Skip to main content

Algebraic Reconstruction of Spatial Distributions of Acoustic Velocities in Tissue from Their Time-of-Flight Profiles

  • Chapter
Acoustical Holography


Two-dimensional distributions of acoustic velocities were measured in transverse sections through intact isolated organs, using reconstruction techniques. Profiles of time-of-flight (TOF) of 10 MHz pulses through the specimen were obtained by rectilinearly scanning two opposing transducers along either side of the specimen in the plane of interest. The received pulses were digitized at a rate of one 8-bit sample-per-10 nanosec, for 512 samples and were analyzed with a computer algorithm which calculated the TOF of the pulse to within ± 10 nanosec. Typically, 256 measurements of TOF were made in each profile scan for each of 37 angles of view separated by 5°, TOF’s through tissue, normalized by TOF through water, were used to calculate velocity within the specimen, using an algebraic reconstruction technique (ART), Images obtained represented acoustic velocities in individual cross sections within the tissue specimen with a resolution of 64 by 64 elements (< 2 mm square), The disadvantage of TOF reconstruction is that transmission scanning is required. Advantages over B- and C-scan imaging are: 1) dynamic changes in gain of receiver are not required, 2) attenuation occurs on only one traversal through tissue, and 3) the absolute value of an important acoustic parameter (velocity) is determined, which may have significant diagnostic value.

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

Access this chapter

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Gordon, R., and G. T. Herman:Reconstruction of pictures from their projections.Comm ACM 14 (12):759–768, 1971.

    Article  MATH  Google Scholar 

  2. Bracewell, R. N., and J. A. Roberts:Aerial smoothing in radio astronomy. Aust J Phys 7 (4):615–640, 1954.

    Article  ADS  Google Scholar 

  3. DeRosier, D. J., and A. Klug:Reconstructions of three-dimensional structures from electron micrographs. Nature 217:130–134, 1968.

    Article  ADS  Google Scholar 

  4. Gordon, R., R. Bender, and G. T. Herman:Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography.J Theor Biol 29:471–481, 1970.

    Article  Google Scholar 

  5. Herman, G. T., and S. Rowland:Resolution in ART: An experimental investigation of the resolving power of an alge-braic picture reconstruction technique. J Theor Biol 33:213–223, 1971.

    Article  Google Scholar 

  6. Robb, R. A., S. A. Johnson, J. F. Greenleaf, M. A. Wondrow, and E. H. Wood:An operator-interactive computer-controlled system for high fidelity digitization and analysis of biomedical images.Proceedings of the Society of Photo- Optical Instrumentation Engineers, August 27–29, 1973, Volume 40, pp 11–26.

    Google Scholar 

  7. Sweeny, D.:Interferometric measurement of three-dimen- sional temperature fields.Mechanical Engineering Ph.D. Thesis, University of Michigan, p 125.

    Google Scholar 

  8. Greenleaf, J. F., S. A. Johnson, S. L. Lee, G. T. Herman, and E. H. Wood:Algebraic reconstruction of spatial distributions of acoustic absorption within tissue from their two-dimensional acoustic projections.Acoustic Holography Vol 5, Plenum Press, New York, 1974, pp 591–603.

    Chapter  Google Scholar 

  9. Gordon, R., and G. T. Herman:Three-dimensional reconstruction from projections: a review of algorithms. International Review of Cytology 38:111–151, 1974.

    Article  Google Scholar 

  10. Kossoff, G., E. K. Fry, and L. Tellins:Average velocity of ultrasound in the human female breast.The Journal of Acoustical Society of America 53 (6):1730–1736, 1973.

    Article  ADS  Google Scholar 

  11. Jellins, L., and G. Kossoff:Velocity compensation in water-coupled breast echography.Ultrasonics 11 (5):223–226, September, 1973.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer Science+Business Media New York

About this chapter

Cite this chapter

Greenleaf, J.F., Johnson, S.A., Samayoa, W.F., Duck, F.A. (1975). Algebraic Reconstruction of Spatial Distributions of Acoustic Velocities in Tissue from Their Time-of-Flight Profiles. In: Booth, N. (eds) Acoustical Holography. Springer, Boston, MA.

Download citation

  • DOI:

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-8218-2

  • Online ISBN: 978-1-4615-8216-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics