, Volume 175, Issue 3, pp 781–789 | Cite as

Deconvolution of isotope signals from bundles of multiple hairs

  • Christopher H. RemienEmail author
  • Frederick R. Adler
  • Lesley A. Chesson
  • Luciano O. Valenzuela
  • James R. Ehleringer
  • Thure E. Cerling
Physiological ecology - Original research


Segmental analysis of hair has been used in diverse fields ranging from forensics to ecology to measure the concentration of substances such as drugs and isotopes. Multiple hairs are typically combined into a bundle for segmental analysis to obtain a high-resolution series of measurements. Individual hair strands cycle through multiple phases of growth and grow at different rates when in the growth phase. Variation in growth of hair strands in a bundle can cause misalignment of substance concentration between hairs, attenuating the primary body signal. We developed a mathematical model based on the known physiology of hair growth to describe the signal averaging caused by bundling multiple hairs for segmental analysis. The model was used to form an inverse method to estimate the primary body signal from measurements of a hair bundle. The inverse method was applied to a previously described stable oxygen isotope chronology from the hair of a murder victim and provides a refined interpretation of the data. Aspects of the reconstruction were confirmed when the victim was later identified.


Stable isotope Mathematical model Inverse methods 



CHR conducted this work as a University of Utah Research Training Group Fellow through NSF award #EMSW21-RTG and as a Postdoctoral Fellow at the National Institute for Mathematical and Biological Synthesis, an Institute sponsored by the National Science Foundation, the US Department of Homeland Security, and the US Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville.

Supplementary material

442_2014_2945_MOESM1_ESM.pdf (2.3 mb)
Supplementary material 1 (PDF 2323 kb)


  1. Ayliffe LK, Cerling TE, Robinson T, West AG, Sponheimer M, Passey BH, Hammer J, Roeder B, Dearing MD, Ehleringer JR (2004) Turnover of carbon isotopes in tail hair and breath CO2 of horses fed an isotopically varied diet. Oecologia 139:11–22Google Scholar
  2. Bar-Joseph Z, Farkash S, Gifford DK, Simon I, Rosenfield R (2004) Deconvolving cell cycle expression data with complementary information. Bioinformatics 20:23–30CrossRefGoogle Scholar
  3. Bowen GJ, Wilkinson B (2002) Spatial distribution of (δ 18 O) in meteoric precipitation. Geology 30(4):315–318CrossRefGoogle Scholar
  4. Bowen GJ, Ehleringer JR, Chesson LA, Stange E, Cerling TE (2007) Stable isotope ratios of tap water in the contiguous United States. Water Resour Res 43:1–12Google Scholar
  5. Cerling TE, Passey BH, Ayliffe LK, Cook CS, Ehleringer JR, Harris JM, Dhidha MB, Kasiki SM (2004) Orphans’ tales: seasonal dietarry changes in elephants from Tsavo National Park, Kenya. Palaeogeogr Palaeoclim Palaeoecol 206:367–376CrossRefGoogle Scholar
  6. Cerling TE, Wittemyer G, Rasmussen HB, Vollrath F, Cerling CE, Robinson TJ, Douglas-Hamilton I (2006) Stable isotopes in elephant hair document migration patterns and diet changes. Proc Natl Acad Sci (USA) 103(2):371–373CrossRefGoogle Scholar
  7. Cerling TE, Ayliffe LK, Dearing MD, Ehleringer JR, Passey BH, Podlesak DW, Torregrossa AM, West AG (2007) Determining biological tissue turnover using stable isotopes: the reaction progress variable. Oecologia 151:175–189PubMedCrossRefGoogle Scholar
  8. Cerling TE, Wittemyer G, Ehleringer JR, Remien CH, Douglas-Hamilton I (2009) History of animals using isotope records (HAIR): a 6-year dietary history of one family of African elephants. Proc Natl Acad Sci (USA) 106:8093–8100CrossRefGoogle Scholar
  9. Chase HB (1954) Growth of the hair. Physiol Rev 34:113–126PubMedGoogle Scholar
  10. Cooper GAA, Kronstrand R, Kintz P (2011) Society of hair testing guidelines for drug testing in hair. Forensic Sci Int 218(1–3):20–24PubMedGoogle Scholar
  11. Crawford K, McDonald RA, Bearhop S (2008) Applications of stable isotope techniques to the ecology of mammals. Mamm Rev 38(1):87–107CrossRefGoogle Scholar
  12. Ehleringer JR, Bowen GJ, Chesson LA, West AG, Podlesak DW, Cerling TE (2008) Hydrogen and oxygen isotope ratios in human hair are related to geography. Proc Natl Acad Sci (USA) 105(8):2788–2793CrossRefGoogle Scholar
  13. Ehleringer JR, Thompson AH, Podlesak DW, Bowen GJ, Chesson LA, Cerling TE, Park T, Dostie P, Schwarcz H (2010) A framework for the incorporation of isotopes and isoscapes in geospatial forensic investigations. In: West JB et al. (eds) Isoscapes: understanding movement, pattern, and process on earth through isotope mapping, chapter 17. Springer, p 357–387. doi: 10.1007/978-90-481-3354-3_17
  14. Henderson GL (1993) Mechanisms of drug incorporation into hair. Forensic Sci Int 63:19–29PubMedCrossRefGoogle Scholar
  15. Kennedy CD, Bowen GJ, Ehleringer JR (2011) Temporal variation of oxygen isotope ratios (δ 18 O) in drinking water: implications for specifying location of origin with human scalp hair. Forensic Sci Int 208:156–166PubMedCrossRefGoogle Scholar
  16. Kligman AM (1959) The human hair cycle. J Invest Dermatol 33:307–316PubMedCrossRefGoogle Scholar
  17. Lebeau MA, Montgomery MA, Brewer JD (2011) The role of variations in growth rate and sample collection on interpreting results of segmental analyses of hair. Forensic Sci Int 210:110–116PubMedCrossRefGoogle Scholar
  18. Lee SH, Kwon OS, Oh JK, Park WS, Moon SE, Eun HC (2005) Bleaching phototrichogram: an improved method for hair growth assessment. J Dermatol 32(10):782–787PubMedGoogle Scholar
  19. Lu P, Nakorchevskiy A, Marcotte E (2003) Expression deconvolution: a reinterpretation of DNA microarray data reveals dynamic changes in cell populations. Proc Natl Acad Sci (USA) 100:10370–10375CrossRefGoogle Scholar
  20. Martínez del Rio C, Wolf N, Carleton SA, Gannes LZ (2009) Isotopic ecology ten years after a call for more laboratory experiments. Biol Rev 84:91–111CrossRefGoogle Scholar
  21. Myers RJ, Hamilton JB (1951) Regeneration and rate of growth of hairs in man. Ann N Y Acad Sci 53:562–568PubMedCrossRefGoogle Scholar
