Study of some components of the influence and formation of blood flow in patients with “slow flow”

Abstract

BACKGROUND:

“Slow flow” is one very important concept in modern fundamental and clinical biomedicine. Slow coronary flow is indicative of delayed filling of the terminal coronary artery vessels, occurring in the absence of significant coronary stenosis. This group patient of patients exhibits a high incidence of disability and represents a significant financial and material burden for the state and the healthcare system in general.

OBJECTIVE:

The primary objective of our study was to examine patients with slow coronary flow.

METHODS:

We studied the standard parameters recommended by the international health care system (electrocardiography (by Medica QRS-12, Germany), through the electrical activity of a patient’s heart by the electrical impulses (beating) of the heart; HC1(Germany); coagulogramma by Coatron M1 (Germany), troponin by AQT 90 (Germany); general blood test we used automatic human counting device HC1(Germany). Also, we investigate the original parameters (non-standard parameters, which we use in this pilot study) that we were first studied for this diagnosis and non-standard parameters.

RESULTS:

A general blood test showed that patients with slow flow had a higher blood leukocyte count than the control group, but the amount of hemoglobin was normal, the hematocrit was much higher than in the control group, and the platelet count was close to the lower limit of clinical standards.

We obtained details of blood flow by coagulation situation, such as prothrombin time, prothrombin index, international normalized ratio, activated partial thromboplastin time, thrombin time, fibrinogen, and rheological properties such as index of erythrocyte aggregability, index of erythrocyte deformability, plasma viscosity, in silico blood rheological index.

CONCLUSSION:

Blood flow can be considered as a superposition of vortices with similar frequencies and wave vectors that change after bifurcations or other obstacles in the vascular network. These factors together determine the conditions for structuring the flow of moving blood. Disruption or alteration of these factors results in slow flow. It has been found that the speed of blood flow in the coronary arteries depends on changes in the number and function of red blood cells. Slow flow is directly influenced by the aggregation and deformation of red blood cells, their number, and plasma viscosity. Consequently, the rheological status plays a crucial role in determining blood flow and its velocity.

Keywords

Slow flow aggregation deformation coagulation/anticoagulation in silico blood rheological index plasma viscosity

1 Introduction

The concept of “slow flow” has recently become an integral to practical and basic medicine. In the early seventies of the last century, a distinctive coronary angiographic feature was identified in individuals with angina pectoris and normal coronary arteries, leading to the characterization of this phenomenon as “slow coronary flow” [1, 2]. Slow coronary flow is recognized as indicative of delayed filling of the terminal coronary arteries, which occurrs in the absence of significant coronary stenosis. Notably, approximately 80–90% of patients with slow coronary flow report recurrent chest pain, with 33% requiring hospital readmission and 2.5% facing a poor prognosis marked by an increased risk of ventricular arrhythmias and cardiovascular mortality [3 –6]. Consequently, these patients require continuous monitoring and regular clinical observation.

This patient group exhibited a high incidence of disability and represented asubstantial financial and physical burden to both the state and the healthcare system. Beyond the socio-economic challenges associated with slow coronary flow, increased interest in the issue has been spurred by advances in digital research methods, the advent of new drugs, and evolving preventive health policies. The current relevance of slow coronary flow research is underlined by the increasing availability of highly regarded scientific articles exploring the development of slow flow in patients. As a result, the study of slow coronary flow has emerged as a major research problem in biomedicine and modern clinical cardiology.

Various theories regarding the pathogenesis of slow flow exist among researchers. Some suggest that slow flow may underlie the pathogenesis of myocardial ischemia associated with endothelial dysfunction of the coronary arteries. Conversely, others associate slow flow with inflammatory responses, impaired microvascular reserve function and subclinical atherosclerosis. Numerous studies support the association of slow flow with impaired blood function, platelet abnormalities, and genetic factors [7 –16]. See Fig. 1.

Fig. 1

The pathogenesis of coronary slow flow. Current understanding posits that Coronary Slow Flow (CSF) may be a potential pathogenic factor in myocardial ischemia. This association is linked to several factors, including endothelial dysfunction in the coronary arteries, inflammatory responses, abnormalities in microvascular reserve function, subclinical atherosclerosis, blood cell and platelet abnormalities, and genetic factors. Copy [15].

