Blood flow is essential for any living organism. Reductions in blood flow lead to tissue ischemia and if severe to tissue necrosis. In the medical literature, much attention is given to aspects like heart failure, blood pressure, vessel stenosis and/or obstruction as important factors for adequate blood flow in the human organism. In this review, we want to give special attention to two aspects, which in our view are also important for optimal blood flow and which are often neglected in the current medical world. We try to explain how blood viscosity and ideal dynamic blood flow patterns play a pivotal role in the maintenance of optimal blood circulation in the human organism.

Newtonian fluids like water or alcohol have a constant viscosity; however, blood is a non-Newtonian fluid, which means that its viscosity is not constant, but will rise exponentially at lower blood velocity. (Figure 1) The organism will always try to prevent high viscosity in order to sustain proper hemodynamics with adequate blood flows via the systemic vascular resistance response [1-4]. Blood viscosity is symbolized by the Greek letter “η” and is expressed in centipoise (cP) or mPa.sec. As blood viscosity varies for different shear rates, it should always be mentioned at which shear rate it is measured. In normal conditions, laminar blood flow exists in the circulatory system. The velocity at which each layer (lamina) moves over its adjacent layer is defined as shear rate; whereas the force to move one layer of blood over the next layer is defined as shear stress. (Figure 2) The viscosity of a fluid is defined by the relationship between shear stress and shear rate. At higher viscosity levels more shear stress is needed to obtain the same shear rate.

Figure 1: The graph shows the constant viscosity of Newtonian fluids and the exponential rise in viscosity of no n-Newtonian fluids such as blood, when shear rate decreases.

Figure 2: The shear rate is the gradient of velocity between two velocities (v1 and v2) of blood layers (dv/dx), whereas shear stress is the force (F), which is necessary to move lamina 1 over lamina 2. The viscosity is defined as the friction between the two blood layers and can be expressed as viscosity=shear stress/shear.

In order to understand the difference between blood flow velocity and shear rate of blood, an appreciation of non-Newtonian characteristics is crucial. In the middle of a blood vessel, the flow velocity is maximal, but shear rate is the lowest. In the middle of the blood stream each layer moves more or less at the same speed; therefore, the shear rate is very low. At the vessel wall, the shear rate is highest because the closest blood layer moves and the vessel wall (endothelium) stands still [5]. (Figure 3) The evolutionary purpose of these differences in shear rate is that high shear rate stimulates endothelial production of prostacyclin and nitric oxide, thereby preventing endothelial dysfunction [6]. The high shear rate at the vessel wall is not only beneficial for the endothelium but will also lower blood viscosity adjacent to the vessel wall, hence lowering the resistance for blood flow. On the other hand, the lower shear rate in the middle of the vessel will increase viscosity, which is required to advance blood through a vessel by preventing turbulence. In this way, blood is transported at the lowest energy due to its non-Newtonian characteristics.

Figure 3: Due to the non-Newtonian properties of blood and the usually laminar flow profile within blood vessels shear rate will be lowest in the middle of a blood vessel, where blood velocity is highest. At the vessel wall shear rate of blood is highest, where blood velocity is lowest.

Thus, shear rate is the strongest determinant of blood viscosity. The second important determinant of blood viscosity (η_b) is the hematocrit (Ht) [7-9]. Figure 4A depicts how blood viscosity exponentially increases at higher hematocrit, whereas Figure 4B shows Ht/η_b, which reflects the rate of oxygen transported for a given cardiopulmonary function. It is clear that if hematocrit increases appreciably and subsequently viscosity rises greatly, blood flow will be hampered, which will lead to diminished oxygen transport despite high levels of hemoglobin. An optimum of hematocrit exists, at which oxygen transport and tissue perfusion is ideal.

Figure 4: Blood viscosity rises exponentially at higher hematocrits (A); therefore, oxygen supply and tissue perfusion in general will diminish at the same rate, when hematocrit is too high (B). An optimum of hematocrit exists, which in women is between 35.5 and 44.9 percent and in men between 38.3 and 48.6 percent. The optimum hematocrit will be at a lower level if viscosity in blood rises due to factors other than hematocrit, for example in chronic inflammation with high levels of large ‘acute phase’ proteins such as fibrinogen.

The third important determinant of blood viscosity is the level of proteins in the blood [10-12]. Normally blood cells have a negative electric charge on their surface, which causes cells to repel each other. Large inflammatory proteins, such as fibrinogen, may overcome these repulsing intercellular forces by binding to specific receptors on the cell surface and creating intercellular bridges. Acting like a glue between cells, these inflammatory proteins will cause sludging of the blood, especially at a low shear rate (Figure 5). The reversible aggregation between blood cells is called rouleaux formation and is considered to be the preliminary stage of thrombus formation [8]. Higher shear rates can disrupt the intercellular bridges of these inflammatory proteins.

