Sleep Medicine Reviews
Volume 13, Issue 5 , Pages 333-343 , October 2009

Understanding sleep-disordered breathing through mathematical modelling

  • Tero Aittokallio

      Affiliations

    • Biomathematics Research Group, Department of Mathematics, University of Turku, FI-20014 Turku, Finland
    • Sleep Research Unit, Department of Physiology, University of Turku, FI-20520 Turku, Finland
    • Corresponding Author InformationCorresponding author. Department of Mathematics, University of Turku, FI-20014 Turku, Finland. Tel.: +358 2 333 6030; fax: +358 2 333 6595.
  • ,
  • Arho Virkki

      Affiliations

    • Biomathematics Research Group, Department of Mathematics, University of Turku, FI-20014 Turku, Finland
    • Sleep Research Unit, Department of Physiology, University of Turku, FI-20520 Turku, Finland
  • ,
  • Olli Polo

      Affiliations

    • Sleep Research Unit, Department of Physiology, University of Turku, FI-20520 Turku, Finland
    • Department of Pulmonary Medicine, Tampere University Hospital, FI-33521 Tampere, Finland

References* 

  1. Young T, Peppard PE, Gottlieb DJ. Epidemiology of obstructive sleep apnea: a population health perspective. Am J Respir Crit Care Med. 2002;165:1217–1239
  2. Hiestand DM, Britz P, Goldman M, Phillips B. Prevalence of symptoms and risk of sleep apnea in the US population: results from the national sleep foundation sleep in America 2005 poll. Chest. 2006;130:780–786
  3. Shahar E, Whitney CW, Redline S, Lee ET, Newman AB, Javier Nieto F, et al. Sleep-disordered breathing and cardiovascular disease: cross-sectional results of the Sleep Heart Health Study. Am J Respir Crit Care Med. 2001;163:19–25
  4. Marin JM, Carrizo SJ, Vicente E, Agusti AG. Long-term cardiovascular outcomes in men with obstructive sleep apnoea-hypopnoea with or without treatment with continuous positive airway pressure: an observational study. Lancet. 2005;365:1046–1053
  5. Gozal D, Kheirandish-Gozal L. Cardiovascular morbidity in obstructive sleep apnea: oxidative stress, inflammation, and much more. Am J Respir Crit Care Med. 2008;177:369–375
  6. Vgontzas AN, Bixler EO, Chrousos GP. Sleep apnea is a manifestation of the metabolic syndrome. Sleep Med Rev. 2005;9:211–224
  7. Redline S, Storfer-Isser A, Rosen CL, Johnson NL, Kirchner HL, Emancipator J, et al. Association between metabolic syndrome and sleep-disordered breathing in adolescents. Am J Respir Crit Care Med. 2007;176:401–408
  8. Seicean S, Kirchner HL, Gottlieb DJ, Punjabi NM, Resnick H, Sanders M, et al. Sleep-disordered breathing and impaired glucose metabolism in normal-weight and overweight/obese individuals: the Sleep Heart Health Study. Diabetes Care. 2008;31:1001–1006
  9. Halbower AC, Mahone EM. Neuropsychological morbidity linked to childhood sleep-disordered breathing. Sleep Med Rev. 2006;10:97–107
  10. Mitchell GS, Douse MA, Foley KT. Receptor interactions in modulating ventilatory activity. Am J Physiol. 1990;259:R911–R920
  11. Cherniack NS. Sleep apnea and its causes. J Clin Invest. 1984;73:1501–1506
  12. Malhotra A, White DP. Obstructive sleep apnoea. Lancet. 2002;360:237–245
  13. Cherniack NS. Apnea and periodic breathing during sleep. N Engl J Med. 1999;341:985–987
  14. Cherniack NS, Longobardo GS. Mathematical models of periodic breathing and their usefulness in understanding cardiovascular and respiratory disorders. Exp Physiol. 2006;91:295–305
