This study retrospectively recruited 523 consecutive patients that underwent diagnostic cardiac catheterization with a catheter-tipped micromanometer to evaluate coronary artery disease, from April 2001 to December 2010. Of these patients, we enrolled 398 eligible patients that met our inclusion and exclusion criteria. The inclusion criteria included age, 20 years or older; status, no experience of hospitalization due to symptomatic HF; or no change in baseline drug therapy during the 1 month prior to enrolment. The exclusion criteria included LVEF, less than 40%; serum creatinine > 2.5 mg/dL or on haemodialysis; acute coronary syndrome requiring urgent revascularization or severe coronary artery stenosis needing early revascularization within 30 days; pacing controlled by factors other than sinus rhythm, including a pacemaker rhythm; haemodynamically significant aortic or mitral valve disease; hypertrophic cardiomyopathy; acute myocardial infarction within the past 3 months; percutaneous coronary intervention or open-heart surgery within the past 3 months; or any serious non-cardiovascular disease, including malignancy. At the time patients underwent cardiac catheterization for this study, we collected data on demographics, laboratory values, cardiac function parameters, and medications. The study endpoint was a composite of unplanned hospital admission for acute decompensated HF, and cardiovascular death. The indication for hospitalization due to acute decompensated HF was dependent on the discretion of each outpatient doctor. No one of such doctors participated in the analysis of obtained data or writing the current paper. Cardiovascular death was defined as death from congestive HF deterioration, coronary artery disease, cardiac arrest, cardiac arrhythmia, myocardial infarction, stroke, or sudden death.

According to the procedure that we previously published [9, 10], LV pressure was measured with a catheter-tipped micromanometer (SPC-454D, Millar Instrument Co., Houston, Texas) and recorded with a polygraph system (RMC-2000 or RMC-3000, Nihon Kohden Inc., Tokyo, Japan). We also recorded LV pressure with a digital data recorder (NR-2000, Keyence, Osaka, Japan), at a sampling interval 2 ms, before injecting contrast material into the LV or coronary artery. From the recorded pressure waves, we determined the peak positive and negative first derivatives of LV pressure (± dP/dt). Furthermore, we calculated a time constant of LV pressure decay during isovolumic relaxation (Tp). Then, we derived the IFLSAF from the LV pressure and dP/dt relationship (phase loop plot), based on the assumptions and procedures previously described by Sugawara et al. [11]. Briefly, the Tp was defined as the negative inverse slope of the line with the best linear fit to the LV pressure and dP/dt relationship, in the phase between the peak -dP/dt and the minimum LV pressure from which the first several data points after peak -dP/dt and those before the minimum LV pressure were excluded. In the Sugawara method, the best linear-fit line was determined with the least squares method and expressed as: -kP + C (where k > 0; and k and C were constants to be estimated). Thus, the Tp was given by 1/k. Sugawara et al. hypothesized that the Tp might be more independent on the LV contraction phase and it might be more sensitive to the deterioration of LV relaxation than the time constant proposed by Weiss et al. [12]. Furthermore, the IFLSAF was defined as a pressure decay, augmented by the effect of the momentum of blood flowing out of the LV during late systole. The area shown in red divided by the vertical distance between (P₀, 0) and point X is equal to the amount of pressure decay augmented by the effect of the momentum of blood (Fig. 1a). We previously defined an IFLSAF ≥ 0.5 mmHg as a significant threshold with prognostic efficacy in patients with coronary artery disease and LVEF ≥ 50% [9, 10]. In the present study, we defined maintenance of IFLSAF as IFLSAF ≥ 0.5 mmHg as in the prior study. Immediately after measuring left-sided pressure with a catheter-tipped micromanometer and right-sided pressure with a fluid-filled system, we also measured cardiac output with the thermodilution method. Then, cardiac output was used to calculate the cardiac index (cardiac output normalized by body size). In addition, we evaluated the effective arterial elastance, defined as the systolic aortic pressure divided by stroke volume. Next, we performed biplane contrast left ventriculography to determine the end-diastolic and end-systolic LV volumes and calculated the LVEF with the method described by Chapman et al. [13]. At the end of cardiac catheterization, we assessed coronary artery disease.

Besides, we collected the echocardiographic findings of study patients which were measured within 2 days prior to their cardiac catheterization study. Left atrial (LA) diameter was adopted as the parameter representing LA size. LV mass was calculated by the Devereux formula [14] and normalized by the body surface area of each patient to be expressed as LV mass index (LVMI). These two parameters were also included in the cardiac function parameters of this study.

