Associations between Left Ventricular Cavity Size and Cardiac Function and Overload Determined by Natriuretic Peptide Levels and a Covariance Structure Analysis

The effects of left ventricular (LV) cavity size on cardiac function and overload have not yet been fully elucidated. We performed a covariance structure analysis and drew theoretical path models to clarify the effects of hemodynamic parameters on the stroke volume index (SVI) as a marker of cardiac function and on the plasma B-type natriuretic peptide (BNP) level as a marker of cardiac overload. We simultaneously measured various hemodynamic parameters and the BNP levels during cardiac catheterization in 1,715 inpatients of our institution. The current path models tested the validity of the Frank-Starling law in patients with heart failure using the SVI, the LV end-systolic volume index (LVESVI) and the LV end-diastolic volume index (LVEDVI). Using the BNP levels, the path models clearly demonstrated that LVESVI substantially augmented cardiac overload, whereas LVEDVI palliated this parameter. These volume indices exerted opposite effects on cardiac function and overload. These results advance the understanding of the relationships between LV cavity size and both cardiac function and overload and indicate the increasing importance of LV diastolic volume in heart failure and the utility of LVESVI as an important marker of cardiac remodeling for further relevant studies.

Concept and results of the proposed path model C. The next theoretical path model proposed is illustrated in Fig. 1 (lower). Path model C was drawn in a parallel manner with LVESVI and LVEDVI. The paths were drawn from the independent to the dependent variables with directional arrows for each regression model, i.e., from LVESVI and LVEDVI to SVI. The associations between the factors (LVESVI and LVEDVI) are illustrated with two-way arrows. The results of this statistical analysis are presented in Supplemental Table 4. A theoretical path model based on covariance structure analysis using two dependent variables in the same equation model was proposed. The final model produced the following regression weights after standardizing all of the variables: SVI was predicted by LVESVI (β: −0.724, 95% CI [−0.863, −0.569], P < 0.001) and LVEDVI (β: 0.727, 95% CI [0.569, 0.871], P < 0.001). We noted that LVESVI and LVEDVI were inversely and positively associated with SVI, respectively. We believe that this model dovetails with the Frank-Starling law.
Concept and results of the proposed path models D and E. Simple path models D and E were proposed as illustrated in Fig. 2 (upper and middle). The paths were drawn from the independent to the dependent variables with directional arrows that demonstrate each regression model. These models were based on whether LVESVI or LVEDVI causatively induced increases in the plasma BNP levels. The results of these statistical analyses are presented in Supplemental Tables 5 and 6. The simple path model for the confirmation factor analysis revealed that LVESVI (β: 0.501, 95% CI [0.465, 0.536], P < 0.001) and LVEDVI were causatively related to Log BNP (β: 0.414, 95% CI [0.374, 0.453], P < 0.001).  Concept and results of the proposed path model F. Next, the theoretical path model illustrated in Fig. 2 (lower) was proposed. The path model was drawn in a parallel manner with LVESVI and LVEDVI. The paths were drawn from the independent to the dependent variables with directional arrows that were used for each regression model, i.e., the models from LVESVI and LVEDVI to Log BNP. The association between the factors LVESVI and LVEDVI was indicated with two-way arrows. The results of this statistical analysis are presented in Supplemental Concept and results of the proposed path model G. The theoretical path model illustrated in Fig. 3 was proposed. LVEDP might stimulate increases in plasma BNP levels. Because LVESVI, LVEDVI, and LVEDP were found to confound each other in the simple regression analysis (Supplemental Table 1), path model "G" was drawn with LVESVI, LVEDVI, and LVEDP in a parallel manner. The paths were drawn from the independent to dependent variables with directional arrows for each regression model, i.e., from LVESVI, LVEDVI, and LVEDP to Log BNP. The associations between the pairs of the factors were linked by two-way arrows. The results of this statistical analysis are presented in Supplemental  Table 7). Additionally, we found that LVEDP was an additional factor that was associated with an increased Log BNP irrespective of LVESVI and LVEDVI.
Analyses of the other patient groups. We also performed the same statistical analyses with the patients from Groups II, III, and IV. We examined the effects of LVESVI and LVEDVI on SVI (path models H-J in Fig. 4; precise data are presented in Supplemental Tables 9, 10, and 11). The results were similar to those from Group I. We also examined the effects of LVESVI, LVEDVI, and LVEDP on Log BNP in the same manner. The proposed path models K-M are illustrated in Fig. 5, and the results are presented in Supplemental Tables 12, 13, and 14, respectively. The results were similar to those from Group I, except for one path from LVEDVI to Log BNP in Group III (path model L). Critical ratios of differences in the significance of the increases in Log BNP between LVESVI and LVEDP. Figure 3 (path model G) and Supplemental Table 8 demonstrate that LVESVI and LVEDP were significantly associated with increases in Log BNP. Finally, we compared the powers of the effects of LVESVI and LVEDP. The critical ratios of the differences between the parameters were examined using a matrix (the full AMOS matrix is not shown because of its size). The results revealed that compared to LVEDP, LVESVI was more strongly associated with Log BNP (P < 0.001).