  15. Marini JJ, Crooke PS. A general mathematical model for respiratory dynamics relevant to the clinical setting. Am Rev Respir Dis. 1993;147:14–24
  16. Hota S, Crooke PS, Adams AB, Hotchkiss JR. Optimal phasic tracheal gas insufflation timing: an experimental and mathematical analysis. Crit Care Med. 2006;34:1408–1414
  17. Dempsey JA, Skatrud JB, Jacques AJ, Ewanowski SJ, Woodson BT, Hanson PR, et al. Anatomic determinants of sleep-disordered breathing across the spectrum of clinical and nonclinical male subjects. Chest. 2002;122:840–851
  18. El-Solh AA, Mador MJ, Ten-Brock E, Shucard DW, Abul-Khoudoud M, Grant BJ. Validity of neural network in sleep apnea. Sleep. 1999;22:105–111
  19. Tsai WH, Remmers JE, Brant R, Flemons WW, Davies J, Macarthur C. A decision rule for diagnostic testing in obstructive sleep apnea. Am J Respir Crit Care Med. 2003;167:1427–1432
  20. Hand D, Mannila H, Smyth P. Principles of data mining. London: The MIT Press; 2001;
  21. Longobardo GS, Gothe B, Goldman MD, Cherniack NS. Sleep apnea considered as a control system instability. Respir Physiol. 1982;50:311–333
  22. Khoo MC, Gottschalk A, Pack AI. Sleep-induced periodic breathing and apnea: a theoretical study. J Appl Physiol. 1991;70:2014–2024
  23. Batzel JJ, Kappel F, Timischl-Teschl S. A cardiovascular-respiratory control system model including state delay with application to congestive heart failure in humans. J Math Biol. 2005;50:293–335
  24. Topor ZL, Vasilakos K, Younes M, Remmers JE. Model based analysis of sleep disordered breathing in congestive heart failure. Respir Physiol Neurobiol. 2007;155:82–92
  25. Tehrani FT. A model study of periodic breathing, stability of the neonatal respiratory system, and causes of sudden infant death syndrome. Med Eng Phys. 1997;19:547–555
  26. Batzel JJ, Tran HT. Modeling instability in the control system for human respiration: applications to infant non-REM sleep. Appl Math Comput. 2000;110:1–51
  27. Fowler AC. Mathematical models in the applied sciences. Cambridge: Cambridge University Press; 1997;
  28. Sériès F. Upper airway muscles awake and asleep. Sleep Med Rev. 2002;6:229–242
  29. Isono S, Feroah TR, Hajduk EA, Brant R, Whitelaw WA, Remmers JE. Interaction of cross-sectional area, driving pressure, and airflow of passive velopharynx. J Appl Physiol. 1997;83:851–859
  30. Tamisier R, Pepin JL, Wuyam B, Smith R, Argod J, Levy P. Characterization of pharyngeal resistance during sleep in a spectrum of sleep-disordered breathing. J Appl Physiol. 2000;89:120–130
  31. Mansour KF, Rowley JA, Meshenish AA, Shkoukani MA, Badr MS. A mathematical model to detect inspiratory flow limitation during sleep. J Appl Physiol. 2002;93:1084–1092
  32. Gold AR, Schwartz AR. The pharyngeal critical pressure. The whys and hows of using nasal continuous positive airway pressure diagnostically. Chest. 1996;110:1077–1088
  33. Sforza E, Petiau C, Weiss T, Thibault A, Krieger J. Pharyngeal critical pressure in patients with obstructive sleep apnea syndrome. Clinical implications. Am J Respir Crit Care Med. 1999;159:149–157
  34. Patil SP, Punjabi NM, Schneider H, O'Donnell CP, Smith PL, Schwartz AR. A simplified method for measuring critical pressures during sleep in the clinical setting. Am J Respir Crit Care Med. 2004;170:86–93
