title: Trabecular bone gradient in rat long bone metaphyses: mathematical modeling and application to morphometric measurements and correction of implant positioning.
abstract: The distribution of trabecular structures in mammalian long bone metaphyses has been insufficiently explored. We show in rats that the trabecular bone structural parameters display a decreasing gradient, toward the diaphysis, that can be defined mathematically. This gradient is applicable for optimizing the reference volume in metabolic studies and for retrospective correction of implant positioning.
  
  
  BACKGROUND
  The mammalian metaphyseal trabecular bone is unevenly distributed. Hence, defining a standard reference volume is critical for morphometric analyses in metaphyseal sites.
  
  
  METHODS
  The distal femoral and proximal tibial metaphyses of adult orchietomized (ORX) or sham-ORX rats were scanned by microCT 6 wk postoperatively. Morphometric analysis based on 3D image data was performed in 450-microm-thick transversal segments defined consecutively from the primary spongiosa toward the diaphysis. The results were subjected to curve-fit analysis. A similar approach was used for proximal tibial metaphyseal sites carrying titanium implants inserted horizontally 6 wk post-ORX and examined 2-12 wk after implantation.
  
  
  RESULTS
  The respective curve-fit analysis in both femur and tibia revealed decreasing linear/quadratic and logarithmic gradients for all morphometric parameters in the sham-ORX animals. The ORX animals showed similar gradients with roughly similar slopes but lower values. For the bone volume (BV/TV) and connectivity (Conn.D) densities, the magnitude of the ORX effect vastly increased toward the diaphysis. The trabecular number was unaffected in ORX femora and tibias. The trabecular thickness showed a constant decrease in the femur and was unchanged in the tibia. These findings are useful for the determination and reporting of reference volumes in morphometric studies. Implementing the curve-fit analysis for retrospective correction of implant positioning revealed differences in BV/TV, Tb.N, Conn.D, and percent implant surface in contact with bone (%OI) between the sham-ORX and ORX rats. These differences were otherwise undisclosed. In addition, a temporal increase in %OI was shown only for the corrected measurements.
  
  
  CONCLUSIONS
  We show the feasibility of modeling trabecular bone structures using mathematical tools. Such modeling may be used as an experimental tool. Moreover, if proven applicable to human skeletal structures, it may be further developed for the diagnosis of metabolic bone diseases and evaluation of therapeutic measures.
authors: Bone Laboratory, Institute of Dental Sciences, Faculty of Dental Medicine, The Hebrew University of Jerusalem, Jerusalem, Israel. yankelg@ekmd.huji.ac.il
authors: Yankel
authors: Y
authors: Gabet
authors: David
authors: D
authors: Kohavi
authors: Thomas
authors: T
authors: Kohler
authors: Mario
authors: M
authors: Baras
authors: Ralph
authors: R
authors: Müller
authors: Itai
authors: I
authors: Bab
mesh_terms: D000818:Animals; D001862:Bone Resorption; D001863:Bone Screws; D005269:Femur / Q000033:anatomy & histology*; D008297:Male; D008954:Models, Biological; D009919:Orchiectomy; D051381:Rats; D013977:Tibia / Q000033:anatomy & histology*