Control of the Left Ventricular Assist Devices for Heart Patients


Collaborators

 

Dr. Marwan A. Simaan (Pitt-UCF)

Dr. James F. Antaki (Pitt-CMU-Cornell))

Dr. J. Robert Boston (Pitt)

Dr. Robert L. Kormos (UPMC)

Dr. Timothy M. Maul (Nemours)

DR. Peter D. Wearden (Nemours)

Dr.  Eduardo Divo (UCF)

Graduate Students: Y-C, Yu (Pitt), L. A. Baloa (Pitt), S. Chen (Pitt),

A. Ferreira (Pitt), D. G. Galati (Pitt), N. V. Zorn (Pitt), Y. Wang (UCF),

G. Faragallah (UCF), V. Vasudevan (UCF)

 

 

 

Heart Patient with an LVAD

Streamliner Axial Flow Blood Pump with Magnetic

Bearings (Univ. of Pittsburgh)

Pediatric LVAD

Diagram of an LVAD in the Cardiovascular System

 

Combined Model of Left Ventricle and Rotary Pump

 

Description: Description: Description: Description: image013

Rotary Pump Connected to Heart

 

 

         

 

Project Summary

 

Heart transplant candidates often wait long periods (300 days or more on the average) before a suitable donor heart becomes available, and many of these candidate die while awaiting heart transplantation. Consequently, the medical community has been placing increased emphasis on the use of mechanical devices that can substitute for, or enhance, the function of the natural heart.  A Left Ventricular Assist Device (LVAD) is such a device.  This device if often used as a bridge to mechanically support a patient while awaiting heart transplantation, or while their natural heart recovers.  But the ultimate use of this device is as a long-term “cure” for heart failure.  In either case, the goal of the LVAD is to provide the patient with as close to a normal lifestyle as possible.  The goal for all concerned is to allow patients to return home and/or to the workforce.

 

An important challenge facing the increased use of LVADs is the development of an appropriate feedback controller for these devices.  The latest generation LVADs is build using turbo-dynamic rotary pumps which require a controller that can adjust the speed of the rotor (pump impeller) to meet the circulatory demand of the patient.  Therefore, in addition to being robust and reliable, an LVAD controller should be able to adapt to the daily activities and the physiological changes of the patient.  In this project we are investigating the theoretical and fundamental issues associated with the development of such a controller.  More specifically, we will continue our ongoing work on the development of a generalized nonlinear dynamic model for the left ventricle of the heart assisted by a rotary LVAD which together collaborate in pumping blood into the circulatory system.  This bio-mechanical model will serve as a simulation platform for understanding the complex interaction between a biological system (the left ventricle of the heart) and a mechanical system (the LVAD).  Our ultimate goal is the development of a robust optimal feedback control algorithm for the LVAD that provides the flexibility needed to incorporate various sensor inputs as available. The principal functions of this feedback controller will be: (1) to determine and maintain appropriate cardiac output, subject to constraints imposed by the device and the patient’s condition, including avoiding ventricular suction; (2) to identify system variables and parameters to monitor the patient's condition, indicating when the patient's cardiovascular status is improving or deteriorating and detecting component failures; (3) to recognize different operating conditions and data environments, responding to changes in the signals available for measurement from the patient and the assist device; (4) to monitor the control strategy (algorithm) itself to avoid uncontrollable situations and inappropriate or dangerous control actions; and (5) to provide a fail-safe mode of operation by entering a preset open-loop operating mode when a hardware or algorithmic failure occurs.

 

The primary intellectual merit of our research is to increase our understanding of fundamental technical issues related to non-conventional complex systems, such as the left ventricle-LVAD system, which involve both electromechanical as well as physiological components. A truly interdisciplinary approach, with expertise from the electrical, mechanical, and biomedical engineering fields as well as the medical profession, is needed to develop the mathematical framework needed to be able to effectively control such a complex system. 

  

The broader impact of our research will primarily be in improving the quality of life for heart patients awaiting heart transplantation.  Any improvement in the existing technology of the left ventricular assist devices will have a tremendous effect on the physical condition and ultimately the recovery of patients suffering from congestive heart failure.   It is hoped that this study, leading to the development of a patient adaptive feedback controller, will provide an opportunity for these patients to leave the hospital, return home, and re-enter the workforce while either awaiting for a donor heart (bridge-to-transplantation), keeping the LVAD permanently (destination-therapy), or hoping that their hearts recover and the LVAD ultimately removed (bridge-to-recovery).   Another important impact of this project is the training of graduate and undergraduate engineering students from various disciplines to work together as a team in this highly interdisciplinary field. 