Figure 5: Fibrinogen is able to create intercellular bridges between red blood cells, which normally repulse each other due to the negative electric charge at their cell surfaces. Rouleaux formation will be seen by microscopy at the lower shear rates.

A lower hematocrit will lead to larger distances between red blood cells and will cause less of an increase in viscosity, when low shear rate occurs (Figure 6). Large inflammatory proteins will be less able to bind adjacent blood cells together, consequently with a reduced likelihood of rouleaux formation.

Figure 6: This graph reflects the relationship between shear rate and blood viscosity for two different hematocrits (resp. 40 and 20%). At higher hematocrits blood viscosity will increase more rapidly and even at higher shear rates rouleaux formation will occur, the preliminary stage of thrombus formation. Normally at shear rates above 50/sec disaggregation occurs and at highest shear rates red cells alter their shape.

The fourth determinant of blood viscosity is the deformability of the red blood cells. This factor becomes important especially during high shear rate [13-14] (Figure 6).

Having explained the interaction between blood flow and blood viscosity it becomes clear how viscosity becomes one of the factors affecting the volume of flow through a vessel, as represented in the Hagen-Poisseuille equation:

Q= ΔP.π.r⁴/8.l x 1/η

where, Q is the volume of flow, ΔP is the pressure gradient, π is a constant, r is the radius of the vessel, l is the length of the vessel and η represents viscosity. Considering Ohm’s equation R=ΔP/Q (in which R represents resistance), we can simply combine the two equations:

R = 8l / πr⁴ x η (= vascular resistance x blood viscosity).

The radius of the vessel is raised to the fourth power reflecting the most efficient treatment for increased peripheral resistance, as observed in vasodilating pharmaceuticals for hypertension. However, in older patients with reduced compliance of the vascular wall, vasodilatation becomes less feasible and the factor of viscosity becomes more important [1,15]. In elderly patients with chronic heart failure, the shear rate decreases due to a failing heart pump and inflammatory proteins are often elevated, both of which lead to increased blood viscosity. These chronic heart failure patients commonly are anemic, which may act as a compensatory mechanism by lowering the total resistance and preserving tissue perfusion [16-17]. This hypothesis is supported by evidence that in several heart failure trials, in which anemia was corrected with erythropoietin drugs, a significant increase in cardiac mortality has been reported [18,19]. Another consequence of the interaction between blood flow and blood viscosity centers around the high levels of inflammatory proteins in chronic inflammatory disorders, resulting in “stickiness of the blood” [10-11]. Therefore, from a theological point of view, the occurrence of anemia in chronic inflammatory disorders should be considered as a compensatory mechanism during states of hyperviscosity caused by elevated levels of inflammatory proteins [20]. Similarly, during pregnancy mild anemia can occur. In the intervillous spaces within the placenta, the maternal and fetal circulation make contact for optimal gas and nutrient exchange between maternal and fetal blood. The flow (shear rate) in these intervillous spaces is low. Due to the non-Newtonian characteristic of blood, this low shear rate will increase blood viscosity. Again, to prevent the deleterious effects of hyperviscosity, the mother’s hematocrit is lowered. Clinical studies have demonstrated that pregnant women who have normal or high hematocrit in the first trimester often develop preeclampsia [21]. By supplying intravenous fluids, blood viscosity is lowered and the growth of the fetus is restored if dysmaturity is present and blood pressure in the mother with preeclampsia decreases [22]. Another example of the physiological importance of blood viscosity is found in cerebrovascular accidents or in post-resuscitation encephalopathy, where cerebral blood flow is enhanced if blood viscosity is lower [23-25]. Furthermore, the occurrence of low blood flow (shear rate) in the left atrium during atrial fibrillation leads to increased blood viscosity, reflected by the appearance of rouleaux formation, visualized by the presence of spontaneous echo contrast(s) in the left atrium during echocardiography [26]. Multiple studies have shown that the presence of spontaneous echo contrast(s) in the left atrium is correlated with the appearance of emboli, consistent with the concept that rouleaux formation is the preliminary stage of thrombus formation [27] (Figure 7).

Figure 7: Presence of spontaneous echo contrast (rouleaux formation between the red blood cells) in the left atrium (LA) and left atrial appendage (LAA) as sign of hyperviscosity. (Ao = aorta).

