Skip to main content

Advertisement

SpringerLink
Log in

Optimizing stimulus waveforms for electroceuticals

  • Prospects
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

There has been a growing interest in the use of electrical stimulation as a therapy across diverse medical conditions. Most electroceutical devices use simple waveforms, for example sinusoidal or rectangular biphasic pulses. Clinicians empirically tune the waveform parameters (e.g. amplitude, frequency) without altering the fundamental shape of the stimulus. In this article, we review computational strategies that have been used to optimize the shape of stimulus waveforms in order to improve clinical outcomes, and we discuss potential directions for future exploration.

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

Adapted from Chang and Paydarfar (2018) with permission

Similar content being viewed by others

References

  • Barto AG, Sutton RS (2017) Reinforcement learning: an introduction. MIT Press, Cambridge

    Google Scholar 

  • Bellman R (1961) Adaptive control processes: a guided tour. Princeton University Press, Princeton

    Book  Google Scholar 

  • Benabid AL, Chabardes S, Mitrofanis J, Pollak P (2009) Deep brain stimulation of the subthalamic nucleus for the treatment of Parkinson’s disease. Lancet Neurol 8(1):67–81

    Article  PubMed  Google Scholar 

  • Bloch-Salisbury E, Indic P, Bednarek F, Paydarfar D (2009) Stabilizing immature breathing patterns of preterm infants using stochastic mechanosensory stimulation. J Appl Physiol 107(4):1017–27

    Article  PubMed  PubMed Central  Google Scholar 

  • Bonaz BL, Bernstein CN (2013) Brain–gut interactions in inflammatory bowel disease. Gastroenterology 144(1):36–49

    Article  PubMed  Google Scholar 

  • Boon P, Vonck K, De Herdt V, Van Dycke A, Goethals M, Goossens L, Van Zandijcke MV, De Smedt T, Dewaele I, Achten R, Wadman W, Dewaele F, Caemaert J, Van Roost D (2007) Deep brain stimulation in patients with refractory temporal lobe epilepsy. Epilepsia 48(8):1551–1560

    Article  PubMed  Google Scholar 

  • Bryson AE, Ho YC (1975) Applied optimal control: optimization, estimation and control. CRC Press, Boca Raton

    Google Scholar 

  • Cameron T (2004) Safety and efficacy of spinal cord stimulation for the treatment of chronic pain: a 20-year literature review. J Neurosurg Spine 100(3):254–267

    Article  Google Scholar 

  • Cassar IR, Titus ND, Grill WM (2017) An improved genetic algorithm for designing optimal temporal patterns of neural stimulation. J Neural Eng 14(6):066013

    Article  PubMed  PubMed Central  Google Scholar 

  • Chang J, Paydarfar D (2014) Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm. J Comput Neurosci 37(3):569–582

    Article  PubMed  PubMed Central  Google Scholar 

  • Chang J, Paydarfar D (2015) Optimal stimulus waveforms for eliciting a spike: How close is the spike-triggered average? In: 2015 7th international IEEE/EMBS conference on neural engineering (NER), pp 414–417

  • Chang J, Paydarfar D (2018) Evolution of extrema features reveals optimal stimuli for biological state transitions. Sci Rep 8:3403

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Clay J, Forger D, Paydarfar D (2012) Ionic mechanism underlying optimal stimuli for neuronal excitation: role of Na+ channel inactivation. PLoS ONE 7(9):e45983

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Dettling M, Lisanby SH (2008) Electroconvulsive therapy for depression. New Engl J Med 358(6):645–646

    Article  CAS  PubMed  Google Scholar 

  • Fain ES, Sweeney MB, Franz MR (1989) Improved internal defibrillation efficacy with a biphasic waveform. Am Heart J 117(2):358–364

    Article  CAS  PubMed  Google Scholar 

  • Fishler MG (2000) Theoretical predictions of the optimal monophasic and biphasic defibrillation waveshapes. IEEE Trans Biomed Eng 47(1):59–67

    Article  CAS  PubMed  Google Scholar 

  • Forger D (2017) Biological clocks, rhythms, and oscillations: the theory of biological timekeeping. MIT Press, Cambridge

