title: Minimal-invasive thermal imaging of a malignant tumor: a simple model and algorithm.
abstract: OBJECTIVE
  This article deals with the development of a minimal-invasive, infrared (IR) (8-12 microm spectral range) imaging technique that would improve upon current methods by using superparamagnetic nanostructured core/shell particles for imaging as well as for therapy. This technique may function as a diagnostic tool, thanks to the ability of specific bioconjugation of these nanoparticles to a tumor's outer surface. Hence, by applying an alternating magnetic field, the authors could cause a selective elevation of temperature of the nanoparticles for +1 - +5 degrees C, enabling tumor's imaging. Further elevation of the temperature over +10 degrees C will cause a necrotic effect, leading to localized irreversible damage to the cancerous site without harming the surrounding tissues. This technique may also serve as a targeted therapeutic tool under thermal feedback control.
  
  
  METHODS
  Under alternative magnetic field, these biocompatible nanoparticles can generate heat, which propagates along the tissue (by thermal conduction), reaching the tissue's surface. Surface temperature distribution can be acquired by an IR camera and analyzed to retrieve nanoparticles' temperature and location within the tissue. An analytical-based steady-state solution for the thermal inverse problem was developed, considering an embedded point heat source. Based on this solution, the authors developed an algorithm that generates solutions for the corresponding forward problem, and based on discovered relations between the problem's characteristic, can derive the depth and temperature of the embedded heat source from the surface temperature profile, derived from the thermal image.
  
  
  RESULTS
  The algorithm was able to compute the heat source depth and power (proportional to its temperature) in two phases. Assuming that the surface temperature profile can be fitted to a Lorentzian curve, the first phase computing the source depth was based on a linear relation between the depth and the FWHM value of the surface temperature profile, which is independent of the source power. This relation varies between different tissues and surface conditions. The second phase computing the power (Q) was based on an exponential relation between the area (A) curve of the surface temperature profile and power (Q), dependent on the depth computed in the first phase. The simulation results show that given the tissue thermal properties, the surface conductance, and the ambient conditions, an inverse solution can be applied retrieving the depth and temperature of a point heat source from a 2D thermal image.
  
  
  CONCLUSIONS
  The predicted depth and heat source power were compared to the actual parameters (which were derived). Differences between the real and estimated values may occur primarily in computing the forward solution, which was used for the estimation itself. The fact that the computation is carried out discretely and the spatial resolution in the radial direction are influencing factors. To improve and eliminate these factors, the resolution may be increased or suitable interpolation and/or smoothing may be applied. Applying this algorithm on a spherical heat source volume may be feasible. A solution for the forward problem was established, yet incorporation of the source radius has to be further examined.
authors.affiliation: Department of Biomedical Engineering, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel.
authors.forename: Iddo M
authors.initials: IM
authors.lastname: Gescheit
authors.forename: Abraham
authors.initials: A
authors.lastname: Dayan
authors.forename: Moshe
authors.initials: M
authors.lastname: Ben-David
authors.forename: Israel
authors.initials: I
authors.lastname: Gannot
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D007259:Infrared Rays; D008954:Models, Biological; D009369:Neoplasms / Q000175:diagnosis* / Q000503:physiopathology*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013817:Thermography / Q000379:methods*