 

 

 

 

Related Recent Publications

 

V.S. Vasudevan, M.A. Simaan, T.M. Maul, and P.D. Wearden, “Aortic Valve Ejection Fraction For Monitoring Heart Contractility in Patients Supported with a Continuous Flow Left Ventricular Assist Device,” American Journal of Cardiovascular and Thoracic Surgery, Volume 4, Issue 2, 2019 (View)

 

V.S. Vasudevan and M.A. Simaan, “A Modified Definition of Ejection Fraction for Continuous Flow Left ventricular Devices as a Determinant for Heart Recovery,”  Proc. of the 2018 American Society for Artificial Internal Organs (ASAIO) 64th Annual Conference, Washington, DC,  June 13-16, 2018, p. 29

 

V.S. Vasudevan and M.A. Simaan, “Cardiac Function Recovery Using Ejection Fraction in the Presence of a Continuous Flow Left Ventricular Assist Device,” Proc. of the 2018 IEEE EMBS International Conference on Biomedical & Health Informatics (BHI), Las Vegas, NV, March 4-7, 2018, pp. 311-314

 

V.S. Vasudevan and M.A. Simaan, “A System of Systems Approach to Patient Treatment with the Left Ventricular Assist Device,” Proc. of the 12th Annual System of Systems Conference, June 18-21, 2017, Waikoloa, HI

 

V.S. Vasudevan, Y. Wang, and M.A. Simaan, “Aortic Valve Dynamics and Blood Flow Control in Continuous Flow Left Ventricular Assist Devices,” Proc. of the 2017 American Control Conference, Seattle, WA, May 24-26, 2017, pp.1456-1461

 

M. A. Simaan, G. Faragallah, and Y. Wang, “Power Control Range of Operation for the Left Ventricular Assist Device in Bridge-to-Recovery Treatment,” Extended Abstract, World Congress on Medical Physics and Biomedical Engineering, Toronto, Canada, June 7-12, 2015

 

Y. Wang, G. Faragallah, and M. A. Simaan, “Detecting of Aortic Valve Dynamics in Bridge-to-Recovery Feedback Control of the Left Ventricular Assist Device,” Proc. of the 13th European Control Conference, Strasbourg, France, June 24-27, 2014, pp. 140-145

 

Y. Wang, and  M.A. Simaan, “A New Method for Detecting Aortic Valve Dynamics during Control of the Rotary Left Ventricular Assist Device Support,” Proc. of the 2014 American Control Conference, Portland, OR, June 4-6, 2014, pp. 5483-5488

 

G. Faragallah and  M.A. Simaan, “An Engineering Analysis of the Aortic Valve Dynamics in Patients with Left Ventricular Assist Devices,” Journal of healthcare Engineering, Vol. 4, No. 3, September 2013, pp. 307-327

 

Y. Wang, and M. A. Simaan, “A Suction Detection System for Rotary Blood Pumps Based on Lagrangian Support Vector Machine Algorithm,” IEEE Journal of Biomedical and Health Informatics, Vol. 17, No. 3, May 2013, pp. 654-663

 

G. Faragallah, Y. Wang, E. Divo and M. A. Simaan, “A New Control System for Left Ventricular Assist Devices Based on Patient-Specific Physiological Demand,” Inverse problems in Science and Engineering, Taylor and Francis, Vol. 20, No. 5, July 2012, pp. 721-734

 

Y. Wang, G. Faragallah, E. Divo, and  M.A. Simaan, “Feedback Control of a Rotary Left Ventricular Assist Device Supporting a Failing Cardiovascular System,” Proc. of the 2012 American Control Conference, Montreal, Canada, June 27-29, 2012, pp. 1137-1142

 

M. A. Simaan, G. Faragallah and Y. Wang and E. Divo, “Left Ventricular Assist Devices: Engineering Design Considerations,” Chapter 2 in Guillermo Reyes, Editor, Ventricular Assist Device, Intech Publishers, 2011, pp. 21-42

 

