Cross-Sectional Profiles and Volume Reconstructions of Soft Tissues Using Laser Beam Measurements

[+] Author and Article Information
Eve Langelier

PERSEUS, Département de génie mécanique, Université de Sherbrooke, Sherbrooke (Québec), J1K 2R1, Canada telephone: (819) 821-8000 ext. 2998, fax: (819) 821-7163 e-mail: eve.langelier@usherbrooke.ca

Daniel Dupuis

Faculté des sciences et de génie–Dean’s office, Universite Laval, Pavillon Adrien-Pouliot, local 1310 Québec, Canada G1K 7P4 Telephone: (418) 656-2131 ext. 12468e-mail: daniel.dupuis@fsg.ulaval.ca

Michel Guillot

MultiSigma Inc, 736 Avenue Godin, Québec, Québec, Canada telephone: (418) 688-4000, fax:(418) 688-4000e-mail: direction@multisigma.com

Francine Goulet

Tissue Engineering Laboratory, Pavillon Notre-Dame, H-401, CHA, Ho⁁pital de l’Enfant-Jésus, 1401 18e rue, Québec (Québec), Canada, G1J 1Z4, telephone: (418) 682-7765, fax:(418) 649-5969e-mail: chgfgo@hermes.ulaval.ca

Denis Rancourt

PERSEUS, Département de génie mécanique, Université de Sherbrooke, Sherbrooke (Québec), J1K 2R1, Canada, telephone: (819) 821-8000 ext.1346, fax: (819) 821-7163e-mail: denis.rancourt@usherbrooke.ca

J Biomech Eng 126(6), 796-802 (Feb 04, 2005) (7 pages) doi:10.1115/1.1824125 History: Received April 28, 2003; Revised May 26, 2004; Online February 04, 2005
Copyright © 2004 by ASME
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Photograph of the laser micrometer. The laser beam sensor rotates around and translates along the specimen to measure its width at different angles and different z positions.
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Flowchart illustrating the reconstruction algorithm. CP stands for “confining polygon” and PA for “parallelepiped area.”
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The origins of the global and local Cartesian reference systems are set by the lower edge of the laser beam (0.00 mm) for a rotation angle θ=0 deg(x axis) and by its COR (y axis). Note that the global system is fixed in space, while the local system rotates with the laser beam. The measured edges of the specimen are referred to as VL and VU,VL being closer to the lower beam edge (0.00 mm), and VU to the upper beam edge (28.00 mm).
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The location of the COR is determined from the data measured at θ=0 and θ=180 deg. Note the reflection of the specimen projection each side of the COR at θ=0 and θ=180 deg. The localization formula is described in the text.
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The reconstructed cross-sectional profile is a polygon (PP) corresponding to the intersection of PAs obtained at Δθ increments between 0 and 180 deg.
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Illustration of three consecutive steps of the iterative process used to obtain the final cross-sectional profile. (a) The initial CP is bounded by the sectioning lines (SLs) obtained at θ=0 and θ=Δθ deg. (b) and (c) Dashed lines are derived from the precedent confining polygon (CPθ−Δθ), while continuous lines represent the PAθ. Circles identify the CPθ−Δθ vertices, while filled circles identify new intersection points. Only the points lying within the PAθ and the CPθ−Δθ define the CPθ.
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Data transposition from the local to the global reference frame. For an angle θ, the profile width is represented by two SLs. BL and BU correspond to the Y intercepts, and M, to the slope of these SLs.
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SLs obtained from VL and VU data for an Allen key measured at 10-deg intervals.
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Volume visualization of a ligament-like cell-seeded collagen matrice produced in vitro. Cross-sectional profiles were reconstructed from data measured at 10-deg intervals, and the volume, from 9 sections obtained at 4-mm intervals along the specimen.
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Reconstructed profile of an Allen key obtained with the initial tested algorithm. Encircled is a magnification of the star-like artifact resulting from the laser beam precision.
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Illustration of the nomenclature used by Lee and Woo 8 adapted here to the new apparatus. The offset (OS) and offsetting angle (γ) are obtained from data measured at rotation angles of 0 deg (A) and 90 deg (B). They are used to calculate R1 and R2 when the COR is located outside of the specimen profile.




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