Biomedical Engineering - Life Support Systems

Completed notes of the course

Complete course

Notes of LIFE SUPPORT SYSTEM Course h eld by prof essor Maria Laura Costantino A.A. 2021/22 Written by Chiara Moreschini Politecnico di Milano 1 2 INDEX 1. I ntroduction to dialysis ................................ ................................ ........................... 4 2. D iffusion ................................ ................................ ................................ .................. 7 3. T echnology of the dialysis ................................ ................................ ..................... 18 4. B lood oxygenation ................................ ................................ ................................ 50 5. ECMO ................................ ................................ ................................ .................... 64 6. D iffusion of gasses inside the oxygenators ................................ ........................... 82 7. D iffusive and convective transport of respisratory gasses in the blood ............... 87 8. M echanical assistance to the heart ................................ ................................ ...... 95 8.1. T otal A rtificial H eart ( TAH ) ................................ ................................ ......... 116 9. P ancreatic assistance ................................ ................................ .......................... 142 A ppendix ................................ ................................ ................................ .................. 150 Some of the material included in this book is a modification of the slides provided by Professor Maria Laura Costantino during the course of Life support systems (Politecnico di Milano, A . A . 2021/22). The author credits Professor Maria Laura Costantino as the providers of the original. 3 4 1. INTRODUCTION TO D I AL Y SIS THE KIDENY The kidneys are complex organs characterized by a very high vascularizatio n ; the blood enters in the kidney by the renal artery , which is connected with the aorta. The main function of the kidney is purifying the blood from the catabolites produced by the metabolism, like urea , creatinine and especially WATER , which will contain many other substances to be eliminated, which are expelled through urination . If the kidneys stop to purify the blood , these solutes 1 are kept inside the body and they can cause many problems , because there is no other organ that can substitute the kidneys in this function . We can live also with just one kidney but we cannot l ive without any. If the kidney stop to work and its functionality goes under 95% of the physiological function the patient has to be put under dialysis . If a percentage lower than 5% of the functionality of the kidney is lost a pharmacologic treatment is sufficient, while for higher losses the dialysis is required. Other functions of the kidneys are: a) Adjustment of hydro - electrol i tic balance; b) Adjustment of the acid - base balance; c) Control of the blood pressure; d) Hormone secretion (erithropoyetine) The dialysis can substitute just the purifying function of the kidney while the other functions are not reverted to normality by dialysis but they are lost. However these functions are secondary and the main function of the kidney is restored . 10% of the western world population suffers from renal pathologies so the socio - economical impact of kidney disease is very large, with number that increase year by year. Mortality related to the impossibility of the patient to undergo dialysis depends mostly on the welfare of the country considered (in many poor countries people cannot afford the tre atments so the mortality is very high, while in richer countries people can undergo dialysis and they can have longer life expectancy). The costs of the dialysis are high due to the fact that all the removable part of the machine must be disposable and c annot be reused due to hygienic reasons (needles 2 , dialyzer membrane, pipes, dialysate, water …). 1 Solutes = substances solved into a solution called solvent . 2 Needles in particular are very expensive because they are not normal needles, because the profile of usual needles would damage the tissues of the patients and would not be indicated for periodic use such as in dialysis. The needles 5 So dialysis is a socio - economical problem much more than a clinical problem, because the mortality is related to the possibility to access the treatments mo re than how much it is related to clinical problems, even if there are side effects. The mortality of patients which undergo the dialysis treatments is mostly due to cardiac disease s due to the increasing work of the heart 3 due to the dialysis treatmen t. The cardiac diseases in these cases are generally damages of the valves of the hearts or damages of the cardiac muscle, in particular d i lated cardio - m y opathy that decreases the elasticity of the cardiac muscle or thickening of the cardiac muscle that reduces the volume of the ventricle. However the cariad diseases tha t can develop from the problems related to dialysis are not foreseeable because they are “gen e related” and they depend very much on the specific characteristics of the patient and how the heart of each patient is, so one patient can develop either a delated cardio - myopathy or an opposite type of damage . used are made in such a way that they do not damage the tissues and do not cause the inflammation of the vascular system but their production is very expensive ( about 100 times the cost of normal needles). 3 The work of the heart is the energy given to the blood under the form of pressure difference and is the energy consumed by the heart during a cardiac cycle. It can be described by the pressure - volume (P - V) relationship of the ventricle during the cycles. Typically the PV curves of dialysis patients are enlarged and shifted to the right part of the diagram. 6 TECHNOLOGY AND DIALYSIS The aim of technology in the dialysis field is to : a) Produce safe devices b) Increase biocompatibility c) Higher therapy tolerability d) Personalized therapy prescription EVOLUTION OF THE DIALYSIS Dialysis is born in 1912 on an empirical approach developed by Kolff , even if it became a clinical practice in the ’50 . The first in vivo dialysis w as performed on animals until the dialyzer was good enough to be tested on people and finally it started to be produced by companies and used in clinical practice. Miniaturization was a very important step in the development of the dialyzer because the circuit should be a low priming volume circuits 4 , otherwise the dialyzer would subtract too much blood from the patient and would cause problems. The development of small devices was instead very useful because they were filled with a small volume of blood and did not subtract too much volume of blood f rom the patient. 