On the mathematical modelling of pain

Neurochemical Research

Volumn 21, Issue 9, 1996, Pages 1133-1140

  Britton, Nicholas F ^a   Skevington, Suzanne M ^b  

^a UNIVERSITY OF BATH   (United Kingdom)

^b University of Bath   (United Kingdom)

Author keywords

computational neuroscience; mathematical modelling; neural networks; Pain; plasticity

Indexed keywords

ARTICLE; MATHEMATICAL MODEL; NERVE CELL PLASTICITY; NOCICEPTION; PAIN; PRIORITY JOURNAL;

ANALGESIA; ANIMALS; AXONS; HUMANS; MODELS, NEUROLOGICAL; MODELS, THEORETICAL; NERVE NET; NEURONAL PLASTICITY; NEURONS; PAIN; REPRODUCIBILITY OF RESULTS;

EID: 0029823630     PISSN: 03643190     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02532424     Document Type: Article

References (53)

1. Verrill, P. 1990. Does the gate control theory of pain supplant all others? Br. J. Hosp. Med. 43:325.
2. Arbib, M. A. 1995. Handbook of Brain Theory and Neural Networks. MIT Press, Cambridge Mass.
3. Bower, J. M., and Beeman, D. 1995. The Book of Genesis. Springer, New York.
4. Eeckman, F. H., and Bower, J. M. (eds). 1993. Computation and Neural Systems. Kluwer, Boston, Mass.
5. Koch, C. and Segev, I. (eds). 1989. Methods in Neuronal Modelling. MIT Press Cambridge Mass.
6. Koch, C., and Poggio, T. 1987. Biophysics of computation; neurons, synapses and membranes. In Edelman, G. M., Gall, W. E. and Cowan, W. M. (eds). 1987. Synaptic Function. Wiley, New York pp 637-698.
7. Segev, I. 1992. Single neuron models: oversimple, complex and reduced. Trends in Neurosci. 15:414-421.
8. Dubner, R., and Beitel, R. E. 1976. Neural correlates of escape behaviour in rhesus monkeys to noxious heat applied to the face. In Advances in Pain Research and Therapy Vol. 1, eds. J. J. Bonica and D. Albe-Fessard, Raven Press, New York pp 155-160.
9. Price, D. D., Barrell, J. J., and Gracely, R. H. 1980. A psychophysical analysis of experiential factors that selectively influence the affective dimension of pain. Pain 8:137-179.
10. Price, D. D., McGrath, P. A., Rafii, A., and Buckingham, B. 1983. The validation of visual analogue scales as ratio scale measures for chronic and experimental pain. Pain 17:45-56.
11. Price, D. D., and Harkins, S. W. 1987. The combined use of visual analogue scales and experimental pain in proving standardised assessment of clinical pain. Clin. J. Pain 3:1-8.
12. 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. 117:500-544.
13. Rinzel, J. 1990. Electrical excitability of cells, theory and experiment: review of the Hodgkin-Huxley foundation. Bull. Math. Biol. 52:5-23.
14. Nelson M., and Rinzel J. 1995. The Hodgkin-Huxley model. Bower J. and Beeman, D. (eds) The Book of Genesis. Springer, New York, Chapter 4, pp 29-52.
15. Davies, S. N., and Lodge, D. 1987. Evidence for the involvement of N-methyl-D-aspartate receptors in 'wind-up' of class 2 neurones in the dorsal horn of the rat. Brain Res. 424:402-406.
16. Dickenson, A. H., and Sullivan, A. F. 1987. Evidence for a role of the NMDA receptors in the frequency-dependent potentiation of deep dorsal horn neurons following C-fibre stimulation. Neuropharmacol. 26:1235-1238.
17. Thompson, S. W. N., and Woolf, C. J. 1991. Primary afferent-evoked prolonged potentials in the spinal cord and their central summation: role of the NMDA receptor. In Proc of the VIth World Congress on Pain, Adelaide. Eds M. R. Bond, J. E. Charlton and C. J. Woolf, Elsevier, Amsterdam.
18. Woolf, C. J., and Thompson, S. W. N. 1991. The induction and maintenance of central sensitisation is dependent on N-methyl-D-aspartic acid receptor activation; implications for the treatment of post-injury pain hypersensitivity states, Pain 44:293-300.
19. Mendell, L. M. 1966. Physiological properties of unmyelinated fibre projections to the spinal cord. Exp. Neurol., 16:316-32.
20. Wilcox, G. L. 1991. Excitatory neurotransmitters and pain. In Proc. of the VIth World Congress on Pain, Adelaide. Eds M. R. Bond, J. E. Charlton and C. J. Woolf, Elsevier, Amsterdam, 97-117.
21. Randall, A. D., Schofield, J. G., and Collingridge, G. L. 1990. Whole-cell, patch-clamp recordings of an NMDA receptor-mediated synaptic current in rat hippocampal slices. Neurosci. Lett. 114:191-196.
22. Watkins, J. C., and Collingridge, G. L. 1989. The NMDA Receptor, Oxford University Press, Oxford.
23. Zador, A., Koch, C., and Brown, T. H. 1990. Biophysical model of a Hebbian receptor channel kinetic behaviour. Proc. Nat. Acad. Sci. USA, 10:6718-0722.
24. 31P-Nuclear Magnetic Resonance Spectroscopy. Journal of Neurochemistry, 55(4):1446-1449.
