Biomedical Engineering 2012 Part 6 doc

The results are continuously compared with those obtained by Parker et al., 2000 where a linear model based robust control algorithm was used see section 1.5.. Although the first applica

techniques, such as spectral analysis; potentially initiating novel approaches for therapy

strategies Incorporating the progressive status of gait quality in a database could advance

the evaluation of therapy strategy efficacy

Database status tracking may be especially useful for a progressive neurodegenerative

disease, such as Parkinson’s disease The status of a Parkinson’s disease patient could be

monitored through wireless accelerometers over durations in excess of 24 hours Continual

monitoring could augment drug therapy dose allocation and efficacy assessment

Improvements in wireless transmission strength, such as conveying the accelerometer signal

to a wireless phone for subsequent transmission to a database, could provide significant

advances in application autonomy Similar to wireless accelerometers providing the basis

for biofeedback with virtual proprioception, wireless accelerometers could provide feedback

insight for deep brain stimulation parameter settings Wireless accelerometer feedback

could provide the basis for temporally optimal deep brain stimulation parameters with the

integration of multi-disciplinary design optimization algorithms

Wireless accelerometer systems for reflex quantification could advance the evaluation of

central and peripheral nervous system trauma The application has been developed with the

intent to alleviate the growing strain on medical resources Advances in machine learning

classification techniques may further augment the impact of the wireless accelerometer

reflex quantification system Future advances envision the integration of machine learning

and wireless accelerometer applications, such as reflex quantification for trauma and disease

status classification

Machine learning incorporates development of software programs, which improve with

experience at a specific task, such as the classification of a phenomenon Machine learning

has been envisioned for optimizing treatment efficacy for medical issues (Mitchell, 1997)

For example, machine learning algorithms have been applied for predicting pneumonia

attributed mortality of hospital patients (Cooper et al 1997) Machine learning intrinsically

utilizes multiple disciplines, such as artificial intelligence, neurobiology, and control theory

Speech recognition software can be derived from machine learning, while incorporating

learning methods such as neural networks (Mitchell, 1997)

Speech recognition has been successfully tested and evaluated in robust applications

Effectively speech recognition techniques incorporate analysis of acoustic waveforms

(Englund, 2004) Similar to the attributes of an acoustic waveform, human movement may

be recognized through the use of a wireless accelerometer representing artificial

proprioception to derive an acceleration waveform The testing and evaluation of activity

classification using the frequency domain of the acceleration waveform has been

demonstrated (Chung et al., 2008) Machine learning classification techniques in

consideration of the derived acceleration waveform may augment the status evaluation of

reflexes; Parkinson’s disease; and gait diagnostic and treatment methods Machine learning

applications respective of virtual proprioception may advance and optimize near

autonomous rehabilitation strategies

The concept of artificial proprioception utilizing wireless accelerometers emphasizes a invasive approach for acquiring movement status characteristics A machine learning algorithm with a tandem philosophy would be advantageous During 2003 at Carnegie Mellon University a machine learning software program called HiLoClient demonstrated the ability to ascertain classification status while incorporating non-invasive methods The HiLoClient software actually enabled researchers to detect, classify, and extrapolate the data statistically turning patterns into predictions from seemingly random generated data (Mastroianni, 2003)

non-Progress relevant to technology applications incorporating artificial proprioception will likely be augmented through tandem advances in the fields of the robotics industry and feedback control theory The field of robotics incorporates a hierarchical control architecture, generally consisting of high, intermediate, and low level control In general biological control systems and robotic control systems are representative of similar control system structures The hierarchical nature of human locomotion provides a relevant example, with the high level representing descending commands from the brain The central pattern generator may be applied to represent the intermediate level of control; and the lower level

of control could encompass proprioceptors, such as muscle spindles and Golgi tendon organs Respective of this control architecture, reflexes provide an important feedback control system (Bekey, 2005)

Progress in the fields of robotics and feedback control theory will likely advance biomedical applications of artificial proprioception, such as the characterization of reflexes and gait The tandem technology evolutions are envisioned to provide substantial improvement in prosthetic applications Alternative strategies and concepts incorporating robotics and feedback control theory should advance virtual proprioception biofeedback applications for augmented rehabilitation methods

8 References

Aiello, E.; Gates, D.; Patritti, B.; Cairns, K.; Meister, M.; Clancy, E & Bonato, P (2005) Visual

EMG biofeedback to improve ankle function in hemiparetic gait, Proc 27th Int

Conf IEEE EMBS, pp 7703-7706, Shanghai, China, Sep., 2005

Aminian, K.; Robert, P.; Buchser, E.; Rutschmann, B.; Hayoz, D & Depairon, M (1999)

Physical activity monitoring based on accelerometry: validation and comparison

with video observation Med Biol Eng Comput., Vol 37, No 3, (May, 1999) 304–308

Auvinet, B.; Berrut, G.; Touzard, C.; Moutel, L.; Collet, N.; Chaleil, D & Barrey, E (2002)

Reference data for normal subjects obtained with an accelerometric device Gait

Posture, Vol 16, No 2, (Oct., 2002) 124–134

Bamberg, S.; Benbasat, A.; Scarborough, D.; Krebs, D & Paradiso, J (2008) Gait analysis

using a shoe-integrated wireless sensor system IEEE Trans Inf Technol Biomed.,

Vol 12, No 4, (Jul., 2008) 413-423

Bekey, G (2005) Autonomous Robots: From Biological Inspiration to Implementation and Control,

MIT Press, Cambridge, MA

Bickley, L & Szilagyi, P (2003) Bates’ Guide to Physical Examination and History Taking, 8 th ed.,

Lippincott Williams and Wilkins, Philadelphia, PA

techniques, such as spectral analysis; potentially initiating novel approaches for therapy

strategies Incorporating the progressive status of gait quality in a database could advance

the evaluation of therapy strategy efficacy

Database status tracking may be especially useful for a progressive neurodegenerative

disease, such as Parkinson’s disease The status of a Parkinson’s disease patient could be

monitored through wireless accelerometers over durations in excess of 24 hours Continual

monitoring could augment drug therapy dose allocation and efficacy assessment

Improvements in wireless transmission strength, such as conveying the accelerometer signal

to a wireless phone for subsequent transmission to a database, could provide significant

advances in application autonomy Similar to wireless accelerometers providing the basis

for biofeedback with virtual proprioception, wireless accelerometers could provide feedback

insight for deep brain stimulation parameter settings Wireless accelerometer feedback

could provide the basis for temporally optimal deep brain stimulation parameters with the

integration of multi-disciplinary design optimization algorithms

Wireless accelerometer systems for reflex quantification could advance the evaluation of

central and peripheral nervous system trauma The application has been developed with the

intent to alleviate the growing strain on medical resources Advances in machine learning

classification techniques may further augment the impact of the wireless accelerometer

reflex quantification system Future advances envision the integration of machine learning

and wireless accelerometer applications, such as reflex quantification for trauma and disease

status classification

Machine learning incorporates development of software programs, which improve with

experience at a specific task, such as the classification of a phenomenon Machine learning

has been envisioned for optimizing treatment efficacy for medical issues (Mitchell, 1997)

For example, machine learning algorithms have been applied for predicting pneumonia

attributed mortality of hospital patients (Cooper et al 1997) Machine learning intrinsically

utilizes multiple disciplines, such as artificial intelligence, neurobiology, and control theory

Speech recognition software can be derived from machine learning, while incorporating

learning methods such as neural networks (Mitchell, 1997)

Speech recognition has been successfully tested and evaluated in robust applications

Effectively speech recognition techniques incorporate analysis of acoustic waveforms

(Englund, 2004) Similar to the attributes of an acoustic waveform, human movement may

be recognized through the use of a wireless accelerometer representing artificial

proprioception to derive an acceleration waveform The testing and evaluation of activity

classification using the frequency domain of the acceleration waveform has been

demonstrated (Chung et al., 2008) Machine learning classification techniques in

consideration of the derived acceleration waveform may augment the status evaluation of

reflexes; Parkinson’s disease; and gait diagnostic and treatment methods Machine learning

applications respective of virtual proprioception may advance and optimize near

autonomous rehabilitation strategies

The concept of artificial proprioception utilizing wireless accelerometers emphasizes a invasive approach for acquiring movement status characteristics A machine learning algorithm with a tandem philosophy would be advantageous During 2003 at Carnegie Mellon University a machine learning software program called HiLoClient demonstrated the ability to ascertain classification status while incorporating non-invasive methods The HiLoClient software actually enabled researchers to detect, classify, and extrapolate the data statistically turning patterns into predictions from seemingly random generated data (Mastroianni, 2003)

non-Progress relevant to technology applications incorporating artificial proprioception will likely be augmented through tandem advances in the fields of the robotics industry and feedback control theory The field of robotics incorporates a hierarchical control architecture, generally consisting of high, intermediate, and low level control In general biological control systems and robotic control systems are representative of similar control system structures The hierarchical nature of human locomotion provides a relevant example, with the high level representing descending commands from the brain The central pattern generator may be applied to represent the intermediate level of control; and the lower level

of control could encompass proprioceptors, such as muscle spindles and Golgi tendon organs Respective of this control architecture, reflexes provide an important feedback control system (Bekey, 2005)

