Hemodynamics

Hemodynamics or haemodynamics are the dynamics of blood flow. The circulatory system is controlled by homeostatic mechanisms of autoregulation, just as hydraulic circuits are controlled by control systems. The hemodynamic response continuously monitors and adjusts to conditions in the body and its environment. Hemodynamics explains the physical laws that govern the flow of blood in the blood vessels.
Blood flow ensures the transportation of nutrients, hormones, metabolic waste products, oxygen, and carbon dioxide throughout the body to maintain cell-level metabolism, the regulation of the pH, osmotic pressure and temperature of the whole body, and the protection from microbial and mechanical harm.
Blood is a non-Newtonian fluid, and is most efficiently studied using rheology rather than hydrodynamics. Because blood vessels are not rigid tubes, classic hydrodynamics and fluids mechanics based on the use of classical viscometers are not capable of explaining haemodynamics.
The study of the blood flow is called hemodynamics, and the study of the properties of the blood flow is called hemorheology.

Blood

Blood is a complex liquid. Blood is composed of plasma and formed elements. The plasma contains 91.5% water, 7% proteins and 1.5% other solutes. The formed elements are platelets, white blood cells, and red blood cells. The presence of these formed elements and their interaction with plasma molecules are the main reasons why blood differs so much from ideal Newtonian fluids.

Viscosity of plasma

Normal blood plasma behaves like a Newtonian fluid at physiological rates of shear. Typical values for the viscosity of normal human plasma at 37 °C is 1.4 mN·s/m². The viscosity of normal plasma varies with temperature in the same way as does that of its solvent water; a 3 °C change in temperature in the physiological range reduces plasma viscosity by about 10%.

Osmotic pressure of plasma

The osmotic pressure of solution is determined by the number of particles present and by the temperature. For example, a 1 molar solution of a substance contains molecules per gram of that substance and at 0 °C it has an osmotic pressure of. The osmotic pressure of the plasma affects the mechanics of the circulation in several ways. An alteration of the osmotic pressure difference across the membrane of a blood cell causes a shift of water and a change of cell volume. The changes in shape and flexibility affect the mechanical properties of whole blood. A change in plasma osmotic pressure alters the hematocrit, that is, the volume concentration of red cells in the whole blood by redistributing water between the intravascular and extravascular spaces. This in turn affects the mechanics of the whole blood.

Red blood cells

The red blood cell is highly flexible and biconcave in shape. Its membrane has a Young's modulus in the region of 106 Pa. Deformation in red blood cells is induced by shear stress. When a suspension is sheared, the red blood cells deform and spin because of the velocity gradient, with the rate of deformation and spin depending on the shear rate and the concentration.
This can influence the mechanics of the circulation and may complicate the measurement of blood viscosity. It is true that in a steady state flow of a viscous fluid through a rigid spherical body immersed in the fluid, where we assume the inertia is negligible in such a flow, it is believed that the downward gravitational force of the particle is balanced by the viscous drag force. From this force balance the speed of fall can be shown to be given by Stokes' law
Where a is the particle radius, ρ_p, ρ_f are the respectively particle and fluid density μ is the fluid viscosity, g is the gravitational acceleration. From the above equation we can see that the sedimentation velocity of the particle depends on the square of the radius. If the particle is released from rest in the fluid, its sedimentation velocity U_s increases until it attains the steady value called the terminal velocity, as shown above.

