重新审视伍尔夫生物传热模型：定向血液焓传输、生物佩克莱数及其对激光诱导热疗的影响
The Wulff bio-heat transfer model revisited: directional blood enthalpy transport, the biological Peclet number, and implications for laser-induced thermal therapy
AI总结：
该研究重新审视伍尔夫生物传热模型，明晰其推导及假设，通过激光诱导热疗基准问题评估该模型，发现血流方向性影响温度场和热损伤程度，定义生物佩克莱数，并提出考虑静脉淤滞的扩展以减轻过度温度上升。
AI中文摘要：
生物传热模型在预测激光诱导热疗（LITT）中的温度场方面起着基础性作用。在连续生物传热模型中，彭尼斯方程是应用最广泛的公式。然而，它将血液灌注视为各向同性体积源，忽略了与血流相关的热能定向传输。伍尔夫模型通过将血液平均焓传输直接纳入热通量克服了这一局限性。本文有两个目标。首先，重新审视伍尔夫最初提出的物理公式，以阐明其推导过程和获得控制方程所需的假设。其次，通过具有代表性的激光诱导热疗基准问题，将所得模型与经典彭尼斯公式进行评估。数值结果表明，考虑血流方向性可能会显著改变预测的温度场和热损伤程度。无量纲分析进一步定义了生物佩克莱数，量化了定向血液焓传输相对于热扩散的大小。最后，提出了一个考虑静脉淤滞的简单扩展，减轻了原始伍尔夫公式预测的过度温度上升。
英文摘要：
Bio-heat transfer models play a fundamental role in predicting temperature fields during laser-induced thermal therapy (LITT). Among continuum bio-heat transfer models, the Pennes equation remains the most widely adopted formulation. However, by representing blood perfusion as an isotropic volumetric source, it neglects the directional transport of thermal energy associated with blood flow. The Wulff model overcomes this limitation by incorporating blood averaged enthalpy transport directly into the heat flux. Despite its physical significance, the derivation of the Wulff formulation and the assumptions required to obtain its governing equation remain only briefly discussed in the original work. The aim of the present work is twofold. First, the physical formulation originally proposed by Wulff is revisited in order to clarify its derivation and the assumptions required to obtain the governing equation. In particular, the physical origin of the modified heat flux is investigated and an equivalent formulation with an independent metabolic source term is discussed. Second, the resulting model is assessed against the classical Pennes formulation through representative laser-induced thermal therapy benchmark problem. The numerical results show that accounting for blood flow directionality may substantially alter the predicted temperature field and the extent of thermal damage. A dimensionless analysis further leads to the definition of a biological Peclet number, which quantifies the magnitude of directional blood enthalpy transport relative to thermal diffusion. Finally, a simple extension accounting for venous stasis is proposed, mitigating the excessive temperature rise predicted by the original Wulff formulation