Progress in the fields of robotics and feedback control theory will likely advance biomedical applications of artificial proprioception, such as the characterization of reflexes and gait The tandem technology evolutions are envisioned to provide substantial improvement in prosthetic applications Alternative strategies and concepts incorporating robotics and feedback control theory should advance virtual proprioception biofeedback applications for augmented rehabilitation methods

8 References

Aiello, E.; Gates, D.; Patritti, B.; Cairns, K.; Meister, M.; Clancy, E & Bonato, P (2005) Visual

EMG biofeedback to improve ankle function in hemiparetic gait, Proc 27th Int

Conf IEEE EMBS, pp 7703-7706, Shanghai, China, Sep., 2005

Aminian, K.; Robert, P.; Buchser, E.; Rutschmann, B.; Hayoz, D & Depairon, M (1999)

Physical activity monitoring based on accelerometry: validation and comparison

with video observation Med Biol Eng Comput., Vol 37, No 3, (May, 1999) 304–308

Auvinet, B.; Berrut, G.; Touzard, C.; Moutel, L.; Collet, N.; Chaleil, D & Barrey, E (2002)

Reference data for normal subjects obtained with an accelerometric device Gait

Posture, Vol 16, No 2, (Oct., 2002) 124–134

Bamberg, S.; Benbasat, A.; Scarborough, D.; Krebs, D & Paradiso, J (2008) Gait analysis

using a shoe-integrated wireless sensor system IEEE Trans Inf Technol Biomed.,

Vol 12, No 4, (Jul., 2008) 413-423

Bekey, G (2005) Autonomous Robots: From Biological Inspiration to Implementation and Control,

MIT Press, Cambridge, MA

Bickley, L & Szilagyi, P (2003) Bates’ Guide to Physical Examination and History Taking, 8 th ed.,

Lippincott Williams and Wilkins, Philadelphia, PA

Bouten, C.; Koekkoek, K.; Verduin, M.; Kodde, R & Janssen, J (1997) A triaxial

accelerometer and portable data processing unit for the assessment of daily

physical activity IEEE Trans Biomed Eng., Vol 44, No 3, (Mar., 1997) 136–147

Busser, H.; Ott, J.; van Lummel, R.; Uiterwaal, M & Blank, R (1997) Ambulatory

monitoring of children’s activities Med Eng Phys., Vol 19, No 5, (Jul., 1997) 440–

445

Chung, W.; Purwar, A & Sharma, A (2008) Frequency domain approach for activity

classification using accelerometer, Proc 30th Int Conf IEEE EMBS, pp 1120-1123,

Vancouver, Canada, Aug., 2008

Clark, M.; Lucett, S & Corn, R (2008) NASM Essentials of Personal Fitness Training, 3 rd ed.,

Lippincott Williams and Wilkins, Philadelphia, PA

Cocito, D.; Tavella, A.; Ciaramitaro, P.; Costa, P.; Poglio, F ; Paolasso, I.; Duranda, E.; Cossa,

F & Bergamasco, B (2006) A further critical evaluation of requests for

electrodiagnostic examinations Neurol Sci., Vol 26, No 6, (Feb., 2006) 419–422

Cooper, G.; Aliferis, C.; Ambrosino, R.; Aronis, J.; Buchanan, B.; Caruana, R.; Fine, M.;

Glymour, C.; Gordon, G.; Hanusa, B.; Janosky, J.; Meek, C.; Mitchell, T.;

Richardson, T & Spirtes, P (1997) An evaluation of machine-learning methods for

predicting pneumonia mortality Artif Intell Med., Vol 9, No 2, (Feb., 1997) 107-138

Cozens, J.; Miller, S.; Chambers, I & Mendelow, A (2000) Monitoring of head injury by

myotatic reflex evaluation J Neurol Neurosurg Psychiatry, Vol 68, No 5, (May,

2000) 581-588

Culhane, K.; O’Connor, M.; Lyons, D & Lyons, G (2005) Accelerometers in rehabilitation

medicine for older adults Age Ageing, Vol 34, No 6, (Nov., 2005), 556–560

Dietz, V (2002) Proprioception and locomotor disorders Nat Rev Neurosci., Vol 3, No 10,

(Oct., 2002) 781-790

Dobkin, B (2003) The Clinical Science of Neurologic Rehabilitation, 2nd ed., Oxford University

Press, New York

Englund, C (2004) Speech recognition in the JAS 39 Gripen aircraft - adaptation to speech at

different G-loads, Royal Institute of Technology, Master Thesis in Speech

Technology, Stockholm, Sweden, Mar., 2004

Fahrenberg, J.; Foerster, F.; Smeja, M & Muller, W (1997) Assessment of posture and

motion by multichannel piezoresistive accelerometer recordings Psychophysiology,

Vol 34, No 5, (Sep., 1997) 607–612

Faist, M.; Ertel, M.; Berger, W & Dietz, V (1999) Impaired modulation of quadriceps

tendon jerk reflex during spastic gait: differences between spinal and cerebral

lesions Brain, Vol 122, No 3, (Mar., 1999) 567–579

Frijns, C.; Laman, D.; van Duijn, M & van Duijn, H (1997) Normal values of patellar and

ankle tendon reflex latencies Clin Neurol Neurosurg., Vol 99 No 1, (Feb., 1997) 31-36

Gurevich, T.; Shabtai, H.; Korczyn, A.; Simon, E & Giladi, N (2006) Effect of rivastigmine

on tremor in patients with Parkinson’s disease and dementia Mov Disord., Vol 21,

No 10, (Oct., 2006) 1663–1666

Hoos, M.; Kuipers, H.; Gerver, W & Westerterp, K (2004) Physical activity pattern of

children assessed by triaxial accelerometry Eur J Clin Nutr., Vol 58, No 10, (Oct.,

2004) 1425–1428

Huang, H.; Wolf, S & He, J (2006) Recent developments in biofeedback for neuromotor

rehabilitation J Neuroeng Rehabil., Vol 3, No 11, (Jun., 2006) 1-12

Jafari, R.; Encarnacao, A.; Zahoory, A.; Dabiri, F.; Noshadi, H & Sarrafzadeh, M (2005)

Wireless sensor networks for health monitoring, Proc 2nd ACM/IEEE Int Conf on

Mobile and Ubiquitous Systems (MobiQuitous), pp 479–481, San Diego, CA, Jul., 2005

Kamen, G & Koceja, D (1989) Contralateral influences on patellar tendon reflexes in young

and old adults Neurobiol Aging, Vol 10, No 4, (Jul.-Aug., 1989) 311-315 Kandel, E.; Schwartz, J & Jessell, T (2000) Principles of Neural Science, 4 th ed., McGraw-Hill,

New York Kavanagh, J.; Barrett, R & Morrison, S (2004) Upper body accelerations during walking in

healthy young and elderly men Gait Posture, Vol 20, No 3, (Dec., 2004) 291–298

Kavanagh, J.; Morrison, S.; James, D & Barrett, R (2006) Reliability of segmental

accelerations measured using a new wireless gait analysis system J Biomech., Vol

39, No 15, (2006) 2863–2872 Keijsers, N.; Horstink, M.; van Hilten, J.; Hoff, J & Gielen, C (2000) Detection and

assessment of the severity of Levodopa-induced dyskinesia in patients with

Parkinson’s disease by neural networks Mov Disord., Vol 15, No 6, (Nov., 2000)

1104–1111 Keijsers, N.; Horstink, M & Gielen, S (2006) Ambulatory motor assessment in Parkinson’s

disease Mov Disord., Vol 21, No 1, (Jan., 2006) 34–44

Koceja, D & Kamen, G (1988) Conditioned patellar tendon reflexes in sprint- and

endurance-trained athletes Med Sci Sports Exerc., Vol 20, No 2, (Apr., 1988)

172-177 Kumru, H.; Summerfield, C.; Valldeoriola, F & Valls-Solé, J (2004) Effects of subthalamic

nucleus stimulation on characteristics of EMG activity underlying reaction time in

Parkinson’s disease Mov Disord., Vol 19, No 1, (Jan., 2004) 94–100

Lebiedowska, M & Fisk, J (2003) Quantitative evaluation of reflex and voluntary activity in

children with spasticity Arch Phys Med Rehabil., Vol 84, No 6, (Jun., 2003) 828-837

Lee, J.; Cho, S.; Lee, J.; Lee, K & Yang, H (2007) Wearable accelerometer system for

measuring the temporal parameters of gait, Proc 29th Int Conf IEEE EMBS, pp

483-486, Lyon, France, Aug., 2007 LeMoyne, R (2005a) UCLA communication, UCLA, NeuroEngineering, Jun., 2005aLeMoyne, R.; Jafari, R & Jea, D (2005b) Fully quantified evaluation of myotatic stretch

reflex, 35th Society for Neuroscience Annual Meeting, Washington, D.C., Nov., 2005b LeMoyne, R & Jafari, R (2006a) Quantified deep tendon reflex device, 36th Society for

Neuroscience Annual Meeting, Atlanta, GA, Oct., 2006a

LeMoyne, R & Jafari, R (2006b) Quantified deep tendon reflex device, second generation,

15th International Conference on Mechanics in Medicine and Biology, Singapore, Dec.,

2006b

LeMoyne, R (2007a) Gradient optimized neuromodulation for Parkinson’s disease, 12th

Annual Research Conference on Aging (UCLA Center on Aging), Los Angeles, CA, Jun.,

2007a LeMoyne, R.; Dabiri, F.; Coroian, C.; Mastroianni, T & Grundfest, W (2007b) Quantified

deep tendon reflex device for assessing response and latency, 37th Society for

Neuroscience Annual Meeting, San Diego, CA, Nov., 2007b

LeMoyne, R.; Dabiri, F & Jafari, R (2008a) Quantified deep tendon reflex device, second

generation J Mech Med Biol., Vol 8, No 1, (Mar., 2008a) 75-85

Bouten, C.; Koekkoek, K.; Verduin, M.; Kodde, R & Janssen, J (1997) A triaxial

accelerometer and portable data processing unit for the assessment of daily

physical activity IEEE Trans Biomed Eng., Vol 44, No 3, (Mar., 1997) 136–147

Busser, H.; Ott, J.; van Lummel, R.; Uiterwaal, M & Blank, R (1997) Ambulatory

monitoring of children’s activities Med Eng Phys., Vol 19, No 5, (Jul., 1997) 440–

445

Chung, W.; Purwar, A & Sharma, A (2008) Frequency domain approach for activity

classification using accelerometer, Proc 30th Int Conf IEEE EMBS, pp 1120-1123,

Vancouver, Canada, Aug., 2008

Clark, M.; Lucett, S & Corn, R (2008) NASM Essentials of Personal Fitness Training, 3 rd ed.,

Lippincott Williams and Wilkins, Philadelphia, PA

Cocito, D.; Tavella, A.; Ciaramitaro, P.; Costa, P.; Poglio, F ; Paolasso, I.; Duranda, E.; Cossa,

F & Bergamasco, B (2006) A further critical evaluation of requests for

electrodiagnostic examinations Neurol Sci., Vol 26, No 6, (Feb., 2006) 419–422

Cooper, G.; Aliferis, C.; Ambrosino, R.; Aronis, J.; Buchanan, B.; Caruana, R.; Fine, M.;

Glymour, C.; Gordon, G.; Hanusa, B.; Janosky, J.; Meek, C.; Mitchell, T.;

Richardson, T & Spirtes, P (1997) An evaluation of machine-learning methods for

predicting pneumonia mortality Artif Intell Med., Vol 9, No 2, (Feb., 1997) 107-138

Cozens, J.; Miller, S.; Chambers, I & Mendelow, A (2000) Monitoring of head injury by

myotatic reflex evaluation J Neurol Neurosurg Psychiatry, Vol 68, No 5, (May,

2000) 581-588

Culhane, K.; O’Connor, M.; Lyons, D & Lyons, G (2005) Accelerometers in rehabilitation

medicine for older adults Age Ageing, Vol 34, No 6, (Nov., 2005), 556–560

Dietz, V (2002) Proprioception and locomotor disorders Nat Rev Neurosci., Vol 3, No 10,

(Oct., 2002) 781-790

Dobkin, B (2003) The Clinical Science of Neurologic Rehabilitation, 2nd ed., Oxford University

Press, New York

Englund, C (2004) Speech recognition in the JAS 39 Gripen aircraft - adaptation to speech at

different G-loads, Royal Institute of Technology, Master Thesis in Speech

Technology, Stockholm, Sweden, Mar., 2004

Fahrenberg, J.; Foerster, F.; Smeja, M & Muller, W (1997) Assessment of posture and

motion by multichannel piezoresistive accelerometer recordings Psychophysiology,

Vol 34, No 5, (Sep., 1997) 607–612

Faist, M.; Ertel, M.; Berger, W & Dietz, V (1999) Impaired modulation of quadriceps

tendon jerk reflex during spastic gait: differences between spinal and cerebral

lesions Brain, Vol 122, No 3, (Mar., 1999) 567–579

Frijns, C.; Laman, D.; van Duijn, M & van Duijn, H (1997) Normal values of patellar and

ankle tendon reflex latencies Clin Neurol Neurosurg., Vol 99 No 1, (Feb., 1997) 31-36

Gurevich, T.; Shabtai, H.; Korczyn, A.; Simon, E & Giladi, N (2006) Effect of rivastigmine

on tremor in patients with Parkinson’s disease and dementia Mov Disord., Vol 21,

No 10, (Oct., 2006) 1663–1666

Hoos, M.; Kuipers, H.; Gerver, W & Westerterp, K (2004) Physical activity pattern of

children assessed by triaxial accelerometry Eur J Clin Nutr., Vol 58, No 10, (Oct.,

2004) 1425–1428

Huang, H.; Wolf, S & He, J (2006) Recent developments in biofeedback for neuromotor

rehabilitation J Neuroeng Rehabil., Vol 3, No 11, (Jun., 2006) 1-12

Jafari, R.; Encarnacao, A.; Zahoory, A.; Dabiri, F.; Noshadi, H & Sarrafzadeh, M (2005)

Wireless sensor networks for health monitoring, Proc 2nd ACM/IEEE Int Conf on

Mobile and Ubiquitous Systems (MobiQuitous), pp 479–481, San Diego, CA, Jul., 2005

Kamen, G & Koceja, D (1989) Contralateral influences on patellar tendon reflexes in young

and old adults Neurobiol Aging, Vol 10, No 4, (Jul.-Aug., 1989) 311-315 Kandel, E.; Schwartz, J & Jessell, T (2000) Principles of Neural Science, 4 th ed., McGraw-Hill,

New York Kavanagh, J.; Barrett, R & Morrison, S (2004) Upper body accelerations during walking in

healthy young and elderly men Gait Posture, Vol 20, No 3, (Dec., 2004) 291–298

Kavanagh, J.; Morrison, S.; James, D & Barrett, R (2006) Reliability of segmental

accelerations measured using a new wireless gait analysis system J Biomech., Vol

39, No 15, (2006) 2863–2872 Keijsers, N.; Horstink, M.; van Hilten, J.; Hoff, J & Gielen, C (2000) Detection and

assessment of the severity of Levodopa-induced dyskinesia in patients with

Parkinson’s disease by neural networks Mov Disord., Vol 15, No 6, (Nov., 2000)

1104–1111 Keijsers, N.; Horstink, M & Gielen, S (2006) Ambulatory motor assessment in Parkinson’s

disease Mov Disord., Vol 21, No 1, (Jan., 2006) 34–44

Koceja, D & Kamen, G (1988) Conditioned patellar tendon reflexes in sprint- and

endurance-trained athletes Med Sci Sports Exerc., Vol 20, No 2, (Apr., 1988)

172-177 Kumru, H.; Summerfield, C.; Valldeoriola, F & Valls-Solé, J (2004) Effects of subthalamic

nucleus stimulation on characteristics of EMG activity underlying reaction time in

Parkinson’s disease Mov Disord., Vol 19, No 1, (Jan., 2004) 94–100

Lebiedowska, M & Fisk, J (2003) Quantitative evaluation of reflex and voluntary activity in

children with spasticity Arch Phys Med Rehabil., Vol 84, No 6, (Jun., 2003) 828-837

Lee, J.; Cho, S.; Lee, J.; Lee, K & Yang, H (2007) Wearable accelerometer system for

measuring the temporal parameters of gait, Proc 29th Int Conf IEEE EMBS, pp

483-486, Lyon, France, Aug., 2007 LeMoyne, R (2005a) UCLA communication, UCLA, NeuroEngineering, Jun., 2005aLeMoyne, R.; Jafari, R & Jea, D (2005b) Fully quantified evaluation of myotatic stretch

reflex, 35th Society for Neuroscience Annual Meeting, Washington, D.C., Nov., 2005b LeMoyne, R & Jafari, R (2006a) Quantified deep tendon reflex device, 36th Society for

