Skip to main content
SpringerLink
Log in

The Mathematical Microscope – Making the Inaccessible Accessible

  • Chapter
  • First Online:
BetaSys

Part of the book series: Systems Biology ((SYSTBIOL,volume 2))

Abstract

In this chapter we introduce a new term, the “mathematical microscope”, as a method of using mathematics in accessing information about reality when this information is otherwise inaccessible. Furthermore, we discuss how models and experiments are related: none of which are important without the other. In the sciences and medicine, a link that is often missing in the chain of a system can be made visible with the aid of the mathematical microscope. The mathematical microscope serves not only as a lens to clarify a blurred picture but more important as a tool to unveil profound truths. In reality, models are most often used in a detective-like manner to investigate the consequences of different hypothesis. Thus, models can help clarify connections and relations. Consequently, models also help to reveal mechanisms and to develop theories. Case studies are presented and the role of mathematical modelling is discussed for type 1 and type 2 diabetes, depression, cardiovascular diseases and the interactions between the combinations of these, the so-called grey triangle in the metabolic syndrome.

If you want to learn about nature … it is necessary to understand the [mathematical] language that she speaks in

Richard P. Feynman

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Confusion about the nature of the heart, the blood and the role of the blood in the body had existed for centuries. Pliny the Elder, who lived from AD 23–79, wrote in a 37-volume treatise entitled Natural History, that “The arteries have no sensation, for they even are without blood, nor do they all contain the breath of life; and when they are cut only the part of the body concerned is paralyzed [...] the veins spread underneath the whole skin, finally ending in very thin threads, and they narrow down into such an extremely minute size that the blood cannot pass through them nor can anything else but the moisture passing out from the blood in innumerable small drops which is called sweat.”

  2. 2.

    In many cultures, physicians, as well as ordinary citizens, had their own beliefs concerning the nature of the heart and circulatory system. While the Greeks believed that the heart was the seat of the spirit, the Egyptians believed the heart was the center of the emotions and the intellect. The Chinese believed the heart was the centre of happiness. Even today in Western culture, remnants of these beliefs can be found in various sayings, “a broken heart”, “follow one’s heart”, “sweetheart”, etc.

  3. 3.

    Anton van Leeuwenhoek’s microscope from 1674 is considered to be the first functioning microscope. He was the first to see and describe the capillaries of the circulatory system.

References

  1. Andersen LG (2009) Modelling the human glucose insulin system. Master thesis (Supervisor Ottesen JT), in progress, Mathematics, Roskilde University, Denmark

    Google Scholar 

  2. Andersen M, Vinther F (2009) The dynamic of the HPA axis. Master thesis (Supervisor Ottesen JT). Mathematics, Roskilde University, Denmark

    Google Scholar 

  3. Bansal P, Wang Q (2008) Insulin as a physiological modulator of glucagon secretion. Am J Physiol Endocrinol Metab 295:E751–E761

    Article  PubMed  CAS  Google Scholar 

  4. Bergman RN, Ider YZ, Bowden CR, Cobelli C (1979) Quantitative estimation of insulin sensitivity. Am J Physiol Endocrinol Metab 236(6):E667–E677

    CAS  Google Scholar 

  5. Besse C, Nicod N, Tappy L (2005) Changes in insulin secretion and glucose metabolism induced by dexamethasone in lean and obese females. Obes Res Feb;13(2):306–311

    Article  PubMed  Google Scholar 

  6. Blasio BFD, Bak P, Pociot F, Karlsen AE, Nerup J (1999) Onset of type 1 diabetes – a dynamical instability. Perspect Diabetes 48:1677–1685

    Google Scholar 

  7. Carroll BJ, Cassidy F, Naftolowitz D, Tatham NE, Wilson WH, Iranmanesh A, Liu PY, Veldhuis JD (2007) Pathophysiology of hypercortisolism in depression. Acta Psychiatr Scand 115 (Suppl 433):90–103