25. McCulloch, W. S., and Pitts, W. 1943. A logical calculus of ideas immanent in nervous activity. Bull. Math. Biophys. 5:115-133.
26. Traub, R. D., Wong, R. K. F., Miles, R., and Michelson, H. 1991. A model of a CA3 hippocampal neurone incorporating voltage clamp data on intrinsic conductances. J. Neurophysiol. 66:635-650.
27. Bachelard, H. S., Morris, P., Taylor, A., and Thatcher, N. 1995. High field MRS studies in brain slices. Magnetic Resonance Imaging 13(8):1223-1226.
28. Fors, U. G. H., Ahlquist, M., Skagerwall, R., Edwall, L., and Haegerstam, G. 1984. Relation between intradental nerve activity and estimated pain in man - a mathematical analysis. Pain 18: 397-408.
29. Fors, U., Ahlquist, M., Edwall, L., and Haegerstam, G. 1986. An evaluation of the usefulness of a mathematical model analyzing the relation between intradental nerve impulse activity and perceived pain in man. International Journal of Biomedical Computing 19:261-277.
30. Fors, U. G. H., Edwall, L. G. A., Haegerstam, G. A. T. 1988. The ability of a mathematical model to evaluate the effects of two pain modulating procedures on pulpal pain in man. Pain 33(2):253-264.
31. Britton, N. F., and Skevington, S. M. 1989. A mathematical model of the Gate Control theory of pain. Journal of Theoretical Biology 137:91-105.
32. Britton, N. F., Chaplain, M. A. J., and Skevington, S. M. 1996. The role of NMDA receptors in painful wind-up: mathematical model. IMA Journal of Maths Appl Med Biol. In press.
33. Melzack, R., and Wall, P. D. 1965. Pain mechanisms: a new theory, Science, 150:971-979.
34. Melzack, R., and Wall, P. D. 1982. The Challenge of Pain, Penguin, Harmondsworth, Middlesex, UK.
35. Nathan, P. W., and Rudge, P. 1974. Testing the gate control theory of pain in man. Journal of Neurology, Neurosurgery and Psychiatry 37:1366-1372.
36. McQuay, H., Carroll, D., and Moore, R. A. 1988. Post-operative orthopaedic pain - the effect of opiate pre-medication and local anaesthetic blocks. Pain 33(3):79-87.
37. Bach, S., Noreng, M. F., and Tjellden, N. U. 1988. Phantom limb pain in amputees during their first 12 months following limb amputation after preoperative lumbar epidural blockade. Pain 33: 297-301.
38. Humphries, S. A., Johnson, M. H., and Long, N. R. 1993. An investigation of the Gate Control theory of pain by ramping-off the experimental pain stimulus of potassium iontophoresis. Abstracts of the 7th World Congress on Pain, Paris, Abs. 1261, International Association for the Study of Pain.
39. Ermentrout, G. B., and Cowan, J. D. 1979. A mathematical theory of visual hallucination patterns. Biol. Cybernetics, 34:137-150.
40. Hillman, P. and Wall, P. D. 1969. Inhibitory and excitatory factors influencing the receptive fields of lamina 5 spinal cord cells. Exp. Brain Res. 9:284-306.
41. Price, D. D. 1988. Psychological and Neural Mechanisms of Pain, Raven Press, New York.
42. Bachelard, H. S., and Badar-Goffer, R. 1993. NMR spectroscopy in neurochemistry. J. Neurochemistry, 61(2):412-429.
43. Bachelard, H. S. 1988. General neurochemistry. Current Opinion in Neurology and Neurosurgery, 1:1091-1095.
44. Hsieh, J. C., Belfrage, M., Stone-Elander, S., Hansson, P., and Ingvar, M. 1995. Central representation of chronic ongoing neuropathic pain studied by positron emission tomography. Pain 63: 225-236.
45. Wilson, M. A., and Bower, J. M. 1989. The simulation of large scale neural networks. In Koch, C. and Segev, I. (eds) Methods in Neuronal Modelling. MIT Press Cambridge Mass. Chapter 9 pp 291-333.
46. Hebb, D. O. 1949. The Organization of Behaviour, Wiley, New York.
47. Lynch, G. 1986. Synapses, circuits and the beginnings of memory. Bradford Books, M.I.T. Press, Cambridge Mass.
48. Stent, G. S. 1973. A physiological mechanism for Hebb's postulate of learning. Proc. Nat. Acad. Sci. 70:997-1001.
49. Marr, D. 1969. A theory of cerebellar cortex. J. Physiol. 202:437-470.
50. Marr, D. 1971. Simple memory: a theory for archicortex. Phil. Trans. Roy. Soc. B 262:23-81.
51. Woolf, C. J., and Thompson, S. W. N. 1991. Slow potentials, receptive field plasticity and pain. In Information Processing in the Somatosensory System. Eds O. Franzen and J. Westman, Macmillan, Chapter 32, 427-437.
52. Campbell, J. N., and Meyer, R. A. 1991. Plasticity of the neural events related to pain. In Information Processing in the Somatosensory System. Eds O. Franzen and J. Westman, Macmillan, Chapter 33, 439-451.
53. Sternbach, R. A. 1983. Ethical considerations in pain research in man. Pages 259-266, in R. Melzack, (ed). Pain Measurement and Assessment, Raven Press, New York.