Association of Preoperative Parameters on Intraoperative Indicators in Myocardial Revascularization Surgery: Insights from a Targeted Complex Network Model

Abstract

Background/Objectives: Myocardial revascularization surgery (MR) is routinely performed in hospitals. However, there is a lack of an algorithm in the scientific literature aimed at predicting intraoperative parameters, such as total surgery time (TST) and cardiopulmonary bypass time (CBT), based on preoperative MR parameters. Therefore, the objective of the present study is to apply a complex network model to predict parameters associated with TST and CBT. Methods: Retrospective data from 124 patients who underwent MR, including medical history, vital signs, and laboratory/biochemical tests, were used, with 30 patients contributing to the construction of the network. Three complex networks were created to study the targets (TST and CBT). The Eigenvector metric was employed to investigate the parameters most relevant to these targets. Results: Regardless of the target, parameters derived from the blood gas analysis followed by erythrogram displayed greater relevance according to the eigenvector metric. However, for TST, the most prominent parameter was Red Blood Cells, while, for CBT, Diastolic Blood Pressure emerged as the most important variable. Conclusion: The targeted complex network model revealed that pulmonary, hemodynamic, and perfusion factors are relevant to the intraoperative parameters of MR. The networks also demonstrated that, although the targets show significant correlation with each other (TST and CBT-r = 0.76; p = 0.000), the importance of the parameters in the networks does not follow the same order. This reiterates the strength of the network in revealing specific information when a particular target is selected.

1. Introduction

The complex network model has been increasingly used to integrate large datasets in an effort to address or predict specific questions, including those within the medical field. The term “Network Medicine” is appearing more frequently in the scientific literature [1,2,3], highlighting the growing importance of the integration between medicine and mathematics. This approach uses network science techniques to explore disease mechanisms, employing various analytical methods such as protein–protein interaction networks, correlation-based networks, gene regulatory networks, and Bayesian networks to identify key molecular interactions [2]. Narrative reviews discuss how this model can assist with complex issues related to general [4] as well as rare diseases [5].

This mathematical tool analyzes systems where elements are interconnected in a non-trivial manner. While the edges represent interactions between the variables incorporated into the network, the nodes correspond to the variables themselves. In a medical analogy, different organs or cells in the body can be thought of as the nodes, with the edges representing the interactions between them, such as the exchange of signals or substances. The eigenvector metric inside this analogy would be used to identify which organs or cells are most influential for overall health, based not only on the number of interactions but also on the importance of those interactions. For instance, even if an organ has few interactions with others, if it is connected to key organs, its impact on the body’s overall functioning would be greater. Inspired by previous studies [6,7,8], our group has adapted this model by targeting specific nodes within the network, assigning weights to direct or indirect interactions with the nodes of interest (i.e., the target) [9,10,11]. However, the inferences from these studies in the medical context remain limited.

Within this context, a medical gap to be addressed is the influence that the preoperative state of patients undergoing coronary artery bypass grafting (CABG) may have on intraoperative parameters. Given that clinical and biochemical parameters are measured as part of the pre-CABG process, it is crucial to understand whether relationships exist between these variables and indicators such as total surgery time (TST) and cardiopulmonary bypass time (CBT). One possible approach to this end would be to apply a targeted complex network model, considering TST and CBT as targets, with the clinical and biochemical parameters forming part of the network’s construction. While this approach is valid, it has not yet been tested, and the scientific literature lacks a study of this nature.

Therefore, this report aims to apply a complex network model to predict parameters associated with TST and CBT. Given the exploratory nature of this study, it is challenging to hypothesize which variables will have the greatest impact on the targets. However, it is anticipated that the model will be effective in achieving this goal, providing insights for future studies involving the analysis of preoperative parameters in CABG intraoperative indicators.

2. Materials and Methods

2.1. Participants

The medical records of patients of both sexes who underwent MR were carefully analyzed by the research team. Considering that the incidence of MR increases with age, we included patients aged 40 years and older. No patient underwent any intervention; only clinical parameters and other necessary information for constructing the network were obtained from the medical records. The study was approved by the Ethics Committee of São Francisco University (CAAE: 55361622.5.0000.5514).