    Google Scholar 

  • Forger DB, Paydarfar D (2004) Starting, stopping, and resetting biological oscillators: in search of optimum perturbations. J Theor Biol 230(4):521–532

    Article  PubMed  Google Scholar 

  • Forger DB, Paydarfar D, Clay JR (2011) Optimal stimulus shapes for neuronal excitation. PLoS Comput Biol 7(7):e1002089

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Foutz TJ, McIntyre CC (2010) Evaluation of novel stimulus waveforms for deep brain stimulation. J Neural Eng 7(6):066008

    Article  PubMed  PubMed Central  Google Scholar 

  • Garratt A (1858) Galvanism for counteracting pain in the extraction of teeth. Boston Med Surg J 59:32–34

    Article  Google Scholar 

  • Gelfand I, Fomin S, Silverman R (2000) Calculus of variations. Courier Dover Publications, Englewood Cliffs

    Google Scholar 

  • Golfetto WA, da Silva Fernandes S (2012) A review of gradient algorithms for numerical computation of optimal trajectories. J Aerosp Technol Manag 4(2):131–143

    Article  Google Scholar 

  • Grill W (2015) Model-based analysis and design of waveforms for efficient neural stimulation. Prog Brain Res 222:147–162

    Article  PubMed  PubMed Central  Google Scholar 

  • Gurvich N, Yuniev G (1947) Restoration of heart rhythm during fibrillation by a condenser discharge. Am Rev Sov Med 4(3):252–256

    CAS  PubMed  Google Scholar 

  • Hodgkin A, Huxley A (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 52(4):500–544

    Article  Google Scholar 

  • Indic P, Gurdziel K, Kronauer RE, Klerman EB (2006) Development of a two-dimension manifold to represent high dimension mathematical models of the intracellular mammalian circadian clock. J Biol Rhythm 21(3):222–232

    Article  Google Scholar 

  • Izhikevich E (2003) Simple model of spiking neurons. IEEE Trans Neural Netw 14(6):1569–1572

    Article  CAS  PubMed  Google Scholar 

  • Jimenez F, Velasco F, Salin-Pascual R, Hernandez JA, Velasco M, Criales JL, Nicolini H (2005) A patient with a resistant major depression disorder treated with deep brain stimulation in the inferior thalamic peduncle. Neurosurgery 57(3):585–592

    Article  PubMed  Google Scholar 

  • Kane K, Taub A (1975) A history of local electrical analgesia. Pain 1(2):125–138

    Article  CAS  PubMed  Google Scholar 

  • Kelley HJ (1962) Methods of gradients. In: Leitmann G (ed) Optimization techniques, chap 6, 5th edn. Academic Press, Inc, New York, pp 206–254

    Google Scholar 

  • Kodoth V, Castro NC, Glover BM, Anderson JM, Escalona OJ, Lau E, Manoharan G (2011) Waveform optimization for internal cardioversion of atrial fibrillation. J Electrocardiol 44(6):689–693

    Article  PubMed  Google Scholar 

  • Kouwenhoven WB (1969) The development of the defibrillator. Ann Intern Med 71(3):449–458

    Article  CAS  PubMed  Google Scholar 

  • Kuncel AM, Grill WM (2004) Selection of stimulus parameters for deep brain stimulation. Clin Neurophysiol 115(11):2431–2441

    Article  PubMed  Google Scholar 

  • Li W, Ripplinger CM, Lou Q, Efimov IR (2009) Multiple monophasic shocks improve electrotherapy of ventricular tachycardia in a rabbit model of chronic infarction. Heart Rhythm 6(7):1020–1027

    Article  PubMed  PubMed Central  Google Scholar 

  • Lown B (1967) Electrical reversion of cardiac arrhythmias. Br Heart J 29(4):469–89

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Lown B, Neuman J, Amarasingham R, Berkovits B et al (1962) Comparison of alternating current with direct electroshock across the closed chest. Am J Cardiol 10(2):223–233

