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Article

Inotrope Analysis for Acute and Chronic Reduced-EF Heart Failure Using Fuzzy Multi-Criteria Decision Analysis

by
Cemre Ozgocmen
1,*,
Ozlem Balcioglu
2,3,
Berna Uzun
3,4,* and
Dilber Uzun Ozsahin
3,5,6
1
Department of Biomedical Engineering, Faculty of Engineering, Near East University, TRNC, Mersin 10, Turkey
2
Department of Cardiovascular Surgery, Faculty of Medicine, Near East University, TRNC, Mersin 10, Turkey
3
Operational Research Center in Healthcare, Near East University, TRNC, Mersin 10, Turkey
4
Department of Mathematics, Faculty of Arts and Sciences, Near East University, TRNC, Mersin 10, Turkey
5
Medical Diagnostic Imaging Department, College of Health Science, University of Sharjah, Sharjah 27272, United Arab Emirates
6
Research Institute for Medical and Health Sciences, University of Sharjah, Sharjah 27272, United Arab Emirates
*
Authors to whom correspondence should be addressed.
Appl. Sci. 2024, 14(11), 4431; https://doi.org/10.3390/app14114431
Submission received: 23 March 2024 / Revised: 7 May 2024 / Accepted: 9 May 2024 / Published: 23 May 2024
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Abstract

Heart failure is a progressive disease that leads to high mortality rates if left untreated, and inotropes are a class of drugs used to treat a type of heart failure where patients have reduced ejection fraction (HFrEF). This study aims to utilize the Fuzzy-Preference Ranking Organization Method for Enrichment Evaluation (F-PROMETHEE), an effectively used multi-criteria decision making (MCDM) technique. To analyze the characteristics of the most often used inotropes for acute HFrEF and chronic HFrEF, we use the same parameters set with distinct importance factors and aims for each property and, therefore, mathematically demonstrate the strengths and weaknesses of each inotrope alternative. As a result, a detailed ranking list for each HFrEF class was obtained, with supplementary information on how each parameter contributed to the ranking of each inotrope. From these results, it was concluded that the F-PROMETHEE method is applicable for evaluating the risks and benefits of various inotropes to determine a starting point for treating an average patient when making a quick decision without complete patient data. As demonstrated in this study, it is possible to easily use the same data set and only change some preference parameters according to individual needs to produce patient-specific results. In this study, we showed that creating a decision-making system that mathematically assists clinical specialists with their decision-making process is feasible.

