Removal kinetics of therapeutic apheresis

Therapeutic apheresis is aimed at removing a blood constituent, be it a cell or a plasma solute. A partial exception is thrombotic thrombocytopaenic purpura (TTP): in this case the objective of apheresis is to replenish the body's stores of ADAMTS13, a protease that degrades von Willebrand factor multimers^{1, 2}. At any rate, it should be appreciated that removal or replenishment follow exactly the same laws; only, the numerical value should be intended either as a percent decrease or as a percent increase, respectively.

Apheresis can be performed with an intermittent flow cell separator, and in this case the removal kinetics obeys the same laws described in the previous paper of this series³, dedicated to exchange transfusion, or with a continuous flow machine. This paper only concerns continuous flow kinetics.

Rationale of plasma exchange

Plasma exchange has been proposed for a wide array of diseases⁴. As already stated, it is supposed to exert its effect by removing pathogenic substances. The efficacy of the removal depends on the following factors.

• - The distribution space of the substance. Red cells are only present intravascularly; 55%, 58%, and 22% of IgG, IgA, and IgM, respectively, is extravascular⁵; bilirubin and ammonia also diffuse in the intracellular space. Obviously, plasma exchange only removes the intravascular portion, unless equilibration between the compartments already occurs during the procedure (see below).

• - Synthetic and catabolic rates. In a steady state, synthesis and catabolism are balanced. However, when immunoglobulins are acutely removed by plasmapheresis, the catabolic rate decreases, in absolute values, because of the lower plasma concentration. In addition, the fractional catabolic rate of IgG is not constant and is lower at low plasma concentrations⁶. As a result, the recovery rate seems faster than expected. In any case, the effects of plasma exchange are transitory^{5, 7} and the recovery rate depends on the catabolic rate and the half-life of the substance. Those values vary widely: e.g., they are 7% and 22 days, respectively, for IgG, and 150% and 0.6 days for FVIII⁵.

• - The equilibration rate between the compartments (intravascular/extravascular space; intracellular/ extracellular space), that constitute the distribution space of a substance. A fast equilibration means a quick rebound. This may also explain why the removal of some substances is lower than expected⁸: e.g., after an exchange transfusion, where 87% of the red cells were removed, bilirubin was still at 60% of the initial concentration⁹. The bilirubin mass-transfer coefficient of the cell membrane has been calculated as 0.2 L/min¹⁰. In contrast, high molecular weight substances, such as immunoglobulins, equilibrate at a rate of 1-3%/hour⁵.

Removal kinetics of continuous flow plasma exchange

The following formula was proposed by Wiener and Wexler for the kinetics of exchange transfusion¹¹, although, in fact, it describes the kinetics of continuous flow plasma exchange:

where v is the total exchanged volume, V is the patient's plasma volume and e is the transcendental number, base of the natural logarithms. The derivation of the formula may be found in Appendix A. Figure 1 shows the relative intravascular concentration of a substance during plasma exchange, as predicted by (1). The curve is exponential and the efficiency of the procedure decreases as the exchanged volume increases.

Figure 1.

Removal of a hypothetical substance during a continuous flow plasma exchange. The curve is based on the following assumptions: the patient's plasma volume remains constant; the substance is only intravascular, or there is no equilibration with the extravascular compartment; synthesis and catabolism can be ignored. In these conditions, approximately 63% or 86% of the substance is removed, when one or two plasma volumes, respectively, have been exchanged.

Formula (1) is only valid when a number of assumptions are valid. In particular, the following two assumptions deserve close scrutiny:

• - the substance to be removed is only intravascular, or the equilibration is slow;

• - the patient's plasma volume remains constant during the procedure.