  35. Patil SP, Schneider H, Marx JJ, Gladmon E, Schwartz AR, Smith PL. Neuromechanical control of upper airway patency during sleep. J Appl Physiol. 2007;102:547–556
  36. Montserrat JM, Farré R, Navajas D. How to use the nasal pressure in clinical practice. Sleep Med. 2003;4:381–383
  37. Ayappa I, Norman RG, Suryadevara M, Rapoport DM. Comparison of limited monitoring using a nasal-cannula flow signal to full polysomnography in sleep-disordered breathing. Sleep. 2004;27:1171–1179
  38. Farré R, Montserrat JM, Rigau J, Trepat X, Pinto P, Navajas D. Response of automatic continuous positive airway pressure devices to different sleep breathing patterns: a bench study. Am J Respir Crit Care Med. 2002;166:469–473
  39. Aittokallio T, Saaresranta T, Polo-Kantola P, Nevalainen O, Polo O. Analysis of inspiratory flow shapes in patients with partial upper-airway obstruction during sleep. Chest. 2001;119:37–44
  40. Saaresranta T, Aittokallio T, Polo-Kantola P, Helenius H, Polo O. Effect of medroxyprogesterone on inspiratory flow shapes during sleep in postmenopausal women. Respir Physiol Neurobiol. 2003;134:131–143
  41. Aittokallio T, Gyllenberg M, Polo O. A model of a snorer's upper airway. Math Biosci. 2001;170:79–90
  42. Gavriely N, Jensen O. Theory and measurements of snores. J Appl Physiol. 1993;74:2828–2837
  43. Fodil R, Ribreau C, Louis B, Lofaso F, Isabey D. Interaction between steady flow and individualised compliant segments: application to upper airways. Med Biol Eng Comput. 1997;35:638–648
  44. Aittokallio T, Gyllenberg M, Saaresranta T, Polo O. Prediction of inspiratory flow shapes during sleep with a mathematic model of upper airway forces. Sleep. 2003;26:857–863
  45. Trinder J, Kay A, Kleiman J, Dunai J. Gender differences in airway resistance during sleep. J Appl Physiol. 1997;83:1986–1997
  46. Thurnheer R, Wraith PK, Douglas NJ. Influence of age and gender on upper airway resistance in NREM and REM sleep. J Appl Physiol. 2001;90:981–988
  47. Rowley JA, Zhou X, Vergine I, Shkoukani MA, Badr MS. Influence of gender on upper airway mechanics: upper airway resistance and Pcrit. J Appl Physiol. 2001;91:2248–2254
  48. Jordan AS, Wellman A, Edwards JK, Schory K, Dover L, MacDonald M, et al. Respiratory control stability and upper airway collapsibility in men and women with obstructive sleep apnea. J Appl Physiol. 2005;99:2020–2027
  49. Anttalainen U, Saaresranta T, Kalleinen N, Aittokallio J, Vahlberg T, Polo O. Gender differences in age and BMI distributions in partial upper airway obstruction during sleep. Respir Physiol Neurobiol. 2007;159:219–226
  50. Farré R, Rigau J, Montserrat JM, Buscemi L, Ballester E, Navajas D. Static and dynamic upper airway obstruction in sleep apnea: role of the breathing gas properties. Am J Respir Crit Care Med. 2003;168:659–663
  51. Thut DC, Schwartz AR, Roach D, Wise RA, Permutt S, Smith PL. Tracheal and neck position influence upper airway airflow dynamics by altering airway length. J Appl Physiol. 1993;75:2084–2090
  52. Huang Y, White DP, Malhotra A. The impact of anatomic manipulations on pharyngeal collapse: results from a computational model of the normal human upper airway. Chest. 2005;128:1324–1330
  53. Huang Y, Malhotra A, White DP. Computational simulation of human upper airway collapse using a pressure-/state-dependent model of genioglossal muscle contraction under laminar flow conditions. J Appl Physiol. 2005;99:1138–1148