1. Introduction

The American Heart Association (AHA) defines heart failure (HF) as a condition in which a patient’s heart muscles cannot pump adequate blood for the oxygen demand of their body to be met [1,2,3]. This means that there is insufficient perfusion of vital organs in their body. HF’s primary causes involve coronary heart disease, defective heart valves, and other illnesses that cause changes in the myocardium structure, like arrhythmias, where it either becomes too rigid due to its increased size or too weak to operate [1,2,3] effectively.
People from all age groups are susceptible to HF, but statistical prevalence is more dominant in elderly patients. The most prevalent symptoms of HF are shortness of breath, constant exhaustion, inability to do exercise, and swelling of the ankles and legs [1,2,3].
HF is a long-term illness that worsens and can even result in death if left untreated, but the underlying cause cannot be cured. However, its symptoms can be managed to provide an adequate quality of life to patients by using a range of medications [1,2,3].
Ejection fraction (EF) is a common measurement of HF patients, and it defines the percentage of blood pumped out of the left ventricle of the heart; 50–70% EF is considered to be normal. There are two sub types of heart failure, preserved EF and reduced EF heart failure, where the presenting sub type creates an important distinction on how the patient needs to be treated [4].
Preserved ejection fraction (HFpEF) usually means that the EF is normal but heart failure is caused by decreased blood intake into the left ventricle during diastole. Therefore, a reduced blood volume is available to the body [5].
Reduced ejection fraction (HFrEF) usually means that although the left ventricle fills with a sufficient volume of blood, the heart muscles cannot contract with sufficient force, so that produced EF is insufficient for the body [5,6].
About 6.2 m people suffer from heart failure in the US [1], and 65% of these patients have preserved ejection fraction while 35% have reduced ejection fraction [7,8]. This study focuses on HFrEF patients, who require a specific type of drug called inotropes to manage the most severe symptoms of heart failure by increasing contractility and thereby reducing hospitalization time [9,10,11,12].
Inotropes, along with their vasopressor effects, aim to improve myocardial contractility and vital organ perfusion to alleviate life-threatening symptoms of HFrEF [9,10,11,12]. There are multiple types of inotropes, which are classified according to how they affect myocardial contractility. Those most widely used in clinical practices are catecholamines and phosphodiesterase inhibitors (PDIs).
Inotropes are meant to act as short- to medium-term assistive drugs, intending to provide hemodynamic stability that will carry the patient to a point where a more invasive or permanent solution can be discussed and realized as necessary. These solutions include coronary revascularization, total heart transplant, left ventricular assist device, intra-aortic balloon pump, extracorporeal membrane oxygenation, etc. Additionally, inotropes can also be used for palliative therapy with patients that are not eligible for any of these options, providing them with a higher quality of life for limited time as their symptoms are somewhat improved when contrasted with not taking inotropes [9,10,11,12].
As was mentioned previously, each inotrope type has its mechanism. Therefore, they each have a different magnitude of preferred and unwanted side effects according to their specific inhibitory and excitatory actions on the myocardium and vascular smooth muscle.
The main consideration points while using inotropes are their side effects and which type can be tolerated best by a patient’s clinical presentation while providing enough pharmaceutical support to alleviate the most severe HFrEF symptoms. The most common side effects include chronotropic, tachycardia, vasodilation, thrombogenesis, myocardial oxygen demand increase, hypertension, peripheral vascular resistance, and many more [9,10,11,12]. Therefore, a careful balance of drugs and dosage arrangement according to the patient’s needs is most important. Due to these side effects, it is in patients’ best interest to utilize this kind of pharmaceutical regimen with as short as small doses as possible, administering only enough to provide hemodynamic stability to avoid side effects related to severe adverse side effects.
This study evaluated inotropes under two main circumstances, namely, patients with acute HFrEF and chronic HFrEF. It is known that the term heart failure contains much more variation than the types above; however, to avoid repetitions of very similar results, we limited our study to these two variations. This was performed for two primary purposes: first, acute and chronic patients have distinct priorities and considerations, and second, the same principles and evaluation methods proposed in this study can be easily integrated into a more individualized decision-making process.
It is important to note that a combination of multiple inotropes at varying doses may prove to be more effective at symptom management and side effect minimization when compared to a single high-dose inotrope. However, this study aims to mathematically determine which inotrope is the best starting point to shape and personalize the medical treatment of an average patient, where simple case-by-case tweaks and modifications to the decision-making system are possible to obtain a patient-specific evaluation.
There are various types of MCDM methodologies proposed for selection problems, which can be categorized into two main groups: compensatory and non-compensatory approaches [13]. Non-compensatory approaches evaluate each criterion individually without allowing for trade-offs between them. Techniques such as TOPSIS, WPM, and SAW belong to this category. On the other hand, compensatory approaches enable trade-offs between criteria by aggregating them to generate an overall score for each alternative. AHP, ELECTRE, and PROMETHEE are examples of compensatory methods. The PROMETHEE method provides performance rankings of alternatives via pairwise comparisons and can be used for both quantitative and qualitative data. By offering a range of preference functions (V-shaped, level, Gaussian, U-shaped, and linear functions) to compute the disparity between alternatives for each criterion, the PROMETHEE technique distinguishes itself from other MCDM techniques, thereby yielding more nuanced outcomes. Endowed with this versatility, decision makers can prioritize alternatives based on their specific preferences, ensuring a more tailored and informed decision-making process. The fuzzy-based PROMETHEE method enables decision makers to analyze selection problems and provide rankings in environments where decision making involves vagueness or subjectiveness. It allows for the use of quantitative and qualitative data, enabling decision makers to consider different types of parameters for their analysis. It can provide computational efficiency and robustness for different scenarios, even with large datasets. Therefore, in this study, we applied the fuzzy PROMETHEE approach to analyze the effectiveness of inotropes in managing both acute and chronic reduced EF heart failure. PROMETHEE has proven itself to be a rational and successful MCDM method preferred by many other researchers for its performance and visual representation capabilities, and fuzzy logic is also highly regarded for its ability to clarify uncertainty or vagueness in decision-making processes. Combining PROMETHEE with fuzzy logic allows for a more robust and flexible approach, specifically when dealing with complex real-world selection problems where crisp data are not available or difficult to obtain. This hybrid supportive approach provides a comprehensive framework that can combine and analyze various types of information and preferences, ultimately leading to more informed and reliable decisions. Therefore, we applied the fuzzy PROMETHEE approach in this study to analyze and provide performance evaluations of inotropes used for acute and chronic reduced EF heart failure. We provide a framework demonstrating the applicability of the MCDM approach to making informed decisions in complex medical scenarios for healthcare practitioners to support personalized treatment strategies and optimize patient outcomes.