Effect of the diffusion rate of the substance

High molecular weight molecules, such as immunoglobulins or low density lipoproteins, equilibrate very slowly^{5, 12}. Accordingly, their removal kinetics follows the one-compartment model at the basis of (1). However, the more a substance is diffusible, the less formula (1) is adequate. The faulty part of the formula is V, the patient's plasma volume. In fact, a perfectly diffusible molecule would behave as if the whole distribution space were exchanged¹². Therefore, V should be intended as the effective distribution space of the substance, i.e. the intravascular volume plus the portion of the extravascular/intracellular volume that equilibrates during the procedure.

Changes in the patient's plasma volume during the procedure

Generally, the plasma removed during the procedure is replaced with an equal volume of saline, albumin and/or colloids. However, this does not guarantee the constancy of the patient's blood volume. Particularly in cases of hyperviscosity syndrome, plasma volume is greatly increased and undergoes acute changes during the procedure¹³. The patient's plasma volume can be estimated with sufficient accuracy by means of a nomogram¹⁴, but this nomogram is not adequate for patients with splenomegaly or paraproteinemia¹⁴. In those cases, it has been suggested¹⁴ that the data collected in the first exchange procedure be used to calculate V, rearranging (1) for this purpose:

where F_R is the residual fraction and ln means the natural logarithm. However, the obtained estimate would be reliable only for the same patient and the same v, at the same paraprotein concentration: i.e. in an exactly identical situation. Moreover, there is no empirical confirmation of the validity of this approach.

The patient's plasma volume also varies when the exchange is not isovolumetric. In this case, the appropriate formula is the following (see Appendix A):

where r is the ratio between the volumes infused and withdrawn and v is the volume withdrawn. Formula (2) assumes that r is constant during the procedure and that the patient's plasma volume decreases or increases, accordingly.

Panel A of figure 2 shows the concentration of a hypothetical substance when r is 0.8 or 1.2, i.e. when the infused volume is 20% less or 20% more than the removed volume. Apparently, the exchange seems more efficient when r >1. However, if the patient's plasma volume rapidly returns to the initial value after the procedure, as it should in most cases, the final results are quite opposite, as illustrated in panel B of figure 2. The formula applied in panel B of figure 2 includes a correction factor equal to the ratio between the final and the initial plasma volumes. After some simplification (see Appendix A), the formula now becomes:

Figure 2.

Residual relative concentration of a hypothetical substance during a plasma exchange. Comparison of an isovolumetric exchange (▪) and a 20% over return (Ä) or a 20% under return (♦). Panel A: results at the end of the procedure. Panel B: results after the the patient’s plasma volume has been restored to normal. Judging from Panel A, over return would seem preferable, but when the effect of the increased plasma volume is subtracted (Panel B), under return emerges as the most effective strategy.

The difference in efficiency between the procedures conducted at different r values progressively increases together with the ratio v/V (Figure 2, panel B). Up to a ratio of 1 (the exchange of one plasma volume), the difference is small and probably not clinically significant. On the other hand, many patients would not tolerate a greater exchange with under return, because of the contraction of the plasma volume. This severely limits the practical applicability of under return.

Other cases in which (1) and (3) are not applicable

Both (1) and (3) assume that the replacement solution mixes immediately and completely with the circulating blood, the anticoagulant does not enter the circulation and its volume is subtracted from the removed volume. In the case of selective removal, there is no replacement solution and the anticoagulant returns to the patient. On the other hand, most immunoadsorption systems use heparin as an anticoagulant, which does not introduce a significant dilution. In fact, the main limitation to the use of (1) in those cases is the efficiency of removal: immunoadsorption systems do not remove 100% of the substance from the processed plasma and the efficiency varies during the procedure¹⁵.

A further source of error is the use of double-lumen catheters: in these cases the first assumption is not valid and part of the replacement solution is immediately removed¹⁶. In centrally placed catheters, the rate of recirculation is generally no greater than 10%, unless the inflow and outflow lines are reversed¹⁶. If the recirculation rate is known, the exchanged volume should be decreased accordingly, before being entered into the formulae.

