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| {{Merge to |Hemodynamics |discuss=Talk:Hemodynamics#Merge from blood flow |date=December 2013}}
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| '''Blood flow''' is the continuous circulation of [[blood]] in the [[cardiovascular system]].
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| This process ensures the transportation of [[nutrients]], [[hormones]], metabolic wastes, [[Oxygen|O<sub>2</sub>]] and [[CO2|CO<sub>2</sub>]] 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 harms.<ref>{{cite book|title=Principles of Anatomy & Physiology, 13th|authors=Gerard J. Tortora, Bryan Derrickson|year=2012|publisher=John Wiley & Sons, Inc.|ignore-isbn-error=true |isbn= 978-0470-56510-0|chapter=The Cardiovascular System: The Blood|pages = 729–732}}</ref>
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| The science dedicated to describe the physics of ''blood flow'' is called [[hemodynamics]]. For the basic understanding it is important to be familiar with anatomy of the cardiovascular system and [[hydrodynamics]]. However it is crucial to mention that, blood is not a [[Newtonian fluid]], and blood vessels are not rigid tubes, so classic hydrodynamics is not capable to explain hemodynamics.<ref>{{cite book|title=Biology and Mechanics of Blood Flows, Part II: Mechanics and Medical Aspects|authors=Joel S. Fieldman, Duong H. Phong, Yvan Saint-Aubin and Luc Vinet|year=2007|publisher=Springer|isbn=978-0-387-74848-1|chapter=Rheology |pages = 119–123}}</ref>
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| ==Blood and its composition.==
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| [[Blood]] is composed of [[Blood plasma|plasma]] and [[Blood#Constituents of human blood|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.<ref>{{cite book|title=Principles of Anatomy & Physiology, 13th|authors=Gerard J. Tortora, Bryan Derrickson|year=2012|publisher=John Wiley & Sons, Inc.|ignore-isbn-error=true|isbn= 978-0470-56510-0|chapter=The Cardiovascular System: The Blood|pages = 729–732}}</ref>
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| ==The mechanics of blood circulation==
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| [[Mechanics]] is the study of motion (or equilibrium) and the [[forces]] that causes it. Blood moves in the blood vessels, while the [[heart]] serves as the pump for the blood. The vessel walls of the heart are elastic and are movable, therefore causing the blood and the wall to exert forces on each other which in turn influence their respective motion. Therefore to understand the mechanics of circulation of the heart, it will be worth the while to go through a review of basic mechanics of fluid, and [[elasticity (physics)|elastic]] solids ([[momentum]]) and the nature of the forces exerted between two moving substances in contact.
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| ==Velocity==
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| The velocity of blood flow is often expressed in cm/s, this value is inversely related to the total cross-sectional area of the blood vessels, and also differs per cross-sections, because in normal condition the blood flow has [[Laminar flow|laminar characteristic]]. Due to this fact the blood flow velocity is the fastest in the middle of the vessel and the slowest at the vessel wall. In most cases the mean velocity is in use.<ref>{{cite book
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| |title=Principles of Anatomy & Physiology, 13th
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| |authors=Gerard J. Tortora, Bryan Derrickson
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| |year=2012
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| |publisher=John Wiley & Sons, Inc.
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| |ignore-isbn-error=true
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| |isbn=978-0470-56510-0
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| |chapter=The Cardiovascular System: Blood Vessels and Hemodynamics
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| |page = 816
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| }}</ref> There are many ways to measure blood flow velocity like videocapillary microscoping with frame to frame analysis or [[Laser Doppler velocimetry|laser Doppler anemometry]].<ref>{{cite journal|doi=10.1063/1.1754319|title=Capillary Blood Cell Velocity in Human Skin Capillaries Located Perpendicularly to the Skin Surface: Measured by a New Laser Doppler Anemometer|year=1996|last1=Stücker|first1=M.|last2=Bailer|first2=V.|last3=Reuther|first3=T|last4=Hoffman|first4= K.|last5=Kellam|first5=K.|last6=Altmeyer|first6=P|journal=Microvasc Research|volume=52|issue=2|pages=188–192|PMID=8901447 }}</ref>
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| Blood velocities in [[arteries]] are higher during [[Systole (medicine)|systole]] than during [[diastole]]. One parameter to quantify this difference is ''pulsatility index'' (PI), which is equal to the difference between the peak systolic velocity and the minimum diastolic velocity divided by the mean velocity during the [[cardiac cycle]]. This value decreases with distance from the heart.<ref>{{cite book
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| |title=Principles of Anatomy & Physiology, 13th
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| |authors=Gerard J. Tortora, Bryan Derrickson
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| |year=2012
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| |publisher=John Wiley & Sons, Inc.