2.2. Data Collection for Mathematical Model Development

The São Francisco de Assis University Hospital database was accessed both digitally and physically to acquire data and create the complex network model. In addition to the network targets (TST and CBT), parameters obtained from the medical history (age, pre-existing diseases or conditions), as well as clinical and biochemical parameters such as heart rate (HR), peripheral oxygen saturation (SpO₂), systolic blood pressure (SBP), diastolic blood pressure (DBP), serum sodium (Na⁺), serum potassium (K⁺), serum lactate (Lac), urea, creatinine, red blood cells (RBC), hemoglobin (Hb), hematocrit (Hct), mean corpuscular volume (MCV), mean corpuscular hemoglobin (MCH), mean corpuscular hemoglobin concentration (MCHC), red cell distribution width (RDW), white blood cells (WBC), segmented neutrophils (Seg.N), basophils (BAS), lymphocytes (LYM), monocytes (MON), and platelets (PLT) were obtained. Considering that some parameters from the blood gas analysis (BGA) were also measured by biochemical tests, the abbreviation BGA was adopted for these, including pH (pH BGA), partial pressure of carbon dioxide (PCO₂ BGA), partial pressure of oxygen (PO₂ BGA), sodium (Na⁺ BGA), potassium (K⁺ BGA), calcium (Ca²⁺ BGA), glucose (Glu BGA), lactate (Lac BGA), hematocrit (Hct BGA), bicarbonate (HCO₃⁻ BGA), standard bicarbonate (HCO₃std BGA), total carbon dioxide (TCO₂ BGA), base excess in the extracellular fluid (BEecf BGA), base excess in blood (BE(b) BGA), oxygen saturation (SO₂c BGA), and total hemoglobin concentration (THbc BGA). The parameters were selected based on their routine use at the hospital where the data were collected. Parameters that were either not routinely recorded or were missing in the patient records were excluded, as the correlation model necessitates complete data for all subjects.

2.3. Complex Network Model

The weighted complex networks method was adopted [6,7,8,9,10,11]. This model was structured to analyze the targets, that is, TST and CBT (Figure 1). Consequently, three distinct complex graphs were obtained, each highlighting one of the aforementioned variables. To construct the network, we utilized connections between variables that exhibited significant correlations by the Pearson product-moment test. Centrality analyses were conducted in a Python environment (version 3.9.3), specifically developed for this study, using the NetworkX 2.5 library [12]. The Shapiro–Wilk test was applied to assess the normality of the data. Data were presented as mean ± standard deviation. Confidence intervals were calculated as $X^{-}$ ± Z * s/√n, where Z is the Z-value for the chosen confidence level (95%).

This study focused particularly on Eigenvector centrality analysis. This metric was used to identify the most important nodes relative to a main node of interest (e.g., TST and CBT). The assignment of weights was carried out following previous studies conducted by our group [9,10,11]. All edges were weighted based on their proximity to the node of interest. Edges directly connected to the node of interest were assigned a weight equal to the corresponding correlation coefficient. Second-degree connections to the node of interest were assigned a weight equivalent to 0.500 of the correlation coefficients, while third- and fourth-degree connections were weighted at 0.250 and 0.125 of the correlation coefficients, respectively. In this approach, the weights represented the strength of the connection, and the Eigenvector centrality analysis calculated the importance of a node based on the importance of its neighbors. The analysis was summarized by the following equation: Ax = λx. The Eigenvector centrality for node i was the i⁰ element of vector x, defined by the equation, where A is the adjacency matrix of graph G with Eigenvalue λ. There exists a unique solution x, in which all entries are positive if λ is the dominant Eigenvalue of the adjacency matrix A [13].

3. Results

In total, 124 medical records were accessed for pre-MR data collection. Given that the complex network model used in this study was based on correlations, only records containing all input parameters required for the network were included in the model’s construction. Consequently, 30 records were selected for analysis. Of these, 11 patients (36%) required three bypass grafts, while 19 patients (64%) needed four bypass grafts.

Table 1. Details about the sample considered in the present study.