In contemporary clinical practice, primary slow flow is recognized as an independent clinical entity. It is important to distinguish primary slow flow, which has functional differences, from secondary slow flow which has a variety of causes. These causes include conditions such as coronary ectasia, coronary stenosis, coronary spasm, structural abnormalities of the heart (including heart failure, congenital heart disease, valvular dysfunction, hypertrophic or dilated cardiomyopathy), cardiac conduction disorders (ventricular preexcitation, atrioventricular conduction disturbances, bundle branch block, atrial fibrillation, cardiac pacing), angioplasty and stenting for acute myocardial infarction, uncontrolled hypertension, severe bradycardia, hypothyroidism, hyperthyroidism, malignancies, autoimmune diseases, inflammatory or immune diseases, local or systemic infections, as well as pulmonary, hepatic, renal, and hematological diseases [17].

The primary objective of our study was to investigate patients with slow coronary flow. In all patients, we pereformed a comprehensive examination of factors that influence the structure of blood flow. Our focus was to identify factors that, in our perspective, contribute to the provocation of primary slow flow. In the course of our work, we aim to present our vision and describe the key mechanisms involved in structuring primary slow flow.

2 Materials and methods

2.1 Patients

We studied 14 patients with slow flow and 10 control patients. Inclusion criteria: patients with “slow flow” patients with acute coronary syndrome, who were angiographically characterized by slow flow in the coronary arteries. Exclusion criteria are: coronary ectasia, coronary artery spasm, coronary artery stenosis, embolism, heart failure, angiography and angioplasty, significant valvular pathology or connective tissue disease. On the basis of informed consent, which was drawn up in accordance with the recommendations of the Declaration of Helsinki on the rights of patients and healthy volunteers involved in biomedical research, the following studies were carried out on all patients and representatives of the control group: ECG, coronarography, clinical blood test, cholangiogram, creatinine, troponin, erythrocyte aggregability, erythrocyte deformability, plasma viscosity, hematocrit, in silico rheological method.

2.2 Methods

We studied the standard parameters recommended by the international health care system (electrocardiography (by Medica QRS-12, Germany), which tracks the electrical activity of a patient’s heart by the electrical impulses (beating) of the heart; HC1 (Germany); coagulogramma by Coatron M1 (Germany), troponin by AQT 90 (Germany); general blood test we used automatic human counting devise HC1(Germany). Also, we investigated the original parameters (non-standard parameters that we are using in this pilot study) that we were first studied for this diagnosis.

2.3 Original Methods for investigate non-standard parameters

2.3.1 Index of erythrocytes aggregability (EAI)

The erythrocyte aggregability index represents the ratio of the area of aggregated erythrocytes to the total area of the erythrocytes. Erythrocyte aggregation was assessed using the recently developed “Georgian technique”, which provides us with direct and quantitative data. Blood samples (4 ml) from the cubital veins were centrifuged and about 0.1 ml blood was diluted 1 : 200 in autologous plasma in the Thoma pipettes pre-rinsed with 5% sodium citrate solution without the addition of any other anticoagulant to the blood under study. After standard mixing the diluted blood was placed into a 0.1 mm high glass chamber. The quantitative index of erythrocyte aggregation, which was assessed with a special program on the Texture Analysis System (TAS-plus, “Leitz, Germany), represented the ratio between aggregated and non-aggregated red blood cells [18 –20].

2.3.2 Erythrocyte deformability index (EDI)

The evaluation of erythrocyte deformability was performed using the nucleopore membrane filter method, which is based on assessing the velocity of the erythrocytes passage through very small pores (5μm, which is a diameter of the smallest capillary) of a filter, at constant pressure (10 cm of water column) and temperature (37°C). To obtain the pure erythrocytes, the blood sample was centrifuged at 3000 rpm, for 15 min. The resulting plasma was aspirated with a micropipette and the remaining blood cells were added with bovine serum albumin (0.2 mg per 5 ml) dissolved in the phosphate buffer. The blood was then centrifuged a second time at 1000 rpm for 5 min. The precipitated erythrocytes, as well as a thin layer of leukocytes and thrombocytes were separated from the phosphate buffer. This process was repeated three times. The purified erythrocyte mass was diluted in the phosphate buffer, with a hematocrit of 10%. The deformability index was evaluated by measuring a velocity of the erythrocyte passage through the filter (mm/min). High-quality polycarbonate filters (with 5μm diameter pores) were used for the measurments [18 –20].

