Skip to main content

Advertisement

SpringerLink
Log in

A review of presented mathematical models in Parkinson’s disease: black- and gray-box models

  • Review Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

Parkinson’s disease (PD), one of the most common movement disorders, is caused by damage to the central nervous system. Despite all of the studies on PD, the formation mechanism of its symptoms remained unknown. It is still not obvious why damage only to the substantia nigra pars compacta, a small part of the brain, causes a wide range of symptoms. Moreover, the causes of brain damages remain to be fully elucidated. Exact understanding of the brain function seems to be impossible. On the other hand, some engineering tools are trying to understand the behavior and performance of complex systems. Modeling is one of the most important tools in this regard. Developing quantitative models for this disease has begun in recent decades. They are very effective not only in better understanding of the disease, offering new therapies, and its prediction and control, but also in its early diagnosis. Modeling studies include two main groups: black-box models and gray-box models. Generally, in the black-box modeling, regardless of the system information, the symptom is only considered as the output. Such models, besides the quantitative analysis studies, increase our knowledge of the disorders behavior and the disease symptoms. The gray-box models consider the involved structures in the symptoms appearance as well as the final disease symptoms. These models can effectively save time and be cost-effective for the researchers and help them select appropriate treatment mechanisms among all possible options. In this review paper, first, efforts are made to investigate some studies on PD quantitative analysis. Then, PD quantitative models will be reviewed. Finally, the results of using such models are presented to some extent.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Andria G, Attivissimo F, Giaquinto N, Lanzolla A, Quagliarella L, Sasanelli N (2006) Functional evaluation of handgrip signals for Parkinsonian patients. IEEE Trans Instrum Meas 55(5):1467–1473. doi:10.1109/TIM.2006.881029

    Article  CAS  Google Scholar 

  2. Asai Y, Nomura T, Abe K, Matsuo Y, Sato S (2003) Classification of dynamics of a model of motor coordination and comparison with Parkinson’s disease data. Biosystems 71(1):11–21. doi:10.1016/S0303-2647(03)00105-9

    Article  PubMed  Google Scholar 

  3. Austin G, Hayward W, Tsai C, Kuykendall A (1965) Parkinsonian tremor: some aspects of an experimental model and its solution. Stereotact Funct Neurosurg 26(3–5):389–403. doi:10.1159/000104056

    CAS  Google Scholar 

  4. Aziz W, Arif M (2006) Genetically optimized hybrid gait dynamics classifier. In: Emerging technologies, 2006. ICET’06. International conference on, 2006. IEEE, pp 765–770 doi:10.1109/ICET.2006.336026

  5. Banaie M, Sarbaz Y, Gharibzadeh S, Towhidkhah F (2008) Huntington’s disease: modeling the gait disorder and proposing novel treatments. J Theor Biol 254(2):361–367. doi:10.1016/j.jtbi.2008.05.023

    Article  PubMed  Google Scholar 

  6. Benjamin CL, Joseph KC (2001) Epidemiology of Parkinson’s disease. BCMJ. 43(3):133–137

    Google Scholar 

  7. Beuter A, Vasilakos K (1995) Tremor: is Parkinson’s disease a dynamical disease? Chaos Interdiscip J Nonlinear Sci 5(1):35–42. doi:10.1063/1.166082

    Article  Google Scholar 

  8. Bryant MS, Rintala DH, Hou JG, Charness AL, Fernandez AL, Collins RL, Baker J, Lai EC, Protas EJ (2011) Gait variability in Parkinson’s disease: influence of walking speed and dopaminergic treatment. Neurol Res 33(9):959–964. doi:10.1179/1743132811Y.0000000044

    Article  PubMed  Google Scholar 

  9. Ciccone CD (2015) Pharmacology in rehabilitation. FA Davis, Philadelphia

    Google Scholar 

  10. Cornford ME, Chang L, Miller B (1995) The neuropathology of Parkinsonism: an overview. Brain Cognit 28:321–341

    Article  CAS  Google Scholar 

  11. Cutsuridis V (2011) Origins of a repetitive and co-contractive biphasic pattern of muscle activation in Parkinson’s disease. Neural Netw 24(6):592–601. doi:10.1016/j.neunet.2011.03.008

    Article  PubMed  Google Scholar 

  12. Cutsuridis V, Perantonis S (2006) A artificial neural network model of Parkinson’s disease bradykinesia. Artif Neural Netw 19(4):354–374. doi:10.1016/j.neunet.2005.08.016

    Article  Google Scholar 

  13. Dargie WW, Christian P (2010) Fundamentals of wireless sensor networks: theory and practice. Wiley, New Jersey

    Book  Google Scholar 

  14. Edwards R, Beuter A, Glass L (1999) Parkinsonian tremor and simplification in network dynamics. Bull Math Biol 61(1):157–177. doi:10.1006/bulm.1998.0086

    Article  CAS  PubMed  Google Scholar 

  15. Ehringer H, Hornykiewicz O (1960) Verteilung von Noradrenalin und Dopamin (3-hydroxytyramin) im Gerhirn des Menschens und ihr Verhalten bei Erkrankugen des extrapyramidalen Systems. Klin Wochenschr 38(24):1236–1239

    Article  CAS  PubMed  Google Scholar 

  16. Factor S, Weiner W (2007) Parkinson’s disease: diagnosis and clinical management. Demos Medical Publishing, New York

    Google Scholar 

  17. Findley LJ (2007) The economic impact of Parkinson’s disease. Parkinsonism Relat Disord. 13(S8–S12). Epub 2007 Aug 16

  18. Fisher A, Memo M, Stocchi F, Hanin I (2007) Advances in Alzheimer’s and Parkinson’s Disease: insights, progress, and perspectives. Springer, USA

    Google Scholar 

  19. Gangadhar G, Joseph D, Srinivasan A, Subramanian D, Shivakeshavan R, Shobana N, Chakravarthy V (2009) A computational model of Parkinsonian handwriting that highlights the role of the indirect pathway in the basal ganglia. Hum Mov Sci 28(5):602–618. doi:10.1016/j.humov.2009.07.008

    Article  CAS  PubMed  Google Scholar 

  20. Glass L, Malta CP (1990) Chaos in multi-looped negative feedbacks systems. J Theor Biol 145(2):217–223. doi:10.1016/S0022-5193(05)80127-4

    Article  CAS  PubMed  Google Scholar 

  21. Golan DE, Tashjian AH, Armstrong EJ (eds) (2011) Principles of pharmacology: the pathophysiologic basis of drug therapy. Lippincott Williams & Wilkins, Philadelphia

    Google Scholar 

  22. Goldberger AL, Amaral LA, Hausdorff JM, Ivanov PC, Peng C-K, Stanley HE (2002) Fractal dynamics in physiology: alterations with disease and aging. Proc Natl Acad Sci 99(suppl 1):2466–2472. doi:10.1073/pnas.012579499

    Article  PubMed  PubMed Central  Google Scholar 

  23. Guthrie M, Myers C, Gluck M (2009) A neurocomputational model of tonic and phasic dopamine in action selection: a comparison with cognitive deficits in Parkinson’s disease. Behav Brain Res 200(1):48–59. doi:10.1016/j.bbr.2008.12.036

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Hadipour-Niktarash A (2006) A computational model of how an interaction between the thalamocortical and thalamic reticular neurons transforms the low-frequency oscillations of the globus pallidus. J Comput Neurosci 20(3):299–320. doi:10.1007/s10827-006-6673-5

    Article  PubMed  Google Scholar 

  25. Haeri M, Sarbaz Y, Gharibzadeh S (2005) Modeling the Parkinson’s tremor and its treatments. J Theor Biol 236(3):311–322. doi:10.1016/j.jtbi.2005.03.014

    Article  PubMed  Google Scholar 

  26. Hassler R (1938) Zur Pathologie der paralysis agitans und des postenzephalitschen Parkinsonismus. J f Psychol u Neurol 48:387–476

    Google Scholar 

  27. Hassler R (1955) The pathological and pathophysiological basis of tremor and parkinsonism. Proceedings of the second international congress on neuropathology. Excerpta Medical Foundation, Amsterdam, pp 29–40

    Google Scholar 

  28. Hausdorff JM (2009) Gait dynamics in Parkinson’s disease: common and distinct behavior among stride length, gait variability, and fractal-like scaling. Chaos Interdiscip J Nonlinear Sci 19(2):026113. doi:10.1063/1.3147408

