Adaptive thermal modeling: a concept for measurement of local blood perfusion in heated tissues

Preliminary results of a new approach for three-dimensional reconstruction of Dynamic AngioThermography (DATG) images based on the inversion of heat equation

Dynamic AngioThermography (DATG) is a contact-plate technique capable of producing a digital representation of breast vascularity. The inception and growth of a tumor are associated with neoangenesis, which may result in a demonstrable alteration in the regional blood flow, while in normal health conditions the vascularity remains unchanged throughout life. DATG, if included in the clinical evaluation for breast cancer, could potentially improve the accuracy of the diagnosis of this disease. Conventional DATG is limited, however, in that it is a projection (i.e. two-dimensional) imaging technique that does not provide any information on the depth and its effect on the pattern of the perfusion revealed by this technique. In fact, the blood pattern is detected by projecting temperature signals on the plate, thus acquiring a digital two-dimensional image. In this article we propose a new approach for extracting information on depth through the inversion of the Fourier heat equation. The idea is to extract the information along the third axis while acquiring and analyzing the temporal sequence during the process of image formation. The method implemented has been tested on a dedicated "electric phantom" and in one in vivo experiment. In spite of the limits of these preliminary tests, the experimental results have shown that this method makes it possible to obtain a 3D representation of the vascularity. Although it appears to be promising, further validation and characterization of our technique are required.

Inverse techniques in hyperthermia: a sensitivity study

Numerical modeling methods and hyperthermia treatment temperature measurements have been used together to reconstruct steady-state tumor temperature distributions. However, model errors will exist which may in turn produce errors in the reconstructed temperature distributions. A series of computer experiments was conducted to study the sensitivity of reconstructed two-dimensional temperature distributions to perfusion distribution modeling errors. Temperature distributions were simulated using a finite element approximation of Pennes' bioheat transfer equation. Relevant variables such as tumor shape, perfusion distribution, and power deposition were modeled. An optimization method and the temperatures "measured" from the simulated temperature distributions were used to reconstruct the tumor temperature distribution. Using this procedure, the sensitivity of the reconstructed tumor temperature distribution to model-related errors, such as the perfusion function, was studied. It was found that: 1) if the problem is conduction dominated, large errors in the perfusion distribution produce only small errors in the reconstructed temperature distribution (maximum error < 1.0 degrees C), and 2) when the actual perfusion distribution contains a small random variation (+/- 15%) which is neglected by the model, the reconstructed temperature distribution will be in good agreement with the actual temperature distribution (maximum error < or = 0.3 degrees.

Recent developments in modeling heat transfer in blood perfused tissues

Successful hyperthermia treatment of tumors requires understanding the attendant thermal processes in both diseased and healthy tissue. Accordingly, it is essential for developers and users of hyperthermia equipment to predict, measure and interpret correctly the tissue thermal and vascular response to heating. Modeling of heat transfer in living tissues is a means towards this end. Due to the complex morphology of living tissues, such modeling is a difficult task and some simplifying assumptions are needed. Some investigators have recently argued that Pennes' interpretation of the vascular contribution to heat transfer in perfused tissues fails to account for the actual thermal equilibration process between the flowing blood and the surrounding tissue and proposed new models, presumably based on a more realistic anatomy of the perfused tissue. The present review compares and contrasts several of the new bio-heat transfer models, emphasizing the problematics of their experimental validation, in the absence of measuring equipment capable of reliable evaluation of tissue properties and their variations that occur in the spatial scale of blood vessels with diameters less than about .2 mm. For the most part, the new models still lack sound experimental grounding, and in view of their inherent complexity, the best practical approach for modeling bio-heat transfer during hyperthermia may still be the Pennes model, providing its use is based on some insights gained from the studies described here. In such cases, these models should yield a more realistic description of tissue locations and/or thermal conditions for which the Pennes' model might not apply.

Towards the estimation of three-dimensional temperature fields from noisy temperature measurements during hyperthermia

The temperatures at most locations are unknown during clinical hyperthermia because temperature data are obtained at only a few discrete locations. In an attempt to further develop a technique for possibly solving this problem, the feasibility of using state and parameter estimation methods to predict three-dimensional temperature fields during hyperthermia treatments is investigated. Previous studies attempting to solve this problem have been limited to only one or two spatial dimensions. This paper investigates some conditions for which an estimation method can predict the complete three-dimensional temperature field for controlled numerical experiments with additive measurement noise. For the range of perfusion patterns considered, results show that the steady-state temperature field can be estimated to within 1 degree C if there is no measurement noise, no model mismatch, and as few as three measurement locations for seven perfusion zones. The addition of measurement noise degrades the performance of this estimation algorithm, especially when the number of measurement locations is small. Use of Tikhonov regularization of order zero significantly improves the performance of the algorithm for these cases. It was found that there is an optimal regularization parameter which maximizes the algorithm performance. This optimal value is a function of the perfusion magnitude and pattern. The present numerical results indicate that the approach used to solve this difficult and ill-posed problem could potentially be extended to estimate the complete temperature field in more realistic clinical conditions, but considerably more progress must be made before that goal can be reached.