Estimation of Whole Blood(WB) and Anti-Hemophiliate Factor using Extended Kalman Filter in PMI Surabaya

Every hospital is required to have a Hospital Blood Bank (HBB), a service unit of the hospital responsible for the availability of blood for safe transfusion, of high quality and sufficient to support health services in the hospital and other health care centers. PMI (Indonesian Red Cross) continues to campaign for blood donations as part of a lifestyle (lifestyle). Every year, PMI set its targets of up to 4.5 million blood bags to meet the national blood needs, adjusted to the standards of the International Health Institute (WHO), which is 2% of the population for each day. With a continuous campaign by PMI, the stability of blood stock and distribution on target must be maintained, and the importance of blood distribution both blood coming from blood donors and blood distributed to PMI or other regional hospitals must be taken into account, therefore a software is required to estimate blood stock.for the blood banks. In this paper an estimation of Whole Blood (WB) and Anti-Hemophiliate Factor (AHF) blood demand was made at PMI Surabaya. Estimation is made because a problem can sometimes be solved by using the previous information or data related to the problem. One estimation method used was Extended Kalman Filter (EKF), an estimation method with a fairly high degree of accuracy. Based on the simulation results, a numerical study was obtained based on the number of iterations, and that with 350 iterations showed a higher accuracy than those with 250 and 150 iterations. The accuracy reached was within the range of 95-98 %.


Introduction
Every hospital is required to have a Hospital Blood Bank (HBB), a service unit in the hospital responsible for the availability of blood for safe transfusion, of high quality and sufficient to support health services in hospitals and other health care centers. (Minister of Health Regulation 83/2014, Chapter III Article 40). HBB is a service unit established by the Hospital Director and can be part of a laboratory in a hospital.
Currently Indonesia still lacks 500 thousand bags of blood. According to WHO the minimum blood requirement in Indonesia shall be 2% of the population or around 5.1 million bags per year. In fact there are currently only 4.5 million bags out of 3, 05 million donors. Based on this, the Minister of Health in 2014-2019, Prof. Dr. dr. Nila F Moeloek, Sp. M (K) hopes that the community will be more involved and become donors, therefore PMI always conducts blood donor activities as often as possible by involving all elements of the society.
With the enactment of the Permenkes 83/2014, the role of hospitals having HBB is increasingly clear, especially in terms of the duties and responsibilities between HBB and UTD, previously unclear. Now by Permenkes (Health Minister Regulations) it has been emphasized that HBB is a hospital service integrated with UTD with clear duties and responsibilities set up, supported by buildings, facilities and infrastructure, equipment and specific personnels, including HR qualifications and job-description as well as the strength of the network of transfusion services between providers and health services, which up to now, has only covered the related institutions without involving the health department (SW) [1]. PMI continues to campaign for blood donations as part of a lifestyle. Every year, PMI sets a target of up to 4.5 million blood bags to meet the national blood needs, as adjusted to the standards of the International Health Institute (WHO), which is 2% of the population for each day.
With a continuous campaign by PMI, the stability of blood stock and distribution on target shall be maintained, and the importance of blood distribution both blood coming from blood donors and blood distributed to PMI or other regional hospitals shall be taken into consideration. Therefore, a software is needed to estimate blood stock for the blood banks. Many studies on estimation are carried out in all scientific fields, including estimation of stock price and profit company [2,3], steam drum water level [4], estimation of AUV trajectory and ASV position [5,6,7], and estimation of missile trajectories [8].
This paper examined the estimation of blood demand for Whole Blood (WB) and Anti-Hemophiliate Factor (AHF) types for the blood banks. Estimation should be made because a problem can sometimes be solved by using the previous information or data related to the problem with a fairly small error. So with the estimation of blood stock, it is expected to reduce errors in the distribution of blood in various regions or hospitals.

Blood Data of Whole Blood (WB) and Anti-Hemophiliate Factor (AHF)
The data of Whole Blood (WB) and Anti-Hemophiliate Factor (AHF) is shown as follows:

Extended Kalman Filter
The Extended Kalman Filter (EKF) algorithm can be seen [9]: Model system and measurement model 1. Initialization

Simulation Result
From the blood data of WB and AHF types in Table 1 and 2, a mathematical function was obtained for the blood supply of WB and AHF types using Mathematica software. The Mathematica software simulation resulted in a function of WB and AHF as follows: from equations (9) and (10), the modified WB and AHF blood stock function model in (9) and (10) is discreted using the finite difference method and obtained as follows:    Figures 1, 2 and 3 show that the estimation results of WB blood stock had high accuracy with an error of less than 2%, indicating that the estimation of the WB stock declined using either estimation of 150, 250, or 350 iterations. So it could be taken into consideration by PMI to get blood donors to avoid the shortage of blood stock of WB type.    Figures 4, 5 and 6 show that the estimation results of AHF blood stock had high accuracy with an error of less than 5%. as we can see in the real graphs. The accuracy of Extended Kalman Filter methods showed no significant difference.So it could be taken into consideration by PMI to get blood donors to avoid theoverload of blood stock of AHF type.  Figure 5. Estimation of AHF Blood Stock using EKF method with 250 iterations  Table 3, it appears that the Extended Kalman Filter method using 350 iteration with RMSE of 0.00251 for WB Blood has higher accuracy than that of 250 and 150 iterations with RMSE of 0.00312 and 0.00381, and using 350 iterations with RMSE of 0.00451 for AHF blood has higher accuracy than that of 250 and 150 iterations with RMSE of 0.00484 and 0.00517. but the difference is not much. Likewise, in Figures 4 and 5 with 150 and 250 iteration. In conclusion, EKF method can be used as a method estimating either WB and AHF blood stock or other blood types.  In general, the methods of Extended Kalman Filter can be used as a method to estimate Whole Blood (WB) and Anti-Hemophiliate Factor (AHF) blood stock with high accuracy. Based on the numeric simulation results above, it is likely that method can also be used to estimate other type of blood stock, so it can support the work of blood transfusion management.

Conclusion
Based Conclusion could be drawn based on the results of the simulation analysis that the EKF method is an effective method for estimating WB and AHF blood stock with excellent accuracy and an error of less than 5%. Thus, its application can support the work of blood bank management.
Open problem. How to implemented Fuzzy Kalman Filter (FKF) for estimation of other type of blood stock in all cities in Indonesia.