Dose Constraints In Imrt
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Dose Constraints In Imrt

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Dose Constraints In Imrt Dose Constraints In Imrt Presentation Transcript

  • The Use of Equivalent Uniform Dose constraints in IMRT Thomas Bortfeld 1 , Christian Thieke 1,2 , Yair Censor 3 1 Department of Radiation Oncology, Massachusetts General Hospital, Boston, USA 2 Department of Medical Physics, Deutsches Krebsforschungszentrum, Heidelberg, Germany, 3 Department of Mathematics, University of Haifa, Israel
  • Outline
    • Projectors in the dose space
      • Max/min dose constraints
      • DVH constraints
      • EUD constraints
    • Optimizing intensities
      • Scaled gradient method
      • POCS
  • Maximum dose constraint Volume Dose D max
  • "Positivity projector": penalty (weight) dose at voxel i in OAR k tolerance dose Penalty function: Constraints: Maximum (tolerance) doses "The spinal cord should get less than 40 Gy."
  • Small penalty ( w ) Volume Dose d max Large penalty ( w ) DVH Volume d max Dose DVH
  • Constraints: Minimum and tolerance doses
  • Volume Dose DVH d max d min
  • Non-intensity-modulated (4 beams, non-coplanar, MLC) Intensity-modulated (9 beams, coplanar) Brainstem Brainstem Target Target Example: Clivus chordoma
  • NTCP = 7% NTCP = 0.7% Example: Clivus chordoma Non-intensity-modulated (4 beams, non-coplanar, MLC) Intensity-modulated (9 beams, coplanar) Brainstem
  • Target volume Lungs Spinal cord Transversal view Target Spinal cord Lung Lung Technique: 9 beams, coplanar, intensity-modulated Example: Thyroid
  • Example: Thyroid
  • Volume Dose DVH d max V max
  • Constraints: Dose-volume constraints "No more than 1/3 of the lung should get more than 15 Gy."
  • Why are DVH constraints non-convex? Critical structure consisting of 2 voxels d 1 d 2 Not more than 50% of the volume (1 voxel) should get more than 30 Gy 30 Gy 30 Gy feasible region d 1 d 2
  • Non-convexity of DVH constraints
    • Even though DVH constraints are not convex, we can easily determine a projection of a dose distribution that violates a DVH constraint, onto the nearest one that fulfills the constraint:
  • Violation of DVH constraint Volume Dose DVH d max V max  d
  • Modified penalty function: Interval constraint projector: Constraints: Dose-volume constraints Bortfeld et al., ICCR 1997
  • “ Proof” that C [0,  dk] { } actually projects onto the nearest dose distribution that fulfills the DVH constraint
    • Assume that N v voxels receive a dose that is too high
    • We need to reduce (down to d max , but not further) the dose in N v voxels
    • Which voxels to choose?
    • The smallest correction is required for the ones with the smallest excess dose above d max , i.e., with dose values between d max and d max +  d
  • Example: Thyroid
    • Even though DVH constraints are not convex, repeated projections onto the feasible space with C [0,  dk] { } converge well and there are no problems with local minima.
      • Q. Wu, R. Mohan et al., Med. Phys. 2002
      • J. Llacer et al., PMB 2003
    • WHY??
  • Volume effect Whole lung: 18 Gy 50% of lung: 35 Gy
  • Volume effect Power-law relationship for tolerance dose (TD): n small: small “volume effect” n large: large “volume effect”
  • Arbitrary (not 0/1) dose distributions 0 25 50 75 100 0 20 40 60 Volume [%] Dose [Gy] 80 100 EUD = The homogeneous dose that gives the same clinical effect Lung: EUD = 25 Gy Spinal Cord: EUD = 52 Gy
  • The EUD Concept for Optimization
    • EUD = equivalent uniform dose
    • Single parameter for each organ
    • Example objectives and constraints:
      • Maximize EUD(target)
      • Minimize EUD(OAR)
      • EUD(OAR) < Tolerance
    • EUD has not yet been fully validated
    • Use hard physical constraints to limit search space
    • Use EUD to find Pareto solutions within the limited search space.
  • Volume effect -> EUD, Power-Law (a-norm) Model “ a -norm” (a=1/n) Mohan et al., Med. Phys. 19(4), 933-944, 1992 Kwa et al., Radiother. Oncol. 48(1), 61-69, 1998 Niemierko, Med. Phys. 26(6), 1100, 1999 Examples:
    • EUD is a convex function of the dose distribution (for a>1 and negative a)
    • Projection onto convex sets (POCS) methods will converge to given EUD-constrained solutions
  • POCS – Projection onto convex set x x d 2 d 1 D Convex set D‘
  • EUD constraint II Volume Dose
  • EUD constraint II Volume Dose
  • EUD projector Extrema on a bounded surface
    • Use Lagrange Multipliers
  • EUD projector: Lagrange multiplier
  • EUD projector
    • Right-hand side is independent of i
    • Exact solution for a =1 and a =2:
  • EUD projector
    • It turns out that this a good approximation for all values of a
    • Easy solution of the implicit equation
    • Is there an exact solution??
    C. Thieke, T. Bortfeld, A. Niemierko and S. Nill, From physical dose constraints to equivalent uniform dose constraints in inverse radiotherapy planning, Medical Physics, 30 (2003), 2332--2339.
  • Initialization Organ Constraint d pres ({organ}) = ... d pres ({organ}) = ... d pres ({organ}) = ... all organs processed? Adjoint dose calculation Dose calculation Calc. objective function converged ? End Max/min DVH EUD no yes no yes
  • POCS – Example Serial Organ
  • POCS – Example Serial/Parallel Organ
  • POCS – Example Target
  • Example: Head and neck case Brainstem Spinal Cord Parotis
  • Results 58.8 61.0 13.1 Max=13.0 Parotis Min=60.0 Max=61 Target 25.5 Max=25.5 Spinal Cord 23 Max=23 Brainstem EUD (Gy) EUD-Constraint (Gy) Organ
  • Results
  • Outline
    • Projectors in the dose space
      • Max/min dose constraints
      • DVH constraints
      • EUD constraints
    • Optimizing intensities
      • Scaled gradient method
      • POCS
  • Pre-calculated D ij matrix Voxel i Bixel j Source Patient
  • Scaled gradient projection technique
    • Newton-like iteration (simultaneous update):
    •  : damping factor
    “ TBNN” – Thieke, Bortfeld, Niemierko, Nill
  • POCS, Censor & Elfving: Scaled gradient projection (TBNN):
  • Physical dose only, Patient 1
  • Physical dose only, Patient 2
  • EUD only, Patient 1
  • EUD only, Patient 2
    • Why doesn’t the TBNN method work for EUD-only constraints
    • Possible answer: EUD violations affect a large number of voxels at the same time, which may lead to oscillations
  • Conclusions
  • Optimization Iteration 1
  • Optimization Iteration 1
  • Optimization Iteration 1
  • Optimization Iteration 1
  • Optimization Iteration 1
  • Optimization Iteration 1
  • Optimization Iteration 2
  • Optimization Iteration 2
  • Optimization Iteration 2
  • Optimization Iteration 2
  • Optimization Iteration 2
  • Optimization Iteration 2
  • Optimization Iteration 2
  • Optimization Iteration 2
  • Optimization Iteration 2
  • Optimization Iteration 3
  • Optimization Iteration 3
  • Optimization Iteration 3
  • Optimization Iteration 3