Continuous data are presented as the mean ± SD, and categorical variables are summarized as the frequency and percentage. We used Cox proportional-hazards models and a stepwise procedure to evaluate the contributions of clinical variables, including cardiac function parameters, to the relative hazard of experiencing the composite endpoint of this study. We adopted two types of models to assess the contribution of IFLSAF: In model 1, all clinical variables were included; in model 2, the pressure parameters and brain natriuretic peptide (BNP) levels were excluded from the variables used in model 1. We used the model 2 to focus on the IFLSAF and other cardiac function parameters. A p value < 0.05 was considered statistically significant. We defined the day of the cardiac catheterization study as the time of patient enrolment in the study. The duration of observation in our prognosis study started at the time of enrolment and ended either at the occurrence of a terminal endpoint or at the last censoring, when the remaining patients had survived the follow-up period without any adverse events. Besides, when the study patients had no experience of concomitant HF but needed percutaneous coronary revascularization or surgical coronary artery bypass grafting, these patients were defined as censored cases at the time of coronary revascularization and the duration between the enrollment and the time of coronary interventions was adopted as the observation period for them. Furthermore, to clarify the extent of the predictive power of the IFLSAF for the endpoint, we performed a time-dependent receiver operating characteristic (ROC) curve analysis, as proposed by Heagerty et al. [15], to determine whether the IFLSAF could predict adverse events in various subsets of patients with different ranges of LVEF (lower limit varied from 40 to 70%; upper limit varied from 50 to 80%). The mean and standard error of the area under the ROC curve was calculated with 1000 datasets, created with the bootstrap resampling method, for each patient subset. In addition, we performed a regular ROC curve analysis to assess the best threshold LVEF value for discriminating whether the LV maintained the IFLSAF. Finally, we assessed correlations using Spearman's correlation coefficient by ranks between the IFLSAF and several clinical parameters, including age, hemoglobin levels, BNP levels, and cardiac pressure parameters, including the mean right atrial pressure (RAP), the mean pulmonary artery pressure (PAP), the mean pulmonary capillary wedge pressure (PCWP), and the mean aortic pressure (AP). We also assessed cardiac function parameters, including the LVEF, the LVMI, the cardiac index, the ± dP/dt, the Tp, and the effective arterial elastance, to clarify the clinical features of the IFLSAF.

All statistical analyses were performed with SPSS version 23.0 software (SPSS Japan Inc., Tokyo). This study was conducted in full accordance with the Declaration of Helsinki, and it received approval from the Institutional Review Boards and Ethics Committees of the Nagoya City University Graduate School of Medical Sciences, Japan.

Of the 523 consecutive patients that underwent diagnostic cardiac catheterization, 125 patients were excluded from the present study, for the reasons described in the method. (Fig. 2) Among 398 patients who were enrolled in this study, 47 patients needed percutaneous coronary revascularization and 2 patients underwent surgical coronary artery bypass grafting during the observation period. All of them did not experience concomitant HF. The characteristics of patients enrolled in this study are shown on the left side of Table 1. The mean age of all patients was 66.9 years, and 96 patients (24.1%) were female. The mean LVEF value was 66.8% and the median BNP level was in the normal range (16.6 pg/ml; interquartile range: 8.5 to 38.6 pg/ml).

In the current study, 14 cardiovascular deaths and 17 hospitalizations for HF were documented during the follow-up period (median follow-up period: 2433.5 days; interquartile range: 1523.0 to 3387.5 days). We analysed the contribution of each parameter to the end point with two multivariate Cox proportional-hazards models (Table 1). When all parameters were included (model 1), the BNP level and the LVMI displayed a significant predictive value of adverse events (log BNP; hazard ratio (HR): 2.847, 95% confidence interval (CI) 1.652–4.906, p < 0.001, LVMI; HR: 1.029, 95% CI 1.002–1.056, p = 0.004, respectively). In model 2, which lacked the BNP level, intracardiac pressure data, and the aortic pressure value, we identified two significant predictors of adverse events; the loss of IFLSAF (HR: 7.798, 95% CI 2.174–27.969; p = 0.002) and the LVMI (HR: 1.031, 95% CI 1.007–1.056, p = 0.012).

Figure 3 is a two-dimensional heat map representation of the predictive power of IFLSAF for the end-point. Each cell represents a subset of patients with the indicated range of LVEF values, and the predictive power is represented with colour: higher power is represented with a darker colour. This analysis demonstrated that maintained LV contractile performance, reflected by the maintenance of IFLSAF, was a highly reliable prognostic indicator (area under the curve ≥ 0.9) in patients with LVEF in the range of 48 to 67%. Furthermore, the ROC curve analysis (Fig. 4) demonstrated that the best threshold LVEF value was 58% for discriminating whether the LV maintained the IFLSAF, with 85.4% sensitivity and 46.7% specificity.

We performed correlation analyses to examine the association between the IFLSAF and age, hemoglobin levels, BNP levels, the effective arterial elastance, the cardiac pressure parameters, as well as other cardiac function parameters shown in Table 1 (Fig. 5). We found that the IFLSAF was strongly correlated with the LVMI, the LVEF level, the peak -dP/dt, and the BNP level (LVMI, r =  − 0.390, p < 0.001; LVEF: r = 0.429, p < 0.001; -dP/dt: r =  − 0.495, p < 0.001; and log BNP: r =  − 0.358, p < 0.001, respectively). In contrast, the hemoglobin level, the peak + dP/dt, and the effective arterial elastance showed significant, but relatively poor correlations with the IFLSAF (hemoglobin: r = 0.131, p = 0.010; + dP/dt: r = 0.197, p < 0.001; effective arterial elastance: r =  − 0.181, p = 0.016, respectively). We found no significant correlation between the IFLSAF and the cardiac index, Tp, or the cardiac pressure parameters.