Abstract
Researchers have been studying the pain sensation extensively in the past few decades. Quantitative simulation and theoretical modeling of pain sensation based on experimental results are necessary for pain research. Many theories have been proposed to explain the mechanism of pain from molecular, cellular, and neuron network perspectives. But some phenomena in pain sensation are not fully understood, including wind-up and ramp-off. This paper focused on the theoretical model of wind-up and ramp-off phenomena in the pain sensation. With the addition of the transduction model, the generation mechanism of wind-up and ramp-off is better explained. The simulations were carried out to analyze the skin pain sensation under the mechanical stimulus, consisting of four different parts: the mechanical model of skin, transduction, transmission, modulation, and perception. The stress distribution on the skin was obtained based on the elastic theory. And the modified Hodgkin and Huxley model and the mathematical model of gate control theory were utilized to analyze the process of transduction, modulation, and perception, respectively. The numerical experiments demonstrated the wind-up occurs with a frequent stimulus of 1 Hz and 2 Hz, and ramp-off appears with the withdrawal of constant mechanical stimulus, which could contribute to the understanding of the pain sensation mechanism.
References
1.
Raja
, S. N.
, Carr
, D. B.
, Cohen
, M.
, Finnerup
, N. B.
, Flor
, H.
, Gibson
, S.
, Keefe
, F. J.
, et al, 2020
, “The Revised International Association for the Study of Pain Definition of Pain: Concepts, Challenges, and Compromises
,” Pain
, 161
(9
), pp. 1976
–1982
. 2.
Lang
, V. A.
, Lundh
, T.
, and Ortiz-Catalan
, M.
, 2021
, “Mathematical and Computational Models for Pain: A Systematic Review
,” Pain Med.
, 22
(12
), pp. 2806
–2817
. 3.
Woolf
, C. J.
, 2010
, “What Is This Thing Called Pain?
,” J. Clin. Invest.
, 120
(11
), pp. 3742
–3744
. 4.
Colloca
, L.
, Ludman
, T.
, Bouhassira
, D.
, Baron
, R.
, Dickenson
, A. H.
, Yarnitsky
, D.
, Freeman
, R.
, et al, 2017
, “Neuropathic Pain
,” Nat. Rev. Dis. Primer
, 3
(1
), p. 17002
. 5.
Murnion
, B. P.
, 2018
, “Neuropathic Pain: Current Definition and Review of Drug Treatment
,” Aust. Prescr.
, 41
(3
), pp. 60
–63
. 6.
Dubin
, A. E.
, and Patapoutian
, A.
, 2010
, “Nociceptors: The Sensors of the Pain Pathway
,” J. Clin. Invest.
, 120
(11
), pp. 3760
–3772
. 7.
Koltzenburg
, M.
, 2000
, “Neural Mechanisms of Cutaneous Nociceptive Pain
,” Clin. J. Pain
, 16
(3 Suppl
), pp. S131
–S138
. 8.
Zhu
, Y. J.
, and Lu
, T. J.
, 2010
, “A Multi-scale View of Skin Thermal Pain: From Nociception to Pain Sensation
,” Philos. Trans. R. Soc. Math. Phys. Eng. Sci.
, 368
(1912
), pp. 521
–559
. 9.
Goldscheider
, A.
, 1894
, Ueber den Schmerz in Physiologischer und Klinischer Hinsicht: Nach Einem Vortrage in der Berliner Militärärztlichen Gesellschaft
, Verlag von August Hirschwald
, Berlin
.10.
Melzack
, R.
, and Wall
, P. D.
, 1965
, “Pain Mechanisms: A New Theory
,” Science
, 150
(3699
), pp. 971
–979
. 11.
Britton
, N. F.
, and Skevington
, S. M.
, 1989
, “A Mathematical Model of the Gate Control Theory of Pain
,” J. Theor. Biol.
, 137
(1
), pp. 91
–105
. 12.
Britton
, N. F.
, Chaplain
, M. A. J.
, and Skevtngtonj
, S. M.
, 1996
, “The Role of N-Methyl-D-Aspartate (NMDA) Receptors in Wind-Up: A Mathematical Model
,” IMA J. Math. Appl. Med. Biol.
, 13
(3
), pp. 193
–205
.13.
Britton
, N.
, Skevington
, S.
, and Chaplain
, M.
, 1995
, “Mathematical Modelling of Acute Pain
,” J. Biol. Syst.
, 3
(04
), pp. 1119
–1124
. 14.