G. Faragallah, E. Divo, and  M.A. Simaan, “A Feedback Controller Based on the Estimation of the Systemic Vascular Resistance of Left Ventricular Assist Devices Patients,” Abstracts of the 19th Congress of the International Society for Rotary Blood Pumps, Louiville, KY, September 8-10, 2011

 

G. Faragallah, Y. Wang, E. Divo, and  M.A. Simaan, “The Aortic Valve Dynamics Role in the Recovery Treatments of Patients with Left Ventricular Assist Devices,” Proc. of the 2011 IEEE Engineering in Medicine and Biology Conference, Boston, MA, USA on August 30 - September 3, 2011, pp. 1339-1342

 

Y. Wang, G. Faragallah, E. Divo, and  M.A. Simaan, “Detection of Ventricular Suction in an Implantable Rotary Blood Pumps Using Support Vector Machines” Proc. of the 2011 IEEE Engineering in Medicine and Biology Conference, Boston, MA, USA on August 30 - September 3, 2011, pp. 3318-3321

 

G. Faragallah, Y. Wang, E. Divo, and  M.A. Simaan, “A New Current-Based Control Model of the Combined cardiovascular and Rotary Left ventricular Assist Device,” Proc. of the 2011 American Control Conference, San Francisco, CA, June 29-July 1, 2011, pp. 4776-4780

 

G. Faragallah, Y. Wang, E. Divo, and M.A. Simaan, “Determination of the Optimal LVAD Pump Speed Range in Bridge to Recovery Treatment Abstracts of the 57th Annual Conference of the American Society for Artificial Internal Organs (ASAIO), Washington, DC, June 10-12, 2011. ASIAO Journal, Vol. 57, No. 2, March-April 2011, p. 97

 

Y. Wang, G. Faragallah, E. Divo, and M.A. Simaan, “Detection of Suction for Rotary Blood Pumps Using Support Vector Machines” Abstracts of the 57th Annual Conference of the American Society for Artificial Internal Organs (ASAIO), Washington, DC, June 10-12, 2011. ASIAO Journal, Vol. 57, No. 2, March-April 2011, p. 102

 

G. Faragallah, Y. Wang, E. Divo, and  M.A. Simaan, “A New Control System for Left Ventricular Assist Devices Based on the Psychological Demand of the Patient,” Proc. of the 7th International Conference on Inverse Problems in Engineering, Orlando, FL, May 4-6, 2011, pp. 250-255

 

I. Sahin, N. Yilmazer and M. A. Simaan, "A Method for Sub-Optimal Fetal Heart Rate Estimation Under Noisy Conditions," IEEE Transactions on Biomedical Engineering, Vol. 57, No. 4, April 2010, pp. 703-883.

 

M. A. Simaan, “Modeling and Control of Rotary Left Ventricular Assist Devices,” Handbook of Automation, Ed. S. Nof, Springer Verlag, 2009, pp. 1409-1422.

 

M. A. Simaan, A. Ferreira, S. Chen, J.F. Antaki, and D.G. Galati, “A Dynamical State Space Representation and Performance Analysis of a Feedback-Controlled Rotary Left Ventricular Assist Device,” IEEE Transactions on Control Systems Technology,  Vol. 17, No. 1, January 2009, pp. 15-28

 

M.A. Simaan, “Modeling and Control of the Heart Left Ventricle Supported with a Rotary Assist Device,” Proc. of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, December 9-12, 2008, pp. 2656-2661

 

M. A. Simaan and J. F. Antaki, Progress with Extremum-Seeking Feedback Controller for a Rotary Blood Pump” Abstracts of the 54th Conference of the American Society for Artificial Internal Organs (ASAIO), San Francisco, CA, June 19 - 21, 2008.

 

Y-C. Yu, M. A. Simaan, S. Mushi, and N.V. Zorn, “Performance Prediction Of A Percutaneous Ventricular Assist System Using Nonlinear Circuit Analysis Techniques,” IEEE Transactions on Biomedical Engineering, Vol. 55, No. 2, 2008, pp. 419-429

 

Y-C Yu, M. A. Simaan, N. V. Zorn, and S. Mushi, “A Nonlinear Model for Flow Estimation and Control in a Percutaneous Heart Assist System,” Proc. of the 2007 American Control Conference, New York, NY, July 11-13, 2007, pp. 2018-2023.