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| |ignore-isbn-error=true
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| |isbn=978-0470-56510-0
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| |title=Laminar flow analysis
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| |chapter=The Cardiovascular System: Blood Vessels and Hemodynamics
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| |page = 817
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| }}</ref>
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| :<math>PI = \frac{v_{systole} - v_{diastole}}{v_{mean}}</math>
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| {| class="wikitable"
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| |+ Relation between blood flow velocity and total cross-section area in human<ref>{{cite book|title=Principles of Anatomy & Physiology, 13th|authors=Gerard J. Tortora, Bryan Derrickson|year=2012|publisher=John Wiley & Sons, Inc.|ignore-isbn-error=true|isbn=978-0470-56510-0|chapter=The Cardiovascular System: Blood Vessels and Hemodynamics|page = 816}}</ref>
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| !Type of blood vessels
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| !Total cross-section area
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| !Blood velocity in cm/s
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| | Aorta || 3–5 cm<sup>2</sup> || 40 cm/s
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| | Capillaries || 4500–6000 cm<sup>2</sup> || 0.03 cm/s<ref>{{cite book|title=Human anatomy & physiology, 9th ed.|authors=Elaine N. Marieb, Katja Hoehn.|year=2013|publisher=Pearson Education,Inc.|isbn= 978-0-321-74326-8|chapter=The Cardiovascular System:Blood Vessels|page = 712}}</ref>
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| |-
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| | Vena cavae inferior and superior || 14 cm<sup>2</sup> || 15 cm/s
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| |-
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| |}
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| ==Stress==
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| When force is applied to a material it starts to deform or move. As the force that is needed to deform a material (e.g. to make a fluid flow) increases with the size of the surface of the material A.<ref name="autogenerated3">{{cite book|authors='caro C.G, Pedley, T.J, Schroter R.C., Seed. W.A.| publisher=Oxford University Press |title=The Mechanics of Circulation |year=1978| pages=3–60, 151–176| ISBN=0-19-263323-6 }}</ref> The magnitude of this force F is proportional to the area A of the portion of the surface. Therefore the quantity (F/A) that is the force per unit area is called the stress. The shear stress that is associated with blood flow through an artery is around 8-12 dynes/cm^2
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| :<math>\sigma = \frac{F}{A}</math>.
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| [[File:Laminar shear.svg|thumb|right|320px|Laminar shear of fluid between two plates. <math>v=u, \tau=\sigma</math>. Friction between the fluid and the moving boundaries causes the fluid to shear (flow). The force required for this action per unit area is the stress. The relation between the stress (force) and the shear rate (flow velocity) determines the viscosity.]]
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| ==Viscosity of plasma==
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| Normal [[Blood plasma|plasma]] behaves like a Newtonian fluid at rates of shear. Typical values for the [[viscosity]] of normal human plasma at 37 °C is 1.2 N·s/m<sup>2</sup>. The viscosity of normal plasma varies with temperature in just the same way as does that of its solvent water, a 5 °C increase of temperature in the physiological range reduces plasma viscosity by about 10%.
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| ==Osmotic pressure of plasma==
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| The osmotic pressure of solution is determined by the number of particles present by the [[temperature]]. For example a 1 molar solution of a substance contains {{val|6.022|e=23}} molecules per liter of that substance and has at 0 °C an osmotic pressure of {{convert|2.27|MPa|atm|abbr=on}}. The osmotic pressure of the [[Blood plasma|plasma]] affects the mechanics of the circulation in several ways. An alteration of the osmotic pressure difference across the membrane of a blood cell will cause a shift of water and a change of the cell volume. The change both in shape and flexibility will affect the mechanical properties of whole blood. A change therefore in plasma [[osmotic pressure]] will alter 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 will affect the mechanics of the whole blood.<ref name="autogenerated3"/>
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| ==Red blood cells==
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| The red blood cell is highly flexible and biconcave in shape. The red cell membrane has a Young's modulus in the region of 106 Pa. The deformation in the red cells is induced by the shear stress. When a suspension is sheared the red cells are seen to deform and spin, because of the velocity gradient, but the rate of deformation and spin depends on the shear-rate and the concentration.
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| This topic can influence the mechanics of the circulation and may complicate the measurement of the 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 the downward [[gravitational]] force of the particle is balanced by the viscous drag force.