Britton
, N. F.
, and Skevington
, S. M.
, 1996
, “On the Mathematical Modelling of Pain
,” Neurochem. Res.
, 21
(9
), pp. 1133
–1140
. 15.
Prince
, K.
, Campbell
, J.
, Picton
, P.
, and Turner
, S.
, 2005
, “A Computational Model of Acute Pain
,” Int. J. Simul. Syst. Sci. Technol.
, 6
(9
), p. 11
.16.
Xu
, F.
, Wen
, T.
, Lu
, T. J.
, and Seffen
, K. A.
, 2008
, “Modeling of Nociceptor Transduction in Skin Thermal Pain Sensation
,” ASME J. Biomech. Eng.
, 130
(4
), p. 041013
. 17.
Xu
, F.
, Lu
, T. J.
, and Seffen
, K. A.
, 2008
, “Skin Thermal Pain Modeling—A Holistic Method
,” J. Therm. Biol.
, 33
(4
), pp. 223
–237
. 18.
Xu
, F.
, Wen
, T.
, Seffen
, K.
, and Lu
, T.
, 2008
, “Modeling of Skin Thermal Pain: A Preliminary Study
,” Appl. Math. Comput.
, 205
(1
), pp. 37
–46
. 19.
Xu
, F.
, Lu
, T. J.
, and Seffen
, K. A.
, 2008
, “Biothermomechanics of Skin Tissues
,” J. Mech. Phys. Solids
, 56
(5
), pp. 1852
–1884
. 20.
Yin
, Y.
, Li
, M.
, Li
, Y.
, and Song
, J.
, 2020
, “Skin Pain Sensation of Epidermal Electronic Device/Skin System Considering Non-Fourier Heat Conduction
,” J. Mech. Phys. Solids
, 138
, p. 103927
. 21.
Hodgkin
, A. L.
, and Huxley
, A. F.
, 1952
, “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve
,” J. Physiol.
, 117
(4
), pp. 500
–544
. 22.
Hodgkin
, A. L.
, and Huxley
, A. F.
, 1952
, “Currents Carried by Sodium and Potassium Ions Through the Membrane of the Giant Axon of Loligo
,” J. Physiol.
, 116
(4
), pp. 449
–472
. 23.
Haeri
, M.
, Asemani
, D.
, and Gharibzadeh
, S.
, 2003
, “Modeling of Pain Using Artificial Neural Networks
,” J. Theor. Biol.
, 220
(3
), pp. 277
–284
. 24.
Minamitani
, H.
, and Hagita
, N.
, 1981
, “A Neural Network Model of Pain Mechanisms: Computer Simulation of the Central Neural Activities Essential for the Pain and Touch Sensations
,” IEEE Trans. Syst. Man Cybern.
, 11
(7
), pp. 481
–493
. 25.
Herrero
, J.
, Laird
, J. M. A
, and Lopez-Garcia
, J. A.
, 2000
, “Wind-Up of Spinal Cord Neurones and Pain Sensation: Much Ado About Something?
,” Prog. Neurobiol.
, 61
(2
), pp. 169
–203
. 26.
Magerl
, W.
, Wilk
, S. H.
, and Treede
, R.-D.
, 1998
, “Secondary Hyperalgesia and Perceptual Wind-Up Following Intradermal Injection of Capsaicin in Humans
,” Pain
, 74
(2–3
), pp. 257
–268
. 27.
Staud
, R.
, Vierck
, C. J.
, Cannon
, R. L.
, Mauderli
, A. P.
, and Price
, D. D.
, 2001
, “Abnormal Sensitization and Temporal Summation of Second Pain (Wind-Up) in Patients With Bromyalgia Syndrome
,” Pain
, 91
(1–2
), pp. 165
–175
. 28.
Humphries
, S. A.
, Johnson
, M. H.
, and Long
, N. R.
, 1996
, “An Investigation of the Gate Control Theory of Pain Using the Experimental Pain Stimulus of Potassium Iontophoresis
,” Percept. Psychophys.
, 58
(5
), pp. 693
–703
. 29.
Brooks
, J.
, and Tracey
, I.
, 2005
, “REVIEW: From Nociception to Pain Perception: Imaging the Spinal and Supraspinal Pathways: Imaging the Spinal and Supraspinal Pathways, J. Brooks and I. Tracey
,” J. Anat.
, 207
(1
), pp. 19
–33
. 30.
Julius
, D.
, and Basbaum
, A. I.