 

S. Chen, A. Ferreira, M.A. Simaan, J. R. Boston, and J. F. Antaki, “Feedback Control of an LVAD Supporting a Failing Cardiovascular System Regulated by the Baroreflex,” Proc. of the 45th IEEE Conference on Decision and Control, San Diego, CA, December 13-15, 2006, pp.655-660.

 

A. Ferreira, S. Chen, M.A. Simaan, J. R. Boston, and J. F. Antaki, “A Discriminant-Analysis-Based Suction Detection System for Rotary Blood Pumps”, Proc. of the 28th IEEE Annual International Conference of Engineering in Medicine and Biology , August 30 - September 3, 2006 in New York, NY, 2006, pp. 5382-5385

 

P.D. Wearden, V.O. Morell, B.B. Keller, S.A. Webber, H.S. Borovetz, S. F. Badylak, J.R. Boston, R.L. Kormos, M.V. Kameneva, M.A. Simaan, T.A. Snyder, H. Tsukui, W.R. Wagner, J.F. Antaki, C. Diao, S. Vandenberghe, J, Gardiner, C.M. Li, D. Noh, D. Paden, B. Paden, J. Wu, G.B. Bearnson, G. Jacobs, J. Kirk, P. Khanwilkar, J.W. Long, S. Miles, J.A. Hawkins, P.C. Kouretas, and R.E. Shaddy, “The PediaFlowTM Pediatric Ventricular Assist Device,” Seminars in Thoracic and Cardiovascular Surgery: Pediatric Cardiac Surgery Annual, Vol. 9, No. 1, 2006, pp. 92-98

 

S. Chen, A. Ferreira, M. A. Simaan, and J. F. Antaki, “A Mathematical Model of a Cardiovascular System Regulated by the Baroreflex,” Proc. of the 2006 American Control Conference, Minneapolis, MN, June 14-17, 2006, pp. 701-706.

 

H.S. Borovetz, S. Badylak, J.R. Boston, C. Johnson, R. Kormos, M.V. Kameneva, M. A. Simaan, T.A. Snyder, H. Tsukui, W. R. Wagner, J. Woolley, J. Antaki, C. Diao, S. Vandenberghe, B. Keller, V. Morell, P. Wearden, S. Webber, J. Gardiner, C.M. Li, D. Paden, B. Paden, S. Snyder, J. Wu, G. Bearnson, J.A. Hawkins, G. Jacobs, J. Kirk, P. Khanwilkar, P. C. Kouretas, J. Long, and R.E. Shaddy, "Towards the Development of a Pediatric Ventricular Assist Device," Cell Transplantation, Vol. 15, pp. S69-S74, 2006

 

A. Ferreira, M.  A. Simaan, J.R. Boston, and J. F. Antaki, “Frequency and Time-Frequency Based Indices for Suction Detection in Rotary Blood Pumps,” Proc. of the 2006 IEEE International  Conference on Acoustics Speech and Signal Processing, Toulouse, France, May 14-19, 2006, Vol. II, pp.1064-1067

 

K-W. Gwak, M. Ricci, S. Snyder, B.E. Paden, J.R. Boston, M. A. Simaan, and J.F. Antaki, "In Vitro Evaluation of Multiobjective Hemodynamic Control of a Heart-Assist Pump,” The American Society for Artificial Internal Organs(ASAIO) Journal, Vol. 51, No. 4, 2005, pp. 329-335.

 

A. Ferreira, M.  A. Simaan, J.R. Boston, and J. F. Antaki, “A Nonlinear State Space Model of a Combined Cardiovascular System and a Rotary Pump,” Proc. of the 44th IEEE Conference on Decision and Control and European Control Conference, Seville, Spain, Dec. 12-15, 2005, pp. 897-902

 

A. Ferreira, S. Chen, D.G. Galati, M.  A. Simaan, and J. F. Antaki, “A Dynamical State Space Representation of a Feedback Controlled Rotary Left Ventricular Assist Device,” Proc. of the 2005 ASME International Mechanical Engineering Congress, Orlando, FL, November 5-11, 2005, Paper IMECE2005-80973

 

Y-C Yu, M. A. Simaan, N. V. Zorn, and S. Mushi, “Model-based Prediction of a Percutaneous Ventricular Assist Device Performance,” Proc. of the 2005 American Control Conference, Portland, OR, June 8-10, 2005, pp. 3835-3840.