4 Priming volume = v olum e required by the device in terms of fluid that have to fill in , in order to fill the device and make it work, otherwise some air would be in the device and there would be the risk of air entering the circulatory system of the patient (“ de - air ” the device). 7 2. D IFFUSION TRANSPORT PHENOMENA IN DIALYSIS The membrane of the dialyzer , which is the most important part, is a permeable (to a certain kind of solute s ) and microporous membrane, through which many transport phenomena takes place to ensure the purification of the blood: a) Mass transfer and convection takes place through the por e s ; b) Diffusion takes places through the solid part of the membrane . Therefore it is really impor tant to study these transport phenomena before analyzing the working principles of the dialysis . THE DIFFUSION PHENOMENON Diffusion is the movement of a particle inside a medium and depending on the viscosity of the medium and the characteristics of a solute the movement will be fast or slow. Diffusion is caused by disordered molecular movements which brings to a complete mixing of the solution. The viscosity depends then on many other factors, such as the temperature of the medium, for example for high temperature the viscosity decreases so the movement of the solute becomes easier. Diffusion is caused by disordered molecular movements which b rings to a complete mixing of the solution. The diffusion velocity depends on the medium, in fact in gasses the diffusion is very fast while in liquids and solids decreases. Generally the diffusion can vary as a function of the temperature , because it a cts on the viscosity of the medium. In gasses and liquids can be accelerated by stir r ing 5 the solution; in this case the diffusion is combined with convection. 5 Stir = agitare 8 • Diffusion à process due to molecule movement over short molecular distances • String à macroscopic process which mobilizes portions of the fluid over much larger distances than the diffusion distances. Due to solution stir r ing diffusion takes place among fluid portions which are newly adjacent. In biological organism, both pure diffusion and diffusive - convective processes takes place. FICK’S LAW Fick developed a law describing the diffusion phenomenon that can however be used also to describe other phenomena because it is very simple: ! ! = # $ ! = − # ' ( ) ! (* ! ! = one - dimensional flow rate # = area across which the diffusion occurs ' = diffusion coefficient that depends on the medium and on the solute considered $ ! = one - dimensional flux per unit of area ) ! = concentration of the solute * = diffusion distance So the Fick’s law says that the flux of solute is proportional to the gradient of concentration of the solute itself, so it depends on the difference of concentration of the solute in two different areas. In multicomponent systems , the diffusion equation has to be written for each species participating to the diffusion process and each one will have different fluxes and velocities depending on the characteristics of the solutes (size, weight , e t c..). STEADY DIFFUSION ACROSS A THI N FILM We consider a solution with two different areas of the solution with concentrations of the solute C 10 and C 1L and we want to find both the diffusion flux and the concentration profile of the solute. The solute diffuses from the high concentration compartment towards the lower concentration compartment. To calculate the concentration profile, the mass balance on a thin layer D z located at some arbitrary position z within the thin film. The mass balanc e in this layer at constant density r is: + ,-./01 233/4/.205-6 7 = 8 9201 -: ;5::/,5-6 560- 0 ℎ 1 .2=19 20 * > − 8 9201 -: ;5::/,5-6 560- 0 ℎ 1 .2=19 20 * + ∆ * > 9 C 10 and C 1L are the concentrations of the solute in the two homo geneously stirred diluted 6 solution. T he global diffusive flow rate (solute volume flow rate) is the product of the diffusive flux j, by the section A through which diffusion takes place: ( ( ∆ * 3 ! # ) (0 = # C $ ! D * − $ ! D * + ∆ * E D ividing by the volume of the film A* D z and considering that being the process in steady state the accumulation is zero , so all the solute that enters the volume exits, it can be written: 0 = − # C $ ! D * − $ ! D * + ∆ * E # ∆ * A fter simplifying and calculating the limit of the function for D z tending to zero (thin film), it can be obtained that: 0 = − ; ;* $ ! Finally combining that expression with Fick’s law we obtain the final relation: − $ ! = ' ; ) ! ;* And for a constant diffusion coefficient: 0 = ' ; " ) ! ; * " W e need to add also the boundary conditions because the equation is a differential equation : * = 0 ) ! = ) !# * = G ) ! = ) ! $ Because the system is in steady state, the concentrations ) !# and ) ! $ are independent of time . This means that the volume of the adjacent solutions is much greater than the volume of film (the concentration of the solute is uniformly distributed in the solutions). 6 We work with diluted solutions be cause we do not want the solutes to meet to many obstacles during their diffusion. 10 F inally we have obtained the concentration profile i ntegrating twice the equation , from which we obtain a linear variation from one side to the other: ) ! = 2 + H* → ) ! = ) !# + ) ! $ − ) !# G * The flux is found by differentiating the concentration profile ; because the system is in steady state , the flux is constant : $ ! = − ' ; ) ! ;* = ' G ( ) !# − ) ! $ ) CO N CENTRATION DEPENDENT DIFFUSION The diffusion coefficient in some cases is not a constant , but it can suddenly drop from a higher value to a much lower one. If an area of the solution has a diffusion coefficient ' " and another area has a diffusion coefficient ' ! it does NOT mean that the flux will be different, because we are under the hypothesis of continuity (steady state) so the flux has to be constant in adjacent area , what will change is the concentration profile of the two areas in order to keep the flux co nstant , in particular where the diffusion coefficient is higher the concertation difference will be lower to keep the flux constant . ' ! < ' " → ! ! = ! " → ∆ ) ! > ∆ ) " Hypothesis to simplify the problem: concentration ) ! % diffusion is slow but above this diffusion is much faster. The interface between the two films occurs when the concentration is ) = ) ! % . 11 To simplify the problem we can use the g lobal concentration profile , which is obtained by neglecting the different a ctual concentration s in each point of the solution but we only interpolate the two concentrations on the boundaries, so that the behavior of the concentration in the zone considered will be a line that connect the concentrations on the boundaries, so we will have a linear con centration profile . To study the problem we can use a trivial approach, so we apply Fick’s law for both compartments and then we make an equalization of the fluxes in the two compartments (under the hypothesis of no accumulation) . In either film a steady state mass balance leads to the same equation: 0 = − ; $ ! ;* As a result, the flux $ ! = constant everywhere in the film. However, in film 1 (left - hand) the high concentration produces a small diffusion coefficient: $ ! = − ' ! ; ) ! ;* Fick’s law in film 1 L $ ! & ! # ;* = − ' ! L ; ) ! ' " ! ' "# → $ ! = ' ! * % ( ) !