    Article  CAS  PubMed  Google Scholar 

  • Lozano AM, Mayberg HS, Giacobbe P, Hamani C, Craddock RC, Kennedy SH (2008) Subcallosal cingulate gyrus deep brain stimulation for treatment-resistant depression. Biol Psychiatry 64(6):461–467

    Article  PubMed  Google Scholar 

  • Luther S, Fenton FH, Kornreich BG, Squires A, Bittihn P, Hornung D, Zabel M, Flanders J, Gladuli A, Campoy L, Cherry EM, Luther G, Hasenfuss G, Krinsky VI, Pumir A, Gilmour RF Jr, Bodenschatz E (2011) Low-energy control of electrical turbulence in the heart. Nature 475(7355):235–239

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Malkin RA, Jackson SR, Nguyen J, Yang Z, Guan D (2006) Experimental verification of theoretical predictions concerning the optimum defibrillation waveform. IEEE Trans Biomed Eng 53(8):1492–1498

    Article  PubMed  Google Scholar 

  • Meregnani J, Clarençon D, Vivier M, Peinnequin A, Mouret C, Sinniger V, Picq C, Job A, Canini F, Jacquier-Sarlin M, Bonaz B (2011) Anti-inflammatory effect of vagus nerve stimulation in a rat model of inflammatory bowel disease. Auton Neurosci Basic Clin 160(1–2):82–89

    Article  CAS  Google Scholar 

  • Merrill DR, Bikson M, Jefferys JG (2005) Electrical stimulation of excitable tissue: design of efficacious and safe protocols. J Neurosci Methods 141(2):171–198

    Article  PubMed  Google Scholar 

  • Mitchell M, Holland JH, Forrest S (1994) When will a genetic algorithm outperform hill climbing. Adv Neural Inf Process Syst 6:51–58

    Google Scholar 

  • Moehlis J, Shea-Brown E, Rabitz H (2006) Optimal inputs for phase models of spiking neurons. J Comput Nonlinear Dyn 1(4):358

    Article  Google Scholar 

  • Nabi A, Moehlis J (2012) Time optimal control of spiking neurons. J Math Biol 64(6):981–1004

    Article  PubMed  Google Scholar 

  • Oakley JC, Prager JP (2002) Spinal cord stimulation: mechanisms of action. Spine 27(22):2574–2583

    Article  PubMed  Google Scholar 

  • Offner F (1946) Stimulation with minimum power. J Neurophysiol 9(5):387–390

    Article  CAS  PubMed  Google Scholar 

  • Park M, Pillow J (2012) Bayesian active learning with localized priors for fast receptive field characterization. Adv Neural Inf Process Syst 25(25):2357–2365

    Google Scholar 

  • Park M, Nassar M, Vikalo H (2013) Bayesian active learning for drug combinations. IEEE Trans Biomed Eng 60(11):3248–3255

    Article  PubMed  Google Scholar 

  • Paydarfar D, Forger DB, Clay JR (2006) Noisy inputs and the induction of on–off switching behavior in a neuronal pacemaker. J Neurophysiol 96(6):3338–3348

    Article  PubMed  Google Scholar 

  • Pontryagin LS, Boltyanskii V, Gamkrelidze R, Mishchenko E (1962) Mathematical theory of optimal processes. Wiley, New York

    Google Scholar 

  • Prugel-Bennett A (2004) When a genetic algorithm outperforms hill-climbing. Theor Comput Sci 320:135–153

    Article  Google Scholar 

  • Rao AV (2009) A survey of numerical methods for optimal control. Adv Astronaut Sci 135(1):497–528

    Google Scholar 

  • Ross P, Corne D (1995) Comparing genetic algorithms, simulated annealing, and stochastic hillclimbing on timetabling problems. In: AISB workshop on evolutionary computing, pp 94–102

  • Sengupta B, Stemmler MB (2014) Power consumption during neuronal computation. Proc IEEE 102(5):738–750

    Article  Google Scholar 

  • Shahriari B, Swersky K, Wang Z, Adams RP, Freitas ND (2015) Taking the human out of the loop: a review of Bayesian optimization. Proc IEEE 104(1):1–24