, 2001
, “Molecular Mechanisms of Nociception
,” Nature
, 413
(6852
), pp. 203
–210
. 31.
Vexler
, A.
, Polyansky
, I.
, and Gorodetsky
, R.
, 1999
, “Evaluation of Skin Viscoelasticity and Anisotropy by Measurement of Speed of Shear Wave Propagation With Viscoelasticity Skin Analyzer1
,” J. Invest. Dermatol.
, 113
(5
), pp. 732
–739
. 32.
Gahagnon
, S.
, Mofid
, Y.
, Josse
, G.
, and Ossant
, F.
, 2012
, “Skin Anisotropy in Vivo and Initial Natural Stress Effect: A Quantitative Study Using High-Frequency Static Elastography
,” J. Biomech.
, 45
(16
), pp. 2860
–2865
. 33.
Joodaki
, H.
, and Panzer
, M. B.
, 2018
, “Skin Mechanical Properties and Modeling: A Review
,” Proc. Inst. Mech. Eng. H
, 232
(4
), pp. 323
–343
. 34.
Thieulin
, C.
, Pailler-Mattei
, C.
, Abdouni
, A.
, Djaghloul
, M.
, and Zahouani
, H.
, 2020
, “Mechanical and Topographical Anisotropy for Human Skin: Ageing Effect
,” J. Mech. Behav. Biomed. Mater.
, 103
, p. 103551
. 35.
Rosicka
, K.
, Hill
, M.
, and Wdowski
, M. M.
, 2021
, “Skin Anisotropy: Finding the Optimal Incision Line for Volar Forearm in Males and Females
,” J. Mech. Behav. Biomed. Mater.
, 124
, p. 104805
. 36.
Birznieks
, I.
, Jenmalm
, P.
, Goodwin
, A. W.
, and Johansson
, R. S.
, 2001
, “Encoding of Direction of Fingertip Forces by Human Tactile Afferents
,” J. Neurosci.
, 21
(20
), pp. 8222
–8237
. 37.
Moy
, G.
, Singh
, U.
, Tan
, E.
, and Fearing
, R. S.
, 2000
, “Human Psychophysics for Teletaction System Design
,” IEEE Trans. Haptics
, 1
(3
), p. 20
. http://hdl.handle.net/1773/3488138.
Timoshenko
, S.
, and Goodier
, J. N.
, 1970
, The Theory of Elasticity
, 3rd ed., McGraw-Hill
, New York
.39.
Li
, J.
, and Chou
, T.-W.
, 1997
, “Elastic Field of a Thin-Film/Substrate System Under an Axisymmetric Loading
,” Int. J. Solids Struct.
, 34
(35–36
), pp. 4463
–4478
. 40.
Yang
, F.
, 2003
, “Thickness Effect on the Indentation of an Elastic Layer
,” Mater. Sci. Eng. A
, 358
(1–2
), pp. 226
–232
. 41.
Connor
, J. A.
, Walter
, D.
, and McKown
, R.
, 1977
, “Neural Repetitive Firing: Modifications of the Hodgkin-Huxley Axon Suggested by Experimental Results From Crustacean Axons
,” Biophys. J.
, 18
(1
), pp. 81
–102
. 42.
Cain
, D. M.
, Khasabov
, S. G.
, and Simone
, D. A.
, 2001
, “Response Properties of Mechanoreceptors and Nociceptors in Mouse Glabrous Skin: An In Vivo Study
,” J. Neurophysiol.
, 85
(4
), pp. 1561
–1574
. 43.
Slugg
, R.
, Meyer
, R.
, and Campbell
, J.
, 2000
, “Response of Cutaneous A-and C-Fiber Nociceptors in the Monkey to Controlled-Force Stimuli
,” J. Neurophysiol.
, 83
(4
), pp. 2179
–2191
. 44.
Slugg
, R. M.
, Campbell
, J. N.
, and Meyer
, R. A.
, 2004
, “The Population Response of A-and C-Fiber Nociceptors in Monkey Encodes High-Intensity Mechanical Stimuli
,” J. Neurosci.
, 24
(19
), pp. 4649
–4656
. 45.
Van Hees
, J.
, and Gybels
, J.
, 1981
, “C Nociceptor Activity in Human Nerve During Painful and Non Painful Skin Stimulation
,” J. Neurol. Neurosurg. Psychiatry
, 44
(7
), pp. 600
–607
. Copyright © 2022 by ASME
You do not currently have access to this content.