N = 30	Mean ± SD or Frequency
Age (years)	66 ± 8
Sex and Age (years)	Female = 26% (67 ± 8)/Male = 74% (65 ± 8)
Conditions or Diseases
Hypertension	87% (Female = 8; Male = 18)
Type 2 Diabetes Mellitus	33% (Female = 3; Male = 7)
Acute Myocardial Infarction	30% (Female = 3; Male = 6)
Dyslipidemia	37% (Female = 1; Male = 10)
Human Immunodeficiency Virus	3% (Female = 0; Male = 1)
Chronic Obstructive Pulmonary Disease	10% (Female = 2; Male = 1)
Depression	3% (Female = 1; Male = 0)
Habits
Smoking	7% (Female = 0; Male = 2)
Former smoker	27% (Female = 1; Male = 6)
Alcohol	3% (Female = 0; Male = 1)
Former drinker	3% (Female = 0; Male = 1)

SD—Standard deviation.

provides details regarding the sample considered in this study. The sample comprised predominantly men, with systemic arterial hypertension as the most common pre-existing disease.

Table 2. Parameters used in the targeted complex network model.

Parameters	Mean ± SD	Confidence Interval
Targets
TST (min)	227.2 ± 41.3	212.4–242.0
CBT (min)	74.7 ± 28.6	64.5–85.0
Vital signs
HR (bpm)	64.7 ± 11.4	60.6–68.8
SpO2 (%)	97.7 ± 1.5	97.2–98.3
SBP (mmHg)	148.0 ± 21.6	140.2–155.7
DBP (mmHg)	77.3 ± 12.4	72.8–81.7
Biochemical data
Na+ Serum (mEq/L)	137.9 ± 2.3	137.0–138.7
K+ Serum (mEq/L)	4.3 ± 0.5	4.1–4.5
Urea (mg/dL)	42.3 ± 22.4	34.3–50.3
Creatinine (mg/dL)	1.0 ± 0.4	0.8–1.1
Lactate (mg/dL)	12.7 ± 5.6	10.6–14.7
Erythrogram
RBC (106/ul)	4.4 ± 0.6	4.1–4.62
Hb (g/dL)	13.2 ± 1.8	12.5–13.91
Hct (%)	39.2 ± 5.2	37.3–41.11
MCV (fl)	90.4 ± 5.0	88.6–92.25
MCH (pg)	30.1 ± 1.8	29.4–30.76
MCHC (mg/dL)	33.4 ± 0.9	33.1–33.77
RDW (%)	13.7 ± 1.3	13.2–14.26
Leukogram
WBC (109/ul)	7810.3 ± 2747.1	6827.3–8793.36
Seg.N (109/L)	53.1 ± 14.7	47.8–58.40
BAS (109/L)	0.1 ± 0.3	0.0–0.26
LYM (109/L)	34.3 ± 12.0	30.0–38.60
PLT (109/L)	219.137 ± 50.047	201.220–237.040
BGA
pH BGA	7.4 ± 0.0	7.3–7.4
PCO2 BGA (mmHg)	38.7 ± 5.8	36.7–40.8
PO2 BGA (mmHg)	137.1 ± 43.8	121.4–152.8
Na+ BGA (mEq/L)	136.5 ± 6.6	134.1–138.9
K+ BGA (mEq/L)	3.8 ± 0.3	3.7–3.9
Ca2+ BGA (mEq/L)	0.9 ± 0.1	0.9–1.0
Glu BGA (mg/dL)	115.2 ± 41.7	100.2–130.1
Lac BGA (mg/dL)	9.9 ± 4.1	8.4–11.4
Hct BGA (%)	35.7 ± 6.2	33.5–38.0
HCO3− BGA (mEq/L)	24.2 ± 2.2	23.4–25.0
HCO3std BGA (mEq/L)	24.6 ± 1.4	24.1–25.2
TCO2 BGA (mEq/L)	25.4 ± 2.3	24.6–26.3
Beecf BGA (mEq/L)	−0.4 ± 2.1	−1.1–0.3
BE(b) BGA (mEq/L)	−0.3 ± 1.8	−1.0–0.3
SO2c BGA (%)	98.0 ± 4.4	96.4–99.5
THbc BGA (g/dL)	11.1 ± 1.9	10.4–11.7

