Mathematical modeling of the brain: Principles and challenges

Neurosurgery

Volumn 62, Issue 5, 2008, Pages 1146-1156

  Tenti, Giuseppe ^a   Sivaloganathan, Siv ^a,b   Drake, James M ^c  

^a UNIVERSITY OF WATERLOO   (Canada)

^b FIELDS INSTITUTE   (Canada)

^c HOSPITAL FOR SICK CHILDREN   (Canada)

Author keywords

Brain biomechanics; Cerebrospinal fluid dynamics; Hydrocephalus; Mathematical modeling

Indexed keywords

ARTICLE; BRAIN BLOOD FLOW; ELECTRICAL POTENTIAL PARAMETERS; HYDROCEPHALUS; MATHEMATICAL MODEL; MEDICAL RESEARCH; OUTCOME ASSESSMENT; PRIORITY JOURNAL; TONOMETRY; ANIMAL; BRAIN; HUMAN; PHYSIOLOGY; REVIEW; THEORETICAL MODEL;

ANIMALS; BRAIN; HUMANS; MODELS, THEORETICAL;

EID: 49049090222     PISSN: 0148396X     EISSN: None     Source Type: Journal    
DOI: 10.1227/01.neu.0000325877.67752.0f     Document Type: Article

References (33)

1. Goldstein SR, Salcman M: Mechanical factors in the design of chronic recording intracortical microelectrodes. IEEE Trans Biomed Eng BME 20:260-269, 1973.
2. Legendy CR, Salcman M: Bursts and recurrences of bursts in the spike trains of spontaneously active striate cortex neurons. J Neurophysiol 53:926-939, 1985.
3. Salcman M: Probability and the brain. Neurosurgery 4:75-82, 1979.
4. Salcman M, Corradino G, Moriyama E, Gettleman RA, Elsner H, Rossman H, Neuberth G: Cerebral blood flow and the thermal properties of the brain: A preliminary analysis. J Neurosurg 70:592-598, 1989.
5. ABAQUS, version 6.3, User's Manual. Pawtucket, Hibbit, Karlsson, and Sorensen, Inc., 2002, vol 2.
6. Biot MA: General theory of three-dimensional consolidation. J Appl Physics 12:155-164, 1941.
7. Bland DR: The Theory of Linear Viscoelasticity. New York, Pergamon Press, 1960.
8. Den Hartog JP: Mechanical Vibrations. New York, Dover Publications, 1956, ed 4.
9. Drake JM, Kestle JR, Milner R, Cinalli G, Boop F, Piatt J Jr, Haines S, Schiff SJ, Cochrane DD, Steinbok P, MacNeil N: Randomized trial of cerebrospinal fluid shunt valve design in pediatric hydrocephalus. Neurosurgery 43:294-305, 1998.
10. Drake JM, Sainte-Rose C: Shunt Book. New York, Blackwell Science Publications Ltd, 1995.
11. Egnor M, Rosiello A, Zheng L: A model of intracranial pulsations. Pediatr Neurosurg 35:284-298, 2001.
12. Egnor M, Wagshul M, Zheng L, Rosiello A: Resonance and synchrony of arterial and CSF pulsations. Pediatr Neurosurg 38:273-276, 2003.
13. Feynman RP: The Character of Physical Laws. Cambridge, The MIT Press, 1965, p 37.
14. Feynman RP: The Feynman Lectures on Physics. Boston, Addison-Wesley, 1963, vol 1, pp 1-2.
15. Frank O: The basic form of arterial pulses [in German]. Machematische Analyse Z Biol 37:483-526, 1899.
16. Fung YC: Biomechanics: Mechanical Properties of Living Tissues. New York, Springer, 1993, ed 2.
17. Klekamp J: The pathophysiology of syringomyelia: Historical overview and current concept. Acta Neurochir (Wien) 144:649-664, 2002.
18. Kyriacou SK, Mohamed A, Miller K, Neff S: Brain mechanics for neuro-surgery: Modeling issues. Biomech Model Mechanobiol 1:151-164, 2002.
19. Lambermont B, Gérard P, Detry O, Kohl P, Potty P, Defraigne JO, D'Orio V, Marcelle R: Comparison between three- and four-element windkessel models to characterize vascular properties of pulmonary circulation. Arch Physiol Biochem 105:625-632, 1997.
20. Lanczos C: Applied Analysis. New York, Dover Publications, 1988, pp 276-279.
21. Lighthill MJ: Physics of gas flows at very high speeds. Nature 178:343, 1956, pp 343-345.
22. Linninger AA, Tsakiris C, Zhu DC, Xenos M, Roycewicz P, Danziger Z, Penn R: Pulsatile cerebrospinal fluid dynamics in the human brain. IEEE Trans Biomed Eng 52:557-565, 2005.
23. Olufsen MS, Nadim A, Lipsitz LA: Dynamics of cerebral blood flow regulation explained using a lumped parameter model. Am J Physiol Regul Integr Comp Physiol 282:R611-R622, 2002.
24. Prandtl L, Tietjens OG: Fundamentals of Hydro- and Aeromechanics. New York, Dover Publications, 1934.
25. Sivaloganathan S, Tenti G, Drake JM: Mathematical pressure volume models of the cerebrospinal fluid. Appl Math Comp 94:243-266, 1998.
26. Smillie A, Sobey I, Molnar Z: A hydro-elastic model of hydrocephalus. J Fluid Mech 539:417-443, 2005.
27. Stastna M, Tenti G, Sivaloganathan S, Drake JM: Brain biomechanics: Consolidation theory of hydrocephalus. Variable permeability and transient effects. Can Appl Math Q 7:111-124, 1999.
28. Stergiopulos N, Westerhof BE, Westerhof N: Total arterial inertance as the fourth element of the windkessel model. Am J Physiol 276:H81-H88, 1999.
29. Tenti G, Drake JM, Sivaloganathan S: Brain biomechanics: Mathematical modeling of hydrocephalus. Neurol Res 22:19-24, 2000.
30. Tenti G, Sivaloganathan S, Drake JM: Brain biomechanics: Steady-state consolidation theory of hydrocephalus. Can Appl Math Q 7:93-110, 1999.
31. Tenti G, Sivaloganathan S, Drake JM: The synchrony of arterial and CSF pulsations is not due to resonance. Pediatr Neurosurg 37:221-222, 2002.
32. Toy SM, Melbin J, Noordergraaf A: Reduced models of arterial systems. IEEE Trans Biomed Eng 32:174-176, 1985.
33. Truesdell C, Muncaster RG: Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas. New York, Academic Press, 1980, p xvi.