[Regular Paper] Model Predictive and Proportional Integral Control of Blood Clotting Speed Using Warfarin when Data are Missing

Abstract

A control theory approach to the management of the blood clotting speed using the anticoagulant Warfarin is investigated. Controllers are developed and analysed using hospital data from patients with chronic conditions under Warfarin anticoagulation treatment. Proportional Integral (PI) and Model Predictive (MPC) controllers are used to estimate treatment decisions. These controllers are adapted in a novel manner, to enable their use with missing or irregularly sampled data. The performance of the controllers is evaluated both using a simulation of the system and by retrospectively comparing actual decisions in the data to those suggested by the control algorithms. It is shown that when the blood clotting speed is within a target range, the decisions suggested by the control algorithms are similar to those actually made (by medical staff), so would likely have led to similar desirable outcomes. When the blood clotting speed is outside the desirable range and too high or too low, the control algorithms on average suggest lower, or higher inputs respectively. These suggestions are likely to lead to improved outcomes.

An Adaptive Model Predictive Controller to Address the Biovariability in Blood Clotting Response During Therapy With Warfarin

“…These methods were individualized with linear regression approaches; however, in recent years, more advanced techniques have also been investigated, including datadriven algorithms based on multiple linear regression, support vector machines, and artificial neural networks [21]. Moreover, closed-loop approaches were proposed, using deadbeat, proportional integral [29], and proportional integral plus [30] controllers. From these works, the need for a flexible but still robust technique has emerged as one of the critical requirements for automated dosing of warfarin.…”

“…Model parameters were preliminarily initialized, and then, estimated when at least 3-4 samples were available; after these steps, the model was no longer updated. In a more recent work, Wilson and colleagues [29] proposed an MPC controller developed using a linear timediscrete model. The controller was specifically developed to address the presence of missing data.…”

“…1) Model used by the control algorithms: As in [29], both controllers employed the following linear time-discrete model to predict INR response: Final values of the two parameters were obtained by averaging these results, while mean and standard deviation were employed to construct a prior to be used by the Adaptive MPC.…”

“…The second benchmark therapy was the MPC approach developed by Wilson and colleagues (Wilson MPC) [29]. Their work aimed at developing an MPC algorithm for the control of INR response focusing on not-uniformly sampled data.…”

“…In this work, Medical Guidelines from [38] and Wilson MPC from [29] were implemented in MATLAB ® reproducing as closely as possible the description available in their respective publications, and then simulated according to the procedure previously described in Section II-A.3 (i.e., with a daily monitoring and therapy adjustment) in order to compare the tested strategies in a fair scenario.…”