Blood viscosity mediates the relationship between blood pressure gradients and blood flow. At a fixed driving pressure, blood flow is indirectly proportional to the viscosity of blood. Blood is a shear-thinning non-Newtonian fluid, meaning its viscosity decreases as the shear rate increases (1, 2). The shear rate is determined by the velocity of blood flow and by the size of the blood vessel. High shear rates are typically present in large arteries with high blood flow velocity, whereas low shear rates are typically present in the microcirculation where blood flow velocity is low. Thus, under normal physiologic conditions, the viscosity of blood within the circulation at any instant or location varies depending on the shear rate within the particular vessel. The rheologic properties of blood depend on hematocrit and plasma constituents (3). As the cellular fraction of blood increases, so does viscosity (4). Plasma expanders, such as hydroxyethyl starch (HES) and albumin, have their own distinct rheologic properties that are different from those of blood (5, 6). A plasma expander used under clinical conditions will alter blood viscosity as a consequence of both hemodilution and its inherent physical properties.
Although blood hyperviscosity caused by diseases such as Waldenström’s macroglobulinemia and polycythemia have been long recognized to produce clinical syndromes with features attributed to vascu-lar insufficiency (7), the pathophysiologic effects of hypothermia-induced blood hyperviscosity have not been adequately studied. Blood viscosity increases by 50% to 300% as temperature is decreased from 37°C to 22°C (8, 9). Often, even lower blood temperatures, in the range of 8°C–12°C, are typically encountered when performing deliberate deep hypothermia for cardiac or thoracic aortic operations requiring temporary circulatory arrest (10, 11). Because the physical characteristics of blood are complex, blood’s rheologic properties at temperatures commonly used for deep hypothermia cannot be reliably predicted based on measurements performed at higher temperatures.
The goal of the present study was to quantify blood viscosity behavior over an expanded range of temperature and hematocrit relevant to the clinical conduct of deep hypothermia. In addition, the temperature-dependent rheologic effects of hemodilution with plasma expanders commonly used in the setting of cardiac operations was quantified. We hypothesized that blood viscosity would be significantly affected by hematocrit, shear rate, temperature, and diluent type under the conditions of deep hypothermia. We further hypothesized that a single mathematical expression predicting the dependence of blood viscosity on each of these variables could be derived from experimental data. The ability to quantify the independent effects of hemodilution, choice of diluent, and shear rate on blood viscosity over a broad temperature range would be useful for predicting and optimizing the rheologic properties of blood with the intention of improving tissue perfusion during deliberate hypothermia under a wide variety of physiologic conditions.
Approval for this study was obtained from the University of Pennsylvania Committee on Studies Involving Human Beings. Blood was obtained from normal, healthy, male (n = 4) and female (n = 2) volunteers who were not on any medications and who provided informed consent. Blood samples used in the experiments were not pooled from more than one individual subject and were not more than 12 h old.
Forty milliliters of blood was drawn by phlebotomy into two 20-mL syringes that contained heparin (0.5 mL of 5,000 IU/mL). The blood was transferred to 50-mL plastic centrifuge tubes (Fisher Scientific, Pittsburgh, PA) and mixed to ensure uniform heparinization. The hematocrit was measured twice using a blood-gas analyzer (NovaStat; Nova Biomedical, Waltham, MA), and the average was recorded. An aliquot of the blood was centrifuged at 3500 rpm for 30 min to separate the autologous plasma fraction. A stock solution with a hematocrit of 40% was prepared with autologous plasma and adjusted until the hematocrit was within ±1%.
Serial dilutions of the stock solution were made to hematocrits of 35%, 30%, 22.5%, and 15%, with a tolerance of ±1%, using one of the four diluents. The four diluents tested were autologous plasma, 0.9% NaCl (saline, Abbott Laboratories, North Chicago, IL), 5% human serum albumin (albumin; Central Laboratories, Swiss Red Cross, Berne, Switzerland), and HES in 0.9% NaCl having an average molecular weight of 450,000 (range 400,000–550,000) and a molar substitution ratio of 0.7 (HES; Abbott Laboratories).