2.3.3 Plasma viscosity

Blood plasma viscosity was examined in a capillary viscometer at 37°C. The diameter of the capillary was about 1.8 mm. Displacement of plasma samplesDisplacement of the plasma samples was induced by the gravitional force related to the difference in niveaux of the plasma under study (without application of additional pressure). To evaluate the plasma viscosity in centipoises (cP), we determined the calibration factor (F). Blood plasma viscosity was calculated by multiplying the time taken for the plasma to pass through the capillary by the instrument calibration factor.

2.3.4 In silico Blood rheological index (BRI)

Abbreviations in this subchapter

BRI – red blood coefficient RBC – erythrocyte

RDW – red cell distribution width

OS – overall size of red cell distribution width

MCH – mean corpuscular hemoglobin

MCV mean corpuscular volume

To study blood rheology, we used a new rheologically significant parameter – the Red Blood Coefficient (BRI). The BRI is a complex indicator that mathematically reflects such indicators as the number of erythrocytes, their overall size, volume, and the amount of haemoglobin in each of them. The calculation of the BRI gives the clinician a comprehensive view of all the independent parameters of the red blood cells involved in the formation of laminar or turbulent flow, depending on blood viscosity. Thus, if we assume that the viscosity of the plasma is constant, then it is the BRI that is responsible for haematology.

If we analyze each of the parameters we are investigating from the point of view of its physical significance, we get that $RDW = \max (OS) / \min (OS),$ (1) as the parameter of red blood cell distribution is the ratio of the largest large red blood cell to the smallest red blood cells. It follows from (1) that $\max (OS) = RDW * \min (OS)$ (2)

On the other hand, if we will multiply the total number of red blood cells by the average haemoglobin, we get the numerical value of haemoglobin $\max (OS) + min (GS) = RBC * MCH$ (3)

It follows from (3) that $\max (OS) = RBC * MCH - \min (OS)$ (4)

On the other hand, the volume of a red blood cell is equal to the sum of all red blood cells with large dimensions and all red blood cells with smaller dimensions divided by “2”, if n is the number of red blood cells with large dimensions, and (RBC – n) is the number of red blood cells with smaller dimensions $MCV = ((max (OS) * n + min (OS) * (RBC - n)) / 2$ (5)

Hence it follows that $\max (GS) * n + \min (GS) * (RBC - n) = 2 MCV .$ (6)

Thus, if we group formulas (2), (4), (6) into a system of equations, we have three unknowns and three easily solvable equations in the system $\begin{matrix} \max (OS) = RDW * \min (OS), \\ \max (OS) = RBC * MCH - \min (OS), \\ \max (OS) * n + \min (OS) \times (RBC - n) = 2 MCV, \end{matrix}$ where max(OS)*n is the coefficient of red blood [18 –20].

2.4 Statistic analysis legal issues

Arithmetical mean, standard deviation and T-Student’s criteria were calculated by Origin 8.1 (Micro Soft., 2023).

All subjects were informed of their inclusion in the study. Informed consent was signed. The Ethical Committee of the Society of Rheologists granted permission for the research protocol (405133029_1, May 29, 2023).

3 Results

A general blood test showed that in patients with slow flow, leukocyte counts were higher than those in the control group, but the amount of hemoglobin was normal, the hematocrit was much higher than in the control group, and the platelet count was close to the lower limit of clinical standards (see Table 1).

Table 1
Mean of count of leukocytes (WBC), hemoglobin (HGB), hematocrit (HCT), thrombocytes (PLT) in patients with “slow flow” and control group. M±m

Type of subjects WBC,×10 unit /1 HGB, g/l HCT, % PLT,×10³ cells/μl

Patients with “slow flow” 9.3±1.2 155±58 45.9±0.5 211±83

Control 5.0±1.7 129±35 44.0±0.5 250±58

Type of subjects	WBC,×10 unit /1	HGB, g/l	HCT, %	PLT,×10³ cells/μl
Patients with “slow flow”	9.3±1.2	155±58	45.9±0.5	211±83
Control	5.0±1.7	129±35	44.0±0.5	250±58

We received details of blood flow by coagulation situation, such as prothrombin time, prothrombin index, international normalized ratio, activated partial thromboplastin time, thrombin time, fibrinogen (see Table 2), and rheological properties such as index of erythrocytes aggregability, index of erythrites deformability, plasma viscosity, in silico blood rheological index (see Table 3).

