title: Laser-assisted straightening of deformed cartilage: numerical model.
abstract: OBJECTIVE
  The potential application of laser cartilage reshaping (LCR) for correction of septal deviations has generated increasing clinical interest, because septoplasty is among the top five most common operations performed. However, few studies have investigated stress fields existing in the nasal septal cartilage during LCR of septal deviations. The objectives of this study were to: (1) formulate a finite-element model describing stress fields in mechanically straightened septal cartilage, (2) calculate stress fields in the septum after a given pattern of laser irradiation produced thermally induced stress relaxation in selected sites, and (3) investigate the dependence of the overall stress relaxation in a straightened septum as a function of the number, location, and size of laser irradiation sites.
  
  
  METHODS
  The cartilagenous nasal septum was modeled as 24 x 24 x 2-mm slab. The deviation was represented as a bulge running along the center of the septum with a maximum elevation of 2 mm above the surface. A straightening deformation was represented in form of displacement boundary condition applied to the bulge convex surface with maximum displacement amplitude at center of the septum. Laser irradiation applied in a pattern of one, two, and three lines parallel to the bulge was assumed. The effect of thermally induced stress relaxation was modeled as a simultaneous change in the cartilage mechanical properties and reduction of strain to zero occurring inside the laser heated zone. The finite-element method was used to calculate stress fields within cross-section of the straightened septum and the force of reaction to the straightening deformation before and after laser irradiation. Calculations were performed for the width and depth of thermally modified zones varying from 0.5 to 3 mm and from 0.5 to 2 mm, respectively. Irradiation of convex and concave sides of the deviation was studied.
  
  
  RESULTS
  The straightening deformation produced a stress field with both regions of tension and compression present. Maximum stress values were obtained on the surface where the straightening deformation was applied. Reaction force decreased with increasing width and depth of the relaxation zones and depends on location and number of these zones. The maximum reduction of reaction force obtained with three zones (3 mm wide and 2 mm deep) optimally placed in regions of stress concentration was 98%. However, using the same pattern of stress relaxation zones but with a depth of only 1 mm produces a reaction force reaction of 91%. Irradiation of convex side of the deviation reduced reaction force approximately twice as much as irradiation of the concave side.
  
  
  CONCLUSIONS
  The present numerical simulation of the stress field in laser-reshaped deviated septum shows highly non-homogeneous stress distributions before and after laser treatment. Using reasonable assumptions on how the mechanical behavior of cartilage changes after heating, the model allows estimation reaction force and its reduction following localized laser irradiation as a function of size and location of laser heated zones.
authors.affiliation: Beckman Laser Institute, University of California Irvine, Irvine, California 92612, USA. dprotsen@uci.edu
authors.forename: Dmitriy E
authors.initials: DE
authors.lastname: Protsenko
authors.forename: Brian J F
authors.initials: BJ
authors.lastname: Wong
mesh_terms: D000465:Algorithms; D020342:Finite Element Analysis; D006801:Humans; D053685:Laser Therapy; D008954:Models, Biological; D009300:Nasal Septum / Q000002:abnormalities* / Q000601:surgery*; D013314:Stress, Mechanical