A Wells-Brookfield Cone/Plate LVTDV-II+ viscometer with a CP-40 cone (Brookfield Laboratories, Stoughton, MA) coupled to a refrigerated recirculating fluid bath to control the temperature of the sample (Cole Parmer, Vernon Hills, IL) was used to measure the viscosity over a range of different temperatures (12). The cone-and-plate viscometer is a precise torque meter that is driven at discrete rotational speeds. A sample of fluid (blood in this case) held between the rotating cone and a stationary flat plate is subjected to a constant rate of shear. The resistance to the rotation of the cone caused by the liquid viscosity produces a torque that is proportional to the shear stress in the fluid. The liquid viscosity is easily calculated from the known shape of the cone, the imposed rate of rotation, and the measured stress-related torque. This method has been used to measure nonhuman blood viscosity over ranges of temperature, shear rate, and hematocrit similar to those used in the present study (13).
The recirculating bath was set to one of the study temperatures (37°, 25°, 15°, 10°, 5°, and 0°C) and allowed to equilibrate. Either a polyethylene glycol and water solution (50/50 vol% mixture for 0°C, 5°C, and 10°C) or water (for 15°C, 25°C, and 37°C) was used in the recirculating bath, The recirculating bath temperature was adjusted until the stainless-steel viscometer sample cup reached the test temperature. Sample cup temperature was measured with a Physitemp BAT-10 thermometer (Physitemp, Clifton, NJ). To ensure measurement accuracy at low temperature, the viscosity of ultrapure water was measured at 2°C and found to be within 2% of published values (14).
With the cup at the desired temperature, 500 μL of diluted blood was added. Another 5-min equilibration period was sufficient for a steady viscosity reading in all cases. The sample viscosity was recorded in units of centipoise (cP) using the following discrete shear rates (in order): 4.5, 7.5, 11.25, 15, 18.75, 22.5, 37.5, 45, 75, 90, 150, 225, 375, and 450 s−1. A limitation of the instrument was that sample viscosity occasionally fell outside the measurement range. In those cases, no value was recorded. Once the viscosities for all possible shear rates were measured, the cup and cone were cleaned and dried thoroughly. This procedure was repeated in triplicate for five hematocrits at six temperatures using four diluents over the range of shear rates for blood samples obtained from the six different subjects. Viscosity measurements were also recorded for the pure diluents under the same conditions.
Each data point was the average of viscosity measurements performed under each specific set of conditions for samples obtained from the six individual subjects. The standard deviations for each data point were all less than 16% (worst case) of the mean and were typically in the range of 4%–8% of the mean value. Because error bars depicting standard deviations would appear small, only mean values were shown on the graphs constructed from the experimental data. Statistical comparisons between groups were performed by using analysis of variance with the Bonferroni correction for post-hoc analysis. Differences were considered statistically significant for P < 0.05 by using the two-tailed test.
Curve fitting was performed by using a Marquardt-Levenberg least-squares algorithm, an iterative nonlinear regression analysis (SigmaPlot, SPSS, Inc., Chicago, IL) until the experimental data were fit to curves with regression coefficients of r > 0.96. The effect of isolated changes in each of the independent variables, hematocrit, temperature, and shear rate were determined for each diluent while maintaining the other variables constant. The resultant mathematical form of the dependence of viscosity on the independent variables was incorporated into a single expression. Correlation analysis using a linear least-squares regression was performed to test the agreement between viscosity values predicted by the model and the viscosity measured using the cone/plate viscometer based on the remaining experimental data that was not used to generate the mathematical model.
The absolute viscosity of blood at a given temperature and shear rate was always less if diluted with 5% albumin or 0.9% NaCl compared with HES or plasma. This was statistically significant (P < 0.05) for all cases with hematocrit ≤ 30%, temperature ≤ 25°C, and shear rate ≤ 90 s−1. The differences in viscosity between 5% albumin and saline hemodilution or between HES and plasma hemodilution were only significant (P < 0.05) at the extremes of the variable ranges with hematocrit = 15%, temperature ≤ 10°C, and shear rate ≤ 45 s−1.