Table 2

Mean of prothrombin time (PT), prothrombin index (PI), international normalized ratio (INR), activated partial thromboplastin time (APTT), thrombin time (TT), fibrinogen (FIB). M±m

Type of subjects	PT, sec	PI, %	INR, unit	APTT, sec	TT, sec	FIB Mg/100 ml
Patients with “slow flow”	20±2	112±21	1.15±0.07	34±1	13±1	450±40
Control	15±1	95±6	0.97±0.02	39±1	11±1	260±58

4 Discussion

A distinguishing feature of the patients was the presence of slow flow. A comprehensive review of current literature underscores that this phenomenon may serve as a response to various pathophysiological processes.

Specialized epithelial cells develop within the intravascular layer of coronary vessels, positioned between the vascular tissue and the plasma. These cells contribute significantly to normal cellular vasodilation and vascular contraction and play a pivotal role in maintaining vascular tone, monocyte adhesion, and vascular homeostasis [21]. Extensive studies suggest that in patients with slow flow, there is a reduction in endothelium-dependent dilatation, indicating that coronary vascular endothelial dysfunction may play a substantial role in the development and progression of the disease [11 , 22–24].

Vascular endothelial cells serve as controllers of vascular tone, regulating local concentrations of circulating vasoactive substances through the synthesis and release of these substances [21 , 25]. Two main types of active substances are secreted by these cells: vascular endothelial contractility factors (including endothelin-1 [ET-1], [26], prostaglandins (PG) [25, 27], angiotensin [ANG], and thromboxane A2 [TXA2]) and vascular endothelial diastolic factors (such as nitric oxide [NO] and prostaglandin I2 [PGI2]). These substances act collaboratively to regulate the dilation and contraction of blood vessels, thereby maintaining vascular tone.

Nitric oxide (NO) and nitric oxide synthase (NOS) play pivotal roles in these processes, exerting potent diastolic effects. Under physiological conditions, endogenous NO is produced by endothelial NO synthase (eNOS), catalyzing the conversion of ammonia and L-arginine molecules into NO and L-guanosine. NO then undergoes conversion to cyclic guanosine monophosphate in smooth muscle cells, activating protein kinases and reducing intracellular Ca2 + . This cascade leads to vasodilation, contributing to the regulation of platelet activity, leukocyte adhesion, and angiogenesis [22].

These findings highlight the intricate role of endothelial cells and the associated biochemical pathways in the context of slow flow and shed light on potential therapeutic targets and avenues for further research.

Our data show that rheological properties play a certain role in the structuring of slow flow. In particular, it is a change in the rigidity of red blood cells against the background of a large increase in blood viscosity. Another factor contributing to the slow flow rate is the aggregability of erythrocytes, which is inherent in many cardiac diseases. All this is exacerbated by the fact that both the vascular factor and the coagulation/anticoagulation system are disturbed.

Vascular endothelial cells orchestrate the control of vascular tone and the regulation of local concentrations of circulating vasoactive substances through the synthesis and release of these substances [21]. These cells actively secrete two different types of substances: vascular endothelial contractile factors, including endothelin-1 (ET-1) [23], prostaglandins (PG), angiotensin (ANG), and thromboxane A2 (TXA2), and vascular endothelial diastolic factors, including nitric oxide (NO) and prostaglandin I2 (PGI2). The harmonious interaction of these substances serves to finely regulate the dilation and contraction of blood vessels, thereby maintaining vascular tone [25].

Nitric oxide (NO) and nitric oxide synthase (NOS) play pivotal roles in this regulatory process, exerting potent dilatative effects. Under normal physiological conditions, endothelial NO synthase (eNOS) catalyzes the conversion of ammonia and L-arginine molecules into NO and L-guanosine. This endogenous NO is subsequently converted to cyclic guanosine monophosphate in smooth muscle cells, activating protein kinases and reducing intracellular Ca2+. The resulting vasodilation plays a crucial role in the complex regulation of platelet activity, leukocyte adhesion, and angiogenesis [22].

