title: Estimating nanoparticle optical absorption with magnetic resonance temperature imaging and bioheat transfer simulation.
abstract: OBJECTIVE
  Optically activated nanoparticle-mediated heating for thermal therapy applications is an area of intense research. The ability to characterise the spatio-temporal heating potential of these particles for use in modelling under various exposure conditions can aid in the exploration of new approaches for therapy as well as more quantitative prospective approaches to treatment planning. The purpose of this research was to investigate an inverse solution to the heat equation using magnetic resonance temperature imaging (MRTI) feedback, for providing optical characterisation of two types of nanoparticles (gold-silica nanoshells and gold nanorods).
  
  
  METHODS
  The optical absorption of homogeneous nanoparticle-agar mixtures was measured during exposure to an 808 nm laser using real-time MRTI. A coupled finite element solution of heat transfer was registered with the data and used to solve the inverse problem. The L2 norm of the difference between the temperature increase in the model and MRTI was minimised using a pattern search algorithm by varying the absorption coefficient of the mixture.
  
  
  RESULTS
  Absorption fractions were within 10% of literature values for similar nanoparticles. Comparison of temporal and spatial profiles demonstrated good qualitative agreement between the model and the MRTI. The weighted root mean square error was <1.5 σMRTI and the average Dice similarity coefficient for ΔT = 5 °C isotherms was >0.9 over the measured time interval.
  
  
  CONCLUSIONS
  This research demonstrates the feasibility of using an indirect method for making minimally invasive estimates of nanoparticle absorption that might be expanded to analyse a variety of geometries and particles of interest.
authors.affiliation: Department of Imaging Physics, The University of Texas MD Anderson Cancer Center , Houston , Texas .
authors.forename: Christopher J
authors.initials: CJ
authors.lastname: MacLellan
authors.forename: David
authors.initials: D
authors.lastname: Fuentes
authors.forename: Andrew M
authors.initials: AM
authors.lastname: Elliott
authors.forename: Jon
authors.initials: J
authors.lastname: Schwartz
authors.forename: John D
authors.initials: JD
authors.lastname: Hazle
authors.forename: R Jason
authors.initials: RJ
authors.lastname: Stafford
mesh_terms: D000042:Absorption; D000465:Algorithms; D020342:Finite Element Analysis; D006046:Gold / Q000737:chemistry; D006979:Hyperthermia, Induced; D008279:Magnetic Resonance Imaging / Q000295:instrumentation / Q000379:methods; D057145:Nanoshells / Q000737:chemistry*; D043942:Nanotubes / Q000737:chemistry*; D055620:Optical Phenomena; D019047:Phantoms, Imaging; D012822:Silicon Dioxide / Q000737:chemistry; D013696:Temperature; D013814:Thermal Conductivity
chemical_list: D006046:Gold; D012822:Silicon Dioxide