# − ) ! % ) In the right - hand film, the concentration is small, and the diffusion coefficient is large $ " = − ' " ; ) " ;* Fick’s law in film 2 L $ " ;* $ & ! = − ' " L ; ) " ' " $ ' " ! → $ " = ' " G − * % ( ) ! % − ) ! $ ) The unknown position * % can be found recognizing that the flux is the same across bot h $ ! = ' ! * % ( ) !# − ) ! % ) = $ " = ' " G − * % ( ) ! % − ) ! $ ) → * % = G 1 + ' " ( ) ! % − ) ! $ ) ' ! ( ) !# − ) ! % ) 12 T he flux becomes: $ ! = $ " = $ = ' ! ( ) !# − ) ! % ) + ' " ( ) ! % − ) ! $ ) G We define the apparent diffusion coefficient : ' ()) = * " ∆ ' " - * % ∆ ' % ∆ ' " - ∆ ' % If the critical concentration equals the average of ) !# e ) ! $ , then the apparent diffusion coefficient will be the arithmetic average of the two diffusion coeffic ients ' ! e ' " . → $ = $ ! = $ " = ' ()) ( ) !# − ) ! $ ) G The flux across the film is constant and is proportional to the concentration gradient . UNSTEADY DIFFUSION IN A SEMI - INFINITE SLAB (FREE DIFFUSION) The unsteady diffusion in a semi - infinite slab 7 (also called free diffusion ) is the study of the diffusion phenomenon in a solution in which an interface with a non - negligible thickness , that affects the way in which the concentration in one compartment of the solution is felt by th e other compartment. The variation in one compartment is not felt in the other compartment because the interface is too thick to let the two compartments communicate. However the diffusion through the slab is possible, so it is permeable (but only to solute small enough) , so if the solution with two different concentration in the compartments is let enough time , the two compartments will reach the same balance concentration. With a semi - infinite slab the problem becomes time - dependent , because the diffusion is not instantaneous like in the case of a thin film, so the concentration in the 2 compartments will change slowly in time. The semi - infinite slab approach refers to a volume of solution starting at an interface and extending a very long way. The aim is to find how the concentration varies in the solution as a result of a concentration change at its interface. In other words, it has to be found the concentration and flux as a function of position and time . Any diffusion problem will behave as if the slab is infinitely thick at short enough times. Example: a thin membrane separates 2 solutions at identical concentration. The system is quiescent at equilibrium. 7 Slab = piastra The semi - infinite slab is a plate with a certain thickness, opposite to the thin film, in whi ch the thickness is negligible . 13 The concentration on the left - hand interface of the thin membrane is suddenly increased . In the first instants, the concentration at the right interface remains unaltered, as if nothing had happened; the membrane in these first instants behaves as if it was infinitely thic k. Instead at larger times the system will move towards the steady state equilibrium. S o diffusion has to be studied in different ways depending on the period considered : - At short times , we study diffusion as if it proceeded ac ross a semi - infinite slab ; - At long times , we study diffusion as if it proceeded across a thin film . à The semi - infinite slab We increase the concentration at the interface of the semi - infinite slab and we maintain that concentration continuously , feeding that solute to the compartment in order to keep the concentration constant. Moreover the concentration is uniform all over the slab. T he concentration at the left interface (x=0) remains constant at ) !# in tim e because we keep feeding the solution with a certain amount of solute such that the concentration at that point remains constant 14 The slab initially contains a uniform concentration of solute ; a t some time t=0 the concentration at the interface is suddenly and abruptly increased to ) !# , although the solute is present at high dilution. The increase produces a time - dependent concentration profile that develops as solute penetrates into the slab. T ime - dependent the concentration in the solution will vary in time until it becomes p roblem à constant in all points after enough time and equal to the concentration imposed on the interface . We start writing the mass balance on the control volume which describes the solute accumulation in the volume, which will be zero if we study the steady state condition: + ,-./01 233/4/.205-6 7 = 8 9201 -: ;5::/,5-6 560- 0 ℎ 1 .2=19 20 * > − 8 9201 -: ;5 : :/,5-6 560- 0 ℎ 1 .2=19 20 * + ∆ * > ( ( ∆ * 3 ! # ) (0 = # C $ ! D * − $ ! D * + ∆ * E W e divide by the A* D z so we isolate the variation of concentration and if we let D z tend to zero we see that the variation of concentration in time depends on the v ariation of the flux across the thickness : ( 3 ! (0 = C $ ! D * + ∆ * − $ ! D * E * + ∆ * − * 5: ∆ * → 0 ( 3 ! (0 = ( $ ! (* Using the definition of derivatives Combining this equation with the Fick’s law and assuming that the diffusion coefficient D is independent of the concentration we get the so called Fick’s II law : $ ! = − ' ; ) ! ;* → ( 3 ! (0 = ' ; " ) ! ; * " Fick’s II law Then we have to impose the boundary conditions to solve the II order differential equation: 0 = 0 2.. * ) ! = ) !. 0 > 0 * = 0 ) ! = ) !# 0 > 0 * = ∞ ) ! = ) !. N.B. rest of the demonstration on the slides (not done in class) 15 DIFFUSION THROUGH A THIN MEMBRANE The diffusion inside the human body happens often through membranes , which acts as the interface between the two solutions that exchange solutes and they are NOT just passive elements but they play a very important role in transport phenomena. Diffusion through a medium, especially if the medium is a solid such as a memb rane, will be much more enhanced if the solute is soluble into the medium, so the solubility is a very important factor while considering diffusion through a membrane, as we will see. The solubility will be taken into account in the diffusion coefficient and will not appear in the equations, but we have to know where it acts. Thin membranes beh ave like thin films (solid) , so to study the concentration profile and the flux, the same approach used to study diffusion through a thin film is used. The only difference is that the membrane is chemically different from the well - stirred solutions that ar e separated by the membrane itself. This fact will have some little consequences in the definition of the boundary conditions. As usual we first write a mass balance on a thin layer 8 : 0 = # C $ ! D * − $ ! D * + ∆ * E this leads to the differential equation: 0 = ' ; " ) ! ; * " To account for the different solubility of the solute in the membrane with respect to the one in the adjacent solutions the boundary conditions can be written as: * = 0 ) !