2. Methodology

Throughout their lives, humans often make quick decisions based on their previous experiences without any scientific exploration of the issue. This intuition-based decision making system is inadequate for other more complicated and intricate problems with many consideration parameters. An unbiased method is far more preferable. At this point, multi-criteria decision analysis (MCDA) methods aid us in making a proper, mathematical evaluation of multiple alternatives. This process is still dependent on the decision maker’s personal preferences and what is most important to them. Thus, numerous optimal solutions are possible with given data depending on the decision maker’s priorities [14].
Sometimes, however, data used in multiple-criteria decision making (MCDM) might contain vague values and non-specific notions that humans naturally use in their everyday lives, and it is not readily possible for a mathematical system to utilize these. Fuzzy logic works precisely on this type of information. It uses multi-valued logic which assigns membership values between [0 and 1], representing values as degrees of truth, compared to binary Boolean logic. Therefore, fuzzy sets make it possible to represent vague and linguistic data in a numerical form [15].
The preference ranking organization method for the enrichment evaluation (PROMETHEE) technique, first created by Brans et al., aims to provide an in-depth ranking of same-class alternatives based on their comparable features/parameters, where each parameter is assigned a different importance level [16]. The PROMETHEE approach process is detailed in Appendix A [17,18,19].
Ordinarily, imprecise/vague data cannot be processed by the PROMETHEE method in a real decision-making environment. Therefore, a hybrid method, called the Fuzzy- based PROMETHEE (F-PROMETHEE) technique, was utilized this study, as it can support decision analysis made with vague or imprecise data.
By utilizing the F-PROMETHEE, we aim to demonstrate that we can create an unbiased and quick starting point for using inotropes in treating an average patient with acute HFrEF or chronic HFrEF. To achieve this, each parameter of these inotropes must be assigned an importance weight according to what is actually most and least important in practice for a clinical specialist when they are evaluating a patient for inotrope use.
Our process of assigning importance weights was aided by published information on this topic [9,10,11,12,20,21,22,23,24,25,26,27,28], and a cardiovascular surgeon’s knowledge and experience were used to obtain a highly effective result.
Subject-relevant properties of inotropes, most commonly used alternatives, and linguistic or numerical quantifiers were all obtained through a careful consideration of 12 different published studies. Almost all the published information discusses inotropes using linguistic quantifiers like “considerable increase” or “decreased slightly”, or comparisons like “at a higher rate than” in order to assess their properties. Furthermore, what became even more difficult was reconciling different descriptions of the same inotropes and their properties between multiple publications. Therefore, useful parameter selection, correct interpretation, and conversion of these notions into our standardized “Very Low–Very High” linguistic fuzzy grading system was assisted and confirmed by a practicing cardiovascular surgeon.
In this study, we utilized a fuzzy linguistic scale to identify the selected parameters of the inotropes and determine the weights of these parameters. (see in Table 1). These linguistic expressions were assigned to fuzzy triangular sets. The 5-point scale of fuzzy linguistic expressions and assigned fuzzy sets used in this study were as follows: Very Low (0, 0, 0.25), Low (0, 0.25, 0.5), Medium (0.25, 0.5, 0.75), High (0.5, 0.75, 1), and Very High (0.75, 1, 1), and (No = 0, Yes = 1) for binary conversions were also determined. In addition, the Yager index was applied. This centroid defuzzification technique successfully converts fuzzy numbers into single numbers, enabling their consideration in the analysis process. The PROMETHEE technique with a Gaussian preference function was utilized. This choice was made because the Gaussian preference function is robust to outliers and extreme values, thereby enabling a more balanced and rational comparison between alternatives. It offers flexibility in deriving preferences for decision makers, considering mean and standard deviation to match the decision context. Gaussian preferences facilitate a smooth transition between preference levels, resulting in a gradual change in preference rather than abrupt shifts. Furthermore, prioritizing alternatives by considering a parameters’ standard deviation ensures that preference values are relatively sensitive, thus establishing the resulting ranking order.
As seen in Table 1, 15 parameters and their importance weights were utilized for each class assessment and 5 inotrope alternatives were compared and placed in a decision matrix.
The inotropes dataset of the chronic HFrEF patients is shown in Table 2.
As seen in Table 1 and Table 2, each parameter is graded from VL to VH according to its importance levels and with Min or Max according to its aim based on the expert’s priorities. The values are also subject to further grading as necessary to be viable for the F-PROMETHEE technique. It is important to note that parameter values are not subject to change when evaluating for different classes.
Thus, it is now possible to utilize the F-PROMETHEE to rank the inotrope alternatives according to acute-phase or chronic-phase HFrEF. They each have different assigned importance weights and parameter aims and are expected to yield different ranking orders.