 

S. Chen, J. F. Antaki, M.  A. Simaan, and J. R. Boston, “Physiological Control of Left ventricular Assist Devices Based on Gradient of Flow,” Proc. of the 2005 American Control Conference, Portland, OR, June 8-10, 2005, pp. 3829-3834.

 

K-W Gwak, M. Ricci, S. Snyder, B. E. Paden, J. R. Boston, M. A. Simaan, and J.F. Antaki, “In-Vitro Evaluation of Multi-Objective Hemodynamic Control of a Heart-Assist Pump,” The American Society for Artificial Internal Organs (ASAIO) Journal, Vol. 51, No. 4, 2005, pp. 329-335.

 

J. Wu, J.F. Antaki, H.S. Borovetz, J. R. Boston, C. Diao, J.A. Hawkins, J. Gardiner, G. Jacobs, M.V. Kameneva, B.B. Keller, P. Khanwilkar, J. Kirk, R. L. Kormos, J. W. Long, C.M. Li, S. Miles, V. Morell, E. Prem, B.E. Paden, D. Paden, R. E. Shaddy, M. A. Simaan, T. A. Snyder, H. Tsukui, S. Vandeberghe, W. R. Wagner, and S. A. Webber, , “Progress with Pediaflow Maglev Pump for Infants and Small Childern: Form to Function,” Abstracts of the 51th Anniversary Conference of the American Society for Artificial Internal Organs, Washington, DC, June 7-9, 2005.

 

H. Borovetz, S. Badylak, J.R. Boston, R. Kormos, M. Kameneva, M. A. Simaan, T. Snyder, H. Tsukui, W. Wagner, J.F. Antaki, C. Diao, S. Vandeberghe, B. Keller, V. Morell, S. Weber, J. Gardiner, C.M. Li, D. Paden, B. Paden, J. Wu, G. Bearneson, J. Hawkins, G. Jacobs, J. Kirk, P. Khanwilkar, J. Long, S. Miles, and R. Shaddy, "The Pediatric ventricular Assist Device (Pediaflow)," Abstracts of the First International Conference on Pediatric Mechanical Circulatory Support Systems and Pediatric Cardiopulmonary Perfusion, Hershey, PA, May 19-22, 2005, p. 48

B. Uber, L.C. Santelices, B. Keller, S. Webber, V. Morell, R.L. Kormos, H.S. Borovetz, M.A. Simaan and J.F, Antaki, "Systematic Decision Support for Optimal Management of PVAD Patients”" Abstracts of the First International Conference on Pediatric Mechanical Circulatory Support Systems and Pediatric Cardiopulmonary Perfusion, Hershey, PA, May 19-22, 2005, p. 68

S. Mushi, Y-C. Yu, M. A Simaan, and N. V. Zorn, “Flow Rate Prediction of a Percutaneous Ventricular Assist Device using Nonlinear Circuit Analysis,” Proc. of the 31st Annual NorthEast BioEngineering Conference, Hoboken, NJ, April 2-3, 2005, pp. 61-62

 

K-W Gwak, M. Ricci, S. Snyder, B. E. Paden, J. R. Boston, M. A. Simaan, and J. F. Antaki, “In-Vitro Evaluation of Multi-Objective Hemodynamic Control of a Heart-Assist Pump,” Proc. of the 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas, Dec. 14-17, 2004, pp. 1069-1074.

 

M. Y. Tabaksblat, A. Z. Hunsberger, M. A. Simaan, R.L. Kormos, J. Gorcsan, S. G. Shroff, and J. F. Antaki, “Towards the Development of a Computer Simulator for Left Ventricular Recovery” Abstracts of the 50th Anniversary Conference of the American Society for Artificial Internal Organs, Washington, DC, June 17-19, 2004, ASIAO Journal, Vol. 50, No. 2, March-April 2004, p. 139.

 

L. C. Santelices, J. F. Antaki, M. A. Dew, M. B. Holm, M. A. Mathier, M. A. Simaan, K. Desai, and R. L. Kormos, “Mobile Decision Support System For Management of LVAD Patients” Abstracts of the 50th Anniversary Conference of the American Society for Artificial Internal Organs, Washington, DC, June 17-19, 2004, ASIAO Journal, Vol. 50, No. 2, March-April 2004, p. 121.