Hemodilution

Hemodilution is the dilution of the concentration of red blood cells and plasma constituents by partially substituting the blood with colloids or crystalloids. It is a strategy to avoid exposure of patients to the potential hazards of homologous blood transfusions.
Hemodilution can be normovolemic, which implies the dilution of normal blood constituents by the use of expanders. During acute normovolemic hemodilution, blood subsequently lost during surgery contains proportionally fewer red blood cells per milliliter, thus minimizing intraoperative loss of the whole blood. Therefore, blood lost by the patient during surgery is not actually lost by the patient, for this volume is purified and redirected into the patient.
On the other hand, hypervolemic hemodilution uses acute preoperative volume expansion without any blood removal. In choosing a fluid, however, it must be assured that when mixed, the remaining blood behaves in the microcirculation as in the original blood fluid, retaining all its properties of viscosity.
In presenting what volume of ANH should be applied one study suggests a mathematical model of ANH which calculates the maximum possible RCM savings using ANH, given the patients weight H_i and H_m.
To maintain the normovolemia, the withdrawal of autologous blood must be simultaneously replaced by a suitable hemodilute. Ideally, this is achieved by isovolemia exchange transfusion of a plasma substitute with a colloid osmotic pressure. A colloid is a fluid containing particles that are large enough to exert an oncotic pressure across the micro-vascular membrane.
When debating the use of colloid or crystalloid, it is imperative to think about all the components of the starling equation:
To identify the minimum safe hematocrit desirable for a given patient the following equation is useful:
where EBV is the estimated blood volume; 70 mL/kg was used in this model and H_i is the patient's initial hematocrit.
From the equation above it is clear that the volume of blood removed during the ANH to the H_m is the same as the BL_s.
How much blood is to be removed is usually based on the weight, not the volume. The number of units that need to be removed to hemodilute to the maximum safe hematocrit can be found by
This is based on the assumption that each unit removed by hemodilution has a volume of 450 mL.
The model assumes that the hemodilute value is equal to the H_m prior to surgery, therefore, the re-transfusion of blood obtained by hemodilution must begin when SBL begins.
The RCM available for retransfusion after ANH can be calculated from the patient's H_i and the final hematocrit after hemodilution
The maximum SBL that is possible when ANH is used without falling below Hm is found by assuming that all the blood removed during ANH is returned to the patient at a rate sufficient to maintain the hematocrit at the minimum safe level
If ANH is used as long as SBL does not exceed BL_H there will not be any need for blood transfusion. We can conclude from the foregoing that H should therefore not exceed s.
The difference between the BL_H and the BL_s therefore is the incremental surgical blood loss possible when using ANH.
When expressed in terms of the RCM
Where RCM_i is the red cell mass that would have to be administered using homologous blood to maintain the H_m if ANH is not used and blood loss equals BLH.
The model used assumes ANH used for a 70 kg patient with an estimated blood volume of 70 ml/kg. A range of H_i and H_m was evaluated to understand conditions where hemodilution is necessary to benefit the patient.

Result

The result of the model calculations are presented in a table given in the appendix for a range of H_i from 0.30 to 0.50 with ANH performed to minimum hematocrits from 0.30 to 0.15. Given a H_i of 0.40, if the H_m is assumed to be 0.25.then from the equation above the RCM count is still high and ANH is not necessary, if BL_s does not exceed 2303 ml, since the hemotocrit will not fall below H_m, although five units of blood must be removed during hemodilution. Under these conditions, to achieve the maximum benefit from the technique if ANH is used, no homologous blood will be required to maintain the H_m if blood loss does not exceed 2940 ml. In such a case, ANH can save a maximum of 1.1 packed red blood cell unit equivalent, and homologous blood transfusion is necessary to maintain H_m, even if ANH is used.
This model can be used to identify when ANH may be used for a given patient and the degree of ANH necessary to maximize that benefit.
For example, if H_i is 0.30 or less it is not possible to save a red cell mass equivalent to two units of homologous PRBC even if the patient is hemodiluted to an H_m of 0.15. That is because from the RCM equation the patient RCM falls short from the equation giving above.
If H_i is 0.40 one must remove at least 7.5 units of blood during ANH, resulting in an H_m of 0.20 to save two units equivalence. Clearly, the greater the H_i and the greater the number of units removed during hemodilution, the more effective ANH is for preventing homologous blood transfusion. The model here is designed to allow doctors to determine where ANH may be beneficial for a patient based on their knowledge of the H_i, the potential for SBL, and an estimate of the H_m. Though the model used a 70 kg patient, the result can be applied to any patient. To apply these result to any body weight, any of the values BLs, BLH and ANHH or PRBC given in the table need to be multiplied by the factor we will call T
Basically, the model considered above is designed to predict the maximum RCM that can save ANH.
In summary, the efficacy of ANH has been described mathematically by means of measurements of surgical blood loss and blood volume flow measurement. This form of analysis permits accurate estimation of the potential efficiency of the techniques and shows the application of measurement in the medical field.