3. Results

The following results were produced from two different datasets, as given in Table 1 and Table 2. They were used to investigate the best inotrope to use for average acute HFrEF and chronic HFrEF patients.
Using the F-PROMETHEE techniques previously discussed for the inotrope evaluations, the ranking list below was obtained. The net ranking results of the inotropes for acute HFrEF patients are shown in Table 3, while the ranking results of the inotropes for chronic HFrEF patients are shown in Table 4.
Within the limitations of the proposed research, Figure 1 and Figure 2 visually illustrate the ranking of each inotrope alternative. The distance between each alternative represents their relative “score” to each other, and this is represented by phi values that can also be found in Table 3 and Table 4. The highest placed inotrope within each figure scored best, and the arrowed line flow represents the next lower rank. For example, looking at Figure 1, it can be said that there is not a big difference in the rankings of dopamine and noradrenaline for the acute HFrEF patients, as there only have several slightly better graded property values that account for the first rank placement of dopamine over noradrenaline.
The divergence of two arrowed lines from dobutamine in Figure 1 and the convergence of two arrowed lines towards adrenaline in Figure 2 represent a distinct type of information that is also useful to visualize and further investigate as necessary. Inotropes that have similar clusters of properties with comparable strengths and weaknesses and are linked directly with each other, and small differences are represented with a deviation in the x axis, like how Dobutamine is slightly more towards the right-hand side compared to dopamine in Figure 2. Milrinone however, despite being second in the ranking, is placed very far away from first place inotrope dopamine due to the fact that milrinone has distinctly different strengths compared to dopamine with respect to the chronic HFrEF analysis. The same is also true for milrinone in Figure 1. as it has distinctly different weaknesses in the acute HFrEF analysis compared to those of adrenaline. In both cases, further investigation of Figure 3 and Figure 4 is required in order to understand what makes these inotropes distinct from each other.
It is possible to further analyze each of the 15 parameters for each inotrope alternative and see which parameters are considered to be their strengths or weaknesses. Visual representations focusing on parameter contributions as they relate to inotrope rankings for acute and chronic HFrEF patients are shown in Figure 3 and Figure 4, respectively. The parameters placed at the top half in Figure 3 and Figure 4 represent the positives and, conversely, those placed at the bottom represent the negative contributing features of given alternatives. Similarly, for each inotrope, the properties with greatest contribution on ranking are placed in order either towards the top of the list if they have a positive contribution or towards the bottom if they have a negative contribution. Furthermore, each blue colored rectangle belonging to each inotrope alternative visually represents the magnitude of contribution that the positive and negative parameters made to the ranking decision, as their placement with respect to the “zero” line and the total area on each side of this line directly represent the positive outranking flow ( Φ + ) and negative outranking flow ( Φ − ) values that were calculated for the ranking tables.
In real-life applications, we understand that a generalized approach might not be optimally beneficial for patient prognosis depending on each patient. This idea will be further elaborated in the discussion section.

