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Overview :
Wilkinson et al developed a mathematical model for predicting
percent parasitemia in a patient with severe falciparum malaria who has received
an exchange transfusion. This can help plan the number and volumes of blood
exchanges required to achieve a targeted parasite load. The authors are from
Northwick Park Hospital and the Hospital for Tropical Diseases in England.
Model: simple one-compartment model
Blood used for exchange transfusions:
(1) whole
blood < 24 hours old (preferred)
(2)
transfusion of packed cells together with fresh frozen plasma in 1:1 ratio
(approximates whole blood; these should not be mixed before exchange but each
product hung separately)
where:
• The default hemoglobin for whole blood was 14.4 g/dL
• The default hemoglobin for packed red blood cells was 24
g/dL.
hemoglobin following exchange transfusion in g/dL =
= (hemoglobin of transfused blood in g/dL) – (((hemoglobin of
transfused blood) – (hemoglobin of patient before exchange)) * EXP((-1) *
(decimal fraction of blood volume exchanged)))
percent parasitemia after parasitemia =
= (percent parasitemia before exchange) * (hemoglobin before
transfusion) / (hemoglobin following exchange) * EXP((-1) * (decimal fraction of
blood volume exchanged))
where:
• Percent parasitemia refers to percent of red blood cells
containing parasites.
By rearranging this:
decimal fraction of blood volume exchanged =
= (-1) * LN((percent parasitemia after exchange) / (percent
parasitemia before) * (hemoglobin following exchange) / (hemoglobin before
exchange)) =
= LN((percent parasitemia before) / (percent parasitemia after)
* (hemoglobin before exchange) / (hemoglobin after exchange))
An exchange of 0.69 blood volume will reduce the percent
parasitemia to about 50% of the original, depending on the hemoglobin of the
transfused blood:
fraction of original parasitemia after an exchange of 0.69 blood
volume =
= (hemoglobin before exchange) / ((hemoglobin of transfused
blood) + (hemoglobin before transfusion))
In a series of 29 patients, the formula tended to overestimate
the final parasitemia. One possible explanation was that patients were receiving
concurrent quinine and other antimalarials concurrently with the exchange
transfusion.
where:
• One other
explanation might be that severe falciparum malaria may show 2 ring forms per
RBC.
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