Kalman Filtered MR Temperature Imaging for Laser Induced Thermal Therapies

The feasibility of using a stochastic form of Pennes bioheat model within a 3-D finite element based Kalman filter (KF) algorithm is critically evaluated for the ability to provide temperature field estimates in the event of magnetic resonance temperature imaging (MRTI) data loss during laser induced thermal therapy (LITT). The ability to recover missing MRTI data was analyzed by systematically removing spatiotemporal information from a clinical MR-guided LITT procedure in human brain and comparing predictions in these regions to the original measurements. Performance was quantitatively evaluated in terms of a dimensionless L2 (RMS) norm of the temperature error weighted by acquisition uncertainty. During periods of no data corruption, observed error histories demonstrate that the Kalman algorithm does not alter the high quality temperature measurement provided by MR thermal imaging. The KF-MRTI implementation considered is seen to predict the bioheat transfer with RMS error <; 4 for a short period of time, Δt <; 10 s, until the data corruption subsides. In its present form, the KF-MRTI method currently fails to compensate for consecutive for consecutive time periods of data loss Δt >; 10 sec.

[1]  Dhiraj Arora,et al.  Constrained Predictive Control of Thermal Therapies for Minimum-Time Delivery of Thermal Dose , 2007, IEEE Transactions on Control Systems Technology.

[2]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[3]  B. Hooper.  Optical-thermal response of laser-irradiated tissue , 1996 .

[4]  C. Moonen,et al.  Real‐time MR‐thermometry and dosimetry for interventional guidance on abdominal organs , 2010, Magnetic resonance in medicine.

[5]  John D Hazle,et al.  Quantitative comparison of thermal dose models in normal canine brain. , 2010, Medical physics.

[6]  Kung-Shan Cheng,et al.  Effective learning strategies for real-time image-guided adaptive control of multiple-source hyperthermia applicators. , 2010, Medical physics.

[7]  H. H. Pennes.  Analysis of tissue and arterial blood temperatures in the resting human forearm. 1948. , 1948, Journal of applied physiology.

[8]  M. Tutt,et al.  High-power high-efficiency X-band AlGaAs/GaAs heterojunction bipolar transistors with undercut collectors , 1997, IEEE Microwave and Guided Wave Letters.

[9]  Nick Todd,et al.  Model predictive filtering for improved temporal resolution in MRI temperature imaging , 2010, Magnetic resonance in medicine.

[10]  Robert L. Galloway,et al.  Optimizing Electrode Placement Using Finite-Element Models in Radiofrequency Ablation Treatment Planning , 2009, IEEE Transactions on Biomedical Engineering.

[11]  Stephen E. Cohn,et al.  The Behavior of Forecast Error Covariances for a Kalman Filter in Two Dimensions , 1991 .

[12]  Dhiraj Arora,et al.  Model-predictive control of hyperthermia treatments , 2002, IEEE Transactions on Biomedical Engineering.

[13]  K. Zou,et al.  Three validation metrics for automated probabilistic image segmentation of brain tumours , 2004, Statistics in medicine.

[14]  J C Browne,et al.  Dynamic data‐driven finite element models for laser treatment of cancer , 2007, Numerical methods for partial differential equations.

[15]  J. Valvano,et al.  BIOHEAT TRANSFER , 1999 .

[16]  J K Potocki,et al.  Concurrent hyperthermia estimation schemes based on extended Kalman filtering and reduced-order modelling. , 1993, International journal of hyperthermia : the official journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group.

[17]  G. Evensen.  Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[18]  Jari P. Kaipio,et al.  Feedforward and feedback control of ultrasound surgery , 2006 .

[19]  Antonio Fasano,et al.  On a mathematical model for laser-induced thermotherapy , 2009 .

[20]  Dongbin Xiu,et al.  On numerical properties of the ensemble Kalman filter for data assimilation , 2008 .