    Article  Google Scholar 

  29. Hausdorff JM, Peng C, Ladin Z, Wei JY, Goldberger AL (1995) Is walking a random walk? Evidence for long-range correlations in stride interval of human gait. J Appl Physiol 78:349–358

    CAS  PubMed  Google Scholar 

  30. Hausdorff JM, Purdon PL, Peng C, Ladin Z, Wei JY, Goldberger AL (1996) Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations. J Appl Physiol 80(5):1448–1457

    CAS  PubMed  Google Scholar 

  31. Hausdorff JM, Mitchell SL, Firtion R, Peng C, Cudkowicz ME, Wei JY, Goldberger AL (1997) Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington’s disease. J Appl Physiol 82(1):262–269

    CAS  PubMed  Google Scholar 

  32. Hausdorff JM, Cudkowicz ME, Firtion R, Wei JY, Goldberger AL (1998) Gait variability and basal ganglia disorders: stride-to-stride variations of gait cycle timing in parkinson’s disease and Huntington’s disease. Mov Disord 13(3):428–437. doi:10.1002/mds.870130310

    Article  CAS  PubMed  Google Scholar 

  33. Hefti F, Weiner WJ (1988) Progress in Parkinson research. Plenum, New York

    Google Scholar 

  34. Hilborn RC (2000) Chaos and nonlinear dynamics: an introduction for scientists and engineers. Oxford University Press, Oxford

    Book  Google Scholar 

  35. Jeon H-S, Han J, Yi W-J, Jeon B, Park KS (2008) Classification of Parkinson gait and normal gait using spatial-temporal image of plantar pressure. In: Engineering in medicine and biology society, 2008. EMBS 2008. 30th annual international conference of the IEEE, 2008. IEEE, pp 4672–4675 doi:10.1109/IEMBS.2008.4650255

  36. Jervis B, Smaglo L, Djebali S (2001) The rapid classification of brain conditions using neural networks. In: Intelligent sensor processing (Ref. No. 2001/050), A DERA/IEE Workshop on, 2001. IET, pp 4/1–4/8 doi:10.1049/ic:20010099

  37. Laitinen LV, Bergenheim AT, Hariz MI (1992) Leksell’s posteroventral pallidotomy in the treatment of Parkinson’s disease. J Neurosurg 76(1):53–61. doi:10.3171/jns.1992.76.1.0053

    Article  CAS  PubMed  Google Scholar 

  38. Lees AJ (2007) Unresolved issues relating to the shaking palsy on the celebration of James Parkinson’s 250th birthday. Mov Disord 22:S17. doi:10.1002/mds.21684

    Article  Google Scholar 

  39. MashhadiMalek M, Towhidkhah F, Gharibzadeh S, Daeichin V, Ahmadi-Pajouh MA (2008) Are rigidity and tremor two sides of the same coin in Parkinson’s disease? Comput Biol Med 38(11):1133–1139. doi:10.1016/j.compbiomed.2008.08.007

    Article  PubMed  Google Scholar 

  40. Mera TO, Filipkowski DE, Riley DE, Whitney CM, Walter BL, Gunzler SA, Giuffrida JP (2013) Quantitative analysis of gait and balance response to deep brain stimulation in Parkinson’s disease. Gait Posture 38(1):109–114. doi:10.1016/j.gaitpost.2012.10.025

    Article  PubMed  PubMed Central  Google Scholar 

  41. Mosley AD, Romaine DS, Samii A (2010) The encyclopedia of Parkinson’s Disease. Infobase Publishing, New York

    Google Scholar 

  42. Mouradian MM (2001) Parkinson’s disease: methods and protocols. Springer, New York

    Book  Google Scholar 

  43. Naismith SL, Lewis SJ (2010) A novel paradigm for modelling freezing of gait in Parkinson’s disease. J Clin Neurosci 17(8):984–987. doi:10.1016/j.jocn.2009.12.006

    Article  PubMed  Google Scholar 

  44. Nanhoe-Mahabier W, Snijders A, Delval A, Weerdesteyn V, Duysens J, Overeem S, Bloem B (2011) Walking patterns in Parkinson’s disease with and without freezing of gait. Neuroscience 182:217–224. doi:10.1016/j.neuroscience.2011.02.061