  54. Xu C, Sin S, McDonough JM, Udupa JK, Guez A, Arens R, et al. Computational fluid dynamics modeling of the upper airway of children with obstructive sleep apnea syndrome in steady flow. J Biomech. 2006;39:2043–2054
  55. Shome B, Wang LP, Santare MH, Prasad AK, Szeri AZ, Roberts D. Modeling of airflow in the pharynx with application to sleep apnea. J Biomech Eng. 1998;120:416–422
  56. Huang Y, White DP, Malhotra A. Use of computational modeling to predict responses to upper airway surgery in obstructive sleep apnea. Laryngoscope. 2007;117:648–653
  57. De Backer JW, Vanderveken OM, Vos WG, Devolder A, Verhulst SL, Verbraecken JA, et al. Functional imaging using computational fluid dynamics to predict treatment success of mandibular advancement devices in sleep-disordered breathing. J Biomech. 2007;40:3708–3714
  58. Casati A, Squicciarini G, Malagutti G, Baciarello M, Putzu M, Fanelli A. Transcutaneous monitoring of partial pressure of carbon dioxide in the elderly patient: a prospective, clinical comparison with end-tidal monitoring. J Clin Anesth. 2006;18:436–440
  59. Parker SM, Gibson GJ. Evaluation of a transcutaneous carbon dioxide monitor (“TOSCA”) in adult patients in routine respiratory practice. Respir Med. 2007;101:261–264
  60. Ward S, Chatwin M, Heather S, Simonds AK. Randomised controlled trial of non-invasive ventilation (NIV) for nocturnal hypoventilation in neuromuscular and chest wall disease patients with daytime normocapnia. Thorax. 2005;60:1019–1024
  61. Tkacova R, Niroumand M, LorenziFilho G, Bradley TD. Overnight shift from obstructive to central apneas in patients with heart failure: the role of PCO2 and circulatory delay. Circulation. 2001;103:238–243
  62. Aittokallio J, Virkki A, Aittokallio T, Saaresranta T, Polo-Kantola P, Polo O. Non-invasive respiratory monitoring during wakefulness and sleep in pre- and postmenopausal women. Respir Physiol Neurobiol. 2006;150:66–74
  63. Aittokallio T, Gyllenberg M, Polo O, Toivonen J, Virkki A. Model-based analysis of mechanisms responsible for sleep-induced carbon dioxide differences. Bull Math Biol. 2006;68:315–341
  64. Zenker S, Rubin J, Clermont G. From inverse problems in mathematical physiology to quantitative differential diagnoses. PLoS Comput Biol. 2007;3:e204
  65. Fink M, Batzel JJ, Tran H. A respiratory system model: parameter estimation and sensitivity analysis. Cardiovasc Eng. 2008;8:120–134
  66. Aittokallio T, Gyllenberg M, Polo O, Virkki A. Parameter estimation of a respiratory control model from noninvasive carbon dioxide measurements during sleep. Math Med Biol. 2007;24:225–249
  67. Prabhakar NR, Peng YJ. Peripheral chemoreceptors in health and disease. J Appl Physiol. 2004;96:359–366
  68. Nattie E. Why do we have both peripheral and central chemoreceptors?. J Appl Physiol. 2006;100:9–10
  69. Virkki A, Polo O, Gyllenberg M, Aittokallio T. Can carotid body perfusion act as a respiratory controller?. J Theor Biol. 2007;249:737–748
  70. Smith CA, Chenuel BJ, Henderson KS, Dempsey JA. The apneic threshold during non-REM sleep in dogs: sensitivity of carotid body vs. central chemoreceptors. J Appl Physiol. 2007;103:578–586
  71. Virkki A, Polo O, Saaresranta T, Laapotti-Salo A, Gyllenberg M, Aittokallio T. Overnight features of transcutaneous carbon dioxide measurement as predictors of metabolic status. Artif Intell Med. 2008;42:55–65