Blood viscosity has a circadian pattern with the highest levels occurring in the early morning hours [28]. This is why according to the rheological point of view, thrombotic coronary and cerebrovascular events often occur in the early morning hours. Lastly, increased blood viscosity will lead to lower shear rate in areas of changing vascular geometry due to the non-Newtonian characteristics of blood and according to the formula:

Shear rate = shear stress/viscosity

A lower shear rate at the vessel wall will lead to endothelial dysfunction, which is a precursor for the development of atherothrombosis [29]. Several small and large clinical studies have demonstrated the close relationship between hemorheological abnormalities and the occurrence of atherothrombosis [30-34]. The chronic inflammatory character of atherothrombosis [35-36] causes higher viscosity, which is also the reason why atherothrombosis occurs more often in other chronic inflammatory disorders like rheumatoid arthritis, psoriasis and other auto-immune disorders [34,37,38]. All these examples demonstrate the clinical importance of blood viscosity for the maintenance of adequate tissue perfusion and the prevention of thrombus formation. Rudolf Virchow described in 1846 his Triad, which leads to thrombosis: stasis of blood, abnormal composition of blood and defects of the vessel wall. Sluggish blood flow is a manifestation of increased blood viscosity. Blood viscosity plays a role in each of the three factors of Virchow’s Triad. At low flow (shear rate), viscosity rises and vice versa. High blood levels of inflammatory proteins can raise viscosity and produce abnormalities to the vessel wall, which will disturb blood flow patterns, leading to low shear regions where blood viscosity will increase and dysfunction of the endothelium will occur, leading to atherothrombosis. More evidence is emerging that autoregulatory mechanisms may be involved to keep blood viscosity at an optimal level for tissue perfusion [4,39]. The French physiologist Claude Bernard described, almost 200 years ago, the importance of a stable “milieu intérieure” in a living organism. Similar to pH, body temperature or osmotic pressure, blood viscosity should also be considered as one of the key determinants of this “milieu intérieure”. Appropriate homeostasis of blood viscosity will optimize tissue perfusion and prevent cardiovascular thrombogenesis.

Preventive and Therapeutic Consequences

Considering the importance of blood viscosity, several preventive and therapeutic options are available for hyperviscosity. Large epidemiological studies have shown that drinking a few extra glasses of water during the night will decrease the chance of an ischemic event [40-41]. The recent COVID-19 pandemic has shown multiple thrombo-embolic complications in these patients and hyperviscosity and high fibrinogen levels have been observed as a prognostic factor for the occurrence of these thrombotic complications [42,43]. We reported that sufficient oral hydration for a week may decrease the chance of thrombotic complications after vaccinating against COVID-19 [44]. One of the pleiotropic effects of statins is that they lower blood viscosity, probably as part of their anti-inflammatory effect [45]. This lowering effect in blood viscosity is one of the reasons why statins appear to have beneficial effects in the treatment of COVID-19 patients [46]. Several years ago, a clinical study revealed that statins given a few days before Coronary Artery Bypass Grafting (CABG) reduced the incidence of atrial fibrillation post-surgery [47]. No obvious explanation was presented; however, in our viewpoint, lowering blood viscosity with statins would decrease the workload of the atrium, reflected in less atrial strain and hence lowering the chance for atrial fibrillation to develop. Reduced blood viscosity will also increase perfusion of the left atrial myocardium. Besides simple hemodilution or administration of statins, efforts should be made to develop drugs, which specifically are targeted to lowering blood viscosity. However, it should be recognized that especially in chronic situations, our body will decrease blood viscosity, such as what is found in the anemia during pregnancy or by the induction of anemia in chronic inflammatory disorders. In these cases, it is important to acknowledge the homeostatic regulation by our body in addressing and treating the anemia. Sometimes a certain level of anemia is better for optimal tissue perfusion [4].

The Blood Flow Follows Preferential Patterns

Similar to the preferential laminar flow in blood vessels, preferential flow patterns exist in the heart to minimize the energy load for efficient contractions. Leonardo da Vinci described the specific aspects of the aortic sinuses, which play an architectural role so that the aortic valve automatically closes after each cardiac contraction [48,49]. (Figure 8) This concept, first discovered by Leonardo da Vinci, has been copied by bioengineers of today when developing aortic ascending root grafts used in the David surgical procedure, in which the aortic valve is spared [50]. The proximal convex shape of the graft mimics the aortic sinuses and helps to create the vortexes, which lead to an optimal closing of the aortic valve.

Figure 8: The vortex in the aortic sinuses, which helps to close the aortic valve after each contraction is depicted schematically in A. This functional anatomy has already been discovered and depicted by Leonardo da Vinci in his drawings around 1500 AD (see B and C).

