HIFU Treatment Time Reduction by
User Controlled Parameter Search
Joshua Coon, Bob Roemer
December 13, 2010
Axial Study
Start with 2 Position Study:
Several Factor to Consider:
1
Heating Times
Treatment Order / Time Sharing
Amount of Overlap
Offset from Tumor Center
2
Distance to Tumor Boundary
Treatment Time Reduction:
Mathematical Formulation
Minimize:
•T_Heat,n and T_Cool,n are the
sum of the nth heating and
cooling times.
•N is the number of positions
Constraints:
•Thermal Dose (TD) is a metric
for tissue damage as a function
of temperature and time
•Temp Limit Impose in healthy
tissue
•Can Solve with Matlab
Optimization Toolbox (fmincon)
Minimizing Treatment Times
Algorithmically
Fix all treatment
parameters
EXCEPT
heating/cooling
times
Run fmincon
search to look
for minimized
times
Compare
starting
parameters to
find the
minimized time
Treatment
Treatment
Treatment
fmincon
fmincon
fmincon
Compare
final times
Lowest
Time
What Does “fmincon” Do?
fmincon = “Function minimization with constraints”
Different “solvers” to select next point: Interior Point, SQP, Active Set, etc.
Starts with
initial “guess”
for optimal
values, x0
Evaluates
finite
differences
and uses for
gradient
search
Revises guess
x0 -> x and
keeps refining
until
tolerances
met
• Function = sum(x) where x is vector of heating and cooling times at each position
• Constraints = Dose inside tumor > 240 CEM
= NT temp limit < 6 degrees C
• Both evaluated in terms of external functions I wrote by fmincon solver
What Does Constraint Function Do?
Input:
heating/
cooling times
Calculate
Temperatures
-> Thermal
Dose for each
voxel
Time / spatial
resolution for
temps a
consideration
Output : Min
Thermal Dose
in tumor/ Max
NT
temperature
Optimal Axial Overlap
Vary axial
spacing
fmincon
Compare
sum final
times
Dependences:
FZ Path (F->B, B->F)
Tumor Size
Perfusion
Spacing
Spacing: 0, 2, 4, 6, 8, 10, 12, 14, 16 mm
Results: Axial Spacing (1x1x16mm^3
tumor)
500
2 Pos F-B, 0.5 Perf
2 Pos B-F, 0.5 Perf
2 Pos F-B, 5.0 Perf
Total Heating Time
• Strong Minimum around
10 mm separation
400
300
200
100
0
0
+/- 1
+/- 2
+/- 3
+/- 4
+/- 5
+/- 6
+/- 7
Distance of Focal Zones from Center of Tumor
+/- 8
Problem: Convergence To Solution
• Fmincon may not always converge to a
solution from a given starting point
• Can happen in cases where starting point is
too far away from function minimum
• Must restart from another point or use
another fmincon “solver”
Problem: Local vs. Global Minima
Problem: Computing Resources Limits
• More than >20,000 hours of computer time
used in last 3 months
• Optimizations run with 2-3 per computer
(larger CPU than CPU on GPU)
– Requires about 3 days to run to completion
• Extensive Study may require even more time
• Best CPUs at CHPC limited to 24 hour
checkout
Future Directions
• Vary offset, power level, perfusion, tumor size
for 2 positions
• Expand Study to 3 positions, 4 positions, and
more if needed.
• Solve computer memory issues currently
limiting region size.
• Will require a lot of computer time