title: Temperature superposition for fast computation of 3D temperature distributions during optimization and planning of interstitial ultrasound hyperthermia treatments.
abstract: OBJECTIVE
  A temperature superposition method has been developed for fast optimisation and planning of interstitial hyperthermia treatments with convectively cooled multi-transducer ultrasound applicators integrated within high dose rate (HDR) brachytherapy catheters.
  
  
  METHODS
  Steady-state temperature distributions produced by individual tubular transducers capable of directional heating were pre-computed using finite element models (FEM) methods. The composite temperature distributions generated by multi-applicator implants were approximated as superposition sums of the pre-computed temperature profiles. Composite temperature distributions produced by the multi-applicator implants were also computed using accurate but computationally expensive FEM methods (considered here as the validation standard). Both methods were used for temperature calculation on a range of test implant geometries and representative patient cases (HDR implants in prostate (n = 13) and cervix (n = 2)), with optimised treatment plans created for the latter.
  
  
  RESULTS
  Difference between temperatures calculated by the superposition and FEM methods was below 0.37°C (95% confidence interval) in test implants at clinically relevant acoustic intensities (0.3-2.0 W/cm²) and blood perfusion (2 kg/m³/s). Difference in 41°C isothermal volumes was below 8.3%. Superposition-based optimisations followed by FEM forward calculations (hybrid plans) were completed 4-7 times faster than FEM-only plans (FEM optimisation + FEM forward). Mean T₉₀, T₅₀ and T₁₀ values from both plans were within 0.3°C, 0.4°C and 0.45°C respectively, and the mean acoustic intensities were within 0.23 W/cm².
  
  
  CONCLUSIONS
  Temperature superposition provides a fast technique for forward or optimised planning of interstitial ultrasound hyperthermia treatments with calculations comparable to more accurate but time consuming FEM methods.
authors.affiliation: Department of Radiation Oncology, University of California, San Francisco, California, USA.
authors.forename: Vasant A
authors.initials: VA
authors.lastname: Salgaonkar
authors.forename: Punit
authors.initials: P
authors.lastname: Prakash
authors.forename: Chris J
authors.initials: CJ
authors.lastname: Diederich
mesh_terms: D002584:Cervix Uteri / Q000601:surgery; D002985:Clinical Protocols; D003198:Computer Simulation; D005260:Female; D020342:Finite Element Analysis; D006801:Humans; D006979:Hyperthermia, Induced / Q000295:instrumentation / Q000379:methods*; D008297:Male; D008962:Models, Theoretical; D011467:Prostate / Q000601:surgery; D013696:Temperature; D014159:Transducers; D014464:Ultrasonic Therapy / Q000295:instrumentation / Q000379:methods*