RESULTS

1
A Model Based Approach To Monitor
TemperatureDuring HIFU Thermal Therapy Guoliang
Ye, Penny Probert Smith, J. Alison Noble, and
Fares Mayia Dept. of Engineering Science,
Parks Road, University of Oxford, Oxford, UK.
ye, pjp, noble_at_robots.ox.ac.uk Dept. of
Medical Physics Clinical Eng., Oxford Radcliffe
Hospitals NHS Trust, Oxford, UK.
Fares.Mayia_at_orh.nhs.uk

• INTRODUCTION
• Temperature is the most critical
  parameter for controlling tissue ablation through
  HIFU. This poster discusses the improvements
  which result from including a model of the
  expected temperature distribution over space and
  time, derived from the heat equation. A Kalman
  filter, a well known stochastic estimator which
  allows the uncertainty in the model and echo
  strain measurements to be modelled explicitly, is
  used to predict temperature through determining
  the contours of constant temperature. Suitable
  model parameters are derived through least
  squares fitting algorithm based on the
  temperature map estimated by echo-strain method.
  The results allow the extent of tissue damage
  caused by heating can be assessed readily.
• THEORY METHOD
• 1. The Heat Model
• Assumptions A Gaussian-shaped heat
  source is introduced in an infinite homogenous
  media with uniform ambient temperature. 1
• The 3D Heat Model across a 2D
  Cross-Section
• where
• t the time since HIFU exposure and
  heating.
• H a constant which determines the
  energy of the heat source.
• tx ty tz the initial Gaussian
  heat source introduced by HIFU

• RESULTS
• The procedure for finding the final
  temperature map
• 1. The initial temperature map, was
  estimated from r.f. images using the echo-strain
  method (Fig. 1), with polynomial fitting of
  displacement.
• 2. The parameter ? is estimated
  using least-squared data fitting along the axial
  and lateral directions respectively, across the
  peak of the temperature map (Fig. 1 right).
• 3. The Kalman filter is applied
  using the estimated value of ?. Figure 3 shows
  final temperature maps under different ratios of
  uncertainty in the model and measurements.
• Fig. 1. Temperature maps (echo-strain method)
  using a least-squared piecewise line fitting
  (left) and a least-squared polynomial (12th
  order) fitting (right). Due to the
  window-averaging factor along the axial
  direction, the elliptic heat distribution has
  been distorted and becomes circular in the left
  image. The right temperature map is more similar
  to the true elliptic heat distribution. The cross
  on the right image indicates the location of the
  data to be used for data fitting (equation 7) in
  Fig. 2.

y
(xr, yr)
(µx,µy)
x
Uc is the contours temperature.
ACKNOWLEDGEMENTS Thanks to the HIFU unit at
Oxford Churchill Hospital, and funding from EPSRC
grant EP/C00633X.