    Article  Google Scholar 

  8. Danielsen M (1998) Modeling of feedback mechanisms which control the heart function in a view to an implementation in cardiovascular models. PhD thesis (Supervisor Ottesen JT), Roskilde University, Denmark

    Google Scholar 

  9. De Gaetano A, Arino O (2000) Mathematical modelling of the intravenous glucose tolerance test. J Math Biol 40:136–168

    Article  PubMed  Google Scholar 

  10. De Gaetano A, Picchini U, Ditlevsen S (2006) Modeling the euglycemic hyperinsulinemic clamp by stochastic differential equations. J Math Biol 53:771–796

    Article  PubMed  Google Scholar 

  11. Ditlevsen S, Picchini U, De Gaetano A (2008) Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics. Math Med Biol 25:141–155

    Article  PubMed  Google Scholar 

  12. Dunbar C, Huiquing L (2000) Proopiomelanocortin (POMC) products in the central regulation of sympathetic and cardiovascular dynamics: studies on melanocortin and opioid interactions. Peptides 21:211–217

    Article  PubMed  CAS  Google Scholar 

  13. Hannesson K, Hansen DF, Nielsen KHM, Christensen KC, Jensen LF (2007) Matematisk modellering af HPA-aksen. Master thesis in Danish (Supervisor Ottesen JT), Mathematics, Roskilde University, Denmark

    Google Scholar 

  14. Jacobsen LH (2009) Mathematical Modelling of Type 1 Diabetes. Bachelor thesis (Supervisor Ottesen JT), Mathematics, Roskilde University, Denmark

    Google Scholar 

  15. Jelic S, Cupic Z, Kolar-Anic L (2005) Mathematical modeling of the hypohtalamic-pituitaryadrenal system activity. Math Biosci 197:173–187

    Article  PubMed  CAS  Google Scholar 

  16. Jerrold AV, Olefsky M, Bergman RN, Prager R (1987) Equivalence of the insulin sensitivity index in man derived by the minimal model method and the euglycemic glucose clamp. J Clin Invest 79:790–800

    Article  Google Scholar 

  17. Kellendonk C, Gass P, Kretz O, Schütz G, Tronche F (2002) Corticosteroid receptors in the brain: gene targeting studies. Brain Res Bull 57(1):73–83

    Article  PubMed  CAS  Google Scholar 

  18. Kyrylov V, Severyanova LA, Vieira A (2005) Modeling Robust Oscillatory Behaviour of the Hypothalamic-Pituitary-Adrenal Axis, IEEE Trans Biomed Eng 52(12):1977–1983

    Article  PubMed  Google Scholar 

  19. Larsson H, Ahren B (1996) Short-term dexamethasone treatment increases plasma leptin independently of changes in insulin sensitivity in healthy women. J Clin Endocrinol Metabol 81:4428–4432

    Article  CAS  Google Scholar 

  20. Marée AFM, Komba M, Dyck C, Labecki M, Finegood MT, Edelstein-Keshet L (2005) Quantifying macrophage defects in type 1 diabetes. J Theor Biol 233:533–551

    Article  PubMed  Google Scholar 

  21. Marée AFM, Komba M, Finegood DT, Edelstein-Keshet L (2008) A quantitative comparison of rates of phagocytosis and digestion of apoptotic cells by macrophages from normal (balb/c) and diabetes-prone (nod) mice. J Appl Physiol 104:157–169. doi:10.1152

    Article  PubMed  Google Scholar 

  22. Marée AFM, Kublik R, Finegood DT, Edelstein-Keshet L (2006b) Modelling the onset of type 1 diabetes: can impaired macrophage phagocytosis make the difference between health and disease? Philos Trans R Soc 364:1267–1282

    Article  Google Scholar 

  23. Marée AFM, Santamaria P, Edelstein-Keshet L (2006a) Modeling competition among autoreactive cd8+ t cells in autoimmune diabetes: implications for antigen specific therapy. Int Immunol 18(7):1067–1077

    Article  PubMed  Google Scholar 

  24. Mari A, Valerio A (1997) A circulatory model for the estimation of insulin sensitivity. Control Eng Pract 5(12):1747–1752

