Mathematics and transfusion medicine - Blood Transfusion

Reverberi R , Reverberi LIt is easy to see that after n cycles:Residual fraction s = 1 − (2). kV When blood is first transfused, on the basis of verysimilar considerations to those above, it can be derivedthat:Residual fraction= ns − k(V + s)1 (3).In the above formulae, only the correction for thedifference between venous and body haematocrit was used.However, a further correction is advisable when thehaematocrit is measured by centrifugation because of thesmall amount of plasma (≈ 2%) that remains entrapped inthe red cell column 8 . In this case k = 0.91 x 0.98 = 0.89.Absolute amount of neonatal red cellsremaining after the exchange transfusionThe volume of the neonatal red cells remaining afterthe exchange cycles (R R) can be derived from formula (2):nR Bcan be derived from (1). The removed volume can beeasily calculated by difference.Venous haematocrit after the exchangetransfusionLet us consider the case in which blood is firstswithdrawn. Let a = and b =1 − a .kVAt each cycle, a fraction equal to a of the donor's redcells present in the circulation will be removed, whilst avolume D Swill be added.Table II shows the situation in the first cycles of anexchange transfusion.As can be seen from the far right column, at each cycle,a term to the power n – 1 is added in parentheses.By definition, we know that:HD=DsSDS× 100 = × 100kV( 1 − b)where H Dis the haematocrit of the transfused blood, andthat:2n−1DSHd= ( 1+b + b + ... + b ) × × 100 ,kVRR s = RB× 1 − , kV nwhere H dis the venous haematocrit (in the patient’scirculation) of the transfused red cells after cycle n.Therefore:or formula (3), as appropriate:d2n−1n( 1 − b) × ( 1 + b+b + ... + b ) × HD= ( 1 − b ) HDH =×RR=RB× s − k(V + s)1 ,nTable II - Volumes of donor red cells (V GR) exchanged during the exchange transfusion. At each cycle, blood is first withdrawn andthen transfused. In the first cycle, no donor red cells are in the circulation during the withdrawal step. D Sis the volumeof donor red cells transfused at each cycleWithdrawal stepTransfusion stepCYCLE Removed V GRRemaining V GRFinal V GR1 0 0 D S2 a × D Sb × D SD S+ b × D S3 a × (1 + b) × D S(b + b 2 ) × D S(1 + b + b 2 ) × D S4 a × (1 + b + b 2 ) × D S(b + b 2 + b 3 ) × D S(1 + b + b 2 + b 3 ) × D S… … … …n a × (1 + b + b 2 +…+ b n-2 ) × D S(b + b 2 +…+ b n-1 ) × D S(1 + b + b 2 +…+ b n-1 ) × D S98Blood Transfus 2007; 5: 93-101 DOI 10.2450/2007.0018-07093-101_reverberi.p65 9809/07/2007, 9.53