    Article  CAS  PubMed  Google Scholar 

  45. National Collaborating Centre for Chronic Conditions (Great Britain) (2006) Parkinson’s disease: national clinical guideline for diagnosis and management in primary and secondary care. Royal College of Physicians, London

    Google Scholar 

  46. Okuno R, Fujimoto S, Akazawa J, Yokoe M, Sakoda S, Akazawa K (2008) Analysis of spatial temporal plantar pressure pattern during gait in Parkinson’s disease. In: Engineering in medicine and biology society, 2008. EMBS 2008. 30th annual international conference of the IEEE, 2008. IEEE, pp 1765–1768 doi:10.1109/IEMBS.2008.4649519

  47. Parkinson J (1817) An essay on the shaking palsy. Whittingham and Rowland for Sherwood, Needly and Jones, London

    Google Scholar 

  48. Pfeiffer RF, Wszolek KZ, Ebadi M (2004) Parkinson’s Disease. CRC Press, Boca Raton

    Google Scholar 

  49. Rai PV (2010) Step by step treatment of Parkinson Disease Paperback: 26 Nov, Jaypee Brothers Medical

  50. Rana AG (2010) 50 Ways Parkinson’s could affect you paperback. Iuniverse Inc, India

    Google Scholar 

  51. Riederer P, Reichmann H, Youdim MBH, Gerlach M (eds) (2006) Parkinson’s disease and related disorders. Springer, Wien. doi:10.1007/978-3-211-45295-0

    Google Scholar 

  52. Rosenbaum RB (2006) Understanding Parkinson’s disease: a personal and professional view. Greenwood Publishing Group, Santa Barbara

    Google Scholar 

  53. Sarbaz Y, Pourhedayat A (2014) Spectral analysis of gait disorders in Huntington’s disease: a new horizon to early diagnosis. J Mech Med Biol. doi:10.1142/S0219519414500018

    Google Scholar 

  54. Sarbaz Y, Banae M, Gharibzadeh S (2007) A computational model for the Huntington disease. Med Hypotheses 68(5):1154–1158. doi:10.1016/j.mehy.2006.06.039

    Article  PubMed  Google Scholar 

  55. Sarbaz Y, Gharibzadeh S, Towhidkhah F, Banaie M, Jafari A (2011) A grey-box artificial neural network model of Parkinson’s Disease using gait signal. Basic Clin Neurosci 2(3):33–42

    Google Scholar 

  56. Sarbaz Y, Towhidkhah F, Gharibzadeh S, Jafari A (2012) Gait spectral analysis: an easy fast quantitative method for diagnosing Parkinson’s Disease. J Mech Med Biol. doi:10.1142/S0219519411004691

    Google Scholar 

  57. Sarbaz Y, Banaie M, Pooyan M, Gharibzadeh S, Towhidkhah F, Jafari A (2012) Modeling the gait of normal and Parkinsonian persons for improving the diagnosis. Neurosci Lett 509(2):72–75. doi:10.1016/j.neulet.2011.10.002

    Article  CAS  PubMed  Google Scholar 

  58. Sarbaz Y, Gharibzadeh S, Towhidkhah F (2012) Pathophysiology of freezing of gait and some possible treatments for it. Med Hypothesis 78(2):258–261. doi:10.1016/j.mehy.2011.10.040

    Article  Google Scholar 

  59. Sarbaz Y, Towhidkhah F, Jafari A, Gharibzadeh S (2012) Do the chaotic features of gait change in Parkinson’s disease? J Theor Biol 307:160–167. doi:10.1016/j.jtbi.2012.04.032

    Article  PubMed  Google Scholar 

  60. Sarbaz Y, Towhidkhah F, Mosavari V, Janani A, Soltanzadeh A (2013) Separating parkinsonian patients from normal persons using handwriting features. J Mech Med Biol. doi:10.1142/S0219519413500309

    Google Scholar 

  61. Sarbaz Y, Gharibzadeh S, Soltanzadeh A, Towhidkhah F (2013) A novel clinical gait test protocol for separating parkinsonian patients from normal persons in early disease stages. J Med Imaging Health Inform 3(1):7–11. doi:10.1166/jmihi.2013.1125