Neuroscience Annual Meeting, Atlanta, GA, Oct., 2006a

LeMoyne, R & Jafari, R (2006b) Quantified deep tendon reflex device, second generation,

15th International Conference on Mechanics in Medicine and Biology, Singapore, Dec.,

2006b

LeMoyne, R (2007a) Gradient optimized neuromodulation for Parkinson’s disease, 12th

Annual Research Conference on Aging (UCLA Center on Aging), Los Angeles, CA, Jun.,

2007a LeMoyne, R.; Dabiri, F.; Coroian, C.; Mastroianni, T & Grundfest, W (2007b) Quantified

deep tendon reflex device for assessing response and latency, 37th Society for

Neuroscience Annual Meeting, San Diego, CA, Nov., 2007b

LeMoyne, R.; Dabiri, F & Jafari, R (2008a) Quantified deep tendon reflex device, second

generation J Mech Med Biol., Vol 8, No 1, (Mar., 2008a) 75-85

LeMoyne, R.; Coroian, C & Mastroianni, T (2008b) 3D wireless accelerometer

characterization of Parkinson’s disease status, Plasticity and Repair in

Neurodegenerative Disorders, Lake Arrowhead, CA, May, 2008b

LeMoyne, R.; Coroian, C.; Mastroianni, T & Grundfest, W (2008c) Accelerometers for

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LeMoyne, R.; Coroian, C & Mastroianni, T (2008d) Virtual proprioception using Riemann

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Pittsburgh, PA, Jul., 2008d

LeMoyne, R.; Coroian, C.; Mastroianni, T.; Wu, W.; Grundfest, W & Kaiser, W (2008e)

Virtual proprioception with real-time step detection and processing, Proc 30th Int

Conf IEEE EMBS, pp 4238-4241, Vancouver, Canada, Aug., 2008e

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Mech Med Biol., Vol 8, No 3, (Sep., 2008f) 317–338

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reflex device for evaluating response and latency using an artificial reflex device,

38th Society for Neuroscience Annual Meeting, Washington, D.C., Nov., 2008g

LeMoyne, R.; Coroian, C.; Mastroianni, T & Grundfest, W (2008h) Quantified deep tendon

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No 4, (Dec., 2008h) 491–506

LeMoyne, R.; Coroian, C & Mastroianni, T (2009a) Quantification of Parkinson’s disease

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LeMoyne, R.; Coroian, C & Mastroianni, T (2009b) Wireless accelerometer system for

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Engineering (CME2009), pp 1-4, Tempe, AZ, Apr., 2009b

LeMoyne, R.; Coroian, C & Mastroianni, T (2009c) Evaluation of a wireless three

dimensional MEMS accelerometer reflex quantification device using an artificial

reflex system, Proc IEEE/ICME International Conference on Complex Medical

Engineering (CME2009), pp 1-5, Tempe, AZ, Apr., 2009c

LeMoyne, R.; Coroian, C.; Mastroianni, T & Grundfest, W (2009d) Wireless accelerometer

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Robust and Optimal Blood-Glucose Control in Diabetes Using Linear Parameter Varying paradigms

Levente Kovács and Balázs Kulcsár

X

Robust and Optimal Blood-Glucose Control

in Diabetes Using Linear Parameter

Varying paradigms

Levente Kovács* and Balázs Kulcsár**

*Dept of Control Engineering and Information Technology, Budapest University of Technology and Economics, Hungary

**Delft Centre for Systems and Control Delft University of Technology, Netherlands

1 Introduction

The normal blood glucose concentration level in the human body varies in a narrow range

(70 - 110 ml/dL) If for some reasons the human body is unable to control the normal

glucose-insulin interaction (e.g the glucose concentration level is constantly out of the above

mentioned range), diabetes is diagnosed The phenomena can be explained by several

causes, most important ones are stress, obesity, malnutrition and lack of exercise

The consequences of diabetes are mostly long-term; among others, diabetes increases the

risk of cardiovascular diseases, neuropathy and retinopathy (Fonyo & Ligeti, 2008)

Consequently, diabetes mellitus is a serious metabolic disease, which should be artificially

regulated This metabolic disorder was lethal until 1921 when Frederick G Banting and

Charles B Best discovered the insulin Nowadays the life quality of diabetic patients can be

enhanced though the disease is still lifelong

The newest statistics of the World Health Organization (WHO) predate an increase of adult

diabetes population from 4% (in 2000, meaning 171 million people) to 5,4% (366 million

worldwide) by the year 2030 (Wild et al., 2004) This warns that diabetes could be the

“disease of the future”, especially in the developing countries (due to stress and unhealthy

lifestyle)

Type I (also known as insulin dependent diabetes mellitus (IDDM)) is one of the four

classified types of this disease (Type II, gestational diabetes and other types, like genetic

deflections are the other three categories of diabetes), and is characterized by complete

pancreatic β-cell insufficiency (Fonyo & Ligeti, 2008) As a result, the only treatment of Type

I diabetic patients is based on insulin injection (subcutaneous or intravenous), usually

administered in an open-loop manner

Due to the alarming facts of diabetes, the scientific community proposed to improve the

treatment of diabetes by investigating the applicability of an external controller In many

biomedical systems, external controller provides the necessary input, because the human

body could not ensure it The outer control might be partially or fully automated The

self-11

regulation has several strict requirements, but once it has been designed it permits not only

to facilitate the patient’s life suffering from the disease, but also to optimize (if necessary)

the amount of the used dosage

However, blood-glucose control is one of the most difficult control problems to be solved in

biomedical engineering One of the main reasons is that patients are extremely diverse in

their dynamics and in addition their characteristics are time varying Due to the inexistence

of an outer control loop, replacing the partially or totally deficient blood-glucose-control

system of the human body, patients are regulating their glucose level manually Based on

the measured glucose levels (obtained from extracted blood samples), they often decide on

their own what is the necessary insulin dosage to be injected Although this process is

supervised by doctors (diabetologists), mishandled situations often appear Hyper-

(deviation over the basal glucose level) and hypoglycaemia (deviation under the basal

glucose level) are both dangerous cases, but on short term the latter is more dangerous,

leading for example to coma

Starting from the 1960s lot of researchers have investigated the problem of the

glucose-insulin interaction and control The closed-loop glucose regulation, as it was several times

formulated (Parker et al., 2000), (Hernjak & Doyle, 2005), (Ruiz-Velazques et al., 2004),

requires three components:

 glucose sensor;

 insulin pump;

 a control algorithm, which based on the glucose measurements, is able to

determine the necessary insulin dosage

1.1 Modelling diabetes mellitus

To design an appropriate control, an adequate model is necessary The mathematical model

of a biological system, developed to investigate the physiological process underling a

recorded response, always requires a trade off between the mathematical and the

physiological guided choices In the last decades several models appeared for Type I

diabetes patients (Chee & Tyrone, 2007)

The mostly used and also the simplest one proved to be the minimal model of Bergman

(Bergman et al., 1979) for Type I diabetes patients under intensive care, and its extension, the

three-state minimal model (Bergman et al., 1981)

However, the simplicity of the model proved to be its disadvantage too, as it is very

sensitive to parameters variance, the plasma insulin concentration must be known as a

function of time and in its formulation a lot of components of the glucose-insulin interaction

were neglected Therefore, extensions of this minimal model have been proposed (Hipszer,

2001), (Dalla Man et al., 2002), (Benett & Gourley, 2003), (Lin et al., 2004), (Fernandez et al.,

2004), (Morris et al., 2004), (de Gaetano & Arino, 2000), (Chbat & Roy, 2005), (Van Herpe et

al., 2006) trying to capture the changes in patient dynamics of the glucose-insulin

interaction, particularly with respect to insulin sensitivity or the time delay between the

injection and absorption Other approximations proposed extensions based on the meal

composition (Roy & Parker, 2006a), (Roy & Parker, 2006b), (Dalla Man et al., 2006a) , (Dalla

Man et al., 2006b)

Beside the Bergman-model other more general, but more complicated models appeared in

the literature (Cobelli et al., 1982), (Sorensen, 1985), (Tomaseth et al., 1996), (Hovorka et al.,

2002), (Fabietti et al., 2006)

1.2 The Sorensen-model

The most complex diabetic model proved to be the 19th order Sorensen-model (Sorensen, 1985) (the current work focuses on a modification of it, developed by (Parker et al., 2000)), which is based on the earlier model of (Guyton et al., 1978) Even if the Sorensen-model describes in a very exact way the human blood glucose dynamics, due to its complexity it was rarely used in research problems

The model was created with a great simplification: glucose and insulin subsystems are disconnected in the basal post absorptive state, which can be fulfilled with no pancreatic insulin secretion Nomenclature and equations can be found in the Appendix of the current book chapter