SD—standard deviation; TST—total surgery time; CBT—cardiopulmonary bypass time; HR—heart rate; SpO₂—peripheral oxygen saturation; SBP—systolic blood pressure; DBP—diastolic blood pressure; Na⁺—serum sodium; K⁺—serum potassium; Lac—serum lactate; RBC—red blood cells; Hb—hemoglobin; Hct—hematocrit; MCV—mean corpuscular volume; MCH—mean corpuscular hemoglobin; MCHC—mean corpuscular hemoglobin concentration; RDW—red cell distribution width; WBC—white blood cells; Seg.N—segmented neutrophils; BAS—basophils; LYM—lymphocytes; MON—monocytes; PLT—platelets; BGA—blood gas analysis; PCO₂ BGA—partial pressure of carbon dioxide; PO₂ BGA—partial pressure of oxygen; Na⁺ BGA—sodium from BGA; K⁺ BGA—potassium from BGA; Ca²⁺ BGA—calcium from BGA; Glu BGA—glucose from BGA; Lac BGA—lactate from BGA; Hct BGA—hematocrit from BGA; HCO₃⁻ BGA—bicarbonate; HCO₃std BGA—standard bicarbonate; TCO₂ BGA—total carbon dioxide; BEecf BGA—base excess in the extracellular fluid; BE(b) BGA—base excess in blood; SO₂c BGA—oxygen saturation; THbc BGA—total hemoglobin concentration.

presents the parameters collected and used for the construction of the targeted complex network. The models are shown in Figure 2 and Figure 3, with TST and CBT as the respective targets. It is noticeable that, regardless of the target, parameters derived from the BGA followed by erythrogram displayed greater relevance according to the eigenvector metric (TST—HCO₃⁻ BGA = 0.2844; TCO₂ BGA = 0.2768; Beecf BGA = 0.2746; Hb = 0.2713; THbc BGA = 0.2698; Hct BGA = 0.2692; Hct = 0.2678; BE(b) BGA = 0.2595; HCO₃std BGA = 0.2510/CTB—Beecf BGA = 0.2875; HCO₃⁻ BGA = 0.2863; THbc BGA = 0.2840; Hct BGA = 0.2836; TCO₂ BGA = 0.2771; BE(b) BGA = 0.2745; HCO₃std BGA = 0.2659; Hb = 0.2502; Hct = 0.2419).

However, for TST, the most prominent parameter was RBC (0.4327), while, for CBT, DBP emerged as the most important variable (0.3819). To facilitate comparison between the network results, Figure 4 shows a ranking of the top ten variables with the highest eigenvector values based on the targets. The Supplementary Materials present all the correlations and the eigenvector values for each parameter within the targets adopted in this study.

4. Discussion

This study demonstrated that the targeted complex network model is a viable approach for investigating the importance of preoperative parameters to intraoperative indicators, such as TST and CBT, in the context of MR surgery. Regardless of the target, parameters from the erythrogram and BGA stood out. However, RBC showed exclusive relevance for TST, while DBP was particularly significant for CBT.

The first point that deserves emphasis in this study lies in the variables adopted, as well as the timing of their collection. The preoperative assessment of patients is crucial before surgeries in general [14] and cardiac surgeries in particular [15,16]. For example, patients with a history of adverse pulmonary conditions (e.g., obstructive or restrictive lung disease, reduced lung capacity) require the monitoring of parameters derived from BGA before cardiac surgery [17]. In this study, however, these parameters were used with the additional purpose of understanding their impact on intraoperative indicators, such as TST and CBT.

The fact that Hct BGA, HCO₃⁻ BGA, HCO₃std BGA, TCO₂ BGA, Beecf BGA, BE(b) BGA, and THbc BGA stood out in both networks indicates that pulmonary, hemodynamic, and perfusion aspects are relevant to the intraoperative indicators of MR. Notably, none of these variables showed a significant correlation with TST or CBT. However, considering that the network allows for a systemic analysis of all the variables included, these parameters gained relevance. In this context, these variables exhibited 12 to 14 significant correlations with other parameters included in the network. This means that BGA-derived parameters were correlated with 33–38% of the parameters included (n = 36, subtracting the variable itself and the targets).