[21]  Sébastien Roujol,et al.  Robust Adaptive Extended Kalman Filtering for Real Time MR-Thermometry Guided HIFU Interventions , 2012, IEEE Transactions on Medical Imaging.

[22]  D. Simon.  Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches , 2006 .

[23]  François Bouttier,et al.  The dynamics of error covariances in a barotropic model , 1993 .

[24]  Ashok Gowda,et al.  MR thermometry‐based feedback control of laser interstitial thermal therapy at 980 nm , 2004, Lasers in surgery and medicine.

[25]  James Demmel,et al.  Applied Numerical Linear Algebra , 1997 .

[26]  S. Cohn.  Dynamics of Short-Term Univariate Forecast Error Covariances , 1993 .

[27]  R M Henkelman,et al.  Ex vivo tissue‐type independence in proton‐resonance frequency shift MR thermometry , 1998, Magnetic resonance in medicine.

[28]  P. Courtier,et al.  Assimilation of Simulated Wind Lidar Data with a Kalman Filter , 1993 .

[29]  R. Todling,et al.  Suboptimal Schemes for Atmospheric Data Assimilation Based on the Kalman Filter , 1994 .

[30]  A Shetty,et al.  Magnetic resonance temperature imaging validation of a bioheat transfer model for laser‐induced thermal therapy , 2011, International journal of hyperthermia : the official journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group.

[31]  Bruno Quesson,et al.  Three‐dimensional spatial and temporal temperature control with MR thermometry‐guided focused ultrasound (MRgHIFU) , 2009, Magnetic resonance in medicine.

[32]  V. Aidala.  Parameter estimation via the kalman filter , 1977 .

[33]  L. R. Dice.  Measures of the Amount of Ecologic Association Between Species , 1945 .

[34]  Robert F. Stengel,et al.  Optimal Control and Estimation , 1994 .

[35]  Luc Bidaut,et al.  Computational infrastructure for the real-time patient-specific treatment of cancer , 2009 .

[36]  Peter S. Maybeck,et al.  Stochastic Models, Estimation And Control , 2012 .

[37]  D. Fuentes,et al.  Kalman Filtered MR Temperature Imaging , 2010 .

[38]  Martin Ehrendorfer,et al.  Four-Dimensional Data Assimilation: Comparison of Variational and Sequential Algorithms , 1992 .

[39]  E Moser,et al.  Temperature- and pH-dependence of proton relaxation rates in rat liver tissue. , 1995, Magnetic resonance imaging.

[40]  Sharon Thomsen,et al.  Rate Process Analysis of Thermal Damage , 1995 .

[41]  K Hynynen,et al.  The feasibility of MRI feedback control for intracavitary phased array hyperthermia treatments. , 1998, International journal of hyperthermia : the official journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group.

[42]  Dhiraj Arora,et al.  Minimum-time thermal dose control of thermal therapies , 2005, IEEE Transactions on Biomedical Engineering.

[43]  Kim Butts Pauly,et al.  MR thermometry , 2008, Journal of magnetic resonance imaging : JMRI.

[44]  Francis A. Duck,et al.  Physical properties of tissue : a comprehensive reference book , 1990 .

[45]  Eric Vicaut,et al.  Real-time magnetic resonance-guided laser thermal therapy for focal metastatic brain tumors. , 2008, Neurosurgery.

[46]  Yusheng Feng,et al.  Adaptive Real-Time Bioheat Transfer Models for Computer-Driven MR-Guided Laser Induced Thermal Therapy , 2010, IEEE Transactions on Biomedical Engineering.

[47]  Amy Henderson Squilacote.  The Paraview Guide , 2008 .

[48]  I. Yaroslavsky,et al.  Treatment planning for MRI‐guided laser‐induced interstitial thermotherapy of brain tumors—The role of blood perfusion , 1998, Journal of magnetic resonance imaging : JMRI.

[49]  Istvan Szunyogh,et al.  A Local Ensemble Kalman Filter for Atmospheric Data Assimilation , 2002 .