The Sorensen-model can be divided in six compartments (brain, heart and lungs, liver, gut, kidney, periphery), and its compartmental representation is illustrated by Fig 1

Fig 1 Compartmental representation of the Sorensen model (Parker et al., 2000)

Transportation is realized with blood circulation assuming that glucose and insulin concentrations of the blood flow leaving the compartment are equal to the concentrations of the compartment The compartments can be divided into capillary and tissue subcompartments, since glucose and insulin from the blood flow entering the compartment are either utilized or transported by diffusion In compartments with small time constant or with no absorption the division into subcompartments is unnecessary

1.3 Control of diabetes mellitus

Regarding the applied control strategies for diabetes mellitus, the palette is very wide (Parker et al., 2001)

Starting from classical control strategies (PID control (Chee et al., 2003), cascade control (Ortis-Vargas & Puebla, 2006)), to soft-computing techniques (fuzzy methods (Ibbini, 2006), neural networks (Mougiakakou et al., 2006), neuro-fuzzy methods (Dazzi et al., 2001)), adaptive (Lin et al., 2004), model predictive (MPC) (Hernjak & Doyle, 2005), (Hovorka et al.,

regulation has several strict requirements, but once it has been designed it permits not only

to facilitate the patient’s life suffering from the disease, but also to optimize (if necessary)

the amount of the used dosage

However, blood-glucose control is one of the most difficult control problems to be solved in

biomedical engineering One of the main reasons is that patients are extremely diverse in

their dynamics and in addition their characteristics are time varying Due to the inexistence

of an outer control loop, replacing the partially or totally deficient blood-glucose-control

system of the human body, patients are regulating their glucose level manually Based on

the measured glucose levels (obtained from extracted blood samples), they often decide on

their own what is the necessary insulin dosage to be injected Although this process is

supervised by doctors (diabetologists), mishandled situations often appear Hyper-

(deviation over the basal glucose level) and hypoglycaemia (deviation under the basal

glucose level) are both dangerous cases, but on short term the latter is more dangerous,

leading for example to coma

Starting from the 1960s lot of researchers have investigated the problem of the

glucose-insulin interaction and control The closed-loop glucose regulation, as it was several times

formulated (Parker et al., 2000), (Hernjak & Doyle, 2005), (Ruiz-Velazques et al., 2004),

requires three components:

 glucose sensor;

 insulin pump;

 a control algorithm, which based on the glucose measurements, is able to

determine the necessary insulin dosage

1.1 Modelling diabetes mellitus

To design an appropriate control, an adequate model is necessary The mathematical model

of a biological system, developed to investigate the physiological process underling a

recorded response, always requires a trade off between the mathematical and the

physiological guided choices In the last decades several models appeared for Type I

diabetes patients (Chee & Tyrone, 2007)

The mostly used and also the simplest one proved to be the minimal model of Bergman

(Bergman et al., 1979) for Type I diabetes patients under intensive care, and its extension, the

three-state minimal model (Bergman et al., 1981)

However, the simplicity of the model proved to be its disadvantage too, as it is very

sensitive to parameters variance, the plasma insulin concentration must be known as a

function of time and in its formulation a lot of components of the glucose-insulin interaction

were neglected Therefore, extensions of this minimal model have been proposed (Hipszer,

2001), (Dalla Man et al., 2002), (Benett & Gourley, 2003), (Lin et al., 2004), (Fernandez et al.,

2004), (Morris et al., 2004), (de Gaetano & Arino, 2000), (Chbat & Roy, 2005), (Van Herpe et

al., 2006) trying to capture the changes in patient dynamics of the glucose-insulin

interaction, particularly with respect to insulin sensitivity or the time delay between the

injection and absorption Other approximations proposed extensions based on the meal

composition (Roy & Parker, 2006a), (Roy & Parker, 2006b), (Dalla Man et al., 2006a) , (Dalla

Man et al., 2006b)

Beside the Bergman-model other more general, but more complicated models appeared in

the literature (Cobelli et al., 1982), (Sorensen, 1985), (Tomaseth et al., 1996), (Hovorka et al.,

2002), (Fabietti et al., 2006)

1.2 The Sorensen-model

The most complex diabetic model proved to be the 19th order Sorensen-model (Sorensen, 1985) (the current work focuses on a modification of it, developed by (Parker et al., 2000)), which is based on the earlier model of (Guyton et al., 1978) Even if the Sorensen-model describes in a very exact way the human blood glucose dynamics, due to its complexity it was rarely used in research problems

The model was created with a great simplification: glucose and insulin subsystems are disconnected in the basal post absorptive state, which can be fulfilled with no pancreatic insulin secretion Nomenclature and equations can be found in the Appendix of the current book chapter

The Sorensen-model can be divided in six compartments (brain, heart and lungs, liver, gut, kidney, periphery), and its compartmental representation is illustrated by Fig 1

Fig 1 Compartmental representation of the Sorensen model (Parker et al., 2000)

Transportation is realized with blood circulation assuming that glucose and insulin concentrations of the blood flow leaving the compartment are equal to the concentrations of the compartment The compartments can be divided into capillary and tissue subcompartments, since glucose and insulin from the blood flow entering the compartment are either utilized or transported by diffusion In compartments with small time constant or with no absorption the division into subcompartments is unnecessary

1.3 Control of diabetes mellitus

Regarding the applied control strategies for diabetes mellitus, the palette is very wide (Parker et al., 2001)

Starting from classical control strategies (PID control (Chee et al., 2003), cascade control (Ortis-Vargas & Puebla, 2006)), to soft-computing techniques (fuzzy methods (Ibbini, 2006), neural networks (Mougiakakou et al., 2006), neuro-fuzzy methods (Dazzi et al., 2001)), adaptive (Lin et al., 2004), model predictive (MPC) (Hernjak & Doyle, 2005), (Hovorka et al.,

2004), or even robust H∞ control were already applied (Parker et al., 2000), (Ruiz-Velazques

et al., 2004), (Kovacs et al., 2006), (Kovacs & Palancz, 2007), (Kovacs et al., 2008)

Most of the applied control methods were focused on the Bergman minimal model (and so

the applicability of the designed controllers was limited due to excessive sensitivity of the

model parameters) On the other hand, for the Sorensen-model, only linear control methods

were applied (H∞ (Parker et al., 2000), (Ruiz-Velazques et al., 2004), MPC (Parker et al.,

1999)) An acceptable compromise between the model’s complexity and the developed

control algorithm could be the parametrically varying system description (Shamma &

Athans, 1991), identification (Lee, 1997), optimal control (Wu et al., 2000), (Balas, 2002) and

diagnosis (Kulcsar, 2005)

1.4 The aim of the current work

The main contribution of the present work is to give a possible solution for nonlinear and

optimal automated glucose control synthesis

Considering the high-complexity nonlinear Sorensen-model a nonlinear model-based

methodology, the LPV (Linear Parameter Varying) technique is used to develop open-loop

model and robust controller design based on H∞ concepts The results are continuously

compared with those obtained by (Parker et al., 2000) where a linear model based robust

control algorithm was used (see section 1.5)

The validity of the Sorensen model is caught inside a polytopic region and the model is built

up by a linear combination of the linearized models derived in each polytopic point

(covering the physiologic boundaries of the glucose-insulin interaction of the

Sorensen-model)

Finally, using induced L2-norm minimization technique, a robust controller is developed for

insulin delivery in Type I diabetic patients The robust control was developed taking input

and output multiplicative uncertainties with two additional uncertainties from those used

by (Parker et al., 2000) Comparative results are given and closed-loop simulation scenarios

illustrate the applicability of the robust LPV control techniques

1.5 Brief review of the article published by (Parker et al., 2000)

As in the current chapter a continuous comparison of the obtained results will be done with

those obtained by (Parker et al., 2000), we considered useful to briefly summarize the

mentioned article

Although the first application of the H∞ theory on the field of diabetic control was that of

(Kienitz & Yoneyama, 1993), the publication of (Parker et al., 2000) can be considered a

pioneer work in applying the H∞ method for glucose-insulin control of Type I diabetic

patients using the fundamental nonlinear Sorensen-model

In (Parker et al., 2000) uncertainty in the nonlinear model was characterized by up to ±40%

variation in eight physiological parameters and by sensitivity analysis it was identified that

three-parameter set have the most significant effect on glucose and insulin dynamics

Controller performance was designed to track the normoglycemic set point (81.1 mg/dL) of

the Sorensen-model in response to a 50 g meal disturbance (using the six hour meal

disturbance function of (Lehmann & Deutsch, 1992)) By this way, glucose concentration

was maintained within ±3.3 mg/dL of set point

The results were compared to the results of (Kienitz & Yoneyama, 1993), who developed an