4. Discussion

It is clear from the obtained ranking results that both acute and chronic HFrEF patient groups would most likely benefit from dopamine, as it was consistently ranked highest on both lists. For the acute HFrEF group, noradrenaline was a very close second. Thus, it might be fair to say that under most circumstances, depending on the patient’s clinical presentation, a choice between either of them should be used as the go-to initial treatment, depending of course on the clinical presentation.
However, when it comes to chronic patients, we can see that noradrenaline drops down to the fourth ranking and milrinone comes in at a close second place, with the same choice considerations as before still withstanding. In contrast, milrinone was ranked as the last choice in the acute group. Dobutamine seems to consistently rank in third place, suggesting that it is an all-around “balanced” drug for this study. Lastly, adrenaline consistently ranked much lower than other inotrope alternatives in both the results (4th and 5th place), which might indicate that it is not the optimal treatment option for both patient groups most of the time.
If we are to further inspect each inotrope’s individual properties, some important distinctions can be drawn between the alternatives. First of all, adrenaline was graded as having high inotropy, which is crucial, a very high vasopressor effect, and a very low vasodilator effect on peripheral vasculature. On the other hand, however, it has a very high tachycardia causation rate, which in turn lends itself to a highly increased myocardial oxygen demand, very great peripheral organ damage, and, most importantly, a very high-grad and possibly quite problematic side effect list which includes pulmonary congestion, lactic acidosis, myocardial ischemia, thermogenesis, and intracranial bleeding. Therefore, some of its most distinct properties suggest it is a beneficial immediate intervention drug, albeit with comparatively significant risks.
Secondly, we can see that noradrenaline has a very similar profile of properties to adrenaline. Both share the same parameter grade for vasodilator and vasopressor effects; noradrenaline has lower inotropy, tachycardia causation, a relatively more preferable side effects list, and much lower chronotropic effect. These properties seem to suggest that noradrenaline is still an immediate intervention drug. Still, it is slightly less aggressive in its benefits and, relative to adrenaline, it has noticeably better proportionate risk factors.
The third inotrope alternative, dopamine, has a higher vasodilator effect, similar vasopressor effect, and yet it still has as good inotropy as adrenaline. With a much lower increase in myocardial oxygen demand, although it still causes high-grade tachycardia rates, it presents a very important distinction: it has a much better diuresis rate, which is highly desirable. Dopamine has much more tolerable side effects, yet it has some unique side effects that may result in congestion and should not be disregarded.
Dobutamine has the same dopamine property grades, with a vasodilator effect and inotropy. Yet, it has a lower vasopressor effect (graded at medium), a significantly lower chronotropic effect, lower tachycardia rates (graded at medium) and, identically to dopamine, much lower peripheral organ damage rates than adrenaline or noradrenaline when used in longer terms. However, it has significantly increased myocardial oxygen demand, the highest amongst all the alternatives, and an almost non-existent diuresis effect. All these factors considered, dobutamine seems to be a drug that should be carefully considered according to a specific patient and their clinical presentation.
Finally, milrinone has some unique properties to consider. Since it has a different effect mechanism, only milrinone can be used with beta blockers, and it has a much longer effective half-life than the other inotropes. It has a modest inotropy, the lowest myocardial oxygen demand, a high-grade vasodilator effect, low vasopressor effect, and similar tachycardia rates as noradrenaline, which is also graded as high. Its main side effect considerations are also distinct, with hypotension being a significant probability. Most importantly, the renal function of a patient may become compromised in time; thus, closely following these effects is very important. In contrast with a drug like adrenaline, milrinone seems to be more effective in long-term use, for which some significant side effects for comorbidity must be avoided.
As previously mentioned, the achieved results show the rankings of two essential and distinct HFrEF variations, which are still incomplete when other sub-categories (dilated, hypertrophic, ischemic, etc.) are also considered. This study aimed to highlight that using the same data to apply MCDM analysis for different patient types can easily result in different ranking lists when there are inherent consideration differences that have been properly accounted for. Therefore, we believe that it would be desirable to create a system whereby a different best result can be obtained by only changing importance factors and parameter aims according to a patient’s specific clinical presentation.
It worth mentioning some parameter exclusions and importance weight decisions that were made in this study. First, some parameters, like long-term mortality rate and re-hospitalization rate, were omitted from our study. This was due to, as far as we are aware, inconsistent and incomplete case studies and meta data analyses on this matter, with each finding ranging from “inotropes greatly increase mortality rate” to “when used as necessary, there is no difference in mortality rate.” Therefore, until a better scientific consensus is attained, it might be best to exclude these parameters [25,26,27].
Secondly, as the actual cost of each inotrope and its importance according to each country’s healthcare system are very subjective from region to region, an importance weight of “Very Low” was assigned to it to keep its impact to a minimum. However, it was not completely omitted from our parameters list as it is considered to be an important aspect of this subject matter’s decision-making process. This assigned importance weight might not most accurately reflect a real-world decision-making process. Yet, as previously discussed, the ability of the presented MCDM framework to be quite easily adapted for different evaluation needs is, in fact, a strength that we would like to again highlight.
If we were to consider how a study of this nature might have a practical impact on clinical decision making in the future, we would have to imagine a series of other studies that would eventually culminate in a comprehensive database of information. These studies would need to further focus on quantifying more parameters, comparing more inotropes, and evaluating different doses and drug combinations, all with respect to the different priorities of different HF types and comorbidities.
The envisioned scale and scope of this type of study would have to rely on working with multiple clinics for sufficient data acquisition and to ensure accuracy of results. As a result, we would obtain a powerful tool that can objectively address the fact that each patient and their needs are different due to that patient’s specific condition and present comorbidities. In the end, a physician could adjust a few values reflecting a patient’s clinical presentation as an input and mathematically determine what the best option would be as suggested accordingly.

5. Conclusions

MCDM, specifically F-PROMETHEE, was shown to be applicable to inotrope selection for patients with reduced ejection fraction heart failure under acute and chronic groups. With highest net ranking values, dopamine and noradrenaline were determined to be the best two options for acute HFrEF patients, while dopamine and milrinone were determined to be the best two options for acute chronic patients. Using MCDM, the strengths and weaknesses of the most prevalent inotrope alternatives were evaluated, compared to each other, and ranked accordingly based on their resulting ranking value. Therefore, a mathematical approach to evaluating the risks and benefits of various inotropes for an average patient is thought to be helpful for clinical specialists that need to make quick decisions without the full patient data.
As this study focused on the most often used inotrope alternatives, we can say that it does not encompass all the possible drugs available on the market. However, it is a logical next step that MCDM can be used for further study, as it was shown to create a ranking from a more comprehensive list of inotropes. Further expanding on the available parameters to increase the accuracy of the obtained ranking list is also possible within this context. Finally, considering the presence of other comorbidities, like kidney failure, diabetes, chronic obstructive pulmonary disease, tachycardia, or anemia, alongside heart failure, in order to evaluate each clinical presentation as a different class may yield more effective treatment options for each patient’s specific needs.
It is noteworthy that the same approach and analysis structure can be very easily adapted toward other multi-criteria healthcare problems, including analyses of other drug types for other types of illnesses.
It is also possible to conclude that simply tailoring the importance weights according to the attending specialist’s judgment and patients’ clinical presentation can create a more personalized decision-making process, which is thought to be of significant value to both patients and doctors.