  72. Aittokallio J, Polo O, Hiissa J, Virkki A, Toikka J, Raitakari O, et al. Overnight variability in transcutaneous carbon dioxide predicts vascular impairment in women. Exp Physiol. 2008;93:880–891
  73. Huang L, Williams JE. Neuromechanical interaction in human snoring and upper airway obstruction. J Appl Physiol. 1999;86:1759–1763
  74. Aittokallio T, Gyllenberg M, Polo O. Adjustment of the human respiratory system to increased upper airway resistance during sleep. Bull Math Biol. 2002;64:3–28
  75. Longobardo G, Evangelisti CJ, Cherniack NS. Introduction of respiratory pattern generators into models of respiratory control. Respir Physiol Neurobiol. 2005;148:285–301
  76. Longobardo GS, Evangelisti CJ, Cherniack NS. Analysis of the interplay between neurochemical control of respiration and upper airway mechanics producing upper airway obstruction during sleep in humans. Exp Physiol. 2008;93:271–287
  77. Belozeroff V, Berry RB, Khoo MC. Model-based assessment of autonomic control in obstructive sleep apnea syndrome. Sleep. 2003;26:65–73
  78. Fowler AC, McGuinness MJ. A delay recruitment model of the cardiovascular control system. J Math Biol. 2005;51:508–526
  79. Younes M, Ostrowski M, Atkar R, Laprairie J, Siemens A, Hanly P. Mechanisms of breathing instability in patients with obstructive sleep apnea. J Appl Physiol. 2007;103:1929–1941
  80. Cooper VL, Pearson SB, Bowker CM, Elliott MW, Hainsworth R. Interaction of chemoreceptor and baroreceptor reflexes by hypoxia and hypercapnia: a mechanism for promoting hypertension in obstructive sleep apnoea. J Physiol. 2005;568:677–687
  81. Lorenzi-Filho G, Drager LF. Obstructive sleep apnea and atherosclerosis: a new paradigm. Am J Respir Crit Care Med. 2007;175:1219–1221
  82. Caples SM, Wolk R, Somers VK. Influence of cardiac function and failure on sleep-disordered breathing: evidence for a causative role. J Appl Physiol. 2005;99:2433–2439
  83. Arzt M, Young T, Finn L, Skatrud JB, Bradley TD. Association of sleep-disordered breathing and the occurrence of stroke. Am J Respir Crit Care Med. 2005;172:1447–1451
  84. West SD, Nicoll DJ, Stradling JR. Prevalence of obstructive sleep apnoea in men with type 2 diabetes. Thorax. 2006;61:945–950
  85. Riha RL, Diefenbach K, Jennum P, McNicholas WT. For the Management Committee of the COST B26 Action on Sleep Apnoea Syndrome Genetic aspects of hypertension and metabolic disease in the obstructive sleep apnoea-hypopnoea syndrome. Sleep Med Rev. 2008;12:49–63
  86. Lee JC, Weissglas-Volkov D, Kyttälä M, Dastani Z, Cantor RM, Sobel EM, et al. WW-domain-containing oxidoreductase is associated with low plasma HDL-C levels. Am J Hum Genet. 2008;83:180–192
  87. Eberhard P. The design, use, and results of transcutaneous carbon dioxide analysis: current and future directions. Anesth Analg. 2007;105:S48–S52
  88. Aittokallio T, Malminen JS, Pahikkala T, Polo O, Nevalainen OS. Inspiratory flow shape clustering: an automated method to monitor upper airway performance during sleep. Comput Methods Programs Biomed. 2007;85:8–18
  89. Popovic RM, White DP. Upper airway muscle activity in normal women: influence of hormonal status. J Appl Physiol. 1998;84:1055–1062

PII: S1087-0792(08)00110-X

doi: 10.1016/j.smrv.2008.09.008

Sleep Medicine Reviews
Volume 13, Issue 5 , Pages 333-343 , October 2009