Discussion
How can relationships between LV cavity size and cardiac function/overload be determined?. Among the hemodynamic factors that are commonly measured during cardiac catheterization, we proposed that LVESVI and LVEDVI are especially important in terms of cardiac performance because these factors directly determine the stroke volume. In the real world, the extent of LV volume enlargement differs between the systolic and diastolic phases in patients with heart failure. The detection of possible associations between LV cavity size and both cardiac function and overload is very difficult, but it is important for improving our understanding of the basic mechanism of heart failure. Naturally, the Frank-Starling law plays a pivotal role in maintaining cardiac output in patients with heart failure, and myocardial stress or overload should theoretically be related to cardiac volume in the systolic and/or diastolic phase.
Clear distinctions between LVESVI and LVEDVI in cardiac function/overload. In this study, we first planned to examine the effect of LVESVI and LVEDVI on SVI, that latter of which was used as a marker of cardiac function. The results of path models A and B both suggested that neither LVESVI nor LVEDVI significantly influenced SVI. Clear distinctions were drawn between the parameters in the next proposed path model (model C). It is important to note that LVESVI and LVEDVI were inversely and positively associated with SVI, respectively. We believe that these results are in absolute accordance with the Frank-Starling law and that increases in LVEDVI improve cardiac function. This study represents the first trial to successfully create an image of the Frank-Starling law on a path diagram based on covariance structure analysis. Next, we examined the possible association between LV cavity size and cardiac overload as estimated by the plasma BNP level. Path models D and E both suggested that both LVESVI and LVEDVI augmented Log BNP. We subsequently drew the theoretical path model F and successfully demonstrated that LVESVI directly caused increases in the plasma BNP levels and that LVEDVI adaptably reduced the plasma BNP levels. The outcome for  LVEDVI in path model F was the opposite of that observed in path model E. Importantly, an increase in LVEDVI decreased cardiac overload as estimated by the plasma BNP level.
In this study, the P-values were significant, but the R 2 values were very low in some of the models for the determination of the plasma BNP. As previously reported, there are actually many factors that are associated with plasma BNP, including aging, gender, renal dysfunction and obesity 16,17,19 . It is thus logical that the R 2 values were relatively small in this study design. Nonetheless, this analysis was planned to focus only on the effects of LVESVI and LVEDVI, and the other factors were essentially irrelevant. Moreover, this study clearly demonstrated that LVESVI is a major component in the determination of Log BNP and that LVEDVI palliated the Log BNP. Therefore, the contribution of SVI to plasma BNP logically cannot be too extensive. Indeed, understandably, the correlation of −0.137 between SVI and Log BNP was significant but relatively small (Supplemental Table 1). Figure 6 presents a graphical representation of the virtual cardiac shapes that occur during heart failure. Naturally, the patterns of enlargement in the systolic and diastolic phases differed between individuals; some patients' LV volume increased dramatically during the end-systolic phase compared with the end-diastolic phase and vice versa. The current study clearly demonstrated that enlargement in the LV systolic phase is harmful for both cardiac function and cardiac overload, whereas enlargement in the LV diastolic phase appears to be compensatory. As illustrated in Fig. 7, when some types of heart disease occur, the cavity size increases during the Analyses of the different study groups. The study population included patients with different underlying cardiac disorders. We considered it important to perform the same analyses in patients with different characteristics. We performed subgroup analyses of Groups II, III, and IV. Importantly, the results for the different groups were nearly identical, which means that the effects of LVESVI and LVEDVI on cardiac function and overload probably occur in patients with different underlying cardiac disorders. Naturally, this conjecture requires future testing with larger groups of patients with each underlying disorder.
Clarifying the role of LVESVI as a powerful indicator of an increase in plasma BNP levels. LVESVI increased Log BNP to a greater extent than did LVEDP. This result reinforced our previous hypothesis that LVESVI is more strongly associated with the plasma BNP levels 10 .
Directions for future studies of diastolic dysfunction. The main purpose of this study was to assess the associations between cavity size in the systolic and diastolic phases and both cardiac function and overload. We recruited the study population from the patients admitted to our hospital without selecting patients based on specific LV ejection fractions. Our results support the compensatory role of diastolic volume in cardiac function and overload. Furthermore, our results might suggest that the restriction of LV diastolic expansion is ultimately undesirable. In the future, our work will focus on clarifying the differences between the factors that are associated with heart failure according to the reduced ejection fraction and the preserved ejection fraction (HFpEF) using path models. Although the pathology and contributing factors for HFpEF have not been fully clarified, covariance structure analysis should help answer the remaining questions.
Usable information and cautionary notes regarding the selection of the optimal surgical treatment for enlarged ventricles. LV volume reduction has become a potential surgical therapy for heart failure patients with enlarged left ventricles. Cardiac remodeling is thought to be repaired by this procedure 20,21 . There is probably no room for doubt about the effects of volume reduction therapy in patients with significantly enlarged ventricular aneurysms owing to myocardial infarction. However, the over-indication of surgical resection for reducing systolic volume might be undesirable if the procedure results in a reduction in diastolic volume. Furthermore, such surgical methods should not be recommended without caution simply because the diastolic volume is elevated. Based on the current information, when considering surgical therapies, the portion with inadequacy in both contraction and dilatation should theoretically be the only area that is considered for surgical excision.
Utility of covariance structure analysis in cardiovascular studies. In this study, we used covariance structure analysis to test a complicated hypothesis. This statistical method is currently used in many fields because of the widespread availability of computer processing facilities. Recently, we successfully used this method in a practical manner 19 . Path models enable us to draw conclusions about which factors we believe to underlie examined measures. This method provides more credible information than multiple regression analysis. However, the basic concept of drawing a path model is important. In this study, we successfully proposed concise and clear path models based on accumulated scientific information and our past experiences.