    Article  Google Scholar 

  62. Schwartz B (2011) The natural history of the Parkinson’s Disease in early stages. Logos Verlag, Berlin

    Google Scholar 

  63. Sekine M, Tamura T, Akay M, Fujimoto T, Togawa T, Fukui Y (2002) Discrimination of walking patterns using wavelet-based fractal analysis. IEEE Trans Neural Syst Rehabil Eng 10(3):188–196. doi:10.1109/TNSRE.2002.802879

    Article  PubMed  Google Scholar 

  64. Sharma N (2008) Biographies of disease. Parkinson’s disease. Greenwood, Santa Barbara

    Google Scholar 

  65. Shine JM, Matar E, Bolitho SJ, Dilda V, Morris TR, Naismith SL, Moore ST, Lewis SJG (2013) Modeling freezing of gait in Parkinson’s disease with a virtual reality paradigm. Gait Posture 38(1):104–108. doi:10.1016/j.gaitpost.2012.10.026

    Article  CAS  PubMed  Google Scholar 

  66. Sofuwa O, Nieuwboer A, Desloovere K, Willems A-M, Chavret F, Jonkers I (2005) Quantitative gait analysis in Parkinson’s disease: comparison with a healthy control group. Arch Phys Med Rehabil 86(5):1007–1013. doi:10.1016/j.apmr.2004.08.012

    Article  PubMed  Google Scholar 

  67. Solly S (1848) The human brain; its structure, physiology and diseases: with a description of the typical forms of brain in the animal kingdom. Lea and Blanchard, Philadelphia

    Google Scholar 

  68. Švehlík M, Zwick EB, Steinwender G, Linhart WE, Schwingenschuh P, Katschnig P, Ott E, Enzinger C (2009) Gait analysis in patients with Parkinson’s disease off dopaminergic therapy. Arch Phys Med Rehabil 90(11):1880–1886. doi:10.1016/j.apmr.2009.06.017

    Article  PubMed  Google Scholar 

  69. Tarsy D, Vitek JL, Starr P, Okun M (eds) (2008) Deep brain stimulation in neurological and psychiatric disorders. Springer, New York

    Google Scholar 

  70. Titcombe MS, Glass L, Guehl D, Beuter A (2001) Dynamics of Parkinsonian tremor during deep brain stimulation. Chaos Interdiscip J Nonlinear Sci 11(4):766–773. doi:10.1063/1.1408257

    Article  Google Scholar 

  71. Tretiakoff C (1919) Contribution a l’etude de l’anatomie pathologic du locus niger de soemmering avec quelques deductions relative a la pathogenie des troubles du tunos musculaire et de la maladie de Parkinson. These pour le doctorat en Medicine. Paris, These de Paris, pp 1–24

  72. Tugwell C (2008) Parkinson’s disease in focus. Pharmaceutical Press, London

    Google Scholar 

  73. Vieregge P, Stolze H, Klein C, Heberlein I (1997) Gait quantitation in Parkinson’s disease: locomotor disability and correlation to clinical rating scales. J Neural Transm 104(2–3):237–248. doi:10.1007/BF01273184

    Article  CAS  PubMed  Google Scholar 

  74. Wang M, Wang B, Zou J, Nakamura M (2012) A new quantitative evaluation method of spiral drawing for patients with Parkinson’s disease based on a polar coordinate system with varying origin. Phys A Stat Mech Appl 391(18):4377–4388. doi:10.1016/j.physa.2012.03.029

    Article  Google Scholar 

  75. West BJ, Latka M (2005) Fractional Langevin model of gait variability. J NeuroEng Rehabil. doi:10.1186/1743-0003-2-24

    PubMed  PubMed Central  Google Scholar 

  76. West BJ, Scafetta N (2003) Nonlinear dynamical model of human gait. Phys Rev E 67(5):051917. doi:10.1103/PhysRevE.67.051917

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering Emerging Technologies, University of Tabriz, Tabriz, Iran

    Yashar Sarbaz & Hakimeh Pourakbari

Authors
  1. Yashar Sarbaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hakimeh Pourakbari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yashar Sarbaz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sarbaz, Y., Pourakbari, H. A review of presented mathematical models in Parkinson’s disease: black- and gray-box models. Med Biol Eng Comput 54, 855–868 (2016). https://doi.org/10.1007/s11517-015-1401-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-015-1401-9

Keywords

Search

Navigation