Author Contributions

Conceptualization, C.O., D.U.O., O.B. and B.U.; methodology, C.O., B.U. and D.U.O.; validation, O.B., B.U. and D.U.O.; formal analysis C.O. and B.U.; investigations C.O., O.B., D.U.O. and B.U.; resources, C.O. and O.B.; data curation, C.O. and O.B.; writing—original draft preparation, C.O., O.B., B.U. and D.U.O.; writing—review and editing O.B., D.U.O. and B.U.; visualization, C.O.; supervision, D.U.O., O.B. and B.U.; project administration D.U.O., O.B. and B.U. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A

After constructing the decision matrix (a matrix that contains the alternatives and their parameters), the PROMETHEE method contains 5 steps to provide a ranking order of same class alternatives as follows [16,17,18]:
  • The preference function P j ( · ) of each criterion j should be defined.
  • Importance weights of each criterion w j = w 1 ,   w 2 ,   … ,   w K where ( j = 1,2 , … , K ) and should be defined as
    t h e   ∑ j = 1 K w j = 1
    where K is the number of criteria.
  • For each of the alternative pairs a t , a t ′ ∈ A , the outranking relation π a t , a t ′ should be determined by
    π a t , a t ′ = ∑ j = 1 K w j . P j f j a t − f j a t ′ ,   A X A → 0,1
    where f j a t denotes the value of the jth criteria of the alternative a t and π a t , a t ′ denotes the preference indices, which shows the preference intensity for an alternative a t in comparison to an alternative a t ′ while counting all criteria simultaneously.
  • The positive outranking flow and negative outranking flows should be determined as follows:
    A positive outranking flow of the alternative a t ,
    Φ + a t = 1 n − 1 ∑ t ′ = 1   t ′ ≠ t   n π a t , a t ′
    A negative outranking flow of the alternative a t ,
    Φ − a t = 1 n − 1 ∑ t ′ = 1   t ′ ≠ t   n π a t ′ , a t
    n denotes the number of alternatives. The Φ + a t defines the strength of alternative a t ∈ A, while the negative outranking flow Φ − a t defines the weakness of alternative a t ∈ A.
PROMETHEE I determines a partial pre-order of the alternatives based on the positive and negative outranking flows. PROMETHEE II determines a complete pre-order of the alternatives based on a net flow. The partial pre-order of the options can be determined based on the following statements:
Via PROMETHEE I, alternative a t is selected to alternative a t ′ ( a t P a t ′ ) if it satisfies statement (A5), below given as
{ Φ + a t ≥ Φ + a t ′   a n d   Φ − a t < Φ − a t ′   o r   Φ + a t > Φ + a t ′   a n d   Φ − a t = Φ − a t ′
a t is indifferent to alternative a t ′ ( a t I a t ′ ) if
Φ + a t = Φ + a t ′   a n d   Φ − a t = Φ − ( a t ′ )
and a t is incomparable to a t ′ ( a t R a t ′ ) if
{ Φ + a t > Φ + a t ′   a n d   Φ − a t > Φ − a t ′
The net outranking flow can be calculated for each alternative by using Equation (A8).
Φ n e t a t = Φ + a t − Φ − a t
Via PROMETHEE II, the complete order with the net flow can be determined as
a t   is   preferred   to   a t ′   ( a t P a t ′ )   if   Φ n e t a t > Φ n e t a t ′
a t   is   indifferent   to   a t ′   ( a t I a t ′ )   if   Φ n e t a t = Φ n e t a t ′
The higher Φ n e t a t value provides the better alternative and the net ranking can be obtained accordingly.

