In this work, we describe a method for determining the peak HR and in patients with chronic heart failure (CHF) at the end of a cardiorespiratory load stress test based on the results obtained at initial test stages. Materials and methods. The research material comprised 149 anonymized records of rhythmograms and oxygen consumption variations in CHF patients (97 men and 52 women). All the patients underwent CPST on a bicycle ergometer using a stepwise load protocol: the load power was raised by 10 W after each 1-minute stage. The testing was conducted at the Almazov National Medical Research Centre.
Symptoms that resulted in test termination included: 1) pain; 2) fatigue; 3) critical changes in the ECG, blood pressure, oxygen saturation (these were continuously monitored by medical personnel).
Following an analysis of the data obtained, a method for calculating peak HR and  where N is the number of analyzed rhythmograms; peak HR is the true peak heart rate.
The as-obtained coefficients for various groups of CHF patients are summarized in Table. It can be seen that the k coefficients included in the regression expression (1) vary significantly depending on the method of group formation.
On the basis of the obtained peak HR value

HR t HR
 an estimate of the duration of the load interval is found: Fig. 2  Results. Fig. 3 shows the range of the relative error when using the proposed method for calculating HR at maximal exercise (1) by the formula where peak HR is the empirical (true) HR value at a peak load; peak HR  is the HR estimate at a peak load obtained using (1). It can be seen from Fig. 3 that, when estimating peak HR values, the relative error does not exceed 10% in most cases. In addition, the use of the proposed method for assessing CPST parameters for different groups of patients gives similar results when combining the groups. Fig. 4 exemplifies the results of approximating changes in the HR during exercise by quadratic dependence for two different patients. The vertical and horizontal axes shows the HR values and the measurement intervals i. Fig. 4, c shows the range of the relative error when determining HR at maximal exercise using a quadratic model determined by analogy with (4).
As shown in Fig. 4, the quadratic model accurately describes the dependence of HR changes across on the load interval. The relative error in estimating HR at a peak load using a quadratic model does not exceed 2% in the vast majority of cases. This result confirms the adequacy of the applied quadratic model of HR changes across the load interval.  is not known, the dependence of the relative error on the load duration is shown in Fig. 6, a. In this case, the duration was predicted on the basis of (2) and (3) as a fraction of the estimate max . t The use of this estimate leads to an increase in the relative error range when estimating the 2 O peak V value (Fig. 6, b). However, under a 70% completion of the CPST protocol, the relative error of the method does not exceed 20% in most cases.
It should be noted that the magnitude of the relative error is determined by several factors associated with the process of recording biological signals. Thus, the registration of electrocardiograms during CPST involves noises associated with the inevitable motor activity of the patient, which affect the quality of generated rhythmograms (false detection or omission of cardiac signals [16,17]

Conclusions.
As a result of the study, a method was proposed for reducing the duration of cardiopulmonary stress testing by means of calculating its final parameters on the basis of data obtained at the initial test stages. This approach allows the risk of exercise intolerance and respective negative complications to be minimized. An empirical linear regression equation was obtained for estimating peak heart rate values. It was found that the coefficients of the regression equation varied significantly depending on the patient gender. When estimating peak heart rate values, the relative error did not exceed 10% in most cases, which renders the method feasible for practical application. For patients suffering from chronic heart failure, the use of quadratic dependence in describing heart rate changes across the load interval of cardiopulmonary stress testing produces an adequate rhythmogram model. A linear regression equation was empirically obtained for assessing peak oxygen consumption 2 O peak .

V
It was found that, after completing 70% of the load protocol, the relative error in estimating the peak oxygen consumption did not exceed 20% in most cases. The magnitude of this error is associated with the process of registering biological signals. Thus, additional research is needed to improve the accuracy of the proposed method for use in medical applications testing the performance of the cardiovascular system.

Authors' contribution
Alexander S. Krasichkov, management of the work and preparation of the paper text. Eliachim Mbazumutima, analysis of the heart rate data. Fabian Shikama, analysis of the oxygen consumption data. Evgeny M. Nifontov, statement of the problem and discussion of the results.