# ,0 = O ) !# * = G ) ! $ ,0 = O ) ! $ W here C !# ,1 and C !2 ,1 are the concentrations IN the membrane while H is the p artition c oefficient (adimensional). The partition coefficient can be either a decreasing or an increasing coefficient depending on the characteristics of the membrane, so the membrane has to be well characterized to study properly the problem. The choice of the correct membrane is fundamental for each application to replicate a certain function. 8 The membrane could actually have a n accumulation of the solute, so that before diffusion the membrane fills with the solute and then starts to allow the passage of the solutes through the other compartments. 16 The concentration profile resulting from these equations is: ) ! = O ) !# + O ( ) ! $ − ) !# ) * G The capacity of the solute to dissolve through the medium has consequences on the concentration profile of the solute and therefore it affects the diffusion capacity of the solutes in the two compartments. The flux can be found combining the concentration profile with Fick’s law : $ ! = ' 0 O G ( ) !# − ) ! $ ) W here membranes are usually characterized through permeability ( P ), which is given by the diffusion coefficient of the membrane times the solubility coefficient of the solute in that membrane : ' 0 O = R S 4 " , T ' 0 O G = R $ U 4 , V P ermeability of the membrane Permeance of the membrane (permeability per unit length) 17 TYPES OF MEMBRANE We can distinguish two main types of membrane based on their structure: • Solid membrane : uniformly thick membrane , also called continuous membrane ; • Porous membrane : membrane which structure is not uniform but there are pores (channels) that connect the two sides of the membrane . I nside the pores there won’t be the membrane material but the fluid of the solution s of the two compartments; the interface of the two flui ds coming from the different compartments will depend on the pressure of each fluid . 18 3. TECHNOLOGY OF THE D IALYSIS HEMODIALYSIS CIRCUIT AND COMPONENTS The main components of the dialyzer are: 1. Artero - venous fistula , from which we suck the blood; 2. Heparin infusion pump; 3. Pump that allows the flow of blood; 4. Filter (dialyzer membrane) , with a blood - ide and a dialy s ate - side 9 ; 5. Dialy s ate circuit ; 6. Artero - v elous fistula , to readmit the blood into the patient. 9 Dialy s ate = fluido dializzante o dializato 19 THE DIALYSATE The dial ys ate circuit is a circuit in which the dialysate flow and the fluid which flows inside it is prepared directly in the hospital. The d i al ys ate is made of: a) Water ; b) Solutes that will enable the fluid to behave in a certain way to promote the transport of solutes from the blood thorough the dialysate membrane by creating a certain osmotic pressure . The best way to optimize the transfer of a solute between the blood and the dialysate is to use the counter - current configuration , which guarantee a uniformity of concentration and the concentration difference is kept almost uniform along the filter. If instead we use a co - current configuration we would have a blood that decrease the concentration along the filter and the dialysate that would increase the concentration along the filter; this would decrease the overall efficiency of the dialysis. During the dialysis we have also to eliminate water , which is one of the main catabolite of our system (together with CO 2 ) and philologically is eliminated by urinating , but in dialysis patient this function is lost. In order to eliminate water the dialysi s uses the convection phenomenon , thanks to the pressure difference present between the blood compartment and the dialysate compartment. 20 The pressure difference needed to create convection is ensured by placing the dialysate pump downstream wrt the direction of the fluid, so that it has a sucking action on the dialysate and it decreases the pressure of the dialy s ate, while the pump acting on the blood is a pushin g pump so it increases the pressure of the blood. In this way we ensure that there is a pressure difference between the two compartments, because the pressure of the blood is increased by its pump while the one of the dialysate is decreased. Blood à pushing pump ( upstream pump ) Dialysate à sucking pump ( downstream pump ) The dialysate coming out from the dialysis cycle is than disposed , because with the actual technology we are not able to filter properly the dialysate and re - use it, in fact the filter to be used should have very particular characteristics that are not achievable yet . THE INLET AND OUTLET OF THE DIAL YSI S CIRCU IT VA SCULAR ACCESS: THE ARTERO - VENOUS FISTULA ( AVF ) The dialyzer, which acts as a filter, must be insert in the blood circuit in order to work, so we need to repeatedly create an access to the circulatory system. The brachial access is the best access that can be used repeatedly, and it was developed the so - called latero - lateral artero - venous fistula . The artero - venous fistula is an access which consist in 2 different input and output: one access in the artery which is the out put of the blood from the body which enters in the machine and one access in the vein which is the in put of the blood again in the body. The system must have 2 different access otherwise there would be no pressure difference so no flow would go in the dialyzer; without pressure difference the whole system wouldn’t work. In the system the re is then a pump that facilitates the flows of the blood in the dialyzer. The artery is used as the output from the body (input of the dialyzer) because the pressure of blood in the artery is higher than the one in the veins so the sucking action 10 produced by the pump of the dialyzer does not cause collapse in the artery, while the vein could collapse due to the low pressure. Artery à higher pressure à output from the body Vein à low er pressure à input in the body 10 Blood pump is upstream w rt the filter but downstream wrt the artery, so it has a sucking action on the blood comping out of the artery (while in the filter it has a pushing effect on the blood). 