Study of the one dimensional and transient bioheat transfer equation: Multi-layer solution development and applications

Abstract

In this work we derive an analytical solution given by Bessel series to the transient and onedimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp).

Q-r curve of thermal tomography and its clinical application on breast tumor diagnosis

“…At present, the medical imaging technologies being commonly used such as magnetic resonance imaging (MRI), X-CT imaging, ultrasonic imaging etc., can provide some related biochemical and pathologic information, nevertheless these technologies have a fundamental constraint, that is they can only display the shape changes of body tissue, but not reflect functional changes of body tissue [19,20]. When the structural lesions emerge in the human body, the qualitative changes of the patient's condition have taken place [21][22][23][24][25].…”

“…In order to mine the valuable 3-dimensional heat distribution data based on temperature distribution of body surface, many research groups have carried out in-depth studies and made a series of achievements [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. This present paper aims to acquire the q-r characteristic curve of the heat intensity varying with depth of tomography based on the temperature distribution characteristics of tumor in different stages.…”

Tumor bed brachytherapy for locally advanced laryngeal cancer: a feasibility assessment of combination with ferromagnetic hyperthermia

“…several centimeters), and body core temperature T0 = 37°C. The solution of equation (2) has been derived previously for these boundary conditions (Rodrigues et al, 2013).…”

“…In addition, heating the tumor bed >40°C will increase blood perfusion eight-fold or more, reaching over 6 kg/s/m 3 in heated muscle (Sekins et al, 1984, Hasgall et al, January 13th, 2015. In order to bracket the range of expected heating profiles, we determine the temperature for a range of blood perfusion scenarios: ωb = 0 kg/s/m 3 using equation (3); ωb = 0.7 kg/s/m 3 (basal perfusion); and ωb = 6 kg/s/m 3 (active perfusion) using the analytical solution derived by Rodrigues et al (Rodrigues et al, 2013). In addition, we determine the therapeutic penetration depth, defined by the distance into tumor bed where Tt ≥40°C.…”

A novel compact microwave radiometric sensor to noninvasively track deep tissue thermal profiles

“…Invasive measurements of core temperature are generally accomplished either with intracavitary devices like rectal, Foley, nasopharyngeal, endotracheal and esophageal probes, or with temperature sensors placed interstitially in the pulmonary artery [11,[13][14][15]. Placement of internal temperature probes is uncomfortable, may require sedation or anesthesia, and is not without risk.…”