(696c) Dynamic Modeling of Cardiovascular System for Optimal Control of Ventricular Assist Devices

Authors: 
Son, J., Clarkson University
Du, Y., Clarkson University
Approximately 5.7 million adults in U.S. have heart failure (HF), and the annual cost of health care services and medications to treat HF is about $30.7 billion [1]. An estimated 150,000 new patients are diagnosed with end-state HF every year. The traditional solution of HF is heart transplantation. However, only few patients are eligible for a transplant due to the limited supply of donor hearts. Ventricular assist device (VAD) has become an established life-saving therapeutic option for end-stage HF patients, which can support the blood circulation as a bridge-to-transplantation [2]. In this work, a lumped parameter model of human cardiovascular circulatory system is developed, which is further combined with a blood pump model to describe the acceleration of the fluid in a mixed flow blood pump. Based on the models of circulatory system and blood pump, an optimization problem is proposed to control the speed profile of VAD, which can find a trade-off between the maximization of the blood flow to satisfy the blood need of human body and the minimization of suction in VADs.
Previous studies have formulated lumped parameter models of human circulatory system, which comprise the left and right ventricle, active left and right atrium, systemic and pulmonary arterial load, and systemic and pulmonary venous return [3, 4]. While these models have shown their potential in clinical applications, such as the speed control of VADs, the application is still limited due to the incapability of accounting for model uncertainty and variability among individual patients. For example, the flow resistance in the systemic arterial system of the cardiac regulatory mechanisms was modeled based on the mean value of systemic arterial pressure. The step to quantify the effect of variations in arterial pressure on the flow resistance was omitted in previously reported works. In addition, to make models tractable and useful, assumption and simplification are generally used, which may consequently induce model mismatch. In order to improve the reliability and credibility of model, it is necessary to account for uncertainty and model mismatch in the models of circulatory system. Therefore, a stochastic lumped model of the human circulatory system is developed in this work using a polynomial chaos expansion theory [5].
Based on the models of circulatory system, feedback controller can be used to adapt the pump speed of VAD to meet the physiologic needs of HF patients. However, control of VAD presents major challenges, since it can create suctions when the impeller speed, and thus flow, exceeds the venous return to the left ventricle. In addition, most of the available control algorithms of VAD uses a pre-selected speed profile, which ignores different demands of oxygen and blood, due to various activities of patients such as exercise or resting [6, 7]. In this work, an adaptive control algorithm is proposed by formulating an optimization problem to tune the pump speed of VAD in a real-time fashion, which can maximally satisfy the physiologic need of patients, while minimizing suction in VADs. The efficiency of the proposed modelling and control algorithm is illustrated with simulations, which will be further studied with a mock human circulatory cardiovascular system.

Reference

[1] B. Ziaeian and G. C. Fonarow, "Epidemiology and aetiology of heart failure," Nature Reviews Cardiology volume, vol. 13, no. 6, p. 368–378, 2016.

[2] D. Timms, "A review of clinical ventricular assist devices," Medical Engineering & Physics, vol. 33, no. 9, pp. 1041-1047, 2011.

[3] R. Amacher, J. Asprion, G. Ochsner, H. Tevaearai, M. J. Wilhelm, A. Plass, A. Amstutz, S. Vandenberghe and M. S. Daners, "Numerical Optimal Control of Turbo Dynamic Ventricular Assist Devices," Bioengineering, vol. 1, no. 1, pp. 22-46, 2014.

[4] E. Lim, S. Dokos, S. L. Cloherty, R. F. Salamonsen, D. G. Mason, J. A. Reizes and N. H. Lovell, "Parameter-Optimized Model of Cardiovascular–Rotary Blood Pump Interactions," IEEE Transactions on Biomedical Engineering, vol. 57, no. 2, pp. 254-266, 2010.

[5] D. Xiu, Numerical Methods for Stochastic Computation: A Spectral Method Approach, Princeton, New Jersey, USA: Princeton University Press, 2010.

[6] T. Pirbodaghi, S. Axiak, A. Weber, T. Gempp and S. Vandenberghe, "Pulsatile control of rotary blood pumps: Does the modulation waveform matter?," The Journal of Thoracic and Cardiovascular Surgery, vol. 144, no. 4, pp. 970-977, 2012.

[7] P. He, J. Bai and D. D. Xia, "Optimum control of the Hemopump as a left-ventricular assist device," Medical & Biological Engineering & Computing, vol. 43, no. 1, pp. 136-141, 2005.