However, the main limit of the above formulae is that the concentration of the substance to be removed is often not linearly related to the clinical symptoms. Moreover, the formulae do not offer clues to the rebound rate.

Removal of pathogenic substances and clinical symptoms

In many immune diseases, a specific pathogenic antibody has not been identified or the evidence of a causal relationship is lacking¹⁷. In the hyperviscosity syndrome of paraproteinemia, the relationship between protein levels and clinical symptoms is not linear and it is different, according to the patient¹⁸. In myasthenia gravis, acetylcholine receptor antibody levels correlate poorly with neuromuscular symptoms, but the changes in antibody concentration seem to predict the clinical course¹⁹.

Rebound and overshoot

“Rebound” is the return to baseline levels. “Overshoot” occurs when baseline levels are exceeded. The recovery of plasma constituents after plasma exchange has been studied in some detail^{8, 20, 21}. Most coagulation factors and complement components C₃ and C₄ usually return to pre-exchange values by 72 hours or less^{8, 20}. IgM, fibrinogen and cholesterol have a prolonged recovery of 1-2 weeks^{8, 20, 21} and it may take IgG more than 2 weeks to return to baseline levels⁸. Many patients, who underwent three or four exchanges of 50% of the plasma volume in 1-2 weeks, developed hypogammaglobulinaemia²⁰. Plasma exchange was also very effective in removing immune complexes²⁰. In rabbits, overshoot was only observed when the immunoadsorption column released antigen, leading to an increased immune response^22-24. However, the behaviour of a particular antibody is unpredictable: in a case of TTP resistant to plasma exchange, ADAMTS13-inhibitor activity increased abruptly more than 3-fold 7 days after beginning the therapy, to decrease under baseline levels after less than 10 days more²⁵. Other cases of overshoot have been documented²⁶ and this led to the concept of synchronisation and pulse therapy^{26, 27}. The idea is that antibody depletion by plasmapheresis induces a proliferation of antibody-producing cells, making them more sensitive to cytotoxic immunosuppression²⁶. However, overshoot is not commonly observed in man²⁸ and a randomised clinical trial failed to show any clinical benefit of pulse/synchronisation in lupus nephritis²⁹.

A comprehensive model of plasma exchange kinetics

Formulae (1) and (3) derive from a one-compartment model and only regard events occurring during the procedure or immediately after. Kellog and Hester¹² developed a more ambitious model, including a second (extravascular) compartment and considering also synthesis and catabolism. The aim was to predict post-exchange events and establish the optimal interval between the procedures. Unfortunately, many variables appearing in their equations, such as those representing lymphatic and transmembrane flow rates, synthesis, and catabolism, are both patient-dependent and unknown. The Authors tried to estimate them in the first procedures, but the predictions did not always agree with actual data. This is not surprising: patients are usually treated with plasma exchange in unstable periods of their clinical course and the synthetic rate, in particular, is subject to change (see above).

Automated red cell exchange

Red cell exchange is used in the treatment or the prevention of complications of sickle cell disease³⁰ and for a few other indications^{4, 13, 31}. Formulae (1) and (2) are also suitable for red cell exchange, provided that the meanings of the variables are changed appropriately: in (1), v becomes the volume of pure red cells removed and transfused and V is the patient's red cell volume; in (2), v becomes the volume of pure red cells removed, V is the patient's red cell volume at the beginning of the procedure, and r is the ratio between the volumes of pure red cells transfused and removed. In this context, formula (3) is not suitable, because the red cell mass of the patient at the end of the procedure does not return rapidly to the baseline value.

Both (1) and (2) assume that the haematocrit of the red cells used for replacement is constant. However, the formuale are not influenced by changes in the blood volume or the haematocrit of the patient, because the autologous red cells are centrifuged before being removed.

On the other hand, in order to apply (1) or (2), the user must take into account the different haematocrit of the blood withdrawn and transfused. Fortunately, the sophisticated software of modern cell separators facilitates this task, performing most of the calculations automatically. The curious reader can, however, find the relevant formulae in Appendix A. Cell separators can also automatically adjust the inflow and outflow rates so as to balance the volumes of red cells exchanged, or even to reach the desired final haematocrit and haemoglobin S concentration. However, in the case of sickle cell disease, cell separators are not programmed to perform the red cell exchange in the most efficient way automatically: the best technique is a three-step procedure^{32, 33}, including a first phase, in which the removed red cells are replaced with albumin and/or saline; a second phase, during which equal volumes of patient and donor red cells are exchanged; a final phase, in which donor red cells are transfused to reach the desired final haematocrit. Figure 3 also shows that the efficiency of the three-step procedure increases as the minimum allowed haematocrit decreases. Apparently, the patients tolerate well the temporary withdrawal of 300-500 mL of red cell concentrates, even at initial haematocrits as low as 20%³³. Particularly in patients with multiple red cell alloantibodies, the possibility to limit the amount of necessary donor blood is invaluable.

Figure 3.

Number of units of red cell concentrates necessary to decrease the haemoglobin S concentration to the desired value, during a red cell exchange. Initial conditions are as follows: haemoglobin S concentration: 70%; blood volume: 3.5L; haematocrit: 30%. The final desired haematocrit is 33%. The average volume and haematocrit of donor red cell concentrates is 300 mL and 65%, respectively. Comparison of a simple exchange (♦), in which donor red cells are transfused in slight excess to reach the desired haematocrit; a two-step exchange (□), in which equal volumes of donor’s and patient’s red cells are initially exchanged, followed by a top-up transfusion to increase the haematocrit; a three-step exchange, in which the patient’s red cells are initially withdrawn without replacement, followed by an isovolumetric exchange and, finally, by a top-up transfusion (▴= minimum allowed haematocrit: 25%; ○ = minimum allowed haematocrit: 20%). The three-step procedure is preferable and its efficiency increases as the minimum allowed haematocrit decreases.

The prediction by computer simulation of the rate of increase of haemoglobin S after the exchange has been attempted with good results in three out of four patients³⁴.

Therapeutic leucapheresis and thrombocytapheresis

Mathematical modelling of therapeutic leucapheresis and thrombocytapheresis is difficult because the efficiency of removal is not 100% and depends on physical properties of the cells (type of white cell; dimension and density of platelets). Moreover, granulocytes have a very rapid turnover in blood and part of them are in a marginated pool³⁵.

Conclusions

When planning the duration and frequency of plasma exchange, it should be considered that the efficiency of plasma exchange decreases as the total exchanged volume increases and that high molecular weight substances require many hours or days to diffuse from the extravascular to the intravascular compartment. Replacing at a lower rate than removing (“under return”) increases the efficiency of the procedure but exposes the patient to hypovolaemia. A similar concept (“three-step exchange”) improves the efficiency of red cell exchange and is clinically safe.

Appendix A – Derivation of the formulae

Removal kinetics of an isovolumetric plasma exchange

If we denote the initial concentration of a substance by C₀, the initial quantity (Q₀) will be, where V is the plasma volume of the patient. During the exchange, Q will vary according to the equation Q = C× V (1). In an infinitesimal time interval dt, equal volumes of plasma will be removed and replaced by the substitution fluid: , and the removed quantity of the substance will be dQ = − k × dt × C. From (1) we can also derive dQ = C × dV + V × dC, but dV = 0 (the patient’s plasma volume is supposed not to change during the procedure). Therefore − k × dt × C = V × dC (2). Dividing by C (supposed ≠ 0) and integrating both terms of (2): $\int \begin{array}{l}C\hfill \\ C_0\hfill \end{array}\frac{dC}{C}=-\frac{k}{V}\int \begin{array}{l}t\hfill \\ 0\hfill \end{array}dt$, we obtain $ln\frac{C}{C_0}=-\frac{k\times t}{V}+A$, where ln denotes the natural logarithm and A is the integration constant. From the case t = 0, we obtain A = 0.