To illustrate shear rate effects, the measured viscosity of blood diluted with 5% albumin to a hematocrit of 22.5% was displayed with individual curves for each temperature (Fig. 1A). These series of curves relating blood viscosity to shear rate were representative of hemodilution with the other diluents as well. The shape of the curves relating blood viscosity to shear rate demonstrated that blood exhibited non-Newtonian behavior at shear rates < 45 s−1 (viscosity dependent on the shear rate), but that blood viscosity was almost independent of shear rate at shear rates > 45 s−1 (Fig. 1A). Decreasing the temperature caused a uniform upward displacement of the curve relating viscosity to shear rate. Hemodilution with plasma or HES caused a greater upward displacement of relating viscosity to shear rate compared with hemodilution with 0.9% NaCl or 5% albumin (not shown).
Recasting data to view the independent effect of temperature on blood viscosity demonstrated that the relationship between temperature and blood viscosity was nonlinear (Fig. 1B). In general, viscosity decreased as a function of increasing temperature, with a steep decline in the viscosity at temperatures ranging from 0°C to 15°C. The effect of temperature on viscosity was less at temperatures ranging from 25°C to 37°C. Decreasing temperature alone could potentially increase the viscosity in excess of 450%, depending on the shear rate, the extent of hemodilution, and the diluent used. For hemodilution with any single diluent, the viscosity was significantly greater (P < 0.021) at lower temperatures (0°C, 5°C, or 10°C), compared with higher temperatures (15°C, 25°C, or 37°C).
For a single diluent, at a constant shear rate and a constant temperature, hemodilution decreased blood viscosity (Fig. 1C). As hematocrit decreased, the greater volume fraction of the diluent caused the samples to behave rheologically more like the corresponding pure diluent and less like whole blood. For the neat diluents themselves, at shear rates ≤ 45 s−1, the viscosity of 5% albumin and plasma were strongly shear rate dependent. In contrast, 0.9% NaCl and HES exhibited Newtonian behavior with viscosity that was independent of shear rate. Viscosity increased as a function of decreasing temperature at all shear rates tested for each of the diluents. The viscosity of HES and plasma were the most sensitive to changes in temperature. Over a temperature range of 37°C–0°C, the viscosity of 0.9% NaCl increased by only 125% (P = 0.0084), whereas the viscosity of the other neat diluents increased by 200% to 400% (P < 0.01 for all cases).
Data demonstrated independent functional effects of shear rate, temperature, and hematocrit on viscosity, as well as individual effects of the different diluents. The mathematical model combining all of these factors was based on the following categorical trends observed for the individual effects of temperature, shear rate, hematocrit, and diluent.
Effect of Temperature
Viscosity decreased with increasing temperature for each combination of shear rate, diluent, and hematocrit. Data (minimum of 132 data points) were fitted to a sigmoidal curve that decayed as temperature increased (minimum value of r2 = 0.942).
Effect of Shear Rate (γ)
Viscosity decreased with increasing shear rate. For sufficiently large shear rates, the viscosity reached a plateau. Data (minimum of 132 data points) were fitted to a curve that decayed as a monotonic exponential in response to increasing shear rate (minimum value of r2 = 0.959).
Effect of Hematocrit
Viscosity increased with increasing hematocrit. Data (minimum of 132 data points) were fitted to a curve with monotonic exponential growth in response to increasing hematocrit (minimum value of r2 = 0.926).
Each diluent had unique rheologic properties that were temperature- and shear rate-dependent. The effects of temperature, shear rate, and hematocrit were analyzed separately for each of the diluents.
The combined parametric effects of hematocrit, temperature, shear rate, and diluent on blood viscosity, determined by curve fitting of the experimental data, were reduced to a single mathematical expression. The formula incorporated the dependence of viscosity on each of the independent variables and was described by Equation 1 :
In this expression, μ is viscosity (cP), γ is shear rate (shear rate−1), Hct is hematocrit (%), and T is temperature (°C). The constants λ, η, α, φ, β, and ξ describe the individual shear, thermal, and volume fraction effects of a particular diluent. Values of the constants were determined using a least-squares algorithm as previously described (Table 1).