Appendix B

Table A1. The raw dataset of inotropes and their properties assessed for acute HFrEF [9,10,11,12,20,21,22,23,24,25,26,27,28].
Table A1. The raw dataset of inotropes and their properties assessed for acute HFrEF [9,10,11,12,20,21,22,23,24,25,26,27,28].
Criteria/AlternativesAdrenaline (β1 > β2 > α)Noradrenaline (β and α)Dopamine (dopa1-2, α1, β1)Dobutamine (β1 > β2 > α)Milrinone (PDE3 Inhibitor)
Cost271 USD/30 mL (30 mg)120 USD/40 mL (40 mg)141 USD/3000 mL (4800 mg)136 USD/3000 mL (6000 mg)55.70 USD/200 mL (200 mg)
Steady-State Blood Concentration Reached In10–15 min5 min5 min10 min20 min
Half-Life 3 min2.4 min2 min2 min2.5 h
Long-Term Use Short (VL)Short (VL)Longer (L)Longer (M)Longer (M)
VasodilatorVLVLLow Dose Yes Low Dose Peripheral YesYes
Vasopressor Peripheral and Pulmonary Yes Yes High Dose Yes Neutral–V. High Dose Peripheral Yes Low
Inotropy 3 (H)2 (M)3 (H)3 (H)2
Chronotropic Effect Positive Minimal Positive Neutral Minimal (L)
Myocardial Oxygen DemandTachycardia Increased Tachycardia Increased Slight IncreaseSignificant Increase Lower
Causes TachyarrhythmiaYes YesYes Yes Mild Yes
Thrombogenic Yes NoNo No No
Diuresis0 1 2 0 0
Peripheral Organ Damage5 3 2 1 1
Side Effects1. Lactic Acidosis
2. Myocardial Ischemia
3. Intracranial Bleeding
4. Hypertension
5. Pulmonary Congestion
6. Hyperglycemia 		1. Increased BP
2. Myocardial Toxicity
3. Hypertension
4. Headache 		1. +PCWP
2. ++Afterload
3. Hypertension		1. Hypotension
2. Low Dose Reduced Afterload
3. May Build Tolerance
4. Myocarditis
5. Peripheral Eosinophilia 		1. Hypotension
2. Renal Funct. Consideration
Effectiveness with Beta BlockersNo NoNo NoYes
(VH: Very High, H: High, M: Moderate, L: Low, VL: Very Low).
Table A2. The raw dataset of inotropes and their properties assessed for chronic HFrEF [9,10,11,12,20,21,22,23,24,25,26,27,28].
Table A2. The raw dataset of inotropes and their properties assessed for chronic HFrEF [9,10,11,12,20,21,22,23,24,25,26,27,28].
Criteria/AlternativesAdrenaline (β1 > β2 > α)Noradrenaline (β and α)Dopamine (dopa1-2, α1, β1)Dobutamine (β1 > β2 > α)Milrinone (PDE3 Inhibitor)
Cost 271 USD/30 mL (30 mg)120 USD/40 mL (40 mg)141 USD/3000 mL (4800 mg)136 USD/3000 mL (6000 mg)55.70 USD/200 mL (200 mg)
Steady-State Blood Concentration Reached In 10–15 min5 min5 min10 min20 min
Half-Life 3 min2.4 min2 min2 min2.5 h
Long-Term UseVLVLLMM
VasodilatorVLVLLow Dose Yes Low Dose Peripheral Yes Yes
Vasopressor Peripheral and Pulmonary Yes YesHigh Dose Yes Neutral—V. High Dose Peripheral Yes Low
Inotropy 32 3 3 2
Chronotropic EffectPositive MinimalPositive Neutral Minimal
Myocardial Oxygen Demand Tachycardia Increased Tachycardia Increased Slight Increase Significant Increase Lower
Causes Tachyarrhythmia YesYes Yes Yes Mild Yes
Thrombogenic Yes No No No No
Diuresis 0 1 2 0 0
Peripheral Organ Damage 5 3 21 1
Side Effects 1. Lactic Acidosis
2. Myocardial Ischemia
3. Intracranial Bleeding
4. Hypertension
5. Pulmonary Congestion
6. Hyperglycemia		1. Increased BP
2. Myocardial Toxicity
3. Hypertension
4. Headache 		1. +PCWP
2. ++Afterload
3. Hypertension 		1. Hypotension
2. Low Dose Reduced Afterload
3. May Build Tolerance
4. Myocarditis
5. Peripheral Eosinophilia		1. Hypotension
2. Renal Funct. Consideration
Effective With Beta Blockers No No No No Yes
(VH: Very High, H: High, M: Moderate, L: Low, VL: Very Low).