Denoting by v the exchanged volume (= k× t), we get:

$$Residual\hspace{0.17em}relative\hspace{0.17em}concentration=e^{-\frac{v}{V}}$$ (3)

where “relative concentration” means the concentration expressed as a fraction of the initial value $\left(\frac{C}{C_0}\right)$.

Removal kinetics of a non-isovolumetric plasma exchange

In this case, dv_in ≠ dv_out, dv_in = k₁ × dt, dv_out = k₂ × dt, and dV = (k₁ − k₂)×dt. The patient’s plasma volume varies in time according to the equation V = V₀ + (k₁ − k₂)×t (4), where V₀ is the plasma volume at the beginning of the procedure. In an infinitesimal time interval dt, the removed quantity of the substance will be dQ = − k₂ × dt × C.

Repeating the steps outlined in the previous paragraph, with the appropriate changes, we have − k₂ × dt × C = (k₁ − k₂)× dt × C + V × dC and $\frac{dC}{C}=-\frac{k_1}{V}\times dt$(5). Substituting the right term of (4) for V and integrating both terms of (5), we get

$$ln\frac{C}{C_0}=\frac{k_1}{k_2-k_1}\times ln\left(1+\frac{k_1-k_2}{V_0}\times t\right)+A.$$

From the case t = 0, we obtain A = 0. Therefore, we have: $\frac{C}{C_0}={\left(1+\frac{k_1-k_2}{V_0}\times t\right)}^{\frac{k_1}{k_2-k_1}}$.

From (4) we know that k₂× t is the volume of plasma removed at time t (v_out).

If we denote by r the ratio v_in/v_out (= k₁/k₂), by means of a few substitutions we get:

$$Residual\hspace{0.17em}relative\hspace{0.17em}concentration={\left(1+\left(\left(r-1\right)\times \frac{v_{out}}{V_0}\right)\right)}^{\frac{r}{1-r}}$$ (7)

where v_out and V₀ have the same meaning as v and V in (3), respectively.

Formula (7) gives the final concentration of the hypothetical substance at the end of the exchange, when the patient’s plasma volume is V₀ + (k₁ − k₂)×t = V₀ + (r − 1)× v_out.

However, in most cases, the plasma volume of the patient will soon return to the initial value.

Therefore, the final concentration of the substance, provided there is no diffusion and no synthesis or catabolism, will be equal to $\frac{V_0+(r-1)\times v_{out}}{V_0}\times C$, or $\left(1+(r-1)\times \frac{v_{out}}{V_0}\right)\times C$.

Substituting the right term of (7) for C we get:

$$Residual\hspace{0.17em}relative\hspace{0.17em}concentration={\left(1+\left((r-1)\times \frac{v_{out}}{V_0}\right)\right)}^{\frac{1}{1-r}}.$$ (8)

Removal kinetics of automated red cell exchange^*

Cell separators separate red cells by centrifugation and remove them at a constant haematocrit, irrespective of the haematocrit of whole blood. Therefore, if we accept the approximation that the red cells used for replacement also have a constant haematocrit, formulae (3) and (7) apply. In (3), v represents the volume of pure red cells removed (equal to the transfused volume) and V is the patient’s red cell volume; in (7), v_out is the volume of pure red cells removed, V₀ is the patient’s red cell volume at the beginning of the procedure, and r is the ratio between the volumes of pure red cells transfused and removed. When planning a red cell exchange for a patient with sickle cell disease, the aim is to decrease the concentration of haemoglobin S under a threshold level and, generally, to increase the haematocrit moderately. We know the following initial values of the patient: blood volume (V, estimated), venous haematocrit (H_V, measured), red cell volume (R_B = H_V × k × V, where k is the correction for the body haematocrit³⁶), concentration of haemoglobin S (HbS₀, measured). We also know the average haematocrit of the red cell concentrates to be used as replacement (H_T), the haematocrit of the red cell concentrates removed by the cell separator (H_R), the final HbS concentration (HbS_F) and haematocrit to be reached (H_F). The unknown variables are: the volume of red cell concentrates to be transfused (V_T) and removed (V_R), and the ratio between them (r). We start with a set of three equations:

$$\frac{Hb{S}_F}{Hb{S}_0}={\left(1+\left((r-1)\times \frac{V_R\times H_R}{R_B}\right)\right)}^{\frac{r}{1-r}}$$ (9)

$$r=\frac{V_T\times H_T}{V_R\times H_R}$$ (10)

$$H_F=\frac{(V_T\times H_T)-(V_R\times H_R)+R_B}{V\times h}$$ (11)

where (9) is simply equation (7) in a more explicit form, (10) is just the definition of r, and (11) is also by definition, provided that the blood volume remains constant or returns to the initial value rapidly, and all transfused red cells survive up to the end of the procedure. By a few substitutions, we obtain:

$$r=\frac{1}{1+\frac{ln\left(\frac{H_F}{H_V}\right)}{ln\left(\frac{Hb{S}_F}{Hb{S}_0}\right)}}$$ (12)

and

$$V_T=\frac{(H_F-H_V)\times V\times h}{\left(1-\frac{1}{r}\right)\times H_T}.$$ (13)

If we do not want to change the patient’s haematocrit, (3) applies:

$$\frac{Hb{S}_F}{Hb{S}_0}=e^{-\frac{V_R\times H_R}{V\times h\times H_V}}.$$ (14)

By definition, we know that $V_T=\frac{V_R\times H_R}{H_T}$. Therefore, solving (14), we obtain:

$$V_T=-V\times h\times \frac{H_V}{H_T}\times ln\left(\frac{Hb{S}_F}{Hb{S}_0}\right).$$ (15)

Two-step or three-step red cell exchange

In a two-step exchange, an isovolumetric red cell exchange is followed by a top-up transfusion to increase the patient’s haematocrit. In this case, the first phase follows (14) and the total volume of donor red cells necessary to decrease the haemoglobin S concentration to HbS_F and to increase the haematocrit to H_F is:

$$V_T=\frac{V\times h}{H_T}\times \left(H_F-\left(1+ln\left(\frac{H_F}{H_V}\times \frac{Hb{S}_F}{Hb{S}_0}\right)\right)\right).$$ (16)

The portion of V_T to be used in the top-up transfusion step (V_U) is:

$$V_U=\frac{V\times h}{H_T}\times (H_F-H_V).$$ (17)

In a three-step exchange, a two-step procedure is preceded by the withdrawal of the patient’s red cells, so as to reach a minimum allowed haematocrit (H_m). In this case the total volume of the donor’s red cells is:

$$V_T=\frac{V\times h}{H_T}\times \left(H_F-H_m\times \left(1+ln\left(\frac{H_F}{H_m}\times \frac{Hb{S}_F}{Hb{S}_0}\right)\right)\right).$$ (18)

The amount of the patient’s red cells to be removed initially (V_P) is:

$$V_P=\frac{V\times h}{H_R}\times (H_V-H_m).$$ (19)

and the portion of V_T to be used in the top-up transfusion step (V_U) is:

$$V_U=\frac{V\times h}{H_T}\times (H_F-H_m).$$ (20)

Appendix B – Programming a spreadsheet^*

(The reader is referred to the previous article³ of this series for a brief introduction to spreadsheets).

Continuous flow plasma exchange –isovolumetric

Open a new sheet. Enter the text, values and formulae listed in table I.

Table I.