  22. O’Brien DM, Wooller MJ (2007) Tracking human travel using stable oxygen and hydrogen isotope analyses of hair and urine. Rapid Commun Mass Spectrom 21(15):2422–2430PubMedCrossRefGoogle Scholar
  23. Passey BH, Cerling TE, Schuster GT, Robinson TF, Roeder BL, Krueger SK (2005) Inverse methods for estimating primary input signals from time-averaged intra-tooth isotope profiles. Geochim Cosmochim Acta 69:4101–4116CrossRefGoogle Scholar
  24. Petzke KJ, Fuller BT, Metges CC (2010) Advances in natural stable isotope ratio analysis of human hair to determine nutritional and metabolic status. Curr Opin Clin Nutr Metab Care 13(5):532–540PubMedCrossRefGoogle Scholar
  25. Rowicka M, Kudlicki A, Tu BP, Otwinowski Z (2007) High-resolution timing of cell cycle- regulated gene expression. Proc Natl Acad Sci (USA) 104:16892–16897CrossRefGoogle Scholar
  26. Sachs H (1995) Theoretical limits of the evaluation of drug concentrations in hair due to irregular hair growth. Forensic Sci Int 70:53–61PubMedCrossRefGoogle Scholar
  27. Sachs H (1997) History of hair analysis. Forensic Sci Int 84:7–16PubMedCrossRefGoogle Scholar
  28. Schwertl M, Auerswald K, Schnyder H (2003) Reconstruction of the isotopic history of animal diets by hair segmental analysis. Rapid Commun Mass Spectrom 17:1312–1318PubMedCrossRefGoogle Scholar
  29. Selavka CM, Rieders F (1995) The determination of cocaine in hair: a review. Forensic Sci Int 70:155–164PubMedCrossRefGoogle Scholar
  30. Siegal-Gaskins D, Ash JN, Crosson S (2009) Model-based deconvolution of cell cycle time- series data reveals gene expression details at high resolution. PLoS Comput Biol 5(8):e1000460PubMedCentralPubMedCrossRefGoogle Scholar
  31. Sponheimer M, Robinson T, Ayliffe L, Roeder B, Hammer J, Passey B, West A, Cerling T, Dearing D, Ehleringer J (2003) Nitrogen isotopes in mammalian herbivores: hair δ 15 N values from a controlled feeding study. Int J Osteoarchaeol 13:80–87CrossRefGoogle Scholar
  32. Staub C (1995) Analytical procedures for determination of opiates in hair: a review. Forensic Sci Int 70:111–123PubMedCrossRefGoogle Scholar
  33. Van Scott EJ, Reinertson RP, Steinmuller RJ (1957) The growing hair root of the human scalp and morphological changes therein following ametropin therapy. J Invest Dermatol 29:197–204CrossRefGoogle Scholar
  34. Vogel CR (2002) Computational methods for inverse problems. Society for Industrial and Applied Mathematics, University City Science Center, Philadelphia. ISBN-10: 0898715075Google Scholar
  35. Wainhaus SB, Tzanani N, Dagan S, Miller ML, Amirav A (1998) Fast analysis of drugs in a single hair. J Am Soc Mass Spectrom 9:1311–1320PubMedCrossRefGoogle Scholar
  36. West AG, Ayliffe LK, Cerling TE, Robinson TF, Karren B, Dearing MD, Ehleringer JR (2004) Short term diet changes revealed using stable carbon isotopes in horse tail-hair. Funct Ecol 18:616–624CrossRefGoogle Scholar
  37. Williams LJ, White CD, Longstaffe FJ (2011) Improving stable isotopic interpretations made from human hair through reduction of growth cycle error. Am J Phys Anthropol 145:125–136PubMedCrossRefGoogle Scholar
  38. Wittemyer G, Cerling TE, Douglas-Hamilton I (2009) Establishing chronologies from isotopic profiles in serially collected animal tissues: an example using tail hairs from African elephants. Chem Geol 263:3–11CrossRefGoogle Scholar
  39. Wolf N, Carleton SA, Martínez del Rio C (2009) Ten years of experimental animal isotopic ecology. Funct Ecol 23(1):17–26CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Christopher H. Remien
    • 1
    Email author
  • Frederick R. Adler
    • 2
    • 3
  • Lesley A. Chesson
    • 3
    • 4
  • Luciano O. Valenzuela
    • 3
    • 4
  • James R. Ehleringer
    • 3
    • 4
  • Thure E. Cerling
    • 3
    • 4
    • 5
  1. 1.National Institute for Mathematical and Biological SynthesisUniversity of TennesseeKnoxvilleUSA
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  3. 3.Department of BiologyUniversity of UtahSalt Lake CityUSA
  4. 4.IsoForensicsSalt Lake CityUSA
  5. 5.Department of GeologyUniversity of UtahSalt Lake CityUSA

Personalised recommendations