Nonlinear regression for only half of the data points of the complete data set yielded correlation coefficients that were highly significant as described for each of the variables. Values of the coefficients giving the best data fit were listed in Table 1. Model predictions correlated well with measured viscosity over the complete range of temperatures, shear rates, and hemodilution for each diluent (minimum value of r2 > 0.92, P < 0.005 for all values). Data pairings were clustered around the line of identity (Fig. 2). The model tended to overestimate the measured viscosity at viscosity values less than 20 cP and underestimate the measured viscosity for values in the range of 40–90 cP.
Microcirculatory blood flow is governed by perfusion pressure, vessel radius, vessel length, and blood viscosity. Autoregulation of regional blood flow is controlled by neural and metabolic factors that influence vascular resistance by modifying perfusion pressure and vasomotor reactivity. Under normal physiologic conditions, blood viscosity plays a passive role in affecting microcirculatory flow. However, changes in blood viscosity have been well known to affect blood flow. Anemia not only decreases the oxygen content of blood, but also decreases blood viscosity promoting an increase in regional blood flow (15, 16). Blood hyperviscosity caused by disease states can limit the ability of autoregulatory mechanisms to augment blood flow resulting in compromised organ perfusion (7). One study suggested that blood hyperviscosity may have been a contributing factor in the pathogenesis of common cardiovascular disease states. The chronic effects of increased blood viscosity have been shown to be associated with anatomic changes in arterial vessel walls, such as increased carotid intima-medial thickness (17). Epidemiologic studies have linked plasma hyperviscosity to an increased risk of ischemic heart disease and stroke (18). Although hypothermia has been well known to increase blood viscosity, the physiologic consequences of hypothermia-induced blood hyperviscosity on organ perfusion is not known. On a more basic level, the effects of hemodilution, type of diluent, and shear rate on blood viscosity at temperatures commonly used during deep hypothermia for cardiac and aortic operations have not been adequately studied.
Blood becomes hyperviscous by at least three mechanisms (7). Polycythemia increases blood viscosity, but anemia is more common in the perioperative setting, particularly with obligatory hemodilution for the conduct of cardiopulmonary bypass. Serum hyperviscosity due to increased plasma protein concentrations in diseases such as Waldenström’s macroglobulinemia and multiple myeloma has also been described to increase the viscosity of blood. Neurologic symptoms in blood hyperviscosity syndromes have been shown to improve in response to treatments such as plasmapheresis directed at decreasing blood viscosity by decreasing the concentration of plasma proteins (19, 20). The third mechanism causing blood hyperviscosity is sclerocythemia or decreased erythrocyte deformability. This mechanism explains many of the pathologic features of sickle cell disease and hereditary spherocytosis. Erythrocyte deformability has been shown to be sensitive to temperature and a decrease in temperature from 37°C to 0°C increased red cell resistance to deformation 2.5- to 3-fold with a resulting increase in blood viscosity (21). Deep hypothermia may compromise microcirculatory blood flow by increasing erythrocyte rigidity, causing red blood cells to resist passage through capillaries, and by increasing the viscosity of blood.
Plasma expanders or hemodiluents have previously been shown to affect blood viscosity under normothermic conditions. Castro et al, (22) demonstrated that HES, in contrast to 5% albumin or 0.9% NaCl, increased blood viscosity, decreased erythrocyte deformability, and increased erythrocyte aggregation in septic patients. Although no laboratory viscometry device truly mimics blood flow conditions within the human vasculature to allow direct clinical interpretation, our study demonstrated that the biophysical characteristics of the diluent were important in determining the temperature and shear rate dependence of blood viscosity. In our experiments, data indicated that plasma protein concentration had a complex role in determining blood rheology. Equal-volume blood dilution with protein-free HES and protein-laden autologous plasma yielded similar effects of blood viscosity, yet HES and plasma were rheologically quite different from one another. The effects of hemodilution and the type of diluent on blood viscosity were magnified during experimental hypothermia (Fig. 1B). Blood viscosity was significantly greater by an average of 50% when hemodilution was performed with HES or plasma, compared with hemodilution with 0.9% NaCl or 5% albumin. The experiments suggested that the choice of hemodiluent used for volume expansion and for priming of the cardiopulmonary bypass circuit for deliberate hypothermia had an important effect on the rheological behavior of plasma and blood viscosity. Preferential use of 0.9% NaCl or 5% albumin for hemodilution to any given hematocrit resulted in lower blood viscosity over a wide range of shear rates and exhibited the least amount of hypothermia-induced hyperviscosity.
Data presented suggested that modulation of the blood viscosity by choice of diluent and degree of hemodilution should permit manipulation of the basic pressure–flow relationship according to the Poiseiulle law for steady laminar flow in blood vessels (Equation 2): where Q is blood flow, ΔP is the pressure gradient across the vessel, r is the vessel radius, μ is blood viscosity, and l is the vessel length. In clinical situations where the driving pressure for blood flow is limited, maximizing blood flow in the presence of intact autoregulatory mechanisms may depend on the ability to reduce blood viscosity. For example, retrograde cerebral perfusion has been advocated as a means for providing metabolic substrate delivery to the brain during the deep hypothermic circulatory arrest (23, 24). The conduct of retrograde cerebral perfusion requires keeping venous pressures at less than 25 mm Hg to decrease the risk of cerebral edema and maintenance of deep hypothermia for brain protection. Under these conditions, the viscosity of the blood used in the retrograde cerebral perfusate would determine the maximum flow rates that could be achieved. Cerebral blood flow has been shown to be inversely related to hematocrit, and decreased in the presence of hypothermia in large part due to changes in blood viscosity (25). Hemodilution from a hematocrit of 35% to 22.5%, that was shown to effectively decrease viscosity by 50% at a temperature of 15°C, would translate to a doubling of the maximum achievable retrograde cerebral perfusion flow rate. In contrast, use of HES or plasma as the hemodiluent instead of 0.9% NaCl or 5% albumin would be predicted to decrease the maximum flow rate that could be achieved at a temperature of 15°C by 50% due to the rheologic properties of the diluent alone. Blood viscosity would also be expected to be an important determinant of tissue perfusion in the clinical situation of hypothermic low flow cardiopulmonary bypass (26). In this situation, low flow resulting in low shear rates would magnify the effects of hypothermia-induced hyperviscosity in the microcirculation. A rational clinical choice of diluent and the degree of hemodilution should be based on the need to maintain tissue blood flow given the anticipated shear rate and thermal conditions combined with the need to carry and transport oxygen to meet anticipated metabolic demands. Optimizing the rheologic properties of blood to promote microcirculatory flow also has the potential to favor tissue perfusion in the presence of arteriovenous shunts in the circulation (27).
The experimental findings of the effects of deep hypothermia and hemodilution on blood viscosity were closely predicted by the model. This leads to the following conclusions. Blood viscosity was predicted to increase approximately 1.2- to 3.5-fold as temperature was reduced from 37°C to 18°C, 1.8- to 5-fold as temperature was reduced from 37°C to 15°C, and 4- to 10-fold as temperature was reduced from 37°C to 0°C, depending on the diluent used. Blood viscosity decreased by a factor of 1.3 to 2.6 as the hematocrit was decreased from 35% to 22.5% and by a factor of 1.5 to 3 as the hematocrit was decreased from 35% to 15%, depending on the diluent used. Below shear rates of 45 s−1, blood viscosity is very sensitive to shear rate. Hemodilution with 0.9% NaCl and 5% albumin had similar effects on viscosity and decreased blood viscosity more than hemodilution with plasma or HES. A mathematical expression was derived that permitted predictions of the independent effects of temperature, shear rate, hematocrit, and diluent on blood viscosity. Although the experimental findings and the mathematical model predicted that decreasing blood viscosity through a variety of techniques had the potential to improve microcirculatory flow during deep hypothermia, actual measures of tissue perfusion in a clinical setting are still required to verify the effects of blood viscosity on the pressure–flow relationship in the intact circulation.
The authors thank Mr. David Barclay for his technical assistance.
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