Mathematics to improve expiry in transfusions

Blood is never transferred directly to the patient. Basically, three products are obtained from the extracted blood: red blood cells, plasma and platelets. These products have a limited lifetime and their expiry times vary: plasma can be stored for up to two years, red blood cells for 28 days, and platelets expire within five days. Managing platelet concentrates is complicated because they expire quickly and because the daily demand is uncertain and no delays are permitted. This means that the person responsible for producing them has to make difficult and sometimes risky decisions: low production entails the risk of patients going untreated; so the general tendency is to generate overproduction, which leads to high expiry rates and an increase in economic costs because these are expensive products.

The Basque Centre for Transfusions and Human Tissue (CVTTH) approached the Mathematical Technology Transfer Group of the UPV/EHU to develop a mathematical tool to optimize the management of stocks of platelet concentrates (PCs). The model was built using past data of 2012, and was validated using past data of 2013: a simulation that gives the results of what would have been the production and expiry following the guidelines of the model was made, and these results were compared with those of the actual demand that occurred in 2013.

The comparison between the results of the model and what happened in 2013 shows that with an annual reduction of 14.42% of the PCs produced (1,472 PCs less) the whole demand would have been met without needing to import any PCs. This would have signified a highly significant reduction of 90.18% of expired PCs with respect to the actual figure (1,460 fewer PCs). Collaterally, an improvement of nearly one day in the average age of the PCs transfused would have been achieved, as a reduction of 65.07% of the five-day-old PCs transfused would be obtained, which is very important from a clinical perspective. This undoubtedly has significant economic repercussions: by applying the rates established in the Basque Country in 2013, the potential savings resulting from cutting production would range between €420,000 and €690,000.  

A complex model which needs to go on being optimized

The expiry of PCs is a global problem that needs to be tackled jointly across the transfusion chain. The Basque Country's transfusion network comprises one production centre, the CVTTH, twelve public hospitals and nine private clinics, even though there are permanent stocks of PCs only in five public hospitals. The information system covers all the organisations except for five private clinics, and includes all the processes in the chain, from donation to transfusion. This means direct, centralised management of 100% of the donations and 94% of the transfusions carried out in the Basque Country. Every year, the CVTTH produces and supplies about 100,000 red blood cell concentrates, 12,000 plasma doses for transfusion and 10,300 PCs.

The model designed for managing PCs in the Basque Country means a single stock in the CVTTH, without taking those of the hospitals into consideration. The model considers that production only takes place on working days although transfusions are made every day of the year. The PCs produced on Monday, Tuesday, Wednesday and Thursday go into stock the following morning with an age of one day, while those produced on Friday go into stock the following Monday with an age of three days, thus reproducing the actual dynamics. At the end of the day once all the transfusions have been made, the expired PCs are discarded. The stock is updated every morning once the expired ones have been deducted and the latest production is incorporated.

The problem raised is no simple one because demand is not stable (it depends on the day of the week). What is more, one has to take into account the effect of Easter, Christmas and the summer public holidays in the mathematical model designed, the rule that specifies the daily limit to be produced is fixed by using a statistical analysis of demand, and the future units that will expire are reckoned through a probabilistic analysis.

"It can be confirmed that this study is useful in gaining a better idea of the production, distribution and transfusion dynamics of PCs in the Basque Country and that, despite its limitations, it allows guidelines to be established," concluded Mikel Lezaun, the group's lead researcher. "In fact, changes have already been introduced into the PC production systematics: mainly, a reduction in production by adjusting it to the day of the week. Now the changes introduced need to be monitored to assess their effectiveness. In the near future the line begun will be pursued further by conducting more exhaustive, more complex studies that reflect the reality better."

Additional information

The UPV/EHU's Mathematical Technology Transfer Group (https://www.ehu.eus/mae/grupottm/) has six PhD holders. The lead researcher is Mikel Lezaun, of the Department of Applied Mathematics and Statistics and Operational Research of the Faculty of Science and Technology. Through research projects the group works in direct contact with companies to resolve any problem in the field of R&D&i. Through the knowledge acquired and its infrastructure the group offers companies and institutions a range of services.

Conference:

MA Pérez Vaquero, C. Gorria, M. Lezaun, FJ López, J Monge, C Eguizabal, MA Vesga. "A strategy for optimally managing the stock of platelet pool on a blood bank by mathematical simulation". Congress of the Real Sociedad de Matemática Española (Royal Spanish Mathematical Society). Granada, February 2-6, 2015