A Generic Bioheat Transfer Thermal Model for a Perfused Tissue

Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN 55455, USA.
Journal of Biomechanical Engineering (Impact Factor: 1.78). 08/2009; 131(7):074506. DOI: 10.1115/1.3127260
Source: PubMed


A thermal model was needed to predict temperatures in a perfused tissue, which satisfied the following three criteria. One, the model satisfied conservation of energy. Two, the heat transfer rate from blood vessels to tissue was modeled without following a vessel path. Three, the model applied to any unheated and heated tissue. To meet these criteria, a generic bioheat transfer model (BHTM) was derived here by conserving thermal energy in a heated vascularized finite tissue and by making a few simplifying assumptions. Two linear coupled differential equations were obtained with the following two variables: tissue volume averaged temperature and blood volume averaged temperature. The generic model was compared with the widely employed empirical Pennes' BHTM. The comparison showed that the Pennes' perfusion term wC(p)(1-epsilon) should be interpreted as a local vasculature dependent heat transfer coefficient term. Suggestions are presented for further adaptations of the general BHTM for specific tissues using imaging techniques and numerical simulations.

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    • "The form of Eq. (1) is very similar to other local thermal nonequilibrium models proposed in the literature [15–18,23]. Noticeable differences includes: a metabolic heat generation term was included in Mahjoob and Vafai [20] but is neglected here since it has been shown to be insignificant in thermal ablation [24]; the heat conduction term in the blood bio-heat equation was ignored in Shrivastava and Vaughan [23] but is preserved here as it could still be comparable to the bulk flow term when the model is used to study the heat transfer between the tissue and the small vessels with a low blood velocity. "
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    ABSTRACT: Ablation techniques have become a widespread choice for the treatment of cancerous tumours, where surgical resection techniques have poor prognosis. However, the extent and the shape of the ablation zone can be significantly affected by heat loss due to blood perfusion, which is difficult both to measure and to model accurately. A two-equation coupled bio-heat model is thus presented here to model the heat exchange between blood flow and its surrounding biological tissue, by considering the vasculature as a porous medium. The cooling effects of different generations of the vasculature are examined separately in the model. It is shown both analytically and computationally that the model behaviour is dependent on a non-dimensional number, γ, so termed here the thermal significance coefficient: for vessels in the highest generation of the vasculature such as big arteries and veins, γ is found to be much larger than unity, indicating that the blood in these large vessels holds a constant temperature, in which case the two-equation coupled bio-heat model can be simplified into the Pennes model; on the other hand, for small vessels in the bottom generation of the vasculature such as arterioles, capillaries, venules, γ is far smaller than unity, suggesting that the blood in small vessels is in continuous equilibrium with tissue temperature, in which case the model is equivalent to the Klinger model. However, most of the temperature equilibration occurs as the blood travels via the middle generations of the vasculature such as terminal artery branches, for which γ is of order unity and hence the two-equation coupled model cannot be further simplified. The implications of this for practical implementation of the bio-heat model are discussed.
    Full-text · Article · Apr 2011 · International Journal of Heat and Mass Transfer
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    • "Desta forma, o sucesso das terapias localizadas de frio e de calor é altamente dependente da compreensão do comportamento da temperatura e do processo térmico que ocorre no interior dos tecidos alvo e adjacente (Karaa et al., 2005). Embora determinações in vivo da temperatura tecidual possam ser empregadas com esse objetivo, ainda existem grandes dificuldades e riscos associados à realização desses procedimentos, principalmente, pelo caráter invasivo, pela imprecisão no controle de diversos parâmetros e pelas limitações das medidas (Trobec et al., 2008; Shrivastava e Vaughan, 2009). Atualmente, um grande número de ferramentas numéricas e computacionais da engenharia tem sido utilizado para conhecer e interpretar os processos e fenômenos biológicos. "

    Full-text · Article · Jan 2011 · Revista Brasileira de Engenharia Biomedica
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    • "In addition, there are serious concerns about the range of these models when so little is known about in vivo vasculature geometry and its trends. The Pennes' model appears to still be applicable in regions where the vasculature geometry is comprised of small, frequent and thermally significant blood vessels [12] "
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    ABSTRACT: Progress in analytical solutions to bioheat transfer problems is stifled by differences in thermal properties between different people and the variance of these properties based on many variables that are difficult to control or account for. Research was conducted to determine an experiment that could measure thermal properties of skin in vivo, with potential use in calculation of skin burn depth based on skin surface temperature distributions. However, the specific vascular morphology and lack of agreement on one particular model led to the belief that thermal property measurement, which depends on the model to be used, would not be accurate enough for the desired clinical use. Moving beyond strict mathematical models, an experiment was designed that could compare the thermal reaction of skin against itself in order to isolate any anisotropies present due the flow of blood in one or more directions. The expected result is that advected blood, which has a specific direction in the capillary bed, diffuses heat better than conduction through the tissue. This would cause an directional difference on the measured heat rate supplied by an external source on the surface of the skin. The absolute value of this difference should be a function of the amount of bloodflow taking place in the capillaries and arterioles. In burned skin, where there is no bloodflow, this difference will be smaller, depending on the depth of the burn. This allows the directional relevance of heat diffusion to be used as a diagnostic tool for determining the depth of burned skin.
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