Maths between the blood bags

‘The rarer the blood, the longer we want to keep it on-shelf’

He seems a bit out of place at Sanquin (but he is not!). As a mathematician, Joost van Sambeeck is working on an algorithmic blood match model.

Joost van SambeeckWhat is a mathematician doing at Sanquin?

Sanquin supplies hospitals with blood products. Ensuring a stable blood supply is one of the blood bank’s primary roles. This not only involves collection centers and donors, but also a board of directors, human resources departments, ICT facilities, logistics. All these logistic processes can be represented in mathematical models, allowing you to calculate an optimal process. That is what I do.

You work at Sanquin, how did that happen?

My professor Dick den Hertog in Tilburg had contacts at Sanquin. He supervised my master’s thesis, which in simple terms was about ‘where do I locate my distribution centers for maximum efficiency in product distribution’. Efficiency is certainly an important factor in terms of optimal blood supply. My previous experience serves Sanquin well.

You are working on the ‘BloodMatch’ project with Mart Jansen as your supervisor in Twente and in Amsterdam.

At Twente University I collaborate in the ‘Center for Healthcare Operations Improvement & Research’. We study how mathematical processes can be applied in healthcare – in hospitals and also the blood bank – to optimise processes. And of course I make a point of being in Amsterdam (Sanquin head office, ed.) too. I need to see and familiarize myself with these processes with my own eyes. You can’t do that with a paper manual. Certainly not with my background. Other than being a blood donor myself, I have no previous experience with blood. I want to discover for myself what the real questions are and what problems Sanquiners encounter in practice. This knowledge is important for the mathematical model I am building. My statistics and algorithms need to be correct. That can be achieved only when I transform the exact reality to mathematics. I want to be right on top of the work.

What exactly is BloodMatch all about?

Donors give blood, patients receive it. That sounds simple enough. But the blood needs to be processed, stored, and then transported to hospitals. Additionally, blood and blood products have a limited shelf life. And not unimportantly: donor and recipient blood should be as similar as possible. We want the best possible match. If patient blood differs too much from donor blood, the patient may produce antibodies against donor antigens (proteins and sugars). This risk is not very high for most antigens, but some antigens, such as A, B and Rhesus D, immediately promote antibody production. Everyone is matched for these antigens. If, for instance, you have antibodies against B in your body, blood with blood type B will immediately be broken down.

This is nothing new, is it?

No, it isn't. But new guidelines were introduced in 2011, specifying how extensively certain patient groups should be matched. If you want to match more blood groups, practical implementation becomes increasingly complex. Especially regular blood transfusion recipients require extensive matching, to prevent these patients from developing problems with the less antigenic blood groups. Thalassaemia patients (congenital blood disease where the body produces insufficient and abnormal haemoglobin, ed.) and patients with sickle cell disease often require additional red blood cells due to a genetic mutation. The question is: how extensively should you match? Of the 300 known blood types, some 20 are actually relevant to blood transfusion. The new guidelines specify which blood types we need to match for which patient populations. The question is whether we will need to match more blood types in the future.

You are answering this question from a patient perspective. There is also the supply side of the donor blood?

Indeed. One side is the demand for typed blood, supply is the other side. These two – supply and demand – should be aligned as closely as possible. This is actually at the heart of the mathematical model we designed. At the same time, it has everything to do with inventory management. The model takes the scarcity of blood into account, for example. Some patients have a (very) rare blood type. When this rare blood type is needed, do we have it in stock? You have a measure of control in calling up donors, but to some degree it is also out of your hands.

And another challenge emerges: blood has a limited shelf life. How does this impact your mathematical model in terms of when to dispense it?

We specifically focused on red blood cells, which have a 35-day shelf life. Because you know one blood type is much rarer than the other, you can weigh the age of blood type against its rarity. The rarer the blood, the longer we want to keep it on shelf, as that will give us more time to use it effectively. We already weigh these considerations to some extent, but in practice it is quite complicated. Our inventory comprises thousands of bags of blood. The oldest are in front, so that you can quickly get to them. The very rare types are kept separate, but the somewhat less rare bags are more quickly included in the bulk. We are trying to design a model that allows us to more effectively tackle this problem – aligning demand and supply on the basis of rarity and availability. The mathematical model then decides which bag of blood should be selected for dispensing.

How does this work out in practice?

If you look at all combinations of these twenty blood groups, you are easily talking about thousands of different blood types. Each blood type is allocated a rarity score between zero and one. This is also a determinator for the moment of dispensing. All bags of blood are allocated two numbers, the basis of which is used to calculate the best blood bag for a specific request from a hospital. A significant benefit is that rare blood bags are now kept in stock for as long as possible, up to the 20-day limit.

What determines this 20-day limit?

If Sanquin transports a bag of blood to the hospital, you want to have some remaining shelf life there. Not that it expires the very next day. That is why we selected this 20-day limit as latest dispensing date. If a blood bag is not very rare, it could be dispensed within, say, five days. If it is very rare, it will be more like 20 days. This is how we try to keep the rare blood types in stock. We dispense them more quickly as they approach their 20th day.

Rarity and time, are these the only factors you need to take into account?

No, more factors are involved. Sanquin collects blood in 136 permanent and mobile locations, processes it in two production centers and then forwards it to some 10 regional hubs for continued distribution to hospitals. Sanquin must take regional characteristics into account when dispensing (rare) blood. Many non-Caucasians live in the urban agglomeration of west-central Netherlands, the Randstad. In many cases, their blood types are slightly different. Sickle-cell disease is more prevalent among this group. That is why in the Randstad distribution centers, we want to have certain rare blood bags available, more so than in the distribution centers for Groningen or Limburg. This aspect, by the way, has not yet been included in our mathematical model. We first pilot the designed model parallel to actual blood dispensing, in order to assess whether it actually improves things. A mathematical model is always a simplified representation of reality. That is why we first test our findings in real life. 

Is Sanquin a deliberate choice for you?

I find this optimal blood matching most fascinating and also socially highly relevant. That appeals to me. I feel strongly about dedicating my mathematical know-how to a socially relevant issue, like improving the health of transfusion recipients. Not through biomedical research, but by modelling, inventory management, by mathematically optimising the complex logistics of blood dispensing.

Has the BloodMatch project been finalised yet?

No, we will go on for at least another year, but already we understand much better how things could be done differently. It would be great to show that the model, which I should say was designed in a collaboration with the entire project team, works so well that it can be implemented. That would be our crowning achievement. •

Joost van Sambeeck studied Operational Research and Management Science at Tilburg University and has worked at Sanquin for three years now in addition to his affiliation with Twente University.