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| From this force balance the speed of fall this can be shown to be given by [[Stokes' law]]
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|
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| :<math>U_s = \frac{2}{9}\frac{\left(\rho_p - \rho_f\right)}{\mu} g\, a^2</math><ref name="autogenerated3"/>
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| 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 terminal velocity (U) as shown above.
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| We have looked at blood flow, [[blood]] composition. Before we look at the main issue, hemodilution let us take a brief history into the use of blood. The [[therapeutic]] use of blood is not a modern phenomenon. [[Egyptians|Egyptian]] writings dates back at least 2000 years suggest oral ingestion of blood as a ‘sovereign remedy’ for leprosy. Experiments with the first intravenous blood transfusions began at the start of the 16th century, and in the last 50 years the field of transfusion medicine has progressed remarkably bringing with it an increase in the use of blood and blood product.<ref>{{cite web | url = http://jic.sagepub.com/content/14/1/20 | title=Bloodless medicine and surgery | accessdate=5 April 2011}}</ref> However the therapeutic use of blood comes with its significant risks which are enormous. As a result many persons are searching for alternatives to transfusion of whole blood. Today bloodless medicine and surgery (BMS) programs have been developed not only for a group of people because of their religious believes but they are also sought after by patient who fear the risks of blood transfusion and desire the best medical care.
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| ==Hemodilution==
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| Hemodilution is the dilution of the concentration of red blood cells and plasma constituents by partially substituting the blood with [[colloid]]s or [[Volume expander|crystalloids]] and it is a strategy to avoid exposure of patients to the hazards of [[Blood transfusion|homologous]] blood transfusions.
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| Hemodilution can be normovolemia which, as we said, implies the dilution of normal blood constituents by the use of expanders. During acute normovolemic hemodilution (ANH) blood subsequently lost during surgery contains proportionally fewer red blood cells per millimetre, 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.
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| There is however the hypervolemic hemodilution (HVH). Here, instead of simultaneously exchanging the patient’s blood as in ANH, hypervolemic technique is carried out by the use of acute preoperative volume expansion without any blood removal. In choosing a fluid, however, we must be sure that when mixed the remaining blood behaves in the microcirculation as the original blood fluid, retaining all its properties of [[viscosity]].<ref>{{cite web | url = http://journals.lww.com/anesthesiology/Abstract/2001/03000/Efficacy_of_Acute_Normovolemic_Hemodilution.13.aspx| publisher=the journal of American society of anesthsiologist inc |title=Efficacy of Acute Normovolemic hemodilution,Accessed as a Function of Blood lost | accessdate=5 April 2011}}</ref>
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| 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. Not to worry. Attached to this document is a glossary of the term used.
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| 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]] (OP). A [[colloid]] is a fluid containing particles that are large enough to exert an oncotic pressure across the micro vascular membrane.
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| When debating the use of colloid or crystalloid, it is imperative to think about all the components of the starling equation:
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| :<math>\ Q = K ( [P_c - P_i]S - [P_c - P_i] )</math>
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| To identify the minimum safe hematocrit desirable for a given patient the following equation is useful:
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| :<math>\ BL_s = EBV \ln \frac{H_i}{H_m} </math>
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| Where EBV is the estimated [[blood]] volume 70 mL/kg was used in this model and Hi (initial hematocrit) is the patient’s initial hematocrit.
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| From the equation above it is clear that the volume of blood removed during the ANH to the Hm is the same as the BLs.
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| The collection of blood needed to be removed is usually based on the weight, not the volume. The number of units that needed to be removed to hemodilute to the maximum safe hematocrite (ANH) can be found by
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| :<math>ANH = \frac {BL_s}{450}</math>
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| This is based on the assumption that each unit removed by hemodilution has a volume of 450 mL (the actual volume of a unit will vary somewhat since completion of collection as we mentioned is dependent on weight and not volume).
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| The model assumes that the hemodilute value to the Hm prior to surgery, therefore the re-transfusion of blood obtained by hemodilution, must begin when SBL begins.
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| The RCM available for retransfusion after ANH (RCMm) can be calculated from the patient's Hi and the final hematocrit after hemodilution(H_m)
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| :<math> RCM = EVB \times (H_i - H_m) </math>
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| The maximum SBL that is possible when ANH is used without falling below Hm(BLH) is found by assuming that all the blood removed during ANH is returned to the patient at a rate sufficient to maintaining the hematocrit at the minimum safe level
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| :<math> BL_H = \frac {RCM_H} {H_m}</math>
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| 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 BL_H should therefore not exceed BL_s.