Instructions for calculating the residual concentration (%) after an isovolumetric plasma exchange

Cell	Text to be entered
A1	Kinetics of continuous flow plasma exchange - isovolumetric
A3	Patient’s blood volume (mL)
A4	Patient’s initial venous haematocrit (%)
A5	Correction factor for the body haematocrit
A6	Exchanged volume (mL)
A8	Patient’s plasma volume (mL)
A9	Exchanged volume (%)
A10	Residual concentration (%)
	Value to be entered
B3	Blood volume of the patient (mL), e.g. 4,500
B4	Initial haematocrit of the patient, e.g. 30
B5	Correction factor for body haematocrit: 0.91
B6	Volume of plasma exchanged (mL), e.g. 3,000
	Formula to be entered
B8	=B3*(1−B4/100*B5)
B9	=B6/B8*100
B10	=EXP(−B6/B8)*100

Cell B8 contains the patient’s plasma volume, as calculated from the blood volume and haematocrit; B9 contains the percentage of the plasma volume exchanged, and B10 the residual concentration of a plasma constituent, calculated as a percentage of the initial value.

Continuous flow plasma exchange –non-isovolumetric

Open a new sheet. Enter the text, values and formulae listed in table II. Cells B9–B11 contain the patient’s plasma volume, the percentage of the plasma volume removed, and the residual concentration of a plasma constituent, respectively.

Table II.

Instructions for calculating the residual concentration (%) after a non-isovolumetric plasma exchange

Cell	Text to be entered
A1	Kinetics of continuous flow plasma exchange – non-isovolumetric
A3	Patient’s blood volume (mL)
A4	Patient’s initial venous haematocrit (%)
A5	Correction factor for the body haematocrit
A6	Removed volume (mL)
A7	Ratio between the infused and the removed volumes
A9	Patient’s plasma volume (mL)
A10	Removed volume (%)
A11	Residual concentration (%)
	Value to be entered
B3	Blood volume of the patient (mL), e.g. 4,500
B4	Initial haematocrit of the patient, e.g. 30
B5	Correction factor for body haematocrit: 0.91
B6	Volume of plasma removed (mL), e.g. 3,000
B7	Ratio between the infused and the removed volumes, e.g. 0.8
	Formula to be entered
B9	=B3*(1−B4/100*B5)
B10	=B6/B9*100
B11	=POWER(1+((B7−1)*B6/B9), 1/(1−B7))*100

Continuous flow red cell exchange –isovolumetric

Open a new sheet. Enter the text, values and formulae listed in table III. Cell B11 contains the patient’s red cell volume; B12 contains the volume of the donor’s red cell concentrate necessary for the exchange.

Table III.

Instructions for calculating the volume of donor red cells necessary to obtain the desired residual concentration of haemoglobin S after an isovolumetric red cell exchange

Cell	Text to be entered
A1	Kinetics of continuous flow red cell exchange – isovolumetric
A3	Patient’s blood volume (mL)
A4	Patient’s initial venous haematocrit (%)
A5	Correction factor for the body haematocrit
A6	Haematocrit of the removed blood (%)
A7	Haematocrit of the transfused blood (%)
A8	Initial concentration of HbS (%)
A9	Desired final concentration of HbS (%)
A11	Patient’s red cell volume (mL)
A12	Volume of red cell concentrate to be exchanged (ml)
	Value to be entered
B3	Blood volume of the patient (mL), e.g. 4,500
B4	Initial haematocrit of the patient, e.g. 30
B5	Correction factor for body haematocrit: 0.91
B6	Haematocrit of the removed blood (%), e.g. 80
B7	Haematocrit of the transfused blood (%), e.g. 60
B8	Initial concentration of HbS (%), e.g. 70
B9	Desired final concentration of HbS (%), e.g. 30
	Formula to be entered
B11	=B3*B4/100*B5
B12	= − B3*B5*B4/B7*LN(B9/B8)

Continuous flow red cell exchange –non-isovolumetric

Open a new sheet. Enter the text, values and formulae listed in table IV. Cell B12 contains the patient’s red cell volume; B13 contains the ratio between the transfused and the removed volumes, and B14 contains the volume of the donor’s red cell concentrate necessary for the exchange.

Table IV.