21 However the arteries are more protected from the surrounding tissues and creating an access to the artery is very difficult and painful. Therefore Cimino and Brescia developed a system that put in connection an artery and a vein ( artero - venous fistula ); in this way, due to the pressure shared by the artery and the vein, the venous wall will change locally its characteristic and will acquire arterial characteristic, so there will be a part of the vein with characteristi c of the artery. In this way the access can be made through the vein, which is superficial and not too difficult to access as an artery but has gained characteristic that avoid its collapse ( arterialization of the vein ). So this vein becomes repeatedly puncturable without damages like a normal vein. The PROBLEMS related to the vascular access which can happen over time are: • Over - maturation of the fistula , which is an enlargement of the fistula that can increase too much the flow of blood during the dialysis ; • Closure of the fistula which means that the fistula reduc es its dimension in time. In order to solve this problem it is necessary to tailor a new fistula in a more proximal position (wrt the heart). However having a too proximal fistula can be a problem because the pressure difference between the artery and the vein reduces as the fistula approa ches the heart (because near the heard the pressure inside the artery and the vein are almost equal) , so the circulation of the blood inside the body would be problematic because the blood would flow through the fistula where the resistance is low and woul d not perfuse the other districts with a higher resistance , because every fluid flows preferentially where the resistance is lower so the perfusion wouldn’t be uniform ; ß hydraulic problem 22 PUMPS OF THE DIALYSIS MACHINE The pumps used in the dialysis for the blood and the dialysate circuits must be VOLUMETRIC PUMPS , that are pumps that work only at a constant flow rate , whatever the downstream resistance is , so they are pumps with v ertical characteristic curves , because t hey work with constant flow rate whatever the prevalence is. The constant flow rate is particularly important on the blood side because we have to know the amount of water eliminated from the blood ; if the flow rate wasn’t constant we couldn’t keep track of the amount of eliminated water . Moreover if the flow wasn’t constant the pressure drop between the compartments would change in time and wouldn’t be constant, so also the exchange of solutes between blood and dialysate wouldn’t be constant so it woul d be difficult to control. So the constant flow rate allow to control properly both the convection of water and the diffusion of the solutes ( à clearance ) , which are the main phenomena acting during dialysis. Moreover volumetric pumps are required because they work at constant flow rate whatever the downstream resistance of the circuit is . In fact during dialysis the hydraulic resistance vary during the session due to the change of viscosity of blood and dialysate (due to the exchange of solutes and water ) . The kidney diseases which require the use dialysis treatment cause an increase of volemy 11 in the patient, which means the volume of the fluids contained in the circulatory system incr eases too much and this causes also an increase of the mean systemic pressure of the patient. 11 Volemy = o verall volume of f luids contained in the circulatory system, which in physiological conditions is about 10% of the mass of the patient. It one of the main actors which produce the mean systemic pressure ( MSP ) of the patient, given by the volemy over the co mpliance. 23 While the patient is undergoing dialysis, the mean systemic pressure drops due to the elimination of the water in excess and the decrease of the volemy, i n fact on e of the risk of the dialysis is the collapse of the patient during the treatment due to the pressure drop. S o the pumps have to work also in condition of pressure change , and this is another reason why we should use volumetric pumps, which can work at constant flow rate even in changing pressure conditions. Moreover the volumetric pumps, in particular the roller pumps used in dialysis, do NOT cause hemolysis , because the rollers of the pump squeeze the pipe in which the blood flows during their rotation in order to push forward the blood and they do not enter in contact with the blood and its particles, so they do not cause damages to them. The volume of blood contained between the two rollers is pu shed foreword without entering directly in contact with the blood, and in this way the shear stresses are minimized . Also the rollers could cause hemolysis if they squeezed too much the pipes and compressed also the particles of blood, but they are designe d in such a way that they do no t compress all the section of the pipes but only a part of it. So VOLUMETRIC PUMPS are needed in dialysis circuits due to the following reasons: 1. To ensure a constant flow rate in order to control water elimination (convection) and solutes clearance (diffusion); 2. To ensure a constant flow rate even if the hydraulic resistance of the downstream circuit vary during the session; 3. To ensure a constant flow rate even if the pressure changes during the session. 4. They do not cause hemolysis ( roller pumps ) because there are not moving parts of the machine in directly contact with the blood. N.B. Hemolysis, which consists in the damage of the red blood cells, cause serious problems related to the following effects: - The membranes of the red blood cells (stroma) separates from the cells and tend to block the kidneys’ surface, causing kidney insuffi ciency; - Hemoglobin tends to exit the red blood cells and move freely in the blood and tend to become toxic for the patient if it is not contained inside the red blood cells. 24 à Hemo l y sis Hemolysis is the damage of the particles contained inside the blood, especially red blood cells . Kidney s just not act as a filter but produce also many substances such as erythropoietin, which are very important for the hemostasis of the blood; since the dialysis is not able to substitute these functions of the kidney it is very important that at least it does not cause hemolysis . The m ain causes of hemolysis are: 1. Mechanical hemolysis : is the one that could happen during dialysis due to the type of pumps used. Blood during dialysis is subjected to high shear stresses and for values higher than a certain threshold the blood could undergo hemolysis, which however could be caused also by too high compression or depression of the blood. The most critical action on the blood is the shear stress, but also compression and de pression could be dangerous, in particular the depression , because it can cause the explosion of blood cells 12 . The maximum shear stress is located at the wall of the pipe in which the blood flows so the most critical point in which mechanical hemolysis ca n happen is the wall ; 2. Thermal hemolysis : because the particles in the blood cannot stand temperature higher than 42 - 43°C; 3. Chemical - physical hemolysis : f or example poison s , drugs, osmotic pressure that could make the particles implode or explode, or oth er chemical - physical agents that damages the particles in the blood. Considering the mechanical hemolysis there is a diagram called Tillman diagrams which divides the areas in which hemolysis happens and does not happen depending on the value of shear stress applied and time of application of the latter. Tilman diagram for hemodialysis Pay attention that it is a bi - logarithmic diagram ( log( t ) and log(t) ) 12 In particular red cells have a biconcave shape and the most critical point in which they often fracture if they undergo a too high depression is the middle , where they are thinner. 