Within the cardiovascular system, NOS expression is localized to the endothelium, the dysfunction of which is thought to underlie most forms of coronary artery disease [28]. NOS, serving as the rate-limiting enzyme for NO synthesis, is classified into three functional types: neurogenic NOS, eNOS, and inducible NOS. Reduced expression of eNOS is particularly implicated in the pathogenesis of coronary artery disease, resulting in decreasewd NO synthesis. Nitric oxide plays a multifaceted role by inhibiting platelet aggregation, attenuating platelet and leukocyte adhesion, and counteracting vascular smooth muscle cell proliferation. The pathophysiological changes resulting from reduced NO synthesis are key events characterizing the course of atherosclerosis [29].

This complex interplay highlights the importance of vascular endothelial cells, NO, and NOS in maintaining vascular homeostasisand provides valuable insights into potential therapeutic targets for conditions associated with slow coronary flow. Other studies have provided insight into the relationship between slow flow and endothelial dysfunction. At rest, plasma endothelial nitric oxide synthase (eNOS) levels were found to be significantly lower in patients with slow flow compared with controls. Furthermore, these eNOS levels were negatively correlated with thrombolysis in exercise-induced myocardial infarction, suggesting a potential role for eNOS in the development and progression of the slow flow phenomenon [30, 31].

Inflammatory cytokines, including interleukin (IL), tumor necrosis factor-α (TNF-α), and C-reactive protein (CRP) are emerging as crucial factors to consider. They play a pivotal role in inflammation, a key player in the pathogenesis and development of blood flow abnormalities [32 –34]. Slow flow has been linked to a chronic inflammatory response that promotes vascular remodelling and increases resistance to blood flow, thereby contributing to the slowing of blood flow [35]. Biomarkers of inflammation have been associated with the severity of blood flow abnormalities [36, 37]. Further evidence supporting the link between slow flow and the vascular inflammatory response comes from studies demonstrating elevated IL-6 levels in patients with slow flow compared to those with normal flow [38, 39]. The platelet-to-lymphocyte ratio is identified as a potential risk factor for the development of slow flow [40].

Endothelial activation and inflammation at the microvascular level may also play a significant role in the pathogenesis of slow flow [41, 42]. Some propose that slow flow may represent an early form of atherosclerosis, referred to as subclinical atherosclerosis, which remains clinically undetectable during a prolonged latent period. Notably, vessels may exhibit morphological changes, including alterations in intima-media thickness associated with cell proliferation during disease progression. Studies have revealed extensive calcification of coronary vessel walls, diffuse intimal thickening, and non-obstructive atherosclerotic changes in the coronary arteries among patients with slow flow [43, 44], indicating potential subclinical atherosclerotic changes.

Some researchers suggest that subclinical atherosclerosis may play a crucial role in the pathogenesis of slow flow. The composition and hemodynamics of blood cells influence the flow and velocity of blood flow in the coronary arteries. Changes in the number and function of various blood cells can affect slow flow dynamics. For example, alterations in red blood cell deformation and aggregation can alter blood viscosity, which influences flow resistance [45, 46]. Numerous studies have demonstrated increased red blood cell distribution width in patients with slow flow compared to controls [47, 48]. Elevated platelet counts in peripheral blood, increased platelet aggregation, and an augmented platelet release response may compromise platelet function. Platelet count, mean platelet volume, platelet distribution width, and platelet levels are significantly higher in patients with slow flow than in controls [49]. Consequently, platelet count and platelet aggregation rate have been identified as independent predictors of slow flow [50]. Furthermore, an increase in the number of eosinophils has been reported in patients with slow flow, which is associated with platelet activation [51]. Taken together, these findings suggest that platelet abnormalities may directly or indirectly contribute to the development of slow flow.

Researchers have recently turned their attention to the genetic predisposition [52 –55]. However, conflicting data have emerged regarding the significance of the eNOS Glu298Asp gene polymorphism in the contractile and diastolic factors of vascular endothelium. Inflammatory factors may contribute to the development of slow flow by enhancing the immune system, as evidenced by significantly higher levels of the IL-1β-511 SNP among patients with slow flow compared to those with normal coronary angiograms [15].

Despite a substantial body of literature devoted to the role of erythrocyte structuring, the contribution of erythrocytes to the formation of slow flow remains not fully understood.