Hematological parameters have been suggested as prognostic or predictive markers in the context of cardiac diseases or surgical procedures. Among these, RDW stands out as one of the parameters of great interest to the scientific community. This variable has been proposed as a novel prognostic marker following myocardial revascularization or cardiac valve surgery [18]. Additionally, this parameter is being studied in other contexts, such as long-term prognostic markers in patients with coronary artery disease [19]. This parameter was not highlighted in our network because it did not show significant correlations with the other parameters (regardless of the target). This does not mean that our study contradicts the literature, but the lack of correlation may be attributed to the low variance of RDW in our sample. However, for TST, RBC was the most prominent parameter.

Apart from their well-established physiological function, erythrocytes have been widely studied in a myriad contexts, including their capacity to act as natural drug carriers [20,21,22], as well as their use as markers of oxidative stress [23] and their relationship with diabetes mellitus [24]. In the surgical context, the analysis of RBC before surgery is relevant to patient blood management [25,26,27,28]. This procedure aims to optimize the patient’s blood health, minimize the need for transfusions, and reduce the risk of complications by managing anemia, coagulation, and overall blood volume. In the context studied in this report, it is possible to suggest that, in addition to being significantly associated with TST, RBC is correlated with 33% of the variables related to this target. These results align with the literature presented on the relevance of patient blood management in the surgical context.

Systemic blood pressure is continuously monitored during the perioperative period, as cardiovascular complications during surgeries are associated with hemodynamic instability [29]. Avoiding hypotension during surgical procedures is a challenge that requires continuous attention from anesthesiologists [30,31]. However, DBP was not significantly correlated with CBT (r = −0.21) but impacted the network targeting this indicator due to its correlation with 41% of the variables included in the network. Nonetheless, it is bold and incorrect to claim that DBP alone predicts CBT. The complex network model presented here indicates the opposite. While monitoring blood pressure during the preoperative, perioperative, and postoperative periods is necessary, its variation can be influenced by multiple parameters. This point was reinforced by the presented network. Additionally, although DBP did not rank among the top 10 variables for TST, it had an eigenvector value of 0.2510 in this network, placing it in the 11th position.

This study is not without limitations. Although the sample size used allowed for the construction of the targeted networks, future multicentric studies with more patients are needed to provide further insights into the context studied here. We acknowledge that a larger number of patients would allow for more robust inferences and strengthen the correlations, and consequently the complex network. Future studies with a larger sample size are necessary to validate the approach proposed here. Additionally, information such as body mass, height, and body mass index were not retrieved, as these details were not always available in the analyzed records. Another limitation is the depth of discussion regarding the results obtained from the networks. Indeed, the networks provide a systemic view of the relationships between the variables included, but they do not directly conclude the impact of modulations in these variables on the adopted target. However, this does not diminish their importance but rather highlights elements viewed from different perspectives, such as the erythrogram as a means of blood patient management. For example, the networks demonstrated that information from the erythrogram may relate to other variables commonly measured before MR surgery, which, together, can help in visualizing the intraoperative indicators of this surgery.

One of the main strengths of this study lies in the use of only significant correlations to obtain the eigenvector metric, as well as the use of specific targets to study a particular problem. Specifically, the network considered a large number of variables, ranging from biochemical parameters to clinical measurements. This strengthens the overall view of the relationship between the parameters commonly analyzed before MR surgery. Further, the networks demonstrated that although the targets were correlated with each other (TST and CBT-r = 0.76; p = 0.000), the importance of the parameters in the networks does not follow the same order. This reiterates the strength of the network in revealing specific information when a particular target is selected. Additionally, all MR surgeries were performed by the same surgical team, adhering to established protocols and guidelines.

5. Conclusions

This study illustrated that the targeted complex network model effectively assesses the significance of preoperative parameters to intraoperative indicators, like TST and CBT, within the scope of MR surgery. Across both targets, parameters derived from the erythrogram and BGA were prominent. Specifically, RBC demonstrated unique importance for TST, while DBP was notably relevant for CBT.