 

J. R. Boston, J. F. Antaki, and M. A. Simaan, "Hierarchical Control for Hearts Assist Devices," IEEE Robotics and Automation Magazine, Vol. 10, No.1, March 2003, pp. 54-64.

 

J. F. Antaki, J. R. Boston and M. A. Simaan, “Control of Heart Assist Devices,” Proc. of the IEEE Conference on Decision and Control, Maui, HI, December 9-12, 2003, pp. 4084-4089.

 

L. A. Baloa, J. R. Boston, M. A. Simaan, and J. F. Antaki, “Performance of an Extended Certainty Weighted Detection Model,” IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, Vol. 33, No. 1, January 2003, pp. 12-22.

 

Y-C. Yu and M. A. Simaan, “Performance Prediction of a Percutaneous Ventricular Assist System – A Nonlinear Circuit Analysis,” Proc. of the 28th Annual Northeast Bioengineering Conference, Philadelphia, PA, April 20-21, 2002, pp.19-20.

 

Y-C. Yu, J. R. Boston, M. A. Simaan, and J. F. Antaki, "Minimally Invasive Estimation of Systemic Vascular Parameters for Artificial Heart Control,” Control Engineering Practice, Vol. 10, March 2002, pp. 277-285.

 

L. Baloa, J. R. Boston, M. A. Simaan, and J. F. Antaki“A Certainty-Weighted Decision Model for the Detection of Suction in VADs,” Proc. of the IEEE Conference on Control Applications and International Symposium on Intelligent Control, Mexico City, Mexico, September 5-7, 2001, pp. 696-701.

 

J. F. Antaki, Z. Wu, D. Liu, M. A. Simaan, and J. R. Boston, “A Multi-Objective Control Algorithm for Turbodynamic Blood Pumps,” Abstracts of the 9th Congress of the International Society for Rotary Blood Pumps, Seattle, Washington, August 17-20, 2001, pp A6.

 

Y-C. Yu, J.R. Boston, M. A. Simaan, and J.F. Antaki, "Minimally Invasive Estimation of Systemic Vascular Parameters,” Annals of Biomedical Engineering, Vol. 29, No. 7, July 2001, pp. 595-606.

 

Y-C. Yu, J. R. Boston, M. A. Simaan, P. J. Miller, and J. F. Antaki, "Pressure-Volume Relationship of a Pulsatile Blood Pump for Ventricular Assist Device Development,” The American Society for Artificial Internal Organs Journal, Vol. 47, No. 3, May-June 2001, pp. 293-301

 

Y-C. Yu, J. R. Boston, M. A. Simaan, and J. F. Antaki, “Minimally Invasive Identification of Ventricular Recovery Index for Weaning Patients from Artificial Heart Support,” Proc. of the IEEE Conference on Decision and Control, Sydney, Australia, December 12-15, 2000, pp. 1799-1803.

 

D. Liu, J. R. Boston, M. A. Simaan, and J. F. Antaki“Multi-Objective Optimal Control of a Heart Assist Device,” Proc. of the IEEE Conference on Decision and Control, Sydney, Australia, December 12-15, 2000, 4857-4858.

 

J. R. Boston, J. F. Antaki, and M. Simaan, "Hierarchical Control for Artificial Hearts," Proc. of the IEEE International Conference on Bio-Informatics and Biomedical Engineering, Arlington, VA, November 8-10, 2000, pp. 376-383.

 

J. R. Boston, L. Baloa, Dehou Liu, M. A. Simaan, S. Choi, and J. F. Antaki“Combination of Data Approaches to Heuristic Control and Fault Detection,” Proc. of the IEEE Conference on Control Applications and International Symposium on Computer-Aided Control Systems Design, Anchorage, AK, September 25-27, 2000, pp. 98-103

 

Y-C. Yu, J. R. Boston, M. A. Simaan, P.J. Miller, and J.F. Antaki, "Modeling and Simulation of a Blood Pump for the Development of a Left Ventricular Assist System Controller,” Kybernetika , Vol. 35, No. 6, October 1999, pp. 651-664.

 

Y-C. Yu, J. R. Boston, M. A. Simaan, and J. F. Antaki, "Estimation of Systemic Vascular Bed Parameters for Artificial Heart Control," IEEE Transactions on Automatic Control, Vol. 43, No. 6, June 1998, pp. 765-778.