H∞ controller based on a third order linear diabetic patient model Performance of (Kienitz

& Yoneyama, 1993)’s controller in response to a meal disturbance was quantitatively similar

to the nominal controller obtained by (Parker et al., 2000) However, the uncertainty-derived controller of (Parker et al., 2000) was tuned to handle significantly more uncertainty than that of (Kienitz & Yoneyama, 1993)

On the other hand, (Parker et al., 2000) underlined that a significant loss in performance appeared applying the potential uncertainty in the model in comparison to the nominal case This could be mostly exemplified by the near physiologically dangerous hypoglycaemic episode, typically characterized as blood glucose values below 60 mg/dL (see Fig 9 and Fig 10 of (Parker et al., 2000) also captured by Fig 2 of the current work) Therefore, our goal was dual: applying nonlinear model-based LPV control methodology to design robust controller for Type I diabetic patients and to design a robust controller by taking into account two additional uncertainties from those used in (Parker et al., 2000), namely sensor noise and worst case design for meal disturbance presented in (Lehmann & Deutsch, 1992) (60 g carbohydrate)

Fig 2 Results obtained by (Parker et al., 2000) (taking from their work)

2 LPV modelling using polytopic description

The chapter suggests using Linear Parameter concepts with optimal and robust control scheme in order to show a candidate for diabetes Type I closed-loop control First, the most important control related definition of such a system class is given Solution of the robust control synthesis by Linear Matrix Inequalities (LMI) is briefly summarized

2.1 LPV system definition

Linear Parameter Varying (LPV) system is a class of nonlinear systems, where the parameter could be an arbitrary time varying, piecewise-continuous and vector valued function denoted by ρ(t), defined on a compact set P In order to evaluate the system, the parameter trajectory is requested to be known either by measurement or by computation A formal definition of the parameter varying systems is given below

2004), or even robust H∞ control were already applied (Parker et al., 2000), (Ruiz-Velazques

et al., 2004), (Kovacs et al., 2006), (Kovacs & Palancz, 2007), (Kovacs et al., 2008)

Most of the applied control methods were focused on the Bergman minimal model (and so

the applicability of the designed controllers was limited due to excessive sensitivity of the

model parameters) On the other hand, for the Sorensen-model, only linear control methods

were applied (H∞ (Parker et al., 2000), (Ruiz-Velazques et al., 2004), MPC (Parker et al.,

1999)) An acceptable compromise between the model’s complexity and the developed

control algorithm could be the parametrically varying system description (Shamma &

Athans, 1991), identification (Lee, 1997), optimal control (Wu et al., 2000), (Balas, 2002) and

diagnosis (Kulcsar, 2005)

1.4 The aim of the current work

The main contribution of the present work is to give a possible solution for nonlinear and

optimal automated glucose control synthesis

Considering the high-complexity nonlinear Sorensen-model a nonlinear model-based

methodology, the LPV (Linear Parameter Varying) technique is used to develop open-loop

model and robust controller design based on H∞ concepts The results are continuously

compared with those obtained by (Parker et al., 2000) where a linear model based robust

control algorithm was used (see section 1.5)

The validity of the Sorensen model is caught inside a polytopic region and the model is built

up by a linear combination of the linearized models derived in each polytopic point

(covering the physiologic boundaries of the glucose-insulin interaction of the

Sorensen-model)

Finally, using induced L2-norm minimization technique, a robust controller is developed for

insulin delivery in Type I diabetic patients The robust control was developed taking input

and output multiplicative uncertainties with two additional uncertainties from those used

by (Parker et al., 2000) Comparative results are given and closed-loop simulation scenarios

illustrate the applicability of the robust LPV control techniques

1.5 Brief review of the article published by (Parker et al., 2000)

As in the current chapter a continuous comparison of the obtained results will be done with

those obtained by (Parker et al., 2000), we considered useful to briefly summarize the

mentioned article

Although the first application of the H∞ theory on the field of diabetic control was that of

(Kienitz & Yoneyama, 1993), the publication of (Parker et al., 2000) can be considered a

pioneer work in applying the H∞ method for glucose-insulin control of Type I diabetic

patients using the fundamental nonlinear Sorensen-model

In (Parker et al., 2000) uncertainty in the nonlinear model was characterized by up to ±40%

variation in eight physiological parameters and by sensitivity analysis it was identified that

three-parameter set have the most significant effect on glucose and insulin dynamics

Controller performance was designed to track the normoglycemic set point (81.1 mg/dL) of

the Sorensen-model in response to a 50 g meal disturbance (using the six hour meal

disturbance function of (Lehmann & Deutsch, 1992)) By this way, glucose concentration

was maintained within ±3.3 mg/dL of set point

The results were compared to the results of (Kienitz & Yoneyama, 1993), who developed an

H∞ controller based on a third order linear diabetic patient model Performance of (Kienitz

& Yoneyama, 1993)’s controller in response to a meal disturbance was quantitatively similar

to the nominal controller obtained by (Parker et al., 2000) However, the uncertainty-derived controller of (Parker et al., 2000) was tuned to handle significantly more uncertainty than that of (Kienitz & Yoneyama, 1993)

On the other hand, (Parker et al., 2000) underlined that a significant loss in performance appeared applying the potential uncertainty in the model in comparison to the nominal case This could be mostly exemplified by the near physiologically dangerous hypoglycaemic episode, typically characterized as blood glucose values below 60 mg/dL (see Fig 9 and Fig 10 of (Parker et al., 2000) also captured by Fig 2 of the current work) Therefore, our goal was dual: applying nonlinear model-based LPV control methodology to design robust controller for Type I diabetic patients and to design a robust controller by taking into account two additional uncertainties from those used in (Parker et al., 2000), namely sensor noise and worst case design for meal disturbance presented in (Lehmann & Deutsch, 1992) (60 g carbohydrate)

Fig 2 Results obtained by (Parker et al., 2000) (taking from their work)

2 LPV modelling using polytopic description

The chapter suggests using Linear Parameter concepts with optimal and robust control scheme in order to show a candidate for diabetes Type I closed-loop control First, the most important control related definition of such a system class is given Solution of the robust control synthesis by Linear Matrix Inequalities (LMI) is briefly summarized

2.1 LPV system definition

Linear Parameter Varying (LPV) system is a class of nonlinear systems, where the parameter could be an arbitrary time varying, piecewise-continuous and vector valued function denoted by ρ(t), defined on a compact set P In order to evaluate the system, the parameter trajectory is requested to be known either by measurement or by computation A formal definition of the parameter varying systems is given below

Definition 1 For a compact P  Rs, the parameter variation set FP denotes the set of all

piecewise continuous functions mapping R + (time) into P with a finite number of

discontinuities in any interval The compact set P  Rs along with the continuous

functions A: Rs Rnn, B: Rs  Rn n u, C: Rs Rny n, D: Rs Rn  y n u represent an

nth order LPV system whose dynamics evolve as:

)(u)(D)(x)(C)(y

)(u)(B)(x)(A)(x

As a result, it can be seen that in the LPV model, by choosing parameter variables, the

system’s nonlinearity can be hidden This methodology is used on different control

solutions, like (Balas, 2002), which gave also a solution of the problem

There are different descriptions of the LPV systems (Kulcsar, 2005) In the affine description

possibility, a part of the x(t) states are equal with the ρ(t) parameters However, due to the

complexity of the Sorensen model, this representation is impossible to be developed

Polytopic representation could be another description of the LPV systems In this case, the

validity of the model is caught inside a polytopic region and the model is built up by a

linear combination of the linearized models derived in each polytopic point

1

i j

1

2

Hence, the LPV system is given by the complex combination of the positive coefficients and

the system Σ-s The polytopic LPV model can be thought as a set of linear models on a

vertex (a convex envelope of LTI systems), where the grid points of the description are LTI

systems The generation of a polytopic model is the derivation around an operating point of

the general nonlinear state-space representation The LPV polytopic model is valid only in a

restricted domain, characterized by the range of the polytope (Kulcsar, 2005)

Therefore, the correct definition of the polytopic region (which is capable to describe the

whole working area of the system) is a key point in this methodology

For a given compact set P  Rs and a continuous bounded matrix function A: Rs Rnn

which describes the x( )A(t))x( ) LPV system (( )P) and for a V Lyapunov function

candidate, it can be written that the time derivative of V(x) (for  P along the LPV

system trajectories) is (Tan, 1997):

 x( ) x ( )A ( t))P PA( t))x( )V

dt

positive definite matrix, such that for  P (Wu et al., 2000):

0))t(PAP))t(

It can be seen that the quadratic stability is a strong form of the robust stability with respect

to time varying parameters as it is true for quick changes of the ρ(t) parameter trajectory and for its definition it is enough a single quadratic Lyapunov-function

