Identification of Controlled-Complexity Thermal Therapy Models Derived from Magnetic Resonance Thermometry Images

Abstract

Medical imaging provides information valuable in diagnosis, planning, and control of therapies. In this paper, we develop a method that uses a specific type of imaging—the magnetic resonance thermometry—to identify accurate and computationally efficient site and patient-specific computer models for thermal therapies, such as focused ultrasound surgery, hyperthermia, and thermally triggered targeted drug delivery. The developed method uses a sequence of acquired MR thermometry images to identify a treatment model describing the deposition and dissipation of thermal energy in tissues. The proper orthogonal decomposition of thermal images is first used to identify a set of empirical eigenfunctions, which captures spatial correlations in the thermal response of tissues. Using the reduced subset of eigenfunction as a functional basis, low-dimensional thermal response and the ultrasound specific absorption rate models are then identified. Once identified, the treatment models can be used to plan, optimize, and control the treatment. The developed approach is validated experimentally using the results of MR thermal imaging of a tissue phantom during focused ultrasound sonication. The validation demonstrates that our approach produces accurate low-dimensional treatment models and provides a convenient tool for balancing the accuracy of model predictions and the computational complexity of the treatment models.

Compression of MR-Thermometry images using reduced-order Karhunen-Loève basis

“…With the reduced KL basis, the original MRI thermal image data is spatially filtered and the MR measurement noises are effectively suppressed. Such property of KLD method also makes it unique to identify the patient-and site-specific accurate thermal response and SAR model of the target [11] However, when the scene of the image changes, the new KL basis functions must be re-identified to accurately capture the correlation, which can be accelerated with existing fast Karhunen-Loève algorithms [16].…”

“…Mathematically, the problem is to find φ(r), such that the projection of all snapshots onto the function φ(r) has the maximum possible value, λ max , on average [11]. Ref.…”

“…Ref. [11] also proved that the KL basis can be found by assuming φ(r) as a linear combination of image snapshots:…”

“…eigenvalue [11]. The first M orthonormal KL basis {φ} M j=1 are used to approximately represent the acquired images T m (r, t) to the desired accuracy, which is given by the following decomposition:…”

Identification of Reduced-Order Thermal Therapy Models Using Thermal MR Images: Theory and Validation

“…The fundamentals of the POD in the context of our objectives are briefly outlined as follows, with further details available in [14]–[18]. …”