25 Every point in the diagram represents the condition of shear stress of a certain point of the circuit and the interval of time which characterize that condition. In order to evaluate the overall condition of the blood cells to establish whether o r not the blood undergoes hemolysis we have to find a total equivalent shear stress and the total equivalent interval of time in which it is maintained. If this total equivalent condition is above the limit of the Tilmann diagram, so in the dangerous zone, the blood will undergo hemolysis, otherwise the blood will be safe. In order to evaluate the total equivalent condition all the points must be referred to the same shear stress (or the same time interval) so that we can sum all the status and obtain th e total equivalent condition. In order to refer all the points to the same shear stress we can transport each point on lines parallel to the limit line of the Tillman diagrams , because all the points on lines with this slope are points with equivalent hemolysis conditions . So for exam ple in the case represented above the point 1 can be transported in point 3 along the dashed line in order to obtain the same shear stress of point 2; then the intervals of time of points 3 and 2 can be sum to obtain the total equivalent interval of time i n which the shear stress 2=3 is maintained; in this case the total equivalent condition is above the limit so the blood undergoes hemolysis . The r ollers of the roller pumps in the dialysis machines compress completely the tubes in which the blood flows, causing tolerable hemolysis . The d iameters of the dialyzer tubes is about ¼ inches (0,6 cm = 6 mm), so they are very small tubes not to insert too much blood in the external circuit and decrease too much the volemy of the patient, otherwise there would be too much pressure drop . Dialysis flow rate = 350 ml/min W 345 X 6 _ 48 = X 9 X : X ;@ → d DG # DG = d A>@ # A>@ No losses or accumulations inside the pump; the flow rate that enters the pump has to exit. d A>@ = d DG # DG # A>@ # DG < # A>@ → d DG > d A>@ So in centrifugal pump the pressure of the blood is increased by decreasing its velocity , thanks to the divergent shape of the pump. The centrifugal pump should be chosen based on the flow rate it has to process, because i f the size or the specific characteristic of the pumps are not chosen correctly some fluid - dynamic problems may arise inside the machines, such as the creation of vortexes inside the pump or an incorrect direction of the flow inside the divergent conduit, that could cause hemolysis . à P rescription by the producer of the range of flow rate in which each pump could be used Moreover the pump has to give th e fluid enough energy (prevalence) to win the a fterloa ds downstream the pump , which are give n in by the sum of all the resistances ( in terms of pressure drops ) the fluid will meet in the circuit downstream the pump. If the pump is not able to give this amount of pressure to the fluid the circulation of the blood inside the system would stop, even if the pump will go on moving without pumping and producing any flow rate. In this case using centrifugal pumps is a safe solution because the pump just keep s rotating even if not producing any flow rate, without heavy consequences (only hemolysis of the blood inside the pump) . 79 Summarizing, centrifugal pumps are used for the oxygenators’ circuits because they are: - No t hemolytic (if chosen for the correct flow rate); - Safe even if the pressur e given to the fluid is not the correct value; - Easy to be controlled . à Miniaturization of the circuits The development of technologies allowed circuit miniatur i zation , facilitated transportation on ECMO and delivery of the therapy with much less use of heparin , thus reducing bleeding risk. The miniaturization of the circuits was very important not only for practical reasons, but also for solving technical problems, such as the m inimization of the priming volume of the machine . “WASH OUT” OF THE CARBON DIOXIDE AND FLOW RATE OF CO 2 We say that during ECMO there is a “ w ash out ” of the CO 2 from the blood, bec a use the D P_CO 2 between gas and blood is really small so the diffusion takes place with a very small velocity because the gradient of concentration is very law (max 45mmHg of D P between the compartments), so we need to “wash out” the CO 2 in the sense that we have to incr ease the gas flow rate so that the gas is always “clean” in terms of CO 2 and the concentration difference between the blood and the gas is always maximized, so that the wash out of the CO 2 can be performed much better in order to increase the efficiency of the exchanges and reduce the duration of the treatment. In this way t he blood interfaces always with clean gasses, so the concentration difference of CO 2 is always maximized and the diffusion is faster. Partial pressure s in the circulator y system (physiological values) Veins Arteries: P_O 2 = 40 mmHg P_O 2 = 100 mmHg P_CO 2 = 46 mmHg P_CO 2 = 40 mmHg When we need to connect the circulatory system with an artificial device to promote the oxygenation , the concentration of the oxygen in the machine is much higher than the physiological concentrations, because the oxygenator’s membrane are not so permeable as the physiological membranes , so we have to maximize the exchanges by increasing the concentration difference . 80 Oxygenators P_O 2 = 380 - 760 mmHg P_CO 2 = 0 mmHg The P_O 2 in the oxygenator changes in a wide range depending on the particular characteristics of the patient and the level of its lungs’ impairment. Inlet fraction of oxygen = FiO 2 = concentration of oxygen inside the air admitted inside the oxygenator ; we could admit either pure oxygen or oxygen mixed with air . The oxygenator has to be changed after some days of use because the improvement of the diffusion by the high flow rate of gasses increases also the clotting of the membrane by the deposition of proteins and ot her blood components on the membrane. N.B. In case of high flow rate of the blood in the fibers, would the fibers be dislocated through preferential path s that the blood would follow? No longer in modern ECMO systems , because in the oxygenators used nowadays the fibers in are spre a d in the oxygenator and maintained at a fixed distance , as if they were a continuous material, so they cannot displace due to the force generated by the flow rate of blood. N.B. After the use of the oxyge nators, they are cleaned by the blood of the patient and then, disposed because they are single - use devices that can be used just on one patient and then cannot be reused but they are disposed. The blood cleaned from the oxygenator is treated and then infu sed back into the patient. N.B. Starting from the Inlet fraction of oxygen ( FiO 2 ) it is possible to compute the partial pressure of the gasses inside the air inflated into the patient: e 50% [/91 h " 50% 259 → [ K % = R @A@ ∙ j5h " + R @A@ ∙ % h " 56 259 ∙ % 259 We don’t have to consider just the percentage of pure oxygen inside the mixture but also the oxygen contained normally into environmental air (about 20%). 