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Applsci 14 04431 g001
Figure 1. Visual representation of inotrope ranking results via F-PROMETHEE for acute HFrEF.
Figure 1. Visual representation of inotrope ranking results via F-PROMETHEE for acute HFrEF.
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Figure 2. Visual representation of inotrope ranking results via F-PROMETHEE for chronic HFrEF.
Figure 2. Visual representation of inotrope ranking results via F-PROMETHEE for chronic HFrEF.
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Figure 3. Fuzzy PROMETHEE evaluation results of the inotropes for acute HFrEF.
Figure 3. Fuzzy PROMETHEE evaluation results of the inotropes for acute HFrEF.
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Figure 4. Fuzzy PROMETHEE evaluation results of the inotropes for chronic HFrEF.
Figure 4. Fuzzy PROMETHEE evaluation results of the inotropes for chronic HFrEF.
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Table 1. Dataset of inotropes and their properties assessed for acute HFrEF [9,10,11,12,20,21,22,23,24,25,26,27,28].
Table 1. Dataset of inotropes and their properties assessed for acute HFrEF [9,10,11,12,20,21,22,23,24,25,26,27,28].
Criteria/AlternativesAim/Imp.WeightsAdrenaline (β1 > β2 > α)Noradrenaline (β and α)Dopamine (dopa1-2, α1, β1)Dobutamine (β1 > β2 > α)Milrinone (PDE3 Inhibitor)
CostMinVL271 USD/30 mL (30 mg)120 USD/40 mL (40 mg)141 USD/3000 mL (4800 mg)136 USD/3000 mL (6000 mg)55.70 USD/200 mL (200 mg)
Steady-State Blood Concentration Reached InMinVH10–15 min5 min5 min10 min20 min
Half-LifeMinM3 min2.4 min2 min2 min2.5 h
Long-Term UseMaxMVLVLLMM
VasodilatorMinHVLVLLLH
Vasopressor MaxVHVHVHHML
Inotropy MaxVHHMHHM
Chronotropic Effect MinMHLHVLL
Myocardial Oxygen DemandMinVHHHMVHVL
Causes TachyarrhythmiaMinVHVHHHMH
Thrombogenic MinHYesNoNoNoNo
DiuresisMaxHVLMHVLVL
Peripheral Organ DamageMinLVHMLVLVL
Side EffectsMinHVHHMLM
Effectiveness with Beta BlockersMaxMNo NoNo NoYes
(VH: Very High, H: High, M: Moderate, L: Low, VL: Very Low).
Table 2. Dataset of inotropes and their properties assessed for chronic HFrEF [9,10,11,12,20,21,22,23,24,25,26,27,28].
Table 2. Dataset of inotropes and their properties assessed for chronic HFrEF [9,10,11,12,20,21,22,23,24,25,26,27,28].
Criteria/AlternativesAim/Imp.WeightsAdrenaline (β1 > β2 > α)Noradrenaline (β and α)Dopamine (dopa1-2, α1, β1)Dobutamine (β1 > β2 > α)Milrinone (PDE3 Inhibitor)
CostMinVL271 USD/30 mL (30 mg)120 USD/40 mL (40 mg)141 USD/3000 mL (4800 mg)136 USD/3000 mL (6000 mg)55.70 USD/200 mL (200 mg)
Steady-State Blood Concentration Reached In MinH10–15 min5 min5 min10 min20 min
Half-LifeMaxM3 min2.4 min2 min2 min2.5 h
Long-Term UseMaxHVLVLLMM
VasodilatorMaxHVLVLLLH
Vasopressor MinVHVHVHHML
Inotropy MaxVHHMHHM
Chronotropic Effect MinMH HVLL
Myocardial Oxygen Demand MinVHHHMVHVL
Causes Tachyarrhythmia MinVHVHHHMH
Thrombogenic MinVHYes No No No No
Diuresis MaxHVLMHVLVL
Peripheral Organ Damage MinVHVHMLVLVL
Side Effects MinVHVHHMLM
Effective With Beta Blockers MaxMNo No No No Yes
(VH: Very High, H: High, M: Moderate, L: Low, VL: Very Low).
Table 3. Obtained inotrope-ranking list via Fuzzy PROMETHEE for acute HFrEF.
Table 3. Obtained inotrope-ranking list via Fuzzy PROMETHEE for acute HFrEF.
RankInotrope Φ n e t Φ + Φ −
1Dopamine0.09990.12960.0297
2Noradrenaline0.09230.12640.0341
3Dobutamine0.01030.09420.0840
4Adrenaline−0.07780.05880.1366
5Milrinone−0.12460.07030.1950
Table 4. Obtained inotrope-ranking list via Fuzzy PROMETHEE for chronic HFrEF.
Table 4. Obtained inotrope-ranking list via Fuzzy PROMETHEE for chronic HFrEF.
RankInotrope Φ n e t Φ + Φ −
1Dopamine0.06320.10370.0405
2Milrinone0.05650.14850.0921
3Dobutamine0.02850.09830.0698
4Noradrenaline0.00810.07820.0701
5Adrenaline−0.15630.02060.1769
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Ozgocmen, C.; Balcioglu, O.; Uzun, B.; Uzun Ozsahin, D. Inotrope Analysis for Acute and Chronic Reduced-EF Heart Failure Using Fuzzy Multi-Criteria Decision Analysis. Appl. Sci. 2024, 14, 4431. https://doi.org/10.3390/app14114431

AMA Style

Ozgocmen C, Balcioglu O, Uzun B, Uzun Ozsahin D. Inotrope Analysis for Acute and Chronic Reduced-EF Heart Failure Using Fuzzy Multi-Criteria Decision Analysis. Applied Sciences. 2024; 14(11):4431. https://doi.org/10.3390/app14114431

Chicago/Turabian Style

Ozgocmen, Cemre, Ozlem Balcioglu, Berna Uzun, and Dilber Uzun Ozsahin. 2024. "Inotrope Analysis for Acute and Chronic Reduced-EF Heart Failure Using Fuzzy Multi-Criteria Decision Analysis" Applied Sciences 14, no. 11: 4431. https://doi.org/10.3390/app14114431

APA Style

Ozgocmen, C., Balcioglu, O., Uzun, B., & Uzun Ozsahin, D. (2024). Inotrope Analysis for Acute and Chronic Reduced-EF Heart Failure Using Fuzzy Multi-Criteria Decision Analysis. Applied Sciences, 14(11), 4431. https://doi.org/10.3390/app14114431

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