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| The difference between the BL_H and the BLs therefore is the incremental surgical blood loss (BL_i) possible when using ANH.
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| :<math>\ {BL_i} = {BL_H} - {BL_s} </math>
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| When expressed in terms of the RCM
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| :<math> {RCM_i} = {BL_i} \times {H_m} </math>
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| 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.
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| The model used assumes ANH used for a 70 kg patient with an estimated blood volume of 70 mL/kg (4900 mL). A range of Hi and Hm was evaluated to understand conditions where hemodilution is necessary to benefit the patient.<ref name="autogenerated1">{{cite web | url = http://ieeexplore.ieee.org/Xplore/login.jsp?reason=login&url=stamp%2Fstamp.jsp%3Ftp%3D%26arnumber%3D1018881 | publisher = IEEE|title=Hemodilution:Modelling and clinincal Aspects | accessdate=5 April 2011}}</ref><ref>{{cite web | url = http://www.anesthesia-analgesia.org/content/80/1/108.full.pdf+html| publisher = anesthesia & analgesia the gold standard in anesthesiology|title=maximum blood savings by acute Normovolemic hemodilution | accessdate=5 April 2011}}</ref>
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| ==Result==
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| The result of the model calculations are presented in a table given in the appendix for a range of Hi from 0.30 to 0.50 with ANH performed to minimum hematocrits from 0.30 to 0.15. Given a Hi of 0.40, if the H_m is assumed to be 0.25.then from the equation above RCM count is still high and ANH is not necessary, if BLs does not exceed 2303 mL, since the hemotocrit will not fall below H_m. though 5 units of blood must be removed during hemodilution. Under these conditions to achieve the maximum benefit from the technique and if ANH is used no homologous blood will be required to maintain the Hm 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, in such a case homologous blood transfusion will be necessary to maintain Hm even if ANH is used.
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| 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.
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| For example if Hi is 0.30 or less it is not possible to save a red cell mass equivalent to 2 unit 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.
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| If Hi is 0.40 one must remove at least 7.5 units of blood during ANH, resulting in an Hm of 0.20 to save 2 units equivalence. Clearly the greater the Hi and the greater the amount of units removed during hemodilution, the more effective ANH is for preventing homologous blood transfusion. The model here is designed to allow doctors determine where ANH may be beneficial for a patient based on their knowledge of the H_i, the potential for SBL and estimate of the Hm. 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
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| :<math> T = \frac {70 \times \text{patient's weight in kg}} {4900} </math>
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| Basically the model we have considered above is designed to predict the maximum RCM that can be saved ANH.
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| 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 it goes to show the application of measurement in the medical field.
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| ==Glossary of terms==
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| {| class="wikitable" style="text-align: center;"
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| ! scope="row" | ANH || Acute Normovolemic Hemodilution
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| ! scope="row" | ANH<sub>u</sub> || Number of Units During ANH
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| ! scope="row" | BL<sub>H</sub> || Maximum Blood Loss Possible When ANH Is Used Before Homologous Blood Transfusion Is Needed
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| ! scope="row" | BL<sub>I</sub> || Incremental Blood Loss Possible with ANH.(BL<sub>H</sub> – BL<sub>s</sub>)
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| ! scope="row" | BL<sub>s</sub> || Maximum blood loss without ANH before homologous blood transfusion is required
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| ! scope="row" | EBV || Estimated Blood Volume(70 mL/kg)
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| ! scope="row" | Hct || Haematocrit Always Expressed Here As A Fraction
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| ! scope="row" | H<sub>i</sub> || Initial Haematocrit
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| ! scope="row" | H<sub>m</sub> || Minimum Safe Haematocrit
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| ! scope="row" | PRBC || Packed Red Blood Cell Equivalent Saved by ANH
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| ! scope="row" | RCM || Red cell mass.
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| ! scope="row" | RCM<sub>H</sub> || Cell Mass Available For Transfusion after ANH
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| ! scope="row" | RCM<sub>I</sub> || Red Cell Mass Saved by ANH
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| ! scope="row" | SBL || Surgical Blood Loss
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| |}
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| <ref name="autogenerated1"/>
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| ==References==
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| {{reflist|colwidth=30em}}
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| [[Category:Cardiovascular physiology]]
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| [[Category:Exercise physiology]]
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| [[Category:Blood]]
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