    Article  Google Scholar 

  25. Nicod N, Giusti V, Besse C, Tappy L (2003) Metabolic adaptations to dexamethasone-induced insulin resistance in healthy volunteers. Obesity Res 11:625–631. doi:10.1038/oby.2003.90

    Article  CAS  Google Scholar 

  26. Nielsen KHM (2009) Exploring Treatment Strategies for Type 1 Diabetes through Mathematical Modelling. Master thesis (Supervisor Ottesen JT), Mathematics, Roskilde University, Denmark

    Google Scholar 

  27. Olufsen MS, Alston AV, Tran HT, Ottesen JT, Novak V (2007) Modeling heart rate regulation – Part I: sit-to-stand versus head-up-tilt. J Cardiovasc Eng. published online doi:10.1007/s10558-007-9050-8

    Google Scholar 

  28. Olufsen MS, Alston AV, Tran HT, Ottesen JT, Novak V (2008) Modeling heart rate regulation, Part I: sit-to-stand versus head-up tilt. J Cardiovasc Eng 8:73–87

    Article  Google Scholar 

  29. Olufsen, MS, Ottesen JT, Tran HT, Ellwein LM, Lipsitz LA, Novak V (2005) Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation. J Appl Physiol 99:1523–1537. Published online March 28, 2005 at http://jap.physiology.org/papbyrecent.shtml

    Article  PubMed  Google Scholar 

  30. Olufsen M, Tran H, Ottesen JT (2004) Modeling cerebral blood flow control during posture change from sitting to standing. J Cardiovasc Eng 4(1):47–58

    Article  Google Scholar 

  31. Olufsen MS, Tran HT, Ottesen JT, Lipsitz LA, Novak V (2006) Modeling baroreflex regulation of heart rate during orthostatic stress. Am J Physiol 291:R1355–R1368

    Article  CAS  Google Scholar 

  32. Ottesen JT (1997a) Non-linearity of baroreceptor nerves. Surv Math Ind 7(3):187–201

    Google Scholar 

  33. Ottesen JT (1997b) Modelling of the baroreflex-feedback mechanism with time-delay. J Math Biol 36:41–63

    Article  PubMed  CAS  Google Scholar 

  34. Ottesen, JT (2000a) Modelling the dynamical baroreflex-feedback control. In: Gyori I (ed) Math Comput Model 31(4–5):167–173

    Google Scholar 

  35. Ottesen JT (2000b) Modeling the dynamical baroreflex-feedback control. Math Comp Mod 31:167–173

    Article  Google Scholar 

  36. Ottesen JT (2000c) General compartmental models of the cardiovascular system. In: Ottesen JT, Danielsen M (eds) Mathematical modelling in medicine. IOS press, Amsterdam, pp 121–138

    Google Scholar 

  37. Ottesen JT (2003) Valveless pumping in a fluid-filled closed elastic tube-system: one-dimensional theory with experimental validation. J Math Biol 46:309–332

    Article  PubMed  CAS  Google Scholar 

  38. Ottesen JT, Danielsen M (2003) Modeling ventricular contraction with heart rate changes. J Theo Biol 22:337–346

    Article  Google Scholar 

  39. Ottesen JT, Olufsen MS (2009) On the track of syncope induced by orthostatic stress – feedback mechanisms regulating the cardiovascular system. Proc IFAC Symp Model Contr Biomed Syst in print

    Google Scholar 

  40. Ottesen JT, Olufsen MS, Larsen J (2004) Applied mathematical models in human. Physiol SIAM

    Google Scholar 

  41. Pagano G, Cavallo-Perin P, Cassader M, Bruno A, Ozzello A, Masciola P, Dall’omo AM, Imbimbo B (1983) An in vivo and in vitro study of the mechanism of prednisone-induced insulin resistance in healthy subjects. J Clin Invest Nov 72(5):1814–1820. doi:10.1172/JCI111141