Within the heart, preferential flow patterns also exist. During diastole, blood flows from the left atrium into the in-flow tract, located posteriorly in the left ventricle. Subsequently the flow turns around at the apex and again with help of an intracavitary vortex, blood is directed towards the out-flow tract at a low energy cost [51-52]. The Bjork-Shiley prosthetic disc valve has a major and a minor orifice. The optimal orientation of the Bjork-Shiley disc prosthesis implanted in the mitral position should be with the major orifice towards the in-flow tract in order to mimic as much as possible the preferential flow pattern in the normal heart [53] (Figure 9).

Figure 9: The optimal position of the Bjork-Shiley tilting disc valve prosthesis is when the greater orifice is directed posteriorly towards the inflow tract; this mimics best the preferential flow pattern in the heart with a normal mitral valve. When the greater orifice of the disc prosthesis is directed towards the septum turbulence inside the left ventricle will occur as well as a significant transmitral gradient.

The mean prosthetic diastolic gradient, calculated using continuous wave Doppler, averages 2.7 mmHg (+/- 0.8 mmHg) for the 27-mm prosthesis in the physiologically correct orientation, but 5.6 mmHg (+/- 0.2 mmHg) for the same size prosthesis in the opposite orientation. Just as the anatomy of the aortic sinuses support the optimal flow conditions during systole, in a similar fashion, the anatomy of the normal mitral valve during diastolic blood flow is oriented according to its preferential pattern. The large anterior leaflet directs blood posteriorly, towards the left ventricular in-flow tract (Figure 10).

Figure 10: The normal mitral valve has a large anterior leaflet and a substantially smaller posterior leaflet in order to direct during diastole blood flow posteriorly towards the inflow tract according to the preferential flow pattern inside the left ventricle. Anatomy and physiology are in perfect harmony.

Recently, we examined the intracavitary flow patterns after mitral valve replacement with the biological Perimount Magna Ease prosthesis, size 27 [54]. Using Color Doppler flow analysis, we demonstrated that the intracavitary flow pattern after implantation of this bioprosthesis did not respect the preferential intracavitary flow pattern, in which the transmitral mean gradient at rest was even higher than in those patients implanted with a similar size Bjork-Shiley prosthesis with optimal orientation. The difference of transmitral gradients became even more pronounced during exercise (Table 1).

Table 1: The asymmetric construction of the Bjork-Shiley tilting disc prothesis, if positioned correctly, mimics better the preferential flow pattern through the normal native mitral valve than the Perimount Magna Ease bioprosthesis. This is reflected in the substantially higher transmitral gradient, which becomes even more pronounced during exercise.

Preventive and Therapeutic Consequences

Considering that preferential flow profiles exist within vessels and within the heart in order to optimize blood flow at the lowest energy cost, the design of artificial grafts and valves should mimic these flow patterns, as well as durability and especially thrombogenicity. Today, during mitral valve surgery all efforts are made to reconstruct the native valve over valve replacement, if the anatomy and conditions are favorable [55]. Mitral valve repair will normally cause less disturbance in the physiological flow patterns as we described above. Physiological flow will prevent pathologically high shear which will activate platelets and increase the risk of thrombosis.

Homeostasis of blood viscosity is necessary to prevent complications linked to the Triad of Virchow and to guarantee optimal flow conditions. Blood viscosity should be considered as one of the basic parameters to keep the “milieu intérieure” stable. Furthermore, preferential flow patterns exist within blood vessels and in the heart. These preferential flow patterns are meant to transport blood at the lowest energy cost and to prevent flow disturbances, which could lead to endothelial dysfunction and platelet activation. Bioengineering of vessel grafts and/or heart valves should not only focus on durability and potential thrombogenicity, but also directed at trying to respect these physiologic preferential flow patterns. We have demonstrated how blood flow, a more precisely shear rate, is strongly determined by whole blood viscosity and that heart valves play an important role in the maintenance of preferential flow patterns. Hemorheology and heart valves are both integrated into the optimization of the human cardiovascular system. A recent clinical study showed that patients with mitral annular calcification have significantly higher levels of whole blood viscosity [56]. Blood viscosity had also an inverse correlation with mitral annular motion velocities. Furthermore, other researchers have demonstrated, when comparing 107 patients with aortic valve sclerosis (AVS) to 100 patients without AVS that whole blood viscosity appears to be independently associated with AVS [57]. Increased blood viscosity places greater shear stress on the valve leaflets which could lead to progress of valve fibrosis. Blood viscosity and preferential flow patterns being both integrated in the maintenance and optimization in the circulation of blood appear not only to be linked with the occurrence of vessel wall abnormalities, such as in atherothrombosis, but also with the occurrence in heart valve degeneration.

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