    Google Scholar 

  • Shan S, Wang GG (2010) Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions. Struct Multidiscip Optim 41(2):219–241

    Article  Google Scholar 

  • Silver D, Huang A, Maddison CJ, Guez A, Sifre L, Van Den Driessche G, Schrittwieser J, Antonoglou I, Panneershelvam V, Lanctot M, Dieleman S, Grewe D, Nham J, Kalchbrenner N, Sutskever I, Lillicrap T, Leach M, Kavukcuoglu K, Graepel T, Hassabis D (2016) Mastering the game of Go with deep neural networks and tree search. Nature 529(7587):484–489

    Article  CAS  PubMed  Google Scholar 

  • Silver D, Schrittwieser J, Simonyan K, Antonoglou I, Huang A, Guez A, Hubert T, Baker L, Lai M, Bolton A, Chen Y, Lillicrap T, Hui F, Sifre L, Van Den Driessche G, Graepel T, Hassabis D (2017) Mastering the game of Go without human knowledge. Nature 550(7676):354–359

    Article  CAS  Google Scholar 

  • Spall JC (2003) Introduction to stochastic search and optimization: estimation, simulation, and control. Wiley, Hoboken

    Book  Google Scholar 

  • Stillings D (1974) A survey of the history of electrical stimulation for pain to 1900. Med Instrum 9:255–259

    Google Scholar 

  • Sun FT, Morrell MJ, Wharen RE (2008) Responsive cortical stimulation for the treatment of epilepsy. Neurotherapeutics 5(1):68–74

    Article  PubMed  PubMed Central  Google Scholar 

  • Tzafriri AR, Lerner EI, Flashner-Barak M, Hinchcliffe M, Ratner E, Parnas H (2005) Mathematical modeling and optimization of drug delivery from intratumorally injected microspheres. Clin Cancer Res 11(2 I):826–834

    CAS  PubMed  Google Scholar 

  • van Maanen MA, Vervoordeldonk MJ, Tak PP (2009) The cholinergic anti-inflammatory pathway: towards innovative treatment of rheumatoid arthritis. Nat Rev Rheumatol 5:229–232

    Article  PubMed  CAS  Google Scholar 

  • von Stryk O, Bulirsch R (1992) Direct and indirect methods for trajectory optimization. Ann Oper Res 37(1):357–373

    Article  Google Scholar 

  • Wilson D, Moehlis J (2014) Optimal chaotic desynchronization for neural populations. SIAM J Appl Dyn Syst 13(1):276–305

    Article  Google Scholar 

  • Wilson D, Moehlis J (2016) Toward a more efficient implementation of antifibrillation pacing. PLoS ONE 11(7):1–28

    CAS  Google Scholar 

  • Wong PK, Yu F, Shahangian A, Cheng G, Sun R, Ho CM (2008) Closed-loop control of cellular functions using combinatory drugs guided by a stochastic search algorithm. Proc Natl Acad Sci 105(13):5105–5110

    Article  CAS  PubMed  Google Scholar 

  • Wongsarnpigoon A, Grill WM (2010) Energy-efficient waveform shapes for neural stimulation revealed with a genetic algorithm. J Neural Eng 7(4):1–20

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Clayton Foundation for Research and NIH R01 GM104987.

Author information

Authors and Affiliations

  1. Department of Neurology, Dell Medical School, The University of Texas at Austin, Austin, TX, 78701, USA

    Joshua Chang & David Paydarfar

  2. The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, 78701, USA

    David Paydarfar

Authors
  1. Joshua Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Paydarfar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joshua Chang.

Additional information

Communicated by Peter J. Thomas.

This article belongs to the Special Issue on Control Theory in Biology and Medicine. It derived from a workshop at the Mathematical Biosciences Institute, Ohio State University, Columbus, OH, USA.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chang, J., Paydarfar, D. Optimizing stimulus waveforms for electroceuticals. Biol Cybern 113, 191–199 (2019). https://doi.org/10.1007/s00422-018-0774-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-018-0774-x

Keywords

Search

Navigation