Defintion 3 For a quadratically stable LPV system ΣP and for zero initial conditions, the induced L2-norm of an LPV system is defined as follows (Tan, 1997):

2 2 L

dd 0P 2

esupsupG

2 2

an X  Rnn, X = XT > 0 such that for all ρ  P

0I)(D)

(C

)(DI

X)(B

)(C)(XB)(XAX)(AL

1 1

T 1 T

T 1 T

1 The function A is quadratically stable over P

2 There exists a β < γ such that GP 2 The matrix inequality (6) can be rewritten in the more familiar Riccati inequality by taking Schur components (Tan, 1997):

L2  , X > 0 and γ >0 constraints, where L2 can be derived from (6):

0I0

)(C

0IX

)(B

)(C)(XB)(XAX)(AL

2 T

T T

3.1 Covering the Sorensen-model with a polytopic region

In case of the 19th order Sorensen model (Fig 1) two inputs: Γmeal (meal disturbance), ΓIVI

(injected insulin amount), and one output, the capillary heart-lungs glucose concentration,

C H

G can be delimited However, we have considered also the peripheral insulin concentration in the capillaries, ICP as an additionally output

Definition 1 For a compact P  Rs, the parameter variation set FP denotes the set of all

piecewise continuous functions mapping R + (time) into P with a finite number of

discontinuities in any interval The compact set P  Rs along with the continuous

functions A: Rs Rnn, B: Rs  Rn n u, C: Rs Rny n, D: Rs Rn  y n u represent an

nth order LPV system whose dynamics evolve as:

)(

u)

(D

)(

x)

(C

)(

y

)(

u)

(B

)(

x)

(A

)(

As a result, it can be seen that in the LPV model, by choosing parameter variables, the

system’s nonlinearity can be hidden This methodology is used on different control

solutions, like (Balas, 2002), which gave also a solution of the problem

There are different descriptions of the LPV systems (Kulcsar, 2005) In the affine description

possibility, a part of the x(t) states are equal with the ρ(t) parameters However, due to the

complexity of the Sorensen model, this representation is impossible to be developed

Polytopic representation could be another description of the LPV systems In this case, the

validity of the model is caught inside a polytopic region and the model is built up by a

linear combination of the linearized models derived in each polytopic point

1

2

Hence, the LPV system is given by the complex combination of the positive coefficients and

the system Σ-s The polytopic LPV model can be thought as a set of linear models on a

vertex (a convex envelope of LTI systems), where the grid points of the description are LTI

systems The generation of a polytopic model is the derivation around an operating point of

the general nonlinear state-space representation The LPV polytopic model is valid only in a

restricted domain, characterized by the range of the polytope (Kulcsar, 2005)

Therefore, the correct definition of the polytopic region (which is capable to describe the

whole working area of the system) is a key point in this methodology

For a given compact set P  Rs and a continuous bounded matrix function A: Rs Rnn

which describes the x( )A(t))x( ) LPV system (( )P) and for a V Lyapunov function

candidate, it can be written that the time derivative of V(x) (for   P along the LPV

system trajectories) is (Tan, 1997):

 x( ) x ( )A ( t))P PA( t))x( )V

dt

positive definite matrix, such that for P (Wu et al., 2000):

0))

t(

PAP

))t

(

It can be seen that the quadratic stability is a strong form of the robust stability with respect

to time varying parameters as it is true for quick changes of the ρ(t) parameter trajectory and for its definition it is enough a single quadratic Lyapunov-function

Defintion 3 For a quadratically stable LPV system ΣP and for zero initial conditions, the induced L2-norm of an LPV system is defined as follows (Tan, 1997):

2 2 L

dd 0P 2

esupsupG

2 2

an X  Rnn, X = XT > 0 such that for all ρ  P

0I)(D)

(C

)(DI

X)(B

)(C)(XB)(XAX)(AL

1 1

T 1 T

T 1 T

1 The function A is quadratically stable over P

2 There exists a β < γ such that GP 2  The matrix inequality (6) can be rewritten in the more familiar Riccati inequality by taking Schur components (Tan, 1997):

L2  , X > 0 and γ >0 constraints, where L2 can be derived from (6):

0I0

)(C

0IX

)(B

)(C)(XB)(XAX)(AL

2 T

T T

3.1 Covering the Sorensen-model with a polytopic region

In case of the 19th order Sorensen model (Fig 1) two inputs: Γmeal (meal disturbance), ΓIVI

(injected insulin amount), and one output, the capillary heart-lungs glucose concentration,

C H

G can be delimited However, we have considered also the peripheral insulin concentration in the capillaries, ICP as an additionally output

Due to the high complexity of the Sorensen-model it was hard to investigate the global

stability of the system (the Lyapunov function is a real function with 19 variables)

Therefore, a solution could be to cover the working region with a set of linear systems and

in this way to investigate the local stability of them

Choosing the polytopic points we have restricted to the physiological meanings of the

variables The first point was the normoglycaemic point (glucose concentration y =GCH =

81.1 mg/dL and calculated insulin concentration C

The glucagon and the additional values were kept at their normoglycaemic value

In the points of the so generated polytopic region (36 points) we have determined one by

one a linearized model and we have analyzed the stability, observability and controllability

properties of them Each system proved to be stable, and partially observable and

controllable (the rank of the respective matrices were all 15 and 14 respectively) (Kovacs,

2008) Finally, we have simulated the so developed polytopic LPV system of the Sorensen

model, and we have compared the results with those obtained by (Parker et al., 2000) After

comparing the results it can be seen (Fig 3) that the LPV model is approximating with an

acceptable error the nonlinear system However, it can be also observed that without an

insulin injection the glucose concentration reaches an unacceptable value for a diabetic

patient Moreover, for the considered polytope the LPV system is stepping out from the

defined region being unable to handle the uncovered region

80 100 120 140 160 180 200

Fig 3 The simulation of the nonlinear Sorensen model (continuous) and the 36 points

polytope region (dashed)

Therefore, we had to extend the glucose concentration region of the considered polytope considering other grid points too, while the insulin concentration grid remained the same:

 glucose concentrations: 25%, 50%, 75%, 100%, 150%, 200%, 300%, 400%;

 insulin concentrations: 0%, 25%, 50%, 100%, 150%, 200%

Using the newly generated polytopic region (48 points) and after the same investigation of each linear model (obtaining the same results: each system proved to be stable and partially observable and controllable) it can be seen that the LPV model remains inside the considered polytopic region (Fig 4) and approximates with an acceptable error the nonlinear system (Kovacs, 2008)

For meal disturbance we have used the same six hour meal disturbance function of (Lehmann & Deutsch, 1992) (Fig 5), filtered with a

60/1s60/1

 first order lag used by (Parker

et al., 2000), while the insulin input was considered zero

It can be seen, that in absence of control the open-loop simulation is going up to a very high glucose concentration value, unacceptable for a Type I diabetic patient

3.2 LPV based robust control of the Sorensen-model

In case of robust control design, the results presented in (Parker et al., 2000) showed that a near hypoglycaemic situation appears for the considered uncertainties (Fig 2) In case of a diabetic patient this could be also a dangerous situation (not only hyperglycaemia)

The aim of the control design is to minimize the meal disturbance level over the performance output for all possible variation of the parameter within the polytope FP

80 100 120 140 160 180 200

Time (min.)

26.6554 26.6554 26.6554

Time (min.)

Fig 4 The simulation of the nonlinear Sorensen model (solid) and the considered polytopic region (dashed)

Due to the high complexity of the Sorensen-model it was hard to investigate the global

stability of the system (the Lyapunov function is a real function with 19 variables)

Therefore, a solution could be to cover the working region with a set of linear systems and

in this way to investigate the local stability of them

Choosing the polytopic points we have restricted to the physiological meanings of the

variables The first point was the normoglycaemic point (glucose concentration y =GCH =

81.1 mg/dL and calculated insulin concentration C

The glucagon and the additional values were kept at their normoglycaemic value

In the points of the so generated polytopic region (36 points) we have determined one by

one a linearized model and we have analyzed the stability, observability and controllability

properties of them Each system proved to be stable, and partially observable and

controllable (the rank of the respective matrices were all 15 and 14 respectively) (Kovacs,

2008) Finally, we have simulated the so developed polytopic LPV system of the Sorensen

model, and we have compared the results with those obtained by (Parker et al., 2000) After

comparing the results it can be seen (Fig 3) that the LPV model is approximating with an

acceptable error the nonlinear system However, it can be also observed that without an

insulin injection the glucose concentration reaches an unacceptable value for a diabetic

patient Moreover, for the considered polytope the LPV system is stepping out from the

defined region being unable to handle the uncovered region

80 100 120 140 160 180 200

Fig 3 The simulation of the nonlinear Sorensen model (continuous) and the 36 points

polytope region (dashed)