At the physical and mathematical level, slow flow involves changes in linear and volumetric velocities, which can be associated with alterations in vascular lumen or changes in the wall without a corresponding change in vascular lumen.

Changes in the vascular lumen are influenced by various physical and elastic factors such as elasticity, plasticity, and deformability. The maintenance of blood flow structure is attributed to the constancy of blood viscosity characteristics, known as viscosity homeostasis. Blood viscosity is influenced by the deformation and aggregation of red blood cells. The dominance of erythrocytes over other cellular elements and plasma makes them particularly significant in terms of blood structuring. The ability of erythrocytes to form aggregates explains the peculiarities of blood flow curves [12 , 55–57].

Conversely, the viscosity of a liquid can vary depending on the presence of particles lacking the ability to deform [11, 58]. Changes in rheological determinants result in increased erythrocyte aggregation, leading to heightened viscosity, while increased deformability contributes to its decrease, and vice versa [59].

As a consequence, the viscosity characteristics of moving blood are closely intertwined with the rheological parameters of red blood cells. In laminar mode, for slowly flowing viscous liquids, velocity exhibits a parabolic dependence with a zero value at the vessel wall. From the perspective of mechanics and materials science, blood can be considered a non-Newtonian fluid, occupying an intermediate state between an emulsion and a suspension [44–60 , 65].

In accordance with the laws of parabola, the velocity distribution in blood flow can be described by the equation $VX (y) = V_{0} - y^{2},$ (7) where the modulus of the velocity vector V₀ in the center of the vessel is calculated from f(x) = y²: V₀ = (1/2 D)² = 1/4D², with D being the diameter of the vessel. As a result, the boundary conditions for V_X (0) = V₀ ∏ / V_X (D/2) = 0. The velocity gradient in the direction perpendicular to the motion vector, representing the relative velocity in the fluid flow tubes or shear velocity ∂Vx/∂y in the vessel lumen (parabolic distribution according to Bernoulli’s principle), is calculated as $\partial Vx / \partial y = 2 y .$ (8)

The shear rate ∂Vx/∂y is then computed on the axis of the vessel where y = 0 and on its wall where y = 1/2*D, also, due to velocity gradients between neighboring layers, a rotational moment of particles arises (Fig. 2).

Fig. 2

a) Velocity profile in the vessel and b) rotation of cells in the vessel.

Thus, the shear rate in the lumen is proportional to the speed of blood flow and follows a linear law from zero in the center to a final value. This shear rate is crucial in determining the internal force for the destruction of erythrocytes. An increase in speed corresponds to a decrease in pressure, and vice versa, as per the Bernoulli equation.

Shear forces are minimal in the central regions of vessels enriched with cellular elements, leading to cell aggregation due to their inherent abilities. These aggregates, primarily of erythrocytes, form in the center, while platelets and leukocytes are pushed to the parietal layer of plasma, where conditions are conducive to their proper function.

In the context of non-Newtonian fluid flow, such as blood, the velocity distribution profile deviates from classical concepts and exhibits a characteristic blunted appearance known as plug flow [1]. In multiphase systems such as blood, particles segregate based on their rheological properties.

The presence of velocity gradients on the surface of non-spherical particles has an orienting effect [8]. When a fluid flows around an obstacle, periodic flow perturbations occur, leading to the formation of counter-rotating vortices (Karman path) [8, 63]. After bifurcations, which can be considered obstacles, flows with multidirectional rotation flow occur in the secondary branches of the vessel. These objective conditions favour the vortex motion of the blood flow, where particles not only move translationally but also rotate along a specific axis, aided by increased viscosity which helps to maintain the wake vortex. Blood flow can therefore be viewed as a superposition of vortices with similar frequencies and wave vectors, changing after bifurcations or other obstacles in the vascular network. Together, these factors determine the conditions for structuring the flow of moving blood. Disruption or alteration of these factors results in slow flow. It has been found that the velocity of the blood flow in coronary arteries depends on changes in the number and function of red blood cells. Slow flow is directly influenced by the aggregation and deformation of red blood cells, their number and plasma viscosity. Consequently, the rheological status plays a crucial role in determining blood flow and its velocity. Our studies revealed that cumulative changes in rheological parameters contribute to the onset of slow blood flow. Further research in this direction is imperative.

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