    Article  CAS  Google Scholar 

  42. Palumbo P, Panunzi S, De Gaetano A (2007) A discrete single delay model for the intra-venous glucose tolerence test. Theor Biol Med Model 4(35):1–16

    Google Scholar 

  43. Panunzi S, Ditlevsen S, Picchini U, De Gaetano A, Mingrone G (2005) A mathematical model of the euglycemic hyperinsulinemic clamp. Theor Biol Med Model 2(44):1–11

    Google Scholar 

  44. Paquot N, Schneiter Ph, Jéquier E,Tappy L (1995) Effects of glucocorticoids and sympathomimetic agents on basal and insulin-stimulated glucose. Metabolism 15(3):231–240

    CAS  Google Scholar 

  45. Perry CG, Spiers A, Cleland SJ, Lowe GDO, Petrie JR, Connell JMC (2003) Glucocorticoids and insulin sensitivity: dissociation of insulin’s metabolic and vascular actions. J Clin Endocrinol Metab 88(12):6008–6014

    Article  PubMed  CAS  Google Scholar 

  46. Picchini U, De Gaetano A, Panunzi S, Ditlevsen S, Mingrone G (2005) A mathematical model of the euglycemic hyperinsulinemic clamp. Theor Biol Med Model 2:4

    Article  Google Scholar 

  47. Pielmeier U, Hann CE, Chase JG, Andreassen S (2008) Glucose-insulin pharmacodynamic surface modeling comparison. Elsevier IFAC, Publications/IFAC Proceedings series, pp 8085–8090

    Google Scholar 

  48. Pielmeier U, Hann CE, McAuley KA, Mann JI, Chase JG, Andreassen S (2009) A glucose-insulin pharmacodynamic surface modeling validation and comparison of metabolic system models. Biomed Signal Process Control in print

    Google Scholar 

  49. Pretty CJ, Chase JG, Lin J, Shaw G, Compte AL, Razak N, Parente J (2009) Corticosteroids and insulin resistance in the ICU. Proceedings of the 7th IFAC symposium on modelling and control in biomedical systems. Aalborg, Denmark

    Google Scholar 

  50. Tappy L, Randin D, Vollenweider P, Vollenweider L, Paquot N, Scherrer U, Nicod P, Jéquier E (1994) Mechanisms of dexamethasone-induced insulin resistance in healthy humans. J Clin Endocrinol Metab 79:1063–1069

    Article  PubMed  CAS  Google Scholar 

  51. Vente W, Olff M, Amsterdam J, Kamphuis J, Emmelkamp P (2003) Physiological differences between burnout patients and healthy controls: blood pressure, heart rate, and cortisol responses. Occup Environ Med 60(Suppl I):i54–i61

    Article  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Science, Systems and Models, Roskilde University, Universitetsvej 1, DK-4000, Roskilde, Denmark

    Johnny T. Ottesen

Authors
  1. Johnny T. Ottesen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Johnny T. Ottesen .

Editor information

Editors and Affiliations

  1. Dept. IMFUFA, Roskilde University, Roskilde, Denmark

    Bernhelm Booß-Bavnbek

  2. University of Southern Denmark, Campusvej 55, Odense M, 5230, Denmark

    Beate Klösgen

  3. Department of Science, Systems and Model, University of Roskilde, Universitetsvej 1, Roskilde, 4000, Denmark

    Jesper Larsen

  4. Glostrup Hospital, Glostrup Research Institute, Ndr. Ringvej 69 2, Glostrup, DK-2600, Denmark

    Flemming Pociot

  5. Skåne University Hospital Malmö entr 72, Lund University Diabetes Center, CRC 91-11 19, Malmö, SE-205 02, Sweden

    Erik Renström

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Ottesen, J.T. (2011). The Mathematical Microscope – Making the Inaccessible Accessible. In: Booß-Bavnbek, B., Klösgen, B., Larsen, J., Pociot, F., Renström, E. (eds) BetaSys. Systems Biology, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6956-9_6

Download citation

Publish with us

Policies and ethics

Search

Navigation