Instructions for calculating the volume of donor red cells necessary to obtain the desired final haematocrit and residual concentration of haemoglobin S after a non-isovolumetric red cell exchange

Cell	Text to be entered
A1	Kinetics of continuous flow red cell exchange – non-isovolumetric
A3	Patient’s blood volume (mL)
A4	Patient’s initial venous haematocrit (%)
A5	Correction factor for the body haematocrit
A6	Haematocrit of the removed blood (%)
A7	Haematocrit of the transfused blood (%)
A8	Initial concentration of HbS (%)
A9	Desired final concentration of HbS (%)
A10	Desired final haematocrit (%)
A12	Patient’s initial red cell volume (mL)
A13	Ratio between the transfused and the removed volumes
A14	Volume of donor red cell concentrate necessary (mL)
	Value to be entered
B3	Blood volume of the patient (mL), e.g. 4,500
B4	Initial haematocrit of the patient, e.g. 30
B5	Correction factor for body haematocrit: 0.91
B6	Haematocrit of the removed blood (%), e.g. 80
B7	Haematocrit of the transfused blood (%), e.g. 60
B8	Initial concentration of HbS (%), e.g. 70
B9	Desired final concentration of HbS (%), e.g. 30
B10	Desired final haematocrit (%), e.g. 33
	Formula to be entered
B12	=B3*B4/100*B5
B13	=1/(1+(LN(B10/B4)/LN(B9/B8)))
B14	=B3*B5*(B10/100−B4/100)/(B7/100*(1−1/B13))

Continuous flow red cell exchange – three-step procedure

Open a new sheet. Enter the text, values and formulae listed in table V. Cell B13 contains the patient’s red cell volume; B14 the volume of patient’s red cells to be removed in the first phase; B15 the volume of the donor’s red cell concentrate to be exchanged in the second phase; B16 the volume of donor red cell concentrate to be transfused at the end; B17 the total volume of the donor’s red cell concentrate needed for the exchange.

Table V.

Instructions for calculating the volume of donor red cells necessary to obtain the desired final haematocrit and residual concentration of haemoglobin S after a three-step red cell exchange

Cell	Text to be entered
A1	Kinetics of continuous flow red cell exchange – non-isovolumetric
A3	Patient’s blood volume (mL)
A4	Patient’s initial venous haematocrit (%)
A5	Correction factor for the body haematocrit
A6	Haematocrit of the removed blood (%)
A7	Haematocrit of the transfused blood (%)
A8	Initial concentration of HbS (%)
A9	Desired final concentration of HbS (%)
A10	Desired final haematocrit (%)
A11	Minimum allowed haematocrit (%)
A13	Patient’s initial red cell volume (mL)
A14	Volume of patient’s red cells to be removed in the first phase (mL)
A15	Volume of donor red cell concentrate to be exchanged in the second phase (mL)
A16	Volume of donor red cell concentrate to be transfused at the end (mL)
A17	Total volume of donor red cell concentrate needed for the exchange (mL)
	Value to be entered
B3	Blood volume of the patient (mL), e.g. 4,500
B4	Initial haematocrit of the patient, e.g. 30
B5	Correction factor for body haematocrit: 0.91
B6	Haematocrit of the removed blood (%), e.g. 80
B7	Haematocrit of the transfused blood (%), e.g. 60
B8	Initial concentration of HbS (%), e.g. 70
B9	Desired final concentration of HbS (%), e.g. 30
B10	Desired final haematocrit (%), e.g. 33
B11	Minimum allowed haematocrit (%), e.g. 25
	Formula to be entered
B13	=B3*B4/100*B5
B14	=B3*B5/B6*100*(B4/100−B11/100)
B15	= − B3*B5*B11/B7*LN(B10/B11*B9/B8)
B16	=B3*B5/B7*100*(B10/100−B11/100)
B17	=B3*B5/B7*100*(B10/100−B11/100*(1+LN(B10/B11*B9/B8)))