Therefore, we had to extend the glucose concentration region of the considered polytope considering other grid points too, while the insulin concentration grid remained the same:

 glucose concentrations: 25%, 50%, 75%, 100%, 150%, 200%, 300%, 400%;

 insulin concentrations: 0%, 25%, 50%, 100%, 150%, 200%

Using the newly generated polytopic region (48 points) and after the same investigation of each linear model (obtaining the same results: each system proved to be stable and partially observable and controllable) it can be seen that the LPV model remains inside the considered polytopic region (Fig 4) and approximates with an acceptable error the nonlinear system (Kovacs, 2008)

For meal disturbance we have used the same six hour meal disturbance function of (Lehmann & Deutsch, 1992) (Fig 5), filtered with a

60/1s60/1

 first order lag used by (Parker

et al., 2000), while the insulin input was considered zero

It can be seen, that in absence of control the open-loop simulation is going up to a very high glucose concentration value, unacceptable for a Type I diabetic patient

3.2 LPV based robust control of the Sorensen-model

In case of robust control design, the results presented in (Parker et al., 2000) showed that a near hypoglycaemic situation appears for the considered uncertainties (Fig 2) In case of a diabetic patient this could be also a dangerous situation (not only hyperglycaemia)

The aim of the control design is to minimize the meal disturbance level over the performance output for all possible variation of the parameter within the polytope FP

80 100 120 140 160 180 200

Time (min.)

26.6554 26.6554 26.6554

Time (min.)

Fig 4 The simulation of the nonlinear Sorensen model (solid) and the considered polytopic region (dashed)

0 50 100 150 200 250 300 350 400 450 500 0

50 100 150 200 250 300

Time (min.)

Fig 5 The glucose emptying function (Lehmann & Deutsch, 1992)

d

zsupsupminG

0 d F K

where d denotes the meal disturbance input and z describes the glucose variation Priory

information is injected to the controller throughout the augmentation of the nominal plant

with extra dynamics, called weighting functions

Therefore, the starting point of the control design was the appropriate choice of the

weighting functions Firstly, we have reproduced the results obtained by (Parker et al., 2000)

with the dangerous near hypoglycemic episode, but using the LPV methodology (on the

polytopic region presented in the previous section) Consequently, the weighting functions

used were the followings:

 The multiplicative uncertainty of the insulin input,

022.0s29.0s

015.0s47.0s

007.0s21.0s63.1

*01.0s

25.0s2.1

1

Wm



However, as we mentioned above, we have additionally taken into account sensor noise too

(neglected in (Parker et al., 2000), by considering it a 1/10000 value) We have considered

that for insulin measurements a 5% error, while for glucose measurements a 2% error is

tolerable (values taken from clinical experience)

As a result, the considered closed-loop interconnection of system can be illustrated by Fig 6,

while the obtained results obtained on the original nonlinear Sorensen-model can be seen in

Fig 7 By the reproduced results of (Parker et al., 2000) we have proved that the obtained controller (designed for the created LPV model) works correctly

Now, we have redesigned the control problem, to minimize the negative effects obtained by (Parker et al., 2000) Moreover, for meal disturbances we focused on the worst case of the (Lehmann & Deutsch, 1992) absorption taking into account a 60 g carbohydrate intake (in comparison with the 50 g carbohydrate considered by (Parker et al., 2000))

To avoid the hypoglycaemic situation and take into account the two additional uncertainties mentioned above, we have extended the control loop with a weighting function for the control signal and an output uncertainty block (Fig 8)

Fig 6 Considered closed-loop interconnection of the reproduced situation of (Parker et al., 2000) extended with additionally considered sensor noise weighting functions

−10 0 10 20

50 100

20 30 40 50

Time (min.)

Fig 7 The LPV based robust controller with induced L2-norm minimization guarantee, using the same weighting functions as in (Parker et al., 2000): in case of the original nonlinear Sorensen model (solid) and the considered polytopic region (dashed) controller

0 50 100 150 200 250 300 350 400 450 500 0

50 100 150 200 250 300

Time (min.)

Fig 5 The glucose emptying function (Lehmann & Deutsch, 1992)

d

zsup

supmin

G

0 d

F K

where d denotes the meal disturbance input and z describes the glucose variation Priory

information is injected to the controller throughout the augmentation of the nominal plant

with extra dynamics, called weighting functions

Therefore, the starting point of the control design was the appropriate choice of the

weighting functions Firstly, we have reproduced the results obtained by (Parker et al., 2000)

with the dangerous near hypoglycemic episode, but using the LPV methodology (on the

polytopic region presented in the previous section) Consequently, the weighting functions

used were the followings:

 The multiplicative uncertainty of the insulin input,

022

0s

29

0s

015

0s

47

0s

0s

52

0s

007

0s

21

0s

63

0

*01

.0

s

25

0s

2

However, as we mentioned above, we have additionally taken into account sensor noise too

(neglected in (Parker et al., 2000), by considering it a 1/10000 value) We have considered

that for insulin measurements a 5% error, while for glucose measurements a 2% error is

tolerable (values taken from clinical experience)

As a result, the considered closed-loop interconnection of system can be illustrated by Fig 6,

while the obtained results obtained on the original nonlinear Sorensen-model can be seen in

Fig 7 By the reproduced results of (Parker et al., 2000) we have proved that the obtained controller (designed for the created LPV model) works correctly

Now, we have redesigned the control problem, to minimize the negative effects obtained by (Parker et al., 2000) Moreover, for meal disturbances we focused on the worst case of the (Lehmann & Deutsch, 1992) absorption taking into account a 60 g carbohydrate intake (in comparison with the 50 g carbohydrate considered by (Parker et al., 2000))

To avoid the hypoglycaemic situation and take into account the two additional uncertainties mentioned above, we have extended the control loop with a weighting function for the control signal and an output uncertainty block (Fig 8)

Fig 6 Considered closed-loop interconnection of the reproduced situation of (Parker et al., 2000) extended with additionally considered sensor noise weighting functions

−10 0 10 20

50 100

20 30 40 50

Time (min.)

Fig 7 The LPV based robust controller with induced L2-norm minimization guarantee, using the same weighting functions as in (Parker et al., 2000): in case of the original nonlinear Sorensen model (solid) and the considered polytopic region (dashed) controller

Fig 8 The augmented system structure using the additional restrictions from those

published in (Parker et al., 2000)

As a result, regarding the weighting functions used in (Parker et al., 2000), we have

modified only the multiplicative uncertainty weighting functions (Wim, Wi) and the

performance weighting function Wperf, while these were chosen only from engineering point

of view Now physiological aspects were taken also into account The frequency response of

the weighting functions can be seen in Fig 9

During the robust control design, a γ = 1.0096 solution was obtained It can be seen (Fig 10)

that the hypoglycaemic situation is avoided and the glucose level is kept inside the normal

80-120 mg/dL range Testing the controller on the original nonlinear Sorensen-model results

are good too Although in this case the glucose results are stepping out the normal range

(160 mg/dL) this is acceptable (and similar to the healthy subjects)

Fig 9 Weighting functions used for the LPV-based induced L2-norm minimization (those

which have been modified from (Parker et al., 2000))

−10 0 10

80 100 120 140

LPV Nonlin

20 30 40

time [min]

LPV Nonlin

Fig 10 The LPV based robust controller (for the case of the considered additional uncertainties) with induced L2-norm minimization guarantee in case of the original nonlinear Sorensen model (solid) and the considered polytopic region (dashed)

4 Conclusions

In the current work a nonlinear model-based LPV control method was applied to design a robust controller for the high complexity Sorensen-model The used methodology is more general than the classical linear H∞ method as it deals directly with the nonlinear model itself From the different descriptions of the LPV systems, polytopic representation was used, where the validity of the model was captured inside a polytopic region In this way the model was built up by a linear combination of the linearized models derived in each considered polytopic point

Using induced L2-norm minimization technique, a robust controller was developed for insulin delivery in Type I diabetic patients Considering the normoglycaemic set point (81.1 mg/dL), a polytopic set was created over the physiologic boundaries of the glucose-insulin interaction of the Sorensen-model

The robust control was developed taking into account input and output multiplicative uncertainties, sensor noise and worst case meal disturbance (as additional restrictions from those applied in (Parker et al., 2000)) The obtained results showed that glucose level can be kept inside a normal range, avoiding hypoglycaemic episode (which was not possible with the control formalism applied in (Parker et al., 2000)) By the given comparative results and closed-loop simulation scenarios it was illustrated the applicability of the robust LPV control techniques

Parameter dependency of the considered weighting functions could be considered in the future, which gives additional design freedom