MR imaging and osteoporosis: Fractal lacunarity analysis of trabecular bone

Annamaria Zaia, Roberta Eleonori, Pierluigi Maponi, Roberto Rossi, Roberto Murri

Research output: Contribution to journalArticlepeer-review


We develop a method of magnetic resonance (MR) image analysis able to provide parameter(s) sensitive to bone microarchitecture changes in aging, and to osteoporosis onset and progression. The method has been built taking into account fractal properties of many anatomic and physiologic structures. Fractal lacunarity analysis has been used to determine relevant parameter(s) to differentiate among three types of trabecular bone structure (healthy young, healthy perimenopausal, and osteoporotic patients) from lumbar vertebra MR images. In particular, we propose to approximate the lacunarity function by a hyperbola model function that depends on three coefficients α, β, and γ, and to compute these coefficients as the solution of a least squares problem. This triplet of coefficients provides a model function that better represents the variation of mass density of pixels in the image considered. Clinical application of this preliminary version of our method suggests that one of the three coefficients, β, may represent a standard for the evaluation of trabecular bone architecture and a potentially useful parametric index for the early diagnosis of osteoporosis.

Original languageEnglish
Pages (from-to)484-489
Number of pages6
JournalIEEE Transactions on Information Technology in Biomedicine
Issue number3
Publication statusPublished - Jul 2006


  • Fractals
  • Lacunarity analysis
  • Magnetic resonance (MR) imaging
  • Osteoporosis
  • Trabecular bone

ASJC Scopus subject areas

  • Health Informatics
  • Health Information Management
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics


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