Recovering the functional form of nonlinear heat transfer by means of thermal imaging

This paper presents a numerical method to address function estimation problems in inverse heat transfer problems using parameter estimation approach without prior information on the functional form of the variable to be estimated. Using an inverse analysis, the functional form of a time-dependent heat transfer coefficient is estimated efficiently and accurately. The functional form of the heat transfer coefficient is assumed unknown and the inverse heat transfer problem should be treated using a function estimation approach by solving sensitivity and adjoint problems during the minimization process. Based on proposing a new sensitivity matrix, however, the functional form can be estimated in an accurate and very efficient manner using a parameter estimation approach without the need for solving the sensitivity and adjoint problems and imposing extra computational cost, mathematical complexity, and implementation efforts. In the proposed sensitivity analysis scheme, all sensitivity coefficients can be computed in only one direct problem solution at each iteration. In this inverse heat transfer problem, the body shape is irregular and meshed using a body-fitted grid generation method. The direct heat conduction problem is solved using the finite-difference method. The steepest-descent method is used as a minimization algorithm to minimize the defined objective function and the termination of the minimization process is carried out based on the discrepancy principle. A test case with three different functional forms and two different measurement errors is considered to show the accuracy and efficiency of the used inverse analysis.

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Application of components analysis in dynamic thermal breast imaging to identify pathophysiologic mechanisms of heat transfer

10.1101/2021.08.16.456538 ◽

2021 ◽

Author(s):

Meir Gershenson ◽

Jonathan P Gershenson

Keyword(s):

Breast Cancer ◽

Heat Transfer ◽

Thermal Imaging ◽

Breast Imaging ◽

Component Analysis ◽

External Stimulus ◽

Time Behavior ◽

Data Set ◽

External Temperature ◽

Components Analysis

Significance: Of the most compelling unsolved issues in the paradigm to create success in the field of breast cancer infrared imaging is localization of direct internal heat of the tumor. The contribution of differential heat production related to metabolism versus perfusion is not understood. Previous work until now has not shown progress beyond identifying veins which are fed by the hot cancer. Employing signal analysis techniques, we probe important questions which may lead to further understanding pathophysiology of heat transfer occurring in the setting of malignancy. Aim: When using thermal imaging to detect breast cancer, the dominant heat signature is that of indirect heat transported in gradient away from the tumor location. Unprocessed images strikingly display vasculature which acts to direct excess heat superficially towards the skin surface before dissipating. In current clinical use, interpretation of thermogram images considers abnormal vascular patterns and overall temperature as indicators of disease. The goal of this work is to present a processing method for dynamic external stimulus thermogram images to isolate and separate the indirect vascular heat while revealing the desired direct heat from the tumor. Approach: In dynamic thermal imaging of the breast, a timed series of images are taken following application of external temperature stimulus (most often cooled air). While the tumor heat response is thought to be independent of the external stimulus, the secondary heat of the veins is known to be affected by vasomodulation. The recorded data is analyzed using independent component analysis (ICA) and principal component analysis (PCA) methods. ICA separates the image sequence into new independent images having a common characteristic time behavior. Resulting individual components are analyzed for correspondence to the presence or lack of vasomodulation. Results: Using the Brazilian visual lab mastology data set containing dynamic thermograms, applying components analysis resulted in three corresponding images: 1. Minimum change as a function of applied temperature or time (suggests correlation with the cancer generated heat), 2. Moderate temperature dependence (suggests correlation with veins affected by vasomodulation) and 3. Complex time behavior (suggests correlation with heat absorption due to high tumor perfusion). All components appear clear and distinct. Conclusions: Applying signal processing methods to the dynamic infrared data, we found three distinct components with correspondence to understood physiologic processes. The two cases shown are self-evident of the capability of the method but are lacking supporting ground truth that is unavailable with such a limited data set. Validation of this proposed paradigm and studying furthering clinical applications has potential to create significant achievement for IR modality in diagnostic imaging.

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