Study limitations.
In this study, the technique used to calculate the LV volumes from single-plane cineangiograms of the LVs is associated with significant limitations.

Conclusion
The path model described in this report was designed to test the validity of the Frank-Starling law in patients with heart failure. When viewing plasma BNP levels as a marker of cardiac overload, LVESVI substantially augmented cardiac overload, whereas LVEDVI palliated it. The current results advance the understanding of the relationships between LV cavity size and both cardiac function and overload. The results of this study are suggestive of the increasing importance of the LV diastolic volume in patients with heart failure and the utility of the LVESVI as an important marker of cardiac remodeling for further relevant studies.

Methods
Study patients. The study patients consisted of 1,715 subjects who were consecutively admitted to our institution with heart disorders from 2012-2015. We simultaneously measured their plasma BNP levels and hemodynamic parameters, which included LVESVI, LVEDVI, LVEDP, and SVI, during cardiac catheterization. The LVESVI and LVEDVI were obtained from left ventriculography (LVG) traces during the end-systolic and end-diastolic phases. The contrast LVG images were acquired at a frame rate of 30 frames per second in the right anterior oblique 30-degree projection. The LVESVI and LVEDVI and the left ventricular ejection fraction were calculated from single-plane cineangiograms by means of the area-length formula using a semi-automated trace method with QAngio XA version 7.1 (Medis medical imaging systems bv, Leiden, The Netherlands). This technique for calculating LV volumes might include methodological limitations. The SVI was calculated using the thermal dilution method and a Swan-Ganz catheter. To evaluate the contributions of LV cavity size to both cardiac function and overload, we divided the patients into different groups. We performed the analyses for each group, and the groups were classified based on the following criteria: Group I consisted of all 1,715 patients who were recruited for this study, and all patients underwent left ventricular catheterization. Among these patients, right ventricular catheterization was performed in 353 patients. Group II consisted of 1,363 patients with all types of IHD. Among these patients, right ventricular catheterization was performed in 135 patients. Group III consisted of 1,080 patients with chronic stable IHD after the exclusion of those with acute coronary syndrome. Among these patients, right ventricular catheterization was performed in 133 patients. Finally, Group IV consisted of 352 patients without IHD. Among these patients, right ventricular catheterization was performed in 218 patients. The study protocol (24-355[7121]) was approved by the Ethics Committee of the Jikei University School of Medicine, and we complied with the routine ethical regulations of our institution. This was a retrospective study, and informed consent could not be obtained from each patient. Instead of obtaining informed consent from each patient, we posted a notice about the study design and contact information at a public location in our institution.