81 MAIN ISSUES OF ECMO The main issues related to ECMO are: a. Efficacy b. Priming volume c. Hemolysis d. Compatibility e. Duration ECMO can be used for no longer than 15 days because of many complications related to: - Decubitus syndrome ; - Dead foot syndrome ; - The oxygenator has to be changed every week because the elemen ts present in the blood accumulate inside the oxygenator and could clot them; - If the patient doesn’t recover after 15 days the chances of survival are very low. 82 6. DIFFUSION OF GASSES INSIDE THE OXYGENATORS ECMO SYSTEMS The membrane of the oxygenators interfaces with the blood side and the gas side (both for continuous and microporous membrane) ; the CO 2 has to be removed from the blood side and O 2 has to be taken in in the blood side . Gas flow rate > blood flow rate The d irections of the flow s are mainly counter - current or cross - current ( à blood perpendicular to the fibers, so that there is a remix of the blood through creation of micro - vortexes), in order to increase or maintain more constant the differences in concentrations of the relevant gasses we want to deal with. DIFFUSION OF GA SSES In general g asses can be analyzed through concentration or partial pressure . For gasses it is much easier to deal with partial pressure when studying diffusion phenomena , instead of the concentration like we did for solid solutes in dialysis , becaus e it is much easier to measure for gasses. à H enry’s law Also gases can diffuse through solutions or membranes . In living organisms diffusion of gases mainly occurs through membranes interfacing a gas mixture and a liquid phase (alveolar membrane) or two liquid phases in which gases are dissolved (vascular membrane: blood and interstitial fluid). When a gas diffus es through a liquid it is necessary to consider the Henry’s law which assesses that at a given temperature the concentration of the gas dissolved in the liquid is proportional to its partial pressure in the liquid: [ l2, ] = ` L [ L Henry’s law : relation between partial pressure and concentration W he re [gas] , is the gas concentration dissolved in a volume of liquid, at standard temperature and pressure conditions (NTP: 0°C and 1 atm), and p g is the partial pressure of the same gas. The coefficient a g is the solubility coefficient which is dependent on the temperature and the kind of liquid. [ L n L = 6 L a o 3 L = [ L ao = ` L [ L 83 By combining the Henry’s law with the Fick’s law , writing the concentration gradient as a function of the partial pressure gradient we obtain: $ L = − ' ` L ( [ L (* S olubility coefficient a independent of the position so it can be taken out from the derivative (it depends mainly on the temperature and on the total pressure 31 ) This is the reason why we have said that the blood should NOT be warmed up after it is oxygenated, because the gasses dissolved in the blood would tend to form bubbles and cause emboli, so the heat exchanger in the oxygenators’ systems must be put before t he oxygenators’ membrane. For the same reason it is also important NOT to over - oxygenate the blood at the end of the treatment . In order to avoid this the blood is continuously remixed, in order to mix oxygenated and non - oxygenated blood and balance the concentrations of oxygen. The blood coming out of the oxygenator is over - oxygenated in order to obtain a final flow rate of blood that is correctly oxygenated, after having mixed with the 20% of the flow rate processed by the aorta, which is unoxygenated. This is the only situat ion in which over - oxygenation is wanted. In all the other applications it is an unwanted effect because it may cause embolization. 31 The fact that the solubility coefficient ! depends mainl y on the temperature and on the total pressure and not by the position can be proved f or example by taking water to boil and observing that the solubility decreases as the temperature increases. 84 Over - oxygenated blood at the end of the circuit could cause emboli so should be avoided, but the over - oxygenation of the blo od coming out of the oxygenator is needed to obtain a correct final concentration of O 2 after having mixed with the aorta blood. Blood has to exit the oxygenator at a higher level of oxygenation (over - oxygenation) in order to obtain complete oxygenation downstream the mixing point in which over - oxygenated and non - oxygenated blood meet. In order to understand how much the blood coming out of the oxygenator should be over - oxygenated in order to obtain a complete oxygenation after the mixture with non - oxygen ated blood, we can use the diagram below , from which starting from the partial pressure of the gasses (O 2 ), the temperature and hematocrit we can obtain the concentration of O 2 in the blood in that condition: 32 Standard hematocrit = 45% → [ h " ] MHDGB = 12 4. K % ;. EFAAC , [ h " ] (N@HNDHB = 20 4. K % ;. EFAAC 32 We use this graph because it is difficult to measure the concentration of gasses inside the blood but it is easy to obtain their partial pressur e and the other parameters. 85 Then we can define the amount of over - oxygenation of the blood coming out of the oxygenator: Y EFAAC ,@A@ = 5 .5019, 456 r Y EFAAC ,AOP = 4 .5019, 456 [ h " ] AOP = ? ⎩ ⎨ ⎧ Y EFAAC , GAG AOP = 1 .5019 456 [ h " ] GAG AOP = 12 4. K % ;. EFAAC Y EFAAC ,@A@ [ h " ] (N@HNDHB = Y EFAAC ,AOP [ h " ] AO P + Y EFAAC , GAG AOP [ h " ] GAG AOP → [ h " ] AOP = 5 ∙ 20 − 12 4 = 22 4. K % ;. EFAAC A mount of over - oxygenation of the blood coming out of the oxygenator DIFFUSION OF GA S SES THROUGH A MEMBRANE When gasses diffuse through a membrane or a liquid we have to take into account the capacity of the gasses to move through these structures. Like for the diffusion/convection of the molecules through a membrane that we saw for dialysis, also the diffusi on of the gasses through a membrane depend s on the molecular weight of the gasses . The membrane can be “ solid ” or made of liquids . It has been experimentally demonstrated that the diffusion coefficient D m of a gas through a membrane is related to the molecular weight of the gas ( Graham’s law ): ' 0 = Z √ y where k is a constant depending on both the material of the membrane and the absolute temperature and M is the molecular weight . Similarly to what was considered about the diffusion of solid solutes, it is necessary to consider how well a gas dissolves in the membrane, with respect to the diffusion of the same gas in the adjacent solutions: also in this case the partition coefficient H has t o be considered. So, the Fick’s law becomes: $ L = − ' 0 O ` L ( [ L ( * 0 86 Also for gasses, like for solid solutes, it is possible to define t he p ermeability P , that is the ability of the gas to permeate the membrane by dissolving into it and moving through it and then passing to the other compartment, on the other side of the membrane and can be thus written as: R = ' 0 O ` 0 and p ermeance P L as: R = * ' Q R ' $ à S ame concepts as for the diffusion of solid solutes in dialysis , but applied for gasse s In Tab.1 the solubility coefficients , for some particular gases in water are listed, at different temperature. It can be noticed that solubility decreases with the increase in temperature . 