Definition of diseases.
The definitions of the diseases were as follows: In brief, IHD was diagnosed based on symptoms, electrocardiography results, blood sampling, and the morphology of the coronary arteries. The patients with IHD included those with clinically stable IHD. Organic stenosis was defined by a ≥ 75% occlusion of the coronary arteries on coronary angiography. Patients with coronary spastic angina were included in the IHD group if the disease activity was stable and a provocation test was planned during hospitalization. Valvular diseases included heart failure caused by moderate valvular disease, and patients who were scheduled for surgery were included in this group. Arrhythmia was defined by the need for catheter ablation, an implantable cardioverter-defibrillator, or cardiac resynchronization therapy, and patients with a pacemaker or syncope were included in this group. Cardiomyopathy was defined when a patient was diagnosed before admission and underwent treatment or if a patient was diagnosed after admission (excluding cases of ischemic cardiomyopathy). Infectious heart disease included pericarditis, myocarditis, and infectious endocarditis. Hypertension, diabetes mellitus, and dyslipidemia were defined as described previously 22 .
Blood sampling and biochemical examination. We used blood sampling and hemodynamic data during the cardiac catheterization. The serum biochemical analyses and the measurements of the plasma BNP levels were performed in a central laboratory at our hospital during the study period. The plasma BNP level was measured as described in previous reports 16,17,19 . In brief, whole blood (5 mL) was collected in tubes containing potassium ethylenediaminetetraacetic acid (1 mg/mL blood). The plasma BNP level was then measured with a rapid enzyme-linked immunosorbent assay (non-extracted) kit using an antibody to human BNP (Shionogi Co. Ltd., Tokyo, Japan). Group III consisted of patients with chronic and stable IHD after excluding patients with acute coronary syndrome because plasma BNP levels noticeably and rapidly increase during the 24 h after the onset of acute myocardial infarction in a monophasic manner and then transiently decrease; moreover, the latter decrease is potentially followed by another increase 2-3 days after onset (depending on the degree of ventricular remodeling), which results in a biphasic profile 23 .
Statistical analysis. Continuous variables are expressed as the means ± the standard deviations (SDs) or the medians with the ranges. Categorical variables are expressed as percentages. Comparisons between two continuous variables were performed using Pearson's product-moment correlation coefficient analysis. The Kolmogorov-Smirnov test was used to determine whether the BNP values were normally distributed. Subsequently, the BNP data were log-transformed (Log BNP) to achieve a normal distribution for the analysis. All statistical analyses were performed using SPSS Statistics version 23.0 (SPSS Inc., Chicago, IL, USA). A path model based on covariance structure analysis was proposed to investigate the relationships between clinical factors in the study population and specifically to identify the factors that most likely exerted causal effects on IHD. The path analyses were performed with IBM SPSS AMOS version 23 (Amos Development Corporation, Meadville, PA, USA). The obtained structural equation models were tested and confirmed at a significance level of P < 0.05. The causality model defined some hierarchical regressions between the hemodynamic parameters and cardiac function/overload. The paths between the variables were drawn from the independent to the dependent variables with directional arrows that were used for every regression model (i.e., arrowhead on one end only). A two-way arrow between two variables indicated a correlation between these variables. For every regression, the total variance in the dependent variable was theorized to be caused either by the independent variables in the model or by extraneous variables (e). Each path had a coefficient that indicated the standardized coefficient of the regressing independent variable on the dependent variable of the relevant path. When obtaining the critical ratios of the differences between parameters, we used AMOS to display the matrix, which included a row and a column for each parameter of the model. Each off-diagonal entry in the matrix provided a statistic for testing the hypothesis that the two-model parameters were equal in the population. The corresponding author had full access to all of the data in the study and takes responsibility for both its integrity and the data analysis.