87 7. DIFFUSIVE AND CONVECTIVE TRANSPORT OF RESPISRATORY GASSES IN THE BLOOD THE BLOOD TISSUE Blood is a tissue consisting of a suspension of cells in aqueous solution, the plasma , which is composed by 90% water and about 7% protein . The number of cells in one ml of human blood is approximately 5×1 0 9 , of which: • approximately 5% are thrombocytes or platelets , which are the cells involved in the coagulation mechanisms; • less than 0.2% are leukocytes or white blood cells , which are the cells involved in immune reactions of the organism ; • The major part of the blood cells is made of erythrocytes or red blood cells , which approximately correspond to 45% in volume of the whole blood of an adult man: this fraction is known as H ematocrit ( Ht ). The red blood cell ( RBC ) is the functional unit of the respiratory gas transport in the blood. It consists of a cell membrane enclosing an aqueous solution whose main components are: a) Na + , K + , Cl - , HCO 3 - ions ; b) Hemoglobin (Hb 4 ) which is present in the solution at approximately 25% by volume (33% by weight) . Hemoglobin is a protein of molecular weight around 67000, whose functional role is to chemically react with the respiratory gases . The hemoglobin molecule contains four functional groups each one capable to form a chemical bond with a oxygen molecule by means of a reversible reaction, to give rise to oxyhemoglobin (Hb 4 O 8 ). The not bonded heme groups are defined as “reduced” and are indicated with RHb. The hemoglobin molecule that reacts with anything containing CO 2 and O 2 . It moves convectively those gasses inside the cardiovascular system by bonding with them. The bonding is reversible and the O 2 and CO 2 can be released by the he moglobin. As soon as the hemoglobin releases the O 2 it bonds with the CO 2 and transport it (and vice versa depending on where it is). The speed of the oxyhemoglobin reaction is high, with respect to the kinetics of oxygen diffusion in the blood, so that in the vast majority of numerical applications, it is reasonable to assume that the reaction is always at the equilibrium . 88 We can de fine hemoglobin capacity for oxygen ( O 2 CAP ), the maximum amount of oxygen that can make a chemical bond with the hemoglobin contained in the whole blood per unit volume. Under physiological arterial conditions, the capacity for oxygen is more than 50 times larger than the capacity of blood to contain oxygen in the dissolved form. This demonstrates the great effectiveness of blood in transporting oxygen. N.B. Blood has to be heparinized when it enters in contact with external machines. OXY - HEMOGLOBIN DISSOCIATION CURVE The degree of oxyhemoglobin saturation , or more simply, saturation ( SO 2 ), refers to the fraction of oxygenated heme groups, with respect to the total number of heme groups available to make a chemical bond with oxygen. In other words, the s aturation indicates how much oxygen is bond to hemoglobin in a given condition: it is a dimensionless quantity whose value is between 0 and 1 (often expressed in percentage te rms). Saturation is influenced by many physicochemical parameters of blood. The capacity of hemoglobin to bind O 2 is described by the oxygen - hemoglobin dissociation (or saturation) c u rve : '5,,-.d1; l2, : [ l2, ] = ` L [ L The reversible reaction between O 2 and hemoglobin is a step by step reaction and does not happen all in one, but it consists in 4 phases, that are represented by the 4 different slopes of the curve in th e saturation curve. 89 The oxygen - hemoglobin dissociation (or saturation) c u rve is represented I a graph where: • Y axis à percentage of saturation of O 2 of the hemoglobin , that reaches a horizontal asymptote because the saturation can reach maximum the 100%, after this value all the remaining O 2 is dissolved into the blood and not bonded to any other hemoglobin cell. This oversaturation is the cause that leads to the formation of emboli ; • X axis à partial pressure of O 2 . T he curve varies in the graph depending mainly on the temperature , but also on the pH : à Effect of the temperature : - If the temperature increases the curve is shifted towards the right and the affinity of hemoglobin and O 2 decreases; instead of this the blood should be warm up before to be oxygenated otherwise we will have formation of emboli ; - If the temperature decreases the curve is shifted towards the left and the affinity of hemoglobin and O 2 increases . à Effect of t he pH : - If the pH increases the curve is shifted towards the left and the affinity of hemoglobin and O 2 increases ; - If the pH decreases the curve is shifted towards the right and the affinity of hemoglobin and O 2 decreases . REACTIONS OF THE CARBON DIOXIDE INSIDE THE BLOOD The presence of CO 2 inside the blood instead is more complicated to be described than the oxygen , because it does not bind only with hemoglobin but it can be present also in the dissolved form , but when it is dissolved in the plasma it can react with many elements , such as the water or the ions (H + and HCO 3 – ) present in the plasma. Those ions are the ones that confer to the blood the correct pH, so if they bind with CO 2 the pH of the blood could change Moreover CO 2 can also react with the proteins present in the blood, however these reactions are much slower wrt to the previous re actions so they can be neglected. Some other reactions involving CO 2 instead take place inside the red blood cells , such as the hemoglobin present inside the red blood cells, but also with the water and some catalyzer contained in the red blood cells. 90 N.B. Hemoglobin is present not only inside the red blood cells but also outside in the blood. CONTINUITY EQUATION AND TRANSPORT OF OXYGEN IN THE BLOOD We want now to study the t ransfer of the gasses inside the blood , not considering any mass transfer through a membrane but just focusing inside the blood side. To study the t ransfer of the gasses inside the blood , so transport inside the same tissue and not crossing membranes or other components, w e need to take into consideration also the reaction elements the gasses enter in contact with inside